What is the magnetic field induction (of earth) when a bar magnet is placed with its axial line   perpendicular to magnetic meridian with North pole facing towards east to achieve neutral point?

In this case two null points are obtained one $N_1$  is in  (N-W  direction ) and another  $N_2$
(S-E  direction)

We know  magnetic field induction at any point is
$B_H=\frac{{\mu }_0}{4\pi }\frac{M}{d^3}\sqrt{1+3{\cos }^2\theta }$
Here   $\tan \theta =\sqrt{2}$

$$\begin{gathered} \because \cos \theta =\frac{1}{\sqrt{3}} \\ {B}_H=\frac{{\mu }_0}{4\pi }\frac{\sqrt{2}M}{d^3} \end{gathered}$$

  Hence key (2) is Correct & Remaining (1),(2),(4) are not correct