The value of x for which the polynomial 2x3 - 9x2 + 12x + 4 is a

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If y = 2x . 32x - 1, then d2ydx2 is equal to :

  • log2log3

  • log18

  • log182y2

  • log18y


2.

If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing, is

  • a constant

  • proportional to the radius

  • inversely proportional to the radius

  • inversely proportional to the surface area


3.

The length of the subtangent to the curve x2 + xy + y2 = 7 at (1, - 3) is :

  • 3

  • 5

  • 35

  • 15


4.

If y = x + x2 + x3 + ... to  where x < 1, then for y < 1dxdy is equal to :

  • y + y2 + y3 + ... to 

  • 1 - y + y2 - y3 + ... to 

  • 1 - 2y + 3y- ... to 

  • 1 + 2y + 3y2 + ... to 


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5.

Twenty two metres are available to fence a flower bed in the form of a circular sector. If the flower bed should have the greatest possible surface area, the radius of the circle must be :

  • 4 m

  • 3 m

  • 6 m

  • 5 m


6.

If y = sinx + sinx + sinx + ... , then dydx is equal to :

  • cosx2y - 1

  • - cosx2y - 1

  • sinx1 - 2y

  • - sinx1 - 2y


7.

Given f(0) = 0 and f(x) = 11 - e- 1x for x  0. Then only one of the following statements on f (x) is true. That is f(x), is :

  • continuous at x = 0

  • not continuous at x = 0

  • both continuous and differentiable at x = 0

  • not defined at x = 0


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8.

The value of x for which the polynomial 2x3 - 9x2 + 12x + 4 is a decreasing function of x, is :

  • - 1 < x < 1

  • 0 < x < 2

  • x > 3

  • 1 < x < 2


D.

1 < x < 2

 fx =  2x3 - 9x2 + 12x + 4On differentiating w.r.t. x, we getf'(x) = 6x2 - 18x + 12For function to be decreasing f'(x) < 0      6 (x2 - 3x + 2) < 0 (x2 - 2x - x + 2) < 0       (x - 2) (x - 1) < 0                      1< x < 2


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9.

The range of the function sinsin-1x + cos-1x, x  1 :

  • [- 1, 1]

  • [1, - 1]

  • {0}

  • {1}


10.

Let f : R  R : f(x) = x2 and g : R  R : g(x) = x + 5, then gof is :

  • (x + 5)

  • (x + 52)

  • (x2 + 52)

  • (x2 + 5)


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