Question(s) from Search: IIT

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)

The inequality |z – 4| < |z – 2| represents the region given by

a) Re(z) ≥ 0

b) Re(z) < 0

c) Re(z) > 0

d) None of these

a) True

b) False

Coefficient of t²⁴ in (1 + t²)¹² (1 + t¹²) (1 + t²⁴) is

a)

b)

c)

d)

If f (x) = |x – 2| and g (x) =  then  for x > 20

a) 0

b) 1

c) 2

d) 4

The value of the integral  is

a)

b)

c)

d)

If tan A  then

a) True

b) False

For a real y, let [y] denote the greatest integer less than or equal to y. Then the function  is

a) Discontinuous at some x

b) Continuous at all x but the derivative  does not exist for some x

c)  exists for all x but the derivative  does not exist for some x

d)  exists for all x

Show that

The position vectors of the point A, B, C, D are  respectively. If the points A, B, C and D lie in a plane, find the value of λ.

If k =  then the numerical value of k is ……….

a)

b)

c)

d)

If f (a) =  then the value of  is

a) – 5

b)

c) 5

d) None of these

Evaluate

a)

b)

c)

d)