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 (a) 32 (b) 31 (c) 64 (d) 1024

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

If (1+x+2x^2)^20=a_0 + a_1x+a_2x^2+....................+a_40x^40 then a_0+a_2+a_4+.............+a_38 is

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 a_1+a_2+a_3+......+a_n=1 AA a_1 > 0, i=1,2,3,......,n, then find the maximum value of a_1 a_2 a_3 a_4 a_5......a_n.