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Question(s) from Search: IIT

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1

Let f : ℝ → ℝ and g : ℝ → ℝ be continuous functions. Then the value of integral  is

a) π

b) 1

c) – 1

d) 0

Let f : ℝ → ℝ and g : ℝ → ℝ be continuous functions. Then the value of integral  is

a) π

b) 1

c) – 1

d) 0

IIT 1990
01:59 min
2

Let  If c is a vector such that  and the angle between  and c is 30° then  is equal to

a)

b)

c) 2

d) 3

Let  If c is a vector such that  and the angle between  and c is 30° then  is equal to

a)

b)

c) 2

d) 3

IIT 1999
03:56 min
3

An anti–aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probability of hitting the plane at the first shot, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

An anti–aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probability of hitting the plane at the first shot, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

IIT 1981
02:45 min
4

The value of the expression  is equal to

a) 2

b)

c) 4

d)

The value of the expression  is equal to

a) 2

b)

c) 4

d)

IIT 1988
02:02 min
5

Let f(x) =  where p is a constant

Then  at x = 0 is

a) p

b)

c)

d) Independent of p

Let f(x) =  where p is a constant

Then  at x = 0 is

a) p

b)

c)

d) Independent of p

IIT 1997
04:22 min
6

 

a)

b)

c)

d)

 

a)

b)

c)

d)

IIT 1997
02:03 min
7

A and B are independent events. The probability that both A and B occur is  and probability that neither of them occur is . Find the probability of the occurrence of A.

A and B are independent events. The probability that both A and B occur is  and probability that neither of them occur is . Find the probability of the occurrence of A.

IIT 1984
04:43 min
8

Let  then  equals

a) tan

b) tan

c) tan

d) tan2

Let  then  equals

a) tan

b) tan

c) tan

d) tan2

IIT 1994
02:33 min
9

 equals

a)

b)

c)

d)

 equals

a)

b)

c)

d)

IIT 2007
01:21 min
10

If  f(x) = x – [x] for every real number x, where [x] is the integral part of x, then  is

a) 1

b) 2

c) 0

d)

If  f(x) = x – [x] for every real number x, where [x] is the integral part of x, then  is

a) 1

b) 2

c) 0

d)

IIT 1998
02:21 min
11

If a and b are two unit vectors such that  are perpendicular to each other then the angle between a and b is

a) 45°

b) 60°

c)

d)

If a and b are two unit vectors such that  are perpendicular to each other then the angle between a and b is

a) 45°

b) 60°

c)

d)

IIT 2003
01:56 min
12

A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point.

A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point.

IIT 1987
04:29 min
13

The length of longest interval in which the function  is increasing is

a)

b)

c)

d)

The length of longest interval in which the function  is increasing is

a)

b)

c)

d)

IIT 2002
01:29 min
14

Let p, q be the roots of the equation , and r and s are roots of the equation . If  are in arithmetic progression then A = .  .  .  .  . , B = .  .  .  .  .

Let p, q be the roots of the equation , and r and s are roots of the equation . If  are in arithmetic progression then A = .  .  .  .  . , B = .  .  .  .  .

IIT 1997
03:26 min
15

Let y =  Find

a)

b)

c)

d) 0

Let y =  Find

a)

b)

c)

d) 0

IIT 1984
02:52 min
16

If

Then  =

a) 0

b) 1

c) 2

d) 3

If

Then  =

a) 0

b) 1

c) 2

d) 3

IIT 2000
02:01 min
17

If  are non-coplanar vectors and
  then a.b1 and a.are orthogonal.

If  are non-coplanar vectors and
  then a.b1 and a.are orthogonal.

IIT 2005
02:29 min
18

Let A be a set containing n elements. A subset P of A is constructed at random. The set A is reconstructed by replacing the elements of P. A subset of Q of A is again chosen at random. Find the probability that P and Q have no elements in common.

Let A be a set containing n elements. A subset P of A is constructed at random. The set A is reconstructed by replacing the elements of P. A subset of Q of A is again chosen at random. Find the probability that P and Q have no elements in common.

IIT 1990
04:10 min
19

The derivative of an even function is always an odd function.

a) False

b) True

The derivative of an even function is always an odd function.

a) False

b) True

IIT 1983
01:33 min
20

If  then

a) Re(z) = 0

b) Im(z) = 0

c) Re(z) = 0, Im(z) > 0

d) Re(z) > 0, Im(z) < 0

If  then

a) Re(z) = 0

b) Im(z) = 0

c) Re(z) = 0, Im(z) > 0

d) Re(z) > 0, Im(z) < 0

IIT 1982
02:07 min
21

a) True

b) False

a) True

b) False

IIT 1983
03:16 min
22

The derivative of  with respect to  at x =  is

a) 0

b) 1

c) 2

d) 4

The derivative of  with respect to  at x =  is

a) 0

b) 1

c) 2

d) 4

IIT 1986
04:19 min
23

If f (x) is differentiable and  , then  equals

a)

b)

c)

d)

If f (x) is differentiable and  , then  equals

a)

b)

c)

d)

IIT 2004
01:33 min
24

 equals

a)

b)

c)

d) 4 f (2)

 equals

a)

b)

c)

d) 4 f (2)

IIT 2007
03:41 min
25

Let z and ω be two non zero complex numbers such that |z| = |ω| and Arg(z) + Arg(ω) = π then z equals

a)  ω

b)  

c)  

d)   

Let z and ω be two non zero complex numbers such that |z| = |ω| and Arg(z) + Arg(ω) = π then z equals

a)  ω

b)  

c)  

d)   

IIT 1995
02:03 min

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