Question(s) from Search: IIT

If  then

tan

a) True

b) False

Evaluate

a)

b)

c)

d)

Let C be the curve  . If H is the set of points on the curve C when the tangent is horizontal and v be the set of all points on the curve C when the tangent is vertical then H  =  . . . . .  and v = . . . . .

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

Show that

The centre of the circle passing through (0, 1) and touching the curve  at (2, 4) is

a)

b)

c)

d) None of these

Determine a positive integer n ≤ 5 such that .

a) 1

b) 2

c) 3

d) 4

If a, b, c, d are distinct vectors satisfying relation  and . Prove that

If two circles  and  intersect in two distinct points, then

a) 2 < r < 8

b) r < 2

c) r = 2

d) r > 2

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)

The left hand derivative of f (x) = [x] sinπx at k, k an integer is

a) (k – 1)π

b) (k – 1)π

c) kπ

d)  kπ

Determine the value of

a)

b)

c)

d)

Let f : ℝ → ℝ be such that f (1) = 3 and  then

 equals

a) 1

b)

c)

d)

For x > 0, let  find the function  and show that . Here .

a)

b)

c)

d)

If two distinct chords drawn from the point (p, q) on the circle  (where pq ≠ 0) are bisected by the X-axis then

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

Evaluate

The sum of the rational terms in the expansion of  is

The integral  dx where [ ] denotes the greatest integer function equals .  .   .

a)

b)  + 1

c)

d)

A non-zero vector a is parallel to the line of intersection of the plane determined by the vectors  and the plane determined by the vectors . The angle between a and  is .  .  .  .  .

A circle is given by , another circle C touches it externally and also the X-axis, then the locus of the centre of C is

a)

b)

c)

d)

Find all solutions of
 in

a)

b)

c)

d)

Let f (x) = sin x and g (x) = ln|x|. If the range of the composition

functions fog and gof are R₁ and R₂ respectively, then

a) R₁ = [ u : −1 ≤ u < 1], R₂ = [ v : − < v < 0 ]

b) R₁ = [ u : − < u < 0 ], R₂ = [ v : −1 ≤ v ≤ 0]

c) R₁ = [ u : −1 < u < 1], R₂ = [ v : − < v < 0 ]

d) R₁ = [ u : −1 ≤ u ≤ 1], R₂ = [ v : − < v ≤ 0 ]