﻿ IIT - JEE Main Important Questions of Application of Integrals | Zigya

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# Application of Integrals

#### Multiple Choice Questions

1.

If one of the diameters of the circle, given by the equation, x2+y2−4x+6y−12=0, is a chord of a circle S, whose centre is at (−3, 2), then the radius of S is:

• 5√2

• 5√3

• 5

• 10

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2.

Let P be the point on the parabola, y2=8x which is at a minimum distance from the centre C of the circle, x2+(y+6)2=1. Then the equation of the circle, passing through C and having its centre at P is:

• x2+y2−4x+8y+12=0

• x2+y2−x+4y−12=0

• x2+y2− 4 x +2y−24=0

• x2+y2− 4 x +2y−24=0

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3.

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is:

• 4/3

• 4/√3

• 2/√3

• √3

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4.

The area (in sq units) of the region described by {x,y): y2 ≤ 2x and y ≥ 4x-1} is

• 7/32

• 5/64

• 15/64

• 15/64

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5.

The area (in sq units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse

• 27/4

• 18

• 27/2

• 27/2

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6.

Let O be the vertex and Q be nay point on the parabola x2 = 8y. If the point P divides the line segment OQ internally in the ratio 1:3 then the locus of P is

• x2= y

• y2 =x

• y2 =2x

• y2 =2x

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7.

If =-1 and x =2 are extreme points of f(x) =α log|x| + βx2 +x, then

• α = -6, β = 1/2

• α = -6, β = -1/2

• α = 2, β = -1/2

• α = 2, β = -1/2

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8.

The area of the region described by A = {(x,y): x2 +y2 ≤ 1 and y2 ≤1-x} is

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9.

Let the population of rabbits surviving at a time t be governed by the differential equation. If p(0) = 100 then p(t) is equal to

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10.

The area (in square units) bounded by the curves y =  2y-x+3 =0, X -axis and lying in the first quadrant is

• 9

• 36

• 18

• 18

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