AIEEE 2004 (Maths) Mock Test

If the lines $2x+3y+1=0$ and $3x-y-4=0$ lie along diameters of a circle of circumference $10\pi ,$ then the equation of the circle is

The intercept on the line $y=x$ by the circle $x^2+y^2-2x=0$ is $AB.$ Equation of the circle on $AB$ as a diameter is

If $a\ne 0$ and the line $2bx+3cy+4d=0$ passes through the points of intersection of the parabolas $y^2=4ax$ and $x^2=4ay,$ then

The eccentricity of an ellipse, with its centre at the origin, is $\frac{1}{2}.$ If one of the directrices is $x=4,$ then the equation of the ellipse is

A line makes the same angle $\theta$ with each of the $x$ and $z$ axes. If the angle $\beta ,$ which it makes with $y$ -axis, is such that ${\sin }^2\beta =3{\sin }^2\theta ,$ then ${\cos }^2\theta$ equals