If the tangent at (1, 1) on y = x(2 - x)2 meets the curve again a

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 Multiple Choice QuestionsMultiple Choice Questions

41.

Angle between y2 = x and x2 = y at the origin is

  • 2 tan-1(3/4)

  • tan-1(4/3)

  • π/2

  • π/4


42.

The distance covered by a particle in t seconds is given by x = 3 + 8t - 4t2. After 1 s its velocity will be

  • 0 unit/s

  • 3 unit/s

  • 4 unit/s

  • 7 unit/s


 Multiple Choice QuestionsShort Answer Type

43.

If the tangent to the parabola y = x(2 - x) at the point (1, 1) intersects the parabola at P. Find the coordinate of P.


 Multiple Choice QuestionsMultiple Choice Questions

44.

The maximum value of xy subject to x + y = 8

  • 8

  • 16

  • 20

  • 24


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45.

A particle moves along a straight line according to the laws = 16- 2t + 3t, where s metres is the distance of the particle from a fixed point at the end of t seconds. The acceleration of the particle at the end of 2s is

  • 36m/s2

  • 34m/s2

  • 36m

  • None of these


46.

The maximum slope of the curve y = - x3 + 3x2 + 2x - 27 is

  • 5

  • - 5

  • 15

  • None of these


47.

For the curve y = xe, the point

  • x = - 1 is a point of minimum

  • x = 0 is a point of minimum

  • x = - 1 is a point of maximum

  • x = 0 is a point of maximum


48.

If the slope of the curve y = axb - x at the point (1, 1) is 2, then

  • a = 1, b = - 2

  • a = - 1, b = 2

  • a = 1, b = 2

  • None of these


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49.

If the tangent at (1, 1) on y = x(2 - x)2 meets the curve again at P, then P is

  • (4, 4)

  • (- 1, 2)

  • (9/4, 3/8)

  • None of these


C.

(9/4, 3/8)

We have,

     y2 = x(2 - x)2            ...(i)

 y2 = x3 - 4x2 + 4x

On differentiating both sides w.r.t. x we get

       2ydydx = 3x2 - 8x + 4           dydx = 3x2 - 8x + 42y dydx1, 1 = 3 - 8 + 42 = - 12

The equation of the tangent at (1, 1) is

y - 1 = - 1/2 (x - 1)

 x +2y - 3 = 0         ...(ii)

On solving Eq. (i) and (ii), we get x = 9/4 and y = 3/8

Hence, the coordinates of Pare (9/4, 3/8).


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50.

If there is an error of K % is measuring the edge of a cube, then the per cent error in estimating its volume is

  • k

  • 3k

  • k3

  • None of these


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