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

112.

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

• 9

• 16

• 49

• 100

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

• $4\mathrm{\pi }$

• $2\mathrm{\pi }$

• $6\mathrm{\pi }$

• $3\mathrm{\pi }$

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

• 4

• 5

• 6

• 8

The slope of the curve y = e^xcos(x), x $\in \left(- \mathrm{\pi }, \mathrm{\pi }\right)$ is maximum at

• x = $\frac{\mathrm{\pi }}{2}$

• $\mathrm{x} = - \frac{\mathrm{\pi }}{2}$

• $\mathrm{x} = \frac{\mathrm{\pi }}{4}$

• x = 0

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

Let f(x) = 2x³ - 5x² - 4x + 3, $\frac{1}{2} \le \mathrm{x} \le 3$. The point at which the tangent to the curve is parallel to the X-axis, is

• (1, - 4)

• (2, - 9)

• (2, - 4)

• (2, - 1)

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 $\frac{\mathrm{\pi }}{3}$, 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

If y = 8x³ - 60x² + 144x + 27 is a decreasing function in the interval

• (- 5, 6)

• $\left(- \infty , 2\right)$

• (5, 6)

• (2, 3)

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

• 0

• 1

• 2

• 1/2