Magnetic lines of force due to a bar magnet do not intersect because

The equation $\sqrt{3} \sin x + \cos x = 4$ has

Among the following,the $CORRECT$ combinations are :
$A.$ $IF_3$ $\rightarrow$ $T$-shaped $(sp^3d)$
$B.$ $IF_5$ $\rightarrow$ Square pyramidal $(sp^3d^2)$
$C.$ $IF_7$ $\rightarrow$ Pentagonal bipyramidal $(sp^3d^3)$
$D.$ $ClO_4^-$ $\rightarrow$ Square planar $(sp^3d)$
Choose the correct answer from the options given below :

The equations of the circle which pass through the origin and make intercepts of lengths $4$ and $8$ on the $x$ and $y$-axes respectively are

Data Entry - Physics

The potential energy between two atoms in a molecule is given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$,where $a$ and $b$ are positive constants and $x$ is the distance between the atoms. The atoms are in stable equilibrium when: