If y = cos-1a2 - x2a2 + x2&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

421.

If z = sec-1x4 + y4 - 8x2y2x2 + y2, then xzy + yzy is equal to

  • cotz

  • 2cotz

  • 2tanz

  • 2secz


422.

If f : R  R is defined byf(x) = 2sinx - sin2x2xcosx, if x  0,                          a , if x = 0, then the value of a so that f is continuous at 0 is

  • 2

  • 0

  • 1

  • 2


423.

x = cos-111 +t2, y = sin-1t1 +t2  dydx = ?

  • 0

  • tan(t)

  • 1

  • sin(t)cos(t)


424.

ddxa tan-1x + blogx - 1x + 1 = 1x4 - 1  a - 2b = ?

  • 1

  • 0

  • - 1

  • 2


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425.

y = easin-1x  1 - x2yn +2 - 2n +1xyn +1 is equal to

  • -n2 +a2yn

  • n2 -a2yn

  • n2 +a2yn

  • -n2 - a2yn


426.

If f : R  R defined byf(x) = 1 + 3x2 - cos2xx2, for x  0k, for x= 0is continuous at x = 0, then k is equal to

  • 1

  • 5

  • 6

  • 0


427.

If f(x) = cosxcos2x. . . cosnx, then f'(x) + r = 1n rtanrxfx = ?

  • f(x)

  • 0

  • - f(x)

  • 2f(x)


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428.

If y = cos-1a2 - x2a2 + x2 + sin-12axa2 + x2,then dydx = ?

  • ax2 + a2

  • 2ax2 + a2

  • 4ax2 + a2

  • a2x2 + a2


C.

4ax2 + a2

y = cos-1a2 - x2a2 + x2 + sin-12axa2 + x2Put x = atanθ  θ = tan-1xa cos-1a2 - a2tan2θa2 + a2tan2θ + sin-12a2tanθa2 + a2tan2θ y = cos-11 - tan2θ1 + tan2θ + sin-12tanθ1 + tan2θ y =  cos-1cos2θ + sin-1sin2θ   cos2θ = 1 - tan2θ1 + tan2θ                                                                        sin2θ = 2tanθ1 + tan2θ  y = 2θ + 2θ y = 4θ y = 4tan-1xadydx = 4 11 + x2a21a = 4 a2a2 + x2 . 1a dydx = 4aa2 + x2


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429.

If fx = sinx + cosx,then fπ4fivπ4 = ?

  • 1

  • 2

  • 3

  • 4


430.

If y = sinmsin-1x, then 1 - x2y2 - xy1 = ?Here, yn denotes dnydxn

  • m2y

  • - m2y

  • 2m2y

  • - 2m2y


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