The energy dissipated by a resistor is \(10 \,mJ\) in \(1\,s\) when an electric current of \(2\, mA\) flows through it. The resistance is \(....... \Omega\) (Round off to the Nearest Integer)

A bullet of mass \(200\,g\) having initial kinetic energy \(90\,J\) is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to \(40\,J\) within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is \(.....m\)

If Rydberg's constant is \(R\), the longest wavelength of radiation in Paschen series will be \(\frac{\alpha}{7 R}\), where \(\alpha=\)____________

Given below are two statements:
Statement I: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.
Statement II: For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon.
In the light of the above statements, choose the correct answer from the options given below:

The percentage error in the calculated volume of a sphere, if there is \(2\%\) error in its diameter measurement, is __________.

Two objects \(A\) and \(B\) are placed at \(15\,cm\) and \(25\,cm\) from the pole in front of a concave mirror having radius of curvature \(40 cm\). The distance between images formed by the mirror is \(..........\,cm\)

A cylindrical tube AB of length \(l\), closed at both ends contains an ideal gas of 1 mol having molecular weight M. The tube is rotated in a horizontal plane with constant angular velocity \( \omega \) about an axis perpendicular to AB and passing through the edge at end A. If \( P_{A} \) and \( P_{B} \) are the pressures at A and B respectively, then (Consider the temperature is same at all points in the tube)

An object \(AB\) is placed \(15\text{ cm}\) on the left of a convex lens \(P\) of focal length \(10\text{ cm}\). Another convex lens \(Q\) is now placed \(15\text{ cm}\) right of lens \(P\). If the focal length of lens \(Q\) is \(15\text{ cm}\), the final image is _______.

In an experiment for determining the gravitational acceleration \(g\) of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure. What is the value of \(g\) at the place? ...... \(m/s^2\)

Train \(A\) and train \(B\) are running on parallel tracks in the opposite directions with speeds of \(36\, km / hour\) and \(72 \,km / hour,\) respectively. A person is walking in train \(A\) in the direction opposite to its motion with a speed of \(1.8\, km / hr\). Speed (in \(ms ^{-1}\) ) of this person as observed from train \(B\) will be close to (take the distance between the tracks as negligible)

An artillery piece of mass \(M_1\) fires a shell of mass \(\mathrm{M}_2\) horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is _______.

The number of air molecules per \(\mathrm{cm}^3\) increased from \(3 \times 10^{19}\) to \(12 \times 10^{19}\). The ratio of collision frequency of air molecules before and after the increase in number respectively is \(.........\)

A tube of length \(50\,cm\) is filled completely with an incompressible liquid of mass \(250\,g\) and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity \(x \sqrt{ F }\) rad \(s ^{-1}\). If \(F\) be the force exerted by the liquid at the other end then the value of \(x\) will be\(....\)