A differentiable function f(x) is defined for all x > 0 and sa

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The equation of the tangent to the curve y = 1 + xy + sin-1sin2x

  • x - y + 1 = 0

  • x + y + 1 = 0

  • 2x - y + 1 = 0

  • x + 2y + 2 = 0


2.

If 2132A- 325- 3 = 1001, then A is equal to :

  • - 1110

  • 1101

  • 1011

  • 0111


3.

The point on the curve y = 2x2 - 6x - 4 at which the tangent is parallel to the x-axis, is :

  • 32, 132

  • - 52, - 172

  • 32, 172

  • 32, - 172


4.

The value of cosx - acosx + acosxsinx + asinx - asinxcosatanxcosacotxcsc2x is equal to :

  • 1

  • sinacosa

  • 0

  • sinxcosx


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5.

Let f be twice differentiable function such that f"(x) = - f(x) and f'(x) = g(x), h(x) = {f(x)}2 + {g(x)}2. If h(5) = 11, then h(10) is equal to :

  • 22

  • 11

  • 0

  • 20


6.

Suppose A is a matrix of order 3 and B = AA-1. If A = - 5, then B is equal to :

  • 1

  • - 5

  • - 1

  • 25


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7.

A differentiable function f(x) is defined for all x > 0 and satisfies f(x3) = 4x4 for all x > 0. The value of f'(8) is :

  • 163

  • 323

  • 1623

  • 3223


B.

323

fx3 = 4x4  x > 0Let x3 = t  x = t13    ft = 4t43On differentiating w.r.t. t, we get        f't = 4 . 43t43 - 1 = 4 . 43t13 f'x3 = 163x313 = 163x f'8 = f'23 = 163 × 2 = 323


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8.

The value of cos2tan-1- 7 is :

  • 4950

  • - 4950

  • 2425

  • - 2425


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9.

If 2- 3i133i- 143i = x + iy, then :

  • x = 3, y = 1

  • x = 2, y = 5

  • x = 0, y = 0

  • x = 1, y = 1


10.

The value of the C410C510Cm11C611C711Cm + 212C812C912Cm + 413 = 0 when m is equal to :

  • 6

  • 5

  • 4

  • 1


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