Vegetative propagation in Pistia occurs by:

In the figure,suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also,let the center disk be rotated on the common axis with an angular speed $\omega$. If unpolarized light is incident on the left disk with an intensity $I_{max}$,the intensity of the beam emerging from the right disk is given by:

$A$ cylindrical rod with one end in a steam chamber and the other end in ice results in the melting of $0.1 \, g$ of ice per second. If the rod is replaced by another with half the length and double the radius of the first,and if the thermal conductivity of the material of the second rod is $1/4$ that of the first,the rate at which ice melts in $g/s$ will be:

Number of moles of $MnO_4^-$ required to oxidize one mole of ferrous oxalate completely in acidic medium will be .............. $moles$.

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by:

The radius of the circle $r = \sqrt{3} \sin \theta + \cos \theta$ is