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JEE Main202227 Jun 2022Morning ShiftMathematicsBinomial TheoremActual

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 coprime to 5 , then k is equal to ______.

Correct answer

0

Step-by-step solution

T r + 1 = C r 60 x 5 1 4 60 - r 5 x 1 3 r For x 10 , 60 - r 2 - r 3 = 10 ⇒    r = 24 Hence coefficient of x 10 will be C 24 60 5 3 Now, exponent of 5 in C 24 60 will be the power of 5 in 60 ! 24 ! 36 !   i.e.   5 14 5 4 · 5 8 = 5 2 i.e. k = 5

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