The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to \(\frac{\mathrm{h}^{2}}{\mathrm{xma}_{0}^{2}}\). The value of \(10 \mathrm{x}\) is ........ . \(\left(\mathrm{a}_{0}\right.\) is radius of Bohr's orbit) (Nearest integer) [Given : \(\pi=3.14]\)

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

List\(I\)	List\(II\)
\(A.\) Cobalt catalyst	\(I.\) \(\left( H _2+ Cl _2\right)\) production
\(B.\)  Syngas	\(II.\) Water gas production
\(C.\) Nickel catalyst	\(III.\) Coal gasification
\(D.\) Brine solution	\(IV.\) Methanol production

Choose the correct answer from the options given below :-

Which of the following linear combination of atomic orbitals will lead to formation of molecular orbitals in homonuclear diatomic molecules [internuclear axis in \(z\)-direction] ?
A. \(2 \mathrm{p}_{\mathrm{z}}\) and \(2 \mathrm{p}_{\mathrm{x}}\)
B. 2 s and \(2 \mathrm{p}_{\mathrm{x}}\)
C. \(3 \mathrm{~d}_{\mathrm{xy}}\) and \(3 \mathrm{~d}_{\mathrm{x}^2-y^2}\)
D. 2 s and \(2 \mathrm{p}_{\mathrm{z}}\)
E. \(2 p_z\) and \(3 d_x{ }^2-y^2\)
Choose the correct answer from the options given below:

Mischmetal is an alloy consisting mainly of

For the thermal decomposition of reaction AB(g), the following is constructed.

The half life of the reaction is 'x' min.
x =_________ min.(Nearest integer)

Given below are two statements: Statement \(I\) : The metallic radius of \(\mathrm{Na}\) is \(1.86 \mathrm{~A}^{\circ}\) and the ionic radius of \(\mathrm{Na}^{+}\)is lesser than \(1.86 \mathrm{~A}^{\circ}\). Statement \(II\) : Ions are always smaller in size than the corresponding elements. In the light of the above statements, choose the correct answer from the options given below :

The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. \(19\)) are _______.

Wheatstone bridge principle is used to measure the specific resistance \(\left(S_1\right)\) of given wire, having length \(L\), radius \(r\). If \(X\) is the resistance of wire, then specific resistance is: \(S_1=X\left(\frac{\pi r^2}{L}\right)\). If the length of the wire gets doubled then the value of specific resistance will be :

The area of the region bounded by \(y^{2}=8 x\) and \(y^{2}=16(3-x)\) is equal to

Number of bridging \(CO\) ligands in \(\left[ Mn _{2}( CO )_{10}\right]\) is .... .

The source that illuminates the double - slit in 'double - slit interference experiment' emits two distinct monochromatic waves of wavelength \(500\,nm\) and \(600\, nm\), each of them producing its own pattern on the screen. At the central point of the pattern when path difference is zero, maxima of both the patterns coincide and the resulting interference pattern is most distinct at the region of zero path difference. But as one moves out of this central region, the two fringe systems are gradually out of step such that maximum due to on wavelength coincides with the minimum due to the other and the combined fringe system becomes completely indistinct. This may happen when path difference in \(nm\) is

A spherical soap bubble of radius \(3\,cm\) is formed inside another spherical soap bubble of radius \(6\,cm\). If the internal pressure of the smaller bubble of radius \(3\,cm\) in the above system is equal to the internal pressure of the another single soap bubble of radius \(r\,cm\). The value of \(r\) is.......

Let \(A =\left\{\theta \in(0,2 \pi): \frac{1+2 i \sin \theta}{1- i \sin \theta}\right.\) is purely imaginary \(\}\). Then the sum of the elements in \(A\) is