What is the position and nature of image formed by lens combination shown in figure? (\(f_1, f_2\) are focal lengths)

In the reported figure, there is a cyclic process \(ABCDA\) on a sample of \(1\, {mol}\) of a diatomic gas. The temperature of the gas during the process \({A} \rightarrow {B}\) and \({C} \rightarrow {D}\) are \({T}_{1}\) and \({T}_{2}\left({T}_{1}\,>\,{T}_{2}\right)\) respectively. Choose the correct option out of the following for work done if processes \(B C\) and \(D A\) are adiabatic.

Identify the correct truth table of the given logical circuit.

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is :

A cord is wound round the circumference of wheel of radius \(r\). The axis of the wheel is horizontal and moment of inertia about it is \(I\). A weight \(mg\) is attached to the end of the cord and falls from rest. After falling through a distance \(h\), the angular velocity of the wheel will be

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ______ \(\times 10^{-1} \mathrm{~J}\).
(Take \(\pi=3.14\))

In the figure shown, the current in the \(10\, V\) battery is close to

An electron in the hydrogen atom initially in the fourth excited state makes a transition to \(\mathrm{n}^{\text {th }}\) energy state by emitting a photon of energy 2.86 eV. The integer value of \(n\) will be ____.

In Young's double slit experiment, monochromatic light of wavelength \(5000\) \(A\) is used. The slits are \(1.0 \mathrm{~mm}\) apart and screen is placed at \(1.0 \mathrm{~m}\) away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is _______ \(10^{-6} \mathrm{~m}\).

A block of mass \(0.1\, kg\) is connected to an elastic spring of spring constant \(640\, Nm^{-1}\) and oscillates in a damping medium of damping constant \(10^{-2}\, kg\,s^{-1}\) . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to ..... \(s\)

Given below are two statements :
Statement (I) : The dimensions of Planck's constant and angular momentum are same.
Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.
In the light of the above statements, choose the most appropriate answer from the options given below :

An inductance coil has a reactance of \(100\, \Omega\). When an \(AC\) signal of frequency \(1000\, Hz\) is applied to the coil, the applied voltage leads the current by \(45^{\circ}\). The self- inductance of the coil is