According to $VSEPR$ theory,

If $g(x) = \int_0^x \cos^4 t \, dt$,then $g(x + \pi)$ equals

The angle between the lines whose direction cosines are given by the equations $l^2+m^2-n^2=0$ and $l+m+n=0$ is

$A$ 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:

$A$ bimetallic strip is formed out of two identical strips,one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_C$ and $\alpha_B$. On heating,the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

The area (in square units) of the region enclosed by the two circles $x^2+y^2=1$ and $(x-1)^2+y^2=1$ is