In Young's double slit experiment how many maxima can be obtained on a screen (including the central maximum) on both sides of the central fringe if $\lambda = 2000\,\mathrm{\AA}$ and $d = 7000\,\mathrm{\AA}$

In Young's double slit experiment, maxima occur for $$d\sin\theta = n\lambda$$ For a real maximum, we need $$\sin\theta \le 1$$ So the largest possible order satisfies $$n \le \frac{d}{\lambda}$$ Substituting the given values, $$\frac{d}{\lambda} = \frac{7000}{2000} = 3.5$$ Hence the maximum integer order is $$n_{\max} = 3$$ So maxima occur for $$n = 0, \pm 1, \pm 2, \pm 3$$ Therefore total number of maxima including the central maximum is $$2\times 3 + 1 = 7$$ This matches option $\mathrm{(B)}$.