The document contains 50 multiple choice questions covering various topics in mathematics including functions, trigonometry, calculus, probability, matrices and linear algebra. The questions test concepts such as one-to-one functions, inverse trigonometric functions, limits, derivatives, integrals, probability, matrices, vectors, and linear transformations.

1. 1) Let f:R R be define as f(x)=x4
. Then f is
(a) One-one onto (b) one-one but not onto
(c) neither one- one nor onto (d) many one onto
2) Value of cos-1
(1/2) +2 Sin-1
(1/2) is
(a) π /8 (b) π /3 (c) 5 π /4 (d) 2
π /3
3) The area enclosed between y=x , x=1 , x=3 and x-axis is:
(a) 2 (b) 9/2 (c) 4 (d) none of these
4) A = {1,2,3} Which of the following is not an equivalence relation on A?
(a) {(1,1),(2,2),(3,3)} (b) {(1,1),(2,2).(3,3),(1,2),(2,1)}
(c) {(1,1),(2,2),(3,3),(2,3),(3,2)} (d) none of these
5) Let f:NN be defined by f(x)=2x for all x ∈ N . Then f is:
(a) One-one (b) onto (c) bijective (d) none of these
6) For a Binomial distribution mean is 9 and Standard deviation is √6. The value of n and p are respectively:
(a) 27, 2/3 (b) 9 ,1/3 (c) 27 ,1/3 (d) 9,2/3
7) For what value of c , the LMV theorem holds in the function f(x)=x2
-2x+3 in [0,5]?
(a) 5/2 (b) √2 (c) 0 (d) -2
8) Sin(sin-1
x+cos-1
x) is equal to (-1≤x ≤1¿
(a) 1 (b) π /2 (c) 0 (d) none of these
9) The degree of differential equation {1+(
dy
dx
)2
}5/3
=d2
y/dx2
is
(a) 1 (b) 3 (c) 5 (d) not defined
10) Direction cosines of i
∧
are:
(a) <0,1,1> (b) <1,0,0> (c) <-1,0,0> (d) none
11) Objective function of a LPP is
(a) constant (b)function to be optimised
(c) relation between variables (d) none of these
12) If A and B are independent events then which one is not true?
(a) P(A/B) = P(A) (b) P(B/A) = P(B) (c) P(A/B) = P(B/A) (d) none of these

2. 13) Suppose X has Binomial Variate B(5,p) and P(X=2)=P(X=3) then p is equal to
(a) 1/5 (b) 1/4 (c)1/3 (d)
1/2
14) A pair of dice is rolled again and again till a total of 5 or 7 is obtained. The chance that a total of 5 comes before a total
of 7 is
(a) 2/5 (b) 3/7 (c) 3/13 (d) none of these
15) If A is a square matrix : A2
=I, Then A-1
is equal to
(a) I (b) O (c) A (d) I+A
16) The number of all possible matrices of order 2×3 with each entry 0 or 1 is
(a) 64 (b) 12 (c) 32 (d) 128
17) If A is a Square matrix of order 2 , the det(adjA) is equal to
(a) 1 (b) detA (c) (detA) 2
(d) not defined
18) The system of equations x+y+Z=6 , x+2y+3z=10 , x+2y+ λ Z =μ has unique solution if
(a) λ=3 (b) λ=3 , μ 10 (c) λ ≠3 (d) λ=3 , μ=10
19) Maximum value of f(x)=SinxCosx is
(a) -1/2 (b) 0 (c) 1/2 (d) none
20) Slope of tangent to the curve y=x3
-x at x=2 is
(a) 6 (b) 0 (c) 11 (d) none
21) Consider a binary operation on Q-{1) defined by a ¿b = a+b-ab . The identity element in Q-{1} is
(a) 1 (b) 0 (c) -1 (d) 2
22) If
2x
4
sin
x
3
sin 11 π
=





+




 −−
, x equals
(a) 5 (b) –5 (c) 25 (d) none of these
23) =++ −−−
3tan2tan1tan 111
(a) 0 (b) ∏ (c) ∏/2 (d) ∏/4
24) An integrating factor of the differential equation
( )0x,
x
y1
y
dx
dy
>
+
=+
is
(a)
x
e
x
(b) x
ex
(c)
x
xe (d)
none of these

3. 25) ( ) ( ) ( )ikkjji

+×+×+ is equal to
(a) 0 (b) 1 (c) 2 (d) none of these
26) If a

and b

are unit vectors and is the angle between them, then
=− ba

(a) 2
sin
θ
(b) 2
sin2
θ
(c) 2
cos2
θ
(d) 2
cos
θ
27) The lines 0
3
2
1
1
1 −
=
−
=
− zyx
and 1
4
0
3
0
2 −
=
−
=
− zyx
are
(a) parallel (b) skew (c) coincident (d) perpendicular
28) The distance between the planes 3x + 2y – 6z – 14 = 0 and 6x + 4y – 12z + 42 = 0 is
(a) 35units (b) 7units (c) 1unit (d) 5unit
29) The sine of angle between 5
4z
4
3y
3
2x −
=
−
=
−
and plane 2x – 2y + z = 5 is
(a) 56
10
(b) 10
2
(c) 25
4
(d) 5
2
30) If P(A ∪ B) = 5/6, P(A ∩ B) = 1/3, P( B ) = 1/2, then A and B are
(a) dependent (b) independent (c) mutually exclusive (d) mutually exhaustive
31) 10 eggs are drawn successively with displacement from a lot containing 10% defective bulb. The probability that there
is at least one defective bulb is
(a)
10
10
9






(b)
10
10
1






(c)
10
10
9
1 





−
(d)
10
10
1
1 





−
32) Volume of cube is increasing at the rate of 9 cu.cm per second. The rate of change of its surface area when its edge
is 6 cm is
(a) 3.6 cm/s (b) 3.6 cm2
/s (c) 6 cm/s (d) 6 cm2
/s
33) The point at which curves x2
= y and y2
= x cut orthogonally is
(a) (0, 0) (b) (1, 1) (c) (2, 2) (d) none of these
34) Line
2
b
y
a
x
=+
touches the curve
2
b
y
a
x
nn
=





+





at (a, b) for
(a) n = 2 (b) n = 3 (c) any value of n (d) no value of n

4. 35) If
( )
1x2x4
1
xf 2
++
=
, then its maximum value is
(a) 4/3 (b) 2/3 (c) 1 (d) ¾
36) If
yxy
ex +
= then dx
dy
=
(a)
( )2
1xlog
2xlog
−
−
(b)
( )2
1xlog
2ylog
−
−
(c)
( )2
1xlog
2xy
−
−
(d) none of these
37) Find the value of
( ) ( )3coteccos2tansec 1212 −−
+ .
(a) 18 (b) ∏/4 (c) 15 (d) 12
38) Value of
4
5
x
4
,
2
xcosxsin
cos 1 ππ
<<




 +−
is
(a) 4
x
π
+
(b) 4
x
π
−
(c)
x
2
−
π
(d)
x
2
+
π
39) A die is thrown 100 times. Getting an even number is considered as success. The variance of the number of a
success is
(a) 10 (b) 20 (c) 25 (d) 50
40) The solution of differential equation
0x4
dx
dy
y9 =+
is
(a)
c
4
x
9
y 22
=+
(b)
c
9
x
4
y 22
=+
(c)
c
9
x
4
y 22
=−
(d)
c
4
x
9
y 22
=−
41) The probability that at least one of the events A and B occur is 0.6. If A and B occur simultaneously with probability 0.2,
then value of
( ) ( )BPAP + is
(a) 1.4 (b) 1.2 (c) 1.3 (d) 1.1
42) A coin is tossed 7 times. The probability that a person wins the toss on more occasions is
(a) 1/4 (b) 5/8 (c) 1/2 (d) 1/7
43) If






=
10
01
I
,






−
=
01
10
J
,






−
=
θθ
θθ
cossin
sincos
B
, then B is also equal to

5. (a) θθ sinJcosI + (b) θθ cosJsinI + (c) θθ sinJcosI − (d) θθ cosIsinJ −
44) The value of
1
1
1
2
2
2
ωω
ωω
ωω
is equal to
(a) 0 (b) 1 (c) 3 (d) none of these
45) The value of determinant
xcosxsin3
xsinxcos2
001
is equal to
(a) cos2x (b) 1 (c) 0 (d) sin2x
46) Value of
∫−
3
3
dx.x
is
(a) 3 (b) 9 (c) 18 (d) 0
47) If
2
1
2cos1
2cos1
y 





−
+
=
θ
θ
, then value of θd
dy
at 4
3π
θ =
is
(a) –2 (b) 2 (c) ±2 (d) 0
48) Value of
∫ +
3
6
tan1
π
π x
dx
is
(a) 10
π
(b) 11
π
(c) 18
π
(d) 12
π
49) Sin-1
(1-x) – 2Sin-1
x= 2
π
, then x is equal to
(a)0 , 1/2 (b)1, 1/2 (c) 0 (d) 1/2
50) On R, the function f(x) =
x1
x
+
is
(a) strictly decreasing (b) strictly increasing (c) increasing (d) decreasing

6. (a) θθ sinJcosI + (b) θθ cosJsinI + (c) θθ sinJcosI − (d) θθ cosIsinJ −
44) The value of
1
1
1
2
2
2
ωω
ωω
ωω
is equal to
(a) 0 (b) 1 (c) 3 (d) none of these
45) The value of determinant
xcosxsin3
xsinxcos2
001
is equal to
(a) cos2x (b) 1 (c) 0 (d) sin2x
46) Value of
∫−
3
3
dx.x
is
(a) 3 (b) 9 (c) 18 (d) 0
47) If
2
1
2cos1
2cos1
y 





−
+
=
θ
θ
, then value of θd
dy
at 4
3π
θ =
is
(a) –2 (b) 2 (c) ±2 (d) 0
48) Value of
∫ +
3
6
tan1
π
π x
dx
is
(a) 10
π
(b) 11
π
(c) 18
π
(d) 12
π
49) Sin-1
(1-x) – 2Sin-1
x= 2
π
, then x is equal to
(a)0 , 1/2 (b)1, 1/2 (c) 0 (d) 1/2
50) On R, the function f(x) =
x1
x
+
is
(a) strictly decreasing (b) strictly increasing (c) increasing (d) decreasing