The two curves x3 - 3xy2 + 2 = 0 and 3x2y - y3 = 2 from Mathemat

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 Multiple Choice QuestionsMultiple Choice Questions

311.

If f(x) = 3sinπx5x, x  02k,            x = 0 is continuous at x = 0, then the value k is

  • π10

  • 3π10

  • 3π2

  • 3π5


312.

If f(x) = 3x - 8, if x  52k,        if x > 5 is continuous, then find k.

  • 4/7

  • 2/7

  • 7/2

  • 3/7


313.

The function f(x) = [x], where [x] denotes greatest integer function, is continuous at

  • 1

  • 4

  • 1.5

  • - 2


314.

If y = log1 - x21 + x2, then dydx is equal to

  • 11 - x4

  • - 4x1 - x4

  • - 4x31 - x4

  • 4x31 - x4


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315.

The two curves x3 - 3xy2 + 2 = 0 and 3x2y - y3 = 2

  • cut at angle π/3

  • touch each other

  • cut at angle π4

  • cut at right angle


D.

cut at right angle

On differentiating x3 - 3xy2 + 2 = 0 w.r.t. x, we get3x2 - 3y2 + 2xyy' = 0  3x2 - 3y2 - 6xyy' = 0 y' = 3x2 - 3y26xy = m1On differentating 3x2y - y3 = 2 w.r.t. x, we get   32xy + x2y' - 3y2y' = 0 6xy + 3x2y' - 3y2y' = 0 y'3x2 - 3y2 + 6xy = 0       y' = - 6xy3x2 - 3y2 = m2Now, m1 × m2 = 3x2 - 3y26xy- 6xy3x2 - 3y2 = - 1Hence, both curves cut at right angle.


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316.

If y = esin-1t2 - 1 and x = esec-11t2 - 1, then dydx is equal to

  • xy

  • - yx

  • yx

  • - xy


317.

If xy = ex - y, then dydx is equal to

  • logxlogx - y

  • exxx - y

  • logx1 + logx2

  • 1y - 1x - y


318.

The function f(x) = [x], where [x] is the greatest integer function, is continuous at

  • 1.5

  • 4

  • 1

  • - 2


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319.

If tan-1x2 + y2 = α, then dydx is equal to

  • - xy

  • xy

  • xy

  • - xy


320.

If y = fxgxhxlmnabc, then dydx is equal to

  • f'xg'xh'xlmnabc

  • lmnfxgxhxabc

  • f'xlag'xmbh'xnc

  • lmnabcf'xg'xh'x


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