If `(1 - x)^-n = a_0 + a_1 x + a_2 x^2 + a_3 x^3 +........,` find the value of, `a_0 + a_1 + a_2 +...... +a_n`.

If (1 - x + x^2)^n = a_0 + a_1 x + a_2x^2 + ..... + a_(2n)x^(2n) then a_0 + a_2 + a_4 + ... + a_(2n) equals

If (1 + x +x^2)^n = a_0 +a_1x + a_2x^2 + ….+a_(2n)x^(2n) then prove that a_0 +a_1 +a_2 + ……a_(2n) = 3^n

If (3 + 7x - 9x^2)^n = a_0 +a_1x + a_2 x^2 + ……+a_(2n)x^(2n) prove the a_0 +a_1 +a_2 + ……+a_(2n) = 1

If (3 + 7x - 9x^2)^n = a_0 +a_1x + a_2 x^2 + ……+a_(2n)x^(2n) prove the a_0 +a_1 +a_2 + ……+a_(2n) = 1

If (1+x)^10 = a0 + a1 x + a2 x^2 + a3 x^3 + a4 x^4 + a5 x^5 + a6 x^6 +.... a10 x^10), then the value of ( a0 - a2 + a4 - a6 + a8 -a10)^2 + (a1 - a3 + a5 -a7 + a9)^2 is :

If (1 + ax + b x^2)^4 = a_0 +a_1 x + a_2 x^2 +...+a_8 x^8 when a,b,a_0,a_1,a_2...,a_8 in R such that a_0+a_1+a_2 != 0 and |(a_0,a_1,a_2),(a_1,a_2,a_3),(a_2,a_0,a_1)| then the value of 5a/b (A) 6 (B) 8 (C) 10 (D) 12

If (1 + ax + b x^2)^4 = a_0 +a_1 x + a_2 x^2 +...+a_8 x^8 when a,b,a_0,a_1,a_2...,a_8 in R such that a_0+a_1+a_2 != 0 and |(a_0,a_1,a_2),(a_1,a_2,a_0),(a_2,a_0,a_1)|=0 then the value of 5a/b (A) 6 (B) 8 (C) 10 (D) 12

If cosx=a_0+a_1 x+a_2x^2+... then the value of a_2 is