Question(s) from Search: IIT

If x, y, z are in Harmonic Progression then show that
 

 =

a)

b)

c)

d)

The points with position vectors  are collinear if

a)

b)

c)

d)

If P (B) =  and  then

P (B ∩ C) is

a)

b)

c)

d)

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 = y (x) and it follows the relation xcosy + ycosx = π then  is

a) – 1

b) π

c) – π

d) 1

Let f be a positive function. Let
 
 where
2k – 1 > 0 then  is

a) 2

b) k

c)

d) 1

Let
,
then  depends on

a) Only x

b) Only y

c) Neither x nor y

d) Both x and y

In a multiple choice question there are four alternative answers out of which one or more is correct. A candidate will get full marks in the question only if he ticks the correct answers. If he is allowed up to three chances to answer the question, find the probability that he will get marks in the question?

Let the Harmonic Mean and Geometric Mean of two positive numbers be in the ratio of 4:5. Then the two numbers are in the ratio .  .  .  .  .