If `(1+x)^n=a_0+a_1x+a_2x^2+....+a_nx^n`, then `(a_0-a_2+.....)^2+(a_1-a_3+.....)^2` is equal to (A)`3^n` (B) `2^n` (C)`((1-2^n)/(1+2^n))` (D) none of these

If (1+x+x^2)^n=a_0+a_1x+a_2x^2+....+a_(2n)x^(2n) , then a_0+a_2+a_4+.....+a_(2n) is

If (1 +x+x^2)^25 = a_0 + a_1x+ a_2x^2 +..... + a_50.x^50 then a_0 + a_2 + a_4 + ... + a_50 is :

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

If (1+x+x^2+x^3)^100=a_0+a_1x+a_2x^2+.......+a_300x^300, then

If (1+x)^5=a_0+a_1x+a2x^2+a_3x^3+a_4x^4+a_5x^5, then the value of (a_0-a_2+a_4)^2+(a_1-a_3+a_5)^2 is equal to 243 b. 32 c. 1 d. 2^(10)

If (1+x)^n=a_0+a_1x+a_2x^2).....+a_nx^n The sum of the series a_(0) +a_(4) +a_(8)+a_(12)+ …… is

If (1-x)^(-n)=a_0+a_1x+a_2x^2+...+a_r x^r+ ,t h e na_0+a_1+a_2+...+a_r is equal to (n(n+1)(n+2)(n+r))/(r !) ((n+1)(n+2)(n+r))/(r !) (n(n+1)(n+2)(n+r-1))/(r !) none of these

If (1 + x +x^2)^n = a_0 +a_1x + a_2x^2 + ….+a_(2n)x^(2n) then prove that a_0 +a_2 +a_4+……+a_(2n) = (3^n +1)/(2)

If (1-x+x^2)^n=a_0+a_1x+a_2x^2+ .........+a_(2n)x^(2n),\ find the value of a_0+a_2+a_4+........+a_(2n)dot

lf (1 + x + x^2 + x^3)^5 = a_0+a_1x +a_2x^2+.....+a_(15)x^15 , then a_(10) equals to