Question(s) from Search: IIT

If a  are linearly dependent and |c|  then

a)

b)

c)

d)

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

 is equal to

a)

b)

c)

d)

If a, b, c are positive real numbers then prove that
 

Let f(x) be a quadratic expression which is positive for all values of x. If g(x) =  then for any real x

a) g (x) < 0

b) g (x) > 0

c) g (x) = 0

d) g (x) ≥ 0

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

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 .  .  .  .  .

If f (x) = , find  from first principle.

a)

b)

c)

d)

If for real number y, [y] is the greatest integer less than or equal to y then the value of the integral   is

a)

b)

c)

d)

If  and  then b is equal to

a)

b)

c)

d)

A box contains two 50 paise coins, 5 twenty five paise coins and a certain number N(≥ 2) of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these coins is less than one rupee and 50 paise.

 and
where α, β ε [π, π]. Values of α, β which satisfy both the equations is/are

a) 0

b) 1

c) 2

d) 4

Given positive integers r > 1, n > 2 and the coefficients of (3r)^th term and (r + 2)^th terms in the binomial expansion of (1 + x)²ⁿ are equal then

a) n = 2r

b) n = 2r + 1

c) n = 3r

d) none of these

The number of distinct real values of λ for which   are coplanar is

a) Zero

b) One

c) Two

d) three

If , then  

a) True

b) False

If in the expansion of (1 + x)^m (1 – x)ⁿ, the coefficients of x and x² are 3 and –6 respectively. then m is

a) 6

b) 9

c) 12

d) 24

If  then  at x = e is .  .  .

a) 0

b)

c) e

d) 1

If  then the expression for  in terms of  is

a)

b)

c)

d)