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 :

" 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 find A and B

If px^(4)+qx^(3)+rx^(2)+sx+t=|{:(x^(2)+3x,x-1,x+3),(x^(2)+1,2-x,x-3),(x^(2)-3,x+4,3x):}| then t is equal to

if (2x - 1)/3 = (x-2)/3 + 1 , then x = ?

If (x ^(2) +x+1) + (x^(2) + 2x +3) + (x^(2) + 3x +5) + ….. + (x ^(2) + 20x + 39) =4500, then x is equal to :

Solve for x , |[x,-6,-1], [ 2,-3x,x-3], [-3, 2x, x+2]| =0.

Let x=|(x1),(x2),(x3)|,A=|(1,-1, 2),( 2, 0, 1),( 3, 2, 1)|a n d B=[(3),( 2),( 1)]dotIfA X=B , Then X is equal to

If the expression |{:(x^2+x+3,1,4),(2x^4+x^3+2x+1,2,3),(x^2+x,1,1):}| is equal to ax^4+bx^3+cx^2+dx+e , then the value of e is equal to

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

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

If a,b,c are in A.P.and f(x)= |(x+a,x^2+1,1),(x+b, 2x^2-1,1),(x+c,3x^2-2 , 1)| , then f'(x) is :