$A$ line passing through the point of intersection of $x+y=4$ and $x-y=2$ makes an angle $\tan ^{-1}\left(\frac{3}{4}\right)$ with the $x$-axis. It intersects the parabola $y^{2}=4(x-3)$ at points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ respectively. Then, $|x_{1}-x_{2}|$ is equal to

Two waves $Y_1 = 0.25 \sin 316 t$ and $Y_2 = 0.25 \sin 310 t$ are propagating in the same direction. The number of beats produced per second is

Consider a block of conducting material of resistivity ' $\rho$ ' as described. Current ' $I$ ' enters at ' $A$ ' and leaves from ' $D$ '. We apply the superposition principle to find the voltage ' $\Delta V$ ' developed between ' $B$ ' and ' $C$ '. The calculation is done in the following steps:
$(i)$ Take current ' $I$ ' entering from ' $A$ ' and assume it to spread over a hemispherical surface in the block.
(ii) Calculate the field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E = \rho j$,where $j$ is the current per unit area at ' $r$ '.
(iii) From the ' $r$ ' dependence of $E(r)$,obtain the potential $V(r)$ at $r$.
(iv) Repeat $(i)$,(ii),and (iii) for current ' $I$ ' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '.
For current entering at $A$,the electric field at a distance ' $r$ ' from $A$ is:

Which of the following alkenes does $NOT$ exhibit cis-trans isomerism?

$P_4O_{10}$ has short and long $P-O$ bonds. The number of short $P=O$ bonds in this compound is

If $5x - 12y + 10 = 0$ and $12y - 5x + 16 = 0$ are two tangents to a circle,then the radius of the circle is