Let f : [- 1, 3] → R be defined as f(x) =&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

171.

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


172.

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


173.

If the derivative of the function f(x) is every where continuous and is given by

fx = bx2 + ax + 4; x  - 1ax2 + b;          x < - 1, then :

  • a = 2, b = - 3

  • a = 3, b = 2

  • a = - 2, b = - 3

  • a = - 3, b = - 2


174.

If f(x + y) = f(x)f(y) for all real x and y, f(6) = 3 and f'(0) = 10, then f'(6) is :

  • 30

  • 13

  • 10

  • 0


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175.

Derivative of sec-111 - 2x2 w . r. t sin-13x - 4x3 is :

  • 14

  • 32

  • 1

  • 23


176.

Let f : R  R be a diiferentiable function Satisfyingf'(3) + f'(2) = 0. Then limx01 + f3 + x - f31 + f2 - x - f21x is equal to :

  • 1

  • e

  • e- 1

  • e2


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177.

Let f : [- 1, 3]  R be defined as f(x) = x + x,  - 1 x < 1  x + x,      1  x < 2  x +x,      2 x 3 where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at :

  • only three points

  • only one point

  • only two points

  • four or more points


A.

only three points

fx = - x - 1, - 1  x < 0x,                 0  x < 12x,               1  x < 2x +2,          2 x < 36,                 x = 3 f(x) is discontinuous at 0, 1, 3.


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178.

If the function f(x) = a|π - x| + 1,     x  5bx - π + 3,     x > 5 is continuous at x = 5, then the value of a - b is

  • - 2π + 5

  • 2π + 5

  • 2π - 5

  • 25 - π


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179.

If fx = x - x4, x  R , where [x] denotes the greatest integer function, then:

  • Both limx4-fx and limx4+fx exist but noot equal

  • f is continuous at x = 4

  • limx4-fx exist but limx4+fx does not exist

  • limx4+fx exist but limx4-fx does not exist


180.

If the function f defined on π6, π3 by f(x) = 2cosx - 1cotx - 1, x  π4k,                       x = π4 is continuous, then k is equal to :

  • 2

  • 12

  • 12

  • 1


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