`x^2\ x\ \ 2y^3\ x\ \ 5x^3y^2` is equal to:
(a)`10 x^2y^5`
(b) `10 x^5y^2`
(c)`10 x^5y^5`
(d) `x^5y^5`

The coefficient of x^2 in -5/3\ x^2y is equal to :- (a) -5/3 (b) -5/3y (c) 5/3 (d) 5/3y

The combined equation of the asymptotes of the hyperbola 2x^2+5x y+2y^2+4x+5y=0 is (a) 2x^2+5x y+2y^2+4x+5y+2=0 (b) 2x^2+5x y+2y^2+4x+5y-2=0 (c) 2x^2+5x y+2y^2=0 (d) none of these

From the points (3, 4), chords are drawn to the circle x^2+y^2-4x=0 . The locus of the midpoints of the chords is (a) x^2+y^2-5x-4y+6=0 (b) x^2+y^2+5x-4y+6=0 (c) x^2+y^2-5x+4y+6=0 (d) x^2+y^2-5x-4y-6=0

Find the greatest common factor (GCF/HCF) of the following polynomials: 2x^3y^2,\ 10 x^2y^3 ,14 x y (ii) 14 x^3y^5,\ 10 x^5y^3,\ 2x^2y^2

The equation of the circle having the intercept on the line y+2x=0 by the circle x^2 + y^2 + 4x + 6y = 0 as a diameter is : (A) 5x^2 + 5y^2 - 8x + 16y =0 (B) 5x^2 + 5y^2 + 8x - 16y =0 (C) 5x^2 + 5y^2 - 8x - 16y =0 (D) 5x^2 + 5y^2 + 8x+- 16y =0

The equation of the circle passing through the point of intersection of the circle x^2+y^2=4 and the line 2x+y=1 and having minimum possible radius is (a) 5x^2+5y^2+18 x+6y-5=0 (b) 5x^2+5y^2+9x+8y-15=0 (c) 5x^2+5y^2+4x+9y-5=0 (c) 5x^2+5y^2-4x-2y-18=0

If the point P(x ,\ y) is equidistant from A(5,\ 1) and B(-1,\ 5) , then (a) 5x=y (b) x=5y (c) 3x=2y (d) 2x=3y

Show that: (x^2+y^2)^5=(x^5-10x^3y^2+5xy^4)^2+(5x^4 y-10x^2y^3+y^5)^2

The general solution of differential equation (x^6y^4+x^2)dy=(1-x^5y^5-x y)dx is (a)In |x|=x y+(x^4y^4)/4+C (b)In |y|=x y+(x^5y^5)/4+C (c)In |y|=x y+(x^5y^5)/2+C (d)In |x|=x y+(x^4y^4)/5+C

If the foci of a hyperbola lie on y=x and one of the asymptotes is y=2x , then the equation of the hyperbola, given that it passes through (3, 4), is (a) x^2-y^2-5/2x y+5=0 (b) 2x^2-2y^2+5x y+5=0 (c) 2x^2+2y^2-5x y+10=0 (d) none of these