If `p(x)=(1+x^2+x^4++x)/(1+x+x^2++x^(n-1)^(2n-2)` is a polynomial in `x ,t h e nn` can be `5` b. `10` c. `20` d. `17`

If p(x)=(1+x^(2)+x^(4)+...+x^(2n-2))/(1+x+x^(2)+...+x^(n-1)) is a polomial in x, then find possible value of n.

If a^2+b^2+c^2=-2a n df(x)= |a+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

D={x:x=2n-1<20 and n in N}

If a^2+b^2+c^2=-2\ a b n df(x)=|1+a^xx(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree- a. 2 b. \ 3 c. \ 0 d. 1

If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e r en in N , then value of a is n b. n-1 c. n+1 d. none of these

Let p_1(x) = x^3 – 2020x^2 + b_1x + c_1 and p_2(x) = x^3 – 2021x^2 + b_2x + c^2 be polynomials having two common roots alpha and beta . Suppose there exist polynomials q_1(x) and q_2(x) such that p_1(x)q_1(x) + p_2(x)q_2(x) = x^2 – 3x + 2 . Then the correct identity is

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

If p x^4\ \ q x^3+r x^2+s x+t=|x^2+3xx-1x+3x+1 2-xx-3x-3x+4 3x|t h e n\ is equal to- a. b. c. d. none