The maximum area of the rectangle that can be inscribed in a circ

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 Multiple Choice QuestionsMultiple Choice Questions

161.

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

  • 0, 

  • - , 0

  • - , 

  • None of the above


162.

If f(x) = kx - sinx, then sin(x)is monotonically increasing, then

  • k > 1

  • k > - 1

  • k < 1

  • k < - 1


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163.

The maximum area of the rectangle that can be inscribed in a circle of radius r, is

  • πr2

  • r2

  • πr24

  • 2r2


D.

2r2

Area of rectangle    A = 2x . 2r2 - x2       = 4xr2 - x2dAdx = 4r2 - 2x2r2 - x2For maximum or minimum put dAdx = 0 x = r2

It can be easily checked that d2Adx2 < 0 for this value of x.

 A is maximum for x = r2 and the maximum value of A is given by

A = 4r2r2 - r22 = 2r2


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164.

The velocity of a particle at time t is given by the relation v = 6t - t26. The distance traveled in 3 s is, if s = 0 at t = 0

  • 392

  • 572

  • 512

  • 332


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165.

The maximum value of function x3 - 12x2 + 36x + 17 in the interval [1, 10] is

  • 17

  • 177

  • 77

  • None of these


166.

The abscissae of the points, where the tangent is to curve y = x3 - 3x2 - 9x + 5 is parallel to x-axis, are

  • x = 0 and 0

  • x = 1 and - 1

  • x = 1 and - 3

  • x = - 1 and 3


167.

The equation of motion of a particle moving along a straight line is s = 2t3 - 9t2 + 12t, where the units of s and t are centimetre and second. The acceleration of the particle will be zero after

  • 32s

  • 23s

  • 12s

  • 1 s


168.

The equation of the tangent to the curve y = 4xex at - 1, - 4e

  • y = - 1

  • y = - 4e

  • x = - 1

  • x = - 4e


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169.

The equation of tangent to the curve y2 = ax2 + b at point (2, 3) is y = 4x - 5, then the values of a and b are

  • 3, - 5

  • 6, - 5

  • 6, 15

  • 6, - 15


170.

For all real x, the minimum value of 1 -  x + x21 +  x + x2 is

  • 0

  • 1/3

  • 1

  • 3


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