The factors of `x^3-1+y^3+3x y` are (a) `(x-1+y)(x^2+1+y^2+x+y-x y)` (b)`(x+y+1)(x^2+y^2+1-x y-x-y)` (c)`(x-1+y)(x^2-1-y^2+x+y+x y)` (d)`3(x+y-1)(x^2+y^2-1)`

The factors of x^(3)-1+y^(3)+3xy are (a) (x-1+y)(x^(2)+1+y^(2)+x+y-xy)( b) (x+y+1)(x^(2)+y^(2)+1-xy-x-y)( c) (x-1+y)(x^(2)-1-y^(2)+x+y+xy)(d)3(x+y-1)(x^(2)+y^(2)-1)

The factors of x^3-x^2y-x y^2+y^3 are (a (x+y)(x^2-x y+y^2) (b) (x+y)(x^2+x y+y^2) (c) (x+y)^2(x-y) (d) (x-y)^2(x+y)

(x + 2) (x + 1) = (x -2) (x -3) (y+3)(y+2)=(y-1)(y-2)

{:("Column" A ,, "Column" B), (225x^(2) - 625 y^(2) = ,, (a) 25(x-2) (x-2)), (x^(2) - x - y - y^(2) = ,, (b) 25(3x- 5y) (3x + 5y)), (x^(2) - x - y^(2) + y = ,, (x + y) (x - y- 1)), (25x^(2) - 100 x + 100 = ,, (d) (x - y) (x + y -1)), (,,(e) (x + y) (x + y - 1)):}

If xa n dy are of same sign, then the value of (x^3)/2cos e c^2(1/2tan^(-1)x/y)+(y^3)/2sec^2(1/2tan^(-1)y/x) is equal to (x-y)(x^2+y^2) (b) (x+y)(x^2-y^2) (x+y)(x^2+y^2)dot (d) (x-y)(x^2-y^2)

The locus of the middle point of the chord of the circle x ^(2) + y ^(2) = a ^(2) such that the chords passes through a given point (x _(1) , y _(1)), is : a) x ^(2) + y ^(2) - x x _(1) - y y _(1) =0 b) x ^(2) + y ^(2) = x _(1) ^(2) + y _(1) ^(2) c) x + y = x _(2) + y _(1) d) x + y = x _(1) ^(2) + y _(1) ^(2)

Factorize : (1) (x+y)(2x+3y)-(x+y)(x+1) (2) (x+y)(2a+b)-(3x-2y)(2a+b)

The solution of 2 (y + 3) - x y(dy)/(dx) = 0 with y =-2, when x =1 is :a) (y + 3) = x ^(2) b) x ^(2) (y + 3) = 1 c) x ^(4) (y + 3) = 1 d) x ^(2) ( y +3) ^(2) = e ^(y +2)

If x and y are of same sign,then the value of (x^(3))/(2)cos ec^(2)((1)/(2)(tan^(-1)x)/(y))+(y^(3))/(2)sec^(2)((1)/(2)(tan^(-1)y)/(x)) is equal to (x-y)(x^(2)+y^(2)) (b) (x+y)(x^(2)-y^(2))(x+y)(x^(2)+y^(2))*(d)(x-y)(x^(2)-y^(2))