If `f(x)=|((1+x)^a,(1+2x)^b,1),(1,(1+x)^a,(1+2x)^b), ((1+2x)^b,1,(1+x)^a)|` then find constant term and coefficient of x

If the polynomial f(x) = |{:((1+x)^(a), (2+x)^(b),1),(1, (1 + x)^(a), (2 + x)^(b)),((2+x)^(b) , 1, (1+x)^(a)) :}| then the constant term of f(x) is

If f(x)= |{:((1+x)^(a),(1+2x)^(b),1),(1,(1+x)^(a),(1+2x)^(b)),((1+2x)^(b),1,(1+x)^(a)):}|, a,b being positive integers then

If f(x)=det[[(1+x)^(a),(1+2x)^(b),11,(1+x)^(a),(1+2x)^(b)(1+2x)^(b),1,(1+x)^(a)(1+2x)^(b),1,(1+x)^(a) term and coefficient of x]]

Consider the polynomial fucntion f(x) = |{:((1+x)^(2),,(1+2x)^(b),,1),(1,,(1+x)^(a),,(1+2x)^(b)),((1+2x)^(b),,1,,(1+x)^(a)):}| a,b being positive integers. the coefficient of x in f(x) is

Consider the polynomial fucntion f(x) = |{:((1+x)^(a),,(1+2x)^(b),,1),(1,,(1+x)^(a),,(1+2x)^(b)),((1+2x)^(b),,1,,(1+x)^(a)):}| a,b being positive integers. The constant term in f(x) is

If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)):}| then

In the expansion of (x^(2)+1+(1)/(x^(2)))^(n),n in N, (a)number of terms is 2n+1 (b)coefficient of constant terms is 2^(n-1) (c)coefficient of x^(2n-1)isn (d)coefficient of x^(2) in n

If f(x) =|(1, x, x+1),(2x, x(x-1), x(x+1)), (3x(x-1), 2(x-1)(x-2), x(x+1)(x-1))| then what is f(-1) +f(0) +f(1) equal to ?

If f(x)=det[[x-2,(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+2)^(3) then coefficient of x in f(x), is ]]