An object is projected with a velocity of $20 \ m/s$ making an angle of $45^\circ$ with the horizontal. The equation for the trajectory is $h = Ax - Bx^2$,where $h$ is height,$x$ is horizontal distance,and $A$ and $B$ are constants. The ratio $A : B$ is $(g = 10 \ m/s^2)$.

The ratio of the magnetic field at the centre of a current-carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be

$A$ conducting rod $AC$ of length $4l$ is rotated about a point $O$ in a uniform magnetic field $\vec{B}$ directed into the paper. $AO = l$ and $OC = 3l$. Then:

Which of the following pairs of substances cannot exist together in a solution?

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Four particles,each of mass $m$,are gently placed on the ring at opposite points of two perpendicular diameters. The new angular velocity of the ring will be:

The rate of steady volume flow of water through a capillary tube of length $l$ and radius $r$,under a pressure difference of $p$ is $V$. This tube is connected with another tube of the same length but half the radius,in series. Then,the rate of steady volume flow through them is (The pressure difference across the combination is $p$.)