The coefficient of `x^n` in `(1+x)^(101)(1-x+x^2)^(100)` is nonzero, then `n` cannot be of the form `3r+1` b. `3r` c. `3r+2` d. none of these

If the coefficient of x^100 isn 1+(1+x)+1+x)^2+(1+x)^3+………+(1+x)^n , (n.-100) is ^201C_101 then n= (A) 100 (B) 200 (C) 101 (D) none of these

If a_(r) is the coefficient of x^(r) in (1-2x+3x^(2))^(n), then sum_(r=0)^(2n)r*a_(r)=

If C_(r) be the coefficients of x^(r) in (1 + x)^(n) , then the value of sum_(r=0)^(n) (r + 1)^(2) C_(r) , is

The coefficients of (r-1)^(th),rh and (r+1)^(th) terms in the expansion of (x+1)^(n) are in the ratio 1:3:5 Find n and r.

If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e r en in N , then value of a is n b. n-1 c. n+1 d. none of these

The coefficients of x^n in the expansion of (1+x)6(2n) and (1+x0^(2n-1) are in the rtio of (A) 1:2 (B) 1:3 (C) 3:1 (D) 2:1

Given positive integers r gt 1, n gt 2 and that the coefficient of (3rd)th and (r+2)th terms in the binomial expansion of (1+x)^(2n) are equal. Then (a) n=2r (b) n=2r+1 (c) n=3r (d) non of these

in If the coefficient of x^(r) and x^(r+1) are equal in the expansion of (1+x)^(2n+1), then find the value of r.

If the coefficient of (r +1)^(th) term in the expansion of (1 +x)^(2n) be equal to that of (r + 3)^(th) term , then