The color of \(KMnO_4\) is due to :

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.

One mole of \(P _4\) reacts with \(8\) moles of \(SOCl _2\) to give \(4\) moles of \(A , x\) mole of \(SO _2\) and \(2\) moles of B. A, B and \(x\) respectively are

The first and second ionisation enthalpies of a metal are \(496\) and \(4560 \;\mathrm{kJ} \mathrm{mol}^{-1},\) respectively. How many moles of \(\mathrm{HCl}\) and \(\mathrm{H}_{2} \mathrm{SO}_{4}\) respectively, will be needed to react completely with \(1\) mole of the metal hydroxide?

Which of the following compound has a \(P-P\) bond ?

Identify \(\mathrm{A}, \mathrm{B}\) and C in the given below reaction sequence.
\(\mathrm{A} \xrightarrow{\mathrm{HNO}_3} \mathrm{~Pb}\left(\mathrm{NO}_3\right)_2 \xrightarrow{\mathrm{H}_2 \mathrm{SO}_4}\) B \(\xrightarrow[\substack{\text { (2) Acetic acid } \\ \text { (3) } \mathrm{K}_2 \mathrm{CrO}_4}]{\substack{\text { (1) Ammonium } \\ \text { acetate }}}\)

In polythionic acid, \(\mathrm{H}_{2} \mathrm{~S}_{\mathrm{x}} \mathrm{O}_{6}(\mathrm{x}=3\) to \(5\) ) the oxidation state(s) of sulphur is/are :

A monochromatic light is incident on a metallic plate having work function \(\phi\). An electron, emitted normally to the plate from a point \(A\) with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point \(B\). The distance between A and B is :
(Given : The magnitude of charge of an electron is e and mass is \(\mathrm{m}, \mathrm{h}\) is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

The de-Broglie's wavelength of electron present in first Bohr orbit of \('H'\) atom is

Consider the triangles with vertices \(A (2,1) B (0,0)\) and \(C ( t , 4), t \in[0,4]\). It the maximum and the minimum perimeters of such triangles are obtained at \(t=\alpha\) and \(t=\beta\) respectively, then \(6 \alpha+21 \beta\) is equal to \(.........\).

Given below are two statements: Statement \((I)\) : \(A\) Buffer solution is the mixture of a salt and an acid or a base mixed in any particular quantities. Statement \((II)\) : Blood is naturally occurring buffer solution whose \(\mathrm{pH}\) is maintained by \(\mathrm{H}_2 \mathrm{CO}_3 / \mathrm{HCO}_3\) concentrations. In the light of the above statements, choose the correct answer from the options given below.

If \(\sum_{ k =1}^{10} K ^{2}\left(10_{ C _{ K }}\right)^{2}=22000 L\), then \(L\) is equal to \(.....\)

Let \(a_{n}\) be the \(n^{\text {th }}\) term of a G.P. of positive terms. If \(\sum\limits_{n=1}^{100} a_{2 n+1}=200\) and \(\sum\limits_{n=1}^{100} a_{2 n}=100,\) then \(\sum\limits_{n=1}^{200} a_{n}\) is equal to