List of practice Questions

Find the next term in the series: 3, 6, 11, 18, 27, ?

Let $ P_n = \alpha^n + \beta^n $, $ P_{10} = 123 $, $ P_9 = 76 $, $ P_8 = 47 $, and $ P_1 = 1 $. The quadratic equation whose roots are $ \frac{1}{\alpha} $ and $ \frac{1}{\beta} $ is:

Population of Town A and B was 20,000 in 1985. In 1989, the population of Town A was 25,000, and Town B had 28,000. What will be the difference in population between the two towns in 1993?

Bittu and Chintu were partners in a firm sharing profit and losses in the ratio of 4:3. Their Balance Sheet as at 31st March, 2024 was as

On $1^{\text {st }}$ April, 2024, Diya was admitted in the firm for $\frac{1}{7}$ share in the profits on the following terms:

New profit sharing ratio between Bittoo, Chintoo and Diya will be $3:3:1$.
Fixed Assets were found to be overvalued by ₹ 1,40,000.
Creditors were paid ₹ 4,20,000 in full settlement.
Diya brought proportionate capital and ₹ 5,60,000 as her share of goodwill premium by cheque.

Prepare Revaluation Account and Partners' Capital Accounts.

Consider a star of mass $ m_2 $ kg revolving in a circular orbit around another star of mass $ m_1 $ kg with $ m_1 \gg m_2 $. The heavier star slowly acquires mass from the lighter star at a constant rate of $ \gamma $ kg/s. In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is $ r $, then its relative rate of change $ \frac{1}{r} \frac{dr}{dt} $ (in s$^{-1}$) is given by:

Order of limiting molar conductivities of these cations at 298 K is:

The electrostatic potential on the surface of a uniformly charged spherical shell of radius $ R = 10 \, \text{cm} $ is 120 V. The potential at the centre of the shell, at a distance 5 cm from the centre, and at a distance 15 cm from the centre of the shell are:

A wire has a resistance of $ 10 \, \Omega $ at $ 20^\circ \text{C} $. If the temperature coefficient of resistance of the material is $ 0.004 \, \text{per}^\circ \text{C} $, what is the resistance of the wire at $ 50^\circ \text{C} $?

If $ A = \begin{pmatrix} 2 & x + 9 \\ 1 & 2x \end{pmatrix} $ is invertible, then $ x \neq $:

A bag contains 4 red and 6 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?

A battery of emf $ E $ and internal resistance $ r $ is connected to a rheostat. When a current of 2A is drawn from the battery, the potential difference across the rheostat is 5V. The potential difference becomes 4V when a current of 4A is drawn from the battery. Calculate the value of $ E $ and $ r $.

Name a metal found in the earth's crust:
(i) in free state and
(ii) in the form of its compound.
State where each of these metals are placed in the reactivity series of metals

Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of $ x $.

(a) Calculate the standard Gibbs energy ($\Delta G^\circ$) of the following reaction at 25°C:
$\text{Au(s) + Ca\(^{2+}$(1M) $\rightarrow$ Au$^{3+}$(1M) + Ca(s)} \)
$\text{E\(^\circ_{\text{Au}^{3+}/\text{Au}} = +1.5 V, E$$^\circ_{\text{Ca}^{2+}/\text{Ca}} = -2.87 V$}\)
$\text{1 F} = 96500 C mol^{-1}$

Define the following:
(i) Cell potential
(ii) Fuel Cell

Calculate the emf of the following cell at 25°C:
\[ \text{Zn(s)} | \text{Zn}^{2+}(0.1M) || \text{Cd}^{2+}(0.01M) | \text{Cd(s)} \] Given: \[ E^\circ_{\text{Cd}^{2+}/\text{Cd}} = -0.40 \, V, \, E^\circ_{\text{Zn}^{2+}/\text{Zn}} = -0.76 \, V \] \[ [\log 10 = 1] \]

Write chemical equations of the following reactions:
(i) Phenol is treated with conc. HNO$_3$
(ii) Propene is treated with B$_2$H$_6$ followed by oxidation by H$_2$O$_2$/OH$^-$
(iii) Sodium t-butoxide is treated with CH$_3$Cl

Give a simple chemical test to distinguish between butan-1-ol and butan-2-ol.

Arrange the following in increasing order of acid strength: phenol, ethanol, water.

An organic compound ‘A’, molecular formula C$_6$H$_6$O oxidises with CrO$_3$ to form a compound ‘B’. Compound ‘B’ on warming with iodine and aqueous solution of NaOH gives a yellow precipitate of compound ‘C’. When compound ‘A’ is heated with conc. H$_2$SO$_4$ at 413 K gives a compound ‘D’, which on reaction with excess HI gives compound ‘E’. Identify compounds ‘A’, ‘B’, ‘C’, ‘D’ and ‘E’ and write chemical equations involved.

(b) Tarnished silver contains Ag$_2$S. Can this tarnish be removed by placing tarnished silverware in an aluminium pan containing an inert electrolytic solution such as NaCl? The standard electrode potential for half-reactions:
\[ \text{Ag}_2\text{S}(s) + 2e^- \rightarrow 2\text{Ag}(s) + \text{S}^{2-} \, \, E^\circ = -0.71 \, V \] \[ \text{Al}^{3+} + 3e^- \rightarrow 2\text{Al}(s) \, \, E^\circ = -1.66 \, V \]

Complete each synthesis by giving missing starting material, reagent or products:

How will you convert the following:
(i) Toluene to benzoic acid
(ii) Ethanol to propan-2-ol
(iii) Propanal to 2-hydroxy propanoic acid

Give IUPAC name of CH$_3$–CH=CH–CHO.

Give a simple chemical test to distinguish between propanal and propanone.