If the radius of a circle be increasing at a uniform rate of 2 cm

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 Multiple Choice QuestionsMultiple Choice Questions

211.

The function f(x) = log1 + x - 2x2 + x is increasing on

  • - 1, 

  • - , 0

  • - , 

  • None of these


212.

The minimum value of x2 + 11 + x2 is at

  • x = 0

  • x = 1

  • x = 4

  • x = 3


213.

The maximum value of 3 cosθ + 4 sinθ is

  • 3

  • 4

  • 5

  • None of these


214.

The function x5 - 5x4 + 5x3 - 1 is

  • neither maximum nor minimum at x = 0

  • maximum at x = 0

  • maximum at x = 1 and minimum at x = 3

  • minimum at x = 0


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215.

If the radius of a circle be increasing at a uniform rate of 2 cm/s. The area of increasing of area of circle, at the instant when the radius is 20 cm, is

  • 70 π cm2/s

  • 70 cm2/s

  • 80 π cm2/s

  • 80 cm2/s


C.

80 π cm2/s

Given, drdt = 2 cm/s, where r be radius of circle and t be the time.Now, area of circle is given by A = πr2.On differentiating w.r.t. t, we get     dAdt = 2πrdrdt dAdt = 2π . 20 . 2 dAdt = 80 π cm2/s

Thus, the rate of change of area of circle with respect to time is 80 π cm2/s.


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216.

The equation of normal at the point (0, 3) of the ellipse 9x2 + 5y2 = 45 is

  • x-axis

  • y-axis

  • y + 3 = 0

  • y - 3 = 0


217.

The maximum value of x1/x is :

  • 1/ee

  • e

  • e1/e

  • 1/e


218.

The function f defined by f(x) = 4x4 - 2x + 1 is increasing for :

  • x < 1

  • x > 0

  • x < 1/2

  • x > 1/2


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219.

A particle moves in a straight line so that s = t, then its acceleration is proportional to :

  • (velocity)3

  • velocity

  • (velocity)2

  • (velocity)3/2


220.

If the line ax + by + c = 0 is a normal to the curve y =1, then :

  • a > 0, b > 0

  • a > 0, b < 0

  • a < 0, b < 0

  • Data is insufficient


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