If x = acosθ + logtanθ2 

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 Multiple Choice QuestionsMultiple Choice Questions

101.

limx0 ex - esinx2x - sinx

  • - 12

  • 12

  • 1

  • 32


102.

If f(x) = sin1 + xx, for x  00                  , for x = 0

where [x] denotes the greatest integer not exceeding x, then limx0-fx is equal to

  • - 1

  • 0

  • 1

  • 2


103.

If f(x) = x - 5,     for x  14x2 - 9, for 1 < x < 23x + 4,  for x  2

then f'(2+) is equal to

  • 0

  • 2

  • 3

  • 4


104.

If 2x2 - 3xy + y2 + x + 2y - 8 = 0, then : dydx is equal to

  • 3y - 4x - 12y - 3x + 2

  • 3y - 4x + 12y + 3x + 2

  • 3y - 4x + 12y - 3x - 2

  • 3y - 4x + 12y + 3x + 2


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105.

If z = logtanx + tany, thensin2xzx + sin2yzy is equal to

  • 1

  • 2

  • 3

  • 4


106.

limx0 1 - exsinxx2 + x3 = ?

  • - 1

  • 0

  • 1

  • 2


107.

If R  R is defined by f(x) = x - 3 + x - 4 for x  R, thenlimx3 -f(x)  = ?

  • - 2

  • - 1

  • 0

  • 1


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108.

If x = acosθ + logtanθ2 and y = asinθ, then dydx = ?

  • cotθ

  • tanθ

  • sinθ

  • cosθ


B.

tanθ

Given that,x = acosθ + logtanθ2 and y = asinθOn differentiating w.r.t. θ respectively, we getdy = a-sinθ + 1tanθ2 . sec2θ2 . 12       = a- sinθ + 1sinθ = acos2θsinθand dy = acosθ dydx = dydx = acosθacos2θsinθ           = tanθ


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109.

x = 1 - y1 + y  dydx is equal to

  • 4x + 12

  • 4x - 1x + 13

  • x - 11 + x3

  • 41 + x3


110.

limxx + 5x +2x + 3 equals

  • e

  • e2

  • e3

  • e5


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