`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

" 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

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

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

The equation |((1+x)^2,(1-x)^2,-(2+x^2)),(2x+1,3x,1-5x),(x+1,2x,2-3x)|+|((1+x)^2,2x+1,x+1),((1-x)^2,3x,2x),(1-2x,3x-2,2x-3)|=0 has has (a) no real solution (b) 4 real solutions (c) two real and two non-real solutions (d) infinite number of solutions, real or non-real

|(2x_1y_1, x_1y_2+x_2y_1, x_1y_3+x_3y_1),(x_1y_2+x_2y_1, 2x_2y_2, x_2y_3+x_3y_2),(x_1y_3+x_3y_1, x_2y_3+x_3y_2, 2x_3y_3)|= (A) 0 (B) 1 (C) -1 (D) none of these

x^((x-1)- 1/2 (x-1)^2+1/3((x-1)^3).- 1/4((x-1)^4).+…….. is equal to (A) 2logx (B) logx (C) x^2 (D) none of these

If y=(x^2-3x+1)/(2x^2-3x+2) , where x is real, the value of y lies between (A) -1leyle5/7 (B) -1/2leyle5/7 (C) 5/7ltylt1 (D) none of these

Let ax^(3) + bx^(2) + cx + d |(x+1,2x,3x),(2x+3,x+1,x),(2-x,3x+4,5x-1)| , then What is the value of a + b + c + d ?

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

lim_(x rarr oo)((x^(2)+2x-1)/(2x^(2)-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo(c)(1)/(2) (d) none of these