$A$ magnetic needle lying parallel to a magnetic field is turned through $60^{\circ}$. The work done on it is $W$. The torque required to maintain the magnetic needle in the position mentioned above is

The balancing length for a cell is $560 \, cm$ in a potentiometer experiment. When an external resistance of $10 \, \Omega$ is connected in parallel to the cell, the balancing length changes by $60 \, cm$. The internal resistance of the cell in ohms is:

$A$ particle of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x$-direction. It enters a region containing a uniform magnetic field $B$ directed along the negative $z$-direction,extending from $x = a$ to $x = b$. The minimum value of $v$ required so that the particle can just enter the region $x > b$ is

If $f:R \to R$ and $g:R \to R$ are defined by $f(x) = 2x + 3$ and $g(x) = x^2 + 7$,then the values of $x$ such that $g(f(x)) = 8$ are

What is the total number of orbitals associated with the principal quantum number $n=3$?

$A$ thin converging lens of focal length $f=25 \ cm$ forms the image of an object on a screen placed at a distance of $75 \ cm$ from the lens. The screen is moved closer to the lens by a distance of $25 \ cm$. The distance through which the object has to be shifted,so that its image on the screen is sharp again,is (in $cm$)