A particle moves along a straight line according to the laws = 16- 2t + 3t, where s metres is the distance of the particle from a fixed point at the end of t seconds. The acceleration of the particle at the end of 2s is

• 36m/s²

• 34m/s²

• 36m

• None of these

The maximum slope of the curve y = - x³ + 3x² + 2x - 27 is

• 5

• - 5

• $\frac{1}{5}$

• None of these

For the curve y = xe, the point

• x = - 1 is a point of minimum

• x = 0 is a point of minimum

• x = - 1 is a point of maximum

• x = 0 is a point of maximum

484.

If the slope of the curve $\mathrm{y} = \frac{\mathrm{ax}}{\mathrm{b} - \mathrm{x}}$ at the point (1, 1) is 2, then

• a = 1, b = - 2

• a = - 1, b = 2

• a = 1, b = 2

• None of these

If the tangent at (1, 1) on y = x(2 - x)² meets the curve again at P, then P is

• (4, 4)

• (- 1, 2)

• (9/4, 3/8)

• None of these

If there is an error of K % is measuring the edge of a cube, then the per cent error in estimating its volume is

• k

• 3k

• $\frac{\mathrm{k}}{3}$

• None of these

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

• $\frac{\mathrm{x}}{\mathrm{a}} + \frac{\mathrm{y}}{\mathrm{b}} = 1$

• $\frac{\mathrm{x}}{\mathrm{a}} - \frac{\mathrm{y}}{\mathrm{b}} = 1$

• ax + by = 1

• ax - by = 1

On the interval [0, 1], the function x²⁵(1- x)⁷⁵ takes its maximum value at the point

• 0

• 1/4

• 1/2

• 1/3

If there is an error of m% in measuring the edge of cube, then the per cent error in estimating its surface area is

• 2 m

• 3 m

• 1 m

• 4 m

The equation of normal to the curve y = (1 + x)^y +sin^-1(sin²(x)) at a = 0 is

• x + y = 1

• x - y = 1

• x + y = - 1

• x - y = - 1