If the coefficient of $x^{10}$ in the binomial expansion of $\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}}+\frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}$ is $5^k \cdot l$, where $l, k \in \mathbf{N}$ and $l$ is co-prime to 5, then k is equal to ____________.

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 June 2022, Shift 1, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

If the coefficient of

x^{10}

in the binomial expansion of

\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}}+\frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}

5^k \cdot l

, where

l, k \in \mathbf{N}

and

l

is co-prime to 5, then k is equal to ____________.

Official answer

NTA final key.