Field of a Magnet & Magnet in a Uniform Field question from MHT CET 2020 (16 Oct, Shift 1)

Answer: (c)

1. The point lies on the axis of one magnet and on the equatorial line of the other, at distance $d$ from both.
2. $B_{\text{axial}} = \dfrac{\mu_0}{4\pi}\dfrac{2M}{d^3}$, $B_{\text{eq}} = \dfrac{\mu_0}{4\pi}\dfrac{M}{d^3}$, and the two fields are perpendicular.
3. $B = \sqrt{B_{\text{axial}}^2 + B_{\text{eq}}^2} = \dfrac{\mu_0}{4\pi}\dfrac{M}{d^3}\sqrt{4+1}$
4. So the answer is (c) $\frac{\mu_0}{4\pi}(\sqrt{5})\frac{M}{d^3}$.