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INFOMATHS PUNE-2014 What is the correct negation of statement (“2 is even dy 13. If ey = sinx and 0 < x < then find in terms of x and – 3 is negative”) dx (a) 2 is odd and – 3 is not negative (a) tan x (b) cot x (b) 2 is odd and – 3 is negative (c) – tan x (d) – cot x (c) 2 is odd or – 3 is not negative 4 (d) 2 is odd or – 3 is negative 14. If f x and g(x) = 2x and f[g(x)] = g[f(x)] x 1 2. Which of the following polynomial best then find the value of x ex 1 x2 approximately equals the function 1 1 x (a) (b) 2, 3 3 (a) 1 + x + x2 (b) x + 2x2 + x3 2 3 2 1 3x x 3x x x (c) 0,1, (d) N.O.T (c) 1 (d) x3 3 2 6 2 6 24 15. Find the square root of – 7 – 24i i 0 4n 3. If A and n N then the value of A 2i 7 i 7 i (a) 3 + 4i (b) (c) (d) 0 i 4i 1 i 1 i 1 0 i 0 (a) (b) 2 x2 16. Find coefficient of x4 in the expansion of 0 i 0 1 1 x x2 0 i 0 1 in ascending power of x (c) (d) (a) 12 (b) - 2 (c) – 4 (d) 6 i 0 1 0 0 2 1 2 4. If A then find the value of |A2009 – 5 A2008| 17. Given A and its transpose of A is 3 5 is (a) – 6 (b) – 4 (c) – 5 (d) N.O.T equal to its inverse then 2 1 1 3 x (a) (b) 5. The minimum value of the if x 0 2 2 1 x (a) 0 (b) 1 (c) 9 (d) 2 1 (c) (d) All of these 6. Find the 4th term in the expansion of (1 – x)3/2 3 1 3 3 3 x (c) x (d) N.O.T (a) 0 (b) a x3 sin x 18. If f x 16 8 find a f x ? 2 1 7. If [ ] denotes the greatest integer less then or equal to (a) 0 (b) – 2a3 (c) 3 (d) 4 x & - 1 x < 0, 0 y < 1, 1 z < 2 then the value of 19. Students in college _____ laptops to do their work determinant (a) are given (b) are gave [ z] [ x] 1 [ y] (c) given (d) were used [ x] [ y ] 1 [ z ] 20. Sachin will ______ degree next year. [ x] [ y ] [ z ] 1 (a) finish (b) finishes (c) finished his (d) finish his (a) [x] (b) [y] (c) [z] (d) None of these 21. Lectures sometimes _____ Saturday. 8. The cube root of 9 3 11 2 is (a) hold on (b) hold at (a) 3 2 (b) 3 3 2 (c) held on (d) held at 22. Dinesh had purchased four pair of shirts even though (c) 3 3 3 2 (d) 3 2 he has short of money. Choose the appropriate f x 9. If xf x find f(x) punctuation. 2 (a) Shirts, Even though he 2 ex (b) Shirts, even though he x -x (a) e (b) e (c) log x (d) (c) shirts, even though, he 2 (d) shirts, even though, he 10. Find the area bounded by the curve y = e2x & between x axis and y axis and line x = 0 to x = 2 1 3 2 1 1 4 1 4 23. 11 0 5 1 1 0 (a) e e (b) e 1 2 2 0 3 2 x e4 e e4 1 then the best approximation of x (c) (d) 4 2 4 (a) - .8599 (b) -.8597 (c) -.8595 (d) -.8588 11. If f(x) = |x|3 then find f’(0) 24. One hundred identical coins, each with probability p (a) 1 (b) 0 (c) 1/2 (d) 1/3 of showing heads are tossed once. If 0 < p < 1 and 12. The differential equation xdy – ydx = 0 represents the probability of heads showing on 50 coins is equal (a) parabola (b) straight line to that heads showing on 51 coins, the value of p is (c) circle (d) hyperbola (a) 1/2 (b) 50/101 (c) 51/101 (d) 49/101 1. 1 INFOMATHS/MCA/PUNE-2014 INFOMATHS 25. Find the value of m for which the given equations 3x 3n 4 n + my = m and 2x – 5y = 20 has solution satisfying (c) (d) N.O.T n 4 1 the condition x > 0, y > 0 15 34. Ram and Shyam have equal number of daughters. (a) , (b) (30, ) There are three cinema tickets which are to be 2 distributed among the daughters of Ram and Shyam. 15 (c) , The probability that the two tickets goes to the 30, (d) N.O.T 2 daughter of one and one ticket goes to another 26. Find the value of x for which the equation daughters is 6/7. Then the number of daughter each 2 2 of Ram and Shyam have x 5x 3 2 x 5x 3 15 has real solution (a) 3 (b) 4 (c) 8 (d) N.O.T (a) 6 (b) 1 35. An ordinary cube has 4 blank faces, one face marked 5 113 5 113 2 and another face marked 3. Then the probability of (c) (d) 2 2 obtaining 12 in 5 throw is 27. For three events A, B and C, P (exactly one of the 5 5 5 (a) (b) (c) (d) N.O.T events A or B occurs) = P (exactly one of the events 1296 1944 2592 B or C occurs) = P (exactly one of the events C or A occurs) = p and P (all the three events occurs 36. 3 z 1 z , where z is complex number, then z 3z 4 simultaneously) = p2 where 0 < p < ½. Then the probability of at least one of the three events A, B find the number of solution of z satisfying the and C occurring is equation 2 2 (a) zero (b) atmost 2 3p 2p p 3p (a) (b) (c) atleast 2 (d) Infinite solution 2 2 37. Satish had stopped car at petrol pump because there 3 p p2 3 p 2 p2 _____ petrol in the tank (c) (d) 2 4 (a) isn’t much (b) wasn’t much 28. A point (p, q) lies on the curve 2y = x2 is nearest to (c) isn’t many (d) wasn’t many the point (4, 1) then the point (p, q) satisfy the 38. There are 120 students in a class, the students opted condition physics are even numbered, and the students opted (a) p < 1, q > 3 (b) p > 1, q < 3 mathematics are divisible by 5 and the students opted (c) p < 3, q < 3 (d) N.O.T chemistry are divisible by 7. Then find the number of 29. Evaluate limit lim n sin 2 n !e equal students which had taken none of the above subjects. x (a) 9 (b) 41 (c) 84 (d) N.O.T (a) (b) /2 (c) 2 (d) N.O.T 39. Three of the six vertices of a regular hexagon are 30. If z = a + ib, the the points z, z and origin (0, 0) chosen of random. The probability that the triangle form with these three vertices is equilateral triangle is (a) Equilateral equal to (b) Isosceles (a) 1/2 (b) 1/5 (c) 1/10 (d) 1/20 (c) right angle 40. All + ve number that are multiple of 3 are put in just (d) Triangle with all three acute angle a position forming an infinite string of digit for 31. India plays two matches each with West Indies and example Australia. In any match the probabilities of India Multiple of 3 : 369121518212427…. getting points 0, 1 and 2 are 0.45, 0.05 and 0.5 in just a position of multiple of 3 respectively. Assuming that the outcomes are 8th digit from the left of string 1 independent, the probability of India getting at least 9th digit from the left of string 8. Then seven point is 200th digit from the left of string (a) 0.8750 (b) 0.0875 (a) 1 (b) 3 (c) 7 (d) N.O.T (c) 0.0625 (d) 0.0250 41. According to above question 32. A students appears for test I, II and III. The student 2000th digit from the left of string is successful if he passes either in tests I and II or (a) 3 (b) 7 (c) 9 (d) N.O.T tests I and III. The probabilities of the students 42. Find the locus of a point which divides the line AB passing in tests I, II and III are p, q and 1/2 1 externally in the ratio :1 . Where A is a point on respectively. If the probability that students is 2 successful is 1/2 then 2 parabola y – 2y – 4x + 5 = 0 from which tangent is (a) p = q = 1 drawn which meets the directrix at B. (b) p = q = 1/2 Then find the locus (c) p = 1, q = 0 (a) (x + 1) (y – 1)2 = - 4 (b) (x –1) (y – 1)2 = - 4 (d) there are infinite values of p and q (c) (x – 2) (y – 1)2 = - 4 (d) N.O.T 3 4 n 43. If AAT = I & det A = 1 then which is correct 33. If X then X is equal to 1 1 (a) A – I = 0 (b) A + I = 0 (c) A – 2I = 0 (d) N.O.T 3n 4n 2 n n (a) (b) 44. If f(x) = 1 for x is a rational number and f(x) = 0 x is n 5 n n n irrational number then lim f x is x 0 (a) 0 2 (b) 1 (c) 1/2 (d) N.O.T INFOMATHS/MCA/PUNE-2014 INFOMATHS 1 45. lim 1 3x x x 0 (a) e-3 (b) e3 (c) 3 (d) -3 46. For the real value of (a, b) the function x lies in (a, b) f x 2 x 5x 9 (a) a = 0, b = 0 (b) a = - , b = 0 1 1 ,b 2 (c) a (d) a , b 1 20 11 47. There were three logistician peoples name Galelio, Newton, Einstein and the anther man Archimeds who challenged them to play a game to check their reasoning ability. Archimeds had 4 blue tickets and 4 yellow tickets. Out of these eight tickets he posted two tickets on the forehead of each of them and put the remaining two in his pocket after that they were asked to guess the colours of tickets on their foreheads. But in terms he saw only the ticket of others but not see the colour of ticket on their own forehead Their replies are Galelio : No Newton : No Einstein : No Galelio : No Newton : Yes then what was the colour of tickets on Newtons forehead (a) both blue (b) both yellow (c) cannot be determined (d) N.O.T 48. If f x c dx 5 2 1 (a) 1/n (b) 1/k (c) k/n (d) N.O.T 55. A particle, moves along a straight line with velocity v(t) = t2 displacement between t = 1 & t = 2 (a) 7/3 (b) 8/3 (c) 9 (d) N.O.T 56. A2 + A + 2I = 0 then which s incorrect (a) A is non-singular (b) A 0 1 (c) A is symmetric (d) A1 A I 2 57. For 3 3 matrix A where all the elements are either 0 or 1. Then the maximum value of |A| cannot exceeds (a) 4 (b) 2 (c) 1 (d) N.O.T 58. If it is, given that the value of a + b = 100 then maximum value of ab is (a) less than 2601 (b) great than 2601 (c) greater than 2601 and less than 2800 (d) less than 2400 59. k persons are distributed over n cells then find the probability that k person are sitting in adjacent to each other in cells n k 1! n k ! (a) (b) n! nk n k 1 k ! (c) (d) N.O.T n! 60. Determinant of A = 11 then determinant of matrix formed by cofactor of the value lie between (a) between 101 to 161 (b) between 200 to 300 (c) between 50 to 100 (d) greater than 150 61. Find volume of y = sec x in first quadrant between 0 then what will be the value of <x< 2c f x dx (a) . 4 (b) 2 (c) - 2 (d) - 1 1 c (a) 5 + c (b) 5 – c (c) c (d) 5 49. Three numbers are choosen randomly from 1 to 100 then find the probability of getting number which are divisible by 2 and 3 4 4 9 (a) (b) (c) (d) N.O.T 25 1155 1024 50. The probability of obtaining 6 first time in repeatedly throw of cube. Then find the probability that six obtained for first time in n 3 (a) 25/36 (b) 1/36 (c) 5/36 (d) N.O.T The standard analogue clock will having the hour hand and minute hand and second hand 51. If we start counting at 00 : 01 then the second hand shown ‘xx’ seconds after that minute hand just passed over the hour hand 5 time, then ‘xx’ equals (a) 5 (b) 16 (c) 27 (d) N.O.T 52. If we start counting at 00 : 01 then the second hand shown ‘xx’ second after that the minute hand just passed over the found hand 8 times, then ‘xx’ equals (a) 16 (b) 28 (c) 26 (d) N.O.T 53. In equation 2x3 + x + n = 0 roots lies between [0, 1] then the value of n (a) lies between 0 & 1 (b) lies between -1 & 1 (c) lies between 2 & 3 (d) N.O.T 54. There are n differents keys find the probability that the particular lock is opened at the kth time when it is given that each key is tried only once ANSWERS 1 C 11 B 21 C 31 B 41 B 51 D 61 A 3 2 C 12 B 22 C 32 C 42 A 52 C 3 A 13 B 23 A 33 D 43 A 53 D 4 A 14 A 24 C 34 B 44 D 54 C 5 X 15 B 25 C 35 C 45 B 55 A 6 B 16 A 26 A 36 B 46 D 56 D 7 C 17 A 27 A 37 B 47 D 57 B 8 D 18 A 28 C 38 A 48 D 58 A 9 D 19 A 29 D 39 C 49 B 59 B 10 D 20 D 30 B 40 B 50 A 60 A INFOMATHS/MCA/PUNE-2014