`" If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x-1,,2x-1):}|=xA +B` then

Without expanding a determinant at any stage, show that |{:(x^(2)+x, x+1, x+2),(2x^(2) +3x-1, 3x, 3x-3),(x^(2) +2x+3, 2x-1, 2x-1):}|=xA+B where A and B are determinants of order 3 not involving x.

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

y=|(x^2+x, x+1, x-2),(2x^2+3x+1, 3x, 3x-3),(x^2+3x+2, 2x-1, 2x-1)| represents (A) a straight line (B) a circle (C) a parabola (D) none of these

x ^ (2) + 2x + 3x = 1

If |{:(x^(2) +x , 3x - 1 , -x + 3),(2x +1 , 2 + x^(2) , x^(3) - 3),(x - 3, x^(2) + 4, 3x):}| = a_(0) + a_(1) x + a_(2) x^(2) + .... + x_(7) x^(7), then the value of a_(0) is

(x^(2)-x)-(1)/(2)(x-3+3x^(2))

[[3x^(2),3x,1x^(2)+2x,2x+1,12x+1,x+2,1]]=(x-1)^(3)

im_(-)>1[(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

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

lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]