If rank of `((x,x,x),(x,x^2,x),(x,x,x+1))` is 1, then

If rank of ([x,x,xx,x^(2),xx,x,x+1]) is 1, then

The constant term of the polynomial |(x+3,x,x+2),(x,x+1,x-1),(x+2,2x,3x+1)| is

The rank of matrix [(x, -1, 0), (0, x, -1), (-1, 0,x)] is 2 then value of x is:

The constant term of the polynormial {|:(x+3,x,x+2),(x,x+1,x-1),(x+2,2x,+3x+1):|} is

Prove that |(1,x,x^2),(x^2,1,x),(x,x^2,1)|=(1-x^2) .

If f(x) = |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1))| , using properties of determinant, find f(2x) - f(x).

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)=|(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 f(5000) is equal to 0 b. 1 c. 500 d. -500

If f(x) =|(1,x,(x+1)),(2x,x(x-1),(x+1)x),(3x(x-1), x(x-1)(x-2),x(x-1)(x+1))| then f(50)+f(51)..f(99) is equal to

If f(x) =|(1,x,(x+1)),(2x,x(x-1),(x+1)x),(3x(x-1), x(x-1)(x-2),x(x-1)(x+1))| then f(50)+f(51)..f(99) is equal to