Question(s) from Search: IIT

The value of  is

a) 0

b) 1

c)

d)

A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability of A and B being selected is at most 0.3. Is it possible that the probability of B being selected is 0.9?

If y is a function of x and ln (x + y) – 2xy = 0 then the value of

y’ (0) is equal to

a) 1

b) – 1

c) 2

d) 0

If  then g(x + π) equals

a) g(x) + g(π)

b) g(x) − g(π)

c) g(x) g(π)

d)

If   are unit vectors, then  does not exceed

a) 4

b) 9

c) 8

d) 6

In a city only two news papers A and B are published. It is known that 25% of the city population read A and 20% read B, while 8% read A and B. It is also known that 30% of those who read A but not B and 40% of those who read B but not A look into the advertisement. 50% of those who read both A and B look into the advertisement. What is the percentage of the population that reads an advertisement?

a) 11

b) 12

c) 13

d) 14

 is equal to

a) 2

b) –2

c)

d)

Let  and u is a unit vector then the maximum value of  is

a)

b)

c)

d)

Given both θ and Ф are acute angles and sinθ =  , cos Ф =  then the value of θ + Ф belongs to

a)

b)

c)

d)

Let x be the Arithmetic Mean and y, z be two Geometric Means between any two positive numbers then

The value of the integral  

a)

b)

c) 3

d) 5

Let  . A vector in the plane of a and b whose projection on c is  is

a)

b) 3

c)

d)

If  and α, β lie between 0 and  find  

a)

b)

c)

d) 2

The product of n positive real numbers is unity. Then their sum is

a) A positive integer

b) Divisible by n

c) Equal to

d) Never less than n

If and , then find  

The integral  equals

a)

b)

c) 1

d)

Using the relation , or otherwise prove that

a) True

b) False

If A > 0, B > 0 and A + B = , then the maximum value of tan A tanB is ……….

a)

b)

c)

d)

Let  be non–coplanar unit vectors equally inclined to one another at an angle θ. If find p, q, r in terms of θ

If  is the unit vector along the incident ray,  is a unit vector along the reflected ray and is a unit vector along the outward drawn normal to the plane mirror at the point of incidence. Find  in terms of  and

True / False

For any three vectors a, b and c
 

a) True

b) False

Multiple choices
For a positive integer n, let
 
.  .  . then

a)

b)

c)

d)

For all ,

a) True

b) False

Let f (x) = |x – 1| then

a) f (x²) = |f (x)|²

b) f (x + y) = f (x) + f (y)

c) f () = |f (x)|

d) None of these