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

If the line lx + my + n = 0 is tangent to the parabola y² = 4ax, then

• mn = al²

• lm = an²

• ln = am²

• None of the above

All the points on the curve y² = 4a$\left|\mathrm{x} + \mathrm{asin}\left(\raisebox{1ex}{$\mathrm{x}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{a}$}\right.\right)\right|$, where the tangent is parallel to the axis of x are lies on

• circle

• parabola

• straight line

• None of these

177.

The length of normal at any point to the curve $\mathrm{y} = \mathrm{c} \cosh \left(\frac{\mathrm{x}}{\mathrm{c}}\right)$ is

• fixed

• $\frac{{\mathrm{y}}^2}{{\mathrm{c}}^2}$

• $\frac{{\mathrm{y}}^2}{\mathrm{c}}$

• $\frac{\mathrm{y}}{{\mathrm{c}}^2}$

The height of right circular cylinder of maximum volume inscribed in a sphere of diameter 2a is

• $2\sqrt{3}\mathrm{a}$

• $\sqrt{3}\mathrm{a}$

• $\frac{2\mathrm{a}}{\sqrt{3}}$

• $\frac{\mathrm{a}}{\sqrt{3}}$

The approximate value of f(x) = x³ + 5x² - 7x + 9 at x = 1.1 is

• 8.6

• 8.5

• 8.4

• 8.3

The point on the curve 6y = x³ + 2 at which y-coordinate is changing 8 times as fast as x-coordinate is

• (4, 11)

• (4, - 11)

• (- 4, 11)

• (- 4, - 11)