If the coefficient of x^ 10 in the binomial expansion of ( x /5^ 1/4 + 5 /x^ 1/3 )^ 60 is 5^ k l, where l, k N and l is co-prime to 5, then k is equal to _____.

JEE Main 2022 Mathematics question

If the coefficient of in the binomial expansion of is , where l, k N and l is co-prime to 5, then k is equal to .

Answer: 5

= . The power of x is (60 − r)/2 − r/3 = 10, so r = 24. The power of 5 is −(60 − 24)/4 + 24/2 = 3, so the

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Question ID VK-034620