The equations of the tangents to the circle $x^2 + y^2 = 13$ at the points whose abscissa is $2$,are

In a triangle,if $b=20, c=21$ and $\sin A=\frac{3}{5}$,then $a$ is equal to :

Let $f(x)=e^x$,$g(x)=\sin ^{-1} x$ and $h(x)=f(g(x))$,then $\frac{h^{\prime}(x)}{h(x)}$ is equal to

Match the appropriate pairs from List-$I$ and List-$II$ :

List-$I$	List-$II$
$1$. Nitrogen molecules	$(A)$ Continuous spectrum
$2$. Incandescent solids	$(B)$ Absorption spectrum
$3$. Fraunhoffer lines	$(C)$ Band spectrum
$4$. Electric arc between iron rods	$(D)$ Emission spectrum

$A$ concave mirror of focal length $f$ (in air) is immersed in water $(\mu = 4/3)$. The focal length of the mirror in water will be

An $LCR$ series circuit with a resistance of $100\,\Omega$ is connected to an ac source of $200\,V$ (r.m.s.) and angular frequency $300\,rad/s$. When only the capacitor is removed,the current lags behind the voltage by $60^\circ$. When only the inductor is removed,the current leads the voltage by $60^\circ$. The average power dissipated is......$W$.