Consider a region R = {(x, y) ∈ R2 : x2 ≤y

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 Multiple Choice QuestionsMultiple Choice Questions

151.

The area of the region described by(x, y)/x2 + y  1 and y  1 - x is

  • π2 - 23

  • π2 + 23

  • π2 + 43

  • π2 - 43


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152.

Consider a region R = {(x, y)  R: xy  2x}. If a line y = α divides the area of region R into two equal parts, then which of the following is true ?

  • 3α2 - 8α + 8 = 0

  • α3 - 6α32 - 16 = 0

  • α3 - 6α2 + 16 = 0

  • 2 - 8α32 + 8 = 0


D.

2 - 8α32 + 8 = 0

04y - y20dy = 20y - y2dy 2y323 - y2204 = 22y323 - y240α 163 - 4 = 223α32 - α24 43 = 223α32 - α24 23 = 8α32 - 3α212 8α32 - 3α2 = 8


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153.

The area in sq unit of the region x, y; 12  y  sinx, 0  x  πis equal to

  • 3 - 2π

  • 3 - π6

  • 3 - π3

  • 3 - π3


154.

The area (in sq. units) of the region A = {x, y) : (x –1) [x]  y  2x, 0  x  2,where [t] denotes the greatest integer function, is :

  • 432 - 12

  • 832 - 1

  • 432 + 1

  • 832 - 12


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155.

The area (in sq. units) of the region A = x, y :x + y  1, 2y2  x :

  • 56

  • 76

  • 13

  • 16


156.

The area (in sq. units) of the region enclosed by the curves y = x2 – 1 and y = 1 – x2 is equal to :

  • 83

  • 72

  • 43

  • 163


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