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INFOMATHS OLD QUESTIONS-CW1 17. SETS & RELATIONS 1. The binary relation on the integers defined by R = {(a, b) : |b – a| 1} is HCU-2012 (a) Reflexive only (b) Symmetric only (c) Reflexive and Symmetric (d) An equivalence relation 2. Set of all subsets is a PUNE-2012 (a) power set (b) equal sets (c) equivalent sets (d) None of these 3. In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is NIMCET-2012 (a) 22 (b) 33 (c) 10 (d) 45 4. Let X be the universal set for sets A and B. If n(A) = 200, n(B) = 300 and n(A ∩ B) = 100, then n(A'∩ B') is equal to 300 provided in n(X) is equal to NIMCET-2011 (a) 600 (b) 700 (c) 800 (d) 900 5. In a college of 300 students, every student reads 5 news papers and every news paper is read by 60 students. The number of news paper is NIMCET-2011 (a) atleast 30 (b) atmost 20 (c) exactly 25 (d) exactly 28 6. If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B? BHU-2011 (a) {(1, 5), (2, 6), (3, 4), (3, 6)} (b) {(1, 6), (3, 4), (5, 2)} (c) {(4, 2), (4, 3), (5, 1)} (d) B A 7. The number of subsets of an n elementric set is BHU-2011 (a) 2n (b) n (c) 2n (d) 18. 19. 20. 21. 22. 23. 1 n 2 2 If A = {a, b, d, l}, B = {c, d, f, m} and C = {a, l, m, o}, then C (A B) is given by BHU-2011 (a) {a, d, l, m} (b) {b, c, f, o} (c) {a, l, m} (d) {a, b, c, d, f, l, m, o} In question 9 and 10, for sets X and Y, X Y is defined as X Y = (X – Y) (Y – X) 9. If P = {1,2, 3, 4}, Q = {2, 3, 5, 8}, R = {3, 6, 7, 9} and S = {2, 4, 7, 10} then (P Q) (R S) is HCU-2011 (a) {4, 7} (b) {1, 5, 6, 10} (c) {1, 2, 3, 5, 6 8, 9, 10} (d) None of the above 10. If X, Y, Z are any three subsets of U, then the subset of U consisting of elements which belong to exactly two of the sets X, Y, Z is HCU-2011 (a) (X Y) (Y Z) (Z X) (b) (X Y) (Y Z) (Z X) (c) ((X Y) Z) – ((X Y) Z) (d) None of the above 11. Let A = {1, 2, 3, 4}. The cardinality of the relation R = {(a,b)| a divides b} over A is : PU CHD-2011 (A) 10 (B) 9 (C) 8 (D) 4 12. If X={8n –7n–1\nN } and Y= {49(n–1)\nN} then: PU CHD-2010 (A) X Y (B) Y X (C) X=Y (D) XUY=N 13. The relation R={(1,1) (2,2), (3,3), (1,2), (2,3), (1,3) } on the set A ={1,2,3} is : PU CHD-2010 (A) reflexive but not symmetric (B) reflexive but not transitive (C) symmetric and transitive (D) neither symmetric nor transitive 14. Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = (3, 6, 9, 12) Then the relation is : PU CHD-2009 (a) reflexive and transitive only (b) reflexive only (c) and equivalence relation (d) reflexive and symmetric only 8. 15. 16. For real numbers x and y, we write xRy x2 y 2 3 24. 25. 26. 27. 28. If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A B and B A are : KIITEE-2010 (a) 299 (b) 992 (c) 100 (d) 18 If A, B and C are three sets such that A B = A C and A B = A C, then KIITEE-2010 (a) A = C (b) B = C (c) A B = (d) A = B In a city 60% read news paper A, 40% read news paper B and 30% read C, 20% read A and B, 30% read A and C, 10% read B and C. Also 15% read paper A, B and C. The percentage of people who do not read any of these news papers is (PGCET – 2009) (a) 65% (b) 15% (c) 45% (d) None of these The total number of relations that exist from the set A with m elements into the set A A is (NIMCET – 2009) (a) m2 (b) m3 (c) m (d) None of these If P = {(4n – 3n - 1) / n N} and Q = {(9n - 9) / n N}, then P Q is equal to (NIMCET – 2009) (a) N (b) P (c) Q (d) None of these A1, A2, A3 and A4 are subsets of a set U containing 75 elements with the following properties : Each subset contains 28 elements; the intersection of any two of the subsets contains 12 elements; the intersection of any three of the subsets contains 5 elements; the intersection of all four subsets contains 1 elements. The number of elements belongs to none of the four subsets is (NIMCET – 2009) (a) 15 (b) 17 (c) 16 (d) 18 From 50 students taking examination in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 Mathematics and Chemistry and atmost 20 Physics and Chemistry. The largest possible number that could have passed all three examinations is (NIMCET - 2009) (a) 10 (b) 12 (c) 9 (d) None of these Let the sets A = {2, 4, 6, 8 …} and B = {3, 6, 9, 12, …} and n (A) = 200, n(B) = 250 then (KIITEE – 2009) (a) n(A B) = 67 (b) n(A B) = 66 (c) n (A B) = 450 (d) n(A B) = 380 Let R be relation on the set of positive integers defined as follows: aRb iff 4a + 5b is divisible by 9 then R is (Hyderabad Central University – 2009) (a) Reflexive only (b) Reflexive and symmetric but not transitive (c) Reflexive and transitive but not symmetric (d) An Equivalence relation The set having only one subset is (Hyderabad Central University – 2009) (a) { } (b) {0} (c) {{}} (d) None of these If R and S are equivalence relations on a set A, then (Hyderabad Central University – 2009) (a) R S is an equivalence relation (b) R S is an equivalence relation (c) Both A and B are true (d) Neither A nor B is true Identify the wrong statement from the following : NIMCET-2010 (a) If A and B are two sets, then A- B= A B (b) If A,B and C are sets, then (A - B) – C = (A – C)-(B - C) (C) If A and B are two sets, then A B= AB (D) If A, B and C are sets, then A B C A B 29. A survey shows that 63% of the Americans like cheese where as 76% like apples. If x% of the Americans lie both cheese and apples, then we have NIMCET-2010 (a) x 39 (b) x63 (c) 39x63 (d) N.O.T 30. Suppose P1, P2, … P30 are thirty sets each having 5 elements and Q1, Q2, …. Qn are n sets with 3 elements each. Let 30 n i 1 j 1 Pi Q j S is an irrational number. Then the relation R is KIITEE-2010 (a) reflexive (b) symmetric (c) transitive (d) None of these If X = {4n – 3n – 1: n N} and Y = {9(n – 1) : n N}, then X Y is equal to KIITEE-2010 (a) X (b) Y (c) N (d) None of these and each element of S belongs to exactly 10 of the Pi S and exactly 9 of the Qj s. Then, n is equal to (MCA : NIMCET - 2008) (a) 15 (b) 3 (c) 45 (d) None 31. 1 If A = {1, 2, 3}, B = {a, b, c, d}. The number of subsets in the Cartesian product of A & B is (Pune– 2007) (a) 212 (b) 27 (c) 12 (d) 7 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 32. 33. 34. 35. 36. 37. In an election 10 per cent of the voters on the voters’ list did not cast their votes and 50 voters cast their ballot papers blank. There were exactly two candidates. The winner was supported by 47 per cent of all the voters in the list and he got 306 more than his rival. The number of voters in the list was (IP University : – 2006) (a) 6400 (b) 6603 (c) 7263 (d) 8900 (e) N.O.T Only one of the following statements given below regarding elements and subsets of the set {2, 3, {1, 2, 3}} is correct. Which one is it? (IP University : – 2006) (a) {2, 3} {2, 3, {1; 2, 3}} (b) 1 (2, 3, {1, 2, 3}} (c) {2, 3} (2, 3, {1, 2, 3}} (d) {1, 2, 3,} {2, 3, {1, 2, 3}} Which set is the subset of all given sets? (Karnataka PG-CET : - 2006) (a) {1, 2, 3, 4, …} (b) {1} (c) {0} (d) { } A set contains (2n + 1) elements. If the number of subsets which contain at most n elements is 4096, then the value of n is (NIMCET – 2009) (a) 28 (b) 21 (c) 15 (d) 6 If set A has 6 elements, B has 4 elements and C has 8 elements, the maximum number of elements in (B – C) (A B) C is (Hyderabad Central University – 2009) (a) 18 (b) 12 (c) 16 (d) 24 Let A be a set with 10 elements. The total number of relations that can be defined on A that are both reflexive and asymmetric is (Hyderabad Central University – 2009) (a) 245 (b) 255 (c) 10 2 11. 12. 13. 14. 15. 16. 1 5 1 5 , 2 2 1 5 1 5 (c) , 2 2 (a) (d) None of these 17. THEORY OF EQUATIONS 1. If the equation x4 – 4x3 + ax2 + bx + 1= 0 has four positive roots then a =? BHU-2012 (a) 6, -4 (b) -6, 4 (c) 6, 4 (d) -6, -4 2. Let P(x) = ax2 + bx + c and Q(x) = - ax2 + bx + c, where ac 0. Then for the polynomial P(x) Q(x) HCU-2012 (a) All its roots are real (b) None of its roots are real (c) At least two of its roots are real (d) Exactly two of its roots are real 3. Let p(x) be the polynomial x3 + ax2 + bx + c, where a, b and c are real constants. If p(–3) = p(2) = 0 and p'(–3) < 0, which of the following is a possible value of c ? PU CHD-2012 (A) – 27 (B) – 18 (C) – 6 (D) – 3 4. Which of the following CANNOT be a root of a polynomial in x of the form 9x5 + ax3 + b, where a and b are integers? PU CHD-2012 (A) – 9 5. (B) – 5 (C) 1 4 (D) 7. 8. 21. PU CHD-2012 (C) 3 7 (D) 1 2 , 2 1 2 ,1 4 7 (B) 1, 2 (D) 1 1, 2 1 5 1 5 , 2 2 1 5 1 5 , 2 2 and x 3 3 4 y are. (MP combined – 2008) 22. 23. If (c) 24. 25. 26. 27. 28. 11 7 1 x y and 9 4 6 x y 1 1 2 , 3 1 1 2 , 3 then (x, y) = (b) (d) (ICET – 2007) 1 1 3 , 2 1 1 3 , 2 The maximum value of the expression 5 + 6x – x2 is (ICET – 2007) (a) 11 (b) 12 (c) 13 (d) 14 2 If one root of the equation ax + bx + c = 0 is double the other root, then, (ICET – 2005) (a) b2 = 9ac (b) 2b2 = 3ac (c) b = 2a (d) 2b2 = 9ac 2 The maximum value of the expression 2 + 5x – 7x is ICET–2005 (a) 2 (d) 1 5 1 5 , 2 2 1 5 1 5 , 2 2 (a) x = 9, y = 1 (b) x = 6, y = 1 (c) x = 6, y = 2 (d) x = 3, y = 2 If x2 + x – 2 is a factor of the polynomial x4 + ax3 + bx2 – 12x + 16 then the ordered pair (a, b) = (ICET – 2007) (a) (-3, 8) (b) (3, - 8) (c) (-3, - 8) (d) (3, 8) (a) The roots of the equation |x2x6 | x 2 are : PU CHD-2010 (A) – 2, 1, 4 (B) 0, 2, 4 (C) 0, 1, 4 (D) – 2, 2, 4 If one root of the equation ax2 + bx + c = 0 is twice the other then : (b) Let , be the roots of the equation (x – a) (x – b) = c, c 0, then the roots of the equation (x + ) (x + ) + c = 0 are (Hyderabad central university - 2009) (a) a, - b (b) – a, b (c) – a, - b (d) a, b The number of roots of the equation |x2 – x - 6| = x + 2 is (NIMCET - 2008) (a) 2 (b) 3 (c) 4 (d) None If esin x – e-sin x – 4 = 0 then the number of real values of x is (KIITEE – 2008) (a) 0 (b) 1 (c) infinite (d) None The values of x and y satisfying the equations: x 2 1 3 y If the roots of the equation ax2 + bx + c = 0 are real and of the form α/ (α -1) and (α + 1) / α then the value of (a + b + c)2 is : PU CHD-2011 (A) b2 – 4ac (B) b2 – 2ac (C) 2b2 – ac (D) b2 – 3ac 2 2 2 If a + b + c = 1, then ab + bc + ca lies in the interval : PU CHD-2011 (C) 10. 20. If a, b, c are real numbers such that a2 + b2 + c2 = 1, then ab + bc + ca PU CHD-2012 (A) 1/2 (B) – 1/2 (C) 2 (D) – 2 (A) 9. 19. If and are the root of 4x2 + 3x + 7 = 0, then the value of 1 is : 3 3 (A) (B) 7 4 6. (c) 18. 1 5 1 5 , 2 2 1 5 1 5 (d) 2 , 2 (b) The roots of the quadratic equation x2 – x – 1 = 0 are (PGCET – 2009) (a) 1 3 1 PU CHD-2010 (A) 2a2 = 3c2 (B) 2b2 = 3ac(C) 2b2 = 9ac (D) b2 = ac 2 If both the roots of the quadratic equation x – 2kx + k2 + k – 5 = 0 are less than 5, then k lies in the interval PU CHD-2009 (a) (5, 6] (b) (6, ) (c) (-, 4) (d) [4, 5] The function f(a) and f(b) are of same sign and f(x) = 0 then the function : PU CHD-2009 (a) has either no root or even number of roots between a and b (b) must have at least one root between a and B (c) has either no root or odd number of roots between a and b (d) has complex root How many real solutions does the equation x7 + 14x5 + 16x3 + 30x – 560 = 0 have? KIITEE-2010 (a) 7 (b) 1 (c) 3 (d) 5 If the rots of the quadratic equation x2 + px + q = 0 are tan 30 and tan 15, respectively, then the value of 2 + q – p is KIITEE-2010 (a) 3 (b) 0 (c) 1 (d)2 The number of real solutions of the equation x2 – 3|x| + 2 = 0 is KIITEE-2010 (a) 2 (b) 4 (c) 1 (d) 3 2 The roots of the quadratic equation x + x – 1 = 0 are PGCET-2010 28 81 (b) 28 81 (c) 81 28 (d) 81 28 The solution of the equation x2/3 – 3x1/3 + 2 = 0 is (Pune – 2007) (a) 1, 2 (b) 1, 8 (c) 2, 6 (d) 1, 4 Which of the following may be true for a quadratic equation ( is real)? (Pune – 2007) INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 29. (a) If is a root, 1/ is also a root (b) If is a root, - is also a root (c) If is a root, i is also a root (d) If i is a root, -i is also a root If a + b + c = 0 then one root of the equation ax2 – bx + c = 0 is (Pune – 2007) (a) 30. 31. (c) 33. 34. 36. 37. (c) ac a (d) n m 1 a b c n m 1 a c b (b) 48. , 2 2 49. 50. 51. 52. Number of real roots of 3x + 15x – 8 = 0 is 53. 1 log 3 7 is 2 (a) 40. 41. 42. 43. (b) If x < - 1 and 2 |x+1| 55. (d) (ICET – 2005) b a (b) c a (c) ac a ab a (d) If and are the roots of |x2 + x + 5| + 6x + 1 = 0 then + (Pune– 2007) (a) 7 (b) –7 (c) 5 (d) –5 x R, The solution set of the inequality |x – 4| + | x – 6| + |x – 8| 15, is (IP. University : Paper – 2006) (a) [1, 11] (b) [2, 12] (c) [0, 10] (d) [3, 10] (e) None of these x R. The solution set of the inequality 10[x] 2 – 17[x] – 6 0 (where [x] denotes the greatest integer less than or equal to) is (IP. University :– 2006) (b) [-1, 2) (c) (0, 3] (d) [-1, 3] The solution set for real x of the equation is (IP. University :– 2006) (d) 2 (e) None of these If a is a positive integer, and the roots of the equation 7x2 – 13x + 2a are rational numbers, then the smallest value of a is (IP. University : Paper – 2006) (a) 1 (b) 2 (c) 3 (d) 4 (e) N.O.T x 2 8x 7 x 2 8x 8 9 (UPMCAT : paper – 2002) (b) x = - 1 (d) None of these If x 1 2 3 1 , then the value of expression 4x3 + 2x2 – 8x + 7, is equal to are 56. 1 ,5 3 BHU-2011 (a) 10 (b) 5 (c) 0 (d) – 2 The number of quadratic equations which remain unchanged by squaring their roots, is BHU-2011 (a) zero (b) four (c) two (d) infinite x - 2x = |2 - 1| + 1, then the value of x is (NIMCET - 2009) (a) –2 (b) 2 (c) 0 (d) none The number of distinct integral values of ‘a’ satisfying the equation 22a – 3(2a + 2) + 25 = 0 is (NIMCET - 2009) (a) 0 (b) 1 (c) 2 (d) 3 The set of real values of x satisfying |x - 1| 3 and |x – 1| 1 is (KIITEE - 2009) (a) [2, 4] (b) [-2, 0] [2, 4] (c) (- , 2] [4, ) (d) None of these If , are non real numbers satisfying x3 – 1 = 0 then the value of 1 1 1 44. (c) 2 1 , 5 3 (a) x = - 1, x = 9 (c) x = 9 (NIMCET - 2009) 5 ,3 2 then x4 + x3 – 4x2 + x + 1 = (a) x2(y2 + y – 2) (b) x2(y2 + y – 3) (c) x2(y2 + y – 4) (d) x2(y2 + y – 6) Which of the following may be true for a quadratic equation ( is real)? Pune-2007 (a) If is a root, 1/ is also a root (b) If is a root, - is also a root (c) If is a root, i is also a root (d) If i is a root, -i is also a root If a + b + c = 0 then one root of the equation ax2 – bx + c = 0 is Pune-2007 54. NIMCET-2011 (a) (–2, –1) (b) (–2, 3) (c) (–1, 3) (d) (3, ∞) If α, β are the roots of the equation x2 − 2x + 4 = 0 then the value of α6 + β6 is NIMCET-2011 (a) 64 (b) 128 (c) 256 (d) 132 5 3, 2 1 x (c) 12 NIMCET-2012 (a) 3 (b) 5 (c) 1 (d) 0 The least integral value of K for which (K–2) x2 + K+ 8x + 4 > 0 for all x R, is NIMCET-2011 (a) 5 (b) 4 (c) 3 (d) 6 Solution set of inequality 1 x yx 8 log x2 4 log x3 2 , 3 1 (a) (b) 2 ,4 8 5 x If (a) [0, 3) (d) (0, π) If 2x4 + x3 – 11x2 + x + 2 = 0, then the value of (a) 0 (b) 1 (c) 2 (d) 3 If a, b are the roots of x2 + px + 1 = 0 and c, d are roots of x2 + qx + 1 = 0, the value of E = (a – c) (b – c) (a + d) (b + d) is (NIMCET - 2008) (a) p2 – q2 (b) q2 – p2 (c) q2 + p2 (d) None (a) (d) None of these 3 39. 47. n m 1 b a c log3 x 2 x 4 log 1 x 2 38. 46. ab a Given a b; The roots of (a – b)x2 – 5(a – b)x + (b – a) = 0 are: (UPMCAT– 2002) (a) Real and equal (b) real and different (c) complex (d) None of these If the real number x when added to its inverse gives the minimum value of the sum, then the value of is equal to NIMCET-2012 (a) – 2 (b) 2 (c) 1 (d) – 1 The equation (cos p – 1)x2 + (cos p) x + sin p = 0 where x is a variable has real roots. Then the interval of p is NIMCET-2012 (a) (0, 2π) (b) (-π, 0) (c) 35. (b) c a If x2 + ax + 10 = 0 and x2 + bx – 10 = 0, have a common root then a2 – b2 equal to (Karnataka PG-CET – 2006) (a) 10 (b) 20 (c) 30 (d) 40 If ax2 + bx + c = 0 lx2 + mx + n = 0 have reciprocal roots then: (UPMCAT– 2002) (a) 32. b a 45. SEQUENCE & SERIES 1. 1 3 7 15 ........ upto n-terms is: 2 4 8 16 PU CHD-2012 1 (A) n 1 n 2 1 (C) 2n n 2 2. is equal to The sum of the series (KIITEE - 2009) 3. (a) 0 (b) 3 + 1 (c) 3 (d) None of these The number of positive real roots for the following polynomial P(x) = x4 + 5x3 + 5x2 – 5x – 6 is (Hyderabad central university - 2009) (D) n 1 1 2n The harmonic mean of two numbers is 4. The arithmetic mean A and geometric mean G of these two numbers satisfy the equation 2A + G2 = 27. The two numbers are : PU CHD-2012 (A) 3, 6 (B) 4, 5 (C) 2, 7 (D) 1, 8 In a geometric progression, (p + q)th term is m and (p - q)th term is n, then pth term is : PU CHD-2011 (A) m/n 3 1 (B) n n 2 (B) mn (C) m / n (D) n/m INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 4. 5. 6. The arithmetic mean of 9 observations is 100 and that of 6 observations is 80, then the combined mean of all the 15 observations will be : PU CHD-2011 (A) 100 (B) 80 (C) 90 (D) 92 If in a GP sum of n terms is 255, the last term is 128 and the common ratio is 2, then the value of n is equal to BHU-2011 (a) 2 (b) 4 (c) 8 (d) 16 If the ratio of the sum of m terms and n terms of an AP be m2 : n2, then the ratio of its mth and nth terms will be BHU-2011 19. 20. 2m 1 2n 1 mn (d) mn mn mn 2m 1 (c) 2n 1 (a) 7. (c) 21. (b) 22. 5 0 is (a) 2 (d) 8 2 BHU-2011 8. (b) 4 (c) 6 Arithmetic mean of two positive numbers is 18 23. 3 and their 24. 4 geometric mean is 15. The larger of the two numbers is 9. 10. 11. HCU-2011 (a) 30 (b) 20 (c) 24 (d) None of the above Let A (x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4) be four points such that x1, x2, x3, x4 and y1, y2, y3, y4 are both in arithmetic progression. Then the area of the quadrilateral ABCD is HCU-2011 (a) 0 (b) greater than 1 (c) less than 1 (d) Depends on the coordinates of A, B, C, D If x, 2x+2, 3x+3 are in G.P then the 4 th term is : PU CHD-2010 (A) 27 (B) –27 (C) 13.5 (D) –13.5 666.......6 2 888.......8 is equal to : n digits 4 n (A) 10 1 9 2 4 n (c) 10 1 9 25. 26. 27. 28. PU CHD-2010 29. n digits 30. 13. 14. (d) 31. b a q p Which of the following statement is correct? PU CHD-2009 (a) A.M. < G.M. < H.M. (b) A.M. > G.M. > H.M. (c) A.M. > G.M. < H.M. (d) H.M. < A.M. < G.M. The sum to infinite terms of the series 2 6 10 14 1 2 3 4 ....... is 3 3 3 3 15. 16. 17. 18. (d) 02 a2 If K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an arithmetic progression then, K is (ICET – 2005) (a) 4 (b) 3 (c) 1 (d) 4 If a > 1, b > 1 and a + b = ab and if 1 1 1 1 1 1 .... y 1 2 .... then a a2 b b x y (ICET – 2005) (a) 0 (b) 2 (c) 1 (d) 3 th If tn is the n term of an arithmetic progression with first term ‘a’ n t 2k k 1 (ICET – 2005) (a) na + (n – 1)d (b) n(a + nd) (c) na + (n + 1)d (d) na + (2n – 1)d In a polygon, the smallest angle is 88 and common difference is 10, the number of sides is : UPMCAT– 2002 (a) 10 (b) 8 (c) 5 (d) N.O.T. 3 10 3 1 3 10 9 (D) 2 3 1 (A) 214 (B) KIITEE-2010 (C) 2. 3 10 2 3 1 In the binomial expansion of (a – b)n, n 5, the sum of 5th and 6th terms is zero. Then a equals: b BHU-2012 n5 (a) 6 H H is P Q 3. NIMCET-2012 (a) 2 (c) ab BINOMIAL THEOREM 1. The coefficient of x3 in the expansion of (1 + x)3 (2 + x2)10 is : PU CHD-2012 (a) 3 (b) 4 (c) 6 (d) 2 Sum up to 10 terms of 1 + 3 + 5 + 7 + …. Is PGCET-2010 (a) 100 (b) 102 (c) 103 (d) 104 Sum of 43 + 83 + 123 + …. + 403 is (PGCET – 2009) (a) 193600 (b) 183600 (c) 194600 (d) 183700 In a geometric progression, if the sum of the first four term is equal to 15 and the sum of the second, third, fourth and fifth terms is 30, then the sixth term equals to (KIITEE – 2009) (a) 16 (b) 32 (c) 48 (d) 64 If H is the Harmonic mean between P and Q, then (b) a2b2 and common difference “d” then, is equal to b a a c a c (b) (c) q p c a c a H1 a H n b is equal to H1 a H n b (NIMCET -2008) (a) n + 1 (b) n – 1 (c) 2n (d) 2n + 3 If nc4, nc5 and nc6 are in arithmetic progression then n is (KIITEE – 2008) (a) 9 (b) 8 (c) 17 (d) 14 If the second term of an arithmetic progression is 20 and its fifth term is double the first then the sum to 20 terms of the series is (ICET – 2007) (a) 64 (b) 108 (c) 1080 (d) 2160 2 1/3 1/9 1/27 If = b then , … = (ICET – 2007) (a) a (b) b (c) 1/a (d) 1/b If m is the arithmetic mean of a1, a2, ….. an then the arithmetic mean of a1 + , a2, + …. an + is (ICET – 2007) (a) m (b) m + (c) m + (d) m The geometric mean between a2 and b2 is ICET – 2005 x 1 4 2n (b) 10 1 9 14 (d) 10n 1 9 NIMCET-2010 (a) If three positive real number a, b, c (c > a) are in H.P., then log (a + c) + log (a – 2b + c) is NIMCET-2011 (a) 2 log (c – b) (b) 2 log (a + c) (c) 2 log (c – a) (d) log a + log b + log c The sum of 112 + 122 +….+ 302 NIMCET-2011 (a) 8070 (b) 9070 (c)1080 (d) 9700 Suppose a, b, c are in A.P. with common difference d. Then e1/c, eb/ac, e1/a are (NIMCET – 2008) (a) A.P. (b) GP. (c) H.P. (d) None If H1, H2, …., Hn are n harmonic means between a and b, a b, (a) |ab| 12. If a, b, c are in A.P., p, q, r are in H. P. and ap, bq, cr in G.P. , then p r r p (d) None of these then the value of The harmonic mean of the roots of the equation 5 2 x 4 5 x 8 2 PQ PQ PQ (b) Q 4 n4 (b) 5 5 (c) n4 7 (d) n5 If nCr-1 = 36, nCr = 84 and nCr+1 = 126, then the value of r is equal to : BHU-2012 (a) 1 (b) 2 (c) 3 (d) 4 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 4. x 2 3 Let 2012 16. and f = fractional part of x. Then x(1 – f) In the Binomial expansion of (a – b)n, n 5, the sum of 5th and 6th HCU-2012 (a) 1 5. (b) 2 (c) 2 3 (d) 7 (a) 6 n5 23 (a) C12 (b) C12 2n If for n N, 1 K 0 21 (c) 0 (d) C10 2 k 2 n A, then the value of K 18. 2 1 K 2n K 2n is K (a) nA (b) –nA If the last term in the Binomial expansion of 1 5/3 3 NIMCET-2012 then the 5th term from the beginning isKIITEE-2010 (a) 210 (b) 420 (c) 105 (d) None of these If (1 + x – 2x2)6 = 1 + a1x + a2x2 + … + a12x12, then the value of a2 + a4 + a6 + … + a12 is (NIMCET – 2009) (a) 1024 (b) 64 (c) 32 (d) 31 15 19. (c) 0 (d) A t n is equal to Let tn = n(n!) then (a) 15! – 1 2 1 If the coefficient of x7 in the expansion of px is qx 1/3 1 2 is 2 log3 8 NIMCET-2011 11 8. (d) n 17. (a) -216 (b) 216 (c) -110 (d) 300 The sum of 20C8 + 20C9 + 21C10 + 22C11 – 23C11 is 22 7. n5 6 KIITEE-2010 Coefficient of xyz-2 in (x – 2y + 3z-1)4 is Pune-2012 6. a equals: b n4 5 (b) (c) 5 n4 terms is zero, then is equal to (KIITEE – 2009) n 1 (b) 16! – 1 (c) 15! + 1 (d) None of these n 20. 11 1 equal to the coefficient of x in the expansion of px , 21. qx 2 -7 The sum of (a) n 2 2n – 1 r 2n r 1 (KIITEE – 2009) Cr is equal to n-1 (b) 2 +1 (c) 2 2n – 1 (d) None of these 1 1 1 .... 1!(n 1)! 3!(n 3)! 5!(n 5)! then (KIITEE – 2009) BHU-2011 (a) pq = 1 9. 10. (b) p 1 q (a) (c) p + q = 1 (d) p – q = 1 The coefficient of x15 the product (x – 1) (2x – 1) (22x – 1) (23x – 1) …. (215 x – 1) is equal to BHU-2011 (a) 2120 – 2108 (b) 2105 – 2121 (c) 2120 – 2105 (d) 2120 – 2104 The nth term of the series (b) (c) 1 7 1 20 2 1 1 ... is 2 13 9 23 22. BHU-2011 20 (a) 5n 3 2 (b) 5n 3 20 (d) 5n 2 3 (c) 20(5n + 3) 11. The remainder when 599 is divided by 13 is : (A) 6 (B) 8 (C) 9 (D) 10 23. If the co–efficient of x7 in the expansion of (a) (c) 15. nn 1 n 1! (b) (d) 49 + 16n – 1 is divisible by (a) 3 (b) 19 (c) 64 (e) None of these (b) - 15C6 (d) 1 Value of 27. integer) depends on Hyderabad Central Univ. – 2009 (a) Value of A (b) Value of n (c) neither A nor n (d) Both A and n In the expression (x + 1) (x + 4) (x + 9) (x + 16) … (x + 400) the coefficient of x19 is (NIMCET – 2008) (a) 2870 (b) 210 (c) 4001 (d) 1900 The sum of the numerical co-efficients in the expansion of n 29. KIITEE-2010 30. (d) 29 31. 5 is n n n i i (for n, a positive sin A1 sin A i 0 i X 2Y 1 3 3 n! 1 n 1 (1 x) x 26. 28. n n (c) 0 25. n! n 1 the constant term is (KIITEE – 2009) (a) 2nCn (b) –2nCn (c) –2nCn-1 (d) None of these What is the value of the ten’s digit in the sum 1! + 2! + 3! + … + 2008! Hyderabad Central Univ. – 2009 (a) 0 (b) 1 (c) 9 (d) 4 PU CHD-2009 an a1 a2 a3 1 1 1 ....... 1 NIMCET-2010 a1 a2 a0 an 1 n 1 15 The middle term in the expansion of PU CHD-2010 nn n! 3 1 x 2 x 24. 11 1 expansion of ax are equal then ab is equal to : 2 bx 14. In the expansion of n PU CHD-2011 the coefficient of x-7 in the 13. (d) None of these The coefficient of a8 b10 in the expansion of (a + b)18 is (KIITEE – 2009) (a) 18C8 (b) 18C10 (c) 218 (d) None of these (KIITEE – 2009) 2 1 ax and bx (A) 1 (B) 2 (C) 3 (D) 4 What is the value of factorial zero (0!)? (a) 10 (b) 0 (c) 1 (d) – 1 If (1+x)n = ao + a1x + a2 x2 +….an xn ,then 2 n1 for even values of n only n! 2 n1 1 1 for odd values of n only n! 2 n1 for all n N n! (a) 15C6 11 12. is equal to 12 is KIITEE – 2008 (a) 212 (b) 1 (c) 2 (d) None The co-efficients of x3 in the expansion of (1 – x + x2)5 is KIITEE – 2008 (a) 10 (b) – 20 (c) – 30 (d) – 50 In the expansion of (1 + x + x2)-3 the coefficient of x6 will be : (MP combined – 2008) (a) 9 (b) 3 (c) 1 (d) – 3 If (1 + x)n = C0 + C1x + C2x2 + … + Cnxn then C0C1 + C1C2 + C2C3 + … + Cn-1 Cn will be equal to: INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (MP combined – 2008) (a) n (c) (b) | (n 2 1) 2n (d) n 1 n 1 2n 1 2 3 x2 1 x 8 128 3 2 x (c) 1 128 (a) 2| n 2n (n 1)(n 1) 45. 46. 3n 32. 1 In the expansion of x , the term independent of x x2 | 3n (a) 33. 3| n | n| 2n (b) | n| 2n (c) 2 n 2 (d) 34. 35. (a) 36. 45 256 (b) If the 5th term of C0 (a) (c) 38. 39. 40. (d) None 2 3 2x x log e 5 3. Pune– 2007 (a) Pune– 2007 4. (a) (b) 2n 1 n 1 (c) IP Univ.– 2006 (d) 225 24! (e) N.O.T 5. 4 10 44. (b) fifth 3 10 2 3 1 2n 1 1 n 1 1 4 x 1/ 2 (c) sixth 1 4 x 1/ 2 2 log e (625 ) 42 ... is (b) loge 5 log e 5 (c) (d) (log e 5)(log e 2) log e 2 (d) (b) 1 60 (1 4 x x 2 ) ex (c) 1 120 is : 1 1 1 1 ... 2 3 2 22 3 2 4 24 MP COMBINED - 2008 (b) 1 x log e 1 2 (d) 1 – loge2 Find the sum of the infinite series If to MP COMBINED - 2008 1 log e 2 (a) e 7. 1 60 (c) e2 (d) e The value of the series : (c) 2n n 1 (log e 2) 2 (log e 2) 2 (log e 2) 4 ... |2 |3 |4 (a) loge2 6. (d) Value of the series: to infinity is : 2 1 The term independent of x in 3x is MP Paper – 2004 x (a) third log e (125 ) 3 infinity is : (a) 2 (b) 1 6 43. MP COMBINED - 2008 1 120 log e 2 C0 C1 C2 ....... is equal to : MP Paper – 2004 1 2 3 2n n 1 2 2 MP COMBINED - 2008 The coefficient of x in the expansion of (1 + x ) (2 + x ) is IP Univ. Paper – 2006 (a) 214 (b) 31 The sum (d) None Coefficient of x5 in the expansion of (e) None of these 42. C r a r is equal to (c) a log e (25) (a) loge 2 2 n1 1 n 1 n 2 1 n 1 226 25! (d) r 1 KIITEE – 2008 ICET – 2005 2 3 3 10 3 1 (d) None r 1 n infinity is : 6 (c) 1 The sum of the series ICET – 2005 1 The sum equals k ! 25 k ! 0 k 12 KIITEE – 2008 is equal to C r 1 EXPONENTIAL AND LOGARITHMIC SERIES 1. If log103 = 0.477, the number of digits in 340 is : PU CHD-2011 (A) 18 (B) 19 (C) 20 (D) 21 2. The sum of the series The remainder in the divisor of 3 by 23 is (a) 13 (b) 12 (c) 14 (d) 15 (12! + 1) is divisible by (a) 11 (b) 13 (c) 14 (d) 7 (c) Cr (a) n.2n-1 + a (b) 0 (d) 8 (d) (b) 49. 64 256 is 10, then, x = (b) 225 25! r 1 n n 5 C C1 C 2 ... n = 2 3 n 1 224 25! n r The value of UPMCAT– 2005 (d) None of these (c) 10C6 (a) 9 (n – 4) (b) 5 (2n – 9) (c) 10n ICET – 2005 (d) (c) 9 2 n 1 n 1 2 n1 1 n 1 (b) 10C3 10 is (d) 1/3 3 1 x 2 , the term independent of x is x 10 48. 40 (a) 41. 45 64 (b) – 6 (a) 6 37. 2 x 2 2 x 68 (c) 45 In the expression equal to : (a) 10C5 If the 21st and 22nd terms in the expression (1 + 6a)24 are equal then a = ICET - 2007 (a) 7/8 (b) 8/7 (c) 5/8 (d) 8/5 The coefficient of x4 in (c) 1/2 10 47. ICET - 2007 (c) (b) 1/4 2| 2n 9 1 2 2 is equal to : UPMCAT– 2005 (a) 1 The coefficient of the term independent of x in the expansion of 3 2 1 2 x 3x is 1 1 (a) 1 (b) 1 2 2 Coefficient of x4 in log (1 + x + x2) is : UPMCAT paper – 2005 (a) 5/12 (b) 13/12 (c) -5/12 (d) N.O.T If b is taken to be positive, then the following series 2 3| n 3n 3 2 x 128 (d) None of these 1 b 1 1 b ......... 2 1 b 1 b 1 b 3 (MP combined – 2008) will be 1 (b) (b) e-2 1 x 2 4 6 8 .... . 1! 3! 5! 7! (c) 1/e MP Paper – 2004 (d) None of these 2 2! .......... inf. coeff. of xn is UPMCAT Paper - 2002 2e (a) n! (d) seventh UPMCAT paper – 2005 (b) 2n e n! (c) 2n e 2n ! (d) e n! PERMUTATIONS & COMBINATIONS 1. How many words can be formed out of the letters of the word ‘PECULIAR’ beginning with P and ending with R ? 6 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. PU CHD-2012 (A) 100 (B) 120 (C) 720 (D) 150 If M = {1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 17, 18}. Then how many subsets of M contains only odd integers. Pune-2012 (a) 26 (b) 212 (c) 211 (d) None of these No. of seven digit integers with sum of digits equal to 10, formed by digits 1, 2, 3 only are Pune-2012 (a) 55 (b) 66 (c) 77 (d) 88 How many nos. between 1 and 10,000 which are either even, ends up with 0 or have the sum of their digits divisible by 9. Pune-2012 (a) 5356 (b) 5456 (c) 5556 (d) 5656 The number of words that can be formed by using the letters of the word Mathematics that start as well as end with T is NIMCET-2012 (a) 80720 (b) 90720 (c) 20860 (d) 37528 The number of different license plates that can be formed in the format 3 English letters (A …. Z) followed by 4 digits (0, 1 ….. 9) with repetitions allowed in letters and digits is equal to NIMCET-2012 (a) 263 × 104 (b) 263 + 104 (c) 36 (d) 263 In which of the following regular polygons, the number of diagonals is equal to number of sides? NIMCET-2012 (a) Pentagon (b) Square (c) Octagon (d) Hexagon 100 ! = 1 2 3 ….. 100 ends exactly in how many zeroes? HCU-2011 (a) 24 (b) 10 (c) 11 (d) 21 Let a and b be two positive integers. The number of factors of 5 a7b are HCU-2011 (a) 2(a+b) (b) a + b + 2 (c) ab + 1 (d) (a + 1) (b + 1) A polygon has 44 diagonals, the number of its sides is NIMCET-2011, PU CHD-2011 (a) 9 (b) 10 (c) 11 (d) 12 The number of ways of forming different nine digit numbers from the number 223355888 by rearranging its digit so that the odd digits occupy even positions is NIMCET-2011 (a) 16 (b) 36 (c) 60 (d) 180 There are n numbered seats around a round table. Total number of ways in which n1(n1 < n) persons can sit around the round table, is equal to BHU-2011 (a) 13. 14. 15. 16. 17. 18. 19. 20. n Cn1 (b) n Pn1 (c) n 21. 22. 23. 24. 25. 26. 27. (a) 6! 5! (b) 30 (c) 5! 4! (d) 7! 5! Total number of divisors of 200 are PGCET-2010 (a) 10 (b) 6 (c) 12 (d) 5 How many different paths in the xy-plane are there from (1, 3) to (5, 6) if a path proceeds one step at a time by going either one step to the right (R) or one step upward (U)? (NIMCET – 2009) (a) 35 (b) 40 (c) 45 (d) None of these There are 10 points in a plane. Out of these 6 are collinear. The number of triangles formed by joining these points is (NIMCET – 2009) (a) 100 (b) 120 (c) 150 (d) None of these A man has 7 friends. The number of ways in which he can invite one or more of his friends to a party is (KIITEE – 2009) (a) 132 (b) 116 (c) 127 (d) 130 The number of ways in which the letter of word ARTICLE can be rearranged so that the odd places are always occupied by consonants is (KIITEE – 2009) (a) 576 (b) 4C3 4! (c) 2(4!) (d) None of these Nine hundred distinct n – digit positive numbers are to be formed using only the digits 2, 5, 7. The smallest value of n for which this is possible is (KIITEE – 2009) (a) 6 (b) 8 (c) 7 (d) 9 Total number of 6 – digit numbers in which all the odd digits and only odd digits appear is (KIITEE – 2009) (a) 28. 29. 30. 31. 32. 33. Cn1 1 (d) n Pn1 1 The number of subsets of a set containing n distinct object is BHU-2011 (a) nC1 + nC2 + nC3 + nC4 + …… + nCn (b) 2n – 1 (c) 2n + 1 (d) nC0 + nC1 + nC2 + ….. + nCn A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is : PU CHD-2011 (A) 216 (B) 600 (C) 240 (D) 3125 Total number of ways in which five + and seven – signs can be arranged in a line such that no two + signs occur together is : PU CHD-2010 (A) 56 (B) 42 (C) 28 (D) 21 All letters of the word AGAIN are permuted in all possible ways and the words so formed (with or without meaning) are written in dictionary order then the 50th word is : PU CHD-2010 (A) NAAGI (B) NAAIG (C) IAANG (D) INAGA How many ways are there to arranged the letters in the word GARDEN with the vowels in alphabetical order? PU CHD-2009 (a) 120 (b) 480 (c) 360 (d) 240 A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is : KIITEE-2010 (a) 346 (b) 140 (c) 196 (d) 280 How many different words can be formed by jumbling the word MISSISSIPPI in which no two S are adjacent? KIITEE-2010 (a) 8.6C4.7C4 (b) 6.78C4 (c) 6.8.7C4 (d) 7.6C4.8C4 The number of ways in which 6 men and 5 women can dine at a roundtable, if no two women are to sit together is given by KIITEE-2010 34. 35. 36. 37. 38. 39. 40. 41. 7 5 (6!) 2 (b) 1 (6!) 2 (c) 6! (d) N.O.T Find the total number of ways a child can be given at least one rupee from four 25 paise coins, three 50 paise coins and two onerupee coins HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 53 (b) 51 (c) 54 (d) 55 How many 5-digit prime numbers can be formed using the digits 3, 5, 7, 2 and 1 once each? HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 1 (b) 5! – 4! (c) 0 (d) 5! If there are 20 possible lines connecting non-adjacent points of a polygon, how many sides does it have? HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 12 (b) 10 (c) 8 (d) 9 From 5 different green balls, four different blue balls and three different red balls, how many combinations of balls can be chosen taking at least one green and one blue ball? HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 60 (b) 3720 (c) 4096 (d) None of these The number of even proper factors of 1008 is HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 24 (b) 22 (c) 23 (d) 25 An eight digit number divisible by 9 is to be formed by using 8 digits out of the digits 0, 1, … 9 without replacement. The number of ways in which this can be done is NIMCET - 2008 (a) 9! (b) 2(7!) (c) 4(7!) (d) 36(7!) The number of ordered pairs (m, n), m, n {1, 2, … 100} such that 7m + 7n is divisible by 5 is NIMCET - 2008 (a) 1250 (b) 2000 (c) 2500 (d) 5000 Twenty apples are to be given among three boys so that each gets atleast four apples. How many ways it can be distributed? KIITEE - 2008 (a) 22C20 (b) 90 (c) 18C8 (d) None The number of arrangements of the letters of the word SWAGAT taking three at a time is KIITEE - 2008 (a) 72 (b) 120 (c) 14 (d) None The number of points (x, y, z) in space, whose each co-ordinate is a negative integer such that x + y + z + 12 = 0 is KIITEE - 2008 (a) 110 (b) 385 (c) 55 (d) None There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls is. KIITEE - 2008 (a) 6 (b) 7 (c) 8 (d) 9 x1, x2, x3 N. The number of solutions of the equations x1. x2. x3 = 24300 is IP Paper – 2006 (a) 480 (b) 512 (c) 560 (d) 756 In how many different ways can the letters of the word DISTANCE can be arranged so that all the vowels come together Karnataka PG-CET paper – 2006 (a) 720 (b) 4320 (c) 4200 (d) 3400 In a chess tournament each of the six players will play every other player exactly once. How many matches will be played during the tournament? Karnataka PG-CET paper – 2006 (a) 12 (b) 15 (c) 30 (d) 36 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 42. 43. (a) 1+cot (c) – 1 – cot In an objective type examination, 120 objective type questions are there : each with 4 options P, Q, R and S. A candidate can choose either one of these options or can leave the question unanswered. How many different ways exist for answering this question paper? NIMCET – 2008 (a) 5120 (b) 4120 (c) 1205 (d) 1204 A four digit number a3a2a1a0 is formed from digits 1 … 9 such that 3. 45. 46. integer smaller than a. The smallest value that a3 can have is (Hyderabad Central University - 2009) (a) 5 (b) 7 (c) 9 (d) 1 Four students have to be chosen – 2 girls as captain and vice – captain and 2 boys as captain and vice – captain. There are 15 eligible girls and 12 eligible boys. In how many ways can they be chosen if Sunitha is sure to be captain? HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 114 (b) 1020 (c) 360 (d) 1848 From city A to B, there are 3 different roads. From B to C there are 5 and from C to D there are 2 different roads. Laxman has to go from A to D attending to some work in B and C on the way and has to come back in the reversed order. In how many ways can he complete his journey if he does not take the exact same path while coming back? HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 250 (b) 870 (c) 90 (d) 100 The number of ways in which 12 blue balls, 12 green balls and one black ball can be arranged in a row with the black ball in the middle and arrangements of the colours of balls being symmetrical about the black ball, is IP Paper – 2006 (a) (c) 47. 24! 2 2 !12 ! 2 24 ! 12 !12 (c) 35. 23. (d) x k mn sec 37 (a) tan 74 (b) (c) cot 8 (d) tan 16 csc 37 cos11 sin11 The value of cos11 sin11 2 5. PU CHD-2012 (A) cos 34° (B) sin 34° (C) cot 56° (D) tan 56° The maximum value of sin(x + /6) + cos(x + /6) in interval (0, /2) is attained at (A) /12 (B) /6 (C) /3 (D) 2 6. If cos+ sin= (C) 7. If sin = (a) 12! 6 ! 6 ! 2 sec (D) cos sin 0 sin cos 0 0 0 1 then = 3 (b) (c) 4 8. If A – B 9. (a) 2 (b) 1 (c) 0 Which of the following is correct? 4 (d) 2 , then (1 + tan A) (1 – tan B) is equal to NIMCET-2012 12! 2 6 ! 6 ! (d) 3 NIMCET-2012 x (b) k m n k kx (d) k mn 2cot (B) Pune-2012 (a) sin 1 > sin 1 (b) sin 1 < sin 1 (c) sin 1 = sin 1 (d) sin1 180 sin1 10. If two towers of heights h1 and h2 subtend angles 60 and 30 respectively at the midpoint of the line joining their feet, then h 1 : h2 is NIMCET-2012 (a) 1 : 2 (b) 1 : 3 (c) 2 : 1 (d) 3 : 1 11. If cos 0 4 4 5 , and sin 5 13 , then tan (2α) = NIMCET-2012 56 (a) 33 TRIGONOMETRY 1. Let be an angle such that 0 < < /2 and tan (/2) is rational. Then which of the following is true? HCU-2012 (a) Both sin (/2) and cos(/2) are rational (b) tan() is irrational (c) Both sin () and cos() are rational (d) none of the above 5 3 , then 4 2 2 A student took five papers in an examination, where the full marks were the same for each paper. The marks obtained by the student in these papers were in the proportion 6:7:8:9:10. The student obtained 3/5 of the total full marks. The number of papers in which the student obtained less than 45 per cent marks is IP Paper – 2006 (a) 2 (b) 3 (c) 4 (d) None of these A set contains (2n + 1) elements. If the number of subsets which contain at most n elements is 4096, then the value of n is (NIMCET – 2009) (a) 28 (b) 21 (c) 15 (d) 6 n n n If c4, c5 and c6 are in arithmetic progression then n is (KIITEE – 2008) (a) 9 (b) 8 (c) 17 (d) 14 If 2 sin sin (A) 63 (b) 65 16 (c) 63 33 (d) 56 12. If sin2x = 1 – sinx, then cos4x + cos2x = 13. (a) 0 (b) 1 (c) 2/3 (d) – 1 The value of cot-1 (21) + cot-1 (13) + cot-1 (-8) is (a) 0 2. 2 cos, then cos– sinis equal to PU CHD-2012 A contractor hires k people for a job and they complete the job in x days. A month later he gets a contract for an identical job. At this time he has with him k + m + n people for the job, the number of days it will require for them to complete it, is IP Paper – 2006 (a) x + m + n 48. (b) cos 37 sin 37 is cos 37 sin 37 The value of HCU-2012 a i 1 2 if ai + 1 is even otherwise i = 0, 1, 2 ai a a 4. i 1 or i 1 2 2 a is the smallest integer larger than a and a is the largest 44. (b) 1-cot (d) – 1+cot 14. (b) π (c) 8 (d) 2 NIMCET-2012 NIMCET-2012 If sin (cos) = cos (sin), then sin 2 = NIMCET-2012 3 (a) 4 15. If cosec 1 (b) 3 A cot A 1 (c) 4 4 (d) 3 5 , then tan A is : 2 BHU-2012 1 sin 2 4 (a) 9 is equal to 3 (b) 5 15 (c) 16 20 (d) 21 HCU-2012 8 INFOMATHS/MCA/MATHS/OLD QUESTIONS 16. The value(s) of cos 7 cos INFOMATHS (a) A = 30°, c = 3 1 , b = 2 3 1 (b) A = 30°, c = 3 1 , b = 2 3 1 (c) B = 30°, c = 1 3 , b = 2 3 1 (d) B = 30°, c = 3 1 , b = 2 3 1 4 5 is (are): cos 7 7 BHU-2012 1 (b) 4 1 1 (c) (d) 8 4 A B C If A + B + C = and x sin sin sin , then : 2 2 2 1 (a) 8 17. BHU-2012 (a) 18. 19. (b) x 12 h tan tan (b) tan tan h cot cot (d) cot cot 1 1 x 4cos 2 1 x 2 8 (a) b 28. (c) x = 1 22. If sin 29. h cos 3 cos x sin x 3 is: (b) 6 (d) The value of 1 tan 15 1 tan 2 15 x 2n n NIMCET-2011 3 6 is NIMCET-2011, BHU-2011 sin (a) 1 30. 31. 3 32. 1 3 (b) (c) n 1 n (b) 6 5 (c) n 1 6 3 33. (d) 2 n 1 n 2 7 (d) n 1 6 n then x is : 3 2 If sin x, cos x and tan x are in GP, then the value of cot 6x – cot2x is: NIMCET-2011 (a) 2 (b) – 1 (c) 1 (d) 0 The greatest angle of the triangle whose three sides are x2 + x + 1, 2x + 1 and x2 – 1 is NIMCET-2011 (1) 150° (2) 90° (3) 135° (4) 120° The general value of θ satisfying the equation 2sin2 θ − 3sin θ − 2 = 0 is NIMCET-2011 (a) (d) x = 0 1 sin 1 x cot 1 , 2 2 2n a (d) ab 2 1 2 x 2 tan 2 1 x (b) (b) a (c) No solutions h sin BHU-2012 x 3 a (c) b The general solution of (a) is : (a) b , then the value of a cos 2θ + b sin 2θ is a NIMCET-2011 10 If the angles of elevation of the top and bottom of a flag staff fixed at the top of a tower at a point distant a from the foot of a tower are and , then height of the flag staff is : BHU-2012 (a) a (sin - sin ) (b) a (cos - cos ) (c) a (cot - cot ) (d) a (tan - tan ) The solution of the equation 2x 3sin 1 2 1 x tan If 1 1 1 (c) x (d) x 8 2 2 If sinx + sin x = 1, then the value of cos x + 3cos x + 3cos x + cos6x is BHU-2012 (a) – 1 (b) 1 (c) – 2 (d) 2 If the angle of elevation of a cloud at a height h above the level of water in a lake is and the angle of depression of its image in the lake is , then the height of the cloud above the surface of the lake is not correct: BHU-2012 (c) 21. 1 8 2 (a) 20. x 27. n In a ABC, cosec A(sin B cos C + cos B sinC) equals BHU-2011 BHU-2012 (a) 0 2 (b) (c) 1 5 3 23. The value of (a) 24. 25. If 3 cos (b) sin x 1 (d) c (a) a 3 2 34. 2 6 1 cos 1 is equal to : 3 2 3 4 (c) 2 4 , then the value of 5 (d) 6 x tan is 2 3 1 BHU-2012 35. If 26. 1 3 2 2 (c) 2 3 (d) (c) 3 (d) 4 1 3 3 sin , then the value of cos 2 5 2 (a) 36. is (a) (c) 3 2 37. The solution of Δ ABC given that B = 45°, C = 105° and c = 2 is NIMCET-2011 9 1 (b) 10 1 10 (c) 3 (d) 10 7 10 From the top of a lighthouse 60 m high with its base at the sealevel, the angle of depression of a boat is 15. The distance of the boat from the foot of the lighthouse is BHU-2011 ] (b) (b) 2 BHU-2011 NIMCET-2011 1 3 2 (d) 0 BHU-2011 2 2 (a) (c) 1 The value of tan 9 - tan 27 - tan 63 + tan 81 is (a) 1 HCU-2011 (a) 1/2 or 2 (b) 1/2 or – 2 (c) 3/4 or – 2 (d) 3/4 or 2 The value of sin 30° cos 45° + cos 30° sin 45° [no correct answer was given in choices, correct answer should be a (b) c 3 1 3 1 60m 3 1 3 1 m (b) (d) 3 1 3 1 60m 3 1 3 1 m The general solution of the trigonometrical equation sinx + cosx = 1 is given by BHU-2011 (a) x = 2n, n = 0, 1, 2, … INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (b) x = 2n + 38. 2 KIITEE-2010 , n = 0, 1, 2, ….. (c) x n 1 (d) x n 1 n 4 n 4 4 51. , n 0, 1, 2,.... , n 0, 1, 2,.... 2 2a 2x 1 1 b cos tan 1 2 2 1 a 1 b 1 x2 52. 42. 43. 45. (d) 1 y x (b) 1 xy 1 1 x y (d) cos 1 e 53. 54. a b 1 ab (b) 4 (c) 3 (d) 55. 1 1 x y (a) 1 (c) (b) 2 2 2 1 (c) 56. 48. Solution of the equation cot x sin 1 cos 4 49. 50. mts (d) None of these sin cos tan 3 45 3 6 (b) 75 mts 3 125 (b) mts (d) 57. If 58. 5 4 (b) (c) x = 0 (e) None of these (d) None of these 3 100 mts mts (b) 90 is (c) 75 (PGCET paper – 2009) (d) 15 1 1 tan 1 tan 1 1 2 1 (2)(3) 1 1 then is equal to ..... tan 1 1 (3)( 4) 1 n(n 1) n n 1 (b) n 1 n2 (MCA : NIMCET – 2009) n n2 (c) (d) n 1 n2 The number of solutions for tan 1 x( x 1) sin 1 x 2 x 1 59. is 60. 1 (a) x = 3 50 tan 1 (a) is 1 3 3 b 6 2, c 2 3 KIITEE-2010 x 3 1 3 (a) zero mts 3 1 3 1 (a) 20 4 2 1 The smallest angle of a ABC whose sides are a = 1, (e) None of these 1 3 1 (d) 3 2 2 75 (b) 3 KIITEE-2010 1 (d) (c) 1 3 (d) 1 3 The elevation of the tower 100 meters away is 30. The length of the tower is (PGCET paper – 2009) 2 equal to mts 3 1 The value of (a) KIITEE-2010 If tan (cos) = cot(sin), then the value of (c) 3 The greatest angle of ABC whose sides are a = 5, b 5 3 and c = 5, is PGCET-2010 (a) 45 (b) 100 (c) 120 (d) 60 (a) (e) None of these 47. 2 (PGCET– 2009) (a) 0 (b) 1 (c) 2 (d) 4 (e) None of these If tan = (1 + 2-x)-1, tan = (1 + 2x+1)-1, then + equals KIITEE-2010 6 is 3 then x is equal to is 100 (e) None of these If cos ( – ) = a, and cos ( – ) = b, then sin2 ( – ) + 2ab cos ( – ) is equal to KIITEE-2010 (a) a2 + b2 (b) a2 – b2 (c) b2 – a2 (d) – a2 – b2 (e) None of these The number of ordered pairs (,) where , (-,) satisfying (a) (d) 120 From a point 100 meters above the ground, the angles of depression of two objects due south on the ground are 60 and 45. The distance between the object is PGCET-2010 (c) 0 (c) (b) 1 50 The value of 3 cot 20 -4 cos 20 is NIMCET-2010 (a) 1 (b) -1 (c) 0 (d) N.O.T If tan A – tan B = x and cot B – cot A = y, then cot (A – B) is equal to KIITEE-2010 cos ( - ) = 1 and 46. ab 1 ab 0 (a) 44. (c) sin cos tan 3 45 6 3 (a) NIMCET-2010 (b) b (c) 90 3 (a) = 2n + (-1)n (b) = n (c) = n + (-1)n (d) = (2n + 1) + 39. The value of cos 10 - sin 10 is BHU-2011 (a) positive (b) negative (c) 0 (d) 1 40. In a triangle ABC, R is circumradius and 2 2 2 2 8R = a +b +c . The triangle ABC is NIMCET-2010 (a) Acute angled (b) Obtuse angled (c) Right angled (d) N.O.T (a) a The value of (a) 0 BHU-2011 41. If sin (b) 60 PGCET-2010 If sin = sin , then the angle and are related by -1 (a) 30 5 If (b) one (c) two tan 1 2 x tan 1 3x (c) 61. 62. 10 2 is (MCA : NIMCET – 2009) (d) infinite , then x is (MCA : NIMCET – 2009) (a) 1/6 (b) 1/3 (c) 1/2 (d) 1/4 If A = cos2 + sin4, then for all values of (MCA : NIMCET – 2009) (a) 1 A 2 2 1 5 tan 1 The value of cot cos ec KIITEE-2010 3 3 6 3 4 5 (a) (b) (c) (d) 17 17 17 17 2 In ABC, a = 2, b = 3 and sin A then B is equal to 3 4 (b) 3 13 A 4 16 (d) 13 A 1 16 3 A 1 4 If sin x + cos (1 – x) = sin (-x), then x satisfies the equation (MCA : NIMCET – 2009) (a) 2x2 – x + 2 = 0 (b) 2x2 – 3x = 0 (c) 2x2 + x – 1 = 0 (d) None of these The equation sin4x + cos4x + sin2 x + = 0 is solvable for (MCA : NIMCET – 2009) -1 -1 -1 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (a) (c) 63. 64. 1 1 2 2 3 1 2 2 66. 75. (a) 0 cos C tan A 0 sin B 0 tan A 76. (a) sin A sin B cos C (b) 0 (c) 1 (d) None of these The number of solution of |cos x| = sin x, 0 x 4, is (MCA : KIITEE – 2009) (a) 8 (b) 2 (c) 4 (d) None of these 2sin x sin 1 2x 1 x 2 77. holds for 78. 68. (a) 17/6 (b) 7/16 If cos-1 x > sin-1x, then (KIITEE – 2009) (d) None of these (c) 6/17 (b) –1 < x < 0 (a) x < 0 1 0 x (d) 1 x 2 69. Consider the function 70. f x sin 2 x 3 3 1 100 1 2n / 2 (b) (b) 1 2n (c) (a b) 2 /(a 2 b 2 ) a b 2 (c) 74. (d) n 1 2n (b) 3 :nZ tan C 7 then the side c is 2 9 85. 3 1 100 86. 87. (d) 1 88. (a b) 2 /(a 2 b 2 ) 89. (b) tan 1 a bc If in a ABC, 3a = b + c then (b) 4 tan 2 2 B C tan , tan 2 2 2 (c) (c) 2 is equal to KIITEE – 2008 (d) None 1 1 tan 1 3 7 (c) (d) None KIITEE – 2008 (b) x [-1, 1] (d) None -1 4 is KIITEE – 2008 (d) None A tower casts a shadow 100, long when the elevation of a source of light is at 45. What is the height of the tower? KARNATAKA - 2007 (a) 100 3 (b) 100m (c) 10m (d) 10 3 m From the top of a light house 360 m height, the angles of depression of the top and bottom of a tower are observed to be 30 and 60 respectively. What is the height of the tower? KARNATAKA - 2007 (a) 200m (b) 210m (c) 190m (d) 240m The greatest angle of a triangle with sides 7, 5 and 3 is KARNATAKA - 2007 (a) 60 (b) 90 (c) 120 (d) 135 For a triangle XYZ, if X 2 , Y = 2, Z 3 1 then X is KARNATAKA - 2007 (a) 45 (b) 60 (c) 75 (d) 30 A wire of length 20 cm is bent so as to form an arc of a circle of radius 12 cm. The angle subtended at the center is KARNATAKA - 2007 (a) 3/5 radians (b) 5/3 radians (c) 1/3 radians (d) 5 radians A circular metallic ring of radius 1 foot is reshaped into a circular arc of radius 80 ft. The area of the sector formed is KARNATAKA - 2007 (a) 20 sq ft. (b) 40 sq. ft (c) 80 sq. ft (d) 60 sq. ft If A, B, C, D are angles of a cyclic quadrilateral then cos A + cos B + cos C + cos D is KARNATAKA – 2007, UP-2002 (a) 1 (b) 0 (c) 2 (d) 3 If x cos - y sin = and x sin + y cos then x2 + y2 ICET - 2007 (a) 2 (b) 2 (c) 2 + 2 (d) 2 – 2 If (0 < < 90 and the matrix inverse than (a) 30 (b) 45 11 b c tan 1 ac ab MCA : KIITEE – 2008 (d) None If (1 + tan 1) (1 + tan2) … (1 + tan 45) = 2n, then the value of n is NIMCET - 2008 (a) 21 (b) 22 (c) 23 (d) 24 The value of sin 12 and 48 sin 54 NIMCET - 2008 (a) sin 30 (b) sin230 (c) sin330 (d) cos3 30 MCA : KIITEE – 2008 (d) None tan 1 (b) 84. 2 a2 b2 (d) None (c) 2 (a) 83. If cos + cos = a, sin + sin = b and is the arithmetic mean between and , then sin 2 + cos 2 is equal to NIMCET - 2008 (a) 73. 3 :nZ (b) 6 2 tan 1 on R. Let x1 and (c) 3 100 (d) 100 / 3 The maximum value of (cos 1) (cos 2) …. (cos n) where 0 1, 2, n /2 and (cot 1) (cot 2) … (cot n) = 1 is NIMCET – 2008 (a) 72. n 2 (c) The value of 82. Two persons are standing at different floors of a tall building and are looking at a statue that is 100 metres far from the building. Angle of inclination of the person at higher floor is 60 and that of the person at lower floor is 45. What is the distance between the two persons? Hyderabad Central University - 2009 (a) 71. 2n (b) 1 80. 1 terms is equal MCA : KIITEE – 2008 cos (cos x) = x is satisfied by (a) x R (c) x [0, ] (KIITEE – 2009) x2 be two real values such that f(x1) = f(x2). Then x1 – x2 is always of the form Hyderabad Central University - 2009 (a) n : n Z (b) 2n : n Z (c) 3 5 sin ...n n n 79. 81. 2 4 (a) 1 (d) The value of (c) 1 1 x , 2 2 3 3 x , 2 2 2 4 tansin 1 cos 1 5 3 (c) x [0, 1] 67. (b) n sin In a ABC, A = 90. Then (a) (MCA : KIITEE – 2009) (a) x (-1, 0) In a ABC, a = 5, b = 4 and (a) 3 1 sin (KIITEE – 2009) has the value sin B cos C The formula The value of to (d) – 1 1 The number of values of the triple t(a, b, c) for which a cos 2x + b sin2x + c = 0 is satisfied by all real x is (MCA : KIITEE – 2009) (a) 0 (b) 2 (c) 3 (d) infinite 0 65. (b) – 3 1 sin 2 A 1 sec 1 2 has no ICET - 2007 (c) 60 (d) 75 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 90. sin f ( ) cos f 2 1 1 (a) 1 1 It (c) 91. 92. cos then sin f() + cos sin 106. 1 0 0 (d) 1 1 0 0 1 UPMCAT : Paper – 2002 0 1 1 0 107. If cosec x + cot x = 2 sin x, where 0 ≤ x ≤ 2π In then: UPMCAT : Paper – 2002 (a) x = π/3, 5 π/3 (b) x = π/3, 5π/6 (c) x = π/3, π (d) None of these 108. In a cyclic quadrilateral ABCD, sin (A + C) is equal to : UPMCAT : Paper – 2002 (a) 1/2 (b) 1 (c) – 1 (d) 0 109. The maximum value of 3cosx + 4sinx + 5 is: UPMCAT : Paper – 2002 (a) 10 (b) 0 (c) 5 (d) None of these If A + C = B, then, tan A tan B tan C = ICET – 2005 (a) tan B – tan A + tan C (b) tan B + tan A – tan C (c) tan B – tan A + tan C (d) tan A + tan B + tan C If a flag staff of 6 metres height, placed on the top of a tower throws a shadow 2 3 of metres along the ground, then, the angle in degrees that the sun makes with the ground is ICET–2005 (a) 30 (b) 45 (c) 60 (d) 75 93. If sin 110. The sides of a triangle are a, b and greatest angle is : (a) 60 (b) 90 (c) 120 111. sin[cot-1 cos(tan-1 y)] is equal to : 15 15 cot 17 sin , then, for 0 < < 90 8 tan 16 sec 17 23 49 (b) 22 49 (c) 18 49 (d) 17 49 The general solution of the equation sin2 – sin2 - 15cos2 = 0 is given by equals IP University : Paper – 2006 (a) n + tan-1 3 or m - tan-1 5 (b) n - tan-1 3 or m + tan-1 5 (c) n - tan-2 2 or m + tan-1 6 (d) n - tan-1 7 or m - tan-1 3 (e) None of these 95. When the length of the shadow of a pole is equal to a height of the pole, then the elevation of source of light is Karnataka PG-CET Paper – 2006 (a) 30 (b) 45 (c) 60 (d) 75 96. If tan A + cot A = 4 then tan4 A + cot4 A is equal to Karnataka PG-CET Paper – 2006 (a) 110 (b) 194 (c) 88 (d) 194 97. If one side of a triangle is double of another side and the angle opposite to these sides differ by 60, then the triangle is Karnataka PG-CET Paper – 2006 (a) right angled (b) an obtuse angled (c) an acute angled (d) None of these 98. If sin A = sin B and cos A = cos B, then Karnataka PG-CET Paper – 2006 (a) A = n + B (b) A = n - B (c) A = 2 n + B (d) A = 2n - B 99. If tan-1 x + tan-1 y = /4, then Karnataka PG-CET Paper – 2006 (a) x + y + xy = 1 (b) x + y – xy = 1 (c) x + y + xy + 1 = 1 (d) x + y – xy + 1 = 0 100. The equation 3 cos x + 4 sin x = 6 has _____ solution Karnataka PG-CET Paper – 2006 (a) finite (b) infinite (c) one (d) no 101. The value of sin x(1 + cos x) is maximum at: MP: MCA Paper - 2004 (a) /3 (b) /2 (c) /6 (d) 3/4 94. 102. 3 tan tan 1 4 4 250 3 1 mts (c) 250 3 1 mts (b) y2 1 y2 2 (c) y2 y 3 (d) None of these 1 1 3 then C is: bc ca abc (b) 60 (c) 30 UPMCAT : Paper – 2002 (d) 45 PROBABILITY 1. All the coefficients of the equation ax2 + bx + c = 0 are determined by throwing a six-sided un-biased dice. The probability that the equation has real roots is HCU-2012 (a) 57/216 (b) 27/216 (c) 53/216 (d) 43/216 2. Suppose 4 vertical lines are drawn on a rectangular sheet of paper. We A4 B4 3. 4. UPMCAT : Paper – 2002 5. 3 1:1 then A is equal to : (b) y 1 y2 2 (a) 90 UPMCAT : Paper – 2002 (a) 103.5 (b) 98.5 (c) 101.5 (d) None of these 105. If two stones are 500 meters apart. The, angle of depressions being 30 and 45 as seen by aeroplane what is the altitude the plane is flying: UPMCAT : Paper – 2002 (a) , then the UPMCAT : Paper – 2002 (d) None of these (a) 112. If (a) 117 (b) 3/7 (c) -1/7 (d) None of these 103. Cos40 + Cos80 + Cos 160 is equal to : UPMCAT : Paper – 2002 (a) -1 (b) 0 (c) 1 (d) N.O.T. 104. A, B, C are in A.P. b:c a2 ab b2 UPMCAT : Paper – 2002 2 ICET – 2005 (a) is equal to : 2x 1 2x 1 2x 1 (a) (b) (c) (d) None of these 2x 3 2x 1 2x 1 ICET - 2007 (b) tan tan1 2 x 4 (d) None of these A1 B1 , lines A2 B2 , A3 B3 and respectively. Suppose two players A and B join two (B) 137 729 (C) 16 81 (D) 137 81 Let P(E) denote the probability of event E. Given P(A) = 1, P(B) 250 3 mts the disjoint pairs of end points within A1 to A4 and B1 to B4 respectively without seeing how the other is marking. What is the probability that the figure thus formed has disconnected loops? HCU-2012 (a) 1/3 (b) 2/3 (c) 3/6 (d) 1/6 In a village having 5000 people, 100 people suffer from the disease Hepatitis B. It is known that the accuracy of the medical test for Hepatitis B is 90%. Suppose the medical test result comes out to be positive for Anil who belongs to the village, then what is the probability that Anil is actually having the disease. HCU-2012 (a) 0.02 (b) 0.16 (c) 0.18 (d) 0.3 Let A, B and C be the three events such that P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(A B) = 0.08, P(A C) = 0.28, P(A B C) = 0.09. If P(A B C) 0.75, then P(B C) satisfies : PU CHD-2012 (A) P(B C) ≤0.23 (B) P(B C) ≤0.48 (C) 0.23 ≤P(B C) ≤0.48 (D) P(B C) ≤0.15 A number is chosen from each of the two sets {1, 2, 3, 4, 5, 6, 7, 8, 9} and {1, 2, 3, 4, 5, 6, 7, 8, 9}. If P denotes the probability that the sum of the two numbers be 10 and Q the probability that their sum be 8, then (P + Q) is PU CHD-2012 (A) 6. name 1 , the values of P(A|B) and P (B|A) respectively are 2 NIMCET-2012 12 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (a) 7. 8. 9. 1 1 , 4 2 (b) 1 1 , 2 4 (c) 1 ,1 2 20. 21. 1 2 (b) 1 2n (c) 1 1 1 , , respectively. If they all 22. 2 3 4 1 2n1 1 2 (b) 49 101 (c) 50 101 23. 24. 25. Let P be a probability function on S = (l1, l2, l3, l4) such that 26. 1 1 1 P l2 , P l3 , P l4 . Then P(l1) is 3 6 9 BHU-2012 (a) 7/18 13. 14. 15. 16. 17. 18. 19. (b) 1/3 (c) 1/6 27. (d) 1/5 The probability that A, B, C can solve problem is 1 1 1 , , 3 3 3 respectively they attempt independently, then the probability that the problem will solved is : BHU-2012 (a) 1/9 (b) 2/9 (c) 4/9 (d) 2/3 In a single throw with two dice, the chances of throwing eight is : BHU-2012 (a) 7/36 (b) 1/18 (c) 1/9 (d) 5/36 A single letter is selected at random from the word “probability”. The probability that it is a vowel, is : BHU-2012 (a) 3/11 (b) 4/11 (c) 2/11 (d) 0 An unprepared student takes a five question true-false exam and guesses every answer. What is the probability that the student will pass the exam if at least four correct answers is the passing grade? HCU-2011 (a) 3/16 (b) 5/32 (c) 1/32 (d) 1/8 Answer questions 17 and 18 using the following text: In a country club, 60% of the members play tennis, 40% play shuttle and 20% play both tennis and shuttle. When a member is chosen at random, What is the probability that she plays neither tennis nor shuttle? HCU-2011 (a) 0.8 (b) 0.2 (c) 0.5 (d) 0.4 If she plays tennis, what is the probability ability that she also plays shuttle? HCU-2011 (a) 2/3 (b) 2/5 (c) 1/3 (d) 1/2 If E is the event that an applicant for a home loan in employed C is the event that she possesses a car and A is the event that the loan application is approved, what does P(A|E C) represent in words? HCU-2011 (a) Probability that the loan is approved, if she is employed and possesses a car (b) Probability that the loan is approved, if she is either employed or possesses a car 28. 29. 9a 11a 13a 15a 17a 1 8 (B) 2 7 (C) 1 625 (D) 16 625 The numbers X and Y are selected at random (without replacement) from the set (1, 2, .....3N). The probability that x2 – y2 is divisible by 3 is : PU CHD-2010 (A) 51 101 7a NIMCET-2011 (a) 1/81 (b) 2/82 (c) 5/81 (d) 7/81 Three coins are thrown together. The probability of getting two or more heads is BHU-2011 (a) 1/4 (b) 1/2 (c) 2/3 (d) 3/8 If four positive integers are taken at random and are multiplied together, then the probability that the last digit is 1, 3, 7 or 9 is : PU CHD-2010 (A) (d) None of these (d) (c) Probability that the loan is approved, if she is neither employed nor possesses a car. (d) Probability that the loan is approved and she is employed, given that she possesses a car An anti-aircraft gun can take a maximum of four slots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth slots are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane then is NIMCET-2011 (a) 0. 5 (b) 0.7235 (c) 0.6976 (d) 1.0 A random variable X has the following probability distribution x 0 1 2 3 4 5 6 7 8 P(X = x) a 3a 5a Then the value of ‘a’ is One hundred identical coins each with probability P of showing up heads re tossed. If 0 < P < 1 and the probability of heads showing on 50 coins is equal to that of heads on 51 coins; then the value of P is NIMCET-2012 (a) 12. 1 2 try to solve the problem, what is the probability that the problem will be solved? NIMCET-2012, MP-2008 (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4 If a fair coin is tossed n times, then the probability that the head comes odd number of times is NIMCET-2012 (a) 11. 1, A determinant is chosen at random from the set of all determinants of matrices of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is NIMCET-2012 (a) 3/16 (b) 3/8 (c) 1/4 (d) None of these Coefficients of quadratic equation ax2 + bx + c = 0 are chosen by tossing three fair coins where ‘head’ means one and ‘tail’ means two. Then the probability that roots of the equation are imaginary is NIMCET-2012 (a) 7/8 (b) 5/8 (c) 3/8 (d) 1/8 A problem in Mathematics is given to three students A, B and C whose chances of solving it are 10. (d) N 1 4N 3 3N 1 5N 3 (B) (C) (D) N 9N 3 3N 9N 3 Probability of happening of an event A is 0.4 Probability that in 3 independent trials, event A happens atleast once is:PU CHD-2009 (a) 0.064 (b) 0.144 (c) 0.784 (d) 0.4 A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A B) is : PU CHD-2009 (a) 3/5 (b) 0 (c) 1 (d) 1/6 India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability f India getting at least 7 points is NIMCET-2010 (a) 0.8750 (b) 0.0875 (c) 0.0625 (d) 0.0250 A coin is tossed three times The probabilities of getting head and tail alternatively is NIMCET-2010 (a) 1/11 (b) 2/3 (c) 3/4 (d) 1/4 One hundred identical coins, each with probability P of showing up a head, are tossed. If 0 < p < 1 and if the probability of heads on exactly 50 coins is equal to that of heads on exactly 51 coins then the value of p, is NIMCET-2010 (a) 1 2 (b) 49 50 (c) 101 101 (d) 51 101 30. A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is KIITEE-2010 (a) 8/3 (b) 3/8 (c) 4/5 (d) 5/4 31. If A and B are events such that 3 P A B , 4 2 1 P A B , P A , then P A B is 3 4 32. 33. 34. 13 KIITEE-2010 (a) 5/12 (b) 3/8 (c) 5/8 (d) 1/4 If A and B are any two mutually exclusive events, then P(A|AB) is equal to (PGCET– 2009) (a) P(AB) (b) P(A)/(P(A) + P(B)) (c) P(B)/P(AB) (d) None of these A man has 5 coins, two of which are double – headed, one is double – tailed and two are normal. He shuts his eyes, picks a coin at random, and tosses it. The probability that the lower face of the coin is a head is (NIMCET – 2009) (a) 1/5 (b) 2/5 (c) 3/5 (d) 4/5 A and B are independent witnesses in a case. The probability that A speaks the truth is ‘x’ and that B speaks the truth is ‘y’. If A and B agree on a certain statement, the probability that the statement is true is (NIMCET – 2009) INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (a) (c) 35. xy xy (1 x)(1 y ) (b) 1 x 1 y xy 1 x 1 y (d) 38. 39. 40. 41. 42. 43. 44. 46. 47. 1 and P ( A ) . 4 65 81 (b) 13 81 (c) 65 324 (d) 1 45 (b) 13 90 (c) 19 90 (d) Then 50. (a) (c) 45 3 2 4 90 210 (b) (b) 1 44 (c) 5 132 (a) 51. 52. 54. 1 1 , 3 4 and 1 . The probability that exactly one 5 56. 57. 58. 59. 60. 5 12 1 6 61. MP COMBINED – 2008 64. 2 (d) None 14 (d) 3 5 2 3 (c) 625 1296 (d) 671 1296 (b) 7 10 (c) 24 91 (d) 67 91 1 3 and the probability that neither of them occurs is 1/6. Then the probability of occurrence of A is. ICET – 2005 (a) 5/6 (b) 1/2 (c) 1/12 (d) 1/18 8 coins are tossed simultaneously. The probability of getting atleast six heads is ICET – 2005 39 256 (b) 29 256 (c) 31 256 (d) 37 256 If two dice are tossed the probability of getting the sum at least 5 is PUNE Paper – 2007 (a) 63. (c) 13 30 Probability of four digit numbers, which are divisible by three, formed out of digits 1, 2, 3, 4, 5 is : MP COMBINED – 2008 (a) 1/5 (b) 1/4 (c) 1/3 (d) 1/2 Let A and B be two events with P(A) = 1/2, P(B) = 1/3 and P(A B) = 1/4 , What is P(A B)? KARNATAKA - 2007 (a) 3/7 (b) 4/7 (c) 7/12 (d) 9/122 If three unbiased coins are tossed simultaneously then the probability of getting exactly two heads is ICET - 2007 (a) 1/8 (b) 2/8 (c) 3/8 (d) 4/8 A person gets as many rupees as the number he gets when an unbiassed 6 – faced die is thrown. If two such dice are thrown the probability of getting Rs. 10 is. ICET - 2007 (a) 1/12 (b) 5/12 (c) 13/10 (d) 19/10 Let E be the set of all integers with 1 in their units place. The probability that a number n chosen from [2, 3, 4, … 50] is an element of E is ICET - 2007 (a) 5/49 (b) 4/49 (c) 3/49 (d) 2/49 A and B independent events. The probability that both A and B (a) 62. (b) 3 10 occur is 5 8 (b) 7 30 An untrue coin is such that when it is tossed the chances of appearing head is twice the chances of appearance of tail. The chance of getting head in one toss of the coin is : MP COMBINED – 2008 (a) 1/3 (b) 1/2 (c) 2/3 (d) 1 The probability of randomly chosing 3 defectless bulbs from 15 electric bulbs of which 5 bulbs are defective, is : MP COMBINED – 2008 (a) 55. 7 132 Different words are written with the letters of PEACE. The probability that both E’s come together is : MP COMBINED – 2008 (a) 1/3 (b) 2/5 (c) 3/5 (d) 4/5 The probability of throwing 6 at least one in four throws of a die is: MP COMBINED – 2008 (a) 53. (d) Probabilities of three students A, B and C to pass an examination student will pass is: 13 108 1 90 4 1 132 are respectively A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even, is. NIMCET - 2008 (a) 4/8 (b) 5/8 (c) 6/8 (d) 7/8 A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is NIMCET - 2008 (a) 4/11 (b) 1/3 (c) 5/12 (d) None A card is drawn from a pack. The card is replaced and the pack is reshuffled. If this is done six times, the probability that 2 hearts, 2 diamonds and 2 club cards are drawn is. KIITEE – 2008 2 Two balls are drawn at random from a bag containing 6 white, 4 red and 5 black balls. The probability that both these balls are black, is : MP COMBINED – 2008 (a) 1/21 (b) 2/15 (c) 2/21 (d) 2/35 6 boys and 6 girls sit in a row randomly. The probability that all the girls sit together is : MP COMBINED – 2008 (a) An anti aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane then is (MCA : NIMCET – 2009) (a) 0.6972 (b) 0.6978 (c) 0.6976 (d) 0.6974 Let A = [2, 3, 4, …., 20, 21] number is chosen at random from the set A and it is found to be a prime number. The probability that it is more than 10 is (MCA : KIITEE – 2009) (a) 9/10 (b) 1/5 (c) 1/10 (d) None of these Find the probability that a leap year will contain either 53 Tuesday or 53 Wednesdays. HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 1/5 (b) 2/5 (c) 2/3 (d) 3/7 Probability that atleast one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A') + P(B') is HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 0.9 (b) 1.15 (c) 1.1 (d) 2 The sum of two positive real numbers is 2a. The probability that product of these two numbers is not less than 3/4 times the greatest possible product is HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 1/2 (b) 1/3 (c) 1/4 (d) 9/16 If two events A and B such that P(A') = 0.3, P(B) = 0.5 and P(A B) = 0.3, then P(B/AB') is : NIMCET - 2008 (a) 1/4 (b) 3/8 (c) 1/8 (d) None A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is. NIMCET - 2008 (a) 3/5 (b) 2/5 (c) 4/5 (d) None A letter is taken at random from the letters of the word ‘STATISTICS’ and another letter is taken at random from the letters of the word ‘ASSISTANT’. The probability that they are the same letter is. NIMCET - 2008 (a) 45. 49. xy events A and B are (NIMCET – 2009) (a) independent but not equally likely (b) mutually exclusive and independent (c) equally likely and mutually exclusive (d) equally likely but not independent. The probability that a man who is 85 yrs. old will die before attaining the age of 90 is 1/3. A1, A2, A3 and A4 are four persons who are 85 yrs. old. The probability that A1 will die before attaining the age of 90 and will be the first to die is (NIMCET – 2009) (a) 37. 1 x 1 y Let A and B be two events such that 1 1 P( A B) , P ( A B ) 6 4 36. 48. xy 1 x 1 y 7 12 (b) 11 12 (c) 1 2 (d) 5 6 A and B play a game of dice. A throws the die first. The person who first gets a 6 is the winner. What is the probability that A wins? PUNE Paper – 2007 (a) 6/11 (b) 1/2 (c) 5/6 (d) 1/6 A player is going to play a match either in the morning or in the afternoon or in the evening all possibilities being equally likely. The probability that he wins the match is 0.6, 0.1 and 0.8 according as if the match is played in the morning, afternoon or in the evening respectively. Given that he has won the match, the probability that the match was played in the afternoon is IP Univ. Paper – 2006 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (a) 65. 66. 69. 70. 71. 72. 73. 3 14 76. (c) 2 27 1 2 (c) 3 13 (b) 1 286 (c) 37 256 2 3 9 (b) (c) 10 16 41 60 (b) 37 60 (c) 31 60 (e) 3. 1 20 (d) 4. 1 3 5. (d) 28 256 6. 7. P A B P A B (b) 9. 10. 11. (d) N.O.T. 12. 13. x '2 y '2 1 (c) 2 2 17 (B) 1 (C) 14. 15. 16. x '2 y '2 1 2 2 x '2 y '2 1 (d) 2 2 17. The number of points (x, y) satisfying (i) 3x - 4y = 25 and (ii) x2 + y2 25 is HCU-2012 (a) 0 (b) 1 (c) 2 (d) infinite 18. 15 (D) (C) 3 (D) 5 (a) x 1 (c) x 2 1 4 17 5 15 2 2 1 y 2 6 1 y 1 6 (b) x 1 2 y 2 (d) None of these If a given point is P(10,10) and the Eq. of circle is (x – 1)2 + (y – 2)2 = 144. Where does the pt. lies Pune-2012 (a) inside (b) on (c) outside (d) None of these The point on the curve y = 6x = x2, where the tangent is parallel to x – axis is NIMCET-2012 (a) (0, 0) (b) (2, 8) (c) (6, 0) (d) (3, 9) If (4, - 3) and (-9, 7) are the two vertices of a triangle and (1, 4) is its centroid, then the area of triangle is NIMCET-2012 (a) (b) 1 2 The lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 square units. Then the equation of this circle is (= 22/7) PU CHD-2012 (A) x2 + y2 + 2x – 2y = 62 (B) x2 + y2 + 2x – 2y = 47 (C) x2 + y2 – 2x + 2y = 47 (D) x2 + y2 – 2x + 2y = 62 The focus of the parabola y2 – x – 2y + 2 = 0 is : PU CHD-2012 (A) (1/4, 0) (B) (1, 2) (C) (3/4, 1) (D) (5/4, 1) The medians of a triangle meet at (0, –3). While its two vertices are (–1, 4) and (5, 2), the third vertex is at PU CHD-2012 (A) (4, 5) (B) (–1, 2) (C) (7, 3) (D) (– 4, – 15) The area of the triangle having the vertices (4, 6), (x, 4), (6, 2) is 10 sq units. The value of x is PU CHD-2012 (A) 0 (B) 1 (C) 2 (D) 3 The position of reflection of point (4, 1) w.r.to line y = x – 1 is Pune-2012 (a) (-4, -1) (b) (1, 2) (c) (2, 3) (d) (3, 4) 6x2 + 12x + 8 – y = 0 has its standard form as? Pune-2012 (d) None of these A bag contains 6 red and 4 green balls. A fair dice is rolled and a number of balls equal to that appearing on the dice is chosen from the urn at random. The probability that all the balls selected are red is. NIMCET – 2008 (a) 1/3 (b) 3/10 (c) 1/8 (d) none A number x is chosen at random from (1, 2, …. 10). The probability that x satisfies the equation (x – 3) (x – 6) (x – 10) = 0 is ICET - 2007 (a) 2/5 (b) 3/5 (c) 3/10 (d) 7/10 (a) x'2 – y'2 = 1 5 2 (B) 3 8. (d) N.O.T. P A B P A B 3 2 The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is : PU CHD-2012 (A) (1/2, 1/2) (B) (1/3, 1/3) (C) (1/4, 1/4) (D) (0, 0) The distance between the parallel lines y = 2x + 4 and 6x = 3y + 5 is PU CHD-2012, NIT-2010 (A) TWO DIMENSIONAL GEOMETRY 1. Find the equation of the graph xy = 1 after a rotation of the axes by 45 degrees anti-clockwise in the new coordinate system (x', y'). HCU-2012 2. A point P on the line 3x + 5y = 15 is equidistant from the coordinate axes. Then P can lie in HCU-2012 (a) Quadrant I only (b) Quadrant I or Quadrant III only (c) Quadrant I or Quadrant II only (d) any Quadrant A circle and a square have the same perimeter. Then HCU-2012 (a) their areas are equal (b) the area of the circle is larger (c) the area of the square is larger (d) the area of the circle is times the area of the square The eccentricity of the ellipse x2 + 4y2 + 8y – 2x + 1 = 0 is : PU CHD-2012 (A) If the events A and B are mutually exclusive then P (A B) is given by : UPMCAT Paper – 2002 (a) P(A) + P(B) (b) P(A)P(B) (c) P(A) P(B/A) (d) N.O.T. If A and B are two events, the prob. that exactly one of them, occurs in given by: UPMCAT Paper – 2002 (c) P A B P A B 78. 1 10 If P(A' B') is equal to 19/60 then P(AB) is equal to UPMCAT Paper – 2002 (a) 77. (d) Prob. of getting an odd number or a no. less than 4 in throwing a dice is : MP– 2004 (a) 1/3 (b) 2/3 (c) 1/2 (d) 3/5 Given A and B are mutually exclusive events. IFP (B) = 0. 15, P(A B) = 0.85, P(A) is equal to UPMCAT Paper – 2002 (a) 0.65 (b) 0.3 (c) 0.70 (d) N.O.T. In a pack of 52 cards, the probability of drawing at random such that it is diamond or card king is : UPMCAT Paper – 2002 (a) 1/26 (b) 4/13 (c) 3/13 (d) 1/4 Given A and B are mutually exclusive events. if: P (A B) = 0.8, P(B) = 0.2 then P(A) is equal to UPMCAT–2002 (a) 0.5 (b) 0.6 (c) 0.4 (d) N.O.T. Two dice are thrown once the probability of getting a sum 9 is given by : UPMCAT Paper – 2002 (a) 1/12 (b) 1/18 (c) 1/6 (d) N.O.T. In a pack of 52 cards. Two cards are drawn at random. The probability that it being club card is : UPMCAT Paper – 2002 (a) 75. (b) 16 256 1 (a) 13 74. 1 15 The probability of getting atleast 6 head in 8 trials is: MP– 2004 (a) 68. (b) The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9 respectively. What is the probability that in 20 years at least one, will be alive? Karnataka PG-CET : Paper – 2006 (a) 0.98 (b) 0.02 (c) 0.72 (d) 0.28 A bag contains 4 white and 3 black balls and a second bag contains 3 white and 3 black balls. If a ball is drawn from each of the bags, then the probability that both are of same colour is : MP Paper – 2004 (a) 67. 1 12 138 2 (b) 319 2 (c) 183 2 (d) 381 2 The equation of the ellipse with major axis along the x-axis and passing through the points (4, 3) and (-1, 4) is NIMCET-2012 (a) 15x2 + 7y2 = 247 (b) 7x2 + 15y2 = 247 (c) 16x2 + 9y2 = 247 (d) 9x2 + 16y2 = 247 If the circles x2 + y2 + 2x + 2ky + 6 = 0 and x2 + y2 + 2ky + k = 0 intersect orthogonally, then k is NIMCET-2012 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 19. 20. (a) 2 of (c) 2 or 3 2 3 2 (b) – 2 or (d) – 2 or 3 2 (a) x(x2 + y2) = a(2x2 + y2) (c) Focus of the parabola x + y – 2xy – 4(x + y – 1) = 0 is NIMCET-2012 (a) (1, 1) (b) (1, 2) (c) (2, 1) (d) (0, 2) If e and er be the eccentricities of a hyperbola and its conjugate, 2 then 2 32. (b) 1 y a x x 1 y 2 a x2 2 x (d) y = atan + x The relation that represents the shaded region in the figure given below is 1 1 r2 2 e e (a) 0 21. 3 2 (b) 1 NIMCET-2012 (d) None of these (c) 2 The straight line passes through the point P 2, 3 and makes an angle of 60 with the x-axis. The length of the intercept on it between the point P and the line 22. 23. 3 (a) tan 5 1 2 (c) tan 11 25. 34. 35. 5 (b) tan 3 1 11 (d) tan 2 1 (b) 5 2 27. 33. 36. The equation of circle passing through (-1, 2) and concentric with x2 + y2 – 2x – 4y – 4 = 0 is : BHU-2012 (a) x2 + y2 – 2x – 4y + 1 = 0 (b) x2 + y2 – 2x – 4y + 2 = 0 2 2 2 2 (c) x + y – 2x – 4y + 4 = 0 (d) x + y – 2x – 4y + 8 = 0 The radius of the circle on which the four points of intersection of the lines (2x – y + 1) (x – 2y + 3) = 0 with the axes lie, is : BHU-2012 (a) 5 26. is : BHU-2012 (a) 1.5 (b) 2.5 (c) 3.5 (d) 4.5 The equation of the straight line passing through the point of intersection of 4x + 3y – 8 = 0 and x + y – 1 = 0, and the point (-2, 5) is : BHU-2012 (a) 9x + 7y – 17 = 0 (b) 4x + 5y + 6 = 0 (c) 3x – 2y + 19 = 0 (d) 3x – 4y – 7 = 0 The angle between the two straight line represented by the equation 6x2 + 5xy – 4y2 + 7x + 13y – 3 = 0 is: BHU-2012 1 24. x 3 y 12 5 (c) 38. 4 2 39. The focal distance of a point on the parabola y2 = 8x is 4. Its ordinates are : BHU-2012 (a) 1 (b) 2 (c) 3 (d) 4 The straight line x cos + y sin = p touches the ellipse 2 28. If the line lx + my = n touches the hyperbola (a) a2l2 – b2m2 = n2 (c) a2l2 + b2m2 = n2 29. For the conic 40. BHU-2012 segments of any focal chord is equal to : BHU-2012 (a) l 30. 31. (b) 2l 2 3 (c) 3 4 (d) 1 4 Point A is a + 2b, P is a and P divides AB in the ratio of 2 : 3. The position vector of B is BHU-2011 (a) 2a – b (b) b – 2a (c) a – 3b (d) b If the position vectors of A and B are a and b respectively, then the position vector of a point P which divides AB in the ratio 1 : 2 is BHU-2011 b 2a 3 b 2a (d) 3 (b) The straight line x y 1 touches the curve a b y = be-x/a at the point 41. l 1 e cos , the sum of reciprocals of the r 1 (c) l (b) 2 x y 2 1 if : 2 a b (b) al – bm = n (d) al + bm = n 3 ab 3 a 2b (c) 3 BHU-2012 (b) p2 = a2 cos2 + b2 sin2 (d) p2 = a2 sin2 + b2 cos2 (a) p2 = a2 cos2 - b2 sin2 (c) p2 = a2 sin2 - b2 cos2 1 (a) x2 y 2 1 if : a 2 b2 HCU-2011 NIMCET-2011 (a) 1 (b) 2 (c) 3 (d) 4 If 2x + 3y – 6 = 0 and 9x+ 6y – 18 = 0 cuts the axes in concyclic points, then the center of the circle is: NIMCET-2011 (a) (2, 3) (b) (3, 2) (c) (5, 5) (d) (5/2, 5/2) The number of distinct solutions (x, y) of the system of equations x2 = y2 and (x – a)2 + y2 = 1 where ‘a’ is any real number, can only be NIMCET-2011 (a) 0, 1, 2, 3, 4 or 5 (b) 0, 1 or 3 (c) 0, 1, 2 or 4 (d) 0, 2, 3 or 4 The vertex of parabola y2 − 8y +19 = x is NIMCET-2011 (a) (3, 4) (b) (4, 3) (c) (1, 3) (d) (3, 1) The eccentricity of ellipse 9x2 + 5y2 − 30y = 0 is NIMCET-2011 (a) 5 (d) 2 2 37. (a) y x (b) |y| |x| (c) y |x| (d) |y| x The area enclosed within the lines |x| + |y| = 1 is 42. 2 (d) l BHU-2011 (a) where it crosses the y-axis (b) where it crosses the x-axis (c) (0, 0) (d) (1, 1) Every homogeneous equation of second degree in x and y represent a pair of lines BHU-2011 (a) parallel to x-axis (b) perpendicular to y-axis (c) through the origin (d) parallel to y-axis The difference of the focal distances of any point on the hyperbola x2 y 2 1 is a 2 b2 The equation of tangent at (2, 2) of the curve xy2 = 4 (4 – x) is : BHU-2012 (a) x – y = 4 (b) x + y = 4 (c) x – y = 2 (d) x + y = 2 A curve given in polar form as r = a(cos() + sec ()) can be written in Cartesian form as HCU-2011 43. 16 BHU-2011 (a) a (b) 2a (c) b (d) 2b If in ellipse the length of latusrectum is equal to half of major axis, then eccentricity of the ellipse is BHU-2011 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (a) 44. 45. 46. 3 2 (b) 1 (c) 2 2 (d) 1 (c) 3 57. An equilateral triangle is inscribed in the parabola y2 = 4ax whose vertex is at the vertex of the parabola. The length of its side is BHU-2011 x 2 58. (a) straight line (b) circle (c) parabola (d) pair of lines The coordinates of the orthocenter of the triangle formed by the lines 2x2 – 2y2 + 3xy + 3x + y + 1 = 0 and 3x + 2y + 1 = 0 are BHU-2011 (c) (b) (d) 59. 60. 3 1 , 5 5 2 1 , 5 5 61. 48. The angle between the asymptotes of the hyperbola 27x – 9y = 24 is NIMCET-2010 (a) 60 (b) 120 (c) 30 (d) 150 49. If any tangent to the ellipse l on the axes, then l = 2 62. X2 Y2 1 intercepts equal length a 2 b2 63. NIMCET-2010 (B) a b (D) N.O.T 2 (A) a2 + b2 (C) (a2 +b2)2 2 64. p b c 50. If a p, b q, c r and a q c = 0, then the value of a b r p q r + p a q b r c 51. 52. 53. 54. 55. 56. 65. is NIMCET-2010 (a) 0 (b) 1 (c) -1 (d) 2 The number of integral values of m for which the x coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer is KIITEE-2010 (a) 2 (b) 0 (c) 4 (d) 1 The pair of straight lines joining the origin to the common point of x2 + y2 = 4 and y = 3x + c perpendicular if c2 is equal to KIITEE-2010 (a) 20 (b) 13 (c) 1/5 (d) 1 Intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as diameter is KIITEE-2010 (a) x2 + y2 + x – y = 0 (b) x2 + y2 – x + y = 0 (c) x2 + y2 + x + y = 0 (d) x2 + y2 – x – y = 0 The locus of a point which moves such that the tangents from it to the two circles x2 + y2 – 5x – 3 = 0 and 3x2 + 3y2 + 2x + 4y – 6 = 0 are equal is KIITEE-2010 (a) 2x2 + 2y2 + 7x + 4y – 3 = 0 (b) 17x + 4y + 3 = 0 2 2 (c) 4x + 4y – 3x + 4y – 9 = 0 (d) 13x – 4y + 15 = 0 If a 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then KIITEE-2010 (a) d2 + (3b – 2c)2 = 0 (b) d2 + (3b + 2c)2 = 0 (c) d2 + (2b – 3c)2 = 0 (d) d2 + (2b + 3c)2 = 0 The distances from the foci of P (a, b) on the ellipse x2 y 2 1 are 9 25 5 (a) 4 b 4 66. 67. 68. 69. 70. KIITEE-2010 (b) It the foci of the ellipse 71. 4 5 a 5 28 13 (b) and the hyperbola coincide, then the value of b2 is 31 13 (c) 30 10 (d) None of these If the lines x – 6y + a = 0, 2x + 3y + 4 = 0 and x + 4y + 1 = 0 are concurrent, then the value of ‘a’ is PGCET-2010 (a) 4 (b) 8 (c) 5 (d) 6 2 the angle between the lines represented by x + 3xy + 2y2 = 0 is PGCET-2010 (a) tan-1(2/3) (b) tan-1(1/3) (c) tan-1(3/2) (d) None of these If the circle 9x2 + 9y2 = 16 cuts the x-axis at (a, 0) and (-a, 0), then a is PGCET-2010 (a) 2/3 (b) 3/4 (c) 1/4 (d) 4/3 The length of the perpendicular drawn from the point (1, 1) on the 15x + 8y + 45 = 0 is (PGCET paper – 2009) (a) 3 (b) 4 (c) 5 (d) 2 The equation of the line passing through the point of intersection 2x – y + 5 = 0 and x + y + 1 = 0 and the point (5, - 2) is (PGCET paper – 2009) (a) 3x + 7y – 1 = 0 (b) x + 2y + 1 = 0 (c) 5x + 6y + 3 = 0 (d) None of these The point of intersection of the lines represented by 2x 2 – 9xy + 4y2 = 0 is (PGCET paper – 2009) (a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1) If y = x + c is a tangent to the circle x2 + y2 = 8, then c is (PGCET paper – 2009) (a) 3 (b) 2 (c) 4 (d) 1 The equation of the parabola whose vertex is (1, 1) and focus is (4, 1) is (PGCET paper – 2009) (a) (y – 1)2 = 12(x – 1) (b) (y – 2)2 = 13(x – 2) (c) (y – 1)2 = 10(x + 1) (d) None of these If the distance of any point (x, y) from the origin is defined as d(x, y)= max (|x|, |y|), then the locus of the point (x, y) where d(x, y) = 1 is MCA : NIMCET – 2009, KIITEE-2010 (a) a square of area 1 sq. unit (b) a circle of radius 1 (c) a triangle (d) a square of area 4 sq. units Let ABC be an isosceles triangle with AB = BC. If base BC is parallel to x-axis and m1, m2 are slopes of medians drawn through the angular points B and C, then (MCA : NIMCET – 2009) (a) m1m2 = - 1/2 (b) m1 + m2 = 0 (c) m1m2 = 2 (d) (m1 – m2)2 + 2m1m2=0 The straight lines on (a) a parabola (c) a hyperbola 17 x2 y 2 1 25 b2 KIITEE-2010 (a) 3 (b) 16 (c) 9 (d) 12 The medians of a triangle meet at (0, - 3) and two vertices are at (1, 4) and (5, 2). Then the third vertex is at KIITEE-2010 (a) (4, 15) (b) (-4, 15) (c) (-4, 15) (d) (4, -15) The length of the perpendicular drawn from the point (3, - 2) on the line 5x – 12y – 9 = 0 is PGCET-2010 (a) 2 (b) a circle (d) a hyperbola x2 y 2 1 144 81 25 BHU-2011 (a) x2 y 2 1 is a 2 b2 KIITEE-2010 4 y 2 4 xy 4 x 2 y 1 4 3 , 5 5 1 5 , 5 4 The locus of a point P(,) moving under the condition that the (a) an ellipse (c) a parabola represents a 47. (d) None of these line y = x + is a tangent to the hyperbola (a) a 3 (b) 2a 3 (c) 4a 3 (d) 8a 3 Two circles x2 + y2 = 5 and x2 + y2 – 6x + 8 = 0 are given. Then the equation of the circle through their point of intersection and the point (1, 1) is BHU-2011 (a) 7x2 + 7y2 – 18x + 4 = 0 (b) x2 + y2 – 3x + 1 = 0 (c) x2 + y2 – 4x + 2 = 0 (d) x2 + y2 – 5x + 3 = 0 The equation 4 5 b 5 x y x y 1 k and , k 0 meet a b a b k (MCA : NIMCET – 2009) (b) an ellipse (d) a circle INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 72. 73. 74. 75. The equation of the line segment AB is y = x, if A and B lie on the same side of the line mirror 2x – y = 1 the image of AB has the equation (MCA : KIITEE - 2009) (a) 7x – y = 6 (b) x + y = 2 (c) 8x + y = 9 (d) None of these The point (-1, 1) and (1, -1) are symmetrical about the line (MCA : KIITEE - 2009) (a) y + x = 0 (b) y = x (c) x + y = 1 (d) None of these The product of perpendiculars drawn from the point (1, 2) to the pair of lines x2 + 4xy + y2 = 0 is (MCA : KIITEE - 2009) (a) 9/4 (b) 9/16 (c) 3/4 (d) None of these The centroid of the triangle whose three sides are given by the combined equation (x2 + 7xy + 12y2) (y – 1) = 0 is (MCA : KIITEE - 2009) (a) (c) 76. 77. 78. 2 ,0 3 7 2 , 3 3 (b) 80. 1 c, c 85. 7 2 , 3 3 86. Two distinct chords drawn from the point (p, q) on the circle x + y2 = px + qy, where pq 0 are bisected by the x-axis then (MCA : KIITEE - 2009) (a) |p| = |q| (b) p2 = 8q2 (c) p2 < 8q2 (d) p2 > 8q2 The length of the latus rectum of the parabola x = ay2 + by + c is (MCA : KIITEE - 2009) (a) a/4 (b) 1/4a (c) 1/a (d) a/3 2 The equation of the tangent to the x – 2y2 = 18 which is perpendicular to the line x – y = 0 (MCA : KIITEE - 2009) (a) x + y = 3 (b) x + y =3/2 25 0 2 (a) x (b) x2 (c) x2 (d) 81. 82. x 2 83. (d) (a) 1 (b) 3 (c) 3y x 3 (d) 3 y (3x 1) (a) y mx 3 1 m 2 (b) y mx 2 3 1 m 2 (c) y mx m 2 3 1 m 2 (d) None The equation of the circle whose two diameters are 2x – 3y + 12 = 0 and x + 4y – 5 = 0 and the area of which is 154 sq. units, will be 22 7 MP COMBINED - 2008 91. 92. If the line hx + ky = 1 touches the circle 93. 94. 95. NIMCET - 2008 (c) 3 y ( x 3) (a) x2 + y2 + 6x – 4y + 36 = 0 (b) x2 + y2 + 3x – 2y + 18 = 0 (c) x2 + y2 – 6x + 4y + 36 = 0 (d) x2 + y2 + 6x – 4y – 36 = 0 The circle x2 + y2 – 2x + 2y + 1 = 0 touches: MP COMBINED - 2008 (a) Only x-axis (b) Only y-axis (c) Both the axes (d) None of the axes 2 y x 1 16 9 x2 y2 1 16 7 is 1 (b) : If y = mx bisects the angle between the lines x2 (tan2 + cos2) + 2xy tan - y2 sin2 = 0 when = /3, then the value of 3m 2 4m 3 y 3x 1 (x 2 y 2 ) 1 a2 , then the locus of the point (h, k) will be: 2 (b) (a) (a) 4 2 (b) 4 2 (c) 4 (d) 8 The equation of any tangent to the circle x2 + y2 – 2x + 4y – 4 = 0 is KIITEE - 2008 as a diameter is Loci of a point equidistant to (2, 0) and x = - 2 is HYDERABAD CENTRAL UNIVERSITY - 2009 (a) y2 = 8x (b) y2 = 4x (c) x2 = 2y (d) x2 = 16y Given two fixed points A(-3, 0) and B(3, 0) with AB = 6, the equation of the locus of point P which moves such that PA + PB = 8 is HYDERABAD CENTRAL UNIVERSITY - 2009 x y 1 8 6 x y 1 (c) 7 16 (c) (p + q, p – q) (d) (3p, 3q) Equation of the common tangent touching the circle (x – 3)2 + y2 = 9 and the parabola y2 = 4x above the x – axis is NIMCET - 2008 89. 2 (a) p q , 3 3 (a) 4 3 (b) 16 (c) 48 (d) None If the common chord of the circles x2 + (y - )2 = 16 and x2 + y2 = 16 subtend a right angle at the origin then is equal to. MCA : KIITEE - 2008 90. 21 x 3x y 0 2 25 x 2 3x y 0 2 25 x 2 x 3y 0 2 25 x 2 3x y 0 2 (b) 88. HYDERABAD CENTRAL UNIVERSITY - 2009 2 NIMCET - 2008 87. The sides of the rectangle of the greatest area that can be inscribed in the ellipse x2 + 2y2 = 8, are given by HYDERABAD CENTRAL UNIVERSITY - 2009 x 2 x 2 x 3y and The coordinates of a point on the line x + y = 3 such that the point is at equal distances from the lines |x| = |y| are KIITEE - 2008 (a) (3, 0) (b) (-3, 0) (c) (0, - 3) (d) None Lines are drawn through the point P (-2, -3) to meet the circle x2 + y2 – 2x – 10y + 1 = 0. The length of the line segment PA, A being the point on the circle where the line meets the circle is. KIITEE - 2008 x y3 2 0 (a) 2, 2 (b) 4,2 2 (c) 2 2 ,4 (d) 4 2 ,4 The equation of the circle having the chord x – y = 1 of the circle 1 1 a, , b, a b is at the point (a) (p, q) 2 (d) If a, b, c are the roots of the equation x3 – 3px2 + 3qx – 1 = 0, then the centroid of the triangle with vertices (d) None of these (c) x + y + 2 = 0 79. 84. (d) 7 3 96. 3 97. 18 (a) x2 + y2 = a2 MP COMBINED - 2008 (b) x2 + y2 = 2a2 (c) x2 + y2 = 1 (d) x2 y2 a2 2 Equation of the circle concentric to the circle x2 + y2 – x + 2y + 7 = 0 and passing through (-1, -2) will be: MP COMBINED - 2008 (a) x2 + y2 + x + 2y = 0 (b) x2 + y2 – x + 2y + 2 = 0 (c) 2(x2 + y2) – x + 2y = 0 (d) x2 + y2 – x + 2y – 2 = 0 For the circle x2 + y2 – 4x + 2y + 6 = 0, the equation of the diameter passing through the origin is: MP COMBINED - 2008 (a) x – 2y = 0 (b) x + 2y = 0 (c) 2x – y = 0 (d) 2x + y = 0 The circle x2 + y2 + 2ax – a2 = 0: (MP COMBINED – 2008) (a) touches x – axis (b) touches y – axis (c) touches both the axis (d) intersects both the axes The circles x2 + y2 + 2g1x + f1y + c1 = 0 and x2 + y2 + g2x + 2f2y + c2 = 0 cut each other orthogonally, then : (MP COMBINED – 2008) (a) 2g1g2 + 2f1f2 = c1 + c2 (b) g1g2 + f1f2 = c1 + c2 (c) g1g2 + f1f2 = 2(c1 + c2) (d) g1g2 + f1f2 + c1 + c2 = 0 If the straight line 3x + 4y = touches the parabola y2 = 12x then value of is INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 98. 99. (MCA : MP COMBINED – 2008) (a) 16 (b) 9 (c) – 12 (d) – 16 2 For the parabola y = 14x, the tangent parallel to the line x + y + 7 = 0 is : (MCA : MP COMBINED – 2008) (a) x + y + 14 = 0 (b) x + y + 1 = 0 (c) 2(x + y) + 7 = 0 (d) x + y = 0 Eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is : (MP COMBINED – 2008) (a) 1/3 (b) 2/3 (c) 4/9 (d) 5/9 2 100. For the ellipse ICET – 2005 (a) incentre (b) orthocenter (c) centroid (d) circumcentre 118. If (0, 0), (2, 2) and (0, a) form a right angled isosceles triangle, then a = ICET – 2005 (a) 4 (b) – 4 (c) 3 (d) – 3 119. The area of the largest rectangle, whose sides are parallel to the coordinate axes, that can be inscribed in the ellipse x2 y 2 1 25 9 2 x y 1 , S1 and S2 are two foci then for 64 36 (a) 10 (b) 20 (c) 30 (d) 20 5 (e) 20 6 120. The orthocenter of the triangle determined by the lines 6x2 + 5xy – 6y2 – 29x + 2y + 28 = 0 and 11x – 2y – 7 = 0 is IP Univ. Paper – 2006 (a) (-4, 5) (b) (4, 4) (c) (6, 7} (d) (2, 1) (e) (-1, 3) 121. a, b, c R. if 2a + 3b + 4c = 0, then the line ax + by + c = 0 passes through the point any point P lying on the ellipse S1P + S2P equals: (MCA : MP COMBINED – 2008) (a) 6 (b) 8 (c) 12 (d) 16 101. The coordinates of the foci of the hyperbola 9x2 – 16y2 = 144 are: (MCA : MP COMBINED – 2008) (a) (0, 4) (b) ( 4, 0) (c) (0, 5) (d) ( 5, 0) 102. The lengths of transverse and conjugate axes of the hyperbola x2 2y2 – 2x + 8y – 1 = 0 will be respectively: (MCA : MP COMBINED – 2008) (a) (c) 2 3 ,2 6 4 3 ,4 6 (b) (d) IP Univ. Paper – 2006 (a) 3 6 (c) 1 1 3, 6 2 2 1 3 , 3 5 5 3 , 2 7 (b) (d) 2 3 , 3 4 1 3 , 7 11 (e) 1 3 , 2 4 122. The distance of the point (x, y) form y-axis is Karnataka PG-CET : Paper 2006 (a) x (b) y (c) |x| (d) |y| 123. If the lines 4x + 3y = 1, y = x + 5 and 5y + bx = 3 are concurrent, then the value of b is Karnataka PG-CET : Paper 2006 (a) 1 (b) 3 (c) 6 (d) 0 124. The system of equations x + y = 2 and 2x + 2y = 3 has Karnataka PG-CET : Paper 2006 (a) No solution (b) a unique solution (c) finitely many solutions (d) infinitely many solutions 125. The radius of the circle 16x2 + 16y2 = 8x + 32y – 257 = 0 Karnataka PG-CET : Paper 2006 (a) 8 (b) 6 (c) 15 (d) None of these 2 126. Axis of the parabola x – 3y – 6x + 6 = 0 is Karnataka PG-CET : Paper 2006 (a) x = - 3 (b) y = - 1 (c) x = 3 (d) y = 1 127. The locus of a point which moves such that the difference of its distances from two fixed points is always a constant is Karnataka PG-CET : 2006 (a) a circle (b) a straight line (c) a hyperbola (d) an ellipse 128. The Eccentricity of a rectangular hyperbola is : MP : MCA Paper – 2003 103. For the given equation x2 + y2 – 4x + 6y – 12 = 0, the centre of the circle is KARNATAKA - 2007 (a) (-2, 3) (b) (-3, 2) (c) (3, - 2) (d) (2, - 3) 104. The circumference of the circle x2 + y2 + 2x + 6y – 12 = 0 is KARNATAKA - 2007 (a) 2 (b) 8 (c) 3 (d) None 105. The locus of a point which moves in a plane such that its distance from a fixed point is equal to its distance from a fixed line is. KARNATAKA - 2007 (a) Parabola (b) Hyperbola (c) Ellipse (d) Circle 106. In parabola y2 = 4kx, if the length of Latus Rectum is 2 then k is KARNATAKA - 2007 (a) +1/2 (b) –1/2 (c) 0 (d) +1/2 or – 1/2 107. The point of intersection of lines (i) x + 2y + 3 = 0 and (ii) 3x + 4y + 7 = 0 is KARNATAKA - 2007 (a) (1, 1) (b) (1, - 1) (c) (-1, 1) (d) (-1, -1) 108. The acute angle between the lines (i) 2x – y + 13 = 0 and (ii) 2x – 6y + 7 = 0 KARNATAKA - 2007 (a) 0 (b) 30 (c) 45 (d) 60 109. If the points (k, - 3), (2, - 5) and (-1, -8) are collinear then K = ICET - 2007 (a) 0 (b) 4 (c) – 2 (d) – 3 110. The equation of the line with slope -3/4 and y – intercept 2 is ICET - 2007 (a) 3x + 4y = 8 (b) 3x + 4y + 8 = 0 (c) 4x + 3y = 2 (d) 3x + 4y = 4 111. If the lines x + 2y + 1 = 0, x + 3y + 1 = 0 and x + 4y + 1 = 0 pass through a point then a + = ICET - 2007 (a) (b) 2 (c) 1/ (d) 1/2 112. Equation of the line passing through the point (2, 3) and perpendicular to the segment joining the points (1, 2) and (-1, 5) is ICET – 2005 (a) 2x – 3y – 13 = 0 (b) 2x – 3y – 9 = 0 (c) 2x – 3y – 11 = 0 (d) 3x + 2y – 12 = 0 113. The two sides forming the right angle of the triangle whose area is 24 sq. cm. are in the ratio 3:4. Then the length of the hypotenuse (in cm) is ICET – 2005 (a) 12 (b) 10 (c) 8 (d) 5 114. The equation of the circle passing through the origin and making intercepts of 4 and 3 or OX and OY respectively is ICET – 2005 (a) x2 + y2 – 3x – 4y = 0 (b) x2 + y2 + 4x + 3y = 0 (c) x2 + y2 + 3x + 4y = 0 (d) x2 + y2 – 4x – 3y = 0 115. The equation of the straight line which cuts off equal intercepts from the axis and passes through the point (1, - 2) is ICET – 2005 (a) 2x + 2y + 1 = 0 (b) x + y + 1 = 0 (c) x + y – 1 = 0 (d) 2x + 2y – 1 = 0 116. If the lines 2x + 3y = 6, 8x – 9y + 4 = 0, ax + 6y = 13 are concurrent, then a = ICET – 2005 (a) 3 (b) – 3 (c) – 5 (d) 5 117. The points of concurrence of medians of a triangle is (a) 3 (b) 2 (c) 3 / 2 (d) 2 129. From a point (x1, y1) two tangent can be drawn on circle x2 + y2 = a2 if: MP : MCA Paper – 2003 (a) x12 y12 a 2 0 (b) x12 y12 a 2 0 (c) x12 y12 a 2 0 (d) None of these 130. The sum of the distance of a point on the ellipse x2 y 2 1 to a 2 b2 its foci is equal to : MP : MCA– 2003 (a) semi major axis (b) major axis (c) semi minor axis (d) minor axis 131. The foci of hyperbola 9x2 – 25y2 + 54x + 50y – 169 = 0 is MP – 2003 (a) (-3, 1) (c) 3 (b) 34,1 2 3 34,1 (d) None of these 132. If two circles x + y + 2g1x + 2f1y + c1 = 0 & x2 + y2 + 2g2x + 2f2y + c2 = 0 will cut each other and satisfies the relation g1 g 2 f1 f 2 2 c1 c2 . Then angle between the circles will be 2 MP : MCA Paper – 2003 (a) π/3 (b) π/2 (c) 3π/2 (d) π/4 2 2 2 133. Two circles x + y + 2gx + c = 0 and x + y2 + 2fy + c = 0 touch each other, then : MP :– 2003 19 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 2 2 3 2 2 (a) g + f = c (b) g + f = c (c) c(g2 + f2) = g2f2 (d) g2 + f2c = g2f2 2 2 134. S1 = x + y – 4x – 6y + 10 = 0 S2 = x2 + y2 – 2x – 2y – 4 Angle between S1 and S2 is UPMCAT : paper – 2002 (a) 90 (b) 60 (c) 45 (d) None of these 135. The equation of line passing through the intersection of lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to 3x – 5y + 27 = 0 is : UPMCAT :– 2002 (a) 5x + 3y + 10 = 0 (b) 5x + 3y + 21 = 0 (c) 5x + 3y + 18 = 0 (d) 5x + 3y + 8 = 0 136. The area of triangle formed by y = m1x + c, y = m2x + c2 and y axis is : UPMCAT : paper – 2002 1 c1 c2 2 m1 m2 2 (a) 1 c1 c2 2 m1 m2 2 (c) 1 c1 c2 2 m1 m2 2 (b) 1 c2 c1 2 m1 m2 2 (d) (a) (c) (b) (b) 13 26 , 5 5 3 4 13 5 (c) 13 (d) None of these 140. If (± 3, 0) be focus of ellipse and semi major axis is 6. Then equ. of ellipse is: UPMCAT :– 2002 (a) (c) (b) x2 y 2 1 27 36 g h b f 0 g f c 2 2 1 , directrix is x + 6 = 0, and has a focus at (0, 2 0) then the eqn. of ellipse is: UPMCAT :– 2002 (a) 3x + 4y + 12x – 36 = 0 (b) 3x + 4y – 12x + 36 = 0 (c) 3x2 + 4y2 – 12x – 36 = 0 (d) None of these 144. The eqn. of the ellipse has its centre at (1, 2), a focus at (6, 2) and passing through the point (4, 6) : UPMCAT :– 2002 2 (a) 2 x 1 45 2 2 (c) 5 y 2 20 2 1 (b) 2 x 1 45 2 (d) 3 x2 cos 2 y2 1 which of the MCA : KIITEE - 2008 (a) directrix (b) eccentricity (c) abscissae of foci (d) abscissae of vertices 149. The sum of the intercepts made on the axes of co-ordinates by any x y 2 is equal to KIITEE - 2008 (a) 4 (b) 8 (c) 2 (d) None 150. If the focus and directrix of a parabola are (-sin , cos ) and x cos + y sin = p respectively, then length of the latus rectum will be: (MP COMBINED – 2008) (a) 2p (b) 4p (c) p2 (d) p(cos – sin ) 151. The distance between the two focii of a hyperbola H is 12. The distance between the two directories of hyperbola H is 3. The acute angle between the asymptotes of H in degrees is IP Univ. Paper – 2006 (a) 30 (b) 40 (c) 45 (d) 60 (e) 70 y 2 20 2 1 1 . All 25 x2 y 2 1 . The area of the 25 9 parallelogram determine by these lines is IP University : Paper - 2006 (a) 21 (b) 28 (c) 40 (d) 56 (e) 60 153. If P, Q, R, S are four distinct collinear points such that PR PS RP RQ k , then, the value of . is RQ SQ PS QS IP University : Paper - 2006 1 k (a) 1 l (ii) abc + 2fgh – af – bg – ch = 0 (iii) af + bg + ch = 0 (iv) af2 = bg2 ; h2 = ab UPMCAT:– 2002 (a) i, ii (b) ii, iv (c) i, iv (d) i, ii and iv 2 e (b) 6 (d) None of these h 143. A ellipse has (a) 10 these lines touch the ellipse a has the eccentric angle 152. L1 || L2. Slope of L1 = 9. Also L3 || L4. Slope of L4 141. If 2x2 – 5xy + 2y2 – 3x + 1 = 0, represents pairs of lines, then the angle between the lines is : UPMCAT : paper – 2002 (a) tan-1 (2/3) (b) tan-1 (4/3) (c) tan-1 (3/4) (d) None of these 142. The condition that eqa. ax2 + by2 + 2gx + 2fy + 2hxy + c = 0 represents a pair of the line is (i) x2 y2 1 25 9 . The sum of the distance of P from the two foci is. tangent to the curve 1 Sq U 12 13 x2 y 2 1 36 45 x2 y 2 1 36 27 (a) 4 (b) 6 2 (c) 4 (d) None 146. The x2 + y2 + 2x = 0, R touches the parabola y2 = 4x externally. Then KIITEE - 2008 (a) > 1 (b) < 0 (c) > 0 (d) None sin 2 following remains constant when varies? (d) N.O.T. (b) 1 (d) None of these 45 148. For the hyperbola 139. If 4x2 + 9y2 + 12xy + 6x ….. + 9y – 4 = 0 represents two parallel lines then the distance between. The lines is: UPMCAT:– 2002 (a) y 2 KIITEE - 2008 138. The area of the region bonded by the curve y = x2 and the line y = x is UPMCAT : paper – 2002 1 Sq U 64 1 (c) Sq U 6 20 2 145. The tangents of the circle x2 + y2 = 4 at the points A and B meet at P(-4, 0). The area of the quadrilateral PAOB where O is the origin is. KIITEE - 2008 8 (d) None of these (a) x 1 147. A point P on the ellipse 137. Reflection of the point P(1, 2) in x + 2y + 4 = 0 is UPMCAT : paper – 2002 13 26 , 5 5 13 26 , 5 5 (c) 2 (c) 1 k (b) 1 k 2 1 k 1 k (d) 1 k 1 k 2 2 (e) N.O.T. 154. P moves on the line y = 3x + 10. Q moves on the parabola y2 = 24x. The shortest value of the segment PQ is IP University - 2006 (a) 7 12 8 (b) (c) 10 7 2 (d) 6 (e) 6 15 155. The line 2x + y – 1 = 0 cuts the curve 5x2 + xy – y2 – 3x – y + 1 = 0 at P and Q. O is the origin. The acute angle between the lines OP and OQ is IP University - 2006 (a) 7 (b) 6 (c) 5 (d) 4 (e) 3 156. The limiting points of the system of coaxial circles of which two members are x2 + y2 + 2x + 4y + 7 = 0 and x2 + y2 + 5x + y + 4 = 0 is: MP : MCA Paper – 2003 (a) (-2, 1) and (0, - 3) (b) (2, 1) and (0, 3) 20 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (c) (4, 1) and (0, 6) (d) None of these 157. The length of common chord of the circles (x – a)2 + y2 = a2 and x2 2 2 + (y – b) = b is : MP : MCA Paper – 2003 (a) 2 a b 2 2 (b) 2ab (c) 9. PU CHD-2011 (A) ab a 2 b2 (C) (d) None of these a 2 b2 10. 158. An arch way is in the shape of a semi ellipse. The road level being the major axis. If the breadth of the road is 30 metres and the height of the arch is 6m at a distance of 2 metre from the side, then find the greatest height of the arch. MP : MCA Paper – 2003 (a) (c) 25 14 14 25 14 7 m (b) m (d) 45 14 14 45 14 7 11. m 12. m 159. The locus midpoint of a chord of the circle x2 + y2 = 4, which subtend angle 90 at the centre. UPMCAT : paper – 2002 (a) x + y + 3 = 0 (b) x2 + y2 = 0 (c) x + y + 2 = 0 (d) x2 + y2 = 2 13. 14. FUNCTIONS 1. x 1 x 3 f x x 2 The range of the function f(x) = 1/(2 – cos3x) = 1 ,1 3 1 3 ,1 1 (B) ,1 3 1 (d) ,1 3 If f = {(1, 1), (2, 3), (0, - 1), (-1, -3)} be a function described by the formula f(x) = ax + b for some integers a, b, then the value of a, b is BHU-2011 (a) a = - 1, b = 3 (b) a = 3, b = 1 (c) a = - 1, b = 2 (d) a = 2, b = - 1 Set A has 3 elements and set B has 4 elements. The number or injection that can be defined from A to B is NIMCET-2010 (a) 144 (b) 12 (c) 24 (d) 64 Let A and B be sets and the cardinality of B is 6. The number of one-to-one functions from A to B is 360. Then the cardinality of A is (Hyderabad Central University – 2009) (a) 5 (b) 6 (c) 4 (d) Can’t be determined Suppose that g(x) = 1 f(x) is (a) 1 + 2x2 (b) 2 + x2 If f x x and f{g(x)} = 3 2 x x, then cos 2 x sin 4 x sin 2 x cos4 x 3. 4. 15. (b) 2 The function (c) 3 Then fof f x log x x2 1 6. 7. 8. (c) 1 1 1 4log 2 x 2 1 1 1 4log 2 x 2 17. (a) [1, 9] (b) [-, 9] (c) [-9, 1] (d) [-9, -1] A function f from the set of natural numbers to integers defined by 18. 19. (d) not defined 20. Let the function f (x) = x2 from the set of integers to the set of integers. Then : PU CHD-2011 (A) f is one-one and onto (B) f is one-one but not onto (C) f is not one-one but onto (D) f is neither one-one nor onto The value of P and Q for which the identity f(x+1) - f (x) = 8x + 3 is satisfied, where f (x) = Px2 + Qx + R, are : PU CHD-2011 (A) P = 2, Q = 1 (B) P = 4, Q = –1 (C) P = –1, Q = 4 (D) P = –1, Q = 1 Let (C) x2 – 2 KIITEE-2010 (a) one-one but not onto (b) onto but not one-one (c) one-one and onto both (d) neither one-one nor onto For real x, let f(x) = x3 + 5x + 1, then KIITEE-2010 (a) f is onto R but not one-one (b) f is one-one and onto R (c) f is neither one-one nor onto R (d) f is one-one but not onto R Let f(x) = [x2 - 3] where [ ] denotes the greatest integer function. Then, the number of points in the interval (1, 2) where the function is discontinuous is (MCA : NIMCET – 2009) (a) 4 (b) 2 (c) 6 (d) None of these Let f(x) = - log2x + 3 and a[1, 4] the f(a) is equal to (MCA : KIITEE - 2009) (a) [1, 3] (b) [2, 4] (c) [1, 2] (d) [1, 9] 21 x x 1 is 2 22. (MCA : KIITEE - 2009) (a) periodic (b) odd (c) even (d) neither odd or even Which of the function is periodic? (MCA : KIITEE - 2009) (a) f(x) = x cos x (b) f(x) = sin (1/x) 23. (D) x2 + 2 f ( x) The function (c) PU CHD-2011 (B) x2 – 1 KIITEE-2010 21. 1 1 f x x 2 2 x 0 , then f(x) = x x (A) x2 is n 1 2 , when n is odd if f x is : n , when n is even 2 (a) 1 (b) - 1 (c) 3 (d) 0 If the function f: [1, ∞) → [1, ∞) is defined by f(x) = 2x(x−1) , then f −1(x) is KIIT-2010, NIMCET-2011 (b) x sin 1 log3 3 The domain of 1 3 1 2 x x 1 is 16. -1, if x is rational f x= . 1, if x is irrational (a) (a) neither an even nor an odd function (b) an even function (c) an odd function (d) a periodic function Pune-2012 5. (d) 4 KIITEE-2010 PU CHD-2012 (A) (–, – 1] [3, ) (B) (–, – 1] (2, 3] (C) [– 1, 2) [3, ) (D) [– 1, 2] If X = {a, b, c, d} then no. of 1–1. Then number of functions from X X are Pune-2012 (a) 64 (b) 13 (c) 24 (d) 16 If R+ is set of all real +ve nos. then F: R+ R+ be defined by f(x) = 3x. Then f(x) is Pune-2012 (a) neither one-one nor onto (b) one-one and onto (c) one-one but not onto (d) onto but not one-one If f :R R, where for x R, then f(2010) is KIITEE-2010 (a) 1 is a real-valued function in the domain : 2. KIITEE-2010 (d) 2 + x (c) 1 + x (e 1) x f ( x) cos x (d) f(x) = {x}, the fractional part of x The function f : R R given by f(x) = 3.2 sin x is (MCA : KIITEE - 2009) INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (a) one – one (c) bijective 24. 25. 26. The domain of the function (a) (b) (c) (d) 28. 29. e | x| e x e x e x 38. then (MCA : KIITEE - 2009) The domain of y 39. x 40. (MCA : KIITEE - 2009) (a) R ~ {1, 2} (b) (-, 2) (c) (-, 1) (2, ) (d) (1, ) If f(x – 1) = 2 x2 – 3x + 1 then f(x + 1) is given by (MCA : KIITEE - 2009) (a) 2x2 + 5x + 1 (b) 2x2 + 5x + 3 (c) 2x2 + 3x + 5 (d) 2x2 + x + 4 If y = log3 x and F = {3, 27}. Then the set onto which the set F is mapped contains (MCA : KIITEE - 2009) (b) {1, 3} (c) {0, 1} If f : [1, ) [2, ) is given by f (a) 1 x2 x x2 4 2 cos x sin x If f ( x) sin x cos x 0 0 (c) 1 ( x) x 1 x then f –1 42. (x) 43. (b) x x2 4 2 44. (d) x x2 4 45. 46. 0 0 1 then f(x + y) is equal to (a) f(x) f(y) (c) f(x) – f(y) (d) None of these 47. Let 33. exists and equals – 1 and f(0) = 1, then, f(2) is Hyderabad Central Univ. – 2009 (a) -1 (b) 2 (c) 0 (d) 1 If f(x) = sin (log x), then, the value of f(xy) + f(x/y) – 2f(x) cos log (y) is Hyderabad Central Univ. – 2009 (a) 0 (b) – 1 (c) 1 (d) – 2 Consider the function f ( x) sin 2 x 3 (c) 35. 2n 3 : nZ (d) n If f(x) + f(1 – x) = 2, then the value of 3 1 2 2000 f f ... f 2001 2001 2001 36. (a) 2000 (b) 2001 (c) 1999 If f(x) is a polynomial satisfying f ( x) x2 1 x2 then the MCA : KIITEE – 2008 (a) one – one (b) one – many (c) many – one (d) onto If f(x) = x2 + 4 and g(x) = x3 – 3 then the degree of the polynomial f[g(x)] ICET - 2007 (a) 6 (b) 5 (c) 3 (d) 3 If f(x) = 2x2 + 5x + 1 and g(x) = x – 4 then { R : g (f()) = 0} = ICET - 2007 (a) {-1/2, 3} (b) {-1/2, -3} (c) {1/2, - 3}(d) {1/2, 3} If f : |R | R and g : |R R| are defined by f(x) = x - (x) and g(x) = (x) for each x in |R where (x) is the greatest integer not exceeding x, then, the range of gof is. ICET – 2005 (a) (b) (0) (c) Z (d) |R The number of injections of the set {1, 2, 3} into the set {1, 2, 3, 4, 5, 6} is ICET – 2005 (a) 10 (b) 30 (c) 60 (d) 120 The number of mappings from {a, b, c} to {x, y} is PUNE - 2007 (a) 3 (b) 6 (c) 8 (d) 9 If f = {(6, 2), (5, 1)}, g = {2, 6), (1, 5)} then f o g = PUNE - 2007 (a) {(6, 6) (5, 5)} (b) (2, 2) (1, 1) (c) {(6, 7) (2, 6) (5, 1) (1, 5} (d) None of these If (x + 2y, x – 2y) = xy then f(x, y) is equal to (KIITEE - 2009) (c) 49. 1 2 (x y 2 ) 8 1 2 (x y 2 ) 2 (b) (d) 1 2 (x y 2 ) 4 1 ( xy) 4 The function f and g are given by f(x) = (x), the fractional part of x and g(x) = 1/2 sin[x], where [x] denotes the integral part of x, then the rage of (g o f) is (MCA : KIITEE - 2009) (a) [-1, 1] (b) {-1, 1} (c) {0} (d) {0, 1} The least period of the function f(x) = [x] + [x + 1/3] + [x + 2/3] – 3x + 10 where [x] denotes the greatest integer x is KIITEE – 2008 (a) 2/3 (b) 1 (c) 1/3 (d) 1/2 LIMITS & CONTINUITY on R. Let x1 and 1. x2 be two real values such that f(x1) = f(x2). Then x1 – x2 is always of the form Hyderabad Central Univ. – 2009 (a) n : n Z (b) 2n : n Z Let f : R R be a mapping such that (a) 48. y f ( x) f ( y ) for all real x and y. If f’(0) 2 32. 34. 41. (d) {0, 2} (KIITEE – 2009) (b) f(x) + f(y) x f 2 by NIMCET - 2008 (a) 63 (b) 65 (c) 67 (d) 68 The number of functions f from the set A = {0, 1, 2} in to the set B = {0, 1, 2, 3, 4, 5, 6, 7} such that f(i) f(j) for i < j and ij A is. NIMCET - 2008 (a) 8C3 (b) 8C3 + 2(8C2) (c) 10C3 (d) None The range of the function f(x) = 7-xPx-3 is MCA : KIITEE – 2008 (a) {1, 2, 3, 4} (b) {1, 2, 3} (c) {1, 2, 3, 4, 5} (d) {3, 4, 5, 6} Let A = {x|-1 < x < 1} = B. If f: A B be bijective then f(x) could be defined as MCA : KIITEE – 2008 (a) |x| (b) sin x (c) x|x| (d) None property of the function f is. (MCA : KIITEE - 2009) x and f(3) = 28, then f(4) is given is x 3x 2 2 equals to 31. 37. f is both one – one and onto f is one – one but not onto f is onto but not one – one f is neither one – one nor onto (a) {0, 3} 30. f ( x) 2 x 1 3 2 x is (MCA : KIITEE - 2009) (a) [1/2, 3/2] (b) (1/2, 3/2) (c) [1/2, ) (d) (-, 3/2] The period of the function f(x) = cosec23x + cot 4x is (MCA : KIITEE - 2009) (a) (b) /8 (c) /4 (d) /3 Let f : R R be a function defined by f ( x) 27. 1 1 f ( x) f f ( x) f x x (b) onto (d) None of these lim (A) 1 (B) –1 x 0 x is : lim 22 2x f x If f (1) = 2 f '(1) = 1 then 3. (a) – 1 (b) 0 (c) 1 (d) 2 F(x) = x + |x|. Then F(x) is continuous for …………. x 1 (a) x = 0 only (c) for all x R except x = 0 MCA : NIMCET - 2008 (d) 1998 PU CHD-2012 (D) Does not exist (C) 2. : nZ is sin x The value of x 1 (b) for all x R (d) None of these Pune-2012 Pune-2012 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 4. π sin x if x 2 What is the value of a for which f x is ax if x > π 2 13. continuous? (a) π 5. (b) π /2 lim 1 x 1/ x n (c) 2/ π 14. NIMCET-2012 (d) 0 (a) 0 (b) 1 (c) e The function f(x) defined by (d) 1/e 15. 16. 17. 18. 10. 19. Let f (2) = 4 and f´ (2) = 1. Then lim x 2 xf 2 2 f x x2 is given 11. PU CHD-2011 1. 0, if x 0 1 x x , if 0 x 1 2 2 1 1 If f x , if x 2 2 2 1 x, if x 1 2 3 1, if x 1 (c) continuous at x = 0 2. (b) - 1 (d) 9/25 lim 2 (c) 0 (c) 1/4 cos x tan x lim (b) 2/4 x 3 x 3 x (d) 1/12 1 1 3 is IP Univ. Paper – 2006 (d) 1 (e) 5/4 (c) 3/4 sin x6 a 6 x a (d) 3 ICET – 2005 (b) 1/3 x 0 lim ICET – 2005 x6 a6 UPMCAT : Paper - 2002 (a) Does not exist at x = 1 (b) 1/2 (c) – 1 (d) 1 f = R R is given by f(x) = x2 + 6x + 2 if x is rational and f(x) = x2 + 5x – 4 otherwise. F is continuous at IP Univ. Paper – 2006 (a) x = R (b) for no x R (c) for only one value of x. (d) for two values of x If y = logex and n is positive integer, then dn y dx n is equal to n (B) (n – 1)x–n (C) (n – 1) ! x–n F(x) = xn then the value of F ' 1 1! (D) (–1)n – 1 (n – 1)! x–n F " 1 2! F "' 1 3! ........... 1 n F n 1 n! is Pune-2012 (b) 2n-1 (c) 0 y e x .e x .e x ........., 0 < x < 1 then 2 3. 1 (b) continuous at x = 1 2 3 (d) 1 1 dy at x is. dx 2 Pune-2012 (d) discontinuous at x = 0 (c) ICET - 2007 8 x 2 x (a) 2n 4. tan x 1 lim 1 2 is equal to The value of lim x 2 x 2 x x (a) + 1 Lt x0 F 1 x 12. (d) 2 PU CHD-2012 BHU-2011 x (c) 1 (c) 3/5 (b) 2 e (A) x Then, f (x) is (a) continuous at ICET - 2007 DERIVATIVES by : (A) 2 (B) –2 (C) –4 (D) 3 (b) 1 (a) 1/4 22. (d) None x( x 1)(2 x 3) Lt x x3 21. (c) – 1 (b) 0- (a) 1/2 20. lim x0 f ( x) is equal to KIITEE - 2008 1 cos 3x lim x / 2 1 cos 5 x 3 NIMCET-2011 (d) none of these (c) –1 is a MCA : NIMCET - 2008 (d) 4 1 x 1 x x (a) 1 x sin x equals to x cos x (b) 1 lim x (a) 0 HCU-2011 (a) no point in (0, 1) (b) at exactly 2 points in (0, 1) (c) at exactly one point in (0, 1) (d) at more than 2 points in (0, 1) Suppose f(x) = [x2] – [x]2 where [x] denotes the largest integer x. Then which of the following statements is true? HCU-2011 (a) f(x) ≥ 0 x R (b) f(x) can be discontinuous at points other than the integral values of x (c) f(x) is a monotonically increasing function (d) f(x) 0 everywhere, except on the interval [0, 1] (a) 0 xn x 0 (c) 3 (b) 1 (a) – 1 x 1 x if x is rational f x 1 x 1 x if x is not rational 2 x (cos x 1)(cos x e x ) sin x , [ x] 0 If f ( x ) x when [.] denotes the greatest [ x] 0 0, (a) 0 (a) f(x) is continuous at x = 0 (b) f(x) has discontinuity of first kind at x = 0 (c) f(x) has discontinuity of second kind at x = 0 (d) f(x) has removable discontinuity at x = 0 Let f(x) be the function defined on the interval (0, 1) by lim (b) 2 integer function then then f is continuous at 9. (d) 1/2 (e) None of these lim The integer n for which (a) 1 BHU-2012 8. (c) 1 finite non – zero number is 1 f x x 1 sin log x 2 , x 0 , then: 3 f x 0, x0 7. (b) 4 KIITEE-2010 x 1 x 1 is equal to : BHU-2012 6. 2 (a) f x 1 lim If f(1) = 1, f ' (1) = 2, then (a) e (b) 4e (c) 3e log(x + y) – 2xy = 0 then y'(0) is (d) 2e Pune-2012 5. BHU-2011 (d) 3 (a) 1 (b) – 1 (c) 2 (d) 0 If f(x) is twice differentiable function. Then f '(x) = g(x), f '(x) = -f (x). if h(x) = f(x)2 + g(x)2, h(1) = 8, h(0) = 2 then h(2) = Pune-2012 23 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 6. (a) 1 (b) 2 (c) 3 f (x) = x|x| and g(x) = sin x then (d) None of these (a) Pune-2012 7. 8. (a) gof(x) differential and its derivative is continuous (b) fog(x) is twice diff. at x = 0 (c) fog(x) is not differentiable (d) None of these If f(a + b) = f(a) × f(b) for all a and b and f(5) = 2, f'(0) = 3, then f'(5) is NIMCET-2012 (a) 2 (b) 4 (c) 6 (d) 8 The derivative of sin 1 1 x2 1 x2 w.r.t. 2x sin 1 2 1 x (c) 17. 18. 9. If (b) 0 (c) 1/x dy x 1 1 x 1 y sec sin , then dx x 1 x 1 19. 20. is : NIT-2008, BHU-2012 (a) 1 10. (b) 0 Let f1(x) = ex, f2(x) = fn+1(x) = of x 1 (c) x 1 e fn x 12. f x f x e 1 , f3(x) = e 2 , …. and in general for any n 1. For any fixed value of n, the value 21. 1 (b) 23. 2x 5 3/ 2 x 2 25. 1 0 p p2 p3 If 26. (b) 28. (c) x (logx + 1) (d) x x Let f(a) = g(a) = k and their nth derivatives f " (a), g" (a) exist and are not equal for some n. lim f a g x f a g a f x g a x a g x f x If x = a sin, y = b cos, then d2y dx 2 (MP COMBINED – 2008) equals: 2 log(log x (logx ) ) x (d) (log x) x(log x-1) If x y e ( x y ) then If dy equals: MP COMB. – 2008 dx ( x y) ( x y) ( x y) (c) (d) x log(ex) x log(ex) log(ex) ( x y) (b) log(ex) x y y y ... (b) x + 1 then (c) 2x – 1 1 1 log x (b) (c) log x (1 log x) 2 (d) If y = 4x3 – 3x2 + 2x – 1, then If (b) 1 1 2 1 x 2 y xx (d) 2x + 1 1 x 1 x x x 1 2 is ICET – 2005 dy ? dx MP– 2004 (d) 3 , then (d) then y log x x (1 log x ) at (b) 2 x ... 1 (1 log x) 2 (c) 2 1 2 1 x dy dx 1 x 1 x y tan 1 ICET - 2007 ICET – 2005 (a) If dy dx dy dx If xy = ex-y, then, (d) 0 24 dy dx 2 (log x) x (log x) x (c) 29. then (d) None (c) 1 then is KIITEE-2010 (c) e (b) (a) KIITEE-2010 (c) 1 y x (logx) (a) 0 x–1 the value of k is (a) 4 (b) 2 16. 27. 1 x x log x x x (b) 0 (log x) x (log x) , where p is constant. PU CHD-2011 (A) P (B) P + P2 (C) p + p3 (D) Independent of p The differential coefficient of xx is BHU-2011 (a) xx logx 2 (a) Then f ′′′ (0) = If (d) 3/2 f ( x) e x , x 0 and f(0) = 0 then f’(0) is (a) x – 1 sin x cos x f x 6 If (a) (d) none of these x3 15. (c) 0 KIITEE – 2008 24. 3 x 3/ 2 2 x 2 5 3/ 2 (c) 2 x x 2 14. (b) e2 (a) 1 d 5 x dx x Let f(x) = 1 2 1 2 (b) log sec(x) x x 2 2 1 2 (c) log cos(x) x (d) None of the above 2 2 sin x If y ( x 1) , they y’(0) is equal to log sec(x) 1 22. NIMCET-2011 13. , x 0 and f(0) = 0 then f’(0) is Hyderabad Central Univ. – 2009 (a) 0 (b) 1 (c) e (d) None of these If f(0) = f '(0) = 0 and f "(x) = tan2x then f(x) is Hyderabad Central Univ. – 2009 (a) 1/2 (a) fn(x) (b) fn(x) fn-1(x) fn-2(x) …. f2(x) f1(x) (c) fn(x) fn-1 (x) (d) fn(x) fn-1(x)fn-2(x) …. f2(x) f1(x) ex Let f : [0, 1] [0, 1] be a function that is twice differentiable in its domain, then the equation f(x) = x has HCU-2011 (a) no solution (b) exactly one solution (c) at least one solution (d) not enough data to say about number of solution (a) f ( x) 2 ex KIITEE – 2008 d f n x is dx Find If (a) x 1 (d) x 1 HCU-2011 11. (d) b sec 2 a b 2 sec3 a 1 (d) x 1 (b) The derivative of f(x) = 3|2 + x| at the point x0 = - 3 is KIITEE-2010 (a) 3 (b) – 3 (c) 0 (d) does not exist Let y be an implicit function of x defined by x2x – 2xx cot y – 1 = 0 then y' (1) equals KIITEE-2010 (a) 1 (b) log2 (c) – log2 (d) – 1 is : BHU-2012 (a) – 1 a sec 2 b2 b sec3 a2 1 2 1 x 2 1 2 1 x2 dy is equal to : dx MP– 2004 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 30. (a) y2 x log x (b) (c) dy log x (d) None of these The value of differential coefficient of to x at x = 2 is : (a) 1/2 (b) -1/5 31. 33. tan 1 1 x with respect 1 x (c) -1/2 11. If 1 2 1 x 2 MP– 2004 12. (d) None of the above F:R R is defined (c) 13. 14. 1 2 15. (d) – 1 In the Interval [0, 1] function x – x + 1 is 2 Pune-2012 4. 5. (a) increasing (b) decreasing (c) neither increasing nor decreasing (d) None of these Normal to the curve y = x3 – 3x + 2 at the point (2, 4) is NIMCET-2012 (a) 9x – y – 14 = 0 (b) x – 9y + 40 = 0 (c) x + 9y – 38 = 0 (d) -9x + y + 22 = 0 The function xx decreases in the interval NIMCET-2012 (a) (0, e) 6. 8. (c) 1 0, e 17. (d) None of these 18. The condition that the curve ax2 + by2 = 1 and a'x2 + b'y2 = 1 should intersect orthogonally is that : BHU-2012 (a) a + b = a' + b' (b) a – b = a' – b' (c) 7. (b) (0, 1) 16. 1 1 1 1 a b a' b' (d) (b) 2/e 1 1 1 1 a b a' b' 2 pq 3 (c) (d) x 1 2 (b) x 1 2 (c) x = 1 (d) x = – 1 The normal to the curve x = a(cos + sin ), y = a (sin - cos ) at any point is such that it BHU-2011 (a) passes through the origin (b) makes a constant angle with the x-axis (c) makes a constant angle with the y-axis (d) is at constant distance from the origin The length of the normal at the point (2, 4) to the parabola y2 = 8x is BHU-2011 (a) 4 2 (b) 4 (c) 6 (d) 2 3 The equation of tangent to the curve y2 = 2x3 – x2 + 3 at the point (1, 4) is BHU-2011 (a) y = 2x (b) x = 2y – 7 (c) y = 4x (d) x = 4y If f(x) satisfies the conditions of Rolle’s theorem is [1, 2] and f(x) (a) (d) 1/e 2r pq 1 2 r h 2 2 1 f ' x dx is equal to pqr 22. 25 (b) 0 (c) 1 f x x 2 2 x (d) 2 20. NIMCET-2011 (b) (d) KIITEE-2010 (a) x = - 2 (b) x = 0 (c) x = 1 (d) x = 2 2 Angle between the tangents to the curve f = x – 5x + 6 at the points (2, 0) and (3, 0) is KIITEE-2010 The minimum value of px + qy when xy = r is 2r pq r 2h The function 2 (a) (b) 19. 21. 9. a / b b / a KIITEE-2010 log e x is : x (c) e (d) The function f(x) = 8x5 – 15x4 + 10x2 has no extreme value at BHU-2011 (a) 3 BHU-2012 (a) 1 2ab / a b is continuous in [1, 2] then If x and y be two real variable, such that x > 0 and xy = 1, then the minimum value of x + y is : BHU-2012 (a) 1 (b) – 1 (c) 2 (d) – 2 The maximum value of ab (b) The volume of a right circular cylinder of height h and radius of base r is BHU-2011 (a) Pune-2012 3. 1 a b 2 1 2 r h 3 4 2 (c) r h 3 if F has local min. at x = - 1 then the value of k is (c) for every real number x, then the minimum (a) k 2 x if x 1 F x 2 x 3 if x 1 (b) 0 x2 1 x2 1 PU CHD-2011 (A) does not exist because f is bounded (B) is not attained even though f is bounded (C) is equal to 1 (D) is equal to –1 If f be the quadratic function defined on [a, b] by f (x) = αx2 + βx + , α ≠ 0, then the real ‘c’ guaranteed by the Langrange’s mean value theorem is equal to : PU CHD-2011 (A) f(x) = |x|, at x = 0 UPMCAT Paper – 2002 (a) is derivable (b) not derivable (c) either may follow (d) None of these If y = f(x) is an odd and differentiable function defined on (- , ) such that f'(3) = - 2, then f’(-3) equals to (NIMCET – 2009) (a) 4 (b) 2 (c) –2 (d) 0 (a) 1 f x value of f : APPLICATION OF DERIVATIVES 1. A particle moves on a coordinate axis with a velocity of v(t) = t2 2t m/sec at time t. The distance (in m) travelled by the particle in 3 seconds if it has started from rest is HCU-2012 (a) 3 (b) 0 (c) 8/3 (d) 4 2. If f (x) = x - 20x + 240x, then f (x) satisfies which of the following? PU CHD-2011 (A) It is monotonically decreasing only in (0, ∞) (B) It is monotonically decreasing every where (C) It is monotonically increasing every where (D) It is monotonically increasing only in (–∞, 0) (d) 1/3 1 x2 1 Differential coefficient of tan is : x 2 2 (a) (b) 2 1 x2 x 1 x 3 10. MP Paper – 2004 1 (c) 32. x y log x 5 2 (b) 6 For the function (c) has a local minimum at 4 (d) 3 f ( x) x ,0 x b, the number c satisfying the mean value theorem is c = 1, then b is (MCA : KIITEE – 2009) (a) 0 (b) 4 (c) 2 (d) 3 The maximum value of the function y = x(x – 1)2, 0 x 2 is (MCA : KIITEE – 2009) INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (a) 23. 24. (c) 27. 28. 29. 30. 7 27 (c) 3 1 ,b 4 8 3 1 a ,b 4 8 a 5 3 , (b) (a) e 34. 2. 3 (b) 3 , (c) 5 , 3 (d) 1 e 3. 4. 5. (d) PU CHD-2012 (A) 6. (2 3 ,6) 1 1 f ( x) dx 14 / 3. , the cubic f(x) is HYDERABAD CENTRAL UNIVERSITY - 2009 (a) x3 + x2 + x + 6 (b) x3 – x2 – x + 10 (c) x3 + x2 + x + 2 (d) x3 + x2 – x + 2 f ( x) a log e|x|bx 2 35. If x (a) (c) 36. 37. 3 1 ,b 4 8 3 1 a ,b 4 8 a 7. has the extremums at x = 1 and x = 3 then KIITEE - 2008 (b) HCU-2012 (a) 1 (b) 2 (c) 0 (d) infinity Let A be an n n-skew symmetric matrix with a11, a22, ….. ann as diagonal entries. Then which of the following is correct? HCU-2012 (a) a11a22 … ann = a11 + a22 + …. + ann (b) a11a22 … ann = (a11 + a22 + …. + ann)2 (c) a11a22 + … + ann = (a11 + a22 + …. + ann)3 (d) all of the above Consider the system of equations 8x + 7y + z = 11 x + 6y + 7z = 27 13x – 4y – 19z = - 20 How many solutions does this system have? HCU-2012 (a) Single (b) Finite (c) Zero (d) Infinite If A is a 3 × 3 matrix such that : e P(x) is a real polynomial of degree three. P(x) = 0 has a double root at x = 2. It has a relative extremum at x = 1. The remaining root of P(x) = 0 is IP Univ. paper – 2006 (a) 4/5 (b) 3/4 (c) 2/3 (d) 1/2 (e) N.O.T If y2 = 8(x + 2) Equ. of tangent at (-1, 3) is : UPMCAT– 2002 (a) y = 2x – 5 (b) y = x + 3 (c) y = x + 5 (d) None of these A cubic f(x) vanishes at x = - 2 and has relative minimum / maximum at x = - 1 and x = 1/3. If 2 3 y t 3 0 6 0 1 A 1 0 and A 4 1 , then the product A 7 is 5 0 8 2 0 The points situated on x = 2y and nearest to (0, 5) are: (MP COMBINED – 2008) (a) (0, 0) (b) ( 2, 2) (2 2 ,4) 2 3 1 3 s are orthogonal, where x, y, z, s and t are real numbers. (d) None 1 (c) e e 1e (b) e Let A be an n n non-singular matrix over ℂ where n 3 is an odd integer. Let a ℝ. Then the equation det(aA) - a det(A) = 0 holds for HCU-2012 (a) All values of a (b) No value of a (c) Only two distinct values of a (d) Only three distinct values of a How many matrices of the form x 2 3 z 3 1 a ,b 4 8 2 (c) 33. 1. 4 27 (d) None of the above 1 32. (d) Equation of the tangent to the curve y = be-x/a at the point where it crosses y – axis is : (MCA : MP COMBINED – 2008) (a) bx + ay = ab (b) ax + by = ab (c) bx + ay = - ab (d) ax + by = - ab The points on the circle x2 + y2 – 2x – 4y + 1 = 0 where the tangents are parallel to x-axis, will be: (MCA : MP COMBINED – 2008) (a) (3, 2), (-1, 2) (b) (-1, 2), (1, 0) (c) (1, 2), (1, 0) (d) (1, 0), (1, 4) The normal to curve y2 = 4ax passing through (a, 2a) is: (MP COMBINED – 2008) (a) x + y = a (b) x + y = 3a (c) x – y = a (d) y = 2a sin x (1 + cos x) is a maximum when x equals : BHU-2011, (MCA : MP COMBINED – 2008) (a) /6 (b) /4 (c) /3 (d) /2 For positive values of x, the minimum value of xx will be: (MP COMBINED – 2008) e 31. 8 27 The function f(x) = 2 sin x + sin 2x, x [0, 2] has absolute maximum and minimum at NIMCET – 2008 (a) 26. (b) The sum of two non zero numbers is 8. the minimum value of the sum of their reciprocal is (KIITEE – 2009) (a) 1/4 (b) 1/8 (c) 1/2 (d) None of these If f(x) = a loge|x| + bx2 + x has the extrema at x = 1 and x = 3 then NIT-2010, HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 25. 5 27 3 1 a ,b 4 8 8. (d) None Let f(x) = cosx + 10x + 3x2 + x3 if -2 x 3, the absolute minimum value of f(x) is KIITEE - 2008 (a) 0 (b) – 15 (c) 3 – 2 (d) None A function y = f(x) has a second derivative f”(x) = 6(x – 1). If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x – 5, then the function is KIITEE - 2008 (a) (x – 1)3 (b) (x + 1)2 (c) (x – 1)2 (d) (x + 1)2 9. 10. MATRICES 26 0 0 1 (B) 1 1 9 2 (C) 1 (D) 10 0 0 11 Consider the following system of linear equations over the real numbers, where x, y and z are variables and b is a real constant : x+y+z=0 x + 2y + 3z = 0 x + 3y + bz = 0 Which of the following statements are true? I. There exists a value of b for which the system has no solution. II. There exists a value of b for which the system has exactly one solution. III. There exists a value of b for which the system has more than one solution. PU CHD-2012 (A) I and II only (B) I and III only (C) II and III only (D) I, II and III The only integral root of the equation 2 y 2 3 2 5 y 6 3 4 10 y 0 is : PU CHD-2012 (A) y = 0 (B) y = 1 (C) y = 2 (D) y = 3 Let N be the set of all 3 3 symmetric matrices. All of whose entries are zero or 1 (Five zero and four 1). Then the no. of matrices in N is Pune-2012 (a) 12 (b) 6 (c) 9 (d) 3 If M & N are square matrices of order "n". Then (M – N)2 = Pune-2012 (a) M2 – 2MN + N2 (b) M2 – N2 (c) M2 – 2NM + N2 (d) M2 – MN – NM + N2 M and N are symmetric matrices of same order then MN – NM is a matrix which is INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS Pune-2012 (a) null (c) skew-symmetric 11. 1 M 1 2 (b) symmetric (d) unit 0 the M50 is equal to 1 21. Pune-2012 1 0 (a) 0 50 1 25 (c) 0 1 12. 13. 14. 15. If matrix 1 3 2 2 4 8 3 5 10 15 2 (b) 17 2 22. is singular the = (c) 31 2 (d) P (d) Let 23. 24. 33 2 If A and B are two square matrices such that B = − A−1BA, then (A + B)2 = NIMCET-2011 (a) 0 (b) A2 + 2AB + B2 (c) A2 + B2 (d) A + B Consider the system of linear equations 3x1 + 7x2 + x3 = 2 x1 + 2x2 + x3 = 3 2x1 + 3x2 + 4x3 = 13 The system has NIMCET-2011 (a) infinitely many solutions (b) exactly 3 solutions (c) a unique solution (d) no solution 1 2 3 25. If A 2 1 2 3 2 1 NIMCET-2012 n 0 1 (c) 0 17. n n (b) 0 1 (d) None of these 2 2 2 1 1 (a) symmetric matrix (b) a skew-symmetric matrix (c) a singular matrix (d) non-singular matrix 26. 18. (b) 1 If the matrices BHU-2011 3 (a) 9 3 (c) 9 (c) 0 (d) 2 1 1 1 A and 3 3 3 2 3 B 1 5 , 4 1 then 27. AB is equal to : BHU-2012 3 9 3 (c) 9 (a) 19. 20. 1 3 1 3 2 3 1 1 1 If A , B 1 5 then AB is equal to 3 3 3 4 1 is equal to : BHU-2012 (a) – 1 , then A is BHU-2011 1 n 0 1 If is cube root of unity, then the value of determinant 1 3 2 1 2 be a 3 3 matrix. Let x and y be the values such that matrix A is singular. What is x + y? HCU-2011 (a) 0 (b) 3 (c) 1/2 (d) 2 1 1 n If A , then A for any natural number n is 0 1 (a) 1 2 3 2 4 1 0 A 2 1 2 x y 1 Pune-2012 (a) – 2 (b) 4 (c) 2 (d) – 4 The number of values of k for which the system of equations (k + 1) x + 8y = 4k and kx + (k + 3)y = 3k – 1 has infinitely many solutions is NIMCET-2012 (a) 0 (b) 1 (c) 2 (d) infinite If is the cube root of unity, then the system of equations x + 2y +z = 0, x + y + 2z = 0 and 2x + y + z = 0 is NIMCET-2012 (a) consistent and has unique solution (b) Consistent and has more than one solution (c) Inconsistent (d) None of these The value of k for which the set of equations 3x + ky – 2z = 0, x + ky + 3z = 0 and 2x + 3y – 4z = 0 has a non-trial solution, is NIMCET-2012 (a) 16. 1 0 (b) 50 1 1 0 (d) 25 1 HCU-2011 (a) 3|B| = 9 (b) |2A| = 32 (c) |AB| = 12 (d) |A + B| = 7 The n n matrix P is idempotent if P2 = P and orthogonal if P'P = I. Which of the following is false? HCU-2011 (a) If P and Q are idempotent n n matrices and PQ= QP = 0, then P + Q is idempotent (b) If P is idempotent then – P is idempotent (c) If P and Q are orthogonal n n matrices then PQ is orthogonal 3 9 3 (d) 9 (b) 1 3 If 1 3 3 (b) 9 3 (d) 9 1 3 1 3 1 3 1 x3 x x2 y y 2 1 y 3 0 , where x, y, z are unequal and non- z z2 1 z3 zero real numbers, then xyz is equal to BHU-2011 1 3 28. If A is a 2 2 real matrix such that A – 3I and A – 4I are not invertible, then A2 is HCU-2011 (a) 12A – 7I (b) 7A – 12I (c) 7A + 10I (d) 12I If A and B are 3 3 matrices with |A| = 4 and |B| = 3, which of the following is generally false? 27 (a) 1 (b) 2 The system of equations ax + y + z = - 1 x + ay + y = - 1 x + y + az = - 1 has not solution if is (a) 1 (c) either – 2 or 1 (e) None of these (e) None of these (c) – 1 (d) – 2 KIITEE-2010 (b) Not – 2 (d) – 2 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 1 0 k 29. Matrix A 2 1 3 k 0 1 is invertible for (a) k = 1 (c) all real k (e) None of these 30. 31. (b) k = - 1 (d) None of these 1 2 The matrix A 1 2 1 2 is 1 2 2 x 2 2 1 x 40. Let 41. 42. 35. The inverse of the matrix (c) A 43. PGCET-2010 94 95 96 (c) 303 If 1 0 1 0 1 0 0 0 1 44. (b) 37. 45. 1 0 0 0 0 1 0 1 0 46. (d) N.O.T 47. 48. 0 1 (b) 1 0 If 49. a unique solution no solution infinite number of solutions finitely many solutions 1 2 2 A , then I + A + A + …. equals to 3 4 1 0 0 1 1 is C2 C5 1 (MCA : KIITEE - 2009) (d) N.O.T (b) 3 x 3 0 is cos sin 0 (b) adj A 1 1 1 1 2 0 1 3 0 0 0 1 (c) A then A-1 is equal to (KIITEE - 2009) (d) N.O.T then the value of |adj A| is equal to (KIITEE - 2009) (a) 5 (b) 1 (c) 0 (d) N.O.T It is given that square matrix A is orthogonal and also that det A is not equal to 1. Then, HYDERABAD CENTRAL UNIVERSITY - 2009 (a) |A| is zero (b) |A| > 1 (c) |A| cannot be determined (d) None of the above If i i 1 1 8 A and B then A equals to i i 1 1 HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 64 B (b) 128 B (c) -128 B (d) -64 B If A is a 3 3 matrix and A’ A = I and |A| = 1 then the value of |(A – 1)| = HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 1 (b) – 1 (c) 0 (d) N.O.T If a, b, c are the roots of x3 + px2 + q = 0, then HYDERABAD CENTRAL UNIVERSITY - 2009 c b a (d) N.O.T 50. (a) p (b) p2 (c) p3 (d) q The following system of equations 6x + 5y + 4z = 0 3x + 2y + 2z = 0 12x + 9y + 8z = 0 has HYDERABAD CENTRAL UNIVERSITY - 2009 (a) no solutions (b) a unique solution (c) more than one but finite number of solution (d) infinite solutions Let a b 3 A be a 2 2 matrix such that A = 0. The sum of c d all the elements of A2 is HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 0 (b) a + b + c + d (c) a2 + b2 + c2 + d2 (d) a3 + b3 + c3 + d3 (NIMCET – 2009) (a) sin cos 0 b c a (NIMCET – 2009) 38. C4 5 a b c If a + b + c 0, then the system of equations (b + c) (y + z) – ax = b – c (c + a) (z + x) – by = c – a (a + b) (x + y) – cz = a – b has (a) (b) (c) (d) If A= (d) 0 (PGCET– 2009) 0 1 0 1 If A = is PGCET-2010 3 1 2 A , then A – 5A + 7l is 1 2 1 (a) 0 0 (c) 0 C1 (MCA : KIITEE - 2009) (c) –5 (d) N.O.T (b) –18 (a) AT 0 0 1 A 0 1 0 1 0 0 (c) A itself 36. C 3 14 5 The sum of two non integral roots of (d) None of these (PGCET– 2009) (a) 5 (c) –(6!) (b) 80 (a) 5 97 98 99 (b) 202 C0 5 4 x KIITEE-2010 (b) a zero matrix (d) an orthogonal matrix The value of the determinant (a) 100 The value of the determinant 5 5 91 92 93 34. 1 0 0 0 , B . If A2 – 2A + I = B, then value A 2 b 4 4 5 KIITEE-2010 2 1 4 3 2 If A , then A + A – A = 3 2 (b) 1 If A is a 3 3 matrix with det (A) = 3, then det (adj A) is (NIMCET – 2009) (a) 3 (b) 9 (c) 27 (d) 6 (a) 0 (a) x = 1 (b) x = (c) x = 2 (d) x = 0 If A is a singular matrix, then A. adj A is (a) 0 1 3 0 x 2 5 (a) a scalar matrix (c) an identity matrix 33. 1 (d) 4 1 2 39. 0 is 1 1 3 0 of b is (Note that I is identity matrix of order 2) (MCA : KIITEE - 2009) (a) 1 (b) 3 (c) –1 (d) 2 KIITEE-2010 (a) unitary (b) orthogonal (c) nilpotent (d) involutory (e) None of these If is a cube root of unity, then a root of the following equation x 1 32. 1 (c) 2 1 2 KIITEE-2010 1 2 3 4 28 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 51. 52. 53. ax + 4y + z = 0, bx + 3y + z = 0, cx + 2y + z = 0 can be a system of equation with nontrivial solutions if a, b, c are in KIITEE–2008 (a) HP (b) AP (c) GP (d) None The system of equations 2x + 3y = 8, 7x – 5y = - 3 and 4x – 6y + = 0 is solvable when is KIITEE – 2008 (a) – 6 (b) – 8 (c) 6 (d) 8 For 3 1 A 1 2 0 6 and If (a) = 4 55. 56. 57. 58. If (b) 8 then A-1 exists of (c) 4 4 1 4 A 3 0 4 3 1 3 KIITEE – 2008 (d) None then A2 is equal to KIITEE – 2008 64. (a) A (b) AT x y If 2x y 2 3 then x y is equal to x y 1 2 (a) – 5 (b) 5 (c) I (d) None The value of the determinant : (a) a, b, c are positive (c) (a + b + c) < 0 The value of the determinant 65. (d) 6 a b c b c a c a b will be negative when MP COMBINED - 2008 (b) a, b, c are negative (d) (a + b + c) > 0 66. ba a ab ca b bc is ab c ca 67. (b) (a + b + c)3 (d) a3 + b3 + c3 – 3abc 1 a bc 59. The value of the determinant : 1 b ca 68. is 1 c ab 60. (a) 0 (c) (a + b + c) If one root of the equation : MP COMBINED - 2008 (b) 1 (d) (1 + a + b + c) x 3 7 2 x 2 0 69. is -9, then other roots are: 7 6 x (a) -2, - 7 61. (b) 2, 7 (c) -2, 7 MP COMBINED - 2008 (d) 2, - 7 70. 5 4 a 14 1 2 If then a and b will be equal to : 1 1 b 17 1 3 MP COMBINED - 2008 (a) 1 a ,b 1 5 (c) a = 1, b = 1 62. If 2 0 0 A 0 2 0 0 0 2 |AB| will be (a) 4 (b) 8 71. (b) a = - 3, b = 4 (d) a = 4, b = - 3 and 1 2 3 B 0 1 3 0 0 2 72. then the value of MP COMBINED - 2008 (c) 16 (d) 32 73. (b) (b) 0 KARNATAKA - 2007 (d) 3 (c) 2 1 2 n A ICET – 2005 , then A = 0 1 1 n 2 n (a) (b) 0 1 0 1 1 2n 1 2 (c) (d) 0 1 0 n 2 k If the matrix ICET – 2005 is invertible, then K 4 10 If (a) 2 MP COMBINED - 2008 (a) (a + b + c) (c) a2 + b2 + c2 – ab – bc – ca then its inverse matrix M-1 will be: 1 4 5 0 2 6 0 0 3 (a) 1 KIITEE – 2008 (c) 4 1 0 0 M 4 2 0 5 6 3 0 0 6 12 3 0 14 6 2 7 1 2 1 3 0 0 1 1 1 (c) 2 (d) 0 0 2 2 1 7 1 1 0 0 3 3 3 1 2 3 4 1 3 3 4 The value of the given determinant is 1 2 4 4 1 2 3 5 (a) (b) A + B exists (d) None 0 4 1 A 2 3 1 2 1 If MP COMBINED - 2008 4 6 5 B 4 1 2 KIITEE – 2008 5 1 1 (a) AB exists (c) BA exists 54. 63. (b) – 5 (c) 10 (d) 5 2 3 , then which of the following is true? If A 1 2 Pune– 2007 (a) A2 – 4 A + I = O (b) A2 + 4A + I = O (c) (A – 4I) (A + I) = O (d) (A + 4I) (A – I) = O A is a square matrix of order 3; then which of the following is not true? |A| means determinant Pune– 2007 (a) | A + A’| = |A| + |A’| (b) |A * A| = |A| |A| (c) |kA| = k3 |A| where k is a constant. (d) |-A| = - |A| If 1 0 0 A 0 1 0 2a 2b 1 then A2 is Pune– 2007 (a) null matrix (b) unit matrix (c) A (d) –A If AB is a zero matrix, then Pune– 2007 (a) A = O or B = O (b) A = O and B = O (c) It is not necessary that either A or B should be O. (d) N.O.T If A is a square matrix of order 3 and entries of A are positive integers then |A| is Karnataka PG-CET– 2006 (a) Different from zero (b) 0 (c) Positive (d) an arbitrary integer If AB = A and BA = B then B2 is equal to Karnataka PG-CET– 2006 (a) A (b) B (c) I (d) 0 The value of 1 2 3 3 5 7 is Karnataka PG-CET– 2006 10 14 20 (a) 20 29 (b) – 2 (c) 0 (d) 5 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 74. 1 0 2 1 what will be the value of A? MP– 2004 1 1 0 1 2 1 2 1 (a) (b) 0 1 1 1 3 1 (c) 1 1 Matrix multiplication is not : MP– 2004 (a) commutative (b) associative (c) distributive (d) Both commutative & associative 76. The matrix 1 1 1 is : 2 1 1 (a) orthogonal (c) singular 1 x x 2 yz 1 y y 2 xz 1 z z xy MP– 2004 (b) 3xyz (d) N.O.T The value of 0 0 2a b a c 2b 80. 52. MP– 2004 2 1 79. 87. (b) unitary (d) None of the above (a) (x + y + z)2 (c) 1 78. 86. (d) None 75. 77. (c) is : 1. a b c MP– 2004 (a) 0 (b) 1 (c) – a – b – c (d) (a + b + c)2 A and B are two matrices where A is a non singular matrix. If AB = 0 then : MP– 2004 (a) B is singular (b) B is non singular (c) B is 0 (d) A is 0 1 P 1 1 1 1 P 1 1 1 1 P The roots of the equation are 81. If (b) 0, 0, - 3 (c) 0, - 3 1 w x w2 1 xw w2 x 1 w w2 (a) – 1 82. 83. 84. 85. (b) 1 2. 3. 2 dx is : 1 x e (a) x 1 (b) (x – 1)2ex (c) (x + 1)ex (d) ex The value of x sin x 1 cos x dx is : The value of x (b) x tan 2 x (d) x cos 2 log xdx is (a) x (log x + 1) (c) log x (x + log x) UPMCAT - 2002 (d) N.O.T 4. UPMCAT - 2002 (a) Identity Matrix (b) Null Matrix (c) NiL potent Matrix (d) N.O.T The eigen vectors of a real symmetric matrix corresponding to different eigen values are HYDERABAD CENTRAL UNIVERSITY - 2009 (a) Singular (b) Orthogonal (c) Non-singular (d) None of the above P, Q are 3 3 matrices. X is 3 1 matrix. PX = 0 has infinitely many solutions, QX = 0 has a unique solution. T be the solution set of P(QX) = 0. S be the solution set of Q(PX) = 0. Then IP Univ.– 2006 (a) both T and S are infinite sets. (b) only T is an infinite1 set. (c) only S is infinite set. (d) both T and S are finite sets. (e) exactly one of S, T is an infinite set. 1 sin x x e dx is equal to 1 cos x 1 x x (a) e tan k 2 2 5. e x (a) e (sin x – cos x) + C (d) 6. cos 2 x y sin 2 x y (b) P Q sin 2 x y cos 2 x y 30 (b) e x sec2 (d) e x tan x k 2 x k 2 (b) ex (cos x – sin x) + C (MCA : MP COMBINED – 2008) 1 x e (sin x cos x) C 2 1 x e (cos x sin x) C 2 1 dx is equal to : x2 a2 (a) log x x 2 a 2 c (c) 1 log x 2 a 2 2 IP Univ.– 2006 2 (MCA : KIITEE – 2009) sin xdx equals: x (c) BHU-2011 (b) x (logx – 1) (d) x (x – log x) (c) ex tan x + k cos x sin x cos y sin y P and Q sin y cos y then sin x cos x (a) PQ QP x 1 BHU-2012 (d) 0, 3 4 2 If A then (A – 2I) (A – 3I) : 1 1 xe x x (a) x cot 2 x (c) x sin 2 0 , then x is equal to : (c) 0 The value of BHU-2012 UPMCAT - 2002 (a) 0, 0, 3 (d) PQ = O for some x, y R (e) None of these All the matrices in this equation are of order 3 3. A1 = P-1 BP, A2 = P-1B2P, |B| = 3. The value of |A12 + A2| is IP Univ.– 2006 (a) 36 (b) 48 (c) 60 (d) 72 If A is a square matrix then A + A| is Karnataka PG-CET– 2006 (a) Unit matrix (b) Null Matrix (c) A (d) Symmetric matrix The following system of linear equations 3x + 2y + z = 3 2x + y + z = 0 6x + 2y + 4z = 6 has HCU-2006 (a) an infinitely many solutions (b) no solution (c) the solution lies on the intersection of the planes x = 2 and y =-2 (d) The solution lies on the plane x + z = 1 (e) None of the above INDEFINITE INTEGRAL 0 0 cos 2 x y sin 2 x y P 2Q sin 2 x y cos 2 x y UPMCAT– 2002 (b) log ( x 2 a2 c (d) None of these INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 7. If x tan 1 x dx 1 2 ( x ) tan 1 x x C 2 values of and are: (b) = 1, 14. (MP COMBINED – 2008) (a) = 0, = 1 (c) = - 1, then 1 2 (d) = 1, (c) 15. 6 The value of the integral (a) 1 (b) 1/2 (c) 3/2 16. (d) 2 The value of the integral (a) log 2 3. NIMCET-2010 17. 18. NIMCET-2010 x (c) log10 e. x loge e x c e (b) loge 10.x loge 4. 2 1 x2 5. 2 (a) 0 7. 1 1 x | x | sin In /4 0 3 x x tan 2 x 1 dx 21. 22. is (c) /4 (d) /2 23. KIITEE-2010 (d) 0 The solution of the differential equation dy x y dx x The value of x sin x (a) 2 1 cos x (b) 3 2 2 (c) 4 2 6 (d) satisfying 11. The value of (a) 0 12. /2 0 (a) 1 13. dx 0 1 tan 2 x (b) 1 a x 5 cos(1 x 4 ) a (1 x ) 24. 25. (d) /2 sin 2 x log(tan x)dx equals: (MP COMBINED – 2008) (b) 1/2 4 (c) 0 (d) (d) 2 y x , x [0, 1], loge x x dx equals e xp " x dx PU CHD-2012 (A) – 3 (B) – 2 (C) – 1 (D) 2 If f is a continuous function on the set of real numbers and if a, b are real numbers, which of the following must be true ? f x dx III. NIMCET – 2008 is (c) /4 MP– 2004 IP Univ.– 2006 (a) 0 (b) 1 (c) 2 (d) 3 (e) 4 Assume that p is a polynomial function on the set of real numbers. II. 2 The smaller of the areas bound by y = 2 – x and x2 + y2 = 4 is (NIMCET – 2009) (a) - 1 (b) - 2 (c) 2 - 1 (d) 2 - 2 dx is equal to : (c) – 1 (b) 1 26. 1 2 b3 f x 3 dx a 3 a 2 10. /2 3 x2 1 x x2 log e 1 x x2 2 b (NIMCET – 2009) dx is 4 2 dx is equal to : 2x e 2 (b) y = x In x + x2 (d) y = x In x + x The value of 0 (d) The area of the plane bounded by the curves I. KIITEE-2010 9. x 3 2 MP– 2004 (a) 0 (b) 1 (c) 4(3 – e) (d) None The area bounded by the curve y = sin x between x = 0 and x = 2 is : MP– 2004 (a) 2 (b) 4 (c) 4 (d) 14 the condition y(1) = 1 is (a) y = In x + x (c) y = xe(x-1) xe (c) 0 x (c) 2 2 If p(0) = p(2) = 3 and p'(0) = p'(2) = –1, then KIITEE-2010 tan n dx, then lim n I n I n 2 equals (b) 1 (b) 2 4 (b) 1 (a) 1/2 8. 3 NIMCET-2010 (a) I3 =I4 (b) I3 > I4 (c) I2 > I1 (d) I1 > I2 The area between the curves y = 2 – x2 and y = x2 is NIMCET-2010 (a) 8/3 (b) 4/3 (c) 2/3 (d) 5/3 The value of IP Univ.– 2006 y = x2, x [1, 2] and y = - x2 + 2x + 4, x [0, 2] is NIMCET–2008 (a) 10/7 (b) 19/3 (c) 3/5 (d) 4/3 2 /4 6. 20. 2 1 The value of (a) 0 dx,I 2 = 2x 3dx,I3 = 2 x dx and I 4 = 2 x dx then 0 equals 0 If I1 = 1 2 1 19. 1 (d) c x +c (d) 2 0 log 10 xdx is (a) (x – 1) loge x + c (MP COMBINED – 2008) equals: (c) 1 1 cos d 1 1 1 log 3 (d) log 3 8 4 (c) (d) (b) 1/2 (a) sinx+cosx 0 3+sin2x dx is (b) log 3 sq. unit 32 sq. unit 3 128 sq. unit 3 2 π 4 2. (b) tan x dx sin x cos x /4 0 2 dx is NIMCET-2010 9-x+ x 3 sq. unit (a) 0 x 16 3 64 3 (a) 1 2 1 2 DEFINITE INTEGRAL 1. (a) 0 (b) 1 (c) a (d) 2a The area enclosed between the curves y = x and y2 = 16x is: (MCA : MP COMBINED – 2008) b 3 a a 3 f x dx f x dx f x dx b 3b b 3a a f x dx 3 f 3x dx PU CHD-2012 (A) I only (B) II only (C) II and III only (D) I, II and III The area of the region bounded by the curves y = |x – 1| and y = 3 – |x| is PU CHD-2012 (A) 2 sq units (B) 3 sq units (C) 4 sq units (D) 6 sq units Area between curve y = 1 - |x| and X-axis Pune-2012 (a) 1 sq. unit (b) 1/2 sq. units (c) 2 sq units (d) 3 sq. units If F(x) is continuous such that area bounded by curve y = F(x) and X – axis gives x = a and x = 0 is Then the value of dx equals : a2 a sin a cos a . 2 2 2 F is 2 Pune-2012 (MCA : MP COMBINED – 2008) 31 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 1 2 (a) 27. (b) a 2 a2 2 (c) (d) 2 (a) 2A + 1 sq. units (c) 2A + 2 sq. units b The value of 39. n 1 is 2 lim sin sin ......... sin n n n n n (b) π (a) 0 1 5 40. 0 2 0 (B) a – b x 6 x (C) b + a (D) |b|–|a| (C) 2 (D) 5/2 dx x 1 I1 2 x dx, I 2 2 x dx, I 3 2 x dx and 3 dx, a < b is : x PU CHD-2011 (A) b – a 2 2 If x a NIMCET-2012 (d) /2 (c) 2 1 28. The value of (b) 2A sq. units (d) A + 2 sq. units PU CHD-2011 1 (A) 1 (B) 3/2 The value of 2 I 4 2 x dx then 3 41. /4 0 1 sin cos d is 9 16sin 2 BHU-2011 NIMCET-2012 (a) I1 = I2 (b) I2 > I1 (c) I3 > I4 1 (a) log 2 10 1 log 3 (c) 20 (d) I4 > I3 /2 29. The value of integral log tan xdx is 0 (b) /2 (a) π sin 2 x 30. The value of NIMCET-2012 (c) /3 sin 1 t dt (d) 0 cos 2 x 0 (a) /4 1 (b) log 5 20 1 log 7 (d) 30 1x 42. cos 1 tdt is The value of e tan 1 x 2 dx BHU-2011 0 (b) /2 NIMCET-2012 (d) None of these (c) 1 (a) e tan 1 x (b) e 1 1 (c) (d) 1 x2 1 x2 tan 1 x /2 31. log tan x dx is equal to : The value of DIFFERENTIAL EQUATIONS 0 (a) 0 32. (b) x/4 For a >1, the value of (c) x/2 0 BHU-2012 (d) 1. dx is a 2 2a cos x 1 (a) 2 (b) 2a (c) a2 1 2. (d) 0 If dy e x y dx dy dy a y 2 dx dx 1 dx Evaluate 2 0 1 x 3. and it is known that for x = 1, y = 1; if x = - 1, (MP COMBINED – 2008) (d) – 1 The solution of the differential equation HCU-2011 (b) 2 (a) - (c) 2 (a) 4x + y + 1 = tan (2x + c) (c) 2(4x + y + 1) = tan (2x + c) Consider the region bounded by the graphs y = e , y = 0, x =1 and x = t, where t < 1.The area of this region is atmost HCU-2011 (a) unbounded (b) e (c) 0 (d) 1n If ‘a’ is a positive integer, then the number of values satisfying 35. 2 a 0 2 4. The solution of the equation 5. (b) (d) four f x t sin tdt , then f'(x) is 6. 0 NIMCET-2011 (a) cos x + x sin x (b) x sin x (c) x cos x (d) 1 37. 2 0 dx x x2 x2 7. 2 [no correct answer was given in choices, correct answer should be π/2 ] NIMCET-2011 (a) 38. 1 2 (b) π (c) 3 (d) 4 If the area bounded by y = x2 and y = x is A sq. units then the area bounded by y = x2 and y = 1 is NIMCET-2011 Integrating factor of 2x 2 y dx x is : dy MP– 2004 (a) x2 (b) 1/x (c) – 1/x (d) 1/y The solution of the differential equation y(2x + y2)dx + x(x + 3y2)dy = 0, is IP Univ.– 2006 (a) x2y + 2xy3 = c (b) 2x2y xy3 = c (c) xy + xy3 = c (d) x2y + xy3 = c. (E) x2y + xy2, = c dy x y z is x dx x y 8. If the solution of the differential equation 9. + y – 1 = Ceu, then the value of u is: (MP COMBINED – 2008) (a) x + y (b) xy (c) x – y (d) x + y + 1 The solution of the differential equation (1 y 2 ) ( x e tan 1y ) 32 (d) (MP COMBINED – 2008) (b) xy = y2 + c (d) x + y3 = c (a) x = y(y2 + c) (c) y = x(y2 + c) x If s t 1 Ce 1 s t Ce t 1 3 dy The solution of the equation : x 2 y y dx NIMCET-2011 36. is : (MP COMBINED – 2008) s t Ce t t (c) s t Ce is (c) three (MCA : MP COMBINED – 2008) (b) 4x + y + 1 = 2 tan (2x + c) (d) tan (4x + y + 1) = 2x + c ds ts dt (a) a 2 cos3x 3 cos x a sin x 20cos x dx 4 3 4 (a) only one (b) two dy (4 x y 1) 2 dx is: (d) x 34. is (MP COMBINED – 2008) (b) (x + a) (1 + ay) = cy (d) (1 – ax) (1 + y) = cy then the value of y will be: (a) e2 (b) e (c) 1 D 33. yx (a) (x + a) (1 – ay) = cy (c) (1 + ax) (1 + y) = cy HCU-2011 Solution of the equation dy 0 dx is: INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 105. The degree of the differential equation (MP COMBINED–2008) 68. 75. 40. 7. 17. (a) e tan1 y x tan 1 y c (b) (c) ye tan1 y tan 1 y c (d) xe tan 1 2 2 dy d y 3 4 2 dx dx y y tan 1 y c The general solution of the differential equation dy x y 2 dx 2 xy Solution of the differential equation (c) (b) (d) 1. dy y sin x is : dx x 2. 3. 4. x3 8. 1 y dx x e 2 tan 1 (a) (c) ye 1 x tan x C y tan 1 xetan 1 x C (d) 2 1 , then that complex i 1' (b) 1 i 1 (c) 1 i 1 (d) 1 i 1 If z2 + z + 1 = 0, where z is a complex number, then the value of 2 2 The value of (b) 6 1 i (c) 12 (d) 18 2 2i (b) 3 + i is PGCET-2010 (c) 1 (d) – 1 z 2 z 0 is 9. The number of solution to the equation 10. (KIITEE - 2009) (a) 2 (b) 3 (c) 4 (d) 1 The area of the triangle whose vertices are I, a, b where i 1 and a, b are the nonreal cube roots of unity, is (MCA : KIITEE – 2009) (a) 11. 12. 3 3 2 (b) 3 3 4 (c) 0 (d) 3 4 If Z2 is purely imaginary when Z is a complex number of constant modules then the number of possible values of Z is KIITEE–2009 (a) 4 (b) infinite (c) 2 (d) 1 If w is an imaginary cube root of unity then (1 + w – w2)7 equals to (KIITEE – 2009) (a) 128 w (b) 128 w2 (c) – 128w (d) –128w2 n 13. y dy 0 14. is BHU-2011 tan 1 (c) 0 KIITEE-2010 1 i 1 (a) 2 dy x 2 y y 4 cos x 0 dx (c) (4x + 6y + 5)dx = (2x + 3y + 4)dy (d) (1 + y2) dx + (x – siny)dy = 0 102. Solution of the differential equation (b) - KIITEE-2010 Which of the following differential equations can be reduced to homogenous form? BHU-2012 (b) 2 (a) 54 d2y dy x2 1 x y e x dx dx 2 d2 y 1 y 2 xy e x x dx y e x x 2 y dx e x dy 0 KIITEE-2010 (a) an ellipse (b) a circle (c) a straight line (d) a parabola If z1 and z2 are two complex numbers such that |z1 + z2| = |z1| + |z2| then arg z1 – arg z2 is equal to” KIITEE-2010 2 dy 0 (b) x y dx (a) z and 1, then z lies on 1 z 3 1 2 1 6 1 z z 2 ..... z 6 is z z z BHU-2012 46. (a) BHU-2012 (d) If The conjugate of a complex number is 7. 45. 4 is 2 number is (a) Clairaut’s form (b) Newtonian form (c) Bernoulli’s form (d) None of these Which of the following differential equation is linear? (d) 1 +2 The value of X + 9X +35X – X + 4 for X = - 5+ 2 NIMCET-2010 (a) 0 (b) -160 (c) 160 (d) -164 3 6. Pune-2012 (c) (c) 2 NIMCET-2010 If |Z + 4| 3 then the maximum value of |z + 1| is KIITEE-2010 (a) 4 (b) 10 (c) 6 (d) 0 determines a family of circle with dy cos x 0 (a) 1 y dx (b) 2 5. 2 44. 1 the value of the 1 is i 1 3 4 (a) (a) fixed radii and center at (0, 1) (b) fixed radii and center at (0, - 1) (c) fixed radius 1 and variable center along X-axis (d) fixed radius 1 and variable center along Y-axis. The differential equation y = px + f(p) is called of : (d) 6 2 1 1 (b) parabola (d) Hyperbola 1 y dy dx y 1 i 1 i (a) 0 Solution of D.E. xdy – ydx = 0 is a D.E. (c) 5 Let 1 be a cube root of unity and i = determinant Pune-2012 31. (b) 4 1 y 2 x2 c 9 4 y 2 x2 c 4 9 (a) circle (c) straight line 2 d3y 3 is dx COMPLEX NUMBERS PU CHD-2012 (A) x(y + cos x) = sin x + C (B) x(y – cos x) = sin x + C (C) x(y + cos x) = cos x + C (D) x(y – cos x) = cos x + C Curve of D.E. xy' = 2y, passing through (1, 2) is also passing through Pune-2012 (a) (1, 2) (b) (4, 24) (c) (24, 4) (d) (4, 8) Solution of D.E. 9yy' + 4x = 0 is Pune-2012 y 2 x2 c 9 4 y 2 x2 c 4 9 2/3 BHU-2011 (a) 3 HCU-2011 (a) y2 = (ln |x| + C)x (b) y = (ln |x| + C)x (c) y2 = (ln |x| + C) (d) y = (ln |x| + C)x2 The differential equation, whose solutions are all the circles in a plane, is given by HCU-2011 (a) (1 + y')2 y'" – 3y'y"2 = 0 (b) xy' + y = 0 (c) (1 + y')2y'" + 3'y"2 = 0 (d) yy" + y'2 + 1 = 0 (a) 24. xe tan1 y tan 1 y c tan 1 1 y tan y C (b) xe (d) y xe tan 1 x 15. C 33 The smallest positive integer n, for which 1 i 1 is 1 i (KIITEE - 2009) (a) 8 (b) 12 (c) 16 (d) None of these Let and be the roots of the equation x2 + x + 1 = 0. The equation whose roots are 19 and 7 is NIMCET – 2008 (a) x2 – x – 1 = 0 (b) x2 + x – 1 = 0 (c) x2 – x + 1 = 0 (d) x2 + x + 1 = 0 The equation |Z + i| - |Z – i| = k represents a hyperbola if KIITEE – 2008 (a) 0 < k < 2 (b) – 2 < k < 2 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS (c) k > 2 16. (d) None (1 ix)(1 2ix) is purely real then the non zero real value of 1 ix 30. KIITEE – 2008 x is 17. (a) 2 (b) 2 (c) 1 (d) – 1 The fourth roots of unity are given as z1, z2, z3 and z4. The value of z12 z 22 z32 z 42 (a) i 1 18. If 20. 21. 31. 1 0 (a) 1 then the value of is : 32 2 (b) 2 (d) 4 24. 26. (b) 2 (d) – 2i (c) 2i PA + PB =2 PC (d) PA + PB +2 PC = O (b) PA + PB + PC = O a , b and c be three non zero vectors, no two of which are collinear and the vector a + b is collinear with c ,while b + c is collinear with a then a + b + c , is equal to NIMCET-2010 3. Let (a) a (b) b (c) c (d) none of these The position vector of A, B, C and D are i j k , 2 i 5 j,3 i 2 j 3k , and i 6 j k then the angle is KIITEE – 2008 AB and CD is between (a) 0 (b) /4 NIMCET-2010 (c) /2 (d) 4. A vector a has components 2p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counterclockwise sense. If, with respect to the new system, a has components p + 1 and 1, then NIMCET-2010 is equal to KIITEE - 2008 (c) p = -1 or p = (a) /3 (b) /4 (c) /5 (d) /6 (e) /7 Let A be the set of all complex numbers that lie on the circle whose radius is 2 and centre lies at the origin. Then B = {1 + 5z|z A} describes HCU-2012 (a) a circle of radius 5 centred at (-1, 0) (b) a straight line 6. The vectors If 7. 1 4 1 i j k 3 3 3 (b) i 4 j k (d) 1 4 1 i j k 3 3 3 The average marks per student in a class of 30 students were 45. On rechecking it was found that marks had been entered wrongly in two cases. After correction these marks were increased by 24 and 34 in the two cases. The corrected average marks per student are NIMCET-2010 (a) 75 (b) 60 (c) 56 (d) 47 8. PU CHD-2012 (B) 2 solutions (D) An infinite number of solutions 8 c is equal to NIMCET-2010 i k (a) i 1 and z = x + iy then the equation z2 = z has The value of complex number a i j , b j k and c make an obtuse angle with the base vector i, then (c) 28. a , b and c are equal in length and taken pairwise make equal angles. If . This set is 27. (d) p = 1 or p = -1 The value of ‘a’ for which the system of equations a3 x + (a + 1 )3 y + (a + 2)3 z = 0 ax + (a + 1) y + (a + 2) z = 0 x+y +z=0 has a non zero solution, is NIMCET-2010 (a) 1 (b) 0 (c) -1 (d) N.O.T j HCU-2012 (a) an unbounded infinite set (b) an infinite bounded set (c) a finite set with |T| > 319 (d) a finite set with |T| < 10 If 1, , 2 be the cube roots of unity, then value of (1 +– 2)7 + (1 – + 2)7 is : PU CHD-2012 (A) – 128 (B) 128 (C) 64 (D) – 64 1 3 5. (c) a circle of radius 5 with centre at (-1, 0). (d) a circle of radius 10 centred at (-1, 0) Consider a set of real numbers T = {t1, t2, ….,} defined as 1 3 1 3 t j 2 2 1 (b) p = 1 or p = 3 (a) p = 0 IP Univ.– 2006 j 29. 2 p 2 p i cos is 7 7 (c) 2. (a) 1 (b) i (c) -i (d) 0 For complex number z, 0 ≤ arg z < 2 . S (A) No solution (C) 4 solutions 2 sin (a) PA + PB = PC i 1 and 4 1 , , , then S {z : z 5 3 5i is 25. 2 VECTORS 1. If C is the middle point of AB and P is any point outside AB, then NIMCET-2010 32 zi z i If z is different from i and |z| = 1 then 1 MP– 2004 i (a) 5/2 (b) 2 5 (c) 5 (d) None If |Z - i| 2 and Z0 = 5 + 3i then the maximum value of |iZ + Z0| is KIITEE – 2008 If The value of p 1 (a) purely imaginary (b) purely real (c) non real with equal real and imaginary parts (d) None 23. (d) If 1, , 2, ……, n-1 are nth roots of unity, then (1 - ) (1 - 2) ….. (1 - n-1) is equal to BHU-2011 (a) n2 (b) 0 (c) 1 (d) n (d) 0 (a) /4 (b) /3 (c) /2 (d) /6 The fourth roots of unity are :. UPMCAAT - 2002 (a) 1, 1, 1, 1 (b) 1, -1, 1, -1 (c) 1, 1, i, i (d) -1, 1, -i, i The radius of a circle given by the equation z z (4 3i) z (4 3i z ) 0 is KIITEE – 2008 (a) (c) 7 22. i e KIITEE–2008 2 (c) BHU-2011 1 1 (b) - 2 6 is (c) -i 1 1 e 1 19. (b) 1 (a) 2 If 8 1 i 1 i is : 2 2 a, b, c 1 b c , then the angle between the vectors a 2 is 3 (a) 4 BHU-2012 34 a b c are non-coplanar unit vectors such that and b KIITEE-2010 (b) 4 (c) 8 (d) 2 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 9. a b c 1 If a . b 0, a . c b . c , and 11. 12. (b) 2 3 3 5 (c) (d) 5 3 (a) 9 (b) 4 a, b, c If 15. 16. 4 non-coplanar (c) a b b c c a (a) a b c (c) 2 a b c unit vectors such that (NIMCET – 2009) 2 (d) 26. 3 (d) a, b are the adjacent sides of a ||gm then ||gm is a: UPMCAT– 2002 (b) square (d) None of these (b) 3/4 (c) 30/4 (d) HYDERABAD CENTRAL UNIVERSITY - 2009 (b) 9 (c) 1 (d) 0 (d) a, b and c are three non-zero vectors, no two of which are a a 2 b is collinear with c Let and b 3 c is , then a 2 b 6 c is HYDERABAD CENTRAL UNIVERSITY - 2009 0 (b) parallel to a b 28. 1 and d .( a b c ) 3 then v is 3 (c) parallel to 3 | c |2 (d) parallel to c A 2 i j 2 k and B i j . If C is a vector such that A C | C |, | C A | 2 2 and the angle between A B and C is 300, then | ( A B ) C | is equal to NIMCET - 2008 1 i j k , j k and i k is minimum is (c) 3 10 2 given by (b) 3 Let (a) then d ( a b ) ( b c ) v( c a ), v( c a ), a If collinear a.c 0 ; and 1 (a) -3 collinear. If The value of for which the volume of parallelepiped formed by the vectors (b) 42sq units (d) N.O.T. a b a b If 3 27. a c a b HYDERABAD CENTRAL UNIVERSITY - 2009 18. (d) None of these (a) 0 .( b c ) a i 2 j 3k , b 2i j k and c is a vector satisfying Karnataka PG-CET– 2006 (d) – 5 (c) 5 a 2 i 3 j 6 k If (a) 6 If a 1, 2,3 and b 2, , 4 are (b) 10 (c) (a) rectangle (c) rthombus KIITEE – 2009 is equal to 1 (a) 0sq units (c) 49 sq units (b) 0 (b) NIMCET - 2008 (c) 5/3 (d) /4 UPMCAT– 2002 3 17. (b) 2/3 Then area of ponallelogram is equal to : The value of x for which the volume of parallelepiped formed by the vectors I + xj + k, j + xk and xi + k is minimum is HYDERABAD CENTRAL UNIVERSITY - 2009 (a) – 3 A and B is If the vectors 3 4 (b) b 3 i 6 j 2 k 25. b c a b c , then the angle between a and b is 2 (a) (d) 6 are (a) 64 (b) 16 (c) 8 (d) None The volume of the tetrahedron whose vertices are P(k, k, k), Q(k + 1, k + 6, k + 36), R(k, k + 2, k + 5), S(k, k, k + 6) is IP Univ.– 2006 (a) 1 (b) 2 (c) 4 (d) 6 (e) 36 14. a , b , c be three vectors such that [ a b c ] = 4 then Let NIMCET – 2009 (c) 8 (d) 8 A B C 0 , | A | 3, | B | 5, | C | 7 then the angle If (a) 12 | a b |2 | b c |2 | c a |2 orthogonal, then the value of is 24. (c) 5 23. 2 (i j ) 3 (d) None of these NIMCET - 2008 (b) 4 [ a b b c c a ] is equal to KIITEE – 2008 (NIMCET – 2009) (b) 21. a, b and c are unit perpendicular vectors, then between (a) /6 B 3i 4k is to be written as the sum of a vector 22. B1 parallel to A i j and a vector B 2 perpendicular to If 4 sin 1 5 3 2 A , then B1 is 3 (a) (i j ) 2 1 (c) (i j ) 2 13. 20. The vector (a) – 6 (c) 90 (d) None of these Area of the parallelogram whose adjacent sides are i + j – k and 2i – j + k is (PGCET– 2009) (b) 2 i 2 j 6 k, KIITEE-2010 3 sin 1 5 (a) 3 i 2 j k ,6 i 3 j k 5 i 7 j k , and (a) 2 + 22 (b) = + 1 (c) = = (d) None of these If 3P and 4P are the resultants of a force 5P, then the angle between 3P and 5P is KIITEE-2010 (a) The value of such that the four points whose position vectors are c a b v a b , then 10. 19. where 29. 3 3 NIMCET - 2008 (a) 2/3 (b) 3/2 (c) 2 (d) 3 The projection of a line segment on the axes of reference are, 3, 4 & 12 respectively. The length of the line segment is KIITEE – 2008 (a) 13 35 (b) 5 (c) 19 3 (d) 19 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 30. The vertices of a triangle ABC are A (-1, 0, 2), B(1, 2, 0) and C(2, 3, 4). The moment of a force of magnitude10 acting at A along AB about C is KIITEE – 2008 (a) 31. 20 6 (b) 50 6 3 (c) 50 40. (d) None 3 41. Let 42. a (a) (c) 33. 34. 35. 36. 37. and c 2 6 , and a ( b c ) be . If , a (b) 3 50i 30 j 70k (b) If angle between 3 , 44. 45. the value of a . b b . c c . a is 2 (a) 3 2 (b) 3 If 3 (d) 2 3 (c) 2 a , b, c are non-coplanar vectors and is a real number, then a 2b 3c, b 4c and 2 1 c are non- NIMCET-2012 (a) All values of (b) All except one value of (c) All except two values of (d) No value of If a, b and c are unit coplanar vectors, then the scalar triple product [2a – b, 2b – c, 2c – a] = NIMCET-2011 (b) 1 (c) 46. Let 3 (d) 3 a x i 3 j k and b 2 x i x j k . Suppose that the angel between a and b is acute and the angle between b and the positive direction of the y-axis lies between 2 and π, then the set of all possible values of x is (b) {–2, –3} (d) {x : x > 0} (a) {1, 2} (c) {x : x < 0} 47. Let NIMCET-2011 v 2 i j k and w i 3 k . If u is a unit vector, then the maximum value of the scalar triple product u v w is NIMCET-2011 48. 49. (a) –1 (b) 10 6 (c) 59 (d) 10 6 If θ is the angle between a and b and |a×b| = |a.b|, then θ is equal to: NIMCET-2011 (a) 0 (b) π (c) π/2 (d) π/4 ABCD is a parallelogram with AC and BD as diagonals. Then AC BD is equal to: NIMCET-2011 HCU-2011 50. 51. are mutually perpendicular, then the value of x is NIMCET-2012 (c) 4 c are unit vectors such that a b c 0 , then and (a) 0 p and q is (b) 2 (d) cot coplanar for p 3 , then the 2 (b) (c) (d) 3 6 6 If the vectors a 1, x, 2 and b x,3, 4 (a) – 2 a, b the vectors 4 (a) 6 39. If (c) -tan NIMCET-2012 2 and (b) tan 50i 30 j 70k p q 1 a and b , then equals 43. 83 and NIMCET-2012 (d) None of the above p q 13 NIMCET-2012 (d) /6 (a) -cot 1 b then. KIITEE – 2008 2 83 (c) Both A and B (c) /4 a.b (d) None 3 a and b is (b) /3 p, q, r are mutually perpendicular unit vectors. d is also a unit vector. If d = u1p + v1q + w1r and d = u2(q r) + v2 (r q) + w2 (p q), then the maximum value of (u1 – u2)2 + (v1 – v2)2 + (w1 – w2)2 equals IP Univ.– 2006 (a) 0 (b) 1 (c) 2 (d) 3 (e) 4 Suppose A = i – j – k, B = i – j + k and C = - i + j + k, where i, j, k are unit vectors. Pick the odd one out among the following: HCU-2012 (a) A (B C) (b) (A B) C (c) A C (d) A B Consider the following equalities formed for any three vectors A, B and C. HCU-2012 I. (A B)C = A(B C) II. (A B) C = A (B C) III. A (B C) = (A B) C IV. A (B + C) = (A B) + (A C) (a) Only I is true (b) I, III and IV are true (c) Only I and IV are true (d) All are true A line makes angles , , and with the four diagonals of a cube. Then the sum cos2 +cos2 +cos2 + cos2 is HCU-2011 (a) 4/3 (b) 0 (c) 1/3 (d) 1 Let A = 2i – 3j + k and B = - i + 2j + k be two vectors. The vector perpendicular to both A and B having length 10 is HCU-2011 (a) 38. be and that between b a b a , b , c be three unit vectors of which b and c are non – If (0 ≤ ≤ π) is the angle between the vectors (d) None parallel. Let the angle between (a) /2 32. a b c 0 , a 3 , b 5 , c 7 , then angle If between the vector 1 1 1 1 1 x 1 y 1 z 1 1 1 1 x y z NIMCET-2012 (b) 3x – y + 2z + 7 = 0 (d) 3x + y + 2z = 7 (a) 2x – y + 3z + 7 = 0 (c) 3x – y + 2z = 7 (b) x + y + z = 1 (c) N 3i j 2k as its normal, is having the vector The coplanar points A, B, C, D are (2 – x, 2, 2), (2, 2 – y, 2), (2, 2, 2 – z) and (1, 1, 1) respectively. Then one the following is true, find it KIITEE – 2008 (a) The equation of the plane passing through the point (1, 2, 3) and (d) – 4 52. 36 (a) 4 AB (b) 3 AB (c) 2 AB (d) AB The vector 2i + j – k is perpendicular to i – 4j + k, if is equal to BHU-2011 (a) 0 (b) – 1 (c) – 2 (d) – 3 If |a| = |b|, then (a + b) . (a – b) is BHU-2011 (a) positive (b) negative (c) unity (d) zero If A = 2i + 2j – k, B = 6i – 3j + 2k, then A B will be given by BHU-2011 (a) 2i – 2j – k (b) 6i – 3j + 2k INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 53. 54. 55. 56. 57. (c) I – 10j – 18 k (d) i + j + k If the position vectors of three points are a – 2b + 3c, 2a + 3b – 4c, - 7b + 10c, then the three points are BHU-2011 (a) collinear (b) coplanar (c) non-coplanar (d) None of these If a = 4i + 2j – 5k, b = - 12i – 6j + 15k, then the vectors a, b are BHU-2011 (a) parallel (b) non-parallel (c) orthogonal (d) non-coplanar If is the angle between vectors a and b, then |a b| = |a . b| when is equal to BHU-2011 (a) 0 (b) 45 (c) 135 (d) 180 If [abc] is the scalar triple product of three vectors a, b and c, then [abc] is equal to BHU-2011 (a) [bac] (b) [cba] (c) [bca] (d) [acb] If be the angle between the vectors 4(i – k) and i +j + k, then is BHU-2011 (a) 58. 2 (b) 3 (c) 4 (d) (a) 3. 4. 5. 6. 7. 1 cos 1 3 a b = 0 implies only 8. BHU-2011 59. 60. 61. 62. 63. (a) a = 0 (b) b = 0 (c) = 90 (d) either a = 0 or b = 0 or = 90 If a and b are two unit vectors and is the angle between them. Then, a + b is a unit vector, if BHU-2011 (a) (c) (b) 3 9. 4 2 (d) 3 2 10. If two vectors a and b are parallel and have equal magnitudes, then BHU-2011 (a) they are not equal (b) they may or may not be equal (c) they have the same sense of direction (d) they do not have the same direction Let ABCD be a parallelogram. If a, b, c be the position vectors of A, B, C respectively with reference to the origin 0, then the position vector of D with reference to 0 is BHU-2011 (a) a + b + c (b) b + c – a (c) c + a – b (d) a + b – c If a and b represent two adjacent sides AB and BC respectively of a parallelogram ABCD, then its diagonals AC and DB are equal to BHU-2011 (a) a + b and a – b (b) a – b and a + b (c) a + 2b and a – 2b (d) 2a + b and 2a – b Let the vectors a, b, c be the position vectors of the vertices P, Q, R of a triangle respectively. Which of the following represents the area of the triangle? BHU-2011 1 ab 2 1 ca (c) 2 (c) 2. 17 19 , , 4 3 3 9 13 , , 4 5 5 12. ) If h is height and r1, r2 are the radii of the end of the frustum of a cone, then the volume of the frustum is BHU-2012 (a) is 2 3 The image of the line from the point P given in Question 37 and it’s reflection P' about the plane 2x + y + z = 6 is given by HCU-2011 The length of the perpendicular from (1, 0, 2) on the line x 1 y 2 z 1 3 2 1 (d) 3x 1 3 y 5 3z 8 4 2 1 x 1 y 2 z 3 (b) 2 1 4 x 1 y 2 z 3 (c) 1 2 2 3x 1 3 y 2 z 8 (d) 2 3 1 (b) (15, 11, 4) (d) (8, 4, 4 3 2 (a) THREE DIMENSIONAL GEOMETRY 1. The image of the point (-1, 3, 4) in the plane x – 2y = 0 is KIITEE-2010 (a) (c) 1 1 12 p 2q 2r , 6 2 p 2q r , 3 3 1 6 2 p q 2r 3 1 1 6 2 p q 2r , 12 p 2q r , 3 3 1 6 2 p q 2r 3 1 1 6 2 p 2q r , 6 2 p 2q r , 3 3 1 12 p 2q 2r 3 (d) (b) 6 3 5 (a) square (b) rectangle (c) rhombus (d) None of these The points A = (1, 2, -1), B = (2, 5, -2), C = (4, 4, -3) and D = (3, 1, -2) are (MCA : KIITEE – 2009) (a) vertices of a square (b) vertices of a rectangle (c) collinear (d) vertices of a rhombus If (1, -1, 0), (-2, 1, 8) and (-1, 2, 7) are three consecutive vertices of a parallelogram then the fourth vertex is (KIITEE – 2009) (a) (0, -2, 1) (b) (1, 0, -1) (c) (1, -2, 0) (d) (2, 0, -1) The points (0, 0, 0), (0, 2, 0), (1, 0, 0), (0, 0, 4) are KIITEE – 2008 (a) vertices of a rectangle (b) on a sphere (c) vertices of a parallelogram (d) coplanar Find the point at which the line joining the points A (3, 1,-2) and B(-2, 7, -4) intersects the XY-plane. HCU-2012 (a) (5, -6, 0) (b) (8, -5, 0) (c) (1, 8, 0) (d) (4, -5, 0) If x + y + z = 0 and x3 + y3 + z3 – kxyz = 0, then only one of the following is true. Which one is it? HCU-2012 (a) k = 3 whatever be x, y and z (b) k = 0 whatever be x, y and z. (c) k = + 1 or -1 or 0 (d) If none of x, y, z is zero, then k = 3 Consider the lines given by (x = a1z + b1, y = c1z + d1) and (x = a2z + b2, y = c2z + d2). The condition by which these lines would be perpendicular is given by HCU-2011 (a) a1c1 – a2c2 + 1 = 0 (b) a1c1 + a2c2 – 1 = 0 (c) a1a2 – c1c2 = 1 (d) a1a2 + c1c2 + 1= 0 The image P' of the point P(p, q, r) in the plane 2x + y + z = 6 HCU-2011 (a) (p, q, - r) (c) 11. (b) If A = (5, -1, 1), B = (7, -4, 7), C = (1, - 6, 10), D = (-1, -3, 4) then ABCD is a (MCA : KIITEE – 2009) (b) 1 bc 2 1 ab bc ca (d) 2 (a) 3 6 2 KIITEE-2010 37 h 3 r 2 1 3r1r2 r22 (b) h 3 r 2 1 3r1r2 r22 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS h (c) 13. 3 r 2 1 r1r2 r22 h (d) 3 r 2 1 BHU-2012 r1r2 r22 (a) If r is a radius and k is thickness of a frustum of a sphere, then its curved surface of frustum is : BHU-2012 1 (a) rk (b) rk 2 14. (c) 2 rk (d) 16. 4 rk The area of the triangle having vertices (1, 2, 3) and (-1, 2, 3) is : BHU-2012 1 107 2 1 (c) 165 2 TRIGONOMETRY 4 5 6 7 D A A D 14 15 16 17 D D C B 24 25 26 27 A * A B 34 35 36 37 D A B C 44 45 46 47 A C B A 54 55 56 57 B D A C 64 65 66 67 B C B D 74 75 76 77 C A B A 84 85 86 87 D B B B 94 95 96 97 B B B A 104 105 106 107 D C C A 8 A 18 A 28 C 38 C 48 A 58 C 68 C 78 D 88 C 98 C 108 D 9 B 19 D 29 C 39 A 49 A 59 B 69 C 79 C 89 B 99 A 109 A 10 D 20 D 30 C 40 C 50 C 60 D 70 A 80 C 90 C 100 D 110 C PROBABILITY 5 6 C D 15 16 + B 25 26 C 35 36 A C 45 46 B A 55 56 A C 65 66 A B 75 76 A D 8 A 18 28 D 38 D 48 C 58 A 68 B 78 C 9 D 19 29 D 39 D 49 A 59 B 69 B 10 A 20 C 30 D 40 C 50 C 60 B 70 B 9 D 19 A 29 D 39 B 49 B 59 B 69 D 79 B 10 D 20 B 30 B 40 A 50 D 60 C 70 N 80 D 2 a 3 b 4 c (b) 2 a 3 b 4 c (c) 2 a 3 b 4 c (d) 2 a 3 b 4 c The straight line through the point (-1, 3, 3) pointing in the direction of the vector (1, 2, 3) hits the xy plane at the point HCU-2011 (a) (2, - 1, 0) (b) (-2, 1, 0) (c) (1, 3, 0) (d) never 1 155 2 1 (d) 187 2 (a) (b) 15. The point of intersection of the line r a b t c and the r a b t1 a b c t2 a b c plane is : ANSWERS (OLD QUESTIONS-CW1) 1 C 11 D 21 C 31 A 1 A 11 C 21 C 31 A 41 CD 51 A 2 A 12 A 22 C 32 A 2 12 A 22 B 32 B 42 B 52 D 3 D 13 A 23 D 33 C 3 A 13 B 23 A 33 C 43 C 53 C 1 A 11 B 21 B 31 A 2 A 12 B 22 C 1 A 11 B 21 C 31 A 41 A 2 B 12 A 22 B 32 A 42 C SETS & RELATIONS 4 5 6 7 B C A C 14 15 16 17 A AC B B 24 25 26 27 B D A B 34 35 36 37 D D B D 8 C 18 B 28 B 9 C 19 D 29 C THEORY OF EQUATIONS 4 5 6 7 8 C B B A C 14 15 16 17 18 A B A C C 24 25 26 27 28 D D C B ABCD 34 35 36 37 38 D C B B C 44 45 46 47 48 B B D ABCD B 54 55 56 D A B 3 B 13 B 23 C 3 C 13 C 23 B 33 D 43 B SEQUENCE & SERIES 4 5 6 7 D C B B 14 15 16 17 A A A B 24 25 26 27 C B C A 4 A 14 B 24 A 34 A 44 B BINOMIAL 5 6 A C 15 16 C B 25 26 B C 35 36 A C 45 46 D C 7 B 17 A 27 A 37 B 47 C 8 A 18 A 28 B 8 A 18 D 28 A 38 A 48 B 9 A 19 C 29 C 9 B 19 B 29 C 39 B 49 C 10 C 20 D 30 C 9 D 19 B 29 B 39 A 49 B 1 C 11 A 21 B 31 D 41 D 51 A 61 D 71 A 81 B 91 A 101 A 111 A 10 C 20 D 30 D 40 BC 50 A 10 D 20 B 30 B 10 A 20 A 30 B 40 A EXPONENTIAL & LOGARITHMIC SERIES 1 2 3 4 5 6 7 C D C B A A D 1 C 11 C 21 C 31 B 41 B 2 A 12 B 22 A 32 C 42 A PERMUTATIONS & COMBINATIONS 3 4 5 6 7 8 9 C C B A A A D 13 14 15 16 17 18 19 D A A B C C D 23 24 25 26 27 28 29 A C D C A C C 33 34 35 36 37 38 39 D C C A C B D 43 44 45 46 47 48 49 D D B B D D D 10 C 20 A 30 C 40 B 50 C 38 2 A 12 B 22 C 32 D 42 A 52 D 62 B 72 D 82 D 92 C 102 C 112 B 1 D 11 D 21 A 31 A 41 A 51 B 61 D 71 C 2 12 A 22 B 32 B 42 D 52 D 62 D 72 D 1 11 A 21 C 31 41 C 51 A 61 C 71 C 2 12 22 A 32 42 B 52 D 62 B 72 A 3 C 13 A 23 D 33 C 43 D 53 C 63 D 73 C 83 C 93 A 103 B 3 13 4 B 14 A D 23 D 33 C 43 D 53 C 63 A 73 D 24 34 A 44 C 54 C 64 B 74 A 7 B 17 27 B 37 C 47 B 57 C 67 D 77 D TWO DIMENSIONAL GEOMETRY 3 4 5 6 7 8 A D D C 13 14 15 16 17 18 A C D C B A 23 24 25 26 27 28 D A C D B A 33 34 35 36 37 38 B D D A B C 43 44 45 46 47 48 B D A A B B 53 54 55 56 57 58 D B B C D B 63 64 65 66 67 68 D B A A C A 73 74 75 76 77 78 B D C D C A INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 81 A 91 C 101 D 111 B 121 E 131 B 141 B 151 D 1 B 11 82 D 92 A 102 A 112 A 122 C 132 B 142 D 152 E 83 C 93 D 103 D 113 B 123 C 133 C 143 C 153 A 1 C 11 C 21 D 31 A 41 A 2 C 12 C 22 D 32 A 42 C 1 D 11 D 21 D 2 C 12 A 22 C 1 D 11 A 21 C 31 C 2 C 12 D 22 B 32 B D A 22 D 32 D 1 11 D 21 3 C 13 B 23 D 33 A 43 B 86 A 96 A 106 D 116 D 126 C 136 A 146 C 156 D FUNCTIONS 5 6 B D 15 16 C A 25 26 A D 35 36 A B 45 46 C B 87 A 97 D 107 D 117 C 127 C 137 B 147 A 157 C 88 A 98 C 108 C 118 A 128 B 138 C 148 C 158 B 89 C 99 B 109 B 119 C 129 A 139 C 149 A 159 D 7 8 9 B C B 17 C 27 A 37 C 47 A 18 B 28 B 38 B 48 C 19 B 29 B 39 C 49 C LIMITS AND CONTINUITY 3 4 5 6 7 8 B C C A A A 13 14 15 16 17 18 E C D B B B 9 B 19 D 3 A 13 D 23 C 33 C 4 B 14 A 24 A 34 A 44 D 85 C 95 D 105 A 115 B 125 D 135 D 145 C 155 E 4 A 14 C 24 B DERIVATIVES 5 6 7 D A C 15 16 17 C D B 25 26 27 C C C 8 B 18 D 28 C 9 B 19 D 29 D APPLICATION OF DERIVATIVES 3 4 5 6 7 8 C C C D C D 13 14 15 16 17 18 B A Bd D A B 23 24 25 26 27 28 C C A A D B 33 34 35 36 37 D D D B A 2 D 12 21 B 31 C 84 A 94 B 104 D 114 D 124 A 134 D 144 B 154 E 2 12 B 22 3 13 B 23 4 14 B 24 MATRICES 5 6 B C 15 16 D B 25 26 7 B 17 C 27 8 A 18 B 28 31 D 41 D 51 B 61 B 71 D 81 C 32 B 42 C 52 D 62 C 72 C 82 B 1 A 10 D 20 A 30 B 40 C 11 B 31 110 A 10 B 20 B 10 A 20 C 16 D 41 1 C 11 C 21 C 1 A 10 B 20 A 30 B 9 A 19 D 29 C 9 D 19 29 90 D 100 D 110 A 120 D 130 B 140 C 150 A 10 C 20 A 30 B C D D B C 33 C 43 B 53 C 63 C 73 B 83 B 34 D 44 B 54 B 64 A 74 C 84 A 35 C 45 55 C 65 C 75 A 85 B 36 D 46 B 56 A 66 D 76 A 86 D 37 C 47 C 57 D 67 A 77 D 87 D 2 B D 38 48 C 58 D 68 A 78 D C 39 B 49 D 59 A 69 B 79 A C 40 B 50 A 60 B 70 C 80 B 18 * 32 INDEFINITE INTEGRATION 3 4 5 6 7 B D C A C 39 C 42 2 12 C DEFINITE INTEGRAL 18 29 11 13 A A C D 17 20 26 27 D B A 3 4 5 6 C D A D 13 14 15 16 A D D C 14 D 31 D C 7 B 17 C 8 D 18 C 41 A 108 C 9 B 19 B 8 C 18 C 9 C 19 D 10 D 20 B 8 B 18 C 28 B 9 D 19 B 29 A 10 C 20 C 30 D (D.E.) DIFFERENTIAL EQUATION 2 3 4 5 6 7 8 9 D B B A B C B 1 A 11 A 21 C 2 B 12 D 22 A 3 C 13 D 23 D 1 B 11 C 21 B 31 C 2 D 12 D 22 B 32 A 3 D 13 C 23 C 33 A COMPLEX NUMBER 4 5 6 7 C C C C 14 15 16 17 D B A D 24 A VECTORS 4 5 6 7 C C D 14 15 16 17 B B B D 24 25 26 27 C A B A THREE DIMENSIONAL-OLD QUESTIONS 1 2 3 4 5 6 B A D B D B 10 C 20 30 39 INFOMATHS/MCA/MATHS/OLD QUESTIONS