HSC Important Questions Bank

Here is a curated list of the most frequently asked questions. Click the '+' button next to any question to add it directly to your task list.

Define moment of inertia. State its SI unit and dimensions.
State and prove the theorem of parallel axes and perpendicular axes.
Derive an expression for the moment of inertia of a thin uniform disc about an axis passing through its center and perpendicular to its plane.
Derive an expression for the kinetic energy of a rolling body.
State and explain the principle of conservation of angular momentum.

Define surface tension and surface energy. Derive the relation between them.
Derive Laplace’s law for a spherical membrane of a bubble.
What is angle of contact? Explain when it is acute and obtuse with diagrams.
State and prove Stokes' Law. Define terminal velocity and derive an expression for it.
State and prove Bernoulli's principle.

State the assumptions of the kinetic theory of gases.
Derive an expression for the pressure exerted by a gas based on kinetic theory.
What is RMS velocity? Show that RMS velocity is proportional to the square root of the absolute temperature.
What is a perfect blackbody? Explain Ferry's blackbody.
State and explain Stefan-Boltzmann law of radiation and Wien's displacement law.

State and explain the First Law of Thermodynamics.
Derive an expression for the work done during an isothermal process.
What is an adiabatic process? Derive an expression for the work done in an adiabatic process.
Explain the working of a Carnot engine and derive the expression for its efficiency.
State the Second Law of Thermodynamics and explain the principle of a refrigerator.

Define Simple Harmonic Motion (S.H.M.). Derive the differential equation for S.H.M.
Derive expressions for displacement, velocity, and acceleration in S.H.M.
Derive the expression for the total energy of a particle performing S.H.M.
What is a simple pendulum? Show that its motion is S.H.M. and derive the expression for its period.
Explain angular S.H.M. and its differential equation.

State the principle of superposition of waves.
What are stationary waves? Explain the formation of stationary waves on a string.
Show that only odd harmonics are present in the vibrations of an air column in a pipe closed at one end.
Explain the phenomenon of beats and derive the expression for the beat frequency.
What is the Doppler effect? State the general expression for the apparent frequency.

State Huygens' principle. Using this principle, prove the laws of reflection and refraction.
What is interference? State the conditions for constructive and destructive interference.
Derive the expression for the path difference and fringe width in Young's double-slit experiment.
What is diffraction? Explain Fraunhofer diffraction at a single slit.
What is resolving power? State Rayleigh's criterion for resolution.

State and prove Gauss's law in electrostatics.
Derive an expression for the electric field intensity due to an infinitely long straight charged wire.
Derive an expression for the potential energy of a system of two charges.
What is a capacitor? Derive the expression for the capacitance of a parallel plate capacitor without a dielectric.
Derive the expression for the energy stored in a capacitor.

State and explain Kirchhoff's laws for an electric network.
Explain the principle of a Wheatstone bridge and derive the balancing condition.
What is a potentiometer? Explain its principle.
How is a potentiometer used to compare the e.m.f.s of two cells?
How is a galvanometer converted into an ammeter and a voltmeter?

State and explain Ampere's circuital law.
Derive an expression for the magnetic field produced by a current in a long straight wire.
Derive an expression for the magnetic field at a point on the axis of a circular current loop.
Derive an expression for the force acting on a current-carrying conductor in a uniform magnetic field.
Explain the principle, construction, and working of a moving coil galvanometer.

Define magnetization and magnetic intensity.
Distinguish between diamagnetic, paramagnetic, and ferromagnetic substances.
Explain the origin of magnetism in materials based on electron theory.
What is hysteresis? Explain the hysteresis loop and define retentivity and coercivity.

State and explain Faraday's laws of electromagnetic induction.
State and explain Lenz's law as a consequence of the principle of conservation of energy.
What is self-inductance and mutual inductance? State their SI units.
Derive an expression for the e.m.f. induced in a straight conductor moving in a uniform magnetic field.
Explain the concept of eddy currents and state their applications.

Derive an expression for the impedance of a series LCR circuit.
What is resonance in an LCR circuit? State the condition for resonance and derive the expression for resonant frequency.
What is the Q-factor of a resonant circuit?
Explain the principle, construction, and working of a transformer.
Derive an expression for the average power in an AC circuit.

Explain the photoelectric effect and state its characteristics.
State Einstein's photoelectric equation and explain the laws of photoelectric emission using it.
What are de Broglie waves? Derive the expression for the de Broglie wavelength.
Explain the Davisson and Germer experiment.

State Bohr's postulates for the hydrogen atom.
Derive the expression for the radius of the nth Bohr orbit and the energy of the electron in it.
What is radioactivity? State the law of radioactive decay.
Define half-life and derive the expression for it.
Explain nuclear fission and nuclear fusion with examples.

Distinguish between intrinsic and extrinsic semiconductors.
Explain the working of a p-n junction diode in forward and reverse bias.
What is rectification? Explain the working of a p-n junction diode as a half-wave and full-wave rectifier.
Explain the working of a Zener diode as a voltage regulator.
Explain the working of a photodiode and a solar cell.

Distinguish between crystalline solids and amorphous solids.
Calculate the number of atoms and packing efficiency in a simple cubic, BCC, and FCC unit cell.
Derive the relationship between molar mass, density, and unit cell edge length.
Explain Schottky defect and Frenkel defect with diagrams.

State and explain Henry's Law and Raoult's Law.
What are colligative properties? Derive the relationship between the elevation of boiling point and the molar mass of the solute.
Define depression in freezing point and derive the expression for the molar mass of solute.
Define osmosis and osmotic pressure. Explain isotonic, hypotonic, and hypertonic solutions.

Explain Arrhenius theory and Bronsted-Lowry theory of acids and bases.
Derive the Ostwald's dilution law for a weak acid and a weak base.
Define pH and pOH. Derive the relationship between them.
What is a buffer solution? Explain its types and mechanism.
Derive the expression for the solubility product.

State and explain the First Law of Thermodynamics.
Derive the expression for the maximum work done during an isothermal reversible expansion of an ideal gas.
Define enthalpy. Derive the relationship between ΔH and ΔU.
State and explain Hess's law of constant heat summation.
State the Second Law of Thermodynamics and define Gibbs free energy.

What is a standard hydrogen electrode (SHE)? Describe its construction and working.
State and explain Kohlrausch's law of independent migration of ions.
Derive the Nernst equation for the e.m.f. of a cell.
Explain the construction and working of a lead accumulator (lead storage cell).
Explain the construction and working of a dry cell.

Distinguish between order and molecularity of a reaction.
Derive the integrated rate law for a first-order reaction.
What is half-life of a reaction? Derive the expression for the half-life of a first-order reaction.
Explain the collision theory of bimolecular reactions.
Derive the Arrhenius equation.

Explain the anomalous behavior of oxygen and fluorine.
Describe the manufacture of sulfuric acid by the contact process.
What are interhalogen compounds? Give their classification and properties.
Explain the structures of XeF2, XeF4, and XeF6.

What are transition elements? Explain their characteristic properties (catalytic property, color, magnetic property).
What is lanthanoid contraction? Explain its causes and consequences.
Compare the properties of lanthanoids and actinoids.

Explain Werner's theory of coordination compounds.
Define ligand, coordination number, and coordination sphere.
Explain the postulates of Valence Bond Theory (VBT) for coordination compounds.
Explain the crystal field splitting in octahedral and tetrahedral complexes.
What is spectrochemical series?

Explain the mechanism of SN1 and SN2 reactions.
Explain the Saytzeff (Zaitsev) rule for elimination reactions.
Write the reactions for the preparation of chloroform from ethanol.
What are Grignard reagents? How are they prepared?
Explain Fittig reaction, Wurtz-Fittig reaction, and Swarts reaction.

Explain the acidic nature of phenols.
Explain Kolbe's reaction and Reimer-Tiemann reaction.
How are primary, secondary, and tertiary alcohols distinguished using Lucas test?
Explain the Williamson synthesis for the preparation of ethers.

Explain Stephen reaction, Rosenmund reduction, and Gattermann-Koch reaction.
Explain Aldol condensation and Cross Aldol condensation.
Explain Cannizzaro reaction and Cross Cannizzaro reaction.
Explain the acidic nature of carboxylic acids.
Explain Hell-Volhard-Zelinsky (HVZ) reaction.

Explain the basic nature of amines.
Explain Gabriel phthalimide synthesis and Hoffmann degradation.
Distinguish between primary, secondary, and tertiary amines using Hinsberg's test.
What is diazotization? Explain the Sandmeyer reaction and Gattermann reaction.

What are carbohydrates? How are they classified?
Explain the structure of glucose and fructose.
What are proteins? Explain the peptide bond and the primary and secondary structure of proteins.
What are enzymes? Explain the lock and key mechanism.
Explain the structure of DNA with a neat diagram.

Define polymer and monomer. How are polymers classified?
Explain the preparation of polythene, Teflon, and neoprene.
What is vulcanization of rubber?
Distinguish between biodegradable and non-biodegradable polymers.

State and explain the principles of green chemistry.
What is nanotechnology?
Explain the synthesis of nanoparticles by the sol-gel process.
Write the applications of nanotechnology.

Prepare the truth table for a given logical statement.
Prove logical equivalences using truth tables (e.g., De Morgan's laws).
Write the converse, inverse, and contrapositive of a given conditional statement.
Find the symbolic form of a given switching circuit and construct its table.

Find the inverse of a matrix using the adjoint method.
Find the inverse of a matrix using elementary row/column transformations.
Solve a system of linear equations using the method of inversion.
Solve a system of linear equations using the method of reduction.

Find the principal solutions and general solution of trigonometric equations.
Prove properties of inverse trigonometric functions.
Solve problems based on the sine rule, cosine rule, and projection rule.

Find the combined equation of a pair of lines.
Find the separate equations of the lines represented by a given homogeneous equation.
Find the acute angle between the lines represented by ax²+2hxy+by²=0.
Find the condition for a general second-degree equation to represent a pair of straight lines.

Prove the section formula for internal and external division.
Prove that the medians of a triangle are concurrent.
Define scalar (dot) product and vector (cross) product. State their properties.
Find the volume of a parallelepiped and tetrahedron using the scalar triple product.

Find the vector and Cartesian equation of a line passing through a point and parallel to a vector.
Find the shortest distance between two skew lines.
Find the vector and Cartesian equation of a plane.
Find the angle between two planes and the distance of a point from a plane.

Formulate a given problem as a Linear Programming Problem (LPP).
Solve the LPP graphically.

Find the derivative of composite, inverse, and logarithmic functions.
Find the derivative of implicit and parametric functions.
Find the second-order derivative of a function.

Find the equation of tangent and normal to a curve.
Find the rate of change of a quantity (e.g., area, volume).
Find the intervals where a function is increasing or decreasing.
Find the local maxima and minima of a function.

Solve integrals using the method of substitution.
Solve integrals using integration by parts.
Solve integrals using the method of partial fractions.

Evaluate definite integrals using the properties of definite integrals.

Find the area of the region bounded by a curve and the x-axis or y-axis.
Find the area of the region between two curves.

Find the order and degree of a differential equation.
Form a differential equation from a given general solution.
Solve a differential equation using the variable separable method.
Solve homogeneous and linear differential equations.

Find the probability mass function (p.m.f.) of a discrete random variable.
Calculate the cumulative distribution function (c.d.f.).
Find the expected value (mean) and variance of a discrete random variable.

State the formula for the binomial distribution, P(X=x).
Find the probability of an event using the binomial distribution.
Find the mean and variance of a binomial distribution.

Describe the structure of an anatropous ovule with a neat, labeled diagram.
Explain the process of double fertilization in angiosperms.
Describe the development of a male gametophyte.
What is pollination? Describe its types.

Describe the structure of a human sperm and ovum with neat, labeled diagrams.
Explain the menstrual cycle with its different phases.
Describe the process of spermatogenesis and oogenesis.

State and explain Mendel's laws (Law of Dominance, Law of Segregation, Law of Independent Assortment).
Explain the concepts of incomplete dominance and co-dominance with examples.
What are sex-linked traits? Explain color blindness and hemophilia.

Describe the structure of DNA as proposed by Watson and Crick with a neat, labeled diagram.
Explain the process of DNA replication (semi-conservative method).
Explain the processes of transcription and translation.
What is a genetic code? State its properties.

Explain the Urey-Miller experiment.
Explain Darwin's theory of natural selection.
What are homologous and analogous organs? Give examples.
What is adaptive radiation? Explain with an example.

Describe the structure of a root hair.
Explain the process of absorption of water by roots.
What is transpiration? Describe the structure of a stomata.

Explain the phases of plant growth.
What are auxins, gibberellins, and cytokinins? State their functions.
Explain the role of macronutrients and micronutrients in plants.

Explain the process of glycolysis and Krebs cycle.
Describe the structure of the human heart with a neat, labeled diagram.
Explain the cardiac cycle.
Explain the structure and function of arteries, veins, and capillaries.

Describe the structure of a neuron with a neat, labeled diagram.
Explain the transmission of a nerve impulse across a synapse.
Describe the structure of the human brain.
Explain the reflex arc with a diagram.

What is immunity? Distinguish between active and passive immunity.
Describe the structure of an antibody.
Explain the life cycle of the malarial parasite (Plasmodium).
What is cancer? Explain its types.

What is animal breeding? Explain inbreeding and outbreeding.
What is tissue culture? Explain its technique.
Explain the process of apiculture (bee-keeping).

What is recombinant DNA technology? Explain its steps.
What are plasmids? Explain their role as vectors.
What is PCR? Explain its steps.
Explain the applications of biotechnology in medicine and agriculture.

What are biotic and abiotic factors?
Explain the different types of population interactions (mutualism, commensalism, parasitism, etc.).
What are population attributes like birth rate, death rate, and sex ratio?

What is an ecosystem? Describe its components.
Explain the concept of a food chain and a food web.
Describe the ecological pyramids (pyramid of number, biomass, and energy).
Explain the carbon cycle and phosphorus cycle.

What are the causes of biodiversity loss?
Explain the difference between in-situ and ex-situ conservation.
What is global warming and the greenhouse effect?
Explain the causes and effects of ozone layer depletion.