Angle between y² = x and x² = y at the origin is

• 2 tan^-1(3/4)

• tan^-1(4/3)

• π/2

• π/4

The distance covered by a particle in t seconds is given by x = 3 + 8t - 4t². After 1 s its velocity will be

• 0 unit/s

• 3 unit/s

• 4 unit/s

• 7 unit/s

If the tangent to the parabola y = x(2 - x) at the point (1, 1) intersects the parabola at P. Find the coordinate of P.

The maximum value of xy subject to x + y = 8

• 8

• 16

• 20

• 24

45.

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

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