Question(s) from Search: IIT

The value of the integral  is

a)

b)

c)

d)

If tan A  then

a) True

b) False

For a real y, let [y] denote the greatest integer less than or equal to y. Then the function  is

a) Discontinuous at some x

b) Continuous at all x but the derivative  does not exist for some x

c)  exists for all x but the derivative  does not exist for some x

d)  exists for all x

Show that

The position vectors of the point A, B, C, D are  respectively. If the points A, B, C and D lie in a plane, find the value of λ.

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

a)

b)

c)

d)

If f (a) =  then the value of  is

a) – 5

b)

c) 5

d) None of these

Evaluate

a)

b)

c)

d)

Let A = . Determine a vector R satisfying  and .

If a, b, c are in Arithmetic Progression then the straight line
 will pass through a fixed point whose coordinates are  . . . . .

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)