41.

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

• Interval	Function
  (-∞, ∞)	x3 – 3x2 + 3x + 3

• Interval	Function
  [2, ∞)	2x3 – 3x2 – 12x + 6

• Interval	Function
  (-∞, 1/3]	3x2 – 2x + 1

• Interval	Function
  (-∞, 1/3]	3x2 – 2x + 1

Suppose f(x) is differentiable x = 1 and 

• 3

• 4

• 5

• 5

Let f be differentiable for all x. If f(1) = - 2 and f′(x) ≥ 2 for x ∈ [1, 6] , then

• f(6) ≥ 8

• f(6) < 8

• f(6) < 5

• f(6) < 5

If f is a real-valued differentiable function satisfying |f(x) – f(y)| ≤ (x – y)² , x, y ∈ R and f(0) = 0, then f(1) equals

• -1

• 0

• 2

• 2

If cos^-1 x - cos^-1 y/2 = α, then 4x² − 4xy cos α + y² is equal to

• 2 sin 2α

• 4

• 4 sin² α

• 4 sin² α

If then the solution of the equation is

A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness than melts at a rate of 50 cm³ /min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is

A particle is projected from a point O with velocity u at an angle of 60^o with the horizontal. When it is moving in a direction at right angles to its direction at O, its velocity then is given by

• u/3

• u/2

• 2u/3

• 2u/3

If a₁, a₂, a₃,…, a_n,… are in G.P., then the determinant

• 1

• 0

• 4

• 4

A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to

• –f(x)

• f(x)

• f(a) + f(a – x)

• f(a) + f(a – x)