The second order derivative of a sin3t with respec

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 Multiple Choice QuestionsMultiple Choice Questions

61.

If y = 2x- 2x2 + 3x - 5, then for x = 2 and x = 0.1, value of y is

  • 2.002

  • 1.9

  • 0

  • 0.9


62.

If the function

fx = x2 - A + 2x + Ax - 2,       for x  22,                                         for x = 2

is continuous at x = 2, then

  • A = 0

  • A = 1

  • A = - 1

  • A = 2


63.

fx = x + - x,      when x  2λ,                       when x = 2

If f (x) is continuous at x = 2 then, the value of λ will be

  • - 1

  • 1

  • 0

  • 2


64.

For what values of x, the function f(x) = x4 - 4x3 + 4x2 + 40 is monotonic decreasing ?

  • 0 < x < 1

  • 1 < x < 2

  • 2 < x < 3

  • 4 < x < 5


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65.

In which of the following functions, Rolle's theorem is applicable

  • f(x) = f(x) = x in - 2 x 2

  • fx = tanx in 0  x  π

  • fx = 1 + x - 223 in 1  x  3

  • fx = xx - 22 in 0  x  2


66.

If y = (1 + x)(1 + x2)(1 + x4)...(1 + x2n) then the value of dydxx = 0 is

  • 0

  • - 1

  • 1

  • 2


67.

f(x) = x + x is continuous for

  • x  - , 

  • x  - ,  - 0

  • only x > 0

  • no value of x


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68.

The second order derivative of a sin3t with respect to cos3t at t = π4 is

  • 2

  • 112a

  • 423a

  • 3a42


C.

423a

Let y = asin3t, x = acos3t

On differentiating w.r.t. t, we get

     dydt = 3asin2tcost, dxdt = - 3acos3tsint dydx = 3asin2tcost- 3acos3tsint dydx = - sintcost - tant

Again, differentiating w.r.t. x, we get

     d2ydx2 = - sec2t . dtdx             = - sec2t- 3acos2tsint = 13acos4tsint d2ydx2t = π4 = 13a124 . 12                         = 253a = 423a


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69.

If x2 + y2 = 1, then

  • yy'' - (2y')2 + 1 = 0

  • yy'' + (y')2 + 1 = 0

  • yy'' - (y')2 - 1 = 0

  • yy'' + 2(y')2 + 1 = 0


70.

The Rolle's theorem is applicable in the interval - 1  x  1 for the function

  • f(x) = x

  • f(x) = x2

  • f(x) = 2x3 + 3

  • f(x) = x


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