The ionization energy of sodium in \(\mathrm{kJ} \mathrm{mol}^{-1}\). If electromagnetic radiation of wavelength \(242 \mathrm{~nm}\) is just sufficient to ionize sodium atom is _______.

\(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\) In an equilibrium mixture, the partial pressures are \(P_{S O_{3}}=43\,\mathrm{kPa} ; \quad P_{O_{2}}=530 \,\mathrm{~Pa}\) and \(\mathrm{P}_{\mathrm{SO}_{2}}=45\, \mathrm{kPa}\) The equilibrium constant \(\mathrm{K}_{\mathrm{p}}=......\times 10^{-2} .\) (Nearest integer)

Number of amine compounds from the following giving solids which are soluble in \(\mathrm{NaOH}\) upon reaction with Hinsberg's reagent is _______.

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)

If \(O _{2}\) gas is bubbled through water at \(303 \;K\), the number of millimoles of \(O _{2}\) gas that dissolve in 1 litre of water is (Nearest Integer) (Given : Henry's Law constant for \(O _{2}\) at \(303 \;K\) is \(46.82 \;k\) bar and partial pressure of \(O _{2}=0.920 \;bar\) ) (Assume solubility of \(O _{2}\) in water is too small, nearly negligible)

When a concentrated solution of sulphanilic acid and 1-naphthylamine is treated with nitrous acid ( 273 K) and acidified with acetic acid, the mass ( g) of 0.1 mole of product formed is _______.
(Given molar mass in \(\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}: 14\), \(\mathrm{O}: 16, \mathrm{~S}: 32)\)

Among the following species, the diamagnetic molecule is

The number of elements in the relation \( R=\{(x,y): 4x^{2}+y^{2}<52, x, y\in Z\} \) is

Let a point \(P\) be such that its distance from the point \((5,0)\) is thrice the distance of \(P\) from the point \((-5,0) .\) If the locus of the point \(P\) is a circle of radius \(r\), then \(4 r ^{2}\) is equal to ...... .

If the system of equations \(x+y+z=2\) \(2 x+4 y-z=6\) \(3 x+2 y+\lambda z=\mu\) has infinitely many solutions, then 

Let the line \(x=-1\) divide the area of the region \(\{(x,y):1+x^{2}\le y\le3-x\}\) in the ratio \(m:n\), \(\gcd(m,n)=1\). Then \(m+n\) is equal to

A thin rod \(MN\), free to rotate in the vertical plane about the fixed end \(N\), is held horizontal . When the end \(M\) is released the speed of this end, when the rod makes an angle \(\alpha \) with the horizontal, will be proportional to ( see figure)

\(A\) and \(B\) decompose via first order kinetics with half-lives \(54.0\, min\) and \(18.0\, min\) respectively. Starting from an equimolar non reactive mixture of \(A\) and \(B\), the time taken for the concentration of \(A\) to become \(16\) times that of \(B\) is ...... \(min.\) (Round off to the Nearest Integer).