'W' g of a non-volatile electrolyte solid solute of molar mass 'M' g \( mol^{-1} \) when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg to 600 mm Hg. If aqueous solution of the electrolyte boils at 375 K and \( K_{b} \) for water is 0.52 K kg \( mol^{-1} \), then the mole fraction of the electrolyte solute \( (X_{2}) \) in the solution can be expressed as
(Given density of water = 1 g/mL and boiling point of water = 373 K)

Mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dil. HCl is _______.
Given : Molar mass of Mg is \(24 \mathrm{~g} \mathrm{~mol}^{-1}\).

When light of wavelength \(248\, nm\) falls on a metal of threshold energy \(3.0 \,eV\), the de-Broglie wavelength of emitted electrons is ............. \(\mathring A\) (Round off to the Nearest Integer). [Use : \(\sqrt{3}=1.73, h =6.63 \times 10^{-34} Js\) \(m _{ e }=9.1 \times 10^{-31} kg ; c =3.0 \times 10^{8} ms ^{-1}\) \(\left.1 eV =1.6 \times 10^{-19} J \right]\)

The absolute configuration of given is :

\(4.0\, L\) of an ideal gas is allowed to expand isothermally into vacuum until the total volume is \(20\, L.\) The amount of heat absorbed in this expansion is \(.....\,L\,atm\)

The standard enthalpy of formation of \(NH_3\) is \(-46.0\, kJ/mol\). If the enthalpy of formation of \(H_2\) from its atoms is \(-436\, kJ/mol\) and that of \(N_2\) is \(-712\, kJ/mol\), the average bond enthalpy of \(N - H\) bond in \(NH_3\) is......\(kJ/mol\)

The correct order of the number of unpaired electrons in the given complexes is \(A.\) \(\left[ Fe ( CN )_6\right]^{3-}\);\(B.\) \(\left[ FeF _6\right]^{3-}\); \(C.\) \(\left[ CoF _6\right]^{3-}\); \(D.\) \(\left[ Cr (\text { oxalate })_3\right]^{3-}\); \(E.\) \(\left[ Ni ( CO )_4\right]\) Choose the correct answer from the options given below:

If a variable line drawn through the intersection of the lines \(\frac{x}{3} + \frac{y}{4} = 1\)  and \(\frac{x}{4} + \frac{y}{3} = 1\) , meets the coordinate axes at \(A\) and \(B,\) \((A \ne B),\)  then the locus of the midpoint of \(AB\)  is

Given below are two statements : Statement \(I :\) \([ Ni ( CN ) 4]^{2-}\) is square planar and diamagnetic complex. with \(dsp ^{2}\) hybridization for \(Ni\) but \(\left[ Ni ( CO )_{4}\right]\) is tetrahedral. paramagnetic and with \(sp ^{3}\)-hybridication for \(Ni\). Statement \(II :\left[ NiCl _{4}\right]^{2-}\) and \(\left[ Ni ( CO )_{4}\right]\) both have same d-electron configuration have same geometry and are paramagnetic. In light the above statements. choose the correct answer form the options given below:

An massless equilateral triangle \(EFG\) of side \('a'\) (As shown in figure) has three particles of mass \(m\) situated at its vertices. The moment of intertia of the system about the line \(EX\) perpendicular to \(EG\) in the plane of \(EFG\) is \(\frac{ N }{20}\, ma ^{2}\) where \(N\) is an integer. The value of \(N\) is

The least count of the main scale of a screw gauge is \(1\, mm\). The minimum number of divisions on its circular scale required to measure \(5\,\mu m\) diameter of a wire is

Consider two vectors \(\overrightarrow{\mathrm{u}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}\) and \(\overrightarrow{\mathrm{v}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\lambda \hat{\mathrm{k}}, \lambda \gt 0\). The angle between them is given by \(\cos ^{-1}\left(\frac{\sqrt{5}}{2 \sqrt{7}}\right)\). Let \(\overrightarrow{\mathrm{v}}=\overrightarrow{\mathrm{v}}_1+\overrightarrow{\mathrm{v}}_2\), where \(\overrightarrow{\mathrm{v}}_1\) is parallel to \(\overrightarrow{\mathrm{u}}\) and \(\overrightarrow{\mathrm{v}}_2\) is perpendicular to \(\overrightarrow{\mathrm{u}}\). Then the value \(\left|\overrightarrow{\mathrm{v}}_1\right|^2+\left|\overrightarrow{\mathrm{v}}_2\right|^2\) is equal to

Consider a force \(\overrightarrow{\mathrm{F}}=-\mathrm{x} \hat{\mathrm{i}}+\mathrm{y} \hat{\mathrm{j}}\). The work done by this force in moving a particle from point \(\mathrm{A}(1,0)\) to \(\mathrm{B}(0,1)\) along the line segment is  (all quantities are in \(SI\) units)