My favourite IIT-JEE Maths question

Although I'm in Class 12,but I couldn't stop myself from taking a glance at this year's JEE Math's questions. I found this question to be very intriguing and so I thought of sharing it with my Brilliant friends.

For $a \in R$ (set of real numbers) , $a \neq -1$ , $lim_{n \to \infty}\frac{1^a+2^a+ \ldots +n^a}{(n+1)^{a-1}[(na+1)+(na+2)+\ldots+(na+n)]}= \frac{1}{60}$ Then $a=?$

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`2 \times 3`	$2 \times 3$
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`\boxed{123}`	$\boxed{123}$

My favourite IIT-JEE Maths question

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