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

• 17

• 177

• 77

• None of these

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

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

• $\frac{3}{2}\mathrm{s}$

• $\frac{2}{3}\mathrm{s}$

• $\frac{1}{2}\mathrm{s}$

• 1 s

The equation of the tangent to the curve y = 4xe^x at $\left(- 1, \frac{- 4}{\mathrm{e}}\right)$

• y = - 1

• $\mathrm{y} = - \frac{4}{\mathrm{e}}$

• x = - 1

• $\mathrm{x} = \frac{- 4}{\mathrm{e}}$

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

For all real x, the minimum value of $\frac{1 - \mathrm{x} + {\mathrm{x}}^2}{1 + \mathrm{x} + {\mathrm{x}}^2}$ is

• 0

• 1/3

• 1

• 3

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

• 3

• 9

• - 9

• - 3

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

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)

If 2x + y + $\mathrm{\lambda }$ = 0 is normal to the parabola y² = 8x, then $\mathrm{\lambda }$, is

• - 24

• 8

• - 16

• 24