Given below are two statements : \(Statement\) \((I)\) :Viscosity of gases is greater than that of liquids. \(Statement\) \((II)\) : Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below :

A current of \(5\; {A}\) is passing through a non-linear magnesium wire of cross-section \(0.04\; {m}^{2}\). At every point the direction of current density is at an angle of \(60^{\circ}\) with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is ....\({V} / {m}\) (Resistivity of magnesium is \(\rho=44 \times 10^{-8}\, \Omega m\))

In a screw gauge, there are \(100\) divisions on the circular scale and the main scale moves by \(0.5\,mm\) on a complete rotation of the circular scale. The zero of circular scale lies \(6\) divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, \(4\) linear scale divisions are clearly visible while \(46^{\text {th }}\) division the circular scale coincide with the reference line. The diameter of the wire is \(...........\times 10^{-2}\,mm\)

The radius of gyration of a uniform rod of length \(l,\) about an axis passing through a point \(\frac{l}{4}\) away from the centre of the rod, and perpendicular to it, is

Given below are two statements: \(Statement\) \(I\) : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. \(Statement\) \(II\) : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water. In the light of the above statements, choose the most appropriate from the options given below

Given below are two statements: Statement \(I\) : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \(\left( E _{1}\right)\) to higher energy orbit \(\left( E _{2}\right)\), is given as \(hf = E _{1}- E _{2}\). Statement \(II\) : The jumping of electron from higher energy orbit \(\left(E_{2}\right)\) to lower energy orbit \(\left(E_{1}\right)\) is associated with frequency of radiation given as \(f\) \(=\left( E _{2}- E _{1}\right) / h\) This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below

The magnetic field associated with a light wave is given, at the origin, by \(B = B_0 [sin\,(3.14 \times 10^7)\,ct\,+\,sin\,(6.28 \times 10^7)\,ct]\) If this light falls on a silver plate having a work function of \(4.7\,eV,\) what will be the maximum kinetic energy of the photo electrons? .............. \(eV\)

Let \(x = x(y)\) be the solution of the differential equation \(2y^2 \dfrac{dx}{dy} - 2xy + x^2 = 0\), \(y > 1\), \(x(e) = e\). Then \(x(e^2)\) is equal to:

Four identical hollow cylindrical columns of mild steel support a big structure of mass \(50 \times 10^{3} {kg}\), The inner and outer radii of each column are \(50\; {cm}\) and \(100 \;{cm}\) respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use \(\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]\)

Two radioactive substances A and B of mass numbers \(200\) and \(212\) respectively, shows spontaneous \(\alpha\)-decay with same \(Q\) value of \(1\) MeV. The ratio of energies of \(\alpha\)-rays produced by A and B is ________.

A plane electromagnetic wave propagates along the \(+x\) direction in free space. The components of the electric field, \(\vec{E}\) and magnetic field, \(\vec{B}\) vectors associated with the wave in Cartesian frame are

A ray of light coming from the point \(P(1,2)\) gets reflected from the point \(\mathrm{Q}\) on the \(\mathrm{x}\)-axis and then passes through the point \(R(4,3)\). If the point \(S(h\), \(\mathrm{k})\) is such that \(\mathrm{PQRS}\) is a parallelogram, then \(\mathrm{hk}^2\) is equal to

The minimum number of elements that must be added to the relation \(R =\{( a , b ),( b , c )\), (b, d) \(\}\) on the set \(\{a, b, c, d\}\) so that it is an equivalence relation, is \(.........\)