Question(s) from Search: IIT

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 we consider only the principal values of the inverse trigonometric functions then the value of

 is

a)

b)

c)

d)

Let g (x) = 1 + x – [ x ] and f (x) =  then for all x,
f (g (x)) is equal to

a) x

b) 1

c) f ( x )

d) g ( x )

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?

Find the value of  at  where
.

a) 1

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.

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

a) Zero

b) One

c) Two

d) three

Multiple choices

Let g (x) be a function defined on [−1, 1]. If the area of the equilateral triangle with the area of its vertices at ( 0, 0) and ( x, g (x)) is  then the function g (x) is

a) g (x) =

b) g (x) =

c) g (x) =

d) g (x) =

Multiple choice

Which of the following expressions are meaningful

a)

b)

c)

d)

Which one of the following is true in a triangle ABC?

a)

b)

c)

d)

Given A =  and f (x) = cosx – x (x + 1). Find the range of f (A).

a)

b)

c)

d)

Find all values of λ such that  and

 where  are unit vectors along the coordinate vectors.

The complex numbers sinx + icos2x and cosx – isin2x are conjugate to each other for

a) a = nπ

b) x = 0

c) x =  

d) None of these

Let OABC be a parallelogram with O as the origin and OC a diagonal. Let D be the midpoint of OA. Using vector method, prove that BD and CO intersect in the same ratio.

For positive integers n₁ and n₂ the value of the expression  where  is real if and only if

a)

b)

c)

d)

Let the angles A, B, C of Δ ABC be in arithmetic progression and
b : c = . Find the angle A.

a)

b)

c)

d)

Determine the value of c so that for all real x the vector cx and  make an obtuse angle with each other.

Let ABC be a triangle such that
 

If A, B, C are in arithmetic progression, determine the values of A, B, C.

a) 30°, 60°, 90°

b) 30°, 75°, 75°

c) 45°, 60°, 75°

d) 60°, 60°, 60°

If f (x) =  and  

then (gof)(x) = …………

a) 0

b) 1

c) 2

d) 3

The lines  and  are diameters of a circle of area 154 square units. Then the equation of the circle is

a)

b)

c)

d)

The largest interval for which  is

a)

b)

c)

d)

The angle between a pair of tangents drawn from a point P to the circle  is 2α. Then the locus of P is

a)

b)

c)

d)

The equation  has

a) No root

b) One root

c) Two equal roots

d) Infinitely many roots