|[x,a,a],[a,x,a],[a,a,x]|=(x+2a)(x-a)^(2)

if f(x)=|[-1,x+2,x+1],[x,x(x-1),x^2],[x^2,x(x-2),2x(x-1)]| then f(99) is equal to (i)0 (ii)990 (iii)2970 (iv)8910

let ax^(6)+bx^(5)+cx^(4)+dx^(3)+ex^(2)+fx+g = |[x+1,x^(2)+2,x^(2)+x],[x^(2)+x,x^(2)+1,x^(2)+2],[x^(2)+2,x^(2)+x,x+1]| then f+g=

Solve |{:(x^(2)-1,,x^(2)+2x+1,,2x^(2)+3x+1),(2x^(2)+x-1,,2x^(2)+5x-3,,4x^(2)+4x-3),(6x^(2)-x-2,,6x^(2)-7x+2,,12x^(2)-5x-2):}| =0

Solve |{:(x^(2)-1,,x^(2)+2x+1,,2x^(2)+3x+1),(2x^(2)+x-1,,2x^(2)+5x-3,,4x^(2)+4x-3),(6x^(2)-x-2,,6x^(2)-7x+2,,12x^(2)-5x-2):}| =0

|[(x-2)^(2), (x-1)^(2), x^(2)], [(x-1)^(2), x^(2), (x+1)^(2)],[x^(2), (x+1)^(2), (x+2)^(2)]|+P^(3)=0 the value of P is

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2) ,((x-1)^2, (x-2)^2, (x-3)^2), ((x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2),((x-1)^2 (x-2)^2, (x-3)^2), (x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), sin(x-x^2)],[sin2x,0,sin(2x^2)]| . Find the value of f^(prime)(0) .

Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), sin(x-x^2)],[sin2x,0,sin(2x^2)]| . Find the value of f^(prime)(0) .