Given, that the abundances of isotopes, \({ }_{54} \mathrm{Fe},{ }_{56} \mathrm{~F}\) and \({ }_{57} \mathrm{Fe}\) are \(5 \%\), \(90 \%\) and \(5 \%\), respectively, the atomic mass of \(\mathrm{Fe}\) is

What is the order of basicity among the following compounds?

Total number of hydroxyl groups present in a molecule of the major product $\mathrm{P}$ is ______

The treatment of galena with ${\mathrm{HNO}}_3$ produces a gas that is

In \(1 \mathrm{~L}\) saturated solution of \(\mathrm{AgCl}\left[K_{\mathrm{sp}} \mathrm{AgCl}=1.6 \times 10^{-10}\right], 0.1\) mole of \(\mathrm{CuCl}\left[K_{\mathrm{sp}}(\mathrm{CuCl})=1.0 \times 10^{-6}\right]\) is added. The resultant concentration of \(\mathrm{Ag}^{+}\)in the solution is \(1.6 \times 10^{-x}\). The value of \(x\) is

A closed vessel contains \(10 \mathrm{~g}\) of an ideal gas \(\mathbf{X}\) at \(300 \mathrm{~K}\), which exerts 2 atm pressure. At the same temperature, \(80 \mathrm{~g}\) of another ideal gas \(\mathbf{Y}\) is added to it and the pressure becomes \(6 \mathrm{~atm}\). The ratio of root mean square velocities of \(\mathbf{X}\) and \(\mathbf{Y}\) at \(300 \mathrm{~K}\) is

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The hydrogen-like species \(\mathrm{Li}^{2+}\) is in a spherically symmetric state \(S_1\) with one radial node. Upon absorbing light the ion undergoes transition to a state \(S_2\). The state \(S_2\) has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
Question:
The state \(S_1\) is

Let $\stackrel{r}{7\overbrace{5\dots 5}7}$ denote the $\left(r+2\right)$ digit number where the first and the last digits are $7$ and the remaining $r$ digits are $5$. Consider the sum $S=77+757+7557+\dots +\stackrel{98}{7\overbrace{5\dots 5}7}$. If $S= \frac{7{\displaystyle \stackrel{99}{\overbrace{5\dots 5 }}}7+m}{n}$, where $m$ and $n$ are natural numbers less than $3000$, then the value of $m+n$ is

The geometries of the ammonia complexes of $\mathrm{N}{\mathrm{i}}^{2+}\mathrm{ },\mathrm{ }\mathrm{P}{\mathrm{t}}^{2+}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }\mathrm{Z}{\mathrm{n}}^{2+}$ respectively, are :

A galvanometer gives full scale deflection with $0·006 A$ current. By connecting it to a $4990 \Omega$ resistance, it can be converted into a voltmeter of range $0-30 V$. If connected to a $\frac{2\mathrm{n}}{249}\mathrm{\Omega }$ resistance, it becomes an ammeter of range $0- 1·5 A$. The value of $n$ is

An organic compound \(\mathbf{P}\) having molecular formula \(\mathrm{C}_6 \mathrm{H}_6 \mathrm{O}_3\) gives ferric chloride test and does not have intramolecular hydrogen bond. The compound \(\mathbf{P}\) reacts with 3 equivalents of \(\mathrm{NH}_2 \mathrm{OH}\) to produce oxime \(\mathbf{Q}\). Treatment of \(\mathbf{P}\) with excess methyl iodide in the presence of \(\mathrm{KOH}\) produces compound \(\mathbf{R}\) as the major product. Reaction of \(\mathbf{R}\) with excess iso-butylmagnesium bromide followed by treatment with \(\mathrm{H}_3 \mathrm{O}^{+}\)gives compound \(\mathrm{S}\) as the major product.
The total number of methyl \(\left(-\mathrm{CH}_3\right)\) group(s) in compound \(\mathbf{S}\) is ________. (consider maximum value if there are two values)

A diatomic ideal gas is compressed adiabatically to \(\frac{1}{32}\) of its initial volume. If the initial temperature of the gas is \(T_i\) \(T_i\) (in kelvin) and the final temperature is \(a T_i\), the value of \(a\) is

A liquid at ${30\mathrm{ }}^{\mathrm{o}}\mathrm{C}$ is poured very slowly into a Calorimeter that is at temperature of ${110\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$ The boiling temperature of the liquid is ${80\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$ It is found that the first $5\mathrm{ }\mathrm{g}\mathrm{m}$ of the liquid completely evaporates. After pouring another $80\mathrm{ }\mathrm{g}\mathrm{m}$ of the liquid the equilibrium temperature is found to be ${50\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$ The ratio of the Latent heat of the liquid to its specific heat will be ______ ${\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$
[Neglect the heat exchange with surrounding]