﻿ IIT - JEE Main Important Questions of Integrals | Zigya

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# Integrals

#### Multiple Choice Questions

1.

The integral  is equal to

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2.

Two sides of a rhombus are along the lines, x−y+1=0 and 7x−y−5=0. If its diagonals intersect at (−1, −2), then which one of the following is a vertex of this rhombus?

• (−3, −9)

• (−3, −8)

• (1/3, -8/3)

• (1/3, -8/3)

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3.

The centres of those circles which touch the circle, x2+y2−8x−8y−4=0, externally and also touch the x-axis, lie on:

• a circle

• an ellipse which is not a circle

• a hyperbola.

• a hyperbola.

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4.

The integral

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5.

The integral   is equal to

• 2

• 4

• 1

• 1

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6.

The number of points having both coordinates as integers that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0) is

• 901

• 861

• 820

• 820

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7.

The integral  dx is equal to

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8.

The Integral  is equal to

• π-4

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9.

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to the additional number of workers x is given by . If the firm employs 25 more workers, then
the new level of production of items is

• 2500

• 3000

• 3500

• 3500

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10.

If ∫f x dx =Ψ (x),then ∫x5 f(x3)dx is equal to

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