If y = sin-13x - 4x3 + cos-14x

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 Multiple Choice QuestionsMultiple Choice Questions

101.

Let f(x)= sin(x), g(x) = x and h(x) = loge(x). If F(x) = (hogof)(x), then F"(x) is equal to

  • csc3x

  • 2cotx2 - 4x2csc2x2

  • 2xcotx2

  • - 2csc2x


102.

If y = tan-14x1 + 5x2 + tan-12 + 3x3 - 2x, then dydx is equal to

  • 51 + 25x2

  • 11 + 25x2

  • 0

  • 51 - 25x2


103.

If y = logax + logxa + logxx + logaa, then dydx is equal to

  • 1x + xloga

  • logax + xloga

  • 1xloga + xloga

  • None of the above


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104.

If y = sin-13x - 4x3 + cos-14x3 - 3x + tan-1E, then dydx is equal to

  • 5

  • 0

  • 21 + x2

  • 11 - x2


B.

0

 Given, sin-13x - 4x3 + cos-14x3 - 3x + tan-1E y = 3sin-1x + 3cos-1x + tan-1E y = 3π2 + tan-1EOn differentiating w.r.t. x, we get  dydx = 0


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105.

If fx = x - 14 + x - 1312 + x - 1520 + x - 1728 + ..., where 0 < x < 2, then f'(x) is equal to

  • 14x2 - x

  • 14x - 22

  • 12 - x

  • 12 + x


106.

If f(x) = sin(x), the derivative of f(log(x)) w.r.t. x is

  • cos(x)

  • f'(log(x))

  • cos(log(x))

  • coslogxx


107.

If f(x + y) = 2 f(x) f(y), f'(5) = 1024log(2) and f(2) = 8,  then the value of f'(3) is

  • 64(log(2))

  • 128(log(2))

  • 256

  • 256log(2)


108.

The number of discontinuities of the greatest integer function f (x) = [x], x  - 72, 100 is equal to

  • 104

  • 100

  • 102

  • 103


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109.

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

  • 3π10

  • 3π5

  • π10

  • 3π2


110.

If y = sincos-1sincos-1x, then dydx at x = 12 is equal to

  • 0

  • - 1

  • 23

  • 1


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