The angles at which the circles `(x-1)^2+y^2=10a n dx^2+(y-2)^2=5` intersect is `pi/6` (b) `pi/4` (c) `pi/3` (d) `pi/2`

The angle subtended by common tangents of two ellipses 4(x-4)^2+25 y^2=100a n d4(x+1)^2+y^2=4 at the origin is (a) pi/3 (b) pi/4 (c) pi/6 (d) pi/2

If the line xcostheta+ysintheta=2 is the equation of a transverse common tangent to the circles x^2+y^2=4 and x^2+y^2-6sqrt(3)x-6y+20=0 , then the value of theta is (a) (5pi)/6 (b) (2pi)/3 (c) pi/3 (d) pi/6

Then angle of intersection of the normal at the point (-5/(sqrt(2)),3/(sqrt(2))) of the curves x^2-y^2=8 and 9x^2+25 y^2=225 is 0 (b) pi/2 (c) pi/3 (d) pi/4

lf the eccentricity of the hyperbola x^2-y^2(sec)alpha=5 is sqrt3 times the eccentricity of the ellipse x^2(sec)^2alpha+y^2=25, then a value of alpha is : (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

If Aa n dB are acute positive angles satisfying the equations 3sin^2A+2sin^2B=1 and 3sin2A-2sin2B=0, then A+2B is equal to (a) pi (b) pi/2 (c) pi/4 (d) pi/6

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

If the tangent at the point P(theta) to the ellipse 16 x^2+11 y^2=256 is also a tangent to the circle x^2+y^2-2x=15 , then theta= (a) (2pi)/3 (b) (4pi)/3 (c) (5pi)/3 (d) pi/3

If (sqrt(3))b x+a y=2a b touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then the eccentric angle of the point of contact is (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

The acute angle between two straight lines passing through the point M(-6,-8) and the points in which the line segment 2x+y+10=0 enclosed between the co-ordinate axes is divided in the ratio 1:2:2 in the direction from the point of its intersection with the x-axis to the point of intersection with the y-axis is: (a) pi/3 (b) pi/4 (c) pi/6 (d) pi/(12)

The length of the longest interval in which the function 3sinx-4sin^3x is increasing is pi/3 (b) pi/2 (c) (3pi)/2 (d) pi