The solution of the differential equation x + y2dy

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 Multiple Choice QuestionsMultiple Choice Questions

101.

The part of straight line y = x + 1 between x = 2 and x = 3 is revolved about x-axis, then the curved surface of the solid thus generated is

  • 37π3

  • 7π2

  • 37π

  • 7π2


102.

The part of circle x2 + y2 = 9 in between y = 0 and y = 2 is revolved about y-axis. The volume of generating solid will be

  • 463π

  • 12π

  • 16π

  • None of these


103.

For 0  x  π, the area between the curve y = sin(x) and x - axis is

  • 1 sq unit

  • 0 sq unit

  • 2 sq unit

  • - 1 sq unit


104.

The area bounded by the curve y2(2a - x) = x3 and the line x = 2a is

  • 3πa2 sq unit

  • 3πa22 sq unit

  • 3πa24 sq unit

  • 6πa25 sq unit


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105.

The area bounded by the curves y2 = 4a2(x - 1) and lines x = 1 and y = 4a is

  • 4a2 sq unit

  • 16a3 sq unit

  • 16a23 sq unit

  • None of these


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106.

The solution of the differential equation x + y2dydx = a2 is

  • x + y2 = a2x2 + C

  • (x + y)2 = a2x + C

  • (x + y)2 = 2a2x + C

  • None of the above


D.

None of the above

Given that, x + y2dydx = a2Put, x + y = v and dydx = dvdx = - 1 v2dvdx - 1 = a2 dvdx = a2 + v2v2 1 - a2a2 + v2dv = dxOn integrating, we get      v - a tan-1va = x + C x +y - a tan-1x +ya = x + C         y = a tan-1x +ya + C


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107.

The area bounded by y = log(x), x-axis and ordinates x = 1, x = 2 is

  • 12log22

  • log(2/e)

  • log(4/e)

  • log(4)


108.

The area of the segment of a circle of radius a subtending an angle of 2α at the centre is :

  • a2α + 12sin2α

  • 12a2sin2α

  • a2α - 12sin2α

  • a2α


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109.

Area bounded by the curve y = loge(x), x = 0, y  0 and x - axis is :

  • 1 sq unit

  • 12 sq unit

  • 2 sq unit

  • None of these


110.

The volume of the solid generated by the revolution of the curve y = a3a2 + x2 about x - axis is :

  • 12π3a2

  • π3a2

  • 12π2a3

  • π2a3


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