The height of the cylinder of maximum volume inscribed in a spher

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 Multiple Choice QuestionsMultiple Choice Questions

221.

The minimum value of 3sinθ + 4cosθ is :

  • 5

  • 1

  • 3

  • - 5


222.

Maximum value of sin(x) - cos(x) is equal to :

  • 2

  • 1

  • 0

  • none of these


223.

If the distance 's' metres traversed by a particle int seconds is given by s = t3 - 3t2, then the velocity of the particle when the acceleration is zero, in m/s is

  • 3

  • - 2

  • - 3

  • 2


224.

If tangent to the curve x = at2, y = 2at is perpendicular to X - axis, then its point of contact is

  • (a, a)

  • (0, a)

  • (0, 0)

  • (a, 0)


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225.

The slope of the tangent to the curve x = 3t2 + 1, y = t3 - 1 at x = 1 is

  • 12

  • 0

  • - 2


226.

The rate ofchange of the surface area ofthe sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to

  • 1r2

  • 1r

  • r2

  • r


227.

For the curve xy = c2, the subnormal at any point varies as

  • x3

  • x2

  • y3


228.

Let the function f : R R be defined by f(x) = 2x + cos(x), then f

  • has maximum at x = 0

  • has minimum at x = π

  • is an increasing function

  • is a decreasing


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229.

The equation to the tangent to the curve y = be- x/a at the point where it crosses the Y-axis is

  • ax + by = 1

  • xa - yb = 1

  • xa + yb = 1

  • ax - by = 1


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230.

The height of the cylinder of maximum volume inscribed in a sphere of radius 'a' is

  • 3a2

  • 2a3

  • a3

  • 2a3


D.

2a3

Let a be the radius and h the height from figurer2 + h24 = a2 h2 = 4a2 - r2Now, v = πr2h = πa2 - h24h           = πa2h - h34 dvdh = πa2 - 3h24 = 0for maximum or minimum h = 2a3 d2vdh2 = - 6h4 < 0 v i s maximum when h = 2a3


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