The area between the curve y = 2x4 - x2, the X-axis and the

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 Multiple Choice QuestionsMultiple Choice Questions

41.

The area of the region bounded by y2 = x and y = x is

  • 13sq. unit

  • 16 sq. units

  • 23 sq. units

  • 1 sq. units


42.

The equation of one of the curves whose slope at any point is equal to y + 2x is

  • y = 2(ex + x - 1)

  • y = 2(ex - x - 1)

  • y = 2(ex - x + 1)

  • y = 2(ex + x + 1)


43.

The area enclosed by y = 3x - 5y = 0, x = 3 and x = 5 is

  • 12 sq units

  • 13 sq units

  • 1312 sq units

  • 14 sq units


44.

The area bounded by the parabolas y = 4x2y = x29 and the line y = 2 is

  • 523 sq units

  • 1023 sq units

  • 1523sq units

  • 2023 sq units


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45.

The slope at any point of a curve y = f(x) is given by dydx = 3x2 and it passes through (-1, 1). The equation of the curve is 

  • y = x3 + 2

  • y = - x3 - 2

  • y = 3x3 + 4

  • y = - x3 + 2


46.

The area enclosed between the curve y = 1 + x2, the y-axis and the straight line y = 5 is given by

  • 143 unit

  • 73 unit

  • 5 sq unit

  • 163


47.

Area bounded by the curve y2 = 16x and line y = mx is 23, then m is equal to

  • 3

  • 4

  • 1

  • 2


48.

Area included between curves y = x2 - 3x + 2 and y = - x2 + 3x - 2 is

  • 16 sq unit

  • 12 sq unit

  • 1 sq unit

  • 13 sq unit


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49.

The area between the curve y = 2x- x2, the X-axis and the ordinates of two minima of the curve is

  • 7/120

  • 9/120

  • 11/120

  • 13/120


A.

7/120

We have,

        y = 2x4 - x2

 dydx = 8x3 - 2xOn putting dydx = 0, we get x = 0, x = ± 1/2Now, d2ydx2 = 24x2 - 2

It can be easily seen that y is minimum for x = ± 1/2

Thus, required area A is given by

A = - 1212ydx = - 12122x4 - x2dx A = 2012x4 - x2dx= 22x55 - x33012 = 7120


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50.

The value of the parameter a such that the area bounded by y = a2x2 + ax + 1, coordinate axes and the line x = 1 attains its least value is equal to

  • - 1

  • - 14

  • - 34

  • - 12


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