\[(a)\;75 ^{\circ} \quad (b)\;45^{\circ} \quad (c)\;15^{\circ} \quad(d)\;60^ {\circ} \]

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Using $s=ut+\large\frac{1}{2}$$at^2$

$\large\frac{a}{\cos \theta}=\frac{1}{2} $$(g \sin \theta)t^2$

$\quad t=\sqrt {\large\frac{2a}{g \sin \theta \cos \theta}}$

$\qquad= \sqrt {\large\frac{4a}{g \sin 2 \theta}}$

t is minimum when $sin\; 2 \theta=1$

$ \theta=45^{\circ}$

Hence b is the correct answer.

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