The functions f, g and h satisfy the relations f'(x) = g (x + 1)

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

141.

If y = sin-12x1 - x2, - 12  x  12, then dydx is equal to

  • x1 - x2

  • 11 - x2

  • 21 - x2

  • 2x1 - x2


142.

The function fx = 2x2 - 1,     if 1  x  4151 - 30x, if 4 < x  5 is not suitable to apply Rolle's theorem, since

  • f(x) is not continuous on [1, 5]

  • f(1) f(5)

  • f(x) is continuous only at x = 4

  • f(x) is not differentiable at x = 4


143.

The number of points at which the function fx = 1logex is discontinuous, is

  • 1

  • 2

  • 3

  • infinitely many


Advertisement

144.

The functions f, g and h satisfy the relations f'(x) = g (x + 1) and g'(x) = h(x - 1). Then, f"(2x) is equal to

  • h(2x)

  • 4h(2x)

  • h(2x - 1)

  • h(2x + 1)


A.

h(2x)

We have,

f'(x) = g(x + 1)

 f''x = g'x + 1But g'x = hx - 1 g'x + 1 = hx + 1 - 1                     = hx         f''x = hx       f''2x = h2x


Advertisement
Advertisement
145.

If f(x) = sin-11 - cos2x2sinx, then f'x is equal to

  • sinx

  • x

  • 0

  • 1


146.

If y xx + 1 + x + 1x, then d2ydx2 at x = 1 is equal to

  • 74

  • 78

  • 14

  • - 78


147.

If 2x + 2y = 2 then the value of dydx at (1, 1) is equal to

  • - 2

  • - 1

  • 0

  • 1


148.

Let y = tan-1secx + tanx. Then dydx is equal to

  • 14

  • 12

  • 1secx + tanx

  • 1sec2x


Advertisement
149.

If s = sec-112x2 - 1 and t = 1 - x2, then dsdt at x = 12 is

  • 1

  • 2

  • - 2

  • 4


150.

If y = f(x) is continuous on [0, 6], differentiable on (0, 6), f(0) = - 2 and f(6) = 16, then at some point between x = 0 and x = 6, f'(x) must be equal to

  • - 18

  • - 3

  • 3

  • 14


Advertisement