The density of ' \(x\) ' \(\mathrm{M}\) solution (' \(\mathrm{x}\) ' molar) of \(\mathrm{NaOH}\) is \(1.12 \mathrm{~g} \mathrm{~mL}^{-1}\). while in molality, the concentration of the solution is \(3 \mathrm{~m}\) ( \(3 \mathrm{molal})\). Then \(\mathrm{x}\) is _______. (Given : Molar mass of \(\mathrm{NaOH}\) is \(40 \mathrm{~g} / \mathrm{mol}\) )

The spin-only magnetic moment value of \(M ^{3+}\) ion (in gaseous state) from the pairs \(Cr ^{3+} / Cr ^{2+}\), \(Mn ^{3+} / Mn ^{2}, Fe ^{3+} / Fe ^{2+}\) and \(Co ^{3+} / Co ^{2+}\) that has negative standard electrode potential, is \(B.M...........\) [Nearest integer]

Match List-I with List-II -

List-I (Separation of)	List-II (Separation Technique)
(A) Aniline from aniline-water mixture	(I) Simple distillation
(B) Glycerol from spent-lye in soap industry	(II) Fractional distillation
(C) Different fractions of crude oil in petroleum industry	(III) Distillation at reduced pressure
(D) Chloroform - Aniline mixture	(IV) Steam distillation

Choose the correct answer from the options given below:

Which one among the following chemical tests is used to distinguish monosaccharide from disaccharide?

The number of species below that have two lone pairs of electrons in their central atom is ..... . (Round off to the Nearest integer) \(SF _{4}, BF _{4}^{-}, CIF _{3}, AsF _{3}, PCl _{5}, BrF _{5}, XeF _{4}, SF _{6}\)

An exothermic reaction \(X \rightarrow Y\) has an activation energy \(30\, kJ \,mol ^{-1}\). If energy change \(\Delta E\) during the reaction is \(-20\, kJ ,\) then the activation energy for the reverse reaction in \(kJ\) is \(...\).(Integer answer)

Consider the following equilibrium, \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_2(\mathrm{g}) \rightleftharpoons \mathrm{CH}_3 \mathrm{OH}(\mathrm{g})\) 0.1 mol of CO along with a catalyst is present in a \(2 \mathrm{dm}^3\) flask maintained at 500 K. Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of \(\mathrm{CH}_3 \mathrm{OH}\) is formed. The \(\mathrm{K}_{\mathrm{p}}^0\) is ______ \(\times 10^{-3}\) (nearest integer).
Given : \(\mathrm{R}=0.08 \mathrm{dm}^3\) bar \(\mathrm{K}^{-1} \mathrm{~mol}^{-1}\)
Assume only methanol is formed as the product and the system follows ideal gas behaviour.

Given,
(A) \(n =5, m_1=-1\)
(B) \(n =3,1=2, m_1=-1, m_{ s }=+\frac{1}{2}\)
The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) respectively are :

Let \(a-2 b+c=1\) If \(f(x)=\left|\begin{array}{lll}{x+a} & {x+2} & {x+1} \\ {x+b} & {x+3} & {x+2} \\ {x+c} & {x+4} & {x+3}\end{array}\right|,\) then

There is a small source of light at some depth below the surface of water (refractive index \(=\frac{4}{3}\) ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly)...........\(\%\) [Use the fact that surface area of a spherical cap of height \(\mathrm{h}\) and radius of curvature \(\mathrm{r} \text { is } 2 \pi \mathrm{rh}]\)

\(40^{\circ}\) of \(HI\) undergoes decomposition to \(H _{2}\) and \(I _{2}\) at \(300\, K . \Delta G ^{\ominus}\) for this decompostion reaction at one atmosphere pressure is \(...\,J\, mol ^{-1} \cdot\) [nearest integer] (Use \(R =8.31\, J\, K ^{-1}\, mol ^{-1} ; \log 2=0.3010\). In \(10=\) \(2.3, \log 3=0.477\) )

Space between two concentric conducting spheres of radii \(a\) and \(b (b > a)\) is filled with \(a\) medium of resistivity \(\rho \). The resistance between the two spheres will be

The number of solutions of the equation \(1 + {\sin ^4}\,x = {\cos ^2}\,3x,x\,\in \,\left[ { - \frac{{5\pi }}{2},\frac{{5\pi }}{2}} \right]\) is