Aluminium reacts with sulfuric acid to form aluminium sulfate and hydrogen. What is the volume of hydrogen gas in liters $\left(\mathrm{L}\right)$ produced at $300 \mathrm{K}$ and $1.0$ atm pressure, when $5.4 \mathrm{g}$ of aluminium and $50.0 \mathrm{mL}$ of $5.0 \mathrm{M}$ sulfuric acid are combined for the reaction? (Use molar mass of aluminium as $27.0 \mathrm{g} {\mathrm{mol}}^{-1}$, $\mathrm{R}=0.082 \mathrm{atm} \mathrm{L} {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$)

The reduction potential $\left({\mathrm{E}}^0\right.$, in $\left.\mathrm{V}\right)$ of ${\mathrm{MnO}}_4^{-}\left(\mathrm{aq}\right)/\mathrm{Mn}\left(\mathrm{s}\right)$ is
\(\left[\right.\)Given: \(E _{\left( MnO _4^{-}( aq ) / MnO _2(s)\right)}^{ o }=1.68 V ;\) \( E _{\left( MnO _2(s) / Mn ^{2+}( aq )\right)}^{ o }=\) \(1.21 V ; E _{\left( Mn ^{2+}( aq ) / Mn ( s )\right)}^{ o }\) \(=-1.03 V]\)
Truncate/round-off the value to TWO decimal places.

One mole of an ideal gas at $300 \mathrm{K}$ in thermal contact with its surroundings expands isothermally from $1.0 \mathrm{L}$ to $2.0 \mathrm{L}$ against a constant pressure of $3.0 \mathrm{atm}$. In this process, the change in entropy of the surroundings $\left(∆{\mathrm{S}}_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r}}\right)$ in $\mathrm{J}\mathrm{ }{\mathrm{K}}^{-1}$ is:
$\left(1 \mathrm{L} \mathrm{atm} = 101.3 \mathrm{J}\right)$

The electrochemical cell shown below is a concentration cell. \(\mathrm{M} \mid \mathrm{M}^{2+}\) (saturated solution of a sparingly soluble salt, \(\left.\mathrm{MX}_{2}\right) \| \mathrm{M}^{2 \perp}\left(0.001 \mathrm{~mol} \mathrm{dm}^{-3}\right) \mid \mathrm{M}\).
The emf of the cell depends on the difference in concentrations of \(\mathrm{M}^{2+}\) ions at the two electrodes. The emf of the cell at \(298 \mathrm{~K}\) is \(0.059 \mathrm{~V}\).
Question:
The solubility product \(\left(\mathrm{K}_{s p} ; \mathrm{mol}^{3} \mathrm{dm}^{-9}\right)\) of \(\mathrm{MX}_{2}\) at \(298 \mathrm{~K}\) based on the information available for the given concentration cell is (take \(2.303 \times \mathrm{R} \times 298 / \mathrm{F}=0.059 \mathrm{~V}\) )

The pair(s) of ions where BOTH the ions are precipitated upon passing ${\mathrm{H}}_2\mathrm{S}$ gas in presence of dilute HCl, is (are)

$2 \mathrm{mol}$ of $\mathrm{Hg}\left(\mathrm{g}\right)$ is combusted in a fixed volume bomb calorimeter with excess of ${\mathrm{O}}_2$ at $298 \mathrm{K}$ and $1 \mathrm{atm}$ into $\mathrm{HgO}\left(\mathrm{s}\right)$. During the reaction, temperature increases from $298.0 \mathrm{K}$ to $312.8 \mathrm{K}$. If heat capacity of the bomb calorimeter and enthalpy of formation of $\mathrm{Hg}\left(\mathrm{g}\right)$ are $20.00 \mathrm{kJ} {\mathrm{K}}^{-1}$ and $61.32 \mathrm{kJ} {\mathrm{mol}}^{-1}$ at $298 \mathrm{K}$, respectively, the calculated standard molar enthalpy of formation of $\mathrm{HgO}\left(\mathrm{s}\right)$ at $298 \mathrm{K}$ is $\mathrm{X} {\mathrm{kJmol}}^{-1}$. The value of $\left|\mathrm{X}\right|$ is___[Given: Gas constant $\mathrm{R}=8.3 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$]

When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its pyranose form is :
\(\mathrm{CHO}-\mathrm{CH}_{2}-\mathrm{CHOH}-\mathrm{CHOH}-\mathrm{CHOH}\) \(-~\mathrm{CH}_{2} \mathrm{OH}\)

One mole of an ideal gas expands adiabatically from an initial state $(T_A, V_0)$ to final state $(T_f, 5V_0)$. Another mole of the same gas expands isothermally from a different initial state $(T_B, V_0)$ to the same final state $(T_f, 5V_0)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $\frac{T_A}{T_B}$?

The trace of a square matrix is defined to be the sum of its diagonal entries. If $A$ is a $2\times 2$ matrix such that the trace of $A$ is $3$ and the trace of  $A^3$ is $-18$ then the value of the determinant of $A$ is_____

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in queue in such a way that exactly four girls stand consecutively in the queue. Then the value of $\frac{\mathrm{m}}{\mathrm{n}}$ is

For any two points \(M\) and \(N\) in the \(X Y\)-plane, let \(\overrightarrow{M N}\) denote the vector from \(M\) to \(N\), and \(\overrightarrow{0}\) denote the zero vector. Let \(P, Q\) and \(R\) be three distinct points in the \(X Y\)-plane. Let \(S\) be a point inside the triangle \(\triangle P Q R\) such that \(\overrightarrow{S P}+5 \overrightarrow{S Q}+6 \overrightarrow{S R}=\overrightarrow{0}\). Let \(E\) and \(F\) be the mid-points of the sides \(P R\) and \(Q R\), respectively. Then the value of \(\frac{\text { length of the line segment } E F}{\text { length of the line segment } E S}\) is ________

The maximum number of possible isomers (including stereoisomers) which may be formed on mono-bromination of $1$-methylcyclohex- $1$-ene using ${\mathrm{Br}}_2$ and $\mathrm{UV}$ light is ___.

In a Young's double slit experiment, a combination of two glass wedges \(A\) and \(B\), having refractive indices 1.7 and 1.5, respectively, are placed in front of the slits, as shown in the figure. The separation between the slits is \(d=2 \mathrm{~mm}\) and the shortest distance between the slits and the screen is \(D=2 \mathrm{~m}\). Thickness of the combination of the wedges is \(t=12 \mu \mathrm{~m}\). The value of \(l\) as shown in the figure is 1 mm . Neglect any refraction effect at the slanted interface of the wedges. Due to the combination of the wedges, the central maximum shifts (in mm ) with respect to O by ______