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Most Important Selected Qs for JEE AdvancedMathematicsBinomial Theorem

If the coefficient of x^8 in the expansion of (2+9 x^3+6 x^4+x^5 )¹⁰ is 5 2^p 3^q where p, q N , then find the value of (p+q) .

Correct answer

14

Step-by-step solution

aligned & (2+x^3(3+x)^2 )¹⁰ & & ¹⁰ C_r 2^ 10-r x^ 3 r (3+x)^ 2 r & & ^ 2 r C_k 3^ 2 r-k x^k & 3 r+k=8 k=2, r=2 & Coefficient of x^8= ¹⁰ C₂ 2^8 ^4 C₂ 3^2=5 2^9 3^5 aligned

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