An infinite number of identical capacitors each of capacitance $1 \mu F$ are connected as shown in the figure. Then,the equivalent capacitance between $A$ and $B$ is .......... $\mu F$.

$A$ $TV$ transmitter has a range of $50 \ km$. The height of the $TV$ transmitter is . . . . . . (Radius of the earth,$R_e = 6.4 \times 10^6 \ m$). (in $m$)

$A$ block of mass $2 \ kg$ is tied to one end of a $2 \ m$ long metal wire of $1.0 \ mm^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is $2 \ mm$, the Young's modulus of the metal is (Acceleration due to gravity $= 10 \ ms^{-2}$)

In the circuit shown below,the $AC$ source has voltage $V = 20 \cos(\omega t)$ with $\omega = 2000 \, rad/sec$. The amplitude of the current will be nearest to.....$A$

$A$ thin prism $P_1$ with angle $4^o$ and made from glass of refractive index $1.54$ is combined with another prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ is......$^o$

If $\overrightarrow{u}=\overrightarrow{a}-\overrightarrow{b}$, $\overrightarrow{v}=\overrightarrow{a}+\overrightarrow{b}$, $|\overrightarrow{a}|=|\overrightarrow{b}|=2$, then $|\overrightarrow{u} \times \overrightarrow{v}|$ is equal to