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) 5π /4 (d) 2π /33) The area enclosed between y=x , x=1 , x=3 and x-axis is:

(a) 2 (b) 9/2 (c) 4 (d) none of these4) 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:N N be defined by f(x)=2x for all x∈N . Then f is:

(a) One-one (b) onto (c) bijective (d) none of these6) 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) 9,2/37) 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-1x+cos-1x) is equal to (-1≤x≤1¿(a) 1 (b)π /2 (c) 0 (d) none of these

9) The degree of differential equation {1+(dydx

)2 }5/3=d2y/dx2 is

(a) 1 (b) 3 (c) 5 (d) not defined

10) Direction cosines of 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

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+λZ =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 sin−1 ( 3x )+sin−1( 4x )=π2 , x equals

(a) 5 (b) –5 (c) 25 (d) none of these

23) tan−11+tan−12+ tan−13=

(a) 0 (b) ∏ (c) ∏/2 (d) ∏/4

24) An integrating factor of the differential equation

dydx

+ y=1+ yx, ( x>0 )

is

(a)

x

ex (b)

ex

x (c) xex

(d) none of these

25) ( i+ j )× ( j+k )×(k+i ) 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 |a−b|=

(a) sinθ2 (b)

2sinθ2 (c)

2cosθ2 (d)

cosθ2

27) The lines

x−11

= y−12

= z−30 and

x−20

= y−30

= z−41 are

(a) parallel (b) skew (c) coincident (d) perpendicular28) 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

x−23

= y−34

= z−45 and plane 2x – 2y + z = 5 is

(a)

106√5 (b)

√210 (c)

45√2 (d)

√25

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) ( 910 )

10

(b) ( 110 )

10

(c)

1−( 910 )10

(d)

1−( 110 )10

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

xa+ yb=2

touches the curve ( xa )

n

+( yb )n

=2 at (a, b) for

(a) n = 2 (b) n = 3 (c) any value of n (d) no value of n

35) If

f ( x )= 1

4 x2+2 x+1 , then its maximum value is

(a) 4/3 (b) 2/3 (c) 1 (d) ¾

36) If xy=ex+ y then

dydx =

(a)

log x−2(log x−1 )2 (b)

log y−2(log x−1 )2 (c)

xy−2(log x−1 )2 (d) none of these

37) Find the value of sec2 ( tan−12 )+cos ec2 (cot−13 ) .

(a) 18 (b) ∏/4 (c) 15 (d) 12

38) Value of

cos−1(sin x+cos x√2 ) , π4 <x<5 π4

is

(a) x+ π4 (b)

x− π4 (c)

π2−x

(d)

π2+x

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 9 ydydx

+4 x=0is

(a)

y2

9+ x

2

4=c

(b)

y2

4+ x

2

9=c

(c)

y2

4− x

2

9=c

(d)

y2

9− x

2

4=c

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 P (A )+P (B ) 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

I=[1 00 1 ]

,

J=[ 0 1−1 0 ]

,

B=[cosθ sinθ−sinθ cosθ ]

, then B is also equal to

(a) I cos θ+J sin θ (b) I sin θ+J cos θ (c) I cos θ−J sinθ (d) J sin θ−I cosθ

44) The value of

|1 ω ω2

ω ω2 1ω2 ω 1

|

is equal to(a) 0 (b) 1 (c) 3 (d) none of these

45) The value of determinant

|1 0 02 cos x sin x3 sin x cos x

| is equal to

(a) cos2x (b) 1 (c) 0 (d) sin2x

46) Value of

∫−3

3

|x|.dx is

(a) 3 (b) 9 (c) 18 (d) 0

47) If

y=( 1+cos2θ1−cos2θ )12

, then value of

dydθ at

θ=3 π4 is

(a) –2 (b) 2 (c) ±2 (d) 0

48) Value of

∫π6

π3

dx1+√ tan x

is

(a)

π10 (b)

π11 (c)

π18 (d)

π12

49) Sin-1(1-x) – 2Sin-1x=

π2 , 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