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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.
2n
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.
14.
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) ½ (B) – ½
(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)
3
10
2
3
1
2.
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
3.
Let
x 2 3
2012
and f = fractional part of x. Then x(1 – f)
is equal to
HCU-2012
H H
is
P Q
(a) 1
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
(b) 2
(c)
2 3 (d) 7
4.
Coefficient of xyz-2 in (x – 2y + 3z-1)4 is
5.
(a) -216
(b) 216
(c) -110
(d) 300
The sum of 20C8 + 20C9 + 21C10 + 22C11 – 23C11 is
Pune-2012
4
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
NIMCET-2012
(a) 22C12
(b) 23C12
1
If for n N,
19.
2
2n
6.
(d) 21C10
(c) 0
k
K 0
2 n
A, then the value of
K
7.
8.
(a)
NIMCET-2011
(b)
(a) nA
(b) –nA
(c) 0
(d) A
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
(c)
20.
1
7
1 20
2 1 1
... is
2 13 9 23
BHU-2011
20
(a)
5n 3
9.
21.
2
(b)
5n 3
20
(d)
5n 2 3
(c) 20(5n + 3)
The remainder when 599 is divided by 13 is :
(A) 6
(B) 8
(C) 9
(D) 10
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!
(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
In the expansion of
1
ax 2 are equal then ab is equal to :
bx
a1 a2 a3
1 1 1
a1 a2
a0
(a)
nn
n!
(b)
n 1
(c)
13.
14.
n
n 1!
PU CHD-2009
an
NIMCET-2010
....... 1
an 1
(d)
n 1
23.
24.
Value of
25.
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
26.
27.
n!
28.
49n + 16n – 1 is divisible by
KIITEE-2010
(a) 3
(b) 19
(c) 64
(d) 29
(e) None of these
In the Binomial expansion of (a – b)n, n 5, the sum of 5th and 6th
29.
a
equals:
BHU-2012, KIITEE-2010
b
n4
5
6
(b)
(c)
(d)
5
n4
n5
terms is zero, then
(a)
n5
6
(c)
n
15.
1
5/3
3
16.
17.
t n is equal to
n 1
(b) 16! – 1
(c) 15! + 1
n
The sum of
(a) n 22n – 1
r
r 1
2n
Cr is equal to
(b) 2n-1 + 1
(c) 22n – 1
2| n
2n
(n 1)(n 1)
n
(b)
2n
2
1
(d)
| (n 2 1)
2n
n 1 n 1
In the expansion of
1
x 2 , the term independent of x
x
(MP combined – 2008)
will be
(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
(a) 15! – 1
18.
30.
then the 5th term from the beginning isKIITEE-2010
Let tn = n(n!) then
KIITEE – 2008
is
3n
log3 8
15
12
(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:
(MP combined – 2008)
(a)
1/3 1
If the last term in the Binomial expansion of 2
is
2
is
n n
n i
i
(for n, a positive
sin A1 sin A
i 0 i
X 2Y
1
3
3
n
n
1
n
1 (1 x)
x
(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
n!
n 1
(d) 1
PU CHD-2011
PU CHD-2010
12.
(KIITEE – 2009)
(c) 0
The middle term in the expansion of
11
11.
the constant term is
22.
the coefficient of x-7 in the
(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
15
n
2 1
If the co–efficient of x7 in the expansion of ax
and
bx
expansion of
3 1
x 2
x
(b) – 15C6
(a) 15C6
11
10.
is equal to
(KIITEE – 2009)
2
2n
K
1 K 2n K is
1
1
1
....
1!(n 1)! 3!(n 3)! 5!(n 5)!
| 3n
(a)
31.
(KIITEE – 2009)
| n| 2n
3| n
(b)
| n| 2n
(c)
3| n
3n
2 n
2
(d)
2| 2n
The coefficient of the term independent of x in the expansion of
9
3 2 1
2 x 3x is
1
1
(a) 1
(b) 1
2
2
(d) None of these
(KIITEE – 2009)
(d) None of these
5
ICET – 2007
(c)
2
1
2
(d) None
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
32.
33.
34.
st
36.
37.
38.
2
x
The coefficient of x in
2 x2
45
45
68
(a)
(b)
(c)
256
64
45
If the 5th term of
2 3
2x
x
(d)
5
log e 5
ICET – 2005
is 10, then, x =
(d) 8
(b)
2
25!
3.
(d)
3 10
3 1
(d)
4.
Pune– 2007
n 1
(a)
2
n 1
(b)
2
n 1
2
24!
(e) N.O.T
5.
2 1
n 1
(b) loge 5
(b)
The term independent of x in
(a) third
42.
(b) fifth
1
4 x
1/ 2
6.
2
n 1
7.
1/ 2
3
x2
1 x
8
128
3 2
x
(c) 1
128
(a)
43.
44.
(b)
1
3 2
x
128
2
is equal to :
UPMCAT– 2005
(b) ¼
(c) ½
(d) 1/3
10
45.
In the expression
equal to :
(a) 10C5
10
46.
The value of
3 1
x 2 , the term independent of x is
x
(b) 10C3
r
r 1
(c) 10C6
n
n
Cr
is equal to
UPMCAT– 2005
(d) None of these
KIITEE – 2008
C r 1
(a) 9 (n – 4) (b) 5 (2n – 9) (c) 10n
is
ex
is :
(c)
(d)
1
60
MP COMBINED – 2008
(c) e2 (d) e
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
(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
n
(b)
2 e
n!
n
(c)
2 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?
PU CHD-2012
(A) 100
(B) 120
(C) 720
(D) 150
2.
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
3.
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
4.
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
5.
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
6.
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
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
(a) 1
...
UPMCAT Paper – 2002
(d) None of these
1 b
1
1 b
.........
2
1 b 1 b 1 b 3
(1 4 x x 2 )
1
120
1 log e 2
2e
(a)
n!
UPMCAT paper – 2005
4 x
42
(log e 2) 2 (log e 2) 2 (log e 2) 4
...
|2
|3
|4
(a) e
(d) seventh
1
1
60
The value of the series :
(c)
2 1
3x is MP Paper – 2004
x
(c) sixth
log e (625 )
log e 5
(c)
(d) (log e 5)(log e 2)
log e 2
(a) loge2
n
(d)
Value of the series:
6
41.
2
to infinity is :
3
10
2
3
1
n 1
(c)
log e (125 )
3
infinity is :
(a) 2
(b) 1
C0 C1 C2
....... is equal to : MP Paper – 2004
The sum
1
2
3
n
MP COMBINED – 2008
1
120
log e 2
(e) None of these
40.
2
2
Coefficient of x5 in the expansion of
(a)
Pune– 2007
The coefficient of x6 in the expansion of (1 + x2)3 (2 + x4)10 is
IP Univ. Paper – 2006
(a) 214
(b) 31
(c)
(d) None
MP COMBINED – 2008
25
2
25!
(c)
log e (25)
(a) loge 2
IP Univ.– 2006
26
(c) a
infinity is :
1
The sum
equals
0 k 12 k ! 25 k !
2
25!
C r a r is equal to
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
64
256
The remainder in the divisor of 340 by 23 is
(a) 13
(b) 12
(c) 14
(d) 15
(12! + 1) is divisible by
(a) 11
(b) 13
(c) 14
(d) 7
(a)
r 1 n
KIITEE – 2008
(a) n.2n-1 + a (b) 0
C
C
C
ICET – 2005
C 0 1 2 ... n =
2
3
n 1
2 n 1
2 n1 1
(a)
(b)
n 1
n 1
n 1
n
2 1
2 1
(c)
(d)
n 1
n 1
25
The sum of the series
r 1
ICET – 2005
is
(c) 9
(b) – 6
1
n
47.
10
4
24
39.
24
If the 21 and 22 terms in the expression (1 + 6a) are equal
then a =
ICET – 2007
(a) 7/8
(b) 8/7
(c) 5/8
(d) 8/5
(a) 6
35.
nd
(d) None
6
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
7.
8.
9.
10.
11.
12.
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.
21.
22.
23.
24.
25.
26.
27.
n
Cn1
(b)
n
Pn1
(c)
n
(a)
28.
29.
30.
31.
32.
33.
n
Cn1 1 (d) 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
(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)
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
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
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
a i 1
2
if ai + 1 is even otherwise © = 0, 1, 2
ai
a a
i 1 or i 1
2 2
a is the smallest integer larger than a and a is the largest
44.
7
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
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
45.
46.
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
24!
(a)
2 2 !12 !
(c)
47.
2 24 !
(d)
12 !12
49.
50.
7.
12!
2 6 ! 6 !
3.
The value of
(c)
4
(d)
2
, then (1 + tan A) (1 – tan B) is equal to
(d) 3
(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
4
4
5
,
and sin
5
13
, then tan (2α) =
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
(b) π
(a) 0
14.
(c) 8
(d)
2
NIMCET-2012
NIMCET-2012
If sin (cos) = cos (sin), then sin 2 =
NIMCET-2012
3
(a)
4
If cosec
1
(b)
3
A cot A
1
(c)
4
4
(d)
3
5
, then tan A is :
2
BHU-2012
20
15
(c)
(d)
16
21
4
5
cos
The value(s) of cos cos
is (are):
7
7
7
4
(a)
9
HCU-2012
16.
3
(b)
5
BHU-2012
17.
1
(a)
8
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) x
8
1
1
1
(b) x
(c) x
(d) x
8
2
2
BHU-2012
5.
6.
If cos+ sin=
18.
2 cos, then cos– sinis equal to
19.
PU CHD-2012
(B)
(b)
4
9.
15.
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
then =
NIMCET-2012
sec 37
(c) cot 8
(d) tan 16
csc 37
cos11 sin11
The value of
cos11 sin11
3
56
(a)
33
cos 37 sin 37
is
cos 37 sin 37
2 sin
1
(a) 2
(b) 1
(c) 0
Which of the following is correct?
(a) tan274 (b)
(A)
0
0
If A – B
HCU-2012
4.
cos
0
8.
is equal to
(b) 1-cot
(d) – 1+cot
sin
0
1
2cot 2
sin
(a) 1+cot
(c) – 1 – cot
sin 0
NIMCET-2012
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
2.
cos
NIMCET-2012
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
If nc4, nc5 and nc6 are in arithmetic progression then n is
(KIITEE – 2008)
(a) 9
(b) 8
(c) 17
(d) 14
5
3
If
, then
4
2
If sin =
(a)
x
(b) k m n
k
kx
(d)
k mn
x
k mn
(D)
Pune-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
(c)
sin
2
12!
(b)
6 ! 6 !
(a) x + m + n
48.
(c)
2 sec
8
If sinx + sin2x = 1, then the value of cos12 x + 3cos10x + 3cos8x +
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:
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
(a)
(c)
20.
21.
h tan tan
(b)
tan tan
h cot cot
(d)
cot cot
h sin
BHU-2012
(c) No solutions
sin
1 1 x
4cos
2
1 x
2x
3sin 1
2
1 x
h cos
29.
1 2 x
2 tan
2
1 x
(b)
(c) x = 1
22.
If
x
(a) 1
30.
31.
3
32.
1
(a) 0
(b)
(c)
(a)
24.
25.
cos 1
The value of
If
3
1
(b)
33.
(c)
be
34.
35.
(d)
6
x
tan is
2
If
26.
2 2
(d)
3
(a) A = 30°, a =
3 1 , b =
(b) A = 30°, a =
3 1 , b =
(c) B = 30°, a =
1 3 , b =
3 1 , b =
2
2
2
2
(a)
36.
3
2
37.
28.
(b) a
The general solution of
3 1
3 1
3 1
3 1
38.
(a)
2n
6
a
(d)
ab
3 cos x sin x 3 is:
(b)
2n
(c) 1
(d) 0
(c) 3
(d) 4
is
1
(b)
10
1
(c)
10
3
(d)
10
7
10
3 1
3 1 60m
3 1
3 1
(b)
m
(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, …
2
, n = 0, 1, 2, …..
(c)
x n 1
(d)
x n 1
n
4
n
4
4
, n 0, 1, 2,....
, n 0, 1, 2,....
If sin = sin , then the angle and are related by
BHU-2011
(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
NIMCET-2011
2
7
(d) n 1
6
n
(b) 2
(b) x = 2n +
NIMCET-2011
(a) b
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
(c)
b
If tan , then the value of a cos 2θ + b sin 2θ is
a
a
(c)
b
n
BHU-2011
The solution of Δ ABC given that B = 45°, C = 105° and c = 2
is
NIMCET-2011
(d) B = 30°, a =
27.
(c)
2
n 1
1
3
3
sin , then the value of cos
2
5
2
]
(b)
(b)
BHU-2011
NIMCET-2011
(a)
The value of tan 9 - tan 27 - tan 63 + tan 81 is
(a)
1 3
n
a
(b)
c
(a) 1
BHU-2012
2
(d) 2
In a ABC, cosec A(sin B cos C + cos B sinC) equals
2 2
1 3
2
n 1
c
(a)
a
HCU-2011
(a) ½ or 2
(b) ½ or – 2
(c) ¾ or – 2
(d) ¾ or 2
The value of sin 30° cos 45° + cos 30° sin 45°
[no correct answer was given in choices, correct answer should
3 1
(c)
BHU-2011
3
2
2
6 1
cos 1
is equal to :
3
2 3
4
, then the value of
5
sin x
(d)
5
4
3
(b)
3
2
6
5
(c) n 1
6
then x is :
3
23.
is
n
BHU-2012
2
6
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)
3
(d) x = 0
1
sin 1 x cot 1 ,
2 2
NIMCET-2011, BHU-2011
BHU-2012
x 3
The value of
sin
is :
(a)
1 tan 15
1 tan 2 15
n
2
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
2
(d)
3
9
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
41. If sin-1
2a
1 b2
2x
cos1
tan 1
2
1 a
1 b2
1 x2
53.
then x is equal to
NIMCET-2010
(a) a
42.
43.
45.
(b) b
1
y
x
1
xy
(b)
54.
(c)
1 1
x y
(d)
cos
1
e
(a)
55.
1 1
x y
is
6
(b)
4
(c)
3
(d)
(c)
56.
equal to
If
(a)
1
(b)
(c)
2
2 2
1
58.
3 2
cot 1 x sin 1
1
5
4
59.
is
KIITEE-2010
49.
50.
51.
x
1
60.
(a) x = 3
(b)
(c) x = 0
(e) None of these
(d) None of these
5
5
2
cot cos ec 1 tan 1
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
(c) 90
(b) 60
The value of
sin cos tan 3 45
6
3
(b) 1
(c)
2
61.
62.
(a)
100
(c)
mts
3 1
(c)
63.
2
3
mts
75
(b)
(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)
(c)
n
n2
(d)
n 1
n2
(b) one
(c) two
tan 1 2 x tan 1 3x
64.
mts
3
is
(MCA : NIMCET – 2009)
(d) infinite
, then x is
(d)
1
1
2
2
3
1
2
2
13
A 1
16
3
A 1
4
(b) – 3 1
(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
cos C
tan A
0
sin B
0
tan A
has the value
(KIITEE – 2009)
sin B cos C
65.
66.
The formula
(d) None of these
10
2
(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
3 1
3
4
(b)
3
13
A
4
16
0
3 1
If sin-1 x + cos-1 (1 – x) = sin-1 (-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)
is
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
50
mts
(MCA : NIMCET – 2009)
(a) 1/6
(b) 1/3
(c) ½
(d) ¼
If A = cos2 + sin4, then for all values of
(MCA : NIMCET – 2009)
(a)
3
3
52.
If
KIITEE-2010
(d) 120
(d)
mts
The number of solutions for
(c)
PGCET-2010
(a) 0
is
(c) 75
(b) 90
(a) 1 A 2
The value of
(a) 30
3
100
3
(a) zero
Solution of the equation
(d)
4 2
(e) None of these
48.
mts
50
tan 1 x( x 1) sin 1 x 2 x 1
1
(d)
3
125
(b)
tan 1
(a)
is
KIITEE-2010
1
mts
(a) 20
57.
1 3
The smallest angle of a ABC whose sides are a = 1,
2
cos
4
75
b 6 2, c 2 3
KIITEE-2010
If tan (cos) = cot(sin), then the value of
(b)
3
(e) None of these
47.
1 3
(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)
(a)
(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
(a)
sin cos tan 3 45
3
6
The value of
(PGCET– 2009)
(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
cos ( - ) = 1 and
46.
a b
(d)
1 ab
The value of 3 cot 200 -4 cos 200 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
(a)
44.
ab
(c)
1 ab
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
2sin 1 x sin 1 2 x 1 x2
holds for
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
(MCA : KIITEE – 2009)
(a) x (-1, 0)
67.
68.
(a) 1
3 3
(c) x [0, 1]
(d) x
,
2
2
1 4
1 2
The value of tansin cos
5
3
(a) 17/6
(b) 7/16
If cos-1 x > sin-1x, then
(c)
(KIITEE – 2009)
(d) None of these
(c) 6/17
1
0 x
(d)
1 x
2
Consider the function
(c)
70.
(c)
75.
(b)
1
(b)
2
(c)
n
1
2n
(a b) 2 /(a 2 b 2 )
(b)
a2 b2
85.
3 1 100
86.
87.
88.
(a b) 2 /(a 2 b 2 )
89.
3
5
sin sin
sin
...n
n
n
n
(b) 1
(c)
n
2
In a ABC, a = 5, b = 4 and
(b) 6
(c) 2
In a ABC, A = 90. Then
(a)
90.
terms is equal
4
tan 1
MCA : KIITEE – 2008
(d) None
92.
(b)
tan
a
bc
If in a ABC, 3a = b + c then
(c)
tan
2
B
C
, tan
2
2
1
1
tan 1
3
7
(c)
4
KIITEE – 2008
is
(d) None
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
sin
f ( )
cos
f
2
1 1
(a)
1 1
It
1 0
0 1
sin 2
A
1
sec
1
2
has no
ICET – 2007
(c) 60
(d) 75
cos
then sin f() + cos
sin
ICET – 2007
1
0
0
(d)
1
(b)
0
1
1
0
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
b
c
tan 1
ac
ab
MCA : KIITEE – 2008
1
KIITEE – 2008
(b) x [-1, 1]
(d) None
(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
(c)
C
7
then the side c is 91.
2
9
(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
(d) None
tan
2
inverse than
(a) 30
(b) 45
MCA : KIITEE – 2008
(a) 3
78.
:nZ
3
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
(a) 0
77.
84.
(d) None
a2 b2
The value of
(b)
(d) 1
to
76.
n
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)
74.
(d)
1
2
73.
:nZ
3 1 100
n/2
(a)
83.
(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.
3
2 tan 1
on R. Let x1 and
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
The value of
82.
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
80.
2
f x sin 2 x
3
(c) 2
cos-1 (cos x) = x is satisfied by
(a) x R
(c) x [0, ]
81.
1
(b)
4
tan
2
79.
(KIITEE – 2009)
(b) –1 < x < 0
(a) x < 0
69.
KIITEE – 2008
1 1
(b) x
,
2 2
(d) None
93.
If
sin
15
15 cot 17 sin
, then, for 0 < < 90
8 tan 16 sec
17
ICET – 2005
is equal to
11
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
(a)
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
(a)
y2 1
y2 2
(b)
(c)
y2
y 3
(d) None of these
94.
102.
3
tan tan 1
4 4
112. If
We
A4 B4
3.
4.
3 1:1 then A is equal to :
5.
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
(b) 250 3 mts
250 3 1 mts
(d) None of these
250 3 1 mts
1
106. tan tan 2 x is equal to :
4
6.
UPMCAT : Paper – 2002
(d) 45
the
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)
1
, the values of P(A|B) and P (B|A) respectively are
2
NIMCET-2012
1 1
(a) ,
4 2
UPMCAT : Paper – 2002
2x 1
2x 1
2x 1
(a)
(b)
(c)
(d) None of these
2x 3
2x 1
2x 1
7.
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) ½ (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
(a) 60
(b) 90
(c) 120
111. sin[cot-1 cos(tan-1 y)] is equal to :
(c) 30
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
(c 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
(c)
a ab b
name
(A)
(a)
110. The sides of a triangle are a, b and
greatest angle is :
(b) 60
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.
UPMCAT : Paper – 2002
2
1
1
3
then C is:
bc ca abc
(a) 90
(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
y2 1
y2 2
2
8.
9.
, then the
1 1
(b) ,
2 4
1
(c) ,1
2
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) ¼
(d) None of these
2
Coefficients of quadratic equation ax + 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
UPMCAT : Paper – 2002
(d) None of these
UPMCAT : Paper – 2002
10.
12
1
(d) 1,
2
1 1 1
, , respectively. If they all
2 3 4
try to solve the problem, what is the probability that the problem
will be solved?
NIMCET-2012, MP-2008
(a) ½
(b) ¼
(c) 1/3
(d) ¾
If a fair coin is tossed n times, then the probability that the head
comes odd number of times is
NIMCET-2012
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
(a)
11.
(b)
1
2n
(c)
1
2
n1
(A)
(d) None of these
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
1
2
(b)
49
101
(c)
50
101
(d)
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.
20.
21.
(b) 1/3
23.
(d) 1/5
27.
1 1 1
The probability that A, B, C can solve problem is , ,
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) ½
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
(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
22.
(c) 1/6
7a
9a
11a
13a
15a
28.
29.
(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
1
8
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) ¾
(d) ¼
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
101
(c)
50
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
3
P A B ,
4
that
2
1
P A B , P A , then P A B is
3
4
32.
33.
34.
KIITEE-2010
(a) 5/12
(b) 3/8
(c) 5/8
(d) ¼
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)
(a)
(c)
35.
xy
xy (1 x)(1 y )
(b)
1 x 1 y
xy 1 x 1 y
(d)
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) ¼
(b) ½
(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
36.
xy
and P ( A )
1
.
4
Then
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)
13
1 x 1 y
Let A and B be two events such that
1
1
P( A B) , P ( A B )
6
4
17a
xy
1 x 1 y
65
81
(b)
13
81
(c)
65
324
(d)
13
108
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
37.
38.
39.
40.
41.
42.
43.
44.
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 ¾ times the greatest
possible product is
HYDERABAD CENTRAL UNIVERSITY – 2009
(a) ½ (b) 1/3
(c) ¼
(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) ¼
(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.
46.
47.
(c)
49.
13
90
(c)
19
90
45 3
2 4
90
2
(b)
1
132
(b)
1
44
(c)
5
132
56.
57.
58.
59.
60.
5
8
61.
1
90
4
64.
2
(d)
7
132
66.
1 1
,
3 4
and
1
. The probability that exactly one
5
(a)
5
12
(b)
7
30
(c)
13
30
(d)
3
5
67.
68.
69.
14
671
1296
(b)
7
10
(c)
24
91
(d)
67
91
1
3
and the probability that neither of them occurs is 1/6.
39
256
(b)
29
256
(c)
31
256
(d)
37
256
7
12
(b)
11
12
(c)
1
2
(d)
5
6
1
12
(b)
1
15
(c)
2
27
(d)
1
10
(e)
1
20
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
3
14
(b)
1
2
(c)
3
13
(d)
1
3
The probability of getting atleast 6 head in 8 trials is: MP– 2004
(a)
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
(d)
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) ½
(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
(a)
MP COMBINED – 2008
625
1296
If two dice are tossed the probability of getting the sum at least 5
is
PUNE Paper – 2007
(a)
65.
(c)
Then the probability of occurrence of A is.
ICET – 2005
(a) 5/6
(b) ½
(c) 1/12
(d) 1/18
8 coins are tossed simultaneously. The probability of getting
atleast six heads is
ICET – 2005
(a)
63.
2
3
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) ¼ (c) 1/3
(d) ½
Let A and B be two events with P(A) = ½, P(B) = 1/3 and P(A
B) = ¼ , 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
oci ssa 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
Probabilities of three students A, B and C to pass an examination
student will pass is:
52.
55.
1
6
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) ½ (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)
(d) None
210
are respectively
51.
(d)
54.
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)
50.
(b)
53.
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
(a)
48.
1
45
(a)
16
256
(b)
1
286
(c)
37
256
(d)
28
256
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) ½
(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
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
70.
71.
72.
73.
(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) ¼
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)
74.
76.
2
(b)
3
9
16 (c) 10
41
60
(b)
37
60
(c)
31
60
(c) P A B P A B
77.
78.
P A B P A B
(b)
9.
(d) N.O.T.
10.
(d) N.O.T.
P A B P A B
11.
12.
13.
(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
14.
15.
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
x '2 y '2
1
(c)
2
2
2.
3.
4.
5.
3
2
(B)
5
2
(C)
1
2
(D)
(B) 1
3
(C)
17.
18.
19.
20.
x 1
(c)
x 2
17 5
15
2
2
1
y 2
6
1
y 1
6
(b)
x 1
y 2
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
2
The point on the curve y = 6x = x , 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
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
(a) 2 of
(c) 2 or
3
2
3
2
(b) – 2 or
(d) – 2 or
3
2
3
2
Focus of the parabola x2 + y2 – 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,
(a) 0
21.
5
(a)
then
1
4
(D)
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
(a)
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
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)
6.
16.
x '2 y '2
1
(b)
2
2
x '2 y '2
(d)
1
2
2
(a) x’ – y’ = 1
2
17
3
8.
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
(a)
The distance between the parallel lines y = 2x + 4 and 6x = 3y + 5
is
PU CHD-2012, NIT-2010
(A)
If P(A’ B’) is equal to 19/60 then P(AB) is equal to
UPMCAT Paper – 2002
(a)
75.
1
13
7.
1
1
r2
2
e
e
(b) 1
(c) 2
NIMCET-2012
(d) None of these
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
The orthocenter of the triangle formed by the lines xy = 0 and x +
y = 1 is :
PU CHD-2012
(A) (1/2, ½)
(B) (1/3, 1/3)
(c) (1/4, ¼)
(D) (0, 0)
between the point P and the line
22.
15
x 3 y 12
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 :
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
23.
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 3
(a) tan
5
1 2
(c) tan
11
24.
25.
(b)
5
2
27.
35.
1 5
(b) tan
3
11
1
(d) tan
2
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
(c) x2 + y2 – 2x – 4y + 4 = 0
(d) x2 + y2 – 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.
34.
5
(c)
(a)
38.
5
(d)
2 2
37.
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
28.
(a) a2l2 – b2m2 = n2
(c) a2l2 + b2m2 = n2
29.
For the conic
40.
x2 y 2
1 if :
a 2 b2
41.
l
1 e cos , the sum of reciprocals of the
r
segments of any focal chord is equal to :
BHU-2012
(a) l
30.
31.
(b) 2l
42.
2
(d)
l
(c)
1
y a x
x
(b)
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
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
(a) x(x2 + y2) = a(2x2 + y2)
32.
1
(c)
l
(b)
y = be-x/a at the point
BHU-2012
(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
If the line lx + my = n touches the hyperbola
1
(a)
x2 y 2
1 if :
a 2 b2
(a) p2 = a2 cos2 - b2 sin2
(c) p2 = a2 sin2 - b2 cos2
(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
43.
1
y a x2 2
x
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
(a)
2
44.
(d) y = atan + x
The relation that represents the shaded region in the figure given
below is
45.
46.
3
2
(b)
1
(c)
2
2
(d)
1
3
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
(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
x
2
4 y 2 4 xy 4 x 2 y 1
represents a
47.
33.
(a) y x
(b) |y| |x| (c) y |x|
(d) |y| x
The area enclosed within the lines |x| + |y| = 1 is
HCU-2011
BHU-2011
(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
(a)
NIMCET-2011
16
4 3
,
5 5
(b)
3 1
,
5 5
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
(c)
1 5
,
5 4
(d)
2 1
,
5 5
61.
48. The angle between the asymptotes of the hyperbola 27x2 – 9y2 = 24
is
NIMCET-2010
(a) 60
(b) 120
(c) 30
(d) 150
X2 Y2
1 intercepts equal length
a 2 b2
49. If any tangent to the ellipse
l on the axes, then l =
62.
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
65.
a b r
p
q
r
+
p a q b r c
51.
52.
53.
54.
55.
56.
is
66.
(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
(c) 4x2 + 4y2 – 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
4
(c) 5 b
5
57.
NIMCET-2010
70.
(b)
4
5 a
5
72.
(d) None of these
The locus of a point P(,) moving under the condition that the
73.
x2 y 2
1 is
a 2 b2
KIITEE-2010
74.
and the hyperbola
75.
(b) a circle
(d) a hyperbola
It the foci of the ellipse
x2 y 2
1
144 81 25
60.
69.
KIITEE-2010
(a) an ellipse
(c) a parabola
59.
68.
71.
line y = x + is a tangent to the hyperbola
58.
67.
x2 y 2
1
25 b2
28
13
(b)
The straight lines
(a)
31
13
(c)
30
10
(c)
76.
77.
(d) None of these
17
x y
x y 1
k and , k 0 meet
a b
a b k
on
(MCA : NIMCET – 2009)
(a) a parabola
(b) an ellipse
(c) a hyperbola
(d) a circle
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) ¾
(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)
coincide, then the value of b2 is
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)
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
the angle between the lines represented by x2 + 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 = - ½
(b) m1 + m2 = 0
(c) m1m2 = 2
(d) (m1 – m2)2 + 2m1m2=0
2
,0
3
7 2
,
3 3
(b)
7 2
,
3 3
(d) None of these
Two distinct chords drawn from the point (p, q) on the circle x2 +
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) ¼a
(c) 1/a
(d) a/3
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
78.
The equation of the tangent to the x – 2y = 18 which is
perpendicular to the line x – y = 0
(MCA : KIITEE – 2009)
(a) x + y = 3
(b) x + y =3/2
2
(c) x + y + 2 = 0
79.
80.
(d)
2
x y3 2 0
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
90.
(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
25
x 2 x 2 x 3y
0
2
x2
(b)
x2
(c)
x2
(d)
81.
82.
x2
83.
(b)
(d)
(a) 1
(c)
3
95.
96.
(d)
7 3
3
84.
the centroid of the triangle with vertices
86.
87.
88.
89.
1 1
a, , b,
a b
and
98.
NIMCET – 2008
is at the point
(a) (p, q)
85.
97.
If a, b, c are the roots of the equation x3 – 3px2 + 3qx – 1 = 0, then
1
c,
c
(b)
(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
If the line hx + ky = 1 touches the circle
NIMCET – 2008
1
y mx m 2 3 1 m 2
92.
94.
x2 y2
1
16
9
x2 y2
1
16
7
is
(b)
(c)
91.
93.
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
y mx 2 3 1 m 2
(x 2 y 2 )
1
a2
,
then the locus of the point (h, k) will be:
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
(c)
1
7 16
(b)
(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
as a diameter is
21
x 2 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
(a)
y mx 3 1 m 2
:
HYDERABAD CENTRAL UNIVERSITY – 2009
(a)
(a)
p q
,
3 3
99.
(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
(a)
3 y 3x 1
(b)
3 y ( x 3)
(c)
3y x 3
(d)
3 y (3x 1)
(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
(MCA : MP COMBINED – 2008)
(a) 16
(b) 9
(c) – 12
(d) – 16
For the parabola y2 = 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
2
Eccentricity of the ellipse 9x + 5y2 – 30y = 0 is :
(MP COMBINED – 2008)
(a) 1/3
(b) 2/3
(c) 4/9
(d) 5/9
100. For the ellipse
x2 y2
1 , S1 and S2 are two foci then for
64 36
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)
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
(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
(a)
2 3 ,2 6
(c)
4 3 ,4 6
(b)
(d)
3 6
1
1
3,
6
2
2
103. For the given equation x + y – 4x + 6y – 12 = 0, the centre of the
circle is
KARNATAKA – 2007
(a) (-2, 3)
(b) (-3, 2) (c) (3, - 2) (d) (2, - 3)
2
2
104. The circumference of the circle x + y + 2x + 6y – 12 = 0 is
KARNATAKA – 2007
2
(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
18
2
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
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
2
2
16x + 16y = 8x + 32y – 257 = 0
Karnataka PG-CET : Paper 2006
(a) 8
(b) 6
(c) 15
(d) None of these
126. Axis of the parabola x2 – 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
(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 – ½
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) ½
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
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
(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
(c)
1 3
,
3 5
5 3
,
2 7
(d)
2 3
,
3 4
1 3
,
7 11
(b)
x12 y12 a 2 0
(c)
x12 y12 a 2 0
(d) None of these
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
2
g1 g 2 f1 f 2
133.
134.
135.
IP Univ. Paper – 2006
(b)
x12 y12 a 2 0
130. The sum of the distance of a point on the ellipse
136.
(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
(a)
(a)
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
Two circles x2 + y2 + 2gx + c = 0 and x2 + y2 + 2fy + c = 0 touch
each other, then :
MP :– 2003
(a) g2 + f2 = c3
(b) g2 + f2 = c
(c) c(g2 + f2) = g2f2
(d) g2 + f2c = g2f2
S1 = x2 + y2 – 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
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
The area of triangle formed by y = m1x + c, y = m2x + c2 and y
axis is :
UPMCAT : paper – 2002
1 c1 c2
(a)
2 m1 m2
2
1 c1 c2
2 m1 m2
2
(c)
1 c1 c2
(b)
2 m1 m2
2
1 c2 c1
2 m1 m2
2
(d)
137. Reflection of the point P(1, 2) in x + 2y + 4 = 0 is
UPMCAT : paper – 2002
(e)
(a)
1 3
,
2 4
(c)
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
13 26
,
5 5
13 26
,
5 5
(b)
13 26
,
5
5
(d) None of these
138. The area of the region bonded by the curve y = x2 and the line y =
x is
UPMCAT : paper – 2002
(a)
19
1
Sq U
64
(b)
1
Sq U
12
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
(c)
1
Sq U
6
(MP COMBINED – 2008)
(a) 2p
(b) 4p
(c) p2
(d) p(cos – sin )
151. The distance between the two oci 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
(d) N.O.T.
139. If 4x2 + 9y2 + 12xy + 6x ….. + 9y – 4 = 0 represents two parallel
lines then the distance between. The lines is: UPMCAT:– 2002
3
(a)
4
(b)
13
5
(c)
13
(d) None of these
13
152. L1 || L2. Slope of L1 = 9. Also L3 || L4. Slope of L4
140. If (± 3, 0) be focus of ellipse and semi major axis is 6. Then equ.
Of ellipse is:
UPMCAT :– 2002
(a)
(c)
x2 y 2
1
36 45
x2 y 2
1
36 27
(b)
x2 y 2
1
27 36
these lines touch the ellipse
a
h
g
h
b
f 0
g
f
c
IP University : Paper – 2006
1 k
(a)
1 l
(c)
(a)
UPMCAT :– 2002
(a) 3x2 + 4y2 + 12x – 36 = 0
(b) 3x2 + 4y2 – 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
(a)
(c)
x 1
45
x 1
20
2
y 2
1 (b)
20
y 2
x 1
45
y 2
20
(a)
1
1 (d) None of these
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
(a)
(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
147. A point P on the ellipse
8
x2 y2
1
25
9
(c)
has the eccentric angle
(a)
KIITEE – 2008
(b) 6
148. For the hyperbola
(c) 5
x
2
cos 2
(d) 3
y
2
sin 2
following remains constant when
varies?
(c)
x
2
(e) N.O.T.
7
12
8
(b)
7
2
(c)
10
6
(d)
(e) 6
15
7
(b)
6
(c)
5
(d)
4
(e)
3
2 a 2 b2
(b)
2ab
ab
a b2
2
(d) None of these
a 2 b2
25 14
14
25 14
7
m
(b)
m
(d)
45 14
14
45 14
7
m
m
1 which of the 159. The locus midpoint of a chord of the circle x2 + y2 = 4, which
subtend angle 90 at the centre.
MCA : KIITEE – 2008
(a) directrix
(b) eccentricity
(c) oci ssa of foci
(d) oci ssa of vertices
149. The sum of the intercepts made on the axes of co-ordinates by any
tangent to the curve
1 k
1 k
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
. The sum of the distance of P from the two foci is.
(a) 10
(d)
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)
(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
+ (y – b)2 = b2 is :
MP : MCA Paper – 2003
2
2
45
1 k
1 k
2
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
0) then the eqn. of ellipse is:
2
1 k
(b)
1 k
2
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
1
143. A ellipse has e , directrix is x + 6 = 0, and has a focus at (0,
2
2
x2 y 2
1 . The area of the
25 9
PR
PS
RP RQ
is
k , then, the value of
.
RQ
SQ
PS QS
(ii) abc + 2fgh – af2 – bg2 – ch2 = 0
(iii) af + bg + ch = 0
(iv) af2 = bg2 ; h2 = ab
UPMCAT:– 2002
(a) ©, ii
(b) ii, iv
(c) ©, iv
(d) ©, ii and iv
2
1
. All
25
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
(d) None of these
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)
(a) x + y + 3 = 0
(c) x + y + 2 = 0
UPMCAT : paper – 2002
(b) x2 + y2 = 0
(d) x2 + y2 = 2
FUNCTIONS
y 2 is equal to KIITEE – 2008
1.
(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:
x 1 x 3
f x
x 2
is a real-valued function in the
domain :
PU CHD-2012
20
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
2.
3.
4.
(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
Then fof
(a) neither an even nor an odd function
(b) an even function
(c) an odd function
(d) a periodic function
The domain of
17.
(a) [1, 9]
(b) [-1, 9] (c) [-9, 1]
(d) [-9, -1]
A function f from the set of natural numbers to integers defined by
-1, if x is rational
f x=
.
1, if x is irrational
1 3
6.
7.
18.
(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
(a)
1 2 x x 1
(c)
1
1 1 4log 2 x
2
(b)
1
1 1 4log 2 x
2
19.
(d) not defined
Let the function f (x) = x 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
9.
(A) x2
(B) x2 – 1 (C) x2 – 2 (D) x2 + 2
The range of the function f(x) = 1/(2 – cos3x) =
21.
(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)
(c)
22.
PU CHD-2011
(A)
(c)
11.
12.
13.
14.
1
,1
3
1
3 ,1
23.
24.
1
3 ,1
1
(d) ,1
3
(B)
25.
(e x 1)
Suppose that g(x) = 1
f(x) is
(a) 1 + 2x2 (b) 2 + x2
If
f x
cos 2 x sin 4 x
sin 2 x cos4 x
The domain of the function
26.
27.
28.
KIITEE-2010
(d) 2 + x
e | x| e x
e x e x
29.
(MCA : KIITEE – 2009)
then
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
The domain of
y
x
x 3x 2
(b) {1, 3}
(c) {0, 1}
If f : [1, ) [2, ) is given by
f
KIITEE-2010
(a) 1
15.
The function
(b) 2
(c) 3
f x log x x 1
is
(a)
KIITEE-2010
21
x
1 x
(d) {0, 2}
1
( x) x
1
x
then f
–1
(x)
(MCA : KIITEE – 2009)
equals to
(d) 4
2
is
2
(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)
(a) {0, 3}
for x R, then f(2010) is
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
(a)
(b)
(c)
(d)
x and f{g(x)} = 3 2 x x, then
(c) 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)
(a) one – one
(b) onto
(c) bijective
(d) None of these
f ( x)
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
x
1 is
2
The function
PU CHD-2011
10.
x
f ( x)
20.
1
1
f x x 2 2 x 0 , then f(x) =
x
x
Let
KIITEE-2010
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) = - 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]
2
8.
is
x 1
2 , when n is odd
if f x
is :
x , when n is even
2
Pune-2012
5.
x
sin 1 log3
3
16.
2
(b)
x x2 4
2
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
x x2 4
2
cos x sin x
If f ( x) sin x
cos x
0
0
(c)
30.
45.
(d)
x x2 4
46.
0
0
1
(a) f(x) f(y)
(c) f(x) – f(y)
(d) None of these
(c)
47.
x y f ( x) f ( y )
f
for all real x and y. If f’(0) 48.
2
2
31.
Let
32.
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
33.
(a)
then f(x + y) is equal to
(KIITEE – 2009)
(b) f(x) + f(y)
Consider the function
f ( x) sin 2 x
3
34.
2n
3
: nZ
(d)
n
If f(x) + f(1 – x) = 2, then the value of
3
35.
(a) 2000
(b) 2001
(c) 1999
If f(x) is a polynomial satisfying
1
f ( x) f f ( x)
x
36.
37.
38.
39.
1
f
x
on R. Let x1 and
41.
42.
43.
44.
lim
sin x
x 0
(B) –1
is :
x
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 ………….
lim
is
4.
(b) for all x R
(d) None of these
Pune-2012
π
sin x if x 2
What is the value of a for which f x
is
ax if x > π
2
continuous?
NIMCET-2012
(a) π
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 © < j and ij A
is.
NIMCET – 2008
(a) 8C3
(b) 8C3 + 2(8C2)
10
(c) C3
(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
1 x2
x 1
x 1
(a) x = 0 only
(c) for all x R except x = 0
x2
PU CHD-2012
(D) Does not exist
(C)
2.
(b) π /2
(c) 2/ π
5.
lim 1 x
6.
(a) 0
(b) 1
(c) e
The function f(x) defined by
1/ x
x
(d) 0
is equal to :
BHU-2012
(d) 1/e
1
f x x 1 sin log x 2 , x 0
3
, then:
f x 0,
x0
7.
then the
property of the function f is.
40.
(d)
1 2
(x y 2 )
4
1
( xy)
4
Pune-2012
MCA : NIMCET – 2008
(d) 1998
f ( x)
The value of
(A) 1
and f(3) = 28, then f(4) is given
Let f : R R be a mapping such that
(b)
The function f and g are given by f(x) = (x), the fractional part of
x and g(x) = ½ 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) ½
(c)
: nZ
1
2
2000
f
f
... f
2001
2001
2001
1 2
(x y 2 )
8
1 2
(x y 2 )
2
LIMITS & CONTINUITY
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
(c)
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)
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
BHU-2012
(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
x 1 x
if x is rational
f x 1
x 1 x if x is not rational
2
then f is continuous at
8.
22
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]
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
9.
x sin x equals to
x cos x
lim
x
(a) 0
10.
21.
NIMCET-2011
(d) none of these
(c) –1
(b) 1
lim
Let f (2) = 4 and f´ (2) = 1. Then
xf 2 2 f x
x2
x 2
22.
is given
by :
23.
PU CHD-2011
(A) 2 (B) –2 (C) –4 (D) 3
11.
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
1.
2.
13.
2
(b) 4
15.
4.
5.
(d) ½
(e) None of these
(cos x 1)(cos x e x )
xn
x 0
is a
6.
sin x
, [ x] 0
If f ( x ) x
when [.] denotes the greatest 7.
[ x] 0
0,
(a) 0
16.
lim
x
lim
(b) 0-
1 cos 3x
x / 2 1 cos 5 x
Lt
x0
(a) ½
lim 2
x 0
x
(a) ¼ (b) 2/4
9.
(c) 0
(d) 3
(c) ¼
10.
3
(a) e
(b) 4e
(c) 3e
log(x + y) – 2xy = 0 then y’(0) is
x 3
(d) 1
F n 1
n!
is
1
dy
at x
is.
dx
2
(d) 2e
(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
Pune-2012
(d) None of these
(a) 1
(b) 2
(c) 3
f (x) = x|x| and g(x) = sin x then
Pune-2012
(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
If
sin 1
1 x2
1 x2
2x
sin 1
2
1 x
w.r.t.
(b) 0
(c) 1/x
is :
(d) x
dy
x 1
1 x 1
y sec1
sin
, then dx
x 1
x 1
of
3 is
IP Univ. Paper – 2006
(e) 5/4
11.
23
(b) 0
Let f1(x) = ex, f2(x) =
fn+1(x) =
(d) 1/12
tan 1 x
n
(d) 1
y e x .e x .e x ........., 0 < x < 1 then
(a) 1
ICET – 2005
(c) ¾
...........
1
is :
NIT-2008, BHU-2012
ICET – 2005
x 3
3!
(d) 9/25
(c) 0
lim
F "' 1
BHU-2012
ICET – 2007
(c) 3/5
(b) 1/3
2!
(b) 2n-1
(a) – 1
8 x 2
x
cos 1 x
8.
(d) 2
(b) 2
F " 1
ICET – 2007
(c) 1
(b) 1
3
20.
(d) None
x( x 1)(2 x 3)
Lt
x
x3
(a) 1
19.
(c) – 1
1 x 1 x
x
(a) 0
18.
lim x0 f ( x) is equal to KIITEE – 2008
(b) 1
(a) – 1
17.
MCA : NIMCET – 2008
(d) 4
(c) 3
integer function then
1!
2
3.
KIITEE-2010
x 1
(c) 1
(b) 2
F ' 1
(D) (–1)n – 1 (n – 1) ! X–n
Pune-2012
finite non – zero number is
(a) 1
(c) (n – 1) ! x–n
F(x) = xn then the value of
Pune-2012
f x 1
x 1
lim
(B) (n – 1)x–n
(d) 3
lim
The integer n for which
is equal to
n
(a) 2n
BHU-2011
(c)
If f(1) = 1, f ‘ (1) = 2, then
(a)
14.
(b) - 1
e
x
(d) discontinuous at x = 0
tan x
1
lim 1 2 is equal to
The value of lim
x 2 x 2
x
x
(a) + 1
dn y
dx n
If y = logex and n is positive integer, then
F 1
x
12.
x6 a6
UPMCAT : Paper – 2002
(a) Does not exist at x = 1 (b) ½
(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
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
(A)
1
(b) continuous at x = 1
2
(c) continuous at x = 0
x a
PU CHD-2012
BHU-2011
x
sin x6 a 6
DERIVATIVES
Then, f (x) is
(a) continuous at
lim
x 1
(c)
x 1
(d)
x 1
x 1
f x
e 1 , f3(x) = e 2 , …. And in general
f
x
e n for any n 1. For any fixed value of n, the value
f
x
d
f n x is
dx
HCU-2011
(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
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
(a) no solution
(b) exactly one solution
(c) at least one solution
(d) not enough data to say about number of solution
12.
24.
d
5
Find
x
dx
x
(c)
2
(log x) x (log x)
x
If
x y e ( x y ) then
(a)
NIMCET-2011
1
3
(a)
x 3/ 2
2 x 2
5 3/ 2
(c) 2 x x
2
5 3/ 2
(b) 2 x x
2
Let f(x) =
26.
f x 6
1
0
p
p2
p3
, 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
15.
(b)
lim
g x f x
x a
(c)
18.
(c) 1
28.
1 then
a
sec 2
b2
b
sec3
a2
(b)
(d)
29.
20.
21.
b
sec 2
a
b
2 sec3
a
30.
31.
y xx
then
32.
33.
(b) e2
(c) 0
(d) 3/2
f ( x) e x , x 0 and f(0) = 0 then f’(0) is
KIITEE – 2008
(b) 0
y x (logx)
then
(log x) x (log x)
(c) e
dy
dx
(d) None
equals:
(b)
is
ICET – 2005
, then
dy
?
dx
MP– 2004
1
2 1 x 2
1
2 1 x2
dy
is equal to :
dx
MP– 2004
(b)
(c)
dy
log x
(d) None of these
The value of differential coefficient of
x 1 x
2
1
2 1 x 2
tan 1
1 x
with respect
1 x
MP Paper – 2004
(c) -1/2
Differential coefficient of
2
x
y log x
tan 1
(d) 1/3
1 x2 1
is :
x
2
(b)
1 x2
MP– 2004
(d) None of the above
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
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
(a) 1
x
1
2
(d) 3
(d)
2
x ...
x
at
(b)
1
2 1 x
y log x
x (1 log x )
y2
x log x
(c)
1
(a)
1 x 1 x
2
(1 log x) 2
(c) 2
1 x 1 x
1
2 1 x
dy
dx
1
(a)
(a)
1 2
1 2
(a) log sec(x) x
(b) log sec(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
If
If
(b) 1
2
KIITEE – 2008
23.
If y = 4x3 – 3x2 + 2x – 1, then
to x at x = 2 is :
(a) ½ (b) -1/5
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
If
(d)
f ( x) e x , x 0 and f(0) = 0 then f’(0) is
(a) ½
22.
log x
(1 log x) 2
is KIITEE-2010
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
If
(c)
(c)
1
19.
(b)
(a)
(d) 2x + 1
ICET – 2005
1
1 log x
y tan 1
ICET – 2007
dy
dx
(a)
If
dy
dx
then
(c) 2x – 1
(b) x + 1
x-y
(a) 0
(d) 0
d2y
dx 2
y y y ...
If x = e , then,
KIITEE-2010
If x = a sin, y = b cos, then
(a)
17.
1
x x log x
x
f a g x f a g a f x g a
the value of k is
(a) 4
(b) 2
16.
27.
(c) xx(logx + 1)
(d) x xx – 1
Let f(a) = g(a) = k and their nth derivatives f “ (a), g” (a) exist and
are not equal for some n.
If
x
y
sin x cos x
Then f ′′′ (0) =
14.
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)
(a) x – 1
(d) none of these
x3
13.
25.
(d) (log x) x(log x-1)
(MP COMBINED – 2008)
2.
2
log(log x (logx ) )
x
F:R R is defined
k 2 x if x 1
F x
2 x 3 if x 1
if F has local min. at x = - 1 then the value of k is
Pune-2012
24
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
(a) 1
(b) 0
(c)
1
2
x = a(cos + sin ), y = a (sin - cos )
at any point is such that it
(d) – 1
3.
In the Interval [0, 1] function x2 – x + 1 is
4.
Pune-2012
(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
5.
(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'
10.
11.
2 pq 3
(b)
(a)
(c)
If
f x
2r pq
(d)
22.
pqr
3
x2 1
x2 1
23.
24.
for every real number x, then the minimum
(c)
13.
1
a b
2
2ab / a b
1 2
r h
3
4 2
(c) r h
3
(a)
14.
(b)
x
1
2
(c) x = 1
The normal to the curve
2
(b)
6
(c)
26.
a / b b / a
27.
r 2h
28.
1 2
(d) r h
2
(b)
x
29.
1
2
30.
(d) x = – 1
25
has a local minimum at
4
(d)
3
f ( x) x ,0 x b, the number c
5
27
(b)
7
27
(c)
8
27
(d)
4
27
3
1
,b
4
8
3
1
a ,b
4
8
a
(b)
3
1
a ,b
4
8
(d) None of the above
The function f(x) = 2 sin x + sin 2x, x [0, 2] has absolute
maximum and minimum at
NIMCET – 2008
(a)
The function f(x) = 8x5 – 15x4 + 10x2 has no extreme value at
BHU-2011
(a)
15.
25.
The volume of a right circular cylinder of height h and radius of
base r is
BHU-2011
x 2
2 x
The sum of two non zero numbers is 8. The minimum value of the
sum of their reciprocal is
(KIITEE – 2009)
(a) ¼
(b) 1/8
(c) ½
(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
(c)
ab
(b)
(d)
f x
(d) 2
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)
(a)
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)
(c) 1
For the function
(a)
value of f :
12.
(b) 0
(d) 1/e
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)
5
is equal to
20.
NIMCET-2011
2r pq
f ' x dx
KIITEE-2010
(a) x = - 2 (b) x = 0
(c) x = 1
(d) x = 2
Angle between the tangents to the curve f = x2 – 5x + 6 at the
points (2, 0) and (3, 0) is
KIITEE-2010
The minimum value of px + qy when xy = r2 is
(a)
1
The function
21.
9.
2
19.
log e x
is :
x
(c) e
KIITEE-2010
(a) 3
BHU-2012
(a) 1
(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)
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
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
5
3
,
3
(b)
3
,
(c)
5
,
3
(d) None
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)
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
1
1e
(b)
e
e
(a) e
31.
33.
34.
36.
e
(2 2 ,4)
(d)
(2 3 ,6)
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) ¾ (c) 2/3
(d) ½ (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
35.
(d)
1
e
The points situated on x2 = 2y and nearest to (0, 5) are:
(MP COMBINED – 2008)
(a) (0, 0)
(b) ( 2, 2)
(c)
32.
1
(c) e e
1
1
7.
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
2
Let f(x) = cosx + 10x + 3x + 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
8.
9.
10.
MATRICES
(c) 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
2.
How many matrices of the form
x
2
3
z
2
3
1
3
s
11.
2
3
y
t
4.
5.
2 y
2
3
2
5 y
6
3
4
10 y
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
2
(b) a11a22 … ann = (a11 + a22 + …. + ann)
(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 :
12.
3 0
6
0 1
A 1 0 and A 4 1 , then the product A 7 is
5 0
8
2 0
15.
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
Pune-2012
(a) null
(b) symmetric
(c) skew-symmetric
(d) unit
1
M 1
2
6.
0
the M50 is equal to
1
13.
14.
1 0
1 0
(a)
(b)
0
50
50 1
1 25
1 0
(c)
(d)
0 1
25 1
1 3 2
If matrix 2 4
8 is singular the =
3 5 10
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)
PU CHD-2012
0
(A) 0
1
0 is :
Pune-2012
are orthogonal, where x, y, z, s and t are real numbers.
3.
x+y+z=0
x + 2y + 3z = 0
x + 3y + bz = 0
Which of the following statements are true?
(c) 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
1
1
9
(C) 1 (D) 10
(B) 2
0
0
11
16.
If
15
2
(b)
17
2
(c)
31
2
(d)
33
2
1 1
n
A
, then A for any natural number n is
0 1
NIMCET-2012
n n
(a)
0 n
Consider the following system of linear equations over the real
numbers, where x, y and z are variables and b is a real constant :
26
1 n
(b)
0 1
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
1 0
0 1
(c)
17.
(d) non-singular matrix
(d) None of these
26.
If is cube root of unity, then the value of determinant
2 1
1
2
1
2
BHU-2011
is equal to :
3
(a)
9
3
(c)
9
BHU-2012
(a) – 1
18.
(b) 1
If the matrices
2 3
1 1 1
If A
, B 1 5 then AB is equal to
3
3
3
4 1
(c) 0
(d) 2
1 1 1
A
and
3 3 3
2 3
B 1 5 ,
4 1
then
27.
If
AB is equal to :
BHU-2012
3
9
3
(c)
9
1
3
(a)
19.
20.
21.
1
3
1
3
P
1
2
3
2
28.
1
3
29.
30.
3
2
1
2
Let
31.
A 2
1
2
3
2
1
y
y
2
z
z2
1 x3
1 y 3 0 , where x, y, z are unequal and non1 z3
(c) – 1
(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
Matrix
(d) – 2
KIITEE-2010
(b) Not – 2
(d) – 2
A 2 1
3
k 0
1
is invertible for
1
2
is
1
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
2
32.
x 2
2
1
x
0 is
1
(a) x = 1
(b) x =
(c) x = 2 (d) x = 0
If A is a singular matrix, then A. adj A is
If
2 1
4
3
2
A
, then A + A – A =
3 2
(a) 0
(b) 1
KIITEE-2010
KIITEE-2010
(b) a zero matrix
(d) an orthogonal matrix
(a) a scalar matrix
(c) an identity matrix
33.
KIITEE-2010
(b) k = - 1
(d) None of these
1
2
The matrix A
1
2
x 1
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
If
x2
(a) k = 1
(c) all real k
(e) None of these
(c) A
PGCET-2010
(d) None of these
91 92 93
34.
The value of the determinant
94 95 96
is PGCET-2010
97 98 99
(a) 100
1 2 3
25.
x
1
3
1 0 k
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) ½
(d) 2
24.
1
3
1
3
BHU-2011
4 1 0
A 2 1 2
x y 1
23.
3
(b)
9
3
(d)
9
zero real numbers, then xyz is equal to
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?
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
(d)
22.
3
9
3
(d)
9
(b)
1
3
, then A is
35.
BHU-2011
(b) 202
The inverse of the matrix
(c) 303
(d) 0
0 0 1
A 0 1 0
1 0 0
(PGCET– 2009)
(a) symmetric matrix
(b) a skew-symmetric matrix
(c) a singular matrix
27
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
1 0 1
0 1 0
0 0 1
(a)
(b)
(c) A itself
36.
1 0 0
0 0 1
0 1 0
(a) |A| is zero
(c) |A| cannot be determined
If
47.
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
(PGCET– 2009)
1
0
0
(c)
0
(a)
37.
0
1
0
1
(b)
0 1
1 0
48.
a b c
b c a
49.
(NIMCET – 2009)
38.
If
a unique solution
no solution
infinite number of solutions
finitely many solutions
1 2
2
A
, then I + A + A + …. equals to
3 4
50.
(NIMCET – 2009)
1 2
(b)
3 4
1 1
(d) 4 3
1
0
2
1 0
(a)
0 1
1
1
2 3
(c)
1
0
2
39.
40.
51.
52.
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
Let
53.
1 0
0 0
, B
. If A2 – 2A + I = B, then value
A
2 b
4 4
The value of the determinant
5
C0
5
C 3 14
5
C1
5
C4
1 is
C2
5
C5
1
5
(a) 0
(c) –(6!)
(b) 80
54.
The sum of two non integral roots of
(MCA : KIITEE – 2009)
(d) N.O.T
3 x 3 0
55.
is
5 4 x
43.
If A =
T
(a) A
sin
cos
0
56.
(MCA : KIITEE – 2009)
(c) –5
(d) N.O.T
(b) –18
(a) 5
cos
sin
0
(b) adj A
0
0
1
(c) A
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
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
4 6
5
B 4
1 2 KIITEE – 2008
5 1 1
If
If
(b) A + B exists
(d) None
0 4 1
A 2 3
1 2 1
(a) = 4
x 2 5
42.
(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
(a) AB exists
(c) BA exists
of b is (Note that I is identity matrix of order 2)
(MCA : KIITEE – 2009)
(a) 1
(b) 3
(c) –1
(d) 2
41.
HYDERABAD CENTRAL UNIVERSITY – 2009
c b a
(d) N.O.T
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)
i i
1 1
8
A
and B
then A equals to
i i
1 1
46.
(d) N.O.T
3 1
2
If A
, then A – 5A + 7l is
1 2
(b) |A| > 1
(d) None of the above
(b) 8
then A-1 exists of
(c) 4
4 1 4
A 3 0 4
3 1 3
(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
45.
(d) None
(c) 4
The value of the determinant :
(KIITEE – 2009)
(d) N.O.T
(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
KIITEE – 2008
KIITEE – 2008
57.
44.
(d) None
then A2 is equal to
then A-1 is equal to
1 1 1
If A= 1 2
0
1 3 0
KIITEE – 2008
58.
then the value of |adj A| is equal to
(a) a, b, c are positive
(c) (a + b + c) < 0
The value of the determinant
(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
ba a ab
ca b bc
is
MP COMBINED – 2008
ab c ca
(a) (a + b + c)
(c) a2 + b2 + c2 – ab – bc – ca
28
(b) (a + b + c)3
(d) a3 + b3 + c3 – 3abc
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
1 a bc
59.
The value of the determinant :
1 b ca
68.
is
1 c ab
60.
MP COMBINED – 2008
(b) 1
(d) (1 + a + b + c)
(a) 0
(c) (a + b + c)
If one root of the equation :
69.
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
x 3 7
2 x 2 0
is -9, then other roots are:
7 6 x
(a) -2, - 7
61.
70.
(b) 2, 7
(c) -2, 7
MP COMBINED – 2008
(d) 2, - 7
5 4 a 14 1 2
If
then a and b will be equal to :
1 1 b 17
1 3
71.
MP COMBINED – 2008
(a)
1
a ,b 1
5
(b) a = - 3, b = 4
(c) a = 1, b = 1
62.
If
2 0 0
A 0 2 0
0 0 2
and
|AB| will be
(a) 4
(b) 8
63.
If
72.
(d) a = 4, b = - 3
1 0 0
M 4 2 0
5 6 3
1 2 3
B 0 1 3
0 0 2
73.
MP COMBINED – 2008
(c) 16
(d) 32
74.
then its inverse matrix M-1 will be:
65.
1 2
n
A
, then A =
0 1
1 n
(a)
0 1
(a) 2
67.
If
(b) – 5
(c) 10
7
is
(b) – 2
Karnataka PG-CET– 2006
(c) 0
3 1
1 1
(d) 5
(d) None
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
1 x
x 2 yz
1 y
y 2 xz
1 z
z xy
MP– 2004
2
(b) 3xyz
(d) N.O.T
1
78.
The value of
0
0
is :
a b c
0
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
ICET – 2005
80.
0
2a b a c
2b
79.
MP– 2004
(b) unitary
(d) None of the above
(a) (x + y + z)2
(c) 1
The roots of the equation are
(d) 5
2 3
, then which of the following is true?
A
1 2
(a) A2 – 4 A + I = O
(c) (A – 4I) (A + I) = O
3
5
75.
77.
n
1
2
n
1 2n
0 1
2 k
If the matrix
is invertible, then K
4 10
(c)
66.
2
0
1
(d)
0
(b)
2
3
(a) orthogonal
(c) singular
ICET – 2005
If
1
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
(c)
KARNATAKA – 2007
(d) 3
(c) 2
Pune– 2007
10 14 20
0 0
6
(a)
(b) 12
3 0
14 6 2
7
1 2 3
1
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
(b) 0
The value of
(a) 20
MP COMBINED – 2008
(a) 1
then A2 is
(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
then the value of
1 4 5
0 2 6
0 0 3
64.
1 0 0
A 0 1 0
2a 2b 1
1 P
1
1
1 P
1
1
1
1 P
1
UPMCAT – 2002
(a) 0, 0, 3
(b) 0, 0, - 3 (c) 0, - 3
(d) 0, 3
Pune– 2007
(b) A2 + 4A + I = O
(d) (A + 4I) (A – I) = O
29
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
81.
If
w
1
xw
w
x 1
w
w2
(a) – 1
82.
83.
84.
85.
If
x w2
1
(b) 1
2
(c)
0 , then x is equal to :
3.
4 2
A
then (A – 2I) (A – 3I) :
1 1
4.
(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.
5.
88.
6.
IP Univ.– 2006
xe x
2
7.
(c) (x + 1)e
e x sec2
(d)
e x tan
UPMCAT– 2002
log x x 2 a 2 c
(b)
x
log (
2
a2 c
1
(d) None of these
log x 2 a 2
2
1 2
1
1
If x tan x dx ( x ) tan x x C then
2
values of and are:
(MP COMBINED – 2008)
(a) = 0, = 1
(b) = 1,
(d) = 1,
1
2
6
1.
The value of the integral
x
1
2
1
2
(a) 1
(b) ½
dx is NIMCET-2010
9-x+ x
3
(c) 3/2
(d) 2
π
4
2.
The value of the integral
(a) log 2
3.
(b) log 3
sinx+cosx
dx is
3+sin2x
0
(c)
NIMCET-2010
1
1
log 3 (d) log 3
8
4
log 10 xdx is
NIMCET-2010
x
e
4.
x
c
e
(b) loge 10.x loge
+c
(d)
1
c
x
If I1 =
1
(b) (x – 1) e
2 x
1
2
2
x
x
x
x
2 dx,I2 = 2 dx,I3 = 2 dx and I 4 = 2 dx then
2
x
(d) e
0
x
2
3
1
2
1
3
1
5.
NIMCET-2010
(a) I3 =I4
(b) I3 > I4
(c) I2 > I1
(d) I1 > I2
2
2
The area between the curves y = 2 – x and y = x is
NIMCET-2010
(a) 8/3
(b) 4/3
(c) 2/3
(d) 5/3
6.
The value of
BHU-2012
x tan
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 :
2
x a2
(c) log10 e. x loge
(b)
x
k
2
DEFINITE INTEGRAL
x sin x
dx is :
The value of
1 cos x
x
2
(b)
sin xdx equals :
(c) = - 1,
dx is :
x
x cot
x
(c)
BHU-2012
(a)
(MCA : KIITEE – 2009)
(a) (x – 1) loge x + c
1 x
e
(a)
x 1
2.
(a)
(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
x 1
e
(d)
cos x sin x
cos y sin y
P
and Q
then
sin x cos x
sin y cos y
The value of
1 sin x x
e dx is equal to
1 cos x
1 x
x
(a) e tan k
2
2
(c)
INDEFINITE INTEGRAL
1.
x
2
(b) x (logx – 1)
(d) x (x – log x)
(a) ex (sin x – cos x) + C
cos 2 x y sin 2 x y
P 2Q
sin 2 x y cos 2 x y
cos 2 x y sin 2 x y
2
(c) P Q
sin 2 x y cos 2 x y
87.
x cos
log xdx is
(c) ex tan x + k
(b)
86.
The value of
(d)
(a) x (log x + 1)
(c) log x (x + log x)
UPMCAT – 2002
(a) PQ QP
x
2
BHU-2011
UPMCAT – 2002
(d) N.O.T
(c) 0
x sin
x | x | sin
/4
3
x x tan 2 x 1 dx
is
4
KIITEE-2010
30
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
(a) 0
7.
In
0
tan dx,
(a) ½
8.
(c) /4
(b) 1
/4
n
then
(d) /2
Assume that p is a polynomial function on the set of real numbers.
2
lim n I n I n 2 equals
If p(0) = p(2) = 3 and p’(0) = p’(2) = –1, then
x
0
(d) 0
The solution of the differential equation
dy x y
dx
x
23.
satisfying
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 ?
the condition y(1) = 1 is
I.
KIITEE-2010
(b) y = x In x + x2
(d) y = x In x + x
(a) y = In x + x
(c) y = xe(x-1)
9.
x sin x
The value of 0
(a)
2
1 cos 2 x
2
(b)
3
4
2
(d)
6
The smaller of the areas bound by y = 2 – x and x + y = 4 is
(NIMCET – 2009)
(a) - 1
(b) - 2
(c) 2 - 1
(d) 2 - 2
11.
The value of
1 tan 2 x
0
(a) 0
12.
/2
0
14.
x 5 cos(1 x 4 )
a
(1 x )
(c)
16
3
64
3
/4
0
2
(d)
25.
1
2
26.
dx equals :
sq. unit
(b)
sq. unit
(d)
tan x
dx
sin x cos x
(b) ½ (c) 1
1 cos d
3
a
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) ½ 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, x = a and x = 0 is
Pune-2012
32
sq. unit
3
128
sq. unit
3
1
(a)
2
27.
a2
(c)
2
a
(b)
2
lim
n 1
2
......... sin
sin sin
is
n n
n
n
(b) π
(a) 0
If
1
(b)
2 2
1
The value of
xe
x
(c)
3 2
(d)
2
3
0
2
2
0
1
2
4 2
I 4 2 x dx then
3
1
dx is equal to :
NIMCET-2012
0
(a) I1 = I2
MP– 2004
18.
19.
1
29.
20.
(a) π
(b) 1
(c) – 1
30.
1 x x2
log e
1 x x2
2
2
(a) 0
(b) 1
(d) 3
sin
NIMCET-2012
(c) /3
(d) 0
cos 2 x
1
t dt
0
y x , x [0, 1],
(a) /4
cos 1 tdt is
0
(b) /2
NIMCET-2012
(d) None of these
(c) 1
/2
31.
The value of
log tan x dx
is equal to :
0
loge x x
dx equals
e
(c) 2
The value of
(d) 2
The area of the plane bounded by the curves
(d) I4 > I3
log tan xdx is
(b) /2
sin 2 x
MP– 2004
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
21.
The value of integral
2
2 x3e x dx is equal to :
(c) I3 > I4
0
0
(a) 0
(b) I2 > I1
/2
(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 value of
NIMCET-2012
I1 2 x dx, I 2 2 x dx, I 3 2 x dx and
2
28.
(d) /2
(c) 2
1
IP Univ.– 2006
(d)
2
The value of
n
(d) 2
equals
a2 a
sin a cos a . Then the
2 2
2
F is
2
value of
(MP COMBINED – 2008)
equals:
3
f x dx f x dx f x dx
2
(a)
17.
(c) 0
4
(a) 0
16.
(d) /2
(MCA : MP COMBINED – 2008)
(a) 0
(b) 1
(c) a
(d) 2a
The area enclosed between the curves y = x and y2 = 16x is:
(MCA : MP COMBINED – 2008)
(a)
15.
(b) ½
a
24.
sin 2 x log(tan x)dx equals: (MP COMBINED – 2008)
(a) 1
13.
2
NIMCET – 2008
(c) /4
(b) 1
a 3
a
2
is
a
III.
10.
dx
b3
II.
2
2
/2
b
f x dx f x 3 dx
b
(NIMCET – 2009)
dx is
(c)
xp " x dx
KIITEE-2010
(c)
(b) 1
22.
(a) 0
32.
IP Univ.– 2006
(e) 4
(b) x/4
For a >1, the value of
(c) x/2
0
(d)
BHU-2012
dx
is
a 2a cos x 1
2
HCU-2011
(a) 2
31
(b)
2a
(c)
a2 1
(d) 0
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
33.
Evaluate
2
(a) e
1
1 x
2
dx
3.
0
HCU-2011
(b)
2
(a) -
(c)
2
35.
2
0
(d)
4.
The solution of the equation
t
s t Ce
t
(c) s t Ce
(a)
5.
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
(b) π
2
The value of
x
The solution of the equation :
3
(d)
(A) b – a
4
x
6 x
41.
The value of
/4
0
(C) b + a
(C) 2
10.
(D) |b|–|a|
11.
(D) 5/2
1
log 5
(b)
20
1
log 7
(d)
30
12.
13.
1x
e tan
The value of
dx
1 x2
14.
BHU-2011
(a)
e tan
x
(b)
e tan
1
1
1
(c)
(d)
2
1 x2
1 x
x
Solution of the equation
yx
(a) (x + a) (1 – ay) = cy
(c) (1 + ax) (1 + y) = cy
2.
If
dy
e x y
dx
1
(a)
etan
(c)
yetan
dy x y z
is x
dx
x y
1
y
)
dy
0 is:
dx
y
1
x tan 1 y c
y
tan 1 y c
(b)
xetan
(d) xe
1
y
tan 1 y
tan 1 y c
y tan 1 y c
The general solution of the differential equation
dy
dy
a y 2
dx
dx
Solution of the differential equation
(c)
15.
(MP COMBINED – 2008)
(b) (x + a) (1 + ay) = cy
(d) (1 – ax) (1 + y) = cy
y 2 x2
c
9
4
y 2 x2
c
4
9
(b)
(d)
y 2 x2
c
9
4
y 2 x2
c
4
9
Solution of D.E. xdy – ydx = 0 is a
Pune-2012
(a) circle
(c) straight line
and it is known that for x = 1, y = 1; if x = - 1,
then the value of y will be:
dy y
sin x is :
dx x
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, 32) (c) (24, 4) (d) (4, 8)
Solution of D.E. 9yy’ + 4x = 0 is
Pune-2012
(a)
is
dy x y 2
dx
2 xy
HCU-2011
(a) y2 = (ln |x| + C)x
(b) y = (ln |x| + C)x
2
2
(c) y = (ln |x| + C)
(d) y = (ln |x| + C)x
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
DIFFERENTIAL EQUATIONS
1.
MP– 2004
(MP COMBINED–2008)
BHU-2011
1
dx
x is :
dy
9.
sin cos
d is
9 16sin 2
1
log 2
(a)
10
1
log 3
(c)
20
42.
y
2
(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. © x2y + xy2, = c
(1 y 2 ) ( x e tan
PU CHD-2011
(B) 3/2
2x
+ 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
dx
(A) 1
(MP COMBINED – 2008)
(b) xy = y2 + c
(d) x + y3 = c
If the solution of the differential equation
x
1
Integrating factor of
PU CHD-2011
(B) a – b
5
8.
dx, a < b is :
x
a
40.
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
(a) 2A + 1 sq. units
(b) 2A sq. units
(c) 2A + 2 sq. units
(d) A + 2 sq. units
b
39.
(c)
s t 1 Cet
t
(d) s t Ce 1
dy
x 2y3
y
dx
(b)
(a) x = y(y2 + c)
(c) y = x(y2 + c)
(d) four
x
If
is :
(MP COMBINED – 2008)
NIMCET-2011
36.
(MCA : MP COMBINED – 2008)
(b) 4x + y + 1 = 2 tan (2x + c)
(d) tan (4x + y + 1) = 2x + c
ds
ts
dt
is
(c) three
dy
(4 x y 1) 2
dx
The solution of the differential equation
(a) 4x + y + 1 = tan (2x + c)
(c) 2(4x + y + 1) = tan (2x + c)
2 cos3x 3
a 2
cos x a sin x 20cos x dx
a
4
3
4
(a) only one (b) two
(d) – 1
(c) 1
is:
Consider the region bounded by the graphs y = ex, 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
34.
(b) e
16.
(MP COMBINED – 2008)
32
D.E.
(b) parabola
(d) Hyperbola
1 y2
dy
determines a family of circle with
dx
y
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
7.
Pune-2012
17.
18.
(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 :
2
(c)
(d)
19.
20.
dy
cos x 0
dx
(b)
8.
d2y
dy
x2
1 x y e x
2
dx
dx
d2 y
1 y 2 xy e x x
dx
dy
x 2 y y 4 cos x 0
dx
y dy 0
is
14.
BHU-2011
21.
y tan 1 xetan
1
x
1
C
(b)
xetan y tan 1 y C
(d)
y xe tan
1
x
C
15.
The degree of the differential equation
2
2
dy d y
3 4 2
dx dx
2/3
2
d3y
3 is
dx
16.
BHU-2011
(a) 3
(b) 4
(c) 5
17.
1 i
2 1 is
i 1 3
1
1 i
(b)
(a) 0
2.
3.
4.
(c) 2
If
z
1
z
3
3
and
2
(b) -
4 is
19.
then z lies on
KIITEE-2010
20.
(c) 0
(d)
6.
The conjugate of a complex number is
(a)
22.
(b)
(c)
1
i 1
(d)
KIITEE – 2008
If
(b) 1
1
1
i
1 0
1 e
1
e
is
KIITEE–2008
(c) –©
(d) 0
then the value of is :
MP– 2004
i
(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, ©, ©
(d) -1, 1, -©, ©
The radius of a circle given by the equation
z z (4 3i) z (4 3i z ) 0 is KIITEE – 2008
–
(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
32 2
(b) 2
(d) 4
If z is different from © and |z| = 1 then
32
zi
z i
is KIITEE –
2008
(a) purely imaginary
(b) purely real
(c) non real with equal real and imaginary parts
(d) None
1
, then that complex
i 1'
KIITEE-2010
1
i 1
1 i
1 is
1 i
(a) 2
(b) 2
(c) 1
(d) – 1
The fourth roots of unity are given as z1, z2, z3 and z4. The value of
(a)
(c) 7
2
If |Z + 4| 3 then the maximum value of |z + 1| is KIITEE-2010
(a) 4
(b) 10
(c) 6
(d) 0
1
i 1
21.
5.
number is
3
4
(d)
(1 ix)(1 2ix)
is purely real then the non zero real value of
1 ix
1
(d) 1 +2
(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
(a)
(c) 0
(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
2
2
(c) x – x + 1 = 0
(d) x + x + 1 = 0
The equation |Z + i| - |Z – i| = k represents a hyperbola if
KIITEE – 2008
(a) 0 < k < 2
(b) – 2 < k < 2
(c) k > 2
(d) None
1
18.
2
1,
3 3
4
The smallest positive integer n, for which
NIMCET-2010
The value of X + 9X +35X – X + 4 for X = - 5+ 2
NIMCET-2010
(a) 0
(b) -160
(c) 160
(d) -164
4
z 2 z 0 is
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
(a) ©
2
1
1
(b)
z12 z 22 z32 z 42
1 the value of the
Let 1 be a cube root of unity and © =
determinant
(d) – 1
(c) 1
x is
(d) 6
COMPLEX NUMBERS
1.
PGCET-2010
n
13.
(c) (4x + 6y + 5)dx = (2x + 3y + 4)dy
(d) (1 + y2) dx + (x – siny)dy = 0
Solution of the differential equation
(c)
(b) 3 + ©
3 3
2
(a)
x3
1
is
(MCA : KIITEE – 2009)
(b)
yetan x tan 1 x C
2i
i 1 and a, b are the nonreal cube roots of unity, is
12.
(a)
2
10.
y e x x 2 y dx e x dy 0
tan
1 i
(d) 18
(KIITEE – 2009)
(a) 2
(b) 3
(c) 4
(d) 1
The area of the triangle whose vertices are I, a, b where
(a)
2
The value of
(c) 12
The number of solution to the equation
11.
1 y dx x e
2
9.
Which of the following differential equations can be reduced to
homogenous form?
BHU-2012
1
(b) 6
(a) 2
dy
0
dx
x y
2
KIITEE-2010
(a) 54
BHU-2012
BHU-2012
1 y
If z + z + 1 = 0, where z is a complex number, then the value of
1 2 1
6 1
z z 2 ..... z 6 is
z
z
z
(a) Clairaut’s form
(b) Newtonian form
(c) Bernoulli’s form
(d) None of these
Which of the following differential equation is linear?
(a)
2
1
i 1
23.
33
If
i 1 and 4 1 , , , then
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
24.
(a) p = 0
KIITEE – 2008
is equal to
(c) p = -1 or p =
(a) 1
(b) ©
(c) –©
(d) 0
For complex number z, 0 ≤ arg z < 2 . S
S {z : z 5 3 5i is
25.
26.
27.
28.
6.
The vectors
. This set is
7.
29.
30.
(b) - 2
(d)
The value of
2 sin
p 1
1
10.
11.
VECTORS
(c)
If C is the middle point of AB and P is any point
outside AB, then
NIMCET-2010
(a) PA + PB = PC
(c)
2.
Let
12.
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
The position vector of A, B, C and D are
AB and CD is
(b) /4
13.
and
b
(d)
2
a . b 0, a . c b . c ,
and
where
KIITEE-2010
(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
3
sin 1
5
(b)
4
sin 1
5
(c) 90
(d) None of these
Area of the parallelogram whose adjacent sides are © + j – k and
2i – j + k is
(PGCET– 2009)
2 3
(b)
3 5
(c)
3 2
(d)
5 3
B 3i 4k is to be written as the sum of a vector
B1 parallel to A i j and a vector B 2 perpendicular to
The vector
If
(NIMCET – 2009)
(b)
2
(i j )
3
(d) None of these
a, b and c are unit perpendicular vectors, then
(a) 9
(b) 4
(c) 8
NIMCET – 2009
(d) 6
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
14.
If
a, b, c
are
non-coplanar
unit
vectors
such
that
b c
a b c
, then the angle between a and b is
2
the new system,
(c)
8
| a b |2 | b c |2 | c a |2
NIMCET-2010
(c) /2
(d)
4.
(b)
i j k , 2 i 5 j,3 i 2 j 3k , and i 6 j k then the angle
between
(a) 0
4
A , then B1 is
3
(a)
(i j )
2
1
(c)
(i j )
2
b is collinear with c ,while b + c
is collinear with a then a + b + c , is equal to NIMCET-2010
(a) a
(b) b
(c) c
(d) none of these
a b c
are non-coplanar unit vectors such that
a b c 1
If
(a)
collinear and the vector a +
3.
1 4 1
i j k
3 3
3
KIITEE-2010
(a)
(d) – 2i
(c) 2i
(d)
c a b v a b , then
2 p
2 p
i cos
is
7
7
(b) 2
i 4 j k
1
b c , then the angle between the vectors a
2
2
BHU-2011
(a) 1
a, b, c
9.
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
6
31.
2
If
3
(a)
4
1 i 1 i
is :
2 2
(c)
(b)
is
8
BHU-2012
(a) 2
c is equal to NIMCET-2010
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
(B) 2 solutions
(D) An infinite number of solutions
The value of complex number
8.
PU CHD-2012
8
1 4 1
i j k
3 3
3
(c)
i k
(a)
i 1 and z = x + iy then the equation z2 = z has
(A) No solution
(c) 4 solutions
a i j , b j k and c make an obtuse
angle with the base vector ©, then
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
If
a , b and c are equal in length and taken pairwise
make equal angles. If
j
1 3 1 3
t j
2
2
(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
(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
j
1
3
5.
IP Univ.– 2006
(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
1
3
(b) p = 1 or p =
a has components p + 1 and 1, then
NIMCET-2010
34
(NIMCET – 2009)
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
4
(a)
15.
3
4
(c)
a b b c c a
2
(d)
(c)
3
3
collinear
then
28.
(a) 0
18.
(b) ¾
(c) 30/4
29.
NIMCET – 2008
(a) -3
(b) 3
(c)
1
(d)
3
30.
The value of such that the four points whose position vectors are
3 i 2 j k ,6 i 3 j k 5 i 7 j k , and
2 i 2 j 6 k,
(a) – 6
20.
NIMCET – 2008
(b) 4
(c) 5
between
(a) /6
(b) 2/3
31.
NIMCET – 2008
(c) 5/3
(d) /4
21.
Let
24.
If
(c) 5
Karnataka PG-CET– 2006
(d) – 5
33.
Then area of ponallelogram is equal to :
UPMCAT– 2002
If
(b) 42sq units
(d) N.O.T.
a b a b
34.
;
a, b
are the adjacent sides of a ||gm then ||gm is a:
(a) rectangle
(c) rhombus
19
3
(b)
50 6
3
(c)
(d) 19
50
(d) None
3
1 1 1
1
x y z
(d) None
UPMCAT– 2002
(b) square
(d) None of these
35.
35
a , b , c be three unit vectors of which b and c are non –
and
(a)
(c)
b 3 i 6 j 2 k
25.
1
1
1
1
1 x 1 y 1 z
a
(a) 0sq units
(c) 49 sq units
20 6
a 2 i 3 j 6 k
(c)
(b) 10
(b) 5
parallel. Let the angle between
orthogonal, then the value of is
(a) 12
and the angle between
32.
a 1, 2,3 and b 2, , 4 are
If the vectors
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
(c)
(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
23.
c
(b) x + y + z = 1
[ a b b c c a ] is equal to KIITEE – 2008
22.
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)
a , b , c be three vectors such that [ a b c ] = 4 then
Let
(d) 8
A and B is
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)
A B C 0 , | A | 3, | B | 5, | C | 7 then the angle
If
(d) parallel to
(a) 13
3
19.
b
A B and C is 300, then | ( A B ) C | is equal to
i j k , j k and i k is minimum is
given by
a
A C | C |, | C A | 2 2
The value of for which the volume of parallelepiped formed by
the vectors
(b) parallel to
that
3 10
2
(d)
is
A 2 i j 2 k and B i j . If C is a vector such
Let
3 | c |2
HYDERABAD CENTRAL UNIVERSITY – 2009
b 3 c
0
a.c 0
and
and
, then a 2 b 6 c is
HYDERABAD CENTRAL UNIVERSITY – 2009
(c) parallel to
a c a b
c
is collinear with
(a)
a i 2 j 3k , b 2i j k and c is a vector
satisfying
a
a 2 b
3
If
1
(d)
a, b and c are three non-zero vectors, no two of which are
Let
collinear. If
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
HYDERABAD CENTRAL UNIVERSITY – 2009
(b) 9
(c) 1
(d) 0
(d) None of these
1
1
and d .( a b c ) 3 then v is
3
(a) 6
27.
(b)
d ( a b ) ( b c ) v( c a ), v( c a ), a
If
.( b c )
(b) 0
(a) – 3
17.
26.
KIITEE – 2009
is equal to
2 a b c
(c)
a b c
(a)
16.
(b)
c
2
6
be . If
,
,
a
and
a ( b c )
3
3
(b)
b
be and that between
1
b then. KIITEE – 2008
2
3
,
2
(d) None
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 = © – j – k, B = © – j + k and C = - © + j + k, where
©, 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
(c) (A B)C = A(B C)
II. (A B) C = A (B C)
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
36.
37.
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 = - © + 2j + k be two vectors. The
vector perpendicular to both A and B having length 10 is
HCU-2011
50i 30 j 70k
(a)
(b)
and
angle between
NIMCET-2011
47.
48.
49.
p 3 , then the
and
50.
are mutually
51.
perpendicular, then the value of x is
NIMCET-2012
(a) – 2
(b) 2
(c) 4
(d) – 4
The equation of the plane passing through the point (1, 2, 3) and
41.
NIMCET-2012
(b) 3x – y + 2z + 7 = 0
(d) 3x + y + 2z = 7
53.
a b c 0 , a 3 , b 5 , c 7 , then angle
If
(a) /2
54.
a and b is
between the vector
42.
52.
N 3i j 2k as its normal, is
(a) 2x – y + 3z + 7 = 0
(c) 3x – y + 2z = 7
(b) /3
(c) /4
NIMCET-2012
(d) /6
If (0 ≤ ≤ π) is the angle between the vectors
55.
a and b , then
a b
56.
equals
a.b
NIMCET-2012
(a) –cot
43.
If
a, b
(c) –tan
(b) tan
(d) cot
57.
c are unit vectors such that a b c 0 , then
and
the value of
a . b b . c c . a is
2
(a)
3
2
(b)
3
If
3
(d)
2
3
(c)
2
58.
a , b, c are non-coplanar vectors and is a real number, then
a 2b 3c, b 4c
the vectors
and
2 1 c
are non-
59.
coplanar for
45.
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
(a) 0
46.
Let
(b) 1 (c)
3
(d)
3
60.
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
36
(a) 4 AB (b) 3 AB (c) 2 AB (d) AB
The vector 2i + j – k is perpendicular to © – 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
(c) I – 10j – 18 k
(d) © + 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(© – k) and © +j + k, then
is
BHU-2011
(a)
NIMCET-2012
44.
NIMCET-2011
2
(b)
(c)
(d)
3
6
6
If the vectors a 1, x, 2 and b x,3, 4
p and q is
having the vector
(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
HCU-2011
40.
AC BD is equal to:
4
(a)
6
39.
p q 1
v 2 i j k and w i 3 k . If u is a unit vector,
Let
then the maximum value of the scalar triple product u v w is
NIMCET-2011
(d) None of the above
p q 13
If
and π,
(b) {–2, –3}
(d) {x : x > 0}
(a) {1, 2}
(c) {x : x < 0}
83
(c) Both A and B
2
then the set of all possible values of x is
50i 30 j 70k
83
38.
and the positive direction of the y-axis lies between
2
(b)
3
(c)
4
(d)
1
cos 1
3
a b = 0 implies only
BHU-2011
(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)
3
2
(b)
4
2
(d)
3
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
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
61.
62.
63.
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
(c)
ca
2
(c)
(d)
1
bc
2
1
(d)
ab bc ca
2
(a)
(b)
11.
(c)
2.
17 19
, , 4
3
3
9 13
, , 4
5 5
(a)
4.
5.
6.
7.
8.
9.
10.
)
The length of the perpendicular from (1, 0, 2) on the line
x 1 y 2 z 1
3
2
1
3.
(a)
(b) (15, 11, 4)
(d) (8, 4, 4
3 6
2
(b)
6 3
5
is
(c)
12.
KIITEE-2010
3 2
(d)
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
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
THREE DIMENSIONAL GEOMETRY
1.
The image of the point (-1, 3, 4) in the plane x – 2y = 0 is
KIITEE-2010
(a)
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
(b)
2 3
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)
h
r
2
1
3r1r2 r22
r12 3r1r2 r22
3
h 2
(d)
r1 r1r2 r22
3
3
h 2
(c)
r1 r1r2 r22
3
If A = (5, -1, 1), B = (7, -4, 7), C = (1, - 6, 10), D = (-1, -3, 4) then
ABCD is a (MCA : KIITEE – 2009)
(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)
13.
If r is a radius and k is thickness of a frustum of a sphere, then its
curved surface of frustum is :
BHU-2012
(a)
14.
h
(b)
1
rk (b) rk
2
(c)
2 rk
(d)
The area of the triangle having vertices (1, 2, 3) and (-1, 2, 3) is :
BHU-2012
1
107
2
1
165
(c)
2
1
155
2
1
187
(d)
2
(a)
(b)
15.
4 rk
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 :
BHU-2012
(a)
16.
2 a 3 b 4 c
(b)
B
28
B
D
29
C
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
ANSWERS (OLD QUESTIONS-CW1)
1
C
11
2
A
12
SETS & RELATIONS 2012
3
4
5
6
7
8
D
B
C
A
C
C
13
14
15
16
17
18
9
C
19
C
21
C
31
10
C
20
37
A
22
C
32
A
23
D
33
A
24
B
34
AC
25
D
35
B
26
A
36
B
27
B
37
D
30
C
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
A
A
1
A
11
C
21
C
31
A
41
CD
51
A
2
12
A
22
B
32
B
42
B
52
D
1
A
11
B
21
B
31
A
C
1
A
11
C
21
B
31
D
41
B
D
B
D
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
A
13
B
23
A
33
C
43
C
53
C
2
A
12
B
22
C
D
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
3
B
13
B
23
C
2
C
12
B
22
A
32
A
42
B
3
A
13
C
23
B
33
B
43
D
4
A
14
B
24
C
34
C
44
C
BINOMIAL
5
6
C
B
15
16
A
D
25
26
A
A
35
36
B
A
45
46
C
B
7
B
17
B
27
C
37
B
47
C
8
A
18
A
28
B
8
A
18
A
28
B
38
A
9
D
19
B
29
B
39
A
49
B
9
A
19
C
29
C
10
C
20
D
30
D
40
BC
50
A
10
D
20
B
30
B
9
B
19
C
29
A
39
A
10
A
20
B
30
A
40
C
5. EXPONENTIAL & LOGARITHMIC SERIES
5
6
7
2
3
4
D
C
B
A
A
D
D
1
1
C
11
C
21
C
31
B
41
B
6. PERMUTATIONS & COMBINATIONS
2
3
4
5
6
7
8
9
A
C
C
B
A
A
A
D
12
13
14
15
16
17
18
19
B
D
A
A
B
C
C
D
22
23
24
25
26
27
28
29
A
A
C
D
C
A
C
C
32
33
34
35
36
37
38
39
C
D
C
C
A
C
B
D
42
43
44
45
46
47
48
49
A
D
D
B
B
D
D
D
1
C
11
A
21
B
31
D
41
D
51
A
61
D
71
A
81
B
91
A
101
A
111
A
2
A
12
B
22
C
32
D
42
A
52
D
62
B
72
D
82
D
92
C
102
C
112
B
3
C
13
B
23
D
33
C
43
D
53
C
63
D
73
C
83
C
93
A
103
B
1
D
11
D
21
A
2
D
12
A
22
B
3
D
13
D
23
D
10
C
20
A
30
C
40
B
50
C
7. TRIGONOMETRY
4
5
6
7
D
A
A
D
14
15
16
17
A
D
C
B
24
25
26
27
A
C
A
B
34
35
36
37
D
A
B
C
44
45
46
47
A
D
B
A
54
55
56
57
B
D
A
C
64
65
66
67
D
C
B
D
74
75
76
77
C
A
B
A
84
85
86
87
D
B
C
B
94
95
96
97
B
B
B
A
104
105
106
107
C
D
C
C
8
A
18
B
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
A
69
A
79
B
89
B
99
A
109
A
8. PROBABILITY
4
5
6
7
B
C
D
B
14
15
16
17
A
B
D
B
24
25
26
27
C
C
D
B
8
A
18
C
28
D
9
D
19
A
29
D
31
A
41
A
51
B
61
D
71
C
32
B
42
D
52
D
62
D
72
D
33
C
43
D
53
C
63
A
73
D
1
11
A
21
C
31
41
C
51
A
61
C
71
C
81
A
91
C
101
D
111
B
121
E
131
B
141
B
151
D
2
12
22
A
32
42
B
52
D
62
B
72
A
82
D
92
A
102
A
112
A
122
C
132
B
142
D
152
E
9. 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
83
84
85
86
87
88
C
A
C
A
A
A
93
94
95
96
97
98
D
B
D
A
D
C
103
104
105
106
107
108
D
D
A
D
D
C
113
114
115
116
117
118
B
D
B
D
C
A
123
124
125
126
127
128
C
A
D
C
C
B
133
134
135
136
137
138
C
D
D
A
B
C
143
144
145
146
147
148
C
B
C
C
A
C
153
154
155
156
157
158
A
E
E
D
C
B
10
D
20
D
30
C
40
C
50
C
60
D
70
A
80
C
90
C
100
D
110
C
1
B
11
10
A
20
C
30
D
38
34
A
44
C
54
C
64
B
74
A
35
A
45
B
55
A
65
A
75
A
36
C
46
A
56
C
66
B
76
D
37
C
47
D
57
C
67
C
77
D
10. FUNCTIONS
4
5
6
7
B
B
D
B
14
15
16
17
A
C
A
C
24
25
26
27
A
D
A
B
34
35
36
37
A
B
C
B
44
45
46
47
C
B
A
C
38
D
48
C
58
A
68
B
78
C
1
C
11
C
21
D
31
A
41
C
2
C
12
C
22
D
32
A
42
B
3
C
13
B
23
A
33
A
43
D
1
D
11
D
21
D
2
C
12
A
22
B
11. LIMITS AND CONTINUITY
3
4
5
6
7
8
B
C
C
A
C
B
13
14
15
16
17
18
E
C
D
B
B
B
23
B
1
D
11
C
21
C
31
C
2
C
12
D
22
B
32
B
3
A
13
D
23
C
33
C
2
D
12
D
A
21
B
22
D
12. DERIVATIVES
4
5
6
7
A
D
A
C
14
15
16
17
C
C
D
B
24
25
26
27
B
C
C
C
39
D
49
A
59
B
69
C
40
C
50
C
60
B
70
B
9
D
19
A
29
D
39
B
49
B
59
B
69
D
79
B
89
C
99
B
109
B
119
C
129
A
139
C
149
A
159
D
10
D
20
B
30
B
40
A
50
D
60
C
70
N
80
D
90
D
100
D
110
A
120
D
130
B
140
C
150
A
8
9
C
B
18
B
28
B
38
C
48
C
19
A
29
B
39
C
10
D
20
D
30
A
40
A
9
A
19
D
10
A
20
C
9
B
19
D
29
D
10
B
20
A
30
B
8
B
18
D
28
C
13. APPLICATION OF DERIVATIVES
3
4
5
6
7
8
C
C
C
D
C
D
13
14
15
16
17
18
B
B
Bd
D
A
B
23
24
25
26
27
28
C
C
A
A
D
B
9
A
19
D
29
C
10
C
20
A
30
B
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
31
C
32
D
1
11
D
21
31
D
41
D
51
B
61
B
71
D
81
C
33
D
2
12
B
22
32
B
42
C
52
D
62
C
72
C
82
B
34
D
3
13
B
23
4
14
B
24
35
B
36
A
A
11
14. MATRICES
5
6
7
B
C
B
15
16
17
D
B
C
25
26
27
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
8
A
18
B
28
D
38
48
C
58
D
68
A
78
D
9
D
19
29
C
39
B
49
D
59
A
69
B
79
A
1
C
11
C
21
C
31
A
41
C
2
C
12
C
22
B
32
C
42
A
1
2
3
C
13
A
23
D
33
C
16. DEFINITE INTEGRAL
4
5
6
7
8
D
A
D
B
D
14
15
16
17
18
D
D
C
C
C
24
25
26
27
28
D
A
A
C
D
34
35
36
37
38
B
D
B
A
B
13
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
B
14
A
15
B
16
17
C
18
C
B
19
C
20
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
21
D
10
C
20
30
C
40
B
50
A
60
B
70
C
80
B
18. COMPLEX NUMBER
4
5
6
7
C
C
C
C
14
15
16
17
D
B
A
D
24
A
19. VECTORS
4
5
6
7
C
C
D
14
15
16
17
B
B
B
D
24
25
26
27
C
A
B
A
20. THREE DIMENSIONAL-OLD QUESTIONS
1
2
3
4
5
6
B
A
D
B
D
B
15. INDEFINITE INTEGRATION
2
3
4
5
6
7
B
B
D
C
A
D
1
A
D
12
9
B
19
B
29
D
39
10
B
20
B
30
A
40
D
C
17. (D.E.) DIFFERENTIAL EQUATION
3
4
5
6
7
8
9
10
39
INFOMATHS/MCA/MATHS/OLD QUESTIONS
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