Q. If A denotes the sum of all the coefficients in the expansion of (1-3x+10x^2 )^n and B denotes the sum of all the coefficients in the expansion of (1+x^2 )^n, then : (1) A=B^3 (2) 3A=B (3) B=A^3 (4) A=3B

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Ans: (1)
Solution: Sum of coefficients in the expansion of
(1-3x+10x^2 )^n=A
then A=(1-3+10)^n=8^n ( put x=1)
and sum of coefficients in the expansion of (1+x^2 )^n=B
then B=(1+1)^n=2^n
A=B^3