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Test: Application of Integrals - 3 - JEE MCQ


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30 Questions MCQ Test - Test: Application of Integrals - 3

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Test: Application of Integrals - 3 - Question 1

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

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Test: Application of Integrals - 3 - Question 2


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Test: Application of Integrals - 3 - Question 3

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The function f(x) has a local minimum at x = 1

Test: Application of Integrals - 3 - Question 4


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Test: Application of Integrals - 3 - Question 5

The length of a longest interval in which the function f (x) = 3 sinx – 4 sin3x is increasing, is

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Test: Application of Integrals - 3 - Question 6


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Test: Application of Integrals - 3 - Question 7


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Test: Application of Integrals - 3 - Question 8


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Test: Application of Integrals - 3 - Question 9

A dynamite blast blows a heavy rock straight up with a launch velocity of 160 m/sec. It reaches a height of  s = 160 t = 16t2  after  t sec. The velocity of the rock when it is  256 m  above the ground on the way up is

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Test: Application of Integrals - 3 - Question 10

Find the area (in sq. units) of the largest rectangle with lower base on the x-axis & upper vertices on thecurve y = 12 – x2

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Test: Application of Integrals - 3 - Question 11


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Test: Application of Integrals - 3 - Question 12

If the point P(a, b) lies on the curve 9y2 = x3 such that the normal to the curve at P makes equal intercepts with the axes. The value of

 (a + 3b) is    

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Test: Application of Integrals - 3 - Question 13

Two curves C1 : y = x2 – 3 and C2 : y = kx2 ,  intersect each other at two different points. The tangent drawn to C2 at one of the points of intersection A (a,y1) , (a > 0) meets C1 again at B(1,y2) . The value of ‘a’ is

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*Multiple options can be correct
Test: Application of Integrals - 3 - Question 14

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*Multiple options can be correct
Test: Application of Integrals - 3 - Question 15

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*Multiple options can be correct
Test: Application of Integrals - 3 - Question 16

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Test: Application of Integrals - 3 - Question 17


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Test: Application of Integrals - 3 - Question 18


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Test: Application of Integrals - 3 - Question 19

If   M (x0, y0) is the point on the curve 3x2 – 4y2 = 72, which is nearest to the line 3x + 2y + 1 = 0, then the value of  (x0 + y0) is equal to

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First of all, we try to locate the points on the curve at which the tangent is parallel to the given line.

 So, differentiating both sides with respect to  x  of   3x2 – 4y2  =  72,  we get




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Test: Application of Integrals - 3 - Question 21


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Test: Application of Integrals - 3 - Question 22


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Test: Application of Integrals - 3 - Question 23


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Test: Application of Integrals - 3 - Question 24


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Test: Application of Integrals - 3 - Question 25

If the exhaustive set of all possible values of c such that f(x) = e2x – (c + 1) ex + 2x + cos 2 + sin 1, is monotonically increasing  for all x ∈ R, is (–∞, λ], then find the value of λ.

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*Multiple options can be correct
Test: Application of Integrals - 3 - Question 26

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Therefore, h(x) is increasing function if f(x) is increasing function, and h(x) is decreasing function if f(x) is decreasing function.

So, correct answer is option A & C.

Test: Application of Integrals - 3 - Question 27


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*Multiple options can be correct
Test: Application of Integrals - 3 - Question 28

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Test: Application of Integrals - 3 - Question 29

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Test: Application of Integrals - 3 - Question 30


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