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

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 Multiple Choice QuestionsMultiple Choice Questions

121.

Let f(x) = 2x3 - 9ax2 + 12a2x + 1, where a > 0. The minimum of f is attained at a point q and the maximum is attained at a point p. If p = q, then a is equal to

  • 1

  • 3

  • 2

  • 0


122.

The difference between the maximum and minimum value of of the function fx = 0xt2 + t + 1dt on [2, 3] is

  • 39/6

  • 49/6

  • 59/6

  • 69/6


123.

If a and b are the non-zero distinct roots of x2 + ax + b = 0, then the minimum value of x2 + ax + b is

  • 2/3

  • 9/4

  • - 9/4

  • - 2/3


124.

The equation of the tangent to the curve (1 + x2)y = 2 - x where it crosses the x-axis, is :

  • x + 5y = 2

  • x - 5y = 2

  • 5x - y = 2

  • 5x + y - 2 = 0


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125.

The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when the side is 10 cm, is:

  • 3 sq cm/s

  • 10 sq cm/s

  • 103 sq cm/s

  • 103 sq cm/s


126.

The function f(x) = 1 - x3 - x5 is decreasing for :

  • 1  x  5

  • x  1

  • x  1

  • all values of x


127.

If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle, is :

  • π

  • π3

  • π4

  • π2


128.

The function y = a(1 - cos(x)) is maximum when x is equal to

  • π

  • π2

  • - π2

  • π6


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129.

The maximum value of logxx is equal to :

  • 2e

  • 1e

  • e

  • 1


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130.

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


D.

inversely proportional to the surface area

Given that, dVdt = k     V = 43πR3On differentiating w.r.t. t, we get      dVdt = 4πR2dRdt dRdt = k4πR2    from Eq. (i)

Thus, Rate of increasing radius is inversely proportional to its surface area.


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