\(6.023 \times 10^{22}\) molecules are present in \(10 \,g\) of a substance \('x'.\) The molarity of a solution containing \(5\, g\) of substance \({ }^{\prime} x ^{\prime}\) in \(2\, L\) solution is.......... \(\times 10^{-3}\)

The number of structural isomers for \(C_6H_{14}\) is

The half-life of radioisotopic bromine \(- 82\) is \(36\) hours. The fraction which remains after one day is _______ \(\times 10^{-2}\). (Given antilog \(0.2006=1.587\) )

Number of moles and number of molecules in \(1.4187\) L of \(SO_2\) at STP respectively are:

The equilibrium constant for the reaction \(\mathrm{SO}_3(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g})\) is \(\mathrm{K}_{\mathrm{C}}=4.9 \times 10^{-2}\). The value of \(\mathrm{K}_{\mathrm{C}}\) for the reaction given below is \(2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_3(\mathrm{~g})\) is _______.

The potential for the given half cell at \(298 \mathrm{~K}\) is \((-)\) _______ \(\times 10^{-2} \mathrm{~V}\). \(2 \mathrm{H}_{(\mathrm{aq})}^{+}+2 \mathrm{e}^{-} \rightarrow \mathrm{H}_2(\mathrm{~g})\) \({\left[\mathrm{H}^{+}\right]=1 \mathrm{M}, \mathrm{P}_{\mathrm{H}_2}=2 \mathrm{~atm}}\) (Given: \(2.303 \mathrm{RT} / \mathrm{F}=0.06 \mathrm{~V}, \log 2=0.3\) )

The Born-Haber cycle for \(\mathrm{KCl}\) is evaluated with the following data : \(\Delta_{f} \mathrm{H}^{\ominus}\) for \(\mathrm{KCl}=-436.7 \,\mathrm{~kJ}\, \mathrm{~mol}^{-1}\) \(\Delta_{\text {sub }} \mathrm{H}^{\ominus}\) for \(\mathrm{K}=89.2 \,\mathrm{~kJ}\, \mathrm{~mol}^{-1}\) \(\Delta_{\text {ionization }} \,\mathrm{H}^{-}\) for \(\mathrm{K}=419.0\, \mathrm{~kJ}\, \mathrm{~mol}^{-1}\) \(\Delta_{\text {electron gain }} \mathrm{H}^{\ominus}\) for \(\mathrm{Cl}_{(\text {e) }}=-348.6 \,\mathrm{~kJ} \,\mathrm{~mol}^{-1}\) \(\Delta_{\mathrm{bond}} \mathrm{H}^{-}\) for \(\mathrm{Cl}_{2}=243.0 \,\mathrm{~kJ} \,\mathrm{~mol}^{-1}\) The magnitude of lattice enthalpy of \(\mathrm{KCl}\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is ..... . (Nearest integer)

The actual value of resistance \(R\), shown in the figure is \(30\,\Omega \). This is measured in an experiment as shown using the standard formula \(R = \frac{V}{I}\) where \(V\) and \(I\) are the readings of the voltmeter and ammeter, respectively. If the measured value of \(R\) is \(5\%\) less, then the internal resistance of the voltmeter is ................. \(\Omega\)

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at \(STP\). Assuming the speed of sound in air at \(STP\) is \(300\; \mathrm{m} / \mathrm{s}\), the frequency difference between the fundamental and second harmonic of this pipe is ___ \(\mathrm{Hz}\)

A body travels \(102.5 \mathrm{~m}\) in \(\mathrm{n}^{\text {th }}\) second and \(115.0 \mathrm{~m}\) in \((n+2)^{\text {th }}\) second. The acceleration is what?

Let \(f: \mathbf{R}-\{0\} \rightarrow(-\infty, 1)\) be a polynomial of degree 2, satisfying \(f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)\). If \(f(K)=-2 K\), then the sum of squares of all possible values of \(K\) is :

The products obtained when chlorine gas reacts with cold and dilute aqueous \(NaOH\) are :

Let the ellipse \(3 x^2+\mathrm{py}^2=4\) pass through the centre \(C\) of the circle \(x^2+y^2-2 x-4 y-11=0\) of radius \(r\). Let \(f_1, f_2\) be the focal distances of the point C on the ellipse. Then \(6 f_1 f_2-r\) is equal to