The area of the region enclosed between parabola y2 = x and the l

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 Multiple Choice QuestionsMultiple Choice Questions

31.

The area of the region bounded by the curve y = x3, its tangent at (1, 1) and X-axis, is

  • 112 sq units

  • 16 sq units

  • 217 sq units

  • 215 sq units


32.

Area of the region bounded by y = x and y = - x + 2 is

  • 4 sq units

  • 3 sq units

  • 2 sq units

  • 1 sq units


33.

The area of the region bounded by the curves y = x2 and x = yis

  • 1/3

  • 1/2

  • 1/4

  • 3


34.

If f(x) = x23, x  0. Then, the area of the region enclosed by the curve y = f (x) and the three lines y = x, x = 1and x = 8 is

  • 632

  • 935

  • 1057

  • 12910


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35.

If f(x) = x1x - 1 + 1x + 1x + 1, x> 1. Then,

  • f(x)  1

  • 1 < f(x)  2

  • 2 < f(x)  3

  • f(x) > 3


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36.

The area of the region enclosed between parabola y2 = x and the line y = mx is 148. Then, the value of m is

  • - 2

  • - 1

  • 1

  • 2


A.

- 2

D.

2

Equation of parabola is y2 = x and line y = mx

For intersection point of both curves put x = y2, we get

         y = my2  ymy - 1 = 0     y = 0 or y = 1mThen, x = 0 or x = 1m2

 Intersection points are 0, 0 and P1m2, 1m

 Required area= 01/mym - y2dy = y22m - y3301m= 12m3 - 13m3 = 16m3 = 148        as given

   16m3 = ± 148  m3 = ± 8Now, if m3 = 8       m3 = 23  m = 2If          m3 = - 8       m3 = - 23  m = - 2


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37.

The area of the region bounded by the curves y = x , y = 1x, x = 2 is

  • 4 - loge2

  • 14 + loge2

  • 3 - loge2

  • 154 - loge2


38.

The area of the region, bounded by the curves y = sin- 1(x) + x(1 - x) and y = sin- 1 (x) - x(1 - x) in the first quadrant, is

  • 1

  • 12

  • 13

  • 14


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39.

The area enclosed between y2 = x and y = x is

  • 23 sq unit

  • 12 unit

  • 13 unit

  • 16


40.

The area bounded by y2 = 4x and x = 4y is

  • 203 sq units

  • 163 sq units

  • 143

  • 103


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