Question(s) from Search: IIT

 equals

a)

b)

c)

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)

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)

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.

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

a)

b)

c)

d)

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 y =  Find

a)

b)

c)

d) 0

If

Then  =

a) 0

b) 1

c) 2

d) 3

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

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.

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

a) False

b) True

If  then

a) Re(z) = 0

b) Im(z) = 0

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

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

a) True

b) False

The derivative of  with respect to  at x =  is

a) 0

b) 1

c) 2

d) 4

If f (x) is differentiable and  , then  equals

a)

b)

c)

d)

 equals

a)

b)

c)

d) 4 f (2)

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)   

The function  is not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuous at x = 0 is

a) a – b

b) a + b

c) lna – lnb

d) None of these

Find the value of

a)

b)

c)

d)

The set of lines  where  is concurrent at the point . . .

If tan θ =  then sin θ is

a)  but not  

b)  or

c)  but not −

d) None of these

Find the sum of the series
 

The set of all points where the function  is differentiable is

a)

b) [0, ∞)

c)  

d)  (0, ∞)

e)  None of these

Given a function f (x) such that
i) it is integrable over every interval on the real axis and
ii) f (t + x) = f (x) for every x and a real t, then show that the integral  is independent of a.

If the algebraic sum of the perpendicular distance from the point
(2, 0), (0, 2) and (1, 1) to a variable straight line be zero then the line passes through a fixed point whose coordinates are