Question(s) from Search: IIT

If x and y are positive real numbers and m and n are any positive integers then

a) True

b) False

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)

If  and , then constants A and B are

a)

b)

c)

d)

If the vectors  form sides BC, CA and AB respectively of a triangle ABC then

a)

b)

c)

d)

Cards are drawn one by one at random from a well shuffled pack of 52 playing cards until 2 aces are drawn for the first time. If N is the number of cards required to be drawn show that
 where 2 < n ≤ 50

If the lengths of the sides of a triangle are 3, 5, 7 then the largest angle of the triangle is

a)

b)

c)

d)

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

a) – 1

b) π

c) – π

d) 1