The angle between the diagonals of a quadrilateral formed by the lines `x/a+y/b=1,x/b+y/a=1,x/a+y/b=2` and `x/b+y/a=2` is (a) `pi/4` (b) `pi/6` (c) `pi/3` (d) `pi/2`

Prove that the diagonals of the parallelogram formed by the lines x/a +y/b=1,x/b+y/a= 1, x/a + y/b = 2 and x/b + y/a = 2 are at right angles . Also find its area (a != b)

If the equation x^3+b x^2+c x+1=0,(b (a) -pi (b) -pi/2 (c) pi/2 (d) pi

The angle between the planes 2x-y+z=6 and x+y+2z=7 is (A) pi/4 (B) pi/6 (C) pi/3 (D) pi/2

The angle of intersection of the curves y=2\ sin^2x and y=cos2\ x at x=pi/6 is (a) pi//4 (b) pi//2 (c) pi//3 (d) pi//6

Area lying in the first quadrant and bounded by the circle x^(2)+y^(2)=4 the line x=sqrt(3)y and x-axis , is (a) pi/2 (b) pi/4 (c) pi/3 (d) pi

The acute angle between the lines joining the origin to the points of intersection of the line sqrt(3)x+y=2 and the circle is x^(2)+y^(2)=4 , is a) pi//2 b) pi//3 c) pi//4 d) pi//6

The angle of intersection between the curves x^(2) = 4(y +1) and x^(2) =-4 (y+1) is (a) pi/6 (b) pi/4 (c) 0 (d) pi/2

The angle between the tangents to the parabola y^2=4a x at the points where it intersects with the line x-y-a=0 is (a) pi/3 (b) pi/4 (c) pi (d) pi/2