Question(s) from Search: IIT

Fill in the blank

The solution of the equation
 is …………..

If  are in Arithmetic Progression where  for all i, show that
 

Show that
 =

Let a, b, c be three non co–planar vectors and p, q, r are vectors defined by the relations
  
Then the value of the expression
 is equal to

a) 0

b) 1

c) 2

d) 3

Fill in the blank

If x < 0, y < 0,  and  then x  ……….. and y  ………..

The sum of the squares of three distinct real numbers which are in Geometric Progression is . If their sum is , show that
 

Show that  =

Let  If d is a unit vector such that  then d equals

a)

b)

c)

d)

(One or more correct answers)
Let E and F are two independent events. The probability that both E and F happen is  and the probability that neither E nor F happens is  , then

a)   

b)    

c)        

d)     

If then x lies in the interval

a) (2, ∞)

b) (1, 2)

c) (−2, −1)

d) None of these

The value of the integral
 is

a)

b)

c) π

d) None of these

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