If the displacements of a particle at time t is given by s2 = at2

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 Multiple Choice QuestionsMultiple Choice Questions

151.

If f(x) = 2x + 42x, then f'(2) is equal to

  • 0

  • - 1

  • 1

  • 2


152.

Let f(x + y) = f(x) f(y) and f(x) = 1 + sin(3x) g(x), where g is differentiable.The f'(x) is equal to

  • 3f(x)

  • g(0)

  • f(x)g(0)

  • 3g(x)


153.

If f(x) = x2 - 9x - 3,    if x  32x + k,    otherwise is continuous at x = 3, then k is equal to :

  • 3

  • 0

  • - 6

  • 16


154.

ddxxx is equal to :

  • logx

  • logex

  • xxlogx

  • xxlogex


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155.

If the displacements of a particle at time t is given by s2 = at2 + 2bt + c, then acceleration varies as :

  • 1s2

  • 1s

  • 1s3

  • s3


C.

1s3

Given that, s = at2 + 2bt +cOn differentiating w.r.t. t, we get     dsdt = 12at2 + 2bt + c2at + 2b dsdt = at +bat2 + 2bt + c = at + bsAgain differentiating, we get    d2sdt2 = sa - at + bdsdts2           = sa - at +bat +bss2           = s2a - at + b2s3           = at2 + 2bt +ca - at + b2s3           = ac - b2s3 Acceleration varies as 1s3.


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156.

Let f(x) be twice differentiable such that f''(x) = - f(x), f'(x) = g(x), where f'(x) and f''(x) represent the first and second derivatives of f(x) respectively. Also, if h(x) = [f(x)]2 + [g(x)]2 and h(S) = 5, then h(10) is equal to :

  • 3

  • 10

  • 13

  • 5


157.

If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is :

  • a constant

  •  s2

  •  1s2

  •  s


158.

If f(x) = 2x - 11 + x - 1, - 1  x < , x  0k,                         x = 0 is continuous everywhere, then k is equal to:

  • 12log2

  • log4

  • log8

  • log2


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159.

If sin-1x + sin-1y = π2, then dydx is equal to :

  • xy

  • - xy

  • yx

  • - yx


160.

If g(x) = min (x, x) where x is a real number, then :

  • g(x) is an increasing function

  • g(x) is a decreasing function

  • g(x) is a constant function

  • g(x) is a continuous function except at x = 0


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