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.

IIT JEE Physics Magnetism and Electromagnetic Induction practice paper with 30 MCQs, answers, explanations and instant score. 30 Questions | 4 Marks Each | No Negative Marking Q1. Unit of magnetic field is: Tesla Weber Henry Ampere Q2. Magnetic force on moving charge is: qvB qE mv²/r IR Q3. Force on current carrying conductor is: BIL qvB IR V/L Q4. Direction of magnetic force is given by: Fleming’s Left Hand Rule Right Hand Rule Lenz Law Ohm’s Law Q5. Magnetic field due to straight wire depends on: Current Distance Both None Q6. Magnetic field at center of circular loop is: μ₀I/2R μ₀I/R μ₀I/4R μ₀IR Q7. Lorentz force depends on: Velocity Charge Magnetic field All Q8. Unit of magnetic flux is: Weber Tesla Henry Joule Q9. Faraday’s law states: emf ∝ flux emf ∝ rate of change of flux emf ∝ current emf ∝ resistance Q10. Lenz law is based on: Conservation of energy Newton law Ohm law Coulomb law Submit Magnetism & Electromagnetic Induction – IIT JEE Notes (Set 3) Magnetic Field Basics Definition A magnetic field is the region around a magnet or current-carrying conductor where magnetic force can be experienced by moving charges or magnetic materials. SI Unit The SI unit of magnetic field is Tesla (T). It is a vector quantity and has both magnitude and direction. Magnetic Force on Moving Charge Lorentz Force F = qvB sinθ The magnetic force depends on charge, velocity, magnetic field, and angle between velocity and field. Important Insight If velocity is parallel to magnetic field, force is zero. If perpendicular, force is maximum. Force on Current Carrying Conductor Formula F = BIL sinθ Where B is magnetic field, I is current, and L is length of conductor. Direction Rule Fleming’s Left Hand Rule gives the direction of force acting on the conductor. Magnetic Field Due to Current Straight Wire B ∝ I / r Magnetic field increases with current and decreases with distance from wire. Circular Loop B = μ₀I / 2R Magnetic field is strongest at the center of the loop. Magnetic Flux Definition Φ = B × A × cosθ Magnetic flux represents the number of magnetic field lines passing through a surface. Unit The SI unit of magnetic flux is Weber (Wb). Electromagnetic Induction (EMI) Faraday’s Law Induced emf is proportional to rate of change of magnetic flux. ε = – dΦ/dt Key Concept Faster change in flux produces larger induced emf. This is widely used in generators. Lenz’s Law Statement The direction of induced current opposes the cause producing it. Important Insight Lenz’s law is based on conservation of energy and prevents violation of energy principles. Induced Current Conditions Induced current is produced when there is a change in magnetic flux through a circuit. Methods to Change Flux Change magnetic field, change area, or change orientation of the loop. Self Inductance Definition Self inductance is the property of a coil to oppose change in current flowing through it. Formula ε = -L (dI/dt) Mutual Inductance Definition It is the property by which a change in current in one coil induces emf in another coil. Application Used in transformers and wireless energy transfer systems. Alternating Current Basics AC Current Current that changes direction periodically is called alternating current. Frequency In India, AC frequency is 50 Hz. Key Exam Concepts Conceptual Traps Magnetic force does no work as it is perpendicular to velocity. Electric field can do work but magnetic field cannot. JEE Strategy Focus on right-hand rules, formulas, and conceptual understanding. Practice numerical problems involving magnetic force and induction carefully.

IIT JEE Physics Electrostatics and Current Electricity practice test with 30 MCQs, solutions, and instant score. 30 Questions | 4 Marks Each | No Negative Marking Q1. SI unit of electric field is: N/C Volt Ohm Ampere Q2. Coulomb’s law force varies as: r 1/r 1/r² r² Q3. Electric field inside a conductor is: Zero Maximum Infinite Constant Q4. Potential difference is defined as: Work per charge Charge per work Energy per time Force per charge Q5. Capacitance unit is: Farad Ohm Volt Ampere Q6. Ohm’s law is: V = IR P = VI F = qE W = qV Q7. Resistance depends on: Length Area Material All of these Q8. Current is defined as: Charge/time Work/time Energy/time Voltage/time Submit Electrostatics & Current Electricity – IIT JEE Notes (Set 2) Electric Charge and Coulomb’s Law Basic Concept Electric charge is a fundamental property of matter. Charges can be positive or negative and interact through electrostatic forces. Like charges repel and unlike charges attract. Coulomb’s Law F = k × (q₁q₂ / r²) The electrostatic force is directly proportional to the product of charges and inversely proportional to the square of the distance between them. This inverse square law is very important for IIT JEE. Electric Field Definition E = F / q Electric field is the force experienced by a unit positive charge placed in the field. Important Points The unit of electric field is N/C. The direction of electric field is the direction of force on a positive charge. Inside a conductor, the electric field is zero due to redistribution of charges. Electric Potential and Potential Difference Electric Potential V = W / q Electric potential is the work done per unit charge in bringing a charge from infinity to a point. Potential Difference It is the difference in potential between two points and is responsible for the flow of current in a circuit. Capacitance Definition C = Q / V Capacitance is the ability of a conductor to store charge. Parallel Plate Capacitor C = ε₀A / d Capacitance increases with plate area and decreases with distance between plates. Electric Current Definition I = Q / t Electric current is the rate of flow of charge through a conductor. Key Concept Current is caused by drift of electrons under an electric field. Though electrons move randomly, an applied field creates a net motion. Ohm’s Law Formula V = IR It states that current is directly proportional to voltage for a conductor at constant temperature. Graph Insight The V-I graph for an ohmic conductor is a straight line, and its slope represents resistance. Resistance and Resistivity Formula R = ρL / A Resistance depends on length, area, and material of the conductor. Important Points Resistance increases with length and decreases with cross-sectional area. Resistivity is a material property and is independent of shape. Combination of Resistors Series Combination R = R₁ + R₂ + R₃ Same current flows through all resistors, and total resistance increases. Parallel Combination 1/R = 1/R₁ + 1/R₂ + 1/R₃ Voltage remains the same across resistors, and total resistance decreases. Electrical Power Formula P = VI = I²R = V²/R Electrical power is the rate at which electrical energy is consumed or converted. Important Insight Higher current or voltage increases power. These formulas are frequently used in numerical problems. Key Exam Concepts Conceptual Traps Electric field inside conductor is zero. Work done depends on angle between force and displacement. Resistance does not depend on current or voltage directly. JEE Strategy Focus on formulas, units, and conceptual clarity. Practice derivations and numerical problems regularly to strengthen understanding.