Question(s) from Search: IIT

If k =  then the numerical value of k is ……….

a)

b)

c)

d)

If  then

tan

a) True

b) False

In a triangle ABC, angle A is greater than angle B. If the measures of angle A and B satisfy the equation , then the measure of angle C is

a)

b)

c)

d)

Prove that C₀ – 2²C₁ + 3²C₂ − .  .  .  + (−)ⁿ  (n + 1)² C_n = 0 for n > 2 where

The maximum value of cos₁ cos₂ cos_{3 ……} cos_nunder the restriction 0  _{1 , 2} , ₃ …. , _n   and cot₁ cot₂ cot_{3 ……} cot_n= 1 is

a)

b)

c)

d)

Let   are the perpendiculars from the vertices of a triangle to the opposite sides, then  

a) True

b) False

The coefficient of x⁹⁹ in the polynomial
(x – 1) (x – 2) .  .  . (x – 100) is

The sum of the rational terms in the expansion of  is

Which of the following functions is periodic?

a) f(x) = x – [x] where [x] denotes the greatest integer less than or equal to the real number x

b) f(x) = sin  x ≠ 0, f(0) = 0

c) f(x) = x cos x

d) None of these

Let f (x) be defined for all x > 0 and be continuous. If f (x) satisfies
f  = f (x) – f (y) for all x and y and f (e) = 1 then

a) f (x) is bounded

b) f  → 0 as x → 0

c) x f  → 0 as x → 0

d) f (x) = lnx

There exists a solution of θ between 0 and 2π that satisfies the equation .

a) True

b) False

The number of values of x where the function
f (x) = cos x + cos () attains the maximum is

a) 0

b) 1

c) 2

d) Infinite

The domain of definition of the function f (x) given by the equation

2^x + 2^y = 2 is

a) 0 < x ≤ 1

b) 0 ≤ x ≤ 1

c)  < x ≤ 0

d)  < x ≤ 1

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 )

Find the value of  at  where
.

a) 1

b)

c)

d)

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) =

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)

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

a)

b)

c)

d)

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 largest interval for which  is

a)

b)

c)

d)

The equation  has

a) No root

b) One root

c) Two equal roots

d) Infinitely many roots

Let a, b, c be real numbers, a ≠ 0. If α is a root of β is a root of  and 0 < α < β then the equation  has a root γ that always satisfies

a) γ =

b) γ =

c) γ = α

d) α < γ < β