The 15 one-mark questions from the May 2022 12th Standard Physics public exam, in paper order, with the correct option marked and a short explanation.
Q1
Which one of the following is the natural nanomaterial ?
- A. Grain of sand
- B. Peacock featherCorrect
- C. Skin of the whale
- D. Peacock beak
Explanation. The bright colours of a peacock feather come from natural nanostructures (photonic crystals) in its barbules, so it is a natural nanomaterial.
Q2
In an electron microscope, the electrons are accelerated by a voltage of 14 kV. If the voltage is changed to 224 kV, then the de-Broglie wavelength associated with the electrons would :
- A. decrease by 4 timesCorrect
- B. increase by 2 times
- C. increase by 4 times
- D. decrease by 2 times
Explanation. \(\lambda = \frac{h}{\sqrt{2meV}} \propto \frac{1}{\sqrt{V}}\). The voltage becomes 224/14 = 16 times, so λ becomes \(\frac{1}{\sqrt{16}} = \frac{1}{4}\) of its value, i.e. it decreases by 4 times.
Q3
The variation of frequency of carrier wave with respect to the instantaneous amplitude of the modulating signal is called :
- A. Phase modulation
- B. Amplitude modulation
- C. Pulse width modulation
- D. Frequency modulationCorrect
Explanation. When the frequency of the carrier wave is varied according to the instantaneous amplitude of the modulating signal, the process is frequency modulation (FM).
Q4
Q factor is equal to ________.
- A. \(\frac{\omega_r L}{R}\)
- B. \(\frac{1}{R}\sqrt{\frac{L}{C}}\)
- C. \(\frac{X_L}{R}\)
- D. All the aboveCorrect
Explanation. At resonance \(Q = \frac{\omega_r L}{R} = \frac{X_L}{R}\), and since \(\omega_r = \frac{1}{\sqrt{LC}}\), \(Q = \frac{1}{R}\sqrt{\frac{L}{C}}\). All three expressions are equal.
Q5
Two metallic spheres of radii 1 cm and 3 cm are given charges of \(-1 \times 10^{-2}\) C and \(5 \times 10^{-2}\) C respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is :
- A. \(1 \times 10^{-2}\) C
- B. \(3 \times 10^{-2}\) CCorrect
- C. \(2 \times 10^{-2}\) C
- D. \(4 \times 10^{-2}\) C
Explanation. Total charge = \(4 \times 10^{-2}\) C. After connection both spheres are at the same potential, so charge ∝ radius (1 : 3). Bigger sphere gets \(\frac{3}{4} \times 4 \times 10^{-2} = 3 \times 10^{-2}\) C.
Q6
Which of the following is an electromagnetic wave ?
- A. β-rays
- B. γ-raysCorrect
- C. α-rays
- D. All of the above
Explanation. γ-rays are high-frequency electromagnetic waves, whereas α-rays and β-rays are streams of charged particles (helium nuclei and electrons).
Q7
An air bubble in glass slab of refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness of the slab is :
- A. 12 cmCorrect
- B. 8 cm
- C. 16 cm
- D. 10 cm
Explanation. Real depth = n × apparent depth. Thickness = 1.5 × 5 + 1.5 × 3 = 7.5 + 4.5 = 12 cm.
Q8
In India electricity is supplied for domestic use at 220 V. It is supplied at 110 V in USA. If the resistance of a 60 W bulb for use in India is R, the resistance of a 60 W bulb for use in USA will be :
- A. R/4Correct
- B. R
- C. R/2
- D. 2R
Explanation. \(R = \frac{V^2}{P}\). For the same power \(R \propto V^2\); halving the voltage (220 V to 110 V) makes the resistance \(\frac{R}{4}\).
Q9
A wire of length \(l\) carrying a current I along the Y direction is kept in a magnetic field given by \(\vec{B} = \frac{\beta}{\sqrt{3}}(\hat{i} + \hat{j} + \hat{k})\) T. The magnitude of Lorentz force acting on the wire is :
- A. \(\sqrt{2}\,\beta I l\)
- B. \(\sqrt{\frac{2}{3}}\,\beta I l\)Correct
- C. \(\sqrt{\frac{1}{2}}\,\beta I l\)
- D. \(\sqrt{\frac{1}{3}}\,\beta I l\)
Explanation. \(\vec{F} = I l\,\hat{j} \times \frac{\beta}{\sqrt{3}}(\hat{i} + \hat{j} + \hat{k}) = \frac{\beta I l}{\sqrt{3}}(\hat{i} - \hat{k})\). Its magnitude is \(\frac{\sqrt{2}}{\sqrt{3}}\beta I l = \sqrt{\frac{2}{3}}\,\beta I l\).
Q10
Emission of electrons by the absorption of heat energy is called ________ emission.
- A. ThermionicCorrect
- B. Photo electric
- C. Secondary
- D. Field
Explanation. When a metal is heated, its free electrons gain enough thermal energy to escape from the surface; this is thermionic emission.
Q11
If a current of 7.5 A is maintained in a wire for 45 seconds then the charge flowing through the wire is :
- A. 6 C
- B. 365.5 C
- C. 3 C
- D. 337.5 CCorrect
Explanation. q = I t = 7.5 × 45 = 337.5 C.
Q12
The charge of cathode ray is :
- A. neutral
- B. positive
- C. not defined
- D. negativeCorrect
Explanation. Cathode rays are streams of electrons; they bend towards the positive plate in an electric field, so they are negatively charged.
Q13
A step-down transformer reduces the supply voltage from 220 V to 11 V and increases the current from 6 A to 100 A. Then its efficiency is :
- A. 0.12
- B. 1.2
- C. 0.9
- D. 0.83Correct
Explanation. Efficiency = output power / input power = \(\frac{11 \times 100}{220 \times 6} = \frac{1100}{1320} \approx 0.83\).
Q14
The electric potential of an electron is given by \(V = V_0 \ln\left(\frac{r}{r_0}\right)\), where \(r_0\) is a constant. If Bohr atom model is valid, then variation of radius of \(n^{th}\) orbit \(r_n\) with the principal quantum number n is :
- A. \(r_n \propto \frac{1}{n^2}\)
- B. \(r_n \propto \frac{1}{n}\)
- C. \(r_n \propto n^2\)
- D. \(r_n \propto n\)Correct
Explanation. Force magnitude = \(e\left|\frac{dV}{dr}\right| = \frac{eV_0}{r}\). Equating it to \(\frac{mv^2}{r}\) gives a constant speed v. With \(mvr = \frac{nh}{2\pi}\), \(r_n \propto n\).
Q15
Transverse nature of light is shown in :
- A. scattering
- B. interference
- C. polarisationCorrect
- D. diffraction
Explanation. Only transverse waves can be polarised; longitudinal waves cannot. So polarisation shows that light is a transverse wave.
