List of practice Questions

For the reaction, \(N_{2}O_{4} \rightleftharpoons 2NO_{2}\) graph is plotted as shown below. Identify correct statements.
A. Standard free energy change for the reaction is 5.40 kJ \(mol^{-1}\). 
B. As \(\Delta G\) in graph is positive, \(N_{2}O_{4}\) will not dissociate into \(NO_{2}\) at all. 
C. Reverse reaction will go to completion. 
D. When 1 mole of \(N_{2}O_{4}\) changes into equilibrium mixture, value of \(\Delta G = -0.84 \text{ kJ mol}^{-1}\). 
E. When 2 mole of \(NO_{2}\) changes into equilibrium mixture, \(\Delta G\) for equilibrium mixture is \(-6.24 \text{ kJ mol}^{-1}\). 

Choose the correct answer from the following.

Identify the correct statements. (Note: Based on options, the question asks to identify INCORRECT statements).
A. Arginine and Tryptophan are essential amino acids.
B. Glycine does not have chiral centre.
C. Proline is a six membered cyclic ring amino acid.
D. Histidine does not contain heterocyclic ring in its structure.
E. Cysteine has characteristic feature of side chain as \(MeS-CH_2-CH_2-\).
An organic compound "P" of molecular formula \(C_7H_{12}O\) (likely \(C_7H_{12}O_2\) or similar based on options), gives positive Iodoform test but negative Tollen's test. When "P" is treated with dilute acid, it produces "Q". "Q" gives positive Tollen's test and also Iodoform test. The structure of "P" is:
An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30\(^\circ\)C. The coefficient of linear expansion of aluminium and steel are \(24 \times 10^{-6}\)/\(^\circ\)C and \(1.2 \times 10^{-5}\)/\(^\circ\)C, respectively. The length of this composite rod when its temperature is raised to 100\(^\circ\)C, is________ cm.
Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceed the activation energy of second reaction by 20 kJ mol\(^{-1}\). If \(k_1\) and \(k_2\) are the rate constants of first and second reaction respectively at 300 K, then \(\ln \frac{k_{2}}{k_{1}}\) will be___. (nearest integer) [\(R=8.3 \text{ J K}^{-1} \text{ mol}^{-1}\)]
  


One mole each of \(A_2(g)\) and \(B_2(g)\) are taken in a 1 L closed flask and allowed to establish the equilibrium at 500 K: \(A_{2}(g)+B_{2}(g) \rightleftharpoons 2AB(g)\). The value of x (missing enthalpy of \(B_2\) or related parameter) is ______ . (Nearest integer)}
  

Consider the reactions: 1. \(NaCl+K_{2}Cr_{2}O_{7}+H_{2}SO_{4} \rightarrow A + ...\) 2. \(A + NaOH \rightarrow B + ...\) 3. \(B + H_{2}SO_{4}+H_{2}O_{2} \rightarrow C + ...\) In the product 'C', X is the number of \(O_{2}^{2-}\) units, Y is the total number of oxygen atoms, and Z is the oxidation state of Cr. The value of \(X+Y+Z\) is__.
  
A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness \( \frac{1}{3}d \) of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is:
In an experiment the values of two spring constants were measured as \(k_1 = (10 \pm 0.2)\) N/m and \(k_2 = (20 \pm 0.3)\) N/m. If these springs are connected in parallel, then the percentage error in equivalent spring constant is:
A uniform solid cylinder of length \(L\) and radius \(R\) has moment of inertia about its axis equal to \(I_1\). A small co-centric cylinder of length \(L/2\) and radius \(R/3\) carved from it has moment of inertia about its axis equal to \(I_2\). The ratio \(I_1/I_2\) is ________.

Consider the following reaction sequence.

Potential energy (V) versus distance (x) is given by the graph. Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.

The pH and conductance of a weak acid (HX) was found to be 5 and \(4\times10^{-5}\) S, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of 1 cm\(^2\) were at a distance of 15 cm apart. The value of the limiting molar conductivity (\(\Lambda_m^\circ\)) is___ S cm\(^2\) mol\(^{-1}\) (nearest integer) (Given: degree of dissociation \(\alpha \ll 1\))
  
Consider a modified Bernoulli equation. \[ P + \frac{A}{Bt^2} + \rho g(h + Bt) + \frac{1}{2} \rho v^2 = \text{constant} \] If t has the dimension of time then the dimensions of A and B are_________ respectively.
A soap bubble of surface tension \(0.04\,\text{N/m}\) is blown to a diameter of \(7\,\text{cm}\). If \((15000 - x)\,\mu\text{J}\) of work is done in blowing it further to make its diameter \(14\,\text{cm}\) \((\pi = 22/7)\), then the value of \(x\) is ________.
The electric field in a plane electromagnetic wave is given by : \( E_y = 69 \sin[0.6 \times 10^3 x - 1.8 \times 10^{11} t] \) V/m. The expression for magnetic field associated with this electromagnetic wave is_________ T.

A thin uniform rod (\(X\)) of mass \(M\) and length \(L\) is pivoted at a height \( \left(\dfrac{L}{3}\right) \) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top is ________. (\(g\) = gravitational acceleration) 

A uniform rod of mass m and length l suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is _______ (g = acceleration due to gravity).

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27 °C to 87 °C. The rate of consumption of the gas is_________ g/s. (Take heat of combustion of gas = \(5.0 \times 10^4\) J/g, specific heat capacity of water = 4200 J/kg.°C).
A current carrying solenoid is placed vertically and a particle of mass m with charge Q is released from rest. The particle moves along the axis of solenoid. If g is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy:

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm\(^2\) and 3 cm\(^2\) respectively. The rate of flow will be ______ cm\(^3\)/s. (take g = 10 m/s\(^2\)).

The reading of the ammeter (\(A\)) in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is ________ A.
A cubical block of density \( \rho_b = 600\,\text{kg/m}^3 \) floats in a liquid of density \( \rho_l = 900\,\text{kg/m}^3 \). If the height of block is \(H = 8.0\,\text{cm}\), then height of the submerged part is ________ cm.
In the Young's double slit experiment the intensity produced by each one of the individual slits is \(I_0\). The distance between two slits is \(2\,\text{mm}\). The distance of screen from slits is \(10\,\text{m}\). The wavelength of light is \(6000\,\text{\AA}\). The intensity of light on the screen in front of one of the slits is ________.
A conducting circular loop of area 1.0 m\(^2\) is placed perpendicular to a magnetic field which varies as B = sin(100t) Tesla. If the resistance of the loop is 100 \(\Omega\), then the average thermal energy dissipated in the loop in one period is_________ J.