Question Sets

Twelve JEE Advanced questions on electrostatic potential and capacitance: a slab and a metal sheet in a charged capacitor, the surface of zero potential round two charges, the space charge of a diode, tilted plates, a match of changes with the energy stored, a metal slab between plates, a potential that makes a saddle, two dielectrics side by side, pulling the plates of a charged capacitor apart, a charged capacitor in a series circuit, the energy of five charges and where the field of a charged ball keeps its energy. Four have one correct option, one matches two lists, four have one or more correct options, and three ask for a number. Every question has a hint and a full worked solution.

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12 questions

Six olympiad questions on combinatorics, geometry and inequalities: seatings with a condition, triangles in a regular polygon, an angle bisector and the circumcircle, AM-GM with weights, the pigeonhole principle and inequalities in a triangle. Four have one correct option and two have one or more correct options. Every question has a hint and a full worked solution.

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6 questions

Twelve JEE Advanced questions on moving charges and magnetism: the field at the centre of a bent wire, the force on a wire along three edges of a cube, the torque on a folded loop, the flux through a toroid, a match of fields at the centres of loops, three parallel wires, a thick slab of current, a mass spectrometer, a short solenoid, a wire that floats on the field of another, a loop shaped like a sector of a ring, and an electron moving away from a long wire. Four have one correct option, one matches two lists, four have one or more correct options, and three ask for a number. Every question has a hint and a full worked solution.

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12 questions

Twelve JEE Advanced questions on integrals and their uses: substitution and integration by parts, the properties of definite integrals, reduction formulas, the Leibniz rule for an integral with variable limits, limits of sums, areas between curves, and an equation for a function given by its integral. Five have one correct option (one of them a match-the-lists question), four have one or more correct options and three ask for a number. Every question has a hint and a full worked solution.

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12 questions

Twelve JEE Advanced questions on electric charges and fields: the flux through a face of a cube, the field of a charged rod and of a charged bowl, the force between a dipole and a point charge, a match of fields with how they fall off, a cavity in a charged sphere, a charge inside a conducting shell, two charged plates, the field of a dipole in any direction, an electron circling a charged wire, three charges in equilibrium and the flux through a washer. Four have one correct option, one matches two lists, four have one or more correct options, and three ask for a number. Every question has a hint and a full worked solution.

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12 questions

Twelve JEE Advanced questions on continuity, differentiability and the uses of derivatives: modulus, greatest-integer and composite functions, the mean value theorem, rates of change, increasing and decreasing functions, greatest and least values, tangents and normals, and counting real roots with calculus. Five have one correct option (one of them a match-the-lists question), four have one or more correct options and three ask for a number. Every question has a hint and a full worked solution.

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12 questions

Six olympiad questions on Class 12 physics: a conductor with a charge in a cavity, a capacitor whose battery is reversed, a proton crossing into a magnetic field, a rod sliding along rails that end in a capacitor, a double slit lit by two colours, and the daughter of a radioactive parent. Three have one correct option and three have one or more. Every question has a hint and a full worked solution.

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6 questions

Twenty JEE Main and JEE Advanced questions on sequences and series: arithmetic and geometric progressions, nth terms and sums, arithmetic and geometric means, infinite geometric series, greatest and least values from the inequality between the arithmetic and geometric means, and sums of squares and cubes of natural numbers. Most have one correct option; four ask for a number and three have one or more correct options. Every question has a hint and a full worked solution.

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20 questions

Ten JEE Main and JEE Advanced questions on waves: the power carried by a wave on a string, the speed of sound in a mixture of gases, a whistle whirled in a circle, a pulse meeting a heavier string, a car heard as it passes, the energy of a standing wave, a standing wave read from its equation, a source moving towards a wall, the length of a pipe from two resonances, and a stretched steel wire. Most have one correct option; two have one or more, and two ask for a number. Every question has a hint and a full worked solution.

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10 questions

Twenty JEE Main and JEE Advanced questions on sets, relations and functions: intervals and set operations, reflexive, symmetric, transitive and equivalence relations, domain and range, one-one and onto functions, composition and inverse, functional equations, counting functions and relations, and reading graphs. Most have one correct option; four ask for a number and three have one or more correct options. Every question has a hint and a full worked solution.

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20 questions

Ten JEE Main and JEE Advanced questions on oscillations: the phase and speed of a body in simple harmonic motion, the distance it travels, springs side by side and end to end, a block on a vertical spring, two blocks joined by a spring, a liquid in a V-shaped tube, a damped pendulum, two motions at right angles and a block that gains mass while it oscillates. Most have one correct option; two have one or more, and two ask for a number. Every question has a hint and a full worked solution.

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10 questions

Twenty JEE Main and JEE Advanced questions on complex numbers and quadratic equations: the algebra of complex numbers, modulus, conjugate and argument, loci and figures in the Argand plane, the polar form and powers, roots and coefficients, the nature and position of roots, forming equations with given roots, common roots and integer roots. Most have one correct option; four ask for a number and three have one or more correct options. Every question has a hint and a full worked solution.

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20 questions

Ten JEE Main and JEE Advanced questions on the kinetic theory of gases: molecular speeds after a process, energy shared among gases in a mixture, the mean free path and collision rate, the Maxwell speed distribution, gases in a tall atmosphere and molecules leaking out of a small hole. Most have one correct option; two have one or more, and two ask for a number. Every question has a hint and a full worked solution.

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10 questions

Ten JEE Main and JEE Advanced questions on thermodynamics: the first law, heat capacities of processes, adiabatic changes fast and slow, cycles, heat engines, refrigerators and heat pumps. Most have one correct option; some have one or more, and two ask for a number. Every question has a hint and a full worked solution.

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10 questions

Ten JEE Main and JEE Advanced questions on the thermal properties of matter: thermal expansion, calorimetry with changes of state, conduction through walls and rods, and radiation. Most have one correct option; some have one or more, and two ask for a number. Every question has a hint and a full worked solution.

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10 questions

Ten JEE Main and JEE Advanced questions on fluids: pressure in still and accelerating liquids, floating, flow and Bernoulli's principle, viscosity and surface tension. Most have one correct option; some have one or more, and two ask for a number. Every question has a hint and a full worked solution.

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10 questions

Ten JEE Main and JEE Advanced questions on motion in a plane: projectiles, relative velocity with rivers, wind and moving carts, and motion on a circle with a changing speed. Most have one correct option; some have one or more, and two ask for a number. Every question has a hint and a full worked solution.

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10 questions

Ten JEE Advanced and Olympiad questions on gravitation: shells and cavities, potential inside a planet, elliptical orbits and Kepler's laws, satellites that change orbit, and systems of stars. Some have one correct option, others one or more. Every question has a hint and a full worked solution.

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10 questions

Ten JEE Advanced and Olympiad questions on rigid bodies: hinged and falling rods, impulses and collisions with rods, rolling with and without slipping, and angular momentum. Some have one correct option, others one or more. Every question has a hint and a full worked solution.

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9 questions

Ten JEE Advanced and Olympiad questions on work, energy, power and collisions: chains and springs, work along a path, bodies joined by springs, and collisions seen from the centre of mass. Some have one correct option, others one or more. Every question has a hint and a full worked solution.

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10 questions

Ten JEE Advanced and Olympiad questions on the laws of motion: springs and strings, friction on stacked and sliding blocks, constraints with pulleys and wedges, and circular motion. Some have one correct option, others one or more. Every question has a hint and a full worked solution.

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10 questions