PYQ Bank

Previous year board exam questions, filtered by subject and year.

319 questions
Feb 2024 · 3 marksmedium

State and explain parallax method for measuring large distances.

Feb 2024 · 3 marksmedium

Derive the kinematic equation v² = u² + 2as using calculus.

Feb 2024 · 3 markshard

Derive an expression for centripetal acceleration.

Feb 2024 · 5 markshard

State the laws of thermodynamics. Explain Carnot engine with a neat diagram.

Feb 2024 · 3 markseasy

Explain the mole concept. Calculate the number of moles in 20g of CaCO₃.

Feb 2024 · 3 markshard

Write the electronic configuration of Cu and Cr. Explain the anomaly.

Feb 2024 · 4 markshard

State Hess's law. Calculate enthalpy change for a reaction using bond energies.

Feb 2024 · 2 markseasy

Explain the concept of pH. Calculate the pH of 0.001M HCl solution.

Feb 2024 · 3 markseasy

If A = {1,2,3}, B = {2,3,4}, find A∪B, A∩B, A-B. Verify n(A∪B) = n(A) + n(B) - n(A∩B).

Feb 2024 · 3 marksmedium

Find the domain and range of f(x) = √(x²-4).

Feb 2024 · 4 markshard

Find the derivative of x³+2x²-5x+7 from first principles.

Feb 2024 · 3 marksmedium

How many 4-letter words can be formed using the letters of 'MATHEMATICS'?

Feb 2024 · 3 markseasy

State the cell theory. Differentiate between prokaryotic and eukaryotic cells.

Feb 2024 · 3 marksmedium

Describe the structure of a dicotyledonous leaf.

Feb 2024 · 4 marksmedium

Explain the mechanism of breathing in humans.

Feb 2024 · 3 marksmedium

Explain the reflex arc with a neat diagram.

Feb 2024 · 4 marksmedium

Derive an expression for moment of inertia of a uniform rod about an axis passing through its centre and perpendicular to its length.

Feb 2024 · 4 marksmedium

State Bernoulli's theorem and derive Bernoulli's equation for an ideal fluid.

Feb 2024 · 4 markshard

Derive the expression for pressure exerted by an ideal gas using kinetic theory.

Feb 2024 · 4 marksmedium

State and explain the first law of thermodynamics. Derive the relation between Cp and Cv.

Feb 2024 · 3 marksmedium

Derive an expression for the time period of a simple pendulum. On what factors does it depend?

Feb 2024 · 4 marksmedium

Explain the formation of stationary waves in a stretched string. Show that nodes and antinodes are formed alternately.

Feb 2024 · 4 marksmedium

Describe Young's double slit experiment. Derive the expression for fringe width.

Feb 2024 · 4 marksmedium

State Gauss's theorem in electrostatics. Using it, derive an expression for electric field due to an infinitely long charged wire.

Feb 2024 · 4 marksmedium

State Kirchhoff's laws. Using them, determine the current in each branch of a given balanced Wheatstone bridge.

Feb 2024 · 4 marksmedium

State Biot-Savart law. Use it to derive the magnetic field at the centre of a circular loop carrying current.

Feb 2024 · 3 markseasy

Distinguish between diamagnetic, paramagnetic and ferromagnetic materials with suitable examples.

Feb 2024 · 4 marksmedium

State Faraday's laws of electromagnetic induction and Lenz's law. Derive the expression for motional emf induced in a conductor moving in a uniform magnetic field.

Feb 2024 · 4 markshard

Derive the expression for impedance of a series LCR circuit. Explain the condition for resonance.

Feb 2024 · 4 marksmedium

Explain the photoelectric effect. Derive Einstein's photoelectric equation and state its physical significance.

Feb 2024 · 4 markshard

State Bohr's postulates. Derive the expression for radius of nth orbit and energy of electron in hydrogen atom.

Feb 2024 · 4 marksmedium

Explain the working of a PN junction diode in forward and reverse bias. Draw its characteristic curves.

Feb 2024 · 2 markseasy

Distinguish between crystalline and amorphous solids with suitable examples.

Feb 2024 · 4 marksmedium

State Raoult's law for volatile liquids. Explain positive and negative deviations from Raoult's law with examples.

Feb 2024 · 3 marksmedium

Define pH and pOH. Derive the relation pH + pOH = 14 at 298 K.

Feb 2024 · 4 marksmedium

State the first and second laws of thermodynamics. Define Gibbs free energy and derive the relation ΔG = ΔH - TΔS.

Feb 2024 · 4 marksmedium

Explain the construction and working of a Daniell cell with a neat diagram. Write the cell reaction.

Feb 2024 · 4 marksmedium

Define rate of chemical reaction. Derive the integrated rate equation for a first order reaction.

Feb 2024 · 3 markseasy

Explain the trends in physical properties of group 16 elements down the group.

Feb 2024 · 4 marksmedium

Explain the general characteristics of transition elements. Why do they exhibit variable oxidation states?

Feb 2024 · 3 markseasy

Define coordination compound. Explain the terms: ligand, coordination number, coordination sphere with examples.

Feb 2024 · 4 markshard

Explain the SN₁ and SN₂ mechanisms of nucleophilic substitution reactions with suitable examples.

Feb 2024 · 3 marksmedium

Explain the methods of preparation of alcohols from alkenes and Grignard reagents.

Feb 2024 · 3 markseasy

Distinguish between aldehydes and ketones using Tollens' reagent and Fehling's solution tests.

Feb 2024 · 3 markseasy

Classify amines with examples. Explain the methods of preparation of primary amines.

Feb 2024 · 3 markseasy

Explain the classification of carbohydrates with examples. What are reducing sugars?

Feb 2024 · 3 markseasy

Classify polymers based on source, structure and type of polymerization.

Feb 2024 · 3 markseasy

Explain the classification of drugs based on pharmacological action. Give one example of each class.

Feb 2024 · 3 markseasy

Explain the different modes of asexual reproduction in plants with examples.

Feb 2024 · 4 markseasy

Draw a labeled diagram of the male reproductive system in humans.

Feb 2024 · 4 marksmedium

State Mendel's laws of inheritance. Explain monohybrid cross with a checkerboard.

Feb 2024 · 4 marksmedium

Describe the structure of DNA as proposed by Watson and Crick. Explain its salient features.

Feb 2024 · 3 marksmedium

Explain the Miller-Urey experiment. What did it demonstrate about the origin of life?

Feb 2024 · 4 marksmedium

Explain the mechanism of water absorption by roots. Differentiate between apoplast and symplast pathways.

Feb 2024 · 3 markseasy

Explain the phases of plant growth. Draw a typical sigmoid growth curve and label its parts.

Feb 2024 · 3 markseasy

Explain the mechanism of breathing in humans. What is the role of the diaphragm?

Feb 2024 · 4 marksmedium

Explain the structure of a neuron. Describe the mechanism of nerve impulse transmission.

Feb 2024 · 4 marksmedium

Explain the structure of HIV with a diagram. Describe the life cycle of HIV.

Feb 2024 · 3 marksmedium

Explain the methods of plant breeding for disease resistance.

Feb 2024 · 4 marksmedium

Explain the steps involved in recombinant DNA technology with a diagram.

Feb 2024 · 3 markseasy

Define population. Explain the different population attributes with examples.

Feb 2024 · 3 markseasy

Define ecosystem. Explain the structure and function of an ecosystem.

Feb 2024 · 3 markseasy

Define biodiversity. Explain the three types of biodiversity with examples.

Feb 2024 · 3 markseasy

Construct the truth table for (p ∧ q) → (p ∨ q). Determine whether it is a tautology, contradiction or contingency.

Feb 2024 · 4 marksmedium

Find the inverse of matrix A = [[2,3],[1,4]] using elementary row transformations.

Feb 2024 · 4 markshard

Prove that sin⁻¹(3/5) + sin⁻¹(8/17) = cos⁻¹(36/85).

Feb 2024 · 3 marksmedium

Show that the equation 2x² - 5xy + 2y² = 0 represents a pair of lines. Find the angle between them.

Feb 2024 · 3 marksmedium

If a = 2i - j + k, b = i + 2j - 3k, find the unit vector perpendicular to both a and b.

Feb 2024 · 3 marksmedium

Find the vector equation of the line passing through (1,2,3) and parallel to the line (x-1)/2 = (y+1)/-3 = (z-2)/4.

Feb 2024 · 4 marksmedium

A furniture dealer deals in tables and chairs. Solve graphically to maximize profit given constraints on wood and labor.

Feb 2024 · 4 markshard

If y = (sin⁻¹x)², prove that (1 - x²)d²y/dx² - x dy/dx = 2.

Feb 2024 · 3 marksmedium

Find the equation of tangent and normal to the curve y = x³ - 2x + 1 at the point where x = 1.

Feb 2024 · 2 markseasy

Evaluate ∫e^x(sin x + cos x) dx.

Feb 2024 · 2 markseasy

Evaluate ∫₀^(π/2) sin²x dx.

Feb 2024 · 3 marksmedium

Find the order and degree of the differential equation (d²y/dx²)² + (dy/dx)³ = 0. Solve the differential equation dy/dx = e^(x+y).

Feb 2024 · 3 marksmedium

A random variable X has the following probability distribution. Find the value of k and P(X ≥ 2).

Feb 2024 · 3 marksmedium

State the conditions for a binomial experiment. If a fair coin is tossed 6 times, find the probability of getting exactly 4 heads.

Feb 2024 · 3 markseasy

Explain the concept of internal energy. State the first law of thermodynamics with mathematical form.

Feb 2024 · 3 markseasy

Distinguish between longitudinal and transverse waves with examples. State the relation between velocity, frequency and wavelength.

Feb 2024 · 4 markshard

Derive the lens maker's formula for a thin lens.

Feb 2024 · 3 markseasy

State Coulomb's law in vector form. Find the force between two charges of +2 μC and -3 μC placed 10 cm apart in air.

Feb 2024 · 2 markseasy

State Ohm's law. Derive the expression for the equivalent resistance of three resistors in series.

Feb 2024 · 2 markseasy

Define magnetic flux. State Gauss's law of magnetism.

Feb 2024 · 3 marksmedium

Explain the energy band theory of solids. Distinguish between conductors, insulators and semiconductors.

Feb 2024 · 2 markseasy

Define atomic mass unit. Calculate the molecular mass of H₂SO₄ and glucose.

Feb 2024 · 3 markseasy

Explain Rutherford's alpha scattering experiment. What conclusions were drawn about the structure of the atom?

Feb 2024 · 3 markseasy

Explain the formation of sigma and pi bonds. Differentiate between them.

Feb 2024 · 3 markseasy

Define oxidation and reduction in terms of oxidation number. Calculate the oxidation number of S in H₂SO₄ and Cr in K₂Cr₂O₇.

Feb 2024 · 3 markseasy

State the periodic law. Explain the trends in atomic radius across a period and down a group.

Feb 2024 · 3 markseasy

Explain the classification of organic compounds based on functional groups with examples.

Feb 2024 · 3 marksmedium

Explain the preparation of methane from Wurtz reaction and decarboxylation.

Feb 2024 · 3 markseasy

State the gas laws. Derive the ideal gas equation PV = nRT.

Feb 2024 · 2 markseasy

Distinguish between physisorption and chemisorption. Give one example of each.

Feb 2024 · 3 marksmedium

Explain the types of radioactive decay with examples: alpha, beta and gamma emission.

Feb 2024 · 3 markseasy

If A = {x: x is a prime number less than 20} and B = {x: x is a multiple of 3 less than 20}, find A∩B and A∪B. Represent on a Venn diagram.

Feb 2024 · 3 marksmedium

Check whether the function f: R → R defined by f(x) = 3x - 5 is one-one and onto.

Feb 2024 · 3 marksmedium

Prove that (sinθ + cosecθ)² + (cosθ + secθ)² = 7 + tan²θ + cot²θ.

Feb 2024 · 2 markseasy

Find the distance between the parallel lines 3x - 4y + 7 = 0 and 6x - 8y + 15 = 0.

Feb 2024 · 2 markseasy

Find the equation of the circle with centre (2,-3) and radius 5 units.

Feb 2024 · 2 markseasy

Evaluate the limit: lim(x→2) (x² - 5x + 6)/(x² - 4).

Feb 2024 · 3 marksmedium

Find the derivative of tan x with respect to x from first principles.

Feb 2024 · 3 markseasy

Evaluate ∫(3x² + 1/x² + √x) dx.

Feb 2024 · 3 marksmedium

A card is drawn from a well shuffled pack of 52 cards. Find the probability that it is either a king or a red card.

Feb 2024 · 3 markseasy

What is the living world? Explain the characteristic features of living organisms.

Feb 2024 · 2 markseasy

What is systematics? Differentiate between taxonomy and systematics.

Feb 2024 · 4 marksmedium

Explain the classification of Kingdom Plantae into divisions with characteristics.

Feb 2024 · 3 markseasy

Explain the salient features of phylum Arthropoda with examples.

Feb 2024 · 3 marksmedium

Explain the structure and function of the endoplasmic reticulum and Golgi apparatus.

Feb 2024 · 3 markseasy

Define carbohydrates. Classify them with examples.

Feb 2024 · 4 marksmedium

Differentiate between mitosis and meiosis with suitable diagrams.

Feb 2024 · 3 marksmedium

Classify plant tissues. Explain the structure and function of meristematic tissues.

Feb 2024 · 4 markshard

Explain the light reaction of photosynthesis. Describe the Z-scheme of electron transport.

Feb 2024 · 4 marksmedium

Explain the process of glycolysis with a flowchart.

July 2024 · 4 marksmedium

A ball is thrown vertically upwards with velocity 20 m/s. Find maximum height and time of flight.

July 2024 · 4 marksmedium

State and explain Huygens' principle. Use it to prove laws of reflection.

July 2024 · 3 marksmedium

Explain periodic trends in ionization enthalpy across a period and down a group.

July 2024 · 2 markseasy

Distinguish between electrophiles and nucleophiles with examples.

July 2024 · 4 markseasy

Prove that sin²θ + cos²θ = 1. Express sin3θ in terms of sinθ.

July 2024 · 5 marksmedium

Describe the stages of mitosis with the help of diagrams.

July 2024 · 3 markseasy

What are hormones? Explain the feedback mechanism of hormone regulation.

July 2024 · 4 markshard

A grindstone of radius 0.5 m rotates with angular speed 40 rad/s. A tool is pressed against it with a force such that the torque due to friction is 10 Nm. Find the time taken for the grindstone to stop if its moment of inertia is 20 kg m².

July 2024 · 3 marksmedium

A capillary tube of internal radius 0.5 mm is dipped vertically in water. If the surface tension of water is 0.072 N/m and angle of contact is 0°, calculate the height to which water rises in the tube.

July 2024 · 3 marksmedium

Calculate the root mean square speed of oxygen molecules at 27°C. Molecular weight of oxygen is 32 g/mol.

July 2024 · 5 markshard

Explain the Carnot cycle with a neat P-V diagram. Obtain the expression for efficiency of a Carnot engine.

July 2024 · 3 marksmedium

A particle performs SHM with amplitude 5 cm and period 2 s. Find its velocity and acceleration when the displacement is 3 cm.

July 2024 · 3 markshard

What are beats? Derive an expression for beat frequency produced by two sound waves of slightly different frequencies.

July 2024 · 4 markshard

What is diffraction of light? Explain the Fraunhofer diffraction pattern due to a single slit.

July 2024 · 4 markshard

Three point charges +2 μC, -3 μC and +4 μC are placed at the vertices of an equilateral triangle of side 0.2 m. Find the net force acting on the +4 μC charge.

July 2024 · 2 markseasy

Derive the expression for the equivalent resistance of three resistors connected in parallel.

July 2024 · 2 markseasy

A long solenoid has 500 turns per metre and carries a current of 2 A. Calculate the magnetic field inside the solenoid.

July 2024 · 3 marksmedium

Define magnetic susceptibility and magnetic permeability. Derive the relation between relative permeability and susceptibility.

July 2024 · 3 marksmedium

A circular coil of radius 10 cm and 50 turns is placed in a magnetic field of 0.5 T perpendicular to its plane. If the field is reduced to zero in 0.1 s, find the induced emf.

July 2024 · 3 marksmedium

A series LCR circuit has R = 10 Ω, L = 0.1 H, C = 10 μF connected to a 230 V, 50 Hz AC supply. Find the impedance and current at resonance.

July 2024 · 3 markshard

Describe Davisson and Germer experiment that confirmed the wave nature of electrons.

July 2024 · 3 markseasy

Distinguish between nuclear fission and nuclear fusion. Give one example of each with equations.

July 2024 · 4 markshard

Explain the working of an NPN transistor as an amplifier in CE configuration.

July 2024 · 3 marksmedium

Explain Schottky and Frenkel defects in crystals with examples.

July 2024 · 3 marksmedium

Derive the relationship between elevation of boiling point and molar mass of solute.

July 2024 · 2 marksmedium

Calculate the pH of 0.1 M acetic acid solution given Ka = 1.8 × 10⁻⁵.

July 2024 · 3 markshard

Calculate the standard enthalpy of formation of CH₄ given that bond energies of C-H, H-H and the enthalpy of sublimation of carbon are known.

July 2024 · 3 marksmedium

Distinguish between electrolytic cells and galvanic cells. Explain Faraday's laws of electrolysis.

July 2024 · 3 markshard

The half-life of a first order reaction is 30 minutes. Calculate the time required for 90% completion of the reaction.

July 2024 · 2 markseasy

Explain the anomalous behaviour of oxygen in group 16.

July 2024 · 3 markshard

Explain the colour of transition metal ions using crystal field theory.

July 2024 · 4 marksmedium

Draw the structures of geometrical isomers of [Pt(NH₃)₂Cl₂]. Explain the difference between geometrical and optical isomerism.

July 2024 · 2 marksmedium

Distinguish between ethyl chloride and chloroform using a chemical test.

July 2024 · 3 markshard

Explain Williamson's synthesis for the preparation of ethers. Write the mechanism.

July 2024 · 4 marksmedium

How are carboxylic acids prepared from alcohols and Grignard reagents? Explain their acidic character.

July 2024 · 3 marksmedium

Describe the carbylamine reaction and coupling reaction of amines with equations.

July 2024 · 3 markseasy

What are vitamins? Classify them with examples. Explain the deficiency diseases.

July 2024 · 2 markseasy

Distinguish between thermoplastics and thermosetting polymers with examples.

July 2024 · 3 marksmedium

Distinguish between soaps and synthetic detergents. How do they clean?

July 2024 · 4 marksmedium

Explain the process of double fertilization in angiosperms. What is its significance?

July 2024 · 5 markshard

Describe the menstrual cycle. Explain the role of hormones in regulating the cycle.

July 2024 · 4 markshard

Explain the chromosomal theory of inheritance. What is linkage and crossing over?

July 2024 · 3 marksmedium

What is the genetic code? Explain its salient features. How is it degenerate?

July 2024 · 3 markshard

What is Hardy-Weinberg principle? Write the equation and state the factors affecting gene frequency.

July 2024 · 3 markshard

Describe the mechanism of phloem transport. Explain the pressure flow hypothesis.

July 2024 · 3 marksmedium

Distinguish between macronutrients and micronutrients. Explain the role of nitrogen in plant nutrition.

July 2024 · 4 markshard

What is cardiac cycle? Explain the stages of cardiac cycle with the help of a diagram.

July 2024 · 3 markshard

Explain the mechanism of hormone action. Distinguish between steroid and peptide hormones.

July 2024 · 4 marksmedium

Describe the life cycle of Plasmodium that causes malaria. How is malaria transmitted?

July 2024 · 3 marksmedium

Describe the methods of animal breeding. What is artificial insemination?

July 2024 · 4 markshard

Describe the process of polymerase chain reaction (PCR) and its applications.

July 2024 · 4 marksmedium

Describe the different types of species interactions with suitable examples.

July 2024 · 4 marksmedium

Describe the carbon cycle with a neat diagram. Why is it called a biogeochemical cycle?

July 2024 · 4 marksmedium

Describe the methods of in situ and ex situ conservation of biodiversity with examples.

July 2024 · 3 marksmedium

Using the laws of logic, prove that (p → q) ∧ (p → r) ≡ p → (q ∧ r).

July 2024 · 2 markseasy

If A is a square matrix, prove that A(Aᵀ) is symmetric. Give an example.

July 2024 · 3 marksmedium

Find the general solution of the equation cos2θ = sinθ.

July 2024 · 2 markseasy

Find the combined equation of the lines x + 2y - 3 = 0 and 2x - y + 1 = 0.

July 2024 · 2 markseasy

Find the projection of vector a = i + 2j + k on vector b = 4i - 3j + 5k.

July 2024 · 3 marksmedium

Find the angle between the line (x-1)/2 = y/3 = (z+1)/-1 and the plane 3x + 4y - 5z = 7.

July 2024 · 4 markshard

Minimize Z = 3x + 2y subject to x + y ≥ 8, 3x + y ≥ 12, x ≥ 0, y ≥ 0 by graphical method.

July 2024 · 3 marksmedium

Find the derivative of tan⁻¹(√((1- cosx)/(1+ cosx))) with respect to x.

July 2024 · 4 markshard

A wire of length 28 m is cut into two pieces to form a square and a circle. Find the lengths of the pieces that minimize the total area enclosed.

July 2024 · 3 marksmedium

Evaluate ∫x² sin x dx using integration by parts.

July 2024 · 3 markshard

Evaluate ∫₀¹ x(1-x)⁵ dx using Beta-Gamma functions.

July 2024 · 3 marksmedium

Solve the differential equation dy/dx + y cot x = sin x.

July 2024 · 3 markshard

In a normal distribution with mean 50 and standard deviation 10, find the probability that X lies between 40 and 60.

July 2024 · 2 marksmedium

The mean and variance of a binomial distribution are 8 and 4.8 respectively. Find n and p.

July 2024 · 3 markshard

Derive the expression for work done in an adiabatic process.

July 2024 · 3 marksmedium

What are stationary waves? Explain the formation of stationary waves in a closed pipe organ.

July 2024 · 3 marksmedium

A convex lens of focal length 20 cm forms a real image at a distance of 30 cm. Find the object distance and magnification.

July 2024 · 2 markseasy

State the principle of superposition for electric forces. Two point charges repel each other with a force F when placed in air. If the distance between them is doubled, what will be the new force?

July 2024 · 2 marksmedium

A wire of resistance 4 Ω is stretched to twice its original length. Find its new resistance.

July 2024 · 4 marksmedium

Explain the principle of a moving coil galvanometer. How is it converted into an ammeter?

July 2024 · 3 marksmedium

Explain the working of a half wave rectifier with a circuit diagram.

July 2024 · 3 marksmedium

Explain the laws of chemical combination with examples.

July 2024 · 3 marksmedium

Explain the quantum numbers. Write all the four quantum numbers for the last electron of sodium atom.

July 2024 · 3 marksmedium

Explain the concept of hybridization. Describe the sp³ hybridization with the example of CH₄.

July 2024 · 2 markseasy

Distinguish between electrochemical cell and electrolytic cell. Give one example of each.

July 2024 · 2 markseasy

Define electronegativity. Explain the trends of electronegativity in the periodic table.

July 2024 · 3 marksmedium

Explain the types of organic reactions: addition, substitution and elimination with one example each.

July 2024 · 2 markseasy

Distinguish between saturated and unsaturated hydrocarbons with suitable tests.

July 2024 · 3 markshard

Calculate the pressure exerted by 2 moles of CO₂ at 27°C in a 5 L container using van der Waals equation.

July 2024 · 2 markseasy

What is Brownian motion? Explain its significance in colloidal systems.

July 2024 · 3 marksmedium

Explain the application of radioisotopes in medicine and agriculture.

July 2024 · 2 marksmedium

Find ∫ dx/(x² - a²) and write the result.

July 2024 · 2 markseasy

Two dice are thrown simultaneously. Find the probability that the sum of the numbers appearing is at least 10.

July 2024 · 3 marksmedium

What are the factors affecting the rate of photosynthesis? Explain Blackman's law of limiting factors.

July 2024 · 3 markseasy

Distinguish between aerobic and anaerobic respiration. Give examples of anaerobic organisms.

Feb 2023 · 2 markseasy

Convert 1 newton into dyne using dimensional analysis.

Feb 2023 · 4 markseasy

State Newton's laws of motion. Explain the concept of inertia with an example.

Feb 2023 · 3 marksmedium

Define SHM. Derive the differential equation of SHM.

Feb 2023 · 2 marksmedium

State Heisenberg's uncertainty principle. Why is it significant only for subatomic particles?

Feb 2023 · 4 marksmedium

Explain VSEPR theory. Predict the geometry of NH₃ and H₂O.

Feb 2023 · 4 marksmedium

What is a redox reaction? Balance the following equation using ion-electron method.

Feb 2023 · 2 marksmedium

Prove that √3 is irrational.

Feb 2023 · 3 marksmedium

Find the equation of the line passing through (2,3) and perpendicular to 3x+4y=12.

Feb 2023 · 4 marksmedium

Explain the structure and function of mitochondria with a labeled diagram.

Feb 2023 · 3 markseasy

Explain the mechanism of enzyme action using lock-and-key model.

Feb 2023 · 4 markshard

Describe the structure and function of nephrons.

Feb 2023 · 3 marksmedium

State and prove the theorem of parallel axes.

Feb 2023 · 3 marksmedium

Explain the molecular theory of surface tension. Define surface energy.

Feb 2023 · 3 marksmedium

State the law of equipartition of energy. Calculate the number of degrees of freedom for monatomic, diatomic and polyatomic gases.

Feb 2023 · 3 marksmedium

Derive an expression for work done during an isothermal expansion of an ideal gas.

Feb 2023 · 4 markshard

Define damped harmonic oscillator. Write the differential equation and discuss the three cases of damping.

Feb 2023 · 3 marksmedium

State the laws of vibrating strings. Verify them experimentally using a sonometer.

Feb 2023 · 3 marksmedium

State Huygens' principle. Using it, prove Snell's law of refraction.

Feb 2023 · 4 markshard

Derive the expression for capacitance of a parallel plate capacitor with a dielectric slab between the plates.

Feb 2023 · 3 marksmedium

Explain the principle of a potentiometer. How is it used to compare the emf of two cells?

Feb 2023 · 3 marksmedium

Obtain an expression for the magnetic field due to a long straight current-carrying conductor using Ampere's circuital law.

Feb 2023 · 2 marksmedium

Explain Curie temperature and its significance for ferromagnetic materials.

Feb 2023 · 3 markshard

Define self-inductance and mutual inductance. Derive an expression for the energy stored in an inductor.

Feb 2023 · 3 marksmedium

Define power factor in an AC circuit. Show that the average power dissipated in a pure inductor is zero.

Feb 2023 · 2 markseasy

Calculate the de Broglie wavelength of an electron accelerated through a potential difference of 100 V.

Feb 2023 · 4 marksmedium

State the radioactive decay law. Derive the relation N = N₀e^(-λt). Define half-life and mean life.

Feb 2023 · 4 marksmedium

With a neat circuit diagram, explain the working of a full wave rectifier.

Feb 2023 · 4 markshard

Calculate the packing efficiency in a face-centered cubic (FCC) unit cell.

Feb 2023 · 3 markseasy

Define molality and molarity. Calculate the molality of a solution containing 10 g of glucose dissolved in 250 g of water.

Feb 2023 · 4 markshard

Explain the concept of buffer solutions. Derive Henderson-Hasselbalch equation for an acidic buffer.

Feb 2023 · 3 marksmedium

What is spontaneous process? Explain the conditions for spontaneity in terms of Gibbs free energy.

Feb 2023 · 4 markshard

State and explain Nernst equation. Calculate the emf of a Zn-Cu cell under standard conditions.

Feb 2023 · 3 marksmedium

Explain Arrhenius equation. How does temperature affect the rate of a reaction?

Feb 2023 · 4 marksmedium

Describe the manufacture of sulphuric acid by contact process.

Feb 2023 · 3 marksmedium

What are lanthanoids? Explain lanthanoid contraction and its consequences.

Feb 2023 · 4 markshard

Explain Valence Bond Theory for the bonding in coordination compounds. Give the hybridization of [Co(NH₃)₆]³⁺.

Feb 2023 · 3 marksmedium

What are Grignard reagents? How are they prepared? Give two important applications.

Feb 2023 · 3 marksmedium

Describe the acidic nature of phenols. How does it differ from alcohols?

Feb 2023 · 4 marksmedium

Explain the mechanism of aldol condensation. Give one example.

Feb 2023 · 3 marksmedium

Explain the basicity of amines. Arrange aniline, methylamine and dimethylamine in increasing order of basic strength.

Feb 2023 · 4 marksmedium

Describe the structure of proteins. Explain the primary, secondary, tertiary and quaternary structures.

Feb 2023 · 4 markshard

Explain the mechanism of free radical addition polymerization with the example of polythene.

Feb 2023 · 2 marksmedium

What are food preservatives? Explain the role of sodium benzoate and sodium metabisulphite as preservatives.

Feb 2023 · 4 marksmedium

Describe the structure of a typical angiosperm ovule with a labeled diagram.

Feb 2023 · 4 marksmedium

Explain the process of oogenesis in humans with a schematic representation.

Feb 2023 · 3 marksmedium

What is codominance? Explain it with the inheritance of ABO blood groups in humans.

Feb 2023 · 3 markshard

Explain the process of transcription in prokaryotes.

Feb 2023 · 4 marksmedium

State Darwin's theory of natural selection. Explain the evidence for evolution from comparative anatomy.

Feb 2023 · 3 markseasy

What is transpiration? Explain the factors affecting transpiration rate.

Feb 2023 · 4 marksmedium

What are plant growth regulators? Explain the physiological effects of auxins.

Feb 2023 · 5 marksmedium

Describe the structure of the human heart with a labeled diagram. Explain the path of blood circulation.

Feb 2023 · 5 marksmedium

Draw a labeled diagram of the human brain and state the functions of each part.

Feb 2023 · 3 markseasy

What is immunity? Distinguish between active and passive immunity with examples.

Feb 2023 · 3 markseasy

What is tissue culture? Explain the technique of micropropagation.

Feb 2023 · 3 markseasy

What are restriction enzymes? Explain their role in genetic engineering.

Feb 2023 · 2 marksmedium

Explain the concept of ecological niche. Differentiate between habitat and niche.

Feb 2023 · 4 marksmedium

Explain the flow of energy through an ecosystem. What is the 10% law?

Feb 2023 · 3 marksmedium

Explain the concept of biodiversity hotspots. Name the four biodiversity hotspots of India.

Feb 2023 · 2 markseasy

Express the following statement in symbolic form: 'If it rains then the match will be cancelled and we will stay home.'

Feb 2023 · 3 marksmedium

Solve the system of equations x + 2y = 5, 3x - y = 8 using matrix inversion method.

Feb 2023 · 3 marksmedium

Solve the trigonometric equation 2sin²θ - 3sinθ + 1 = 0 for θ in [0, 2π].

Feb 2023 · 4 markshard

Find the joint equation of lines passing through the origin and perpendicular to the lines represented by ax² + 2hxy + by² = 0.

Feb 2023 · 3 markshard

Prove that the scalar triple product [a b c] = 0 if and only if the vectors are coplanar.

Feb 2023 · 2 markseasy

Find the distance of the point (2,3,4) from the plane 2x + y - 2z + 5 = 0.

Feb 2023 · 2 markseasy

Define the feasible region in LPP. What are corner points? Explain their significance.

Feb 2023 · 3 marksmedium

Differentiate x^sinx with respect to x using logarithmic differentiation.

Feb 2023 · 2 markseasy

Show that the function f(x) = x³ - 3x² + 3x + 2 is always increasing.

Feb 2023 · 3 marksmedium

Evaluate ∫dx/(x² + 4x + 13).

Feb 2023 · 4 markshard

Using the property of definite integral, evaluate ∫₀^(π/2) log(sin x) dx.

Feb 2023 · 4 markshard

Solve the differential equation (x² - y²) dx + 2xy dy = 0.

Feb 2023 · 3 markseasy

Define probability distribution of a random variable. Find the mean and variance for the distribution of a fair die.

Feb 2023 · 4 markshard

For a binomial distribution, prove that mean = np and variance = npq.

Feb 2023 · 2 markseasy

Distinguish between isothermal and adiabatic processes with examples.

Feb 2023 · 4 marksmedium

Derive Newton's formula for the velocity of sound in air. Explain Laplace's correction.

Feb 2023 · 3 marksmedium

Explain total internal reflection with conditions and applications.

Feb 2023 · 4 marksmedium

Define electric dipole moment. Derive the expression for electric field on the axial line of an electric dipole.

Feb 2023 · 3 marksmedium

Explain the concept of resistivity and conductivity. How does resistivity of a conductor vary with temperature?

Feb 2023 · 3 markshard

Derive the expression for the magnetic field at a point on the axis of a bar magnet.

Feb 2023 · 3 markseasy

Distinguish between intrinsic and extrinsic semiconductors. Explain doping with examples.

Feb 2023 · 3 marksmedium

What is limiting reagent? In the reaction 2H₂ + O₂ → 2H₂O, if 4 g of H₂ reacts with 32 g of O₂, identify the limiting reagent.

Feb 2023 · 3 marksmedium

State de Broglie's principle. Calculate the de Broglie wavelength of an electron moving with velocity 2 × 10⁶ m/s.

Feb 2023 · 4 markshard

Using MOT, predict the bond order and magnetic nature of O₂ and N₂.

Feb 2023 · 4 markshard

What are redox reactions? Balance the equation KMnO₄ + FeSO₄ + H₂SO₄ → K₂SO₄ + MnSO₄ + Fe₂(SO₄)₃ + H₂O by ion-electron method.

Feb 2023 · 2 marksmedium

Explain electron gain enthalpy. Why does chlorine have the highest negative electron gain enthalpy?

Feb 2023 · 2 marksmedium

Define the terms: homolytic and heterolytic fission. Give examples of each.

Feb 2023 · 3 markshard

Describe the mechanism of electrophilic addition of bromine to ethene.

Feb 2023 · 3 marksmedium

Explain the liquefaction of gases using the critical temperature concept.

Feb 2023 · 3 marksmedium

Explain the classification of colloids based on the physical state of dispersed phase and dispersion medium.

Feb 2023 · 2 markseasy

Define half-life. The half-life of a radioactive isotope is 10 days. How much of a 100 g sample remains after 30 days?

Feb 2023 · 4 markshard

Define equivalence relation. Show that the relation R = {(a,b): a - b is divisible by 3} on the set of integers is an equivalence relation.

Feb 2023 · 4 markshard

Find the general solution of the equation sinθ + sin3θ + sin5θ = 0.

Feb 2023 · 2 markseasy

Show that the points (1,2), (3,4) and (5,6) are collinear by distance formula.

Feb 2023 · 2 markseasy

If y = e^x sin x, find dy/dx.

Feb 2023 · 3 marksmedium

Evaluate ∫cos²x dx from 0 to π/2.

Feb 2023 · 4 markshard

State and explain Bayes' theorem. In a class, 60% are boys and 40% are girls. 80% of boys and 90% of girls pass an exam. Find the probability that a randomly chosen student who passed is a boy.

Feb 2023 · 3 marksmedium

Explain the taxonomic hierarchy with suitable examples.

Feb 2023 · 4 markshard

Describe the life cycle of a fern plant with a neat diagram.

Feb 2023 · 2 markseasy

Differentiate between chordates and non-chordates with examples.

Feb 2023 · 4 marksmedium

Draw a labeled diagram of a plant cell. Explain the functions of any three organelles.

Feb 2023 · 3 marksmedium

Explain the structure of proteins. What are essential and non-essential amino acids?

Feb 2023 · 4 markshard

Describe the anatomy of a dicot stem with a labeled diagram.

Feb 2023 · 3 marksmedium

Differentiate between C3 and C4 plants with examples.

Feb 2023 · 4 markshard

Describe the Krebs cycle. How many ATP molecules are produced from one glucose molecule during aerobic respiration?

July 2023 · 3 markseasy

Define work, energy, and power. State work-energy theorem.

July 2023 · 3 marksmedium

Derive the relationship between Kp and Kc. Give one example each of homogeneous and heterogeneous equilibrium.

July 2023 · 4 markshard

Evaluate ∫(3x²+2x-1)dx as a limit of sum.

July 2023 · 4 marksmedium

Draw a labeled diagram of the human heart showing the flow of blood.

July 2023 · 2 markseasy

State the law of conservation of angular momentum. Give two real-life examples.

July 2023 · 3 markshard

State Stokes' law. Derive an expression for terminal velocity of a sphere falling through a viscous fluid.

July 2023 · 2 markseasy

Define entropy. State the second law of thermodynamics in terms of entropy.

July 2023 · 3 markseasy

Define electric potential. Derive an expression for electric potential due to a point charge.

July 2023 · 3 marksmedium

What are unit cells? Explain the seven crystal systems.

July 2023 · 3 marksmedium

What are interhalogen compounds? Give their types and examples.

July 2023 · 3 marksmedium

Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y = 5 and making equal intercepts on the axes.

July 2023 · 2 markseasy

Evaluate lim(x→0) (sin 3x)/(2x).

July 2023 · 2 markseasy

Explain binomial nomenclature with examples. Who proposed this system?

July 2023 · 4 markshard

Explain the stages of meiosis I with the help of diagrams.