Question(s) from Search: IIT

Six boys and six girls sit in a row at random. Find the probability that the six girls sit together,

Given A =  for all values of θ, then

a) 1 ≤ A ≤ 2

b)  ≤ A ≤ 1

c)  ≤ A ≤ 1

d)  ≤ A ≤

If a, b, c are in Arithmetic Progression and are in Harmonic Progression then prove that either or a, b and  are in Geometric Progression.

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)

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)