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JEE Main Heat, Waves, Optics & Modern: practice questions with solutions

16 questions on Atoms, Calorimetry, Dual Nature of Matter, Kinetic Theory of Gases, Nuclei, Ray Optics, Semiconductor Electronics, Sound Waves, Thermodynamics, Wave Optics, Waves on a String. Try each one first, then open the solution.

Tip: solve on paper before opening a solution. Once you open it, that question is counted as practised and won't appear in your HeyGyan tests.
ThermodynamicsMedium

Q1. An ideal monoatomic gas is heated at constant pressure. What fraction of the heat supplied is converted into work done by the gas?

  1. 2/5
  2. 3/5
  3. 2/3
  4. 1/3
Show answer and solution

Answer: (A) 2/5

SolutionQ = nCₚΔT = (5/2)nRΔT and W = nRΔT. So W/Q = 1/(5/2) = 2/5.
Common trap3/5 is the fraction going into internal energy, not work.
Sound WavesHard

Q2. An organ pipe open at both ends has a fundamental frequency of 300 Hz. If one end is closed, what is the frequency of its second overtone?

  1. 450 Hz
  2. 600 Hz
  3. 750 Hz
  4. 900 Hz
Show answer and solution

Answer: (C) 750 Hz

SolutionOpen pipe: v/2L = 300 Hz, so the closed pipe's fundamental is v/4L = 150 Hz. A closed pipe has only odd harmonics. The second overtone is the 5th harmonic: 5 × 150 = 750 Hz.
Common trap450 Hz is the first overtone. 900 Hz uses the open-pipe harmonic series.
Ray OpticsMedium

Q3. A glass lens (μ = 1.5) has focal length 20 cm in air. What is its focal length when immersed in water (μ = 4/3)?

  1. 20 cm
  2. 40 cm
  3. 60 cm
  4. 80 cm
Show answer and solution

Answer: (D) 80 cm

SolutionLensmaker: 1/f ∝ (μ_rel − 1). In air: 0.5. In water: 1.5/(4/3) − 1 = 1/8. So f increases by 0.5 ÷ 1/8 = 4 times: 80 cm.
Common trapUsing (1.5 − 4/3) = 1/6 instead of the relative index ratio.
Dual Nature of MatterEasyNumerical

Q4. Light of wavelength 300 nm falls on a metal with work function 2.13 eV. What is the stopping potential in volts? (Use hc = 1240 eV·nm; round to the nearest integer.)

Numerical value question: type the answer, no options.

Show answer and solution

Answer: 2

SolutionPhoton energy = 1240/300 ≈ 4.13 eV. Maximum KE = 4.13 − 2.13 = 2.00 eV. Stopping potential = 2 V.
Common trapReporting energy in eV and potential in V as different numbers. For electrons they are equal.
NucleiMedium

Q5. The activity of a radioactive sample falls to 1/8 of its initial value in 15 days. What fraction of the original sample decays in the first 10 days?

  1. 1/4
  2. 1/2
  3. 3/4
  4. 7/8
Show answer and solution

Answer: (C) 3/4

Solution1/8 = (1/2)³, so 3 half-lives = 15 days and T½ = 5 days. In 10 days (2 half-lives), 1/4 remains, so 3/4 has decayed.
Common trap1/4 is the fraction remaining, not the fraction decayed.
Wave OpticsEasy

Q6. In Young's double-slit experiment, the fringe width is 0.6 mm in air. What is it when the whole apparatus is immersed in water (μ = 4/3)?

  1. 0.45 mm
  2. 0.6 mm
  3. 0.8 mm
  4. 0.3 mm
Show answer and solution

Answer: (A) 0.45 mm

SolutionFringe width β = λD/d, and the wavelength in water is λ/μ. So β' = 0.6 × 3/4 = 0.45 mm.
Common trapMultiplying by μ instead of dividing gives 0.8 mm.
Kinetic Theory of GasesMediumNumerical

Q7. At what temperature (in K) will the rms speed of oxygen molecules equal the rms speed of hydrogen molecules at 300 K?

Numerical value question: type the answer, no options.

Show answer and solution

Answer: 4800

Solutionv_rms = √(3RT/M), so T/M must be equal. T_O₂ = 300 × (32/2) = 4800 K.
Common trapUsing √16 = 4 instead of 16 gives 1200 K. Temperature scales with M directly, not with √M.
AtomsMedium

Q8. What is the ratio of the wavelength of the first line of the Balmer series to that of the first line of the Lyman series of hydrogen?

  1. 5 : 27
  2. 27 : 5
  3. 4 : 3
  4. 9 : 4
Show answer and solution

Answer: (B) 27 : 5

Solution1/λ = R(1/n₁² − 1/n₂²). Lyman (2→1): 3R/4. Balmer (3→2): 5R/36. λ ratio = (3/4)/(5/36) = 27/5.
Common trap5 : 27 is the ratio of energies (or 1/λ), not wavelengths.
Dual Nature of MatterMediumNumerical

Q9. An electron accelerated through 100 V has a de Broglie wavelength of 1.227 Å. Through what potential difference (in volts) must it be accelerated for a wavelength of 0.6135 Å?

Numerical value question: type the answer, no options.

Show answer and solution

Answer: 400

Solutionλ ∝ 1/√V. Halving the wavelength needs √V to double, so V = 4 × 100 = 400 V.
Common trapAssuming λ ∝ 1/V gives 200 V.
CalorimetryMedium

Q10. 10 g of ice at 0 °C is mixed with 10 g of water at 50 °C. What is the final temperature of the mixture? (Latent heat of fusion = 80 cal/g, specific heat of water = 1 cal/g °C)

  1. 0 °C
  2. 5 °C
  3. 10 °C
  4. 25 °C
Show answer and solution

Answer: (A) 0 °C

SolutionMelting all the ice needs 10 × 80 = 800 cal. Cooling the water to 0 °C releases only 10 × 50 = 500 cal. So only 6.25 g of ice melts and the mixture stays at 0 °C.
Common trap25 °C is the simple average, which ignores the latent heat of melting.
Ray OpticsMedium

Q11. A prism with refracting angle 60° has refractive index √2. What is its angle of minimum deviation?

  1. 15°
  2. 30°
  3. 45°
  4. 60°
Show answer and solution

Answer: (B) 30°

Solutionμ = sin((A + δ)/2)/sin(A/2). So sin((60° + δ)/2) = √2 × sin 30° = 1/√2, giving (60° + δ)/2 = 45° and δ = 30°.
Common trap45° is the half-angle (A + δ)/2, not δ itself.
Semiconductor ElectronicsEasy

Q12. Both inputs of a NAND gate are joined together. The circuit behaves as which gate?

  1. AND
  2. OR
  3. NOT
  4. NOR
Show answer and solution

Answer: (C) NOT

SolutionWith both inputs equal to A, the output is NOT(A · A) = NOT A. So it works as a NOT gate (inverter).
Common trapAssuming the gate keeps its AND-like behaviour when inputs are joined.
AtomsEasyNumerical

Q13. A sample of hydrogen atoms is excited to the n = 4 level. What is the maximum number of different spectral lines it can emit while returning to the ground state?

Numerical value question: type the answer, no options.

Show answer and solution

Answer: 6

SolutionEach pair of levels gives one line: n(n − 1)/2 = 4 × 3/2 = 6 lines.
Common trapAnswering 3, which is the number of lines from a single atom jumping one level at a time.
Waves on a StringEasy

Q14. A stretched string has a fundamental frequency of 200 Hz. If its tension is made 4 times, with nothing else changed, what is the new fundamental frequency?

  1. 100 Hz
  2. 200 Hz
  3. 400 Hz
  4. 800 Hz
Show answer and solution

Answer: (C) 400 Hz

Solutionf = (1/2L)√(T/μ), so f ∝ √T. Four times the tension doubles the frequency: 400 Hz.
Common trap800 Hz assumes frequency is directly proportional to tension.
Ray OpticsEasy

Q15. What is the critical angle for light going from a medium of refractive index √2 into air?

  1. 30°
  2. 45°
  3. 60°
  4. 90°
Show answer and solution

Answer: (B) 45°

Solutionsin C = 1/μ = 1/√2, so C = 45°.
Common trapUsing sin C = μ, which is greater than 1 and impossible.
Dual Nature of MatterMedium

Q16. A proton and an alpha particle have the same kinetic energy. What is the ratio of their de Broglie wavelengths, λ_proton : λ_alpha?

  1. 1 : 1
  2. 1 : 2
  3. 2 : 1
  4. 4 : 1
Show answer and solution

Answer: (C) 2 : 1

Solutionλ = h/√(2mK). With equal K, λ ∝ 1/√m. The alpha particle is 4 times heavier, so λ_p/λ_α = √4 = 2.
Common trap4 : 1 uses λ ∝ 1/m, which is true only for equal speeds.

Frequently asked questions

Which Heat, Waves, Optics & Modern chapters are covered here?

This page covers Atoms, Calorimetry, Dual Nature of Matter, Kinetic Theory of Gases, Nuclei, Ray Optics, Semiconductor Electronics, Sound Waves, Thermodynamics, Wave Optics, Waves on a String. Questions follow the JEE Main pattern, with multiple-choice and numerical value types.

Are these previous year JEE questions?

No. These are original JEE Main-level practice questions written on the latest pattern, with solutions and the common trap for each.