The height of right circular cylinder of maximum volume inscribed

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 Multiple Choice QuestionsMultiple Choice Questions

171.

If x + y = k is normal to y2 = 12x, then k is

  • 3

  • 9

  • - 9

  • - 3


172.

A particle moves along a straight line according to the law s = 16 - 2t + 3t3, where s metres is the distance of the particle from a fixed point at the end of t second. The acceleration of the particle at the end of 2s is

  • 3.6 m/s2

  • 36 m/s2

  • 36 km/s2

  • 360 m/s2


173.

Divide 10 into two parts such that the sum of double of the first and the square of the second is minimum

  • (6, 4)

  • (7, 3)

  • (8, 2)

  • (9, 1)


174.

If 2x + y + λ = 0 is normal to the parabola y2 = 8x, then λ, is

  • - 24

  • 8

  • - 16

  • 24


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175.

If the line lx + my + n = 0 is tangent to the parabola y2 = 4ax, then

  • mn = al2

  • lm = an2

  • ln = am2

  • None of the above


176.

All the points on the curve y2 = 4ax + asinxa, where the tangent is parallel to the axis of x are lies on

  • circle

  • parabola

  • straight line

  • None of these


177.

The length of normal at any point to the curve y = c coshxc is

  • fixed

  • y2c2

  • y2c

  • yc2


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178.

The height of right circular cylinder of maximum volume inscribed in a sphere of diameter 2a is

  • 23a

  • 3a

  • 2a3

  • a3


C.

2a3

Let the radius and height of the cylinder are r and h, respectively.

In AOM,r2 + h24 = a2         h2 = 4a2 - r2Now,      V = πr2h = πa2h - 14h3For max or min,dVdx = πa2 - 34h2 = 0 h = 23aNow, d2Vdx2 = - 6h4 < 0So, V is maximum at h = 2a3


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179.

The approximate value of f(x) = x3 + 5x2 - 7x + 9 at x = 1.1 is

  • 8.6

  • 8.5

  • 8.4

  • 8.3


180.

The point on the curve 6y = x3 + 2 at which y-coordinate is changing 8 times as fast as x-coordinate is

  • (4, 11)

  • (4, - 11)

  • (- 4, 11)

  • (- 4, - 11)


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