A spherical iron ball ofradius 10 cm, coated with a layer of ice

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71.

A spherical iron ball ofradius 10 cm, coated with a layer of ice of uniform thickness, melts at a rate of 100 π cm/min. The rate at which the thickness of decreases when the thickness of ice is 5 cm, is

  • 1 cm/min

  • 2 cm/min

  • 1376 cm/min

  • 5 cm/min


A.

1 cm/min

Given,      dVdt = 100 π cm3/min  ddt43πr3 = 100π        3r2drdt = 300π4π drdtr = 5 = 3004 × 3 × 25                      = 1 cm/min


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72.

If ax2 + bx + 4 attains its minimum value - 1 at x = 1, then the values of a and bare respectively

  • 5, - 10

  • 5, - 5

  • 5, 5

  • 10, - 5


73.

The function f(x) = (9 - x2)2 increases in

  • - 3, 0  3, 

  • - , - 3  3, 

  • - , - 3  0, 3

  • (- 3, 3)


74.

Let gx = 2e,             if x  1logx - 1, if x > 1. The equation  of the normal to y = g(x) at the point (3, log(2)), is

  • y - 2x = 6 + log(2)

  • y + 2x = 6 + log(2)

  • y + 2x = 6 - log(2)

  • y + 2x = - 6 + log(2)


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75.

If a and b are positive numbers such that a > b, then the minimum value of asecθ - btan0 < θ < π2 is

  • 1a2 - b2

  • 1a2 + b2

  • a2 + b2

  • a2 - b2


76.

If the curves x2a2 + y212 = 1 and y3 = 8x  intersect at right angle, then the value of a is equal to

  • 16

  • 12

  • 8

  • 4


77.

If the function f(x) = x-12ax2 + 36a2x - 4(a > 0) attains its maximum and minimum at x = p and x = q respectively and if 3p = q2, then a is equal to

  • 16

  • 136

  • 13

  • 18


78.

The equation of the tangent to the curve y = 4ex4 at the point where the curve crosses y-axis is equal to

  • 3x + 4y = 16

  • 4x + y = 4

  • x + y = 4

  • 4x - 3y = - 12


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79.

The diagonal of a square is changing at the rate of 0.5 cms-1. Then, the rate of change of area, when the area is 400 cm2 is equal to

  • 202 cm2/s

  • 102 cm2/s

  • 1102 cm2/s

  • 102 cm2/s


80.

The equation of the tangent to the curve x- 2.xy + y2 + 2x + y - 6 = 0 at (2, 2) is

  • 2x + y - 6 = 0

  • 2y + x - 6 = 0

  • x + 3y - 8 = 0

  • 3x + y - 8 = 0


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