List of practice Questions

Two moles each of the gases P$_2$, Q$_2$ and PQ are present in a vessel at equilibrium. If 1 mole each of P$_2$ and Q$_2$ is added at equilibrium, then determine the composition (in mole) of each species at the new equilibrium.

Heat of atomisation of CH$_4$(g) and C$_2$H$_6$(g) are $x$ kJ/mol and $y$ kJ/mol respectively. Find the maximum wavelength of photon required to dissociate C–C bond in C$_2$H$_6$.

If for Li$^{2+}$ ion, electron is in transition between energy levels such that sum of principal quantum numbers is 4 and difference is 2, then find the wavelength (in cm) emitted for transition between these energy levels.
[Given: $R = 1.1 \times 10^5\ \text{cm}^{-1}$]

Correct order of 2$^{nd}$ ionisation energy is:

Among the species O$_2^+$, N$_2^-$, N$_2^{2-}$ and O$_2^-$ which have same bond order as well as paramagnetic in nature.

Element X is the lightest element of group 7 of periodic table which forms oxo-anion in +6 oxidation state. The colour of potassium salt of the oxo-anion is:

In general tests of Ba$^{2+}$ and Ca$^{2+}$ give the respective tests as:

Select incorrect option:

Statement-I: Two different aldehydes on cross aldol condensation always give four products.
Statement-II: Among benzaldehyde and acetophenone, only acetophenone reacts with semicarbazide.

Let $f(x)=|\log_e x|-|x-1|+5$. Statement 1: $f(x)$ is differentiable for all $x\in(0,\infty)$
Statement 2: $f(x)$ is increasing in $(1,\infty)$
Statement 3: $f(x)$ is decreasing in $(0,1)$
Which of the following is correct?

Disk \( m_1 = 5 \, \text{kg} \) \& radius \( r_1 = 10 \, \text{cm} \) and disk \( m_2 = 10 \, \text{kg} \) \& radius \( r_2 = 50 \, \text{cm} \) are arranged as shown in the figure. Find the moment of inertia about an axis through the common tangent and parallel to the plane of the disks.

An \( \alpha \)-particle with KE 7.9 MeV is projected towards a stationary target nucleus of \( Z = 79 \). Find the distance of closest approach.

Statement-I: Fluid exerts pressure on the surface of a solid in contact with it. Statement-II: The excess potential energy of molecules at the surface of a liquid leads to surface tension. Which of the following is correct?

For the reaction given below at 25°C: \[ \text{A}_2 \rightleftharpoons 2\text{A} \] Find \( K_p \). Given \( \Delta G^\circ_A = -50.384 \, \text{kJ/mol} \) and \( \Delta G^\circ_{A_2} = -100 \, \text{kJ/mol} \).

Statement-I: Sucrose is dextrorotatory and upon hydrolysis, it becomes laevorotatory. Statement-II: Sucrose on hydrolysis gives glucose and fructose such that the laevorotation of glucose is more than dextrorotation of fructose. Which of the following is correct?

Which of the following statement is correct regarding the nature and directive influence of \( \text{NO}_2 \) group in nitrobenzene?

Bohr’s radius of H-atom is \( 2.12 \times 10^{-10} \) m. Calculate the energy of electron at this level.

Which of the following statement is correct regarding an element having atomic number 79?

Sodium extract of organic compound of 0.1 g is treated with chlorine water and \( \text{CCl}_4 \) which dissolves in organic solvent to produce a violet colour. Upon treatment with \( \text{AgNO}_3 \), a yellow ppt. of 0.12 g is produced. Calculate the percentage of halide in the organic compound.

The number of values of \( x \) satisfying \( \tan^{-1}(4x) + \tan^{-1}(6x) = \frac{\pi}{6} \) and \( x<\left[ \frac{-1}{2\sqrt{6}} , \frac{1}{2\sqrt{6}} \right] \) is:

The value of \[ \int_{\frac{\pi}{2}}^{\pi} \frac{1}{\left\lfloor x \right\rfloor + 4} \, dx \] where \( \left\lfloor x \right\rfloor \) denotes the greatest integer function, is:

If \[ \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \sqrt{5\beta}}{2} \] then the value of \( (\alpha + \beta) \) is: