limx→22 -  2 + x21/3 - (4

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 Multiple Choice QuestionsMultiple Choice Questions

371.

If fx = log1 + x1 - x and gx = 3x +x31 + 3x2, then fog(x) is equal to

  • - f(x)

  • 3f(x)

  • [f(x)]3

  • None of these


372.

Let f(x) be differentiable on the interval (0, ) such that f(1) =1 and limtt2fx - x2ftt - x = 1 for each x > 0. Then, f(x) is equal to

  • 13x + 23x2

  • - x3 + 4x23

  • - 1x

  • - 1x + 2x2


373.

The number of points, where f(x) = [sin(x) + cos(x)] (where [] denotes the greatest integerfunction) and x  (0, 2) is not continuous, is

  • 3

  • 4

  • 5

  • 6


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374.

limx22 -  2 + x21/3 - (4 - x)1/3  is equal to

  • 2 . 3-1/2

  • 3 . 2-4/3

  • - 3 . 24/3

  • None of the above


C.

- 3 . 24/3

limx22 -  2 + x21/3 - (4 - x)1/3  00  form =limx20 -  122 + x0 - 13 . - 1(4 - x)1/3 = limx2- 3(4 - x)2/322 +x= - 32 × 4 - 2232 + 2= - 32 × 2232 = - 3 . 232 - 2= - 3 . 24/3


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375.

If 2a + 3b + 6c = 0, then the equation ax2 + bx + c = 0 has atleast one real root in

  • (0, 1)

  • 0, 12

  • 14, 12

  • None of the above


376.

If f(x) = sinπx2, if x < 13 - 2x,   if x  1, then f(x) has

  • local minimum at x = 1

  • local maximum at x = 1

  • Both local maximum and local minimum at x = 1

  • None of the above


377.

Let f : R  R be a differentiable function and f(1) = 4. Then, the value of limx14fx2tx - 1dt is

  • 8f'(1)

  • 4f'(1)

  • 2f'(1)

  • f'(1)


378.

If f''(x) = - f(x) and g(x) = f'(x) anf F(x) = fx22 + x22 and given that F(5) = 5, then the value of F(10) is

  • 15

  • 0

  • 5

  • 10


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379.

A function g defined for all real x > 0 satisfies g(1) = 1, g'(x2) = x3 for all x > 0, then value of g(4) is

  • 133

  • 3

  • 675

  • None of these


380.

A particle moving on a curve has the position at a time t is given by x = f'(t)sin(t) + f'(t)cos(t), y = f'(t)cos(t) - f'(t)sin(t), where f is a twice differentiable function. Then, the velocity of the particle at time t is

  • f'(t) + f''(t)

  • f'(t) - f''(t)

  • f'(t) + f'''(t)

  • f'(t) - f''(t)


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