If `(1+x-2x^2)^6=1+a_1 x+a_2 x^2+a_2 x^3+.........`, then the value of `a_2+a_4+a_6+......+a_12` will be

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 roots of an equation x^n-1=0 are 1,a_1,a_2,........,a_(n-1) then the value of (1-a_1)(1-a_2)(1-a_3)........(1-a_(n-1)) will be (a) n (b) n^2 (c) n^n (d) 0

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 (1+x)^5=a_0+a_1x+a_2x^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)

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 x=2+2^(2/3)+2^(1/3) , then the value of x^3-6x^2+6x 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_0),(a_2,a_0,a_1)|=0 then the value of 5a/b (A) 6 (B) 8 (C) 10 (D) 12

Let a1,a2,a3 ...... a11 be real numbers satisfying a_1 =15, 27-2a_2 > 0 and a_k= 2a_(k-1) - a_(k-2) for k=3,4,.....11 If (a1^2 +a2^2.......a11^2)/11 = 90 then find the value of (a_1+a_2....+a_11)/11

If a_1+a_2+a_3+...+a_n=1AAa_i>0,i=1,2,3, ,n , then find the maximum value of a_1 a_2a_3a_4a_5.... a_n.

Consider an A. P .a_1,a_2,a_3,..... such that a_3+a_5+a_8 =11and a_4+a_2=-2 then the value of a_1+a_6+a_7 is.....