Which of the following ions is the strongest oxidizing agent? (Atomic Number of \(\mathrm{Ce}=58, \mathrm{Eu}=63, \mathrm{~Tb}=65, \mathrm{Lu}=71\) )

The heat of atomization of methane and ethane are \(360\,kJ/mol\) and \(620\,kJ/mol,\) respectively. The longest wavelength of light capable of breaking the \(C - C\) bond is (Avogadro number \(= 6.02 \times  10^{23},\) \(h = 6.62 \times 10^{-34}\,Js\) )

Given

Reaction	Energy Change (in \(kJ\) )
\(Li(s) \to  Li(g)\)	\(161\)
\(Li(g) \to  Li^+(g)\)	\(520\)
\(\frac {1}{2}F_2(g)\,\to F(g)\)	\(77\)
\(F(g) + e^- \to F^-(g)\)	(Electron gain enthalpy)
\(Li^+ (g) + F^-(g) \to  LiF(s)\)	\(-1047\)
\(Li (s) + \frac {1}{2}F_2(g)\to LiF(s)\)	\(-617\)

Based on data provided, the value of electron gain enthalpy of fluorine would be.....\(kJ\,mol^{-1}\)

Which hydrogen in compound\((E)\) is easily replaceable during bromination reaction in presence of light? \(\mathop {C{H_3} - }\limits_\delta  \mathop {C{H_2} - }\limits_\gamma  \mathop {CH = }\limits_\beta  \mathop {C{H_2}}\limits_\alpha  \)                     \((E)\)

Which among the following purification methods is based on the principle of "Solubility" in two different solvents?

A stream of electrons from a heated filaments was passed two charged plates kept at a potential difference \(V\, esu.\) If \(e\) and \(m\) are charge and mass of an electron, respectively, then the value of \(h/\lambda ,\) (where \(\lambda\) is wavelength associated with electron wave) is given by :

The stepwise formation of \(\left[ Cu \left( NH _{3}\right)_{4}\right]^{2+}\) is given below \(Cu ^{2+}+ NH _{3} \stackrel{ K _{1}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)\right]^{2+}\) \(\left[ Cu \left( NH _{3}\right)\right]^{2+}+ NH _{3} \stackrel{ K _{2}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)_{2}\right]^{2+}\) \(\left[ Cu \left( NH _{3}\right)_{2}\right]^{2+}+ NH _{3} \stackrel{ K _{3}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)_{3}\right]^{2+}\) \(\left[ Cu \left( NH _{3}\right)_{3}\right]^{2+}+ NH _{3} \stackrel{ K _{4}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)_{4}\right]^{2+}\) The value of stability constants \(K _{1}, K _{2}, K _{3}\) and \(K _{4}\) are \(10^{4}, 1.58 \times 10^{3}, 5 \times 10^{2}\) and \(10^{2}\) respectively. The overall equilibrium constants for dissociation of \(\left[ Cu \left( NH _{3}\right)_{4}\right]^{2+}\) is \(x \times 10^{-12}\) The value of \(x\) is ............... (Rounded off to the nearest integer)

The minimum distance of a point on the curve \(y = x^2 - 4\) from the origin is

Given below are two statements: Statement \((I)\) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account. Statement \((II)\) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below:

If \(\int \sin ^{-1}\left(\sqrt{\frac{x}{1+x}}\right) d x=A(x) \tan ^{-1}(\sqrt{x})+B(x)+C\) where \(C\) is a constant of integration, then the ordered pair \(( A ( x ), B ( x ))\) can be

The integral \(\int_{\frac{\pi }{{12}}}^{\frac{\pi }{4}} {\frac{{8\,\cos \,2x}}{{{{\left( {\tan \,x + \cot \,x} \right)}^3}}}\,dx} \) equals

If \(10 \sin ^4 \theta+15 \cos ^4 \theta=6\), then the value of \(\frac{27 \operatorname{cosec}^6 \theta+8 \sec ^6 \theta}{16 \sec ^8 \theta}\) is:

Let \(\vec{a}=\hat{i}+2 \hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}-\hat{k}\). Let \(\hat{c}\) be a unit vector in the plane of the vectors \(\vec{a}\) and \(\vec{b}\) and be perpendicular to \(\vec{a}\). Then such a vector \(\hat{c}\) is :