If 1 - x2 + 1 - y2 = 

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Domain of y = cot-1x is

  • - , 0

  • 0, 

  • - , 

  • None of these


2.

If limx0log3 + x - log3 - xx = k, then the value of k will be

  • 0

  • - 13

  • 23

  • - 23


3.

For the function 3x4 - 8x3 + 12x2 - 48x + 25 in the interval [1, 3]. The value of maxima and minima are

  • 16, - 39

  • - 16, 39

  • 6, - 9

  • None of these


4.

f(x) = x3 - 27x + 5 is an increasing function when

  • x < - 3

  • x >3

  • x  - 3

  • x <3


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5.

In the interval 0, π2 function log(sin(x)) is

  • increasing

  • decreasing

  • neither increasing nor decreasing

  • None of the above


6.

A cone of maximum volume is being cut from sphere, then ratio between height of cone and diameter of sphere is

  • 23

  • 13

  • 34

  • 14


7.

The nth derivative of e2x + 5 is

  • 22nn! e2x + 5

  • 2n e2x + 5

  • 22n e2x + 5

  • 2nn e2x + 5


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8.

If 1 - x2 + 1 - y2 = ax - y, then dydx is equal to

  • 1 - x21 - y2

  • 1 - y21 - x2

  • x2 - 11 - y2

  • y2 - 11 - x2


B.

1 - y21 - x2

1 - x2 + 1 - y2 = ax - yPut x = sinθ and y = sinϕ 1 - sin2θ + 1 - sin2ϕ = asinθ - sinϕ cosθ + cosϕ = asinθ - sinϕ 2cosθ + ϕ2 . cosθ + ϕ2 = a2cosθ + ϕ2 . sinθ - ϕ2 cotθ - ϕ2 = a θ - ϕ = 2cot-1a sin-1x - sin-1y = 2cot-1aOn differentiating w.r.t. x, we get dydx = 1 - y21 - x2 = 1 - y21 - x2


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9.

Function f(x) = x - 1,   x < 22x - 3, x  2 is continuous function for

  • all real values of x

  • only x = 2

  • only real values of x, when x  2

  • the integer values of x


10.

If g(x) = x2 + x - 2 and gof(x) = 2x2 - 5x+ 2, then f(x) is equal to

  • 2x - 3

  • 2x + 3

  • 2x2 + 3x + 1

  • 2x2 - 3x - 1


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