If `1/(1+2x+x^2)= 1+a_1x+a_2x^2+…..` then the value of `a_r` is (A) `2` (B) `r+1` (C) `r` (D) `2r`

If (1+2x +3x^2)^10 = a_0 +a_1x +a_2x^2 + ……+a_20x^20 then a_1 = ?

If cotA+cotB+cotC = k(1/x^2+1/y^2+1/z^2) then the value of k is (A) R^2 (B) 2R (C) /_\ (D) a^2+b^2+c^2

If (1+2x+3x^2)^10=a_0+a_1x+a_2x^2+……..+a_20x^20 then (A) a_1=20 (B) a_2=210 (C) a_3=1500 (D) a_20=2^3.3^7

If (1+x) ^(15) =a_(0) +a_(1) x +a_(2) x ^(2) +…+ a_(15) x ^(15), then the value of sum_(r=1) ^(15) r . (a_(r))/(a _(r-1)) is-

If (1+x-2x^2)^8 = 1 + a_1x + a_2x^2 + ……+ a_16 x^16 , then a_1 +a_3 + a_5 + ……+a_15 = ?

If (1+x+x^2)^n=a_0+a_1x+a_2x^2++a_(2n)x_(2n), find the value of a_0+a_6++ ,n in Ndot

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

If d/(dx){x^n-a_1x^(n-1)+a_2x^(n-2)++(-1)^n a_n}e^x=x^n e^x , then the value of ar, 0 < r ≤ n, is equal to

Given (1-2x+5x^2-10 x^3)(1+x)^n=1+a_1x+a_2x^2+ and that a1 ^2=2a_2 then the value of n is.

If A_r=|(1,r,2^r),(2,n,n^2),(n,(n(n+1))/2 ,2^(n+1))| , then the value of sum_(r=1)^n A_r is n (b) 2n (c) -2n (d) n^2