If log (1 + x) -  2x2 + x is increasing, then

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 Multiple Choice QuestionsMultiple Choice Questions

301.

If f'(x) > 0, x  R, f'(3) = 0 and g(x) = ftan2x - 2tanx + 4, 0 < x < π2, then g(x) is increasing in

  • 0, π4

  • π6, π3

  • 0, π3

  • π4, π2


302.

The radius of a cylinder is increasing at the rate of 2 m/s and its height is decreasing at the rate of 3 m/s. When the radius is 3 m and height is 5 m, then the volume of the cylinder would change at the rate of

  • 87π m3/s

  • 33π m3/s

  • 27π m3/s

  • 15π m3/s


303.

The values of a, if f(x) =2ex - ae-x + 2a +1x - 3  increases x, are in

  • [0, )

  • (- , 0]

  • - , 

  • 1, 


304.

A cylindrical tank of radius 2 m is being filled with rice at the rate of 314 cubic m/h. The depth ofthe rice is increasing at the rate of

  • 25 cubic m/h

  • 0.25 cubic m/h

  • 1 cubic m/h

  • 34 cubic m/h


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305.

The distance of the point on the curve x2 = 2y, which is nearest to the pont (0, 5) is

  • 3

  • 4

  • 22

  • None of these


306.

The minimum value of x - αx - β is

  • 0

  • αβ

  • 14α - β2

  • - 14α - β2


307.

The equation of tangent to the curve 6y = 7 - x3 at (1, 1) is

  • 2x + y = 3

  • x + 2y = 3

  • x + y = 1

  • x + y + 2 = 0


308.

The maximum value of xy subject to x + y = 7 is

  • 10

  • 12

  • 494

  • 554


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309.

The family of curves in which the sub-tangent at any point to any curve is double the abscissa is given by

  • x = Cy2

  • y = Cx2

  • x2 = Cy2

  • y2 = Cx2


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310.

If log (1 + x) -  2x2 + x is increasing, then

  • 0 < x < 

  • -  < x < 0

  • -  < x < 

  • - 1 < x < 2


C.

-  < x < 

Let fx = log1 + x - 2x2 + x2f'x  = 11 + x _ 22 + x + 2x2 + x2For increasing function, f'x > 0 2 + x2 - 22 + x1 + x + 2x1 + x > 0 4 + x2 + 4x - 4 - 5x -2x2 + 2x +2x2  > 0x2  > 0This shows x lies between -  to 


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