\[(a)\;83.5\;KW \quad (b)\;97.5\;KW \quad (c)\;60.5\;KW \quad (d)\;73.5\;KW\]

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$\sin \theta=\large\frac{5}{13}$

$\cos \theta=\sqrt {1-\sin ^ \theta}$

$\qquad= \sqrt {1-\bigg(\large\frac{5}{13}\bigg)^2}$

$\qquad=\large\frac{12}{13}$

Force against which the engine has to work

$F=mg \sin \theta+\mu mg \cos \theta$

$\quad=6500 \times 9.8 \bigg[\large\frac{5}{13}+\frac{1}{12} \times \frac{12}{13}\bigg]$

$\quad=29400 \;N$

Engine power $=Fv$

$\quad=29400 \times 2.5 \qquad 9km/hr=2.5 m/s$

$\quad=73500 \;W$

$\quad=73.5 KW$

Hence d is the correct answer.

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