The hybridisations of the atomic orbitals of nitrogen in \(\mathrm{NO}_{2}^{-}, \mathrm{NO}^{+} _2\) and \(\mathrm{NH}_{4}{ }^{+}\)respectively are.

The wave function \((\Psi)\) of \(2 s\) is given by \(\Psi_{2 s}=\frac{1}{2 \sqrt{2 \pi}}\left(\frac{1}{a_0}\right)^{1 / 2}\left(2-\frac{ r }{ a _0}\right) e ^{- r / 2 a _0}\) At \(r=r_0\), radial node is formed. Thus, \(r_0\) in terms of \(a_0\)

The standard enthalpy of formation \((\Delta _f\,H^o_{298})\) for methane, \(CH_4\) is \(-74.9\,kJ\,mol^{-1}\) . In order to calculate the average energy given out in the formation of a \(C - H\) bond from this it is necessary to know which one of the following?

Assume that the radius of the first Bohr orbit of hydrogen atom is \(0.6 \mathring A\). The radius of the third Bohr orbit of \(He ^{+}\)is \(..................\) picometer. (Nearest Integer)

The major product of the following reaction is \(C{H_3}C \equiv CH\xrightarrow[{(ii)\,Dl}]{{(i)\,DCl\,\,(1\,equiv)}}\)

What is the major product formed by \(HI\) on reaction with \({image}\)

The molar solubility of \(\mathrm{Zn}(\mathrm{OH})_{2}\) in \(0.1 \,\mathrm{M} \,\mathrm{NaOH}\) solution is \(\mathrm{x} \times 10^{-18} \,\mathrm{M}\). The value of \(\mathrm{x}\) is ...... . (Nearest integer) (Given : The solubility product of \(\mathrm{Zn}(\mathrm{OH})_{2}\) is \(\left.2 \times 10^{-20}\right)\)

It is noticed that \( Pb^{2+} \) is more stable than \( Pb^{2+} \) but \( Sn^{2+} \) is less stable than \( Sn^{4+} \). Observe the following reactions:
\( PbO_{2} + Pb \rightarrow 2PbO; \Delta_{r}G^{\circ} (1) \)
\( SnO_{2} + Sn \rightarrow 2SnO; \Delta_{r}G^{\circ} (2) \)
Identify the correct set from the following.

Each side of a box made of metal sheet in cubic shape is \('a'\) at room temperature \('T'\), the coefficient of linear expansion of the metal sheet is \(^{\prime} \alpha^{\prime}\). The metal sheet is heated uniformly, by a small temperature \(\Delta T\), so that its new temperature is \(T +\Delta T\). Calculate the increase in the volume of the metal box.

Concentrated \(HNO _{3}\) reacts with Iodine to give

The molar conductivities at infinite dilution of barium chloride, sulphuric arid and hydrochloric acid are \(280,860\) and \(426 \,Scm ^{2}\) \(mol ^{-1}\) respectively. The molar conductivity at infinite dilution of barium sulphate is \(...... \,S cm ^{2} mol ^{-1}(\) Round off to the Nearest Integer).

Copper reduces \(NO _{3}^{-}\) into \(NO\) and \(NO _{2}\) depending uponthe concentration of \(HNO _{3}\) insolution. (Assuming fixed \(\left[ Cu ^{2+}\right]\) and \(\left. P _{ NO }= P _{ NO _{2}}\right),\) the \(HNO _{3}\) concentration at which the thermodynamic tendency for reduction of \(NO _{3}^{-}\) into \(NO\) and \(NO _{2}\) by copper is same is \(10^{ x }\, M\). The value of \(2 x\) is ...... . \(\left[\right.\) Given \(, E_{C u^{2+} / C u}^{o}=0.34\, V , E _{ NO _{3}^{-} / NO_2 }^{\circ}=0.96\, V\) (Rounded-off to the nearest integer) \(E _{ NO _{3} / NO _{2}}^{\circ}=0.79 \,V\) and at \(298 \,K\)  \(\left.\frac{ RT }{ F }(2.303)=0.059\right]\)

From the circuit given below, the capacitance between terminals \(A\) and \(B\) shown in the circuit is ______ \(\mu\)F.
(take \(C_1=C_2=C_3=1\) \(\mu\)F and \(C_4=2\) \(\mu\)F.)