Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation energy of second reaction by 20 kJ mol⁻¹. If \( k_{1} \) and \( k_{2} \) are the rate constants of first and second reaction respectively at 300 K, then \( ln \frac{k_{2}}{k_{1}} \) will be ______.(nearest integer) [\( R=8.3 \, J \, K^{-1} \, mol^{-1} \)]

Consider the following pairs of electrons \((A)\) \((a)\) \(n=3,1=1, m_{l}=1, m_{s}=+\frac{1}{2}\) \(\quad (b)\) \(n =3,1=2, m _{l}=1, m _{s}=+\frac{1}{2}\) \((B)\) \((a)\) \(n =3,1=2, m _{l}=-2, m _{s}=-\frac{1}{2}\) \(\quad (b)\) \(n =3,1=2, m _{l}=-1, m _{s}=-\frac{1}{2}\) \((C)\) \((a)\) \(n=4,1=2, m_{l}=2, m_{s}=+\frac{1}{2}\) \(\quad (b)\) \(n =3,1=2, m _{l}=2, m _{s}=+\frac{1}{2}\) The pairs of electron present in degenerate orbitals is/are...... .

An unsaturated hydrocarbon \(X\) on ozonolysis gives \(A.\) Compound \(A\) when warmed with ammonical silver nitrate forms a bright silver mirror along the sides of the test tube. The unsaturated hydrocarbon \(X\) is ..... .

Consider the following reactions in which all the reactants and products are present in gaseous state
\(2xy \rightleftharpoons x_2 + y_2 \quad K_1 = 2.5\times 10^5\)
\(xy + \dfrac{1}{2}z_2 \rightleftharpoons xyz \quad K_2 = 5\times 10^{-3}\)
The value of \(K_3\) for the equilibrium \(\dfrac{1}{2}x_2 + \dfrac{1}{2}y_2 + \dfrac{1}{2}z_2 \rightleftharpoons xyz\) is:

What is the number of unpaired electron(s) in the highest occupied molecular orbital of the following species : \(N _2: N _2^{+} ; O _2 ; O _2^{+}\)?

The total number of anti bonding molecular orbitals, formed from \(2 \mathrm{s}\) and \(2 \mathrm{p}\) atomic orbitals in a diatomic molecule is _______.

Consider the following elements. Which of the following is/are true about \(\mathrm{A}^{\prime}, \mathrm{B}^{\prime}, \mathrm{C}^{\prime}\) and \(\mathrm{D}^{\prime}\) ? \(A\). Order of atomic radius: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(B\). Order of metallic character: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(C\). Size of the element : \(\mathrm{D}^{\prime}<\mathrm{C}^{\prime}<\mathrm{B}^{\prime}<\mathrm{A}^{\prime}\) \(D\). Order of ionic radius : \(\mathrm{B}^{\prime+}<\mathrm{A}^{\prime+}<\mathrm{D}^{\prime+}<\mathrm{C}^{\prime+}\) Choose the correct answer from the options given below :

Match List - I with List - II.

List - I	List - II
(A) Young’s Modulus	(I) \(M L^{-1} T^{-1}\)
(B) Torque	(II) \(M L^{-1} T^{-2}\)
(C) Coefficient of Viscosity	(III) \(M^{-1} L^3 T^{-2}\)
(D) Gravitational Constant	(IV) \(M L^2 T^{-2}\)

Choose the correct answer from the options given below :

\(\sum_{r=1}^{20}\left(r^{2}+1\right)(r !)\) is equal to:

If \({E}\) and \({H}\) represents the intensity of electric field and magnetising field respectively, then the unit of \(E/H\) will be :

A beam of light consisting of two wavelengths \(7000\; \mathring A\) and \(5500 \;\mathring A\) is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is \(2.5\,mm\) and the distance between the plane of slits and the screen is \(150\,cm\). The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is \(n \times 10^{-5}\,m\). The value of \(n\) is .............

\(\frac{x}{x+4}\) is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its \((i)\) third permitted energy level to the second level and \((ii)\) the highest permitted energy level to the second permitted level. The value of \(x\) will be.

A wire of resitance \(R\) and length \(L\) is cut into \(5\) equal part. if these parts are joined parts are joined paralley, than result resistance will be: