The maximum value of the function $f(x) = 3x^3 - 18x^2 + 27x - 40$ on the set $S = \{x \in R : x^2 + 30 \le 11x\}$ is

$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $g / 8$,then the ratio of the masses $m_1 : m_2$ is

Two wires of the same material and length but diameters in the ratio $1:2$ are stretched by the same force. The elastic potential energy per unit volume for the wires,when stretched by the same force,will be in the ratio: (in $:1$)

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment is:

$A$ balloon is filled with $500 \ m^3$ of helium gas at $27^{\circ}C$ and $1 \ atm$ pressure. What will be the volume of helium at $3^{\circ}C$ and $0.5 \ atm$ pressure in $m^3$?

$A$ sinusoidal carrier voltage of frequency $1.5\,MHz$ and amplitude $50\,V$ is amplitude modulated by a sinusoidal voltage of frequency $10\,kHz$ producing $50\%$ modulation. The lower and upper side-band frequencies in $kHz$ are: