Application of Integrals - 4 - Free MCQ Practice Test with solutions, JEE

Give the correct order of initials T or F for following statements. Use T if statement is true and F if it is false.

Statement-1: If f : R → R and c ∈ R is such that f is increasing in (c – δ, c) and f is decreasing in (c, c + δ) then f has a local maximum at c. Where δ is a sufficiently small positive quantity.

Statement-2 : Let f : (a, b) → R, c ∈ (a, b). Then f can not have both a local maximum and a point of inflection at x = c.

Statement-3 : The function f (x) = x² | x | is twice differentiable at x = 0.

Statement-4 : Let f : [c – 1, c + 1] → [a, b] be bijective map such that f is differentiable at c then f^–1 is also differentiable at f (c).

The set of values of p for which the equation |ln x|–px = 0 possess three distinct roots is

Which one of the following functions Rolle’s theorem is applicable?

For which one of the following function Rolle's theorem is  applicable?

The curve  y - e^xy + x = 0  has a vertical tangent at  :

where [x] and {x} denotes the greatest integer and fraction part function.

P and Q are two points on a circle of centre C and radius α, the angle PCQ being 2θ then the radius of the circle inscribed in the triangle CPQ is maximum when

Let  P be the point on the curve  4x² + a²y² =  4a², 0 < a² < 8  whose distance from  Q(0, – 2) is greatest. If  R  is the reflection of  P  in the x-axis then find the least distance of  R  from the line  3x – 4y + 7 = 0 is

A right triangle is drawn in a semicircle of radius 1/2 with one of its legs along the diameter. The maximum area of the triangle is