IIT JEE Physics Practice Paper – Electrostatics (Set 12) Instructions Total Questions: 20 | Marks: 4 each | No Negative Marking Q1. Coulomb’s law is: F = kq₁q₂/r² F = ma V = IR None Q2. Electric field unit: N/C Volt Joule Ampere Q3. Electric field direction is: Direction of force on positive charge Negative charge Opposite force None Q4. Electric potential unit: Volt Ampere Tesla None Q5. Potential difference is: Work per unit charge Charge per work Force per charge None Q6. Electric field inside conductor: Zero Maximum Constant Infinite Q7. Capacitance unit: Farad Henry Ohm None Q8. Capacitance formula: C = Q/V V = IR F = ma None Q9. Energy stored in capacitor: ½CV² CV V²/C None Q10. Electric field lines: Never intersect Intersect Parallel always None Q11. Gauss law states: Φ = Q/ε₀ F = ma V = IR None Q12. Electric flux unit: Nm²/C Volt Joule None Q13. Force between like charges: Repulsive Attractive Zero None Q14. Potential due to point charge: kq/r kqr q/r² None Q15. Equipotential surface: Same potential Different potential Zero potential None Q16. Work on equipotential surface: Zero Maximum Minimum None Q17. Electric field due to infinite sheet: Constant Zero Infinite None Q18. Electric field due to point charge ∝ 1/r² r² r None Q19. Parallel plate capacitor field: Uniform Zero Infinite None Q20. Dielectric increases: Capacitance Resistance Current None Submit Electrostatics – IIT JEE Notes (Set 12) Electric Charge Basic Concept Electric charge is a fundamental property of matter responsible for electric forces. There are two types of charges: positive and negative. Like charges repel each other, while unlike charges attract. Quantization of Charge Charge exists in discrete units: q = ne, where e = 1.6 × 10⁻¹⁹ C. Coulomb’s Law Formula F = k (q₁q₂) / r² Explanation The electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Electric Field Definition Electric field is the force experienced by a unit positive charge placed in a region. Formula E = F / q Due to Point Charge E = kq / r² Electric Field Lines Properties Electric field lines originate from positive charges and terminate on negative charges. They never intersect and indicate direction of the electric field. Key Insight Closer field lines indicate stronger electric field. Electric Potential Definition Electric potential is the work done per unit charge in bringing a charge from infinity to a point. Formula V = kq / r Potential Difference Concept Potential difference is the work done per unit charge in moving a charge between two points. Relation V = W / q Equipotential Surfaces Definition Surfaces having the same electric potential at every point. Key Insight No work is done in moving a charge along an equipotential surface. Electric Field in Conductors Important Concept In electrostatic equilibrium, the electric field inside a conductor is zero. Charge Distribution Charge resides on the surface of the conductor. Gauss’s Law Statement The total electric flux through a closed surface is equal to the charge enclosed divided by permittivity. Formula Φ = Q / ε₀ Electric Flux Definition Electric flux is the measure of electric field passing through a surface. Formula Φ = EA cosθ Unit Nm²/C Capacitance Definition Capacitance is the ability of a system to store charge. Formula C = Q / V Unit Farad (F) Parallel Plate Capacitor Formula C = ε₀A / d Key Insight Capacitance increases with area and decreases with separation between plates. Energy Stored in Capacitor Formula U = (1/2)CV² Alternative Forms U = (1/2)QV = Q² / (2C) Dielectrics Concept Dielectric materials increase capacitance by reducing effective electric field between plates. Effect C increases by factor K (dielectric constant). Electric Field Due to Charge Distributions Infinite Line Charge E ∝ 1/r Infinite Plane Sheet Electric field is constant and does not depend on distance. Force and Motion of Charges Force F = qE Key Insight Positive charges move along field lines, while negative charges move opposite. Important Relationships Relation Between E and V E = -dV/dx Field Direction Electric field always points from higher potential to lower potential. Conceptual Insights Key Understanding Electric field and potential are closely related but not the same. Field represents force, while potential represents energy per unit charge. Common Mistakes Students often confuse electric field with electric potential and assume both behave similarly. Important Exam Concepts Conceptual Traps Electric field inside conductor is zero. Equipotential surfaces are perpendicular to electric field lines. JEE Strategy Focus on formulas, diagrams, and problem-solving involving Gauss’s law and capacitors. Practice numerical problems on electric field and potential thoroughly.

Instructions Total Questions: 20 | Marks: 4 each | No Negative Marking Q1. Magnetic field unit is: Tesla Weber Henry Ampere Q2. Magnetic field lines form: Closed loops Open lines Straight lines None Q3. Magnetic dipole moment unit: A·m² Tesla Weber Newton Q4. Torque on magnetic dipole: τ = mB sinθ τ = mB τ = B/m None Q5. Magnetic field at center of circular loop: μ₀I/2R μ₀I/R μ₀IR None Q6. Diamagnetic substances have: Negative susceptibility Positive Zero Infinite Q7. Paramagnetic substances have: Small positive susceptibility Negative Zero None Q8. Ferromagnetic substances: Strongly attracted Weakly Repelled None Q9. Magnetic permeability relates to: Medium Charge Velocity None Q10. Earth behaves like: Bar magnet Capacitor Inductor None Q11. Magnetic declination is: Angle between geographic and magnetic north Dip angle Inclination None Q12. Magnetic inclination is: Angle with horizontal Vertical angle Declination None Q13. Magnetic field due to straight wire: μ₀I/2πr μ₀I/r μ₀Ir None Q14. Magnetic moment of loop: IA IR I² None Q15. Magnetic field inside solenoid: μ₀nI μ₀I μ₀n None Q16. Hysteresis loop shows: Energy loss Energy gain Constant energy None Q17. Retentivity means: Retain magnetism Lose magnetism Increase field None Q18. Coercivity is: Reverse field needed Forward field Zero field None Q19. Magnetic field lines are denser where: Field is strong Weak Zero None Q20. Magnetic field due to long solenoid is: Uniform inside Zero Infinite None Submit Magnetism & Matter – IIT JEE Notes (Set 11) Introduction to Magnetism Basic Concept Magnetism is a physical phenomenon produced by moving electric charges and intrinsic magnetic moments of particles. It results in attractive or repulsive forces between objects. In classical physics, magnetism is closely related to electricity, forming the basis of electromagnetism. Magnetic Field A magnetic field is the region around a magnet or current-carrying conductor where a magnetic force can be experienced. It is represented by magnetic field lines and denoted by B. The SI unit of magnetic field is Tesla (T). Magnetic Field Lines Properties Magnetic field lines are imaginary lines used to represent the direction and strength of a magnetic field. They always form closed loops, emerging from the north pole and entering the south pole outside the magnet, and continuing inside the magnet from south to north. Important Insight The density of field lines indicates the strength of the magnetic field. Closer lines indicate a stronger field, while widely spaced lines indicate a weaker field. Magnetic Dipole and Dipole Moment Magnetic Dipole A magnetic dipole consists of two equal and opposite magnetic poles separated by a small distance. A bar magnet is a classic example of a magnetic dipole. Magnetic Dipole Moment The magnetic dipole moment (m) is a vector quantity defined as the product of pole strength and separation distance. For a current loop, it is given by m = IA, where I is current and A is area. Torque on a Magnetic Dipole Formula τ = mB sinθ Explanation When a magnetic dipole is placed in a uniform magnetic field, it experiences a torque that tends to align it with the field. The torque is maximum when the dipole is perpendicular to the field. Magnetic Field Due to Current Straight Current-Carrying Wire The magnetic field at a distance r from a long straight conductor carrying current I is given by B = μ₀I / 2πr. This shows that the field decreases with increasing distance from the wire. Circular Current Loop The magnetic field at the center of a circular loop is B = μ₀I / 2R, where R is the radius of the loop. This field is stronger than that of a straight wire at the same distance. Solenoid A solenoid is a long coil of wire. The magnetic field inside a long solenoid is uniform and given by B = μ₀nI, where n is the number of turns per unit length. Outside the solenoid, the field is nearly zero. Earth’s Magnetism Concept The Earth behaves like a giant bar magnet with its magnetic south pole near the geographic north pole and vice versa. This allows a compass needle to align along the north-south direction. Magnetic Elements Magnetic declination is the angle between geographic north and magnetic north. Magnetic inclination (or dip) is the angle made by the Earth’s magnetic field with the horizontal plane. Magnetic Properties of Materials Diamagnetic Substances Diamagnetic materials have a small negative magnetic susceptibility and are weakly repelled by magnetic fields. Examples include bismuth and copper. Paramagnetic Substances Paramagnetic materials have a small positive susceptibility and are weakly attracted by magnetic fields. Examples include aluminum and platinum. Ferromagnetic Substances Ferromagnetic materials have very large positive susceptibility and are strongly attracted by magnetic fields. They can retain magnetism even after the external field is removed. Examples include iron, cobalt, and nickel. Magnetic Permeability and Susceptibility Magnetic Permeability Magnetic permeability (μ) measures how easily a material can support the formation of a magnetic field within itself. Magnetic Susceptibility It indicates how much a material will become magnetized in an external magnetic field. It is positive for paramagnetic and ferromagnetic materials and negative for diamagnetic materials. Hysteresis Loop Concept When a ferromagnetic material is magnetized and demagnetized, the magnetic field (B) does not follow the same path with magnetizing field (H). This lag is called hysteresis. Energy Loss The area of the hysteresis loop represents energy loss per cycle due to magnetic reversal. This is important in transformer cores and electrical machines. Retentivity and Coercivity Retentivity It is the ability of a material to retain magnetism after the external magnetic field is removed. Materials with high retentivity are used for permanent magnets. Coercivity It is the reverse magnetic field required to reduce the magnetization of a material to zero. Materials with high coercivity are used for making permanent magnets. Magnetic Field Strength and Flux Magnetic Flux Magnetic flux (Φ) is defined as the total number of magnetic field lines passing through a surface. It is given by Φ = BA cosθ. Unit The SI unit of magnetic flux is Weber (Wb). Applications

Instructions Total Questions: 20 | Marks: 4 each | No Negative Marking Q1. Time period of SHM is: T = 2π/ω T = ω/2π T = ω² None Q2. Acceleration in SHM is: Proportional to displacement Constant Zero Random Q3. Maximum velocity occurs at: Mean position Extreme Anywhere None Q4. Maximum acceleration occurs at: Extreme position Mean position Anywhere None Q5. Frequency is: 1/T T T² None Q6. Energy in SHM is: Constant Increasing Decreasing Zero Q7. Kinetic energy maximum at: Mean position Extreme Both None Q8. Potential energy maximum at: Extreme Mean Both None Q9. Angular frequency ω is: 2πf f/2π 1/f None Q10. SHM restoring force is: -kx kx Zero Constant Q11. Spring time period is: 2π√(m/k) 2π√(k/m) √(m/k) None Q12. Pendulum time period is: 2π√(l/g) 2π√(g/l) l/g None Q13. Phase difference unit: Radian Meter Joule None Q14. SHM graph is: Sinusoidal Linear Parabolic None Q15. Amplitude is: Maximum displacement Minimum displacement Average None Q16. SHM velocity is zero at: Extreme Mean Both None Q17. SHM acceleration zero at: Mean Extreme Both None Q18. SHM is example of: Periodic motion Linear motion Random motion None Q19. Total energy in SHM ∝ Amplitude² Frequency Velocity None Q20. SHM occurs due to: Restoring force Constant force Zero force None Submit Simple Harmonic Motion (SHM) & Oscillations – IIT JEE Notes (Set 10) Simple Harmonic Motion (SHM) Definition Simple Harmonic Motion is a type of periodic motion in which the restoring force is directly proportional to displacement and acts towards the mean position. Restoring Force F = -kx The negative sign indicates that the force is always directed towards the equilibrium position. Basic Equations of SHM Displacement x = A sin(ωt + φ) Velocity v = ω√(A² – x²) Acceleration a = -ω²x Time Period and Frequency Time Period T = 2π/ω Frequency f = 1/T Angular Frequency ω = 2πf Energy in SHM Total Energy E = (1/2)kA² Total energy remains constant throughout the motion. Kinetic Energy Maximum at mean position and zero at extreme positions. Potential Energy Maximum at extreme positions and minimum at mean position. Important Positions in SHM Mean Position Displacement = 0, velocity is maximum, acceleration is zero. Extreme Position Displacement = maximum, velocity is zero, acceleration is maximum. Spring-Mass System Time Period T = 2π√(m/k) Key Insight Time period depends on mass and spring constant, not on amplitude. Simple Pendulum Time Period T = 2π√(l/g) Important Point Valid only for small oscillations. Phase and Phase Difference Phase Represents the state of oscillation at any instant. Unit Radian Phase Difference Difference in phase between two oscillating particles. Graphical Representation Displacement-Time Graph Sinusoidal curve. Velocity-Time Graph Also sinusoidal but shifted by π/2. Acceleration-Time Graph Opposite phase to displacement. Characteristics of SHM Periodic Motion Motion repeats after equal time intervals. Oscillatory Nature Motion occurs about a fixed mean position. Important Relationships Maximum Velocity vₘₐₓ = ωA Maximum Acceleration aₘₐₓ = ω²A Energy Relation Total energy ∝ Amplitude² Conceptual Insights Key Understanding Velocity and acceleration are not constant. Both vary continuously during motion. Common Mistakes Students often assume acceleration is maximum at mean position, which is incorrect. Important Exam Concepts Conceptual Traps Time period of SHM does not depend on amplitude. Frequency remains constant for given system. JEE Strategy Focus on formulas, graphs, and understanding relation between displacement, velocity, and acceleration.

Instructions Total Questions: 20 | Marks: 4 each | No Negative Marking Q1. Wave speed is given by: v = fλ v = λ/f v = f/λ None Q2. Frequency unit is: Hertz Joule Watt Newton Q3. Sound waves are: Longitudinal Transverse Both None Q4. Speed of sound increases with: Temperature Pressure Volume None Q5. Echo occurs due to: Reflection of sound Refraction Diffraction None Q6. Pitch depends on: Frequency Amplitude Speed None Q7. Loudness depends on: Amplitude Frequency Velocity None Q8. Doppler effect is change in: Frequency Speed Wavelength only None Q9. Beats are produced due to: Interference Reflection Refraction None Q10. Resonance occurs when: Frequency matches natural frequency Different frequency Zero frequency None Q11. Unit of wavelength is: Meter Second Hertz Joule Q12. Standing waves are formed due to: Superposition Reflection Diffraction None Q13. Node is point of: Zero displacement Maximum displacement Infinite displacement None Q14. Antinode is: Maximum displacement Zero displacement No wave None Q15. Wave frequency remains same during: Refraction Reflection Both None Q16. Intensity of wave ∝ Amplitude² Frequency Speed None Q17. Ultrasonic waves have frequency: >20 kHz 20 kHz None Q19. Mechanical waves require: Medium Vacuum Both None Q20. Electromagnetic waves are: Transverse Longitudinal Both None Submit Waves & Sound – IIT JEE Notes (Set 9) Basic Wave Concepts Wave Definition A wave is a disturbance that transfers energy from one place to another without transferring matter. Wave Equation v = fλ Where v is wave speed, f is frequency, and λ is wavelength. Types of Waves Mechanical Waves Require a medium to propagate. Example: sound waves. Electromagnetic Waves Do not require a medium and can travel in vacuum. Example: light waves. Sound Waves Nature Sound waves are longitudinal waves consisting of compressions and rarefactions. Speed of Sound Depends on temperature and medium. In air, speed increases with temperature. Frequency, Pitch and Loudness Frequency Number of oscillations per second. Unit is Hertz (Hz). Pitch Determined by frequency. Higher frequency means higher pitch. Loudness Depends on amplitude of the wave. Doppler Effect Concept Apparent change in frequency due to relative motion between source and observer. Key Insight Frequency increases when source approaches and decreases when it moves away. Reflection of Sound Echo Echo is the reflection of sound from a distant surface. Condition Minimum distance required for echo is about 17 meters for distinct hearing. Superposition of Waves Principle When two waves overlap, resultant displacement is the sum of individual displacements. Application Used in interference and formation of standing waves. Standing Waves Formation Formed by superposition of two waves traveling in opposite directions. Nodes and Antinodes Nodes: zero displacement points. Antinodes: maximum displacement points. Beats Concept Beats are periodic variations in intensity due to interference of two waves of slightly different frequencies. Frequency Beat frequency = |f₁ – f₂| Resonance Concept Occurs when frequency of external force matches natural frequency of system. Effect Results in maximum amplitude of vibration. Intensity of Sound Relation Intensity ∝ Amplitude² Key Insight Doubling amplitude increases intensity four times. Range of Sound Audible Range 20 Hz to 20 kHz. Infrasonic Below 20 Hz. Ultrasonic Above 20 kHz. Wave Properties Reflection Wave bounces back from a surface. Refraction Change in direction when wave enters different medium. Diffraction Bending of waves around obstacles. Important Exam Concepts Conceptual Traps Frequency remains constant during reflection and refraction. Speed and wavelength may change. JEE Strategy Focus on formulas, graph interpretation, and conceptual clarity. Practice numerical problems on Doppler effect and standing waves.

Instructions Total Questions: 20 | Marks: 4 each | No Negative Marking Q1. First law of thermodynamics is: ΔQ = ΔU + W PV = nRT Q = mcΔT None Q2. Internal energy depends on: Temperature Volume Pressure Shape Q3. Isothermal process means: Constant temperature Constant pressure Constant volume None Q4. Adiabatic process has: No heat exchange Constant heat Infinite heat None Q5. Efficiency of Carnot engine depends on: Temperature Pressure Volume Work Q6. PV = constant applies to: Isothermal Adiabatic Isochoric None Q7. Work done in isochoric process is: Zero Maximum Minimum Infinite Q8. Heat capacity unit is: J/K J K W Q9. Ideal gas obeys: PV = nRT F = ma V = IR None Q10. Entropy measures: Disorder Energy Work Power Q11. Specific heat depends on: Substance Mass Volume None Q12. Adiabatic equation is: PV^γ = constant PV = constant V = IR None Q13. γ = Cp/Cv is called: Heat capacity ratio Work ratio Energy ratio None Q14. Kelvin scale zero is: Absolute zero Boiling point Melting point None Q15. Heat flows from: High to low temperature Low to high Same None Q16. Carnot efficiency is maximum when: Temperature difference is large Small Zero None Q17. Isobaric process means: Constant pressure Constant temp Constant volume None Q18. Zeroth law defines: Thermal equilibrium Work Energy None Q19. Work done by gas is positive when: Expansion Compression Constant None Q20. Internal energy of ideal gas depends on: Temperature only Volume Pressure None Submit Thermodynamics – IIT JEE Notes (Set 8) First Law of Thermodynamics Statement The first law states that heat supplied to a system is used to change its internal energy and to do work. Formula: ΔQ = ΔU + W Key Insight It is based on the law of conservation of energy. Internal Energy Definition Internal energy is the total energy of all molecules in a system. Important Point For an ideal gas, internal energy depends only on temperature, not on pressure or volume. Isothermal Process Concept In this process, temperature remains constant. Relation PV = constant Key Insight Heat supplied is completely converted into work done. Adiabatic Process Concept No heat exchange occurs between system and surroundings. Equation PVγ = constant Key Insight Temperature changes due to work done. Isochoric Process Concept Volume remains constant. Important Point Work done is zero since there is no change in volume. Isobaric Process Concept Pressure remains constant. Work Done W = PΔV Heat Capacity Definition Heat required to raise temperature of a substance by 1 K. Units J/K Types Specific heat, molar heat capacity, Cp and Cv. Ratio of Heat Capacities Formula γ = Cp / Cv Key Insight Important for adiabatic processes and speed of sound calculations. Ideal Gas Equation Formula PV = nRT Key Insight Relates pressure, volume, temperature, and number of moles. Work Done in Thermodynamics Concept Work done by a gas is positive during expansion and negative during compression. Graph Insight Area under PV curve represents work done. Second Law of Thermodynamics Statement Heat cannot flow from a colder body to a hotter body without external work. Key Insight Introduces concept of irreversibility and efficiency limits. Entropy Definition Entropy is a measure of disorder or randomness of a system. Formula ΔS = Q / T Key Insight Entropy always increases in irreversible processes. Carnot Engine Efficiency η = 1 – (T₂ / T₁) Important Point Efficiency depends only on temperatures of source and sink. Heat Transfer Modes Conduction, convection, and radiation. Key Insight Heat always flows from higher temperature to lower temperature. Zeroth Law of Thermodynamics Statement If two systems are in thermal equilibrium with a third system, they are in equilibrium with each other. Application Basis for temperature measurement. Important Exam Concepts Conceptual Traps Work done is zero in isochoric process. Internal energy of ideal gas does not depend on pressure or volume. JEE Strategy Focus on process-based questions, PV diagrams, and conceptual clarity rather than rote formulas.

IIT JEE SET 7 WAVES & THERMODYNAMICS Physics Practice Paper Set 7 Waves · Sound · Thermodynamics · Kinetic Theory Questions: 30 Marks per correct: +4 Negative marking: None Max Score: 120 Suggested Time: 60 min 📋 Instructions Each question carries 4 marks. There is NO negative marking in this set. Select one option per question. Only your last selected option will be recorded. Click “Submit Paper” after attempting all questions. Unattempted questions will be counted as wrong (0 marks). Results with detailed explanations appear immediately after submission. Question 01 A string of length \(L\) is fixed at both ends and vibrates in its 3rd harmonic. The ratio of the wavelength of the standing wave to the length of the string is: A\( \dfrac{2}{3} \) B\( \dfrac{3}{2} \) C\( \dfrac{1}{3} \) D\( \dfrac{2}{1} \) Question 02 A train moving at 30 m/s emits a whistle of frequency 600 Hz. If the speed of sound is 330 m/s, the apparent frequency heard by a stationary observer standing behind the train is: A545.5 Hz B660 Hz C600 Hz D500 Hz Question 03 Two sound waves of frequencies 256 Hz and 260 Hz superpose. The number of beats heard per second is: A2 B4 C8 D516 Question 04 An open organ pipe of length 0.5 m resonates at its fundamental frequency. If speed of sound is 340 m/s, the fundamental frequency is: A170 Hz B340 Hz C680 Hz D85 Hz Question 05 The intensity of sound at a point is \(10^{-8}\) W/m². If the threshold intensity is \(10^{-12}\) W/m², the sound level in decibels is: A20 dB B40 dB C80 dB D60 dB Question 06 A closed organ pipe of length \(L\) produces its first overtone at the same frequency as the fundamental of an open pipe of length \(L’\). The ratio \(L : L’\) is: A1 : 2 B3 : 4 C2 : 3 D3 : 2 Question 07 A wave is represented by \(y = 5\sin(2\pi t – \frac{\pi x}{3})\) (SI units). The phase velocity of the wave is: A3 m/s B6 m/s C\(\dfrac{2}{3}\) m/s D\(2\pi\) m/s Question 08 In a stationary wave, the distance between two consecutive nodes is 0.3 m. The wavelength of the wave is: A0.15 m B0.3 m C0.6 m D1.2 m Question 09 The speed of sound in a gas at 27°C is \(v\). At what temperature (in °C) will the speed be \(2v\)? A54°C B108°C C927°C D1200°C Question 10 The tension in a string is quadrupled. The speed of the transverse wave in it will become: ADouble BHalf CFour times DSame Question 11 For an ideal gas undergoing an isothermal process, which of the following remains constant? APressure BVolume CInternal energy DEntropy Question 12 One mole of a monatomic ideal gas is taken through an adiabatic process. The ratio \(\gamma = C_p / C_v\) for a monatomic ideal gas is: A\(\dfrac{7}{5}\) B\(\dfrac{5}{3}\) C\(\dfrac{4}{3}\) D\(\dfrac{3}{2}\) Question 13 The work done by a gas in an isothermal expansion from volume \(V_1\) to \(V_2\) at temperature \(T\) is: A\(nRT \ln\!\left(\dfrac{V_2}{V_1}\right)\) B\(nRT(V_2 – V_1)\) C\(\dfrac{nR(T_2 – T_1)}{\gamma – 1}\) DZero Question 14 A Carnot engine operates between temperatures 500 K and 300 K. Its efficiency is: A40% B60% C30% D20% Question 15 According to the equipartition theorem, the internal energy of one mole of a diatomic gas (rigid) at temperature \(T\) is: A\(\dfrac{3}{2} RT\) B\(\dfrac{5}{2} RT\) C\(3 RT\) D\(2 RT\) Question 16 The rms speed of oxygen molecules at 27°C is approximately (M = 32 g/mol, R = 8.314 J/mol·K): A483 m/s B684 m/s C200 m/s D961 m/s Question 17 During an adiabatic process, the relation between pressure and volume is \(PV^\gamma = \text{const}\). For this process, the work done by the gas is: A\(\dfrac{P_1 V_1 – P_2 V_2}{\gamma – 1}\) B\(nRT\ln\!\left(\dfrac{V_2}{V_1}\right)\) C\(P(V_2 – V_1)\) DZero Question 18 A gas absorbs 600 J of heat and does 250 J of work. The change in internal energy of the gas is: A350 J B−350 J C850 J D600 J Question 19 The mean free path of a gas molecule is inversely proportional to: ATemperature BSquare of molecular diameter CNumber density \(\times\) diameter squared DPressure only Question 20 In a \(p\text{-}V\) diagram, an isochoric process is represented by: AA horizontal line BA curve \(pV = \text{const}\) CA vertical line DA curve \(pV^\gamma = \text{const}\) Question 21 Two waves \(y_1 = A\sin(\omega t)\) and \(y_2 = A\sin(\omega t + \phi)\) are superposed. For completely destructive interference, \(\phi\) must be: A\(0, 2\pi, 4\pi\ldots\) B\(\pi, 3\pi, 5\pi\ldots\) C\(\dfrac{\pi}{2}, \dfrac{3\pi}{2}\ldots\) DAny value of \(\phi\) Question 22 The velocity of sound in air at STP is about 332 m/s. At 100°C (373 K), the speed will be approximately: A366 m/s B332 m/s C432 m/s D664 m/s Question 23 Which of the following processes is represented by \(\Delta U = 0\)? AAdiabatic process BIsochoric process CIsothermal process (ideal gas) DIsobaric process Question 24 For a diatomic ideal gas, the ratio of the slope of the adiabatic curve to the slope of the isothermal curve (at the same point on the \(p\text{-}V\) diagram) is: A\(\dfrac{7}{5}\) B\(\dfrac{5}{3}\) C\(\dfrac{5}{7}\) D1 Question 25 The Doppler effect is NOT observed when: AThe source moves towards the observer BThe observer moves towards the source CBoth move perpendicular to the line joining them DThe medium moves between them Question 26 The number of degrees of freedom for a rigid diatomic molecule is: A3 B5 C6 D7 Question 27 A string vibrates in 4 loops when 36 g is suspended. To make it vibrate in 6 loops, the mass suspended should be: A16 g B24 g C64 g D9 g Question 28 For an ideal gas, at constant pressure, the graph of volume vs absolute temperature is: AA parabola BA straight line through the origin CA hyperbola DA horizontal line Question 29 If the pressure of a gas is doubled at constant volume, the rms speed of the gas molecules becomes: ASame B\(\sqrt{2}\) times CDouble D4 times Question 30 The second law of thermodynamics implies that: AEnergy is always conserved BHeat flows spontaneously from

IIT JEE Physics Practice Paper – Modern Physics (Set 6) Instructions Total Questions: 20 | Marks: 4 each | No Negative Marking Q1. Photoelectric effect proves: Particle nature of light Wave nature Both equally None Q2. Einstein photoelectric equation is: hν = φ + KE E = mc² V = IR None Q3. Threshold frequency depends on: Material Intensity Distance Time Q4. Work function is: Minimum energy to remove electron Maximum energy Kinetic energy None Q5. de Broglie wavelength is: h/p p/h hv None Q6. Planck constant unit is: J·s J W N Q7. Energy of photon is: hν mv² mc² None Q8. Compton effect proves: Particle nature Wave nature Both None Q9. Bohr model applies to: Hydrogen atom All atoms Molecules None Q10. Energy levels in atom are: Quantized Continuous Infinite None Q11. Radius of Bohr orbit proportional to: n² n 1/n None Q12. Nuclear force is: Short range Long range Infinite None Q13. Binding energy is: Energy to break nucleus Energy released Kinetic energy None Q14. Half-life depends on: Nature of substance Temperature Pressure Volume Q15. Radioactive decay is: Random Predictable Periodic None Q16. Mass-energy relation: E = mc² V = IR F = ma None Q17. Pair production requires: High energy photon Low energy photon Electron None Q18. Semiconductor conductivity increases with: Temperature Pressure Volume None Q19. Diode allows current in: One direction Both None Random Q20. Transistor is used for: Amplification Storage Reflection None Submit Modern Physics – IIT JEE Notes (Set 6) Photoelectric Effect Concept The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency falls on it. It proves the particle nature of light. Einstein Equation hν = φ + KE(max) Where h is Planck’s constant, ν is frequency, φ is work function, and KE is kinetic energy of emitted electrons. Work Function and Threshold Frequency Work Function Minimum energy required to remove an electron from the surface of a metal. Threshold Frequency The minimum frequency required to initiate photoelectric emission. It depends only on the material. de Broglie Hypothesis Concept Every moving particle has wave nature associated with it. Formula λ = h/p Where λ is wavelength and p is momentum. Photon and Energy Quantization Photon Energy E = hν Key Insight Energy of light is quantized and comes in discrete packets called photons. Compton Effect Concept Scattering of X-rays by electrons leads to an increase in wavelength. Importance It confirms the particle nature of light and conservation of momentum. Bohr Model of Atom Postulates Electrons revolve in fixed orbits with quantized energy levels. Energy Levels E ∝ -1/n² Radius of Orbit r ∝ n² Atomic Spectra Concept When electrons transition between energy levels, they emit or absorb photons of specific wavelengths. Key Insight Each element has a unique spectral signature. Nuclear Physics Basics Nuclear Force Short-range force that holds protons and neutrons together inside nucleus. Binding Energy Energy required to separate a nucleus into individual nucleons. Radioactivity Decay Law N = N₀e^(-λt) Half-Life Time required for half of the radioactive substance to decay. It depends only on the nature of the nucleus. Key Insight Radioactive decay is random and unaffected by external conditions. Mass-Energy Equivalence Formula E = mc² Application Used to explain nuclear reactions like fission and fusion. Pair Production and Annihilation Pair Production A high-energy photon converts into an electron-positron pair in presence of a nucleus. Annihilation Electron and positron combine to produce energy in the form of photons. Semiconductors Types Intrinsic and Extrinsic (n-type and p-type). Key Insight Conductivity increases with temperature, unlike metals. Diodes and Transistors Diode Allows current to flow in one direction only. Transistor Used for amplification and switching in electronic circuits. Important Exam Concepts Conceptual Traps Intensity affects number of electrons emitted, not their energy. Frequency controls energy in photoelectric effect. JEE Strategy Focus on formulas, graphs, and conceptual clarity. Practice numerical problems on photoelectric effect and radioactive decay.

Go to Notes IIT JEE Practice Series Physics Practice PaperWaves & Oscillations 30 Concept-Based Questions | JEE Main & Advanced Level 📋 5 Parts ❓ 30 Questions ⏱ 60 Minutes 🏆 120 Marks ➕ +4 / No Negative 📌 Instructions Each question carries +4 marks for a correct answer. There is no negative marking. Select one option per question. Unattempted questions carry 0 marks. Click Submit Paper after attempting all questions to view your score and explanations. Topics: Simple Harmonic Motion, Wave Motion, Sound Waves, Doppler Effect, Superposition & Beats. Part I Simple Harmonic Motion — Fundamentals Q 01 A particle executes SHM with amplitude \(A\) and angular frequency \(\omega\). The ratio of maximum acceleration to maximum velocity is: A \(\dfrac{\omega}{A}\) B \(\omega A\) C \(\omega\) D \(\dfrac{A}{\omega}\) Q 02 In SHM, the total mechanical energy of a particle at displacement \(x\) from the mean position is: A \(\dfrac{1}{2}m\omega^2 x^2\) B \(\dfrac{1}{2}m\omega^2(A^2 – x^2)\) C \(\dfrac{1}{2}m\omega^2 A^2\) D \(m\omega^2 A^2\) Q 03 A particle in SHM has velocity \(v_1\) at displacement \(x_1\) and velocity \(v_2\) at displacement \(x_2\). The amplitude of oscillation is: A \(\sqrt{\dfrac{v_1^2 x_2^2 – v_2^2 x_1^2}{v_1^2 – v_2^2}}\) B \(\sqrt{\dfrac{v_1^2 x_1^2 – v_2^2 x_2^2}{v_2^2 – v_1^2}}\) C \(\sqrt{x_1^2 + x_2^2}\) D \(\sqrt{\dfrac{v_1^2 + v_2^2}{x_1^2 + x_2^2}}\) Q 04 The time period of a simple pendulum on the surface of a planet where gravitational acceleration is \(\dfrac{g}{4}\) compared to Earth is: A Same as on Earth B Half of Earth’s value C Double of Earth’s value D Four times Earth’s value Q 05 For a spring-mass system with spring constant \(k\) and mass \(m\), if the spring is cut into \(n\) equal parts and one part is used with the same mass, the new time period is: A \(T\sqrt{n}\) B \(\dfrac{T}{\sqrt{n}}\) C \(nT\) D \(\dfrac{T}{n}\) Q 06 The phase difference between displacement and velocity of a particle executing SHM is: A \(0\) B \(\pi\) C \(\dfrac{\pi}{2}\) D \(\dfrac{\pi}{4}\) Part II Simple Harmonic Motion — Advanced Q 07 Two particles perform SHM with the same amplitude and frequency but with a phase difference of \(\dfrac{\pi}{3}\). The maximum resultant displacement when they are superimposed is: A \(A\) B \(\sqrt{3}A\) C \(2A\) D \(\sqrt{2}A\) Q 08 A particle executes SHM: \(x = 5\sin\!\left(2\pi t + \dfrac{\pi}{4}\right)\) cm. The displacement at \(t = 0\) and the initial direction of motion are respectively: A \(5\sqrt{2}/2\) cm, towards positive \(x\) B \(5\) cm, towards positive \(x\) C \(5\sqrt{2}/2\) cm, towards negative \(x\) D \(0\) cm, towards positive \(x\) Q 09 A mass \(m\) is suspended from two springs of spring constants \(k_1\) and \(k_2\) connected in parallel. The angular frequency of oscillation is: A \(\sqrt{\dfrac{k_1 k_2}{m(k_1+k_2)}}\) B \(\sqrt{\dfrac{k_1+k_2}{m}}\) C \(\sqrt{\dfrac{k_1 k_2}{m}}\) D \(\sqrt{\dfrac{k_1-k_2}{m}}\) Q 10 In SHM, the kinetic energy equals the potential energy at what displacement from mean position? A \(A\) B \(\dfrac{A}{2}\) C \(\dfrac{A}{\sqrt{2}}\) D \(0\) Q 11 The number of times KE of a particle in SHM becomes maximum in one complete oscillation is: A 1 B 2 C 4 D 3 Q 12 A pendulum clock runs fast in summer and slow in winter. The correct reason is: A Air density changes with season B Thermal expansion increases \(L\) in summer, increasing \(T\); the clock runs slow in summer C Gravity changes with temperature D Amplitude increases in summer Part III Wave Motion & Progressive Waves Q 13 A transverse wave is described by \(y = A\sin(kx – \omega t)\). The wave speed is: A \(A\omega\) B \(\dfrac{k}{\omega}\) C \(\dfrac{\omega}{k}\) D \(\dfrac{\omega^2}{k}\) Q 14 The speed of a transverse wave in a stretched string depends on which pair of quantities? A Tension and amplitude B Tension and linear mass density C Frequency and amplitude D Wavelength and frequency only Q 15 Two waves of intensities \(I_1\) and \(I_2\) interfere. The ratio of maximum to minimum intensity when \(I_1 : I_2 = 4 : 1\) is: A 9 : 1 B 4 : 1 C 5 : 3 D 25 : 1 Q 16 The equation of a stationary wave is \(y = 2A\cos(kx)\sin(\omega t)\). The distance between two adjacent nodes is: A \(\lambda\) B \(\dfrac{\lambda}{4}\) C \(\dfrac{\lambda}{2}\) D \(2\lambda\) Q 17 A wave pulse travels from medium 1 to medium 2, where wave speed in medium 2 is greater. At the boundary, the reflected pulse will have: A Phase change of \(\pi\) B No phase change C Phase change of \(\pi/2\) D Phase change of \(2\pi\) Q 18 The power transmitted by a transverse wave on a string is proportional to: A \(A\omega\) B \(A^2\omega^2\) C \(A^2\omega\) D \(A\omega^2\) Part IV Sound Waves & Resonance Q 19 The speed of sound in an ideal gas is given by \(v = \sqrt{\dfrac{\gamma P}{\rho}}\). If the temperature is doubled at constant pressure, the speed of sound becomes: A \(\sqrt{2}\,v\) C \(2v\) C \(\dfrac{v}{\sqrt{2}}\) D \(4v\) Q 20 An open organ pipe of length \(L\) resonates at its fundamental frequency. If it is half-submerged in water (effectively becoming a closed pipe of length \(L/2\)), the fundamental frequency: A Doubles B Halves C Remains the same D Becomes four times Q 21 Two tuning forks of frequencies 256 Hz and 260 Hz are sounded together. The number of beats heard per second is: A 516 B 2 C 4 D 8 Q 22 In a closed organ pipe, the ratio of frequencies of the fundamental and second overtone is: A 1 : 3 B 1 : 2 C 1 : 5 D 1 : 4 Q 23 A sound wave of intensity \(I\) has a sound level of 40 dB. If the intensity is increased to \(100I\), the new sound level is: A 60 dB B 4000 dB C 80 dB D 140 dB Q 24 The displacement node in a standing sound wave corresponds to a: A Pressure node B Pressure antinode C Zero pressure variation D Maximum particle velocity Part V Doppler Effect, Superposition & Mixed Concepts Q 25 A source of sound moves toward a stationary observer with velocity \(v_s\).

IIT JEE Physics Practice Paper – Optics (Set 4) Instructions Total Questions: 30 | Marks: 4 each | No Negative Marking Q1. Refractive index is defined as: c/v v/c λ/v f/v Q2. Snell’s law is: n₁sinθ₁ = n₂sinθ₂ θ₁ = θ₂ n₁ = n₂ None Q3. Critical angle occurs when: Refraction angle = 90° Incident angle = 90° Both equal None Q4. Mirror formula is: 1/f = 1/v + 1/u v = u + f f = v/u None Q5. Power of lens is: 1/f f v/u None Q6. Unit of power of lens: Diopter Watt Joule Newton Q7. Total internal reflection occurs when: Denser to rarer medium Rarer to denser Same medium None Q8. Image formed by plane mirror is: Virtual and erect Real Inverted None Q9. Magnification of mirror is: -v/u v/u u/v None Q10. Dispersion of light is due to: Different refractive indices Same speed Reflection Absorption Q11. Speed of light is maximum in: Vacuum Water Glass Air Q12. Concave mirror focal length sign: Negative Positive Zero Infinite Q13. Convex mirror forms image: Virtual Real Both None Q14. Lens formula is: 1/f = 1/v – 1/u 1/f = 1/v + 1/u v = u + f None Q15. Optical fiber works on: Total internal reflection Reflection Refraction Diffraction Q16. Young’s double slit experiment proves: Wave nature of light Particle nature Energy conservation None Q17. Fringe width depends on: Wavelength Mass Charge None Q18. Diffraction occurs when: Aperture size comparable to wavelength Very large aperture No aperture None Q19. Polarization proves: Transverse nature of light Longitudinal nature Particle nature None Q20. Coherent sources have: Same frequency Different frequency Random phase None Q21. Brewster angle relates to: Polarization Diffraction Reflection None Q22. Optical path = n × distance distance 1/n None Q23. Convex lens produces real image when: Object beyond F At F Inside F None Q24. Interference maxima condition: Path difference = nλ (n+½)λ λ/2 None Q25. Diffraction pattern central maxima is: Brightest Dark Same None Q26. Wavefront is: Surface of constant phase Constant velocity Constant energy None Q27. Huygens principle explains: Wave propagation Particle motion Energy loss None Q28. Angular magnification depends on: Focal length Mass Charge None Q29. Telescope works on: Refraction Diffraction Polarization None Q30. Microscope magnification depends on: Focal length Velocity Charge None Submit Optics – IIT JEE Notes (Set 4) Refractive Index Definition Refractive index (n) is defined as the ratio of speed of light in vacuum to speed of light in a medium. Formula: n = c / v Key Insight Higher refractive index means light travels slower in that medium. Refraction and Snell’s Law Law n₁ sinθ₁ = n₂ sinθ₂ Important Points Light bends towards normal when entering denser medium and away from normal when entering rarer medium. Total Internal Reflection (TIR) Conditions 1. Light must travel from denser to rarer medium 2. Angle of incidence must be greater than critical angle Applications Optical fibers, diamond sparkle, mirage formation Mirror Formula and Magnification Formula 1/f = 1/v + 1/u Magnification m = -v/u Key Insight Negative magnification indicates inverted image. Lens Formula and Power Lens Formula 1/f = 1/v – 1/u Power of Lens P = 1/f (in meter) Unit Diopter (D) Image Formation by Lenses Convex Lens Forms real image when object is beyond focal point and virtual image when inside focal length. Concave Lens Always forms virtual, erect, and diminished image. Dispersion of Light Concept White light splits into colors due to different refractive indices for different wavelengths. Key Insight Violet deviates most, red deviates least. Interference of Light Condition Constructive interference: path difference = nλ Destructive interference: path difference = (2n+1)λ/2 Young’s Double Slit Experiment Demonstrates wave nature of light. Diffraction Concept Bending of light around edges or through small apertures. Key Insight Occurs when aperture size is comparable to wavelength. Polarization Concept Polarization proves that light is a transverse wave. Brewster’s Law tanθ = n Wavefront and Huygens Principle Wavefront A surface of constant phase. Huygens Principle Every point on a wavefront acts as a source of secondary wavelets. Optical Instruments Microscope Magnification depends on focal length of objective and eyepiece. Telescope Used for viewing distant objects, works on refraction or reflection. Important Exam Concepts Conceptual Traps Light speed changes but frequency remains constant during refraction. Magnetic field does not affect light path. JEE Strategy Focus on sign conventions, formulas, and diagram-based understanding. Practice numerical problems regularly.