Spin only magnetic moment of an octahedral complex of \(\mathrm{Fe}^{2+}\) in the presence of a strong field ligand in \(B.M.\) is \(.....\)

The bond dissociation enthalpy of \(\mathrm{X}_2 \Delta \mathrm{H}_{\text {bond }}\) calculated from the given data is _______ \(\mathrm{kJ} \mathrm{mol}^{-1}\). (Nearest integer)
\(\begin{aligned}
& \mathrm{M}^{+} \mathrm{X}^{-}(\mathrm{s}) \rightarrow \mathrm{M}^{+}(\mathrm{g})+\mathrm{X}^{-}(\mathrm{g}) \Delta \mathrm{H}_{\text {lattice }}^*=800 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{M}(\mathrm{~s}) \rightarrow \mathrm{M}(\mathrm{~g}) \Delta \mathrm{H}_{\text {sub }}^{\circ}=100 \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{aligned}\)
\(\mathrm{M}(\mathrm{~g}) \rightarrow \mathrm{M}^{+}(\mathrm{g})+\mathrm{e}^{-}(\mathrm{g}) \Delta \mathrm{H}_{\mathrm{i}}=500 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
\(\mathrm{X}(\mathrm{~g})+\mathrm{e}^{-}(\mathrm{g}) \rightarrow \mathrm{X}^{-}(\mathrm{g}) \Delta \mathrm{H}_{\mathrm{eg}}^*=-300 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
\(\mathrm{M}(\mathrm{~s})+\frac{1}{2} \mathrm{X}_2(\mathrm{~g}) \rightarrow \mathrm{M}^{+} \mathrm{X}^{-}(\mathrm{s}) \Delta \mathrm{H}_f^{\circ}=-400 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
[Given : \(\mathrm{M}^{+} \mathrm{X}^{-}\)is a pure ionic compound and X forms a diatomic molecule \(\mathrm{X}_2\) in gaseous state]

Given below are two statements: Statement \(I\) : The decrease in first ionization enthalpy from \(B\) to \(Al\) is much larger than that from \(Al\) to \(Ga\). Statement \(II\) : The d orbitals in Ga are completely filled. In the light of the above statements, choose the most appropriate answer from the options given below

Given below are two statements:
Statement-I : Compound (X), shown below , dissolves in \(NaHCO _3\) solution and has two chiral carbon atoms


Statement - II : Compound (Y), shown below, has two carbons with \(sp ^3\) hybridization, one carbon with \(sp ^2\) and one carbon with sp hybridization

In the light of the above statements, choose the correct answer from the options given below :

If the equilibrium constant for \(A \rightleftharpoons B+C\) is \(K _{ eq }^{(1)}\) and that of \(B + C \rightleftharpoons P \quad\) is \(K _{ eq }^{(2)},\) the equilibrium constant for \(A \rightleftharpoons P\) is :-

The maximum prescribed concentration of copper in drinking water is ........ \(ppm\)

\(\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})\) is a first order reaction.
\(\begin{array}{|l|l|l|}\hline \text{Time} & T & \infty \\\hline \mathbf{P}_{\text {system }} & \mathrm{P}_{\mathrm{t}} & \mathrm{P}_{\infty} \\\hline\end{array}\)
The reaction was started with reactant A only. Which of the following expression is correct for rate constant k ?

\(LED\) is constructed from \(Ga-As-P\) semiconducting material. The energy gap of this \(LED\) is \(1.9\, eV\). Calculate the wavelength of light emitted and its colour. \(\left[ h =6.63 \times 10^{-34} \;Js \right.\) and \(\left. c =3 \times 10^{8}\; ms ^{-1}\right]\)

Let \(\mathrm{A}\,(\sec \theta, 2 \tan \theta)\) and \(\mathrm{B}\,(\sec \phi, 2 \tan \phi)\), where \(\theta+\phi=\pi / 2\), be two points on the hyperbola \(2 \mathrm{x}^{2}-\mathrm{y}^{2}=2\). If \((\alpha, \beta)\) is the point of the intersection of the normals to the hyperbola at \(\mathrm{A}\) and \(\mathrm{B}\), then \((2 \beta)^{2}\) is equal to ..... .

Let a differentiable function \(f\) satisfy \(f ( x )+\int \limits_3^{ x } \frac{ f ( t )}{ t } dt =\sqrt{ x +1}, x \geq 3\). Then \(12 f (8)\) is equal to:

The binding energy for the following nuclear reactions are expressed in MeV .
\({ }_2 He ^3+{ }_0 n ^1 \rightarrow{ }_2 He ^4+20 MeV\)
\({ }_2 He ^4+{ }_0 n ^1 \rightarrow{ }_2 He ^5-0.9 MeV\)
If \(X _3, X _4, X _5\) denote the stability of \({ }_2 He ^3,{ }_2 He ^4\) and \({ }_2 He ^5\), respectively, then the correct order is :

\(\lim _{x \rightarrow 0} \frac{\int_{0}^{x^{2}}(\sin \sqrt{t}) dt }{x^{3}}\) is equal to

If \(\lim _{n \rightarrow \infty}\left(\sqrt{n^{2}-n-1}+n \alpha+\beta\right)=0\) then \(8(\alpha+\beta)\) is equal to :