Let f(x) = [3 sin2(10x + 11) - 7]2 for x ∈ R. Then, the

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 Multiple Choice QuestionsMultiple Choice Questions

111.

If s = 2t3 - 6t2 + at + 5 is the distance travelled by a particle at time t and if the velocity is - 3 when its acceleration is zero, then the value of a is

  • - 3

  • 3

  • 4

  • - 4


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112.

Let f(x) = [3 sin2(10x + 11) - 7]2 for x  R. Then, the maximum value of the function f is

  • 9

  • 16

  • 49

  • 100


C.

49

f(x) = [3 sin2(10x + 11) - 7]2 will have maximum value when sin2(10x + 11) has minimum value.

    sin2θ is always + ve

  Minimum value of sin2(10 x + 11) = 0     Maximum value of f(x) = (- 7)2 = 49 


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113.

If a circular plate is heated uniformly, its area expands 3c times as fast as its radius, then the value of c when the radius is 6 units, is

  • 4π

  • 2π

  • 6π

  • 3π


114.

The minimum valuje of 2x3 - 9x2 + 12x + 4 is

  • 4

  • 5

  • 6

  • 8


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115.

The slope of the curve y = excos(x), x  - π, π is maximum at

  • x = π2

  • x = - π2

  • x = π4

  • x = 0


116.

The equation of tangent to the curve y = x3 - 6x + 5 at (2, 1) is

  • 6x - y - 11 = 0

  • 6x - y - 13 = 0

  • 6x + y + 11 = 0

  • 6x - y + 11 = 0


117.

Let f(x) = 2x3 - 5x2 - 4x + 3, 12  x  3. The point at which the tangent to the curve is parallel to the X-axis, is

  • (1, - 4)

  • (2, - 9)

  • (2, - 4)

  • (2, - 1)


118.

Two sides of triangle are 8 m and 56 m in length. The angle between them is increasing at the rate 0.8=08  rad/s. When the angle between sides of fixed length is π3, the rate at which the area of the triangle is increasing, is

  • 0. 4 m2/s

  • 0.8 m2/s

  • 0 . 6 m2/s

  • 0.04 m2/s


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119.

If y = 8x- 60x2 + 144x + 27 is a decreasing function in the interval

  • (- 5, 6)

  • - , 2

  • (5, 6)

  • (2, 3)


120.

The minimum value of the function max (x, x) is equal to

  • 0

  • 1

  • 2

  • 1/2


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