Application of Integrals - 1 - JEE MCQ
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Application of Integrals - 1 - Question 1
For which one of the following function Rolle's theorem is applicable?
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Application of Integrals - 1 - 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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Application of Integrals - 1 - 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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Application of Integrals - 1 - 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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Application of Integrals - 1 - 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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Application of Integrals - 1 - 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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Application of Integrals - 1 - 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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Application of Integrals - 1 - 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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