If a line in space makes angles $\alpha, \beta,$ and $\gamma$ with the coordinate axes, then the value of $\cos 2\alpha + \cos 2\beta + \cos 2\gamma + \sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ is equal to:

The pressure versus temperature graph of an ideal gas is as shown in the figure. The density of the gas at point $A$ is ${\rho _0}$. The density at point $B$ will be

$A$ parallel beam of fast-moving electrons is incident normally on a narrow slit. $A$ screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is $\text{CORRECT}$?

The set of values of $x$ for which the inequalities $x^2-3x-10 < 0$ and $10x-x^2-16 > 0$ hold simultaneously,is

If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below it,then (both $x$ and $h$ being much smaller than the radius of the earth)

$A$ point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9 \ m$ and $25 \ m$ respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is