The current in the windings of a toroid is $2.0\,A$. There are $400$ turns and the mean circumferential length is $40\,cm$. If the magnetic field inside the toroid is $1.0\,T$,the relative permeability is near to:

Let $P, Q, R$ and $S$ be the points on the plane with position vectors $-2 \hat{i}-\hat{j}$,$4 \hat{i}$,$3 \hat{i}+3 \hat{j}$ and $-3 \hat{i}+2 \hat{j}$ respectively. Then the quadrilateral $PQRS$ must be a

$A$ body of mass $5\, kg$ moving with a velocity $10\, m/s$ collides with another body of mass $20\, kg$ at rest and comes to rest. The velocity of the second body after the collision is ......... $m/s$.

On a new scale of temperature (which is linear) called the $W$ scale,the freezing and boiling points of water are $39\,^{\circ}W$ and $239\,^{\circ}W$ respectively. What will be the temperature on the new scale,corresponding to a temperature of $39\,^{\circ}C$ on the Celsius scale? ............ $^{\circ}W$

The value of $k$,if $(1,2)$ and $(k,-1)$ are conjugate points with respect to the ellipse $2x^2 + 3y^2 = 6$ is:

The product of the lengths of perpendiculars drawn from any point on the hyperbola $x^2 - 2y^2 - 2 = 0$ to its asymptotes is