In the circuit shown in the figure,the power dissipated as heat in the $6\,\Omega$ resistor is $6\,W$. What is the value of resistance $R$ in the circuit? $\Omega$

Given the circle $C$ with the equation $x^2+y^2-2x+10y-38=0$. Match the List-$I$ with the List-$II$ given below concerning $C$.

$A$. The equation of the polar of $(4, 3)$ with respect to $C$	$I$. $y + 5 = 0$
$B$. The equation of the tangent at $(9, -5)$ on $C$	$II$. $x = 1$
$C$. The equation of the normal at $(-7, -5)$ on $C$	$III$. $3x + 8y = 27$
$D$. The equation of the diameter passing through $(1, -5)$ and $(1, 3)$	$IV$. $x = 9$

$A$ particle of charge '$q$' and mass '$m$' moves in a circular orbit of radius '$r$' with angular speed '$\omega$'. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

$(a+b) \cdot (b+c) \times (a+b+c)$ is equal to

If $200 \text{ MeV}$ of energy is released in the fission of one nucleus of ${}_{92}^{236}U$,the number of nuclei that must undergo fission to release an energy of $1000 \text{ J}$ is

$A$ crystal is made up of metal ions $M_1$ and $M_2$ and oxide ions. Oxide ions form a $ccp$ lattice structure. The cation $M_1$ occupies $50 \%$ of octahedral voids and the cation $M_2$ occupies $12.5 \%$ of tetrahedral voids of the oxide lattice. The oxidation numbers of $M_1$ and $M_2$ are,respectively: