If the coefficients of x^5 and x^6 are equal in the expansion of (a+ x 5 )⁶⁵ , then the coefficient of x^2 in the expansion of (a+ x 5 )^4 is

Step-by-step solution

Coefficient of x^5= ⁶⁵ C ₅ a⁶⁰ ( 1 5 )^5= ⁶⁵ C ₅ a⁶⁰ 5^5 Coefficient of x^6= ⁶⁵ C ₆ ( 1 5 )^6 a⁵⁹= ⁶⁵ C ₆ a⁵⁹ 5^6 aligned & ^ ^6 C₅ a⁶⁰ 5^5 = ⁶⁵ C ₆ a⁵⁹ 5^6 & a= ⁶⁵ C ₆ ⁶⁵ C ₅ 5 = 5!60! 59!6! 1 5 a=2 & (a+ x 5 )^4= (2+ x 5 )^2 aligned Coefficient of x^2 is ^4 C₂ 2^2 ( 1 5 )^2= 4! 2!2! 2^2 5^2 = 24 25