y = Aex + Be2x + Ce3x satisfies the differential equation f

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

71.

3 - x21 - 2x + x2exdx = exfx + c  fx

  • 1 + x1 - x

  • 1 - x1 + x

  • 1 - xx - 1

  • x - 11 + x


72.

cotxsinxcosxdx = - fx + c  fx

  • 2tanx

  • - 2tanx

  • - 2cotx

  • 2cotx


73.

- π2π2log2 - sinθ2 + sinθ is equal to

  • 0

  • 1

  • 2

  • - 1


74.

The area bouned by y = x2 + 2, x-axis, x = 1 and x = 2 is

  • 163

  • 173

  • 133

  • 203


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75.

022x - 22x - x2dx is equal to

  • 0

  • 2

  • 3

  • 4


76.

Integrating factor of (x + 2y3)dydx = y2 is

  • e1y

  • e- 1y

  • y

  • - 1y


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77.

y = Aex + Be2x + Ce3x satisfies the differential equation

  • y''' - 6y'' + 11y' - 6y = 0

  • y''' + 6y'' + 11y' + 6y = 0

  • y''' + 6y'' - 11y' + 6y = 0

  • y''' - 6y'' - 11y' + 6y = 0


A.

y''' - 6y'' + 11y' - 6y = 0

Given that,      y = Aex + Be2x + Ce3x       ...iOn differentiating both sides w.r.t x, we get     y' = Aex + 2Be2x + 3Ce3x y' = y + Be2x + 2Ce3x       ...iiAgain differentiating both sides w.r.t x, we get    y'' = y' + 2Be2x + 6Ce3xFrom Eq. (ii)Be2x = y' - y - 2Ce3x y'' = y' + 2y' - 2y - 4Ce3x + 6Ce3x     y'' = 3y' - 2y + 2Ce3x      ...iiiAgain differentiating both sides w.r.t x, we get2Ce3x = y'' - 3y' + 2y y''' = 6y'' - 11y' + 6y y''' - 6y'' + 11y' - 6y = 0


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78.

Observe the following statements

A. Integrating factor of dydx + y = x2 is ex

R. Integrating factor of dydx + Pxy = Qx is ePxdx

  • A is true, R is false

  • A is false, R is true

  • A is true, R is true, R  A

  • Both are false


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79.

For any integer n > 1, the number of positive divisors of n is denoted by d(n). Then, for a prime P, d (d (d(P)7)) is equal to

  • 1

  • 2

  • 3

  • p


80.

k = 1513 + 23 + .... + k31 + 3 + 5 + ... + 2k - 1 is equal to

  • 22.5

  • 24.5

  • 28.5

  • 32.5


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