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Application of Integrals - 2 - JEE MCQ


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30 Questions MCQ Test - Application of Integrals - 2

Application of Integrals - 2 for JEE 2024 is part of JEE preparation. The Application of Integrals - 2 questions and answers have been prepared according to the JEE exam syllabus.The Application of Integrals - 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Application of Integrals - 2 below.
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Application of Integrals - 2 - Question 1

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).

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Application of Integrals - 2 - Question 2

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

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Application of Integrals - 2 - Question 6


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Application of Integrals - 2 - Question 7

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

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Application of Integrals - 2 - Question 9


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Application of Integrals - 2 - Question 10

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

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Application of Integrals - 2 - Question 11


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Application of Integrals - 2 - Question 12

The curve  y - exy + x = 0  has a vertical tangent at  :

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Application of Integrals - 2 - Question 15

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

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Application of Integrals - 2 - Question 16

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

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Application of Integrals - 2 - Question 20


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Application of Integrals - 2 - Question 21

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    

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Application of Integrals - 2 - Question 29

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

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