The speed verses time graph for a particle is shown in the figure. The distance travelled (in \(m\) ) by the particle during the time interval \(t=0\) to \(t=5\, s\) will be

A rod of linear mass density ' \(\lambda\) ' and length ' \(L\) ' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :

Blocks of masses \(m , 2 m , 4 m\) and \(8 m\) are arranged in a line on a frictionless floor. Another block of mass \(m ,\) moving with speed \(v\) along the same line (see figure) ollides with mass \(m\) in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass \(8 m\) starts moving the total energy loss is \(p \%\) of the original energy. Value of \('p'\) is close to

Two capacitors of capacities \(2 {C}\) and \({C}\) are joined in parallel and charged up to potential \({V}\). The battery is removed and the capacitor of capacity \(C\) is filled completely with a medium of dielectric constant \({K}\). The potential difference across the capacitors will now be

In the experiment of calibration of voltmeter, a standard cell of \(e.m.f\,\,1.1\,volt\) is balanced against \(440\,cm\) of potential wire. The potential difference across the ends of resistance is found to balance against \(220\,cm\) of the wire. The corresponding reading of voltmeter is \(0.5\,volt.\) The error in the reading of volmeter will be .................. \(volt\)

A piece of bone of an animal from a ruin is found to have \(^{14}C\) activity of \(12\) disintegrations per minute per gm of its carbon content. The \(^{14}C\) activity of a living animal is \(16\) disintegrations per minute per gm. How long ago nearly did the animal die? ............\(years\) (Given halflife of \(^{14}C\) is \(t_{1/2} = 5760\,years\) )

Match the LIST-I with LIST-II

List-I	List-II
A. Planck's constant	I. \(ML^2T^{-2}\)
B. Stopping potential	II. \(T^{-1}\)
C. Work function	III. \(ML^2T^{-1}\)
D. Threshold frequency	IV. \(ML^2T^{-3}A^{-1}\)

Choose the correct answer from the options given below:

Glycerine of density \(1.25 \times 10^3\,kg\,m ^{-3}\) is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends is \(10\,cm ^2\) and \(5\,cm ^2\) and pressure drop across its length is \(3\,Nm ^{-2}\). The rate of flow of glycerine through the pipe is \(x \times 10^{-5} m ^3 s ^{-1}\). The value of \(x\) is \(..............\).