If a ball is thrown vertically upwards and the height 's' reached in time 't' is given by s = 22t - 11t², then the total distance travelled by the ball is

• 44 units

• 33 units

• 11 units

• 22 units

The sum of two positive numbers is given. If the sum of their cubes is minimum, then

• they are equal

• one is twice the other

• they are unequal

• one is thrice the other

The perimeter of a sectoris a constant. Ifits area is to be maximum, then the sectorial angle is

• $\frac{{\mathrm{\pi }}^{\mathrm{c}}}{6}$

• $\frac{{\mathrm{\pi }}^{\mathrm{c}}}{4}$

• 4^c

• 2^c

The tangent to the curve xy = 25 at any point on it cuts the coordinate axes at A and B, then the area of the $∆$OAB is

• 50 sq units

• 25 sq units

• 75 sq units

• 100 sq units

The length of the subtangent, ordinate and the subnormal are in

• AP

• HP

• GP

• Arithmetico-geometric progression

The maximum value of xe^-x is

• e

• $\frac{1}{\mathrm{e}}$

• - e

• - $\frac{1}{\mathrm{e}}$

The maximum area of a rectangle that can be inscribed in a circle of radius 2 units is

• $8\mathrm{\pi } \mathrm{sq} \mathrm{units}$

• 4 sq units

• 5 sq units

• 8 sq units

If the length of the subtangent at any point to the curve xyⁿ = a is proportional to the abscissa, then n is

• any non-zero real number

• 2

• - 2

• 1

699.

The function f(x) = $\frac{\mathrm{x}}{3} + \frac{3}{\mathrm{x}}$ decreases in the interval

• (- 3, 3)

• $\left(- \infty , 3\right)$

• $\left(3, \infty \right)$

• (- 9, 9)

The tangent to the curve y = x³ + 1 at (1, 2) makes an angle $\mathrm{\theta }$ with y-axis, then the value of $\tan \left(\mathrm{\theta }\right)$ is

• $- \frac{1}{3}$

• 3

• - 3

• $\frac{1}{3}$