If x = f(t) and y = g(t) are differentiable functions of t, then

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The maximum value of fx = logxxx  0, x  1 is

  • e

  • 1e

  • e2

  • 1e2


2.

If g(x) is the inverse function of f(x) and f'x = 11 +x4, then g'(x) is

  • 1 + [g(x)]4

  • 1 - [g(x)]4

  • 1 + [f(x)]4

  • 11 + g(x)4


3.

The inverse of the matrix 10033052- 1 is

  • - 13- 30031092- 3

  • - 13- 3003- 10- 9- 23

  • - 133003- 10- 9- 23

  • - 13- 300- 3- 10- 9- 23


4.

If the function f(x) = tanπ4 + x1x for x  0 is  = K for x = 0 continuous at x = 0, then K = ?

  • e

  • e- 1

  • e2

  • e- 2


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5.

For a invertible matrix A if A(adjA) = 100010 then A =

  • 100

  • - 100

  • 10

  • - 10


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6.

If x = f(t) and y = g(t) are differentiable functions of t, then d2ydx2 is

  • f't . g''t - g't . f''tf't3

  • f't . g''t - g't . f''tf't2

  • g't . f''t - f't . g''tf't3

  • g't . f''t + f't . g''tf't3


A.

f't . g''t - g't . f''tf't3

Given, x = f(t) and y = g(t)On differentiating both sides w.r.t. 't', we getdxdt = f't and dydt = g'tWe know that, dydx = dydtdxdt                   dydx = g'tf'tAgain, differentiating both sides w.r.t. 'x', we getd2ydx2 = f't . g''t - g't . f''tf't2 . dtdxd2ydx2 = f't . g''t - g't . f''tf't3


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7.

If α and β are roots of the equation x2 + 5x - 6 = 0, then the value of tan-1α - tan-1β is

  • π2

  • 0

  • π

  • π4


8.

If the volume of spherical ball is increasing at the rate of 4π cm3/s, then the rate of change of its surface area when the volume is 288 π cm3, is

  • 43π cm2/s

  • 23π cm2/s

  • 4π cm2/s

  • 2π cm2/s


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9.

If f(x) = = logsec2xcot2x for x  0= K                         for x = 0 is continuous at x = 0, then K is

  • e- 1

  • 1

  • e

  • 0


10.

If the inverse of the matrix α14- 1231623 does not exist, then the value of α is

  • 1

  • - 1

  • 0

  • - 2


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