If \(C\) and \(V\) represent capacity and voltage respectively then what are the dimensions of \(\lambda,\) where \(\frac{ C }{ V }=\lambda ?\)

A certain amount of gas of volume \(V\) at \(27^{o}\,C\) temperature and pressure \(2 \times 10^{7} \;Nm ^{-2}\) expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be  (Use \(\gamma=1.5\) )

A physical quantity \(P\) is given as \(P=\frac{a^2 b^3}{c \sqrt{d}}\) The percentage error in the measurement of \(a, b, c\) and \(d\) are \(1 \%, 2 \%, 3 \%\) and \(4 \%\) respectively. The percentage error in the measurement of quantity \(P\) will be \(.......\%\)

A positive ion \(A\) and a negative ion \(B\) has charges \(6.67 \times 10^{-19} \mathrm{C}\) and \(9.6 \times 10^{-10} \mathrm{C}\), and masses \(19.2 \times 10^{-27} \mathrm{~kg}\) and \(9 \times 10^{-27} \mathrm{~kg}\) respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is \(P \times 10^{45}\), where the value of 10\(P\) is _______.
(Take \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-1}\) and universal gravitational constant as \(6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}\) )
Assume that charge may not be an integral multiple of electrons.

A circular loop of radius \(20\text{ cm}\) and resistance \(2\ \Omega\) is placed in a time varying magnetic field \(\vec{B} = (2t^2 + 2t + 3)\text{ T}\). At \(t = 0\), for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at \(t = 3\text{ s}\) is \(\dfrac{\alpha}{50}\text{ A}\). The value of \(\alpha\) is _______.
(Take \(\pi = 22/7\))

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 \(\pi=3.14]\)

The average energy released per fission for the nucleus of \({ }_{92}^{235} U\) is 190 MeV . When all the atoms of 47 g pure \({ }_{92}^{235} U\) undergo fission process, the energy released is \(\alpha \times 10^{23} MeV\). The value of \(\alpha\) is ___________.
(Avogadro Number \(=6 \times 10^{23}\) per mole)

Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is \(M,\) radius of its top, \(R\) and height, \(H\), then its moment of inertia about its axis is

A metal block of base area \(0.20\,m ^2\) is placed on a table, as shown in figure. A liquid film of thickness \(0.25\,mm\) is inserted between the block and the table. The block is pushed by a horizontal force of \(0.1\,N\) and moves with a constant speed. If the viscosity of the liquid is \(5.0 \times 10^{-3} \;Pa-s\), the speed of block is \(.........\times 10^{-3}\,m / s\)

Match the List \(I\) with List \(II\)

LIST \(I\)	LIST \(II\)
\(A\) Intrinsic Semiconductor	\(I\) Fermi-level near conduction band
\(B\) \(n-\)type semiconductor	\(II\) Fermi-level at middle
\(C\) \(p-\) type semiconductor	\(III\) Fermi-level near valence band
\(D\) Metals	\(IV\) Fermi-level inside conduction band

Choose the correct answer from the options given below: