Which of the following sets are not convex? A) `{(x,y):8x^2+6y^2leq24}` B) `{(x,y): 6 leq x^2+y^2 leq 36}` C) `{(x,y): ygeq3, ygeq 30}` D) `{(x,y): x^2leqy}`

Make a rough sketch of the region given below and find its area using integration {(x,y): 0 leq y leq x^2+3,0 leq y leq 2x+3,0 leq x leq 3} .

Factorize each of the following expressions : 54 x^6y+2x^3y^4 , 8x^2y^3-x^5

Using integration, find the area of the region: {(x , y):9x^2+y^2lt=36\ "and"\ 3x+ygeq6}

Find the area of the region given by x+y le 6, x^2+y^2 le 6y and y^2 le 8x .

Find the area of the region given by x+y le 6, x^2+y^2 le 6y and y^2 le 8x .

Which of the following is a homogeneous differential equation? (4 x+6 y+5) d y-(3 y+2 x+4) d x=0 x y d x-(x^3+y^3) d y=0 (x^3+2 y^2) d x+2 x y d y=0 y^2 d x+(x^2-x y-y^2) d y=0

Solve the following systems of inequation graphically: 2x+ygeq8,\ x+2ygeq8,\ x+ylt=6

Find the equation of the circle which intersects each of the following circles orthogonlly x^2 + y^2 + 4x + 2y + 1 = 0 . 2(x^2 + y^2) + 8x + 6y - 3 = 0, x^2 + y^2 + 6x -2y - 3 =0.

Let f(x)=1+x , 0 leq x leq 2 and f(x)=3−x , 2 lt x leq 3 . Find f(f(x)) .

The following are the steps involved in factorizing 64 x^(6) -y^(6) . Arrange them in sequential order (A) {(2x)^(3) + y^(3)} {(2x)^(3) - y^(3)} (B) (8x^(3))^(2) - (y^(3))^(2) (C) (8x^(3) + y^(3)) (8x^(3) -y^(3)) (D) (2x + y) (4x^(2) -2xy + y^(2)) (2x - y) (4x^(2) + 2xy + y^(2))