$A$ wire of resistance $4\,\Omega$ is stretched to twice its original length. The resistance of the stretched wire would be ................ $\Omega$.

Three point charges $+q, -2q$ and $+q$ are placed at points $(x = 0, y = a, z = 0)$,$(x = 0, y = 0, z = 0)$ and $(x = a, y = 0, z = 0)$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

The point of contact of the circles $x^2+y^2+2x+2y+1=0$ and $x^2+y^2-2x+2y+1=0$ is

If the area of the auxiliary circle of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ $(a>b)$ is twice the area of the ellipse,then the eccentricity of the ellipse is

If $A+C=2B$,then $\frac{\cos C-\cos A}{\sin A-\sin C}$ is equal to

The equations of the normals at the ends of the latus rectum of the parabola $y^2 = 4ax$ are given by