In the expansion of x 4 5 + x - 1 5 n , the coeficient of the 8 t h and 19 t h terms are equal. The term independent of x is given by

Question

In the expansion of x 4 5 + x - 1 5 n , the coeficient of the 8 t h and 19 t h terms are equal. The term independent of x is given by, C 21 27, C 20 25, C 21 25, C 22 27

MARKS App · Accepted Answer

Since there is no constant term the coefficient of 8 th and 19 th term are same as the binomial coefficients of 8 th and 19 th term. C 7 n = n C 18 ⇒ n = 7 + 18 = 25 T n + 1 = 25 C r x 4 5 25 - r r - 1 5 r C r 25 x 4 5 ( 25 - r ) - r 5 To be independent of x , 100 - 5 r 5 = 0 ⇒ r = 20 Hence, the required term is C 20 25

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