Which of the following must hold good for the expansion of the binomial (x^4+ 1 x^3 )¹⁵ ?

Step-by-step solution

T _ r+1 ¹⁵ C _r ( x ^4 )^ (15-r) ( X ⁻³ )^r= ¹⁵ C _ r x ^ 80-7 r (A) for the term independent of x, 60-7 r=0 r is not an integer there is no term independent of x . (B) n=15 is odd ^ n C _ r will be maximum if r = n -1 2 or r = n +1 2 i.e. r=7 or r=8 binomial coefficient of 8^ th and 9 th terms will be greatest (C) for the cofficient of x³² ; 60-7 r=32 r=4 cofficient of X ³² is = ¹⁵ C for the coeff. of x⁻¹⁷ ; 60-7 r=-17 ; r=11 coeff. of x ⁻¹⁷ is = ¹⁵ C ₁₁= ¹⁵ C ₄ (C) is correct (D) If x= 2 , T_ r+1 = ¹⁵ C_r 2^ 60-7