Identify the logic gate given in the circuit.

In an experiment to verify Stokes law, a small spherical ball of radius \(r\) and density \(\rho\) falls under gravity through a distance \(h\) in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of \(h\) is proportional to : (ignore viscosity of air)

The current flowing through a conductor connected across a source is \(2\,A\) and \(1.2\,A\) at \(0^{\circ}\,C\) and \(100^{\circ}\,C\) respectively. The current flowing through the conductor at \(50^{\circ}\,C\) will be \(......\times 10^2\,mA\).

A spring stretches by \(2\) mm when it is loaded with a mass of \(200\) g. From equilibrium position the mass is further pulled down by \(2\) mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g \(= 10\) m/s\(^2\))

A thin disc of mass \(M\) and radius \(R\) has mass per unit area \(\sigma (r) = kr^2\) where \(r\) is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is

A thin \(1 \,m\) long rod has a radius of \(5\, mm\). A force of \(50\,\pi kN\) is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is \(0.01\, mm\), which of the following statements is false ?

Match List \(I\) (Wavelength range of electromagnetic spectrum) with List \(II\) (Method of production of these waves) and select the correct option from the options given below the lists

List \(I\)	List \(II\)
\((1)\) \(700\, nm\) to \(1\,mm\)	\((i)\) Vibration of atoms and molecules
\((2)\) \(1\,nm\) to \(400\, nm\)	\((ii)\) Inner shell electrons in atoms moving from one energy level to a lower level
\((3)\) \( < 10^{-3}\,nm\)	\((iii)\) Radioactive decay of the nucleus
\((4)\) \(1\,mm\) to \(0.1\,m\)	\((iv)\) Magnetron valve

A wire of density \(9 \times 10^{-3} \,kg\, cm ^{-3}\) is stretched between two clamps \(1\, m\) apart. The resulting strain in the wire is \(4.9 \times 10^{-4}\). The lowest frequency of the transverse vibrations in the wire is......\(HZ\) (Young's modulus of wire \(Y =9 \times 10^{10}\, Nm ^{-2}\) ), (to the nearest integer),

Given below are two statements: Statement \(I:\) If \(E\) be the total energy of a satellite moving around the earth, then its potential energy will be \(\frac{E}{2}\). Statement \(II:\) The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy \(E\). In the light of the above statements, choose the most appropriate answer from the options given below

In the circuit shown here, the point '\(C\)' is kept connected to point '\(A\)' till the current flowing through the circuit becomes constant. Afterward, suddenly, point '\(C\)' is disconnected from point '\(A\)' and connected to point '\(B\)' at time \(t = 0\). Ratio of the voltage across resistance and the inductor at \(t = L/R\) will be equal to:

Given below are two statements Statement \(I\) : The electric force changes the speed of the charged particle and hence changes its kinetic energy: whereas the magnetic force does not change the kinetic energy of the charged particle Statement \(II\) : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below