Given below are two statements : One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : \(n - p - n\) transistor permits more current than a \(p-n-p\) transistor Reason \(R\) : Electrons have greater mobility as a charge carrier Choose the correct answer from the options given below

Two long current carrying thin wires, both with current \(I\), are held by insulating threads oflength \(L\) and are in equilibrium as shown in the figure, with threads making an angle '\(\theta\)' with the vertical. If wires have mass \(\lambda\) per unit length then the value of \(l\) is 
(\(g =\) gravitational acceleration)

The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is \(31.4 \,cm\). The diameter of wire is measured as \(2.4 \,cm\). The resistivity of the given wire is measured as \(x \times 10^{-3} \,\Omega cm\). The value of \(x\) is_______ [Take \(\pi=3.14]\)

Consider the following statements : \(A.\) Atoms of each element emit characterstics spectrum. \(B.\) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit. \(C.\) The density of nuclear matter depends on the size of the nucleus. \(D.\) A free neutron is stable but a free proton decay is possible. \(E.\) Radioactivity is an indication of the instability of nuclei. Choose the correct answer from the options given below 

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of \(\left[M^a L^b T^c\right]\). If \(b=-3\), the value of \(c\) is ________

When a gas filled in a closed vessel is heated by raising the temperature by \(1^{\circ} C\), its pressure increase by \(0.4 \%\). The initial temperature of the gas is ..........\(K\)

The total internal energy of two mole monoatomic ideal gas at temperature \(T=300\,K\) will be ...........\(J\). \(\text { (Given } R =8.31\,J / mol.K )\)

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of \(T\). The total internal energy, \(U\) of a mole of this gas, and the value of \(\gamma\left(=\frac{ C _{ P }}{ C _{ v }}\right)\) given, respectively, by

A thin convex lens \(L\) (refractive index \(= 1.5\)) is placed on a plane mirror \(M\). When a pin is placed at \(A\), such that \(OA = 18\, cm\), its real inverted image is formed at \(A\) itself, as shown in figure. When a liquid of refractive index \({\mu _1}\) is put between the lens and the mirror, the pin has to be moved to \(A’\). such that \(OA’ = 27\,cm\), to get its inverted real image at \(A'\) itself. The value of \({\mu _1}\) will be

A diverging lens with magnitude of focal length \(25\ cm\) is placed at a distance of \(15\ cm\) from a converging lens of magnitude of focal length \(20\ cm\). A beam of parallel light falls on the diverging lens. The final image formed is

A rectangular loop of sides \(12 \mathrm{~cm}\) and \(5 \mathrm{~cm}\), with its sides parallel to the \(x\)-axis and \(y\)-axis respectively moves with a velocity of \(5 \mathrm{~cm} / \mathrm{s}\) in the positive \(\mathrm{x}\) axis direction, in a space containing a variable magnetic field in the positive \(z\) direction. The field has a gradient of \(10^{-3} \mathrm{~T} / \mathrm{cm}\) along the negative \(\mathrm{x}\) direction and it is decreasing with time at the rate of \(10^{-5} \mathrm{~T} / \mathrm{s}\). If the resistance of the loop is \(6 \mathrm{~m} \Omega\), the power dissipated by the loop as heat is _______ \(\times 10^{-9} \mathrm{~W}\).