If the coefficient of x 10 in the binomial expansion of is , where l, k N and l is co-prime to 5, then k is equal to _____________. ...

Given Binomial Expansion = ( x 5^1 4 + x 5^1 3 )^60 General term T_r + 1 = ^60C_r\,.\,( x^1/2 5^1/4 )^60 - r\,.\,( 5^1/2 x^1/3 )^r = ^60C_r\,.\,5^( r 4 - 15 + r 2 )\,.\,x^( 30 - r 2 - r 3 ) = ^60C_r\,.\,5^( 3r - 60 4 )\,.\,x^( 180 - 5r 6 ) For x 1...

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If the coefficient of x10 in the binomial expansion of x 51 : null (Mathematics) | DivineJEE

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Mathematics

If the coefficient of x¹⁰ in the binomial expansion of ${\left( {{{\sqrt x } \over {{5^{{1 \over 4}}}}} + {{\sqrt 5 } \over {{x^{{1 \over 3}}}}}} \right)^{60}}$ is ${5^k}\,.\,l$ , where l, k $\in$ N and l is co-prime to 5, then k is equal to _____________.

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