Answer: (A) 50h

Explanation

The energy of a photon is given by the relation E = hf, where h is Planck’s constant and f is the frequency of the photon.
Here, $f = 50$ Hz, so the energy is:
$$E = h \times 50 = 50h \text{ J}$$

Hence, the correct answer is 50h J.

Exam Facts

• Photon energy formula: $E = hf$
• Planck’s constant (h): 6.626×10−34 J·s
• Frequency (f) is measured in Hertz (Hz).
• Photon momentum: $p = \frac{h}{\lambda}$​
• Relation between wavelength and frequency: $c = f\lambda$, where $c = 3 \times 10^8$ m/s.
• Max Planck introduced the quantum theory in 1900.
• Albert Einstein explained the photoelectric effect (1905) using the photon concept, earning the 1921 Nobel Prize in Physics.

Answer: (B) 24 m/s

Explanation

When equal distances are covered at different speeds, the average speed is the harmonic mean of the two speeds, not the arithmetic mean.$$\text{Average Speed}=\frac{2v_1v_2}{v_1+v_2}$$$$=\frac{2\times20\times30}{20+30} =\frac{1200}{50}=24\ \text{m/s}$$

Hence, the correct answer is 24 m/s.

Exam Facts

• Average speed = Total distance ÷ Total time.
• For equal distances, average speed $=\dfrac{2v_1v_2}{v_1+v_2}$​​ (Harmonic Mean).
• For equal time intervals, average speed $=\dfrac{v_1+v_2}{2}$(Arithmetic Mean).
• SI unit of speed: metre per second (m/s).
• Speed is a scalar quantity, whereas velocity is a vector quantity.
• Average speed depends on the total distance travelled, while average velocity depends on the net displacement.

Answer: (A) Zero

Explanation

In circular motion, the gravitational force always acts towards the center of the circle (centripetal direction), while the planet’s instantaneous displacement is along the tangent to the orbit. Since the angle between force and displacement is 90°, the work done is zero at every point of the motion. Therefore, the total work done over half the circumference is also zero.

Exam Facts

• Work done: $W = Fs\cos\theta$
• If force is perpendicular to displacement ($\theta = 90^\circ$), then work done = 0.
• In uniform circular motion, centripetal force always acts towards the centre of the circle.
• Gravitational force provides the centripetal force for planetary motion.
• Although gravity does no work in circular motion, it continuously changes the direction of velocity.
• Kinetic energy of a planet remains constant in a uniform circular orbit because no work is done.
• Newton’s Law of Universal Gravitation: $F=\dfrac{GMm}{r^2}$​

Answer: (D) Silicon

Explanation

A semiconductor is a material whose electrical conductivity lies between that of a conductor and an insulator. Silicon (Si) is the most widely used semiconductor because its conductivity can be controlled by doping with suitable impurities. Iron, zinc, and mercury are all conductors.

Exam Facts

• Silicon (Si) and Germanium (Ge) are the most common elemental semiconductors.
• Atomic number of Silicon: 14.
• Silicon belongs to Group 14 (Carbon family) of the Periodic Table.
• The conductivity of semiconductors increases with increase in temperature, unlike metals.
• Doping with pentavalent impurities produces n-type semiconductors, while trivalent impurities produce p-type semiconductors.
• Silicon is the basic material used in ICs (Integrated Circuits), transistors, diodes, solar cells, and computer chips.
• Gallium Arsenide (GaAs) is an important compound semiconductor used in high-speed electronic and optoelectronic devices.

Answer: (C) Low pressure and high temperature

Explanation

A real gas behaves nearly like an ideal gas at low pressure and high temperature because the gas molecules are far apart and intermolecular forces become negligible. Under these conditions, the assumptions of the ideal gas model are approximately valid.

Exam Facts

• Ideal Gas Equation: $PV = nRT$
• An ideal gas has negligible molecular volume and no intermolecular forces.
• Real gases show maximum deviation from ideal behavior at high pressure and low temperature.
• The compressibility factor (Z) is 1 for an ideal gas; for real gases, $Z \neq 1$.
• The van der Waals equation explains the behavior of real gases by considering molecular size and intermolecular attraction.
• Hydrogen (H₂) and Helium (He) exhibit behavior closest to an ideal gas under ordinary conditions.
• Boyle’s Law:$P \propto \frac{1}{V}$ (constant temperature); Charles’ Law:$V \propto T$ (constant pressure).

Answer: (B) 1/10 Ωcm

Explanation

The resistivity of a wire is given by:$$\rho=\frac{RA}{L}$$

Given:

• $R = 10\,\Omega$
• $L = 1\,\text{m} = 100\,\text{cm}$
• $A = 1\,\text{cm}^2$

$$\rho=\frac{10\times1}{100}=0.1\,\Omega\text{cm}=\frac{1}{10}\,\Omega\text{cm}$$

Hence, the correct answer is (A) 1/10 Ωcm.

Exam Facts

• Resistivity: $\rho=\dfrac{RA}{L}$ρ=LRA​
• SI unit of resistivity: ohm-metre (Ω·m).
• In the CGS system, resistivity may be expressed as Ω·cm.
• Resistivity is a material property and does not depend on the length or cross-sectional area of the conductor.
• Resistance increases with length and decreases with cross-sectional area.
• For metallic conductors, resistance increases with temperature.
• Silver has the lowest resistivity among common metals, followed by copper.

Answer: (B) Released

Explanation

When two liquid drops merge, the total surface area decreases. Since surface energy is directly proportional to surface area, the total surface energy of the system decreases. The decrease in surface energy is released as heat or other forms of energy.

Exam Facts

• Surface energy is the energy required to increase the surface area of a liquid.
• Surface tension (T) is the force acting per unit length along the liquid surface.
• Surface energy is directly proportional to surface area.
• A liquid tends to minimize its surface area; therefore, free liquid drops are nearly spherical.
• Smaller drops merging into a larger drop reduces surface area, making the process energetically favorable.
• SI unit of surface tension: N/m (also equal to J/m²).
• Surface tension decreases with increase in temperature and becomes zero at the critical temperature.

Answer: (D) Volume

Explanation

When a water drop breaks into smaller drops, the total volume remains conserved because no water is lost. However, the total surface area increases, which also increases the surface energy. Therefore, only the sum of the volumes of the two smaller drops equals the volume of the original drop.

Exam Facts

• Volume of a sphere: $V=\dfrac{4}{3}\pi r^3$
• Surface area of a sphere: $A=4\pi r^2$
• When a liquid drop splits into smaller drops, volume is conserved.
• Breaking a drop increases the total surface area.
• Since surface energy is proportional to surface area, surface energy also increases after splitting.
• Extra energy is required (absorbed) to break a liquid drop into smaller drops.
• Conversely, when small drops merge into a larger drop, surface area decreases and energy is released.

Answer: (A) 12.5 Ω

Explanation

The maximum equivalent resistance is obtained when all the resistors are connected in series.

For a series combination,$$R = R_1 + R_2 + R_3 = 5 + 4.5 + 3 = 12.5\ \Omega$$

Hence, the maximum resistance is 12.5 Ω.

Exam Facts

• In a series circuit, equivalent resistance is the sum of all resistances: $R = R_1 + R_2 + R_3 + \cdots$
• In a parallel circuit, equivalent resistance is always less than the smallest individual resistance.
• In a series circuit, the same current flows through all resistors.
• In a parallel circuit, the potential difference (voltage) across each resistor is the same.
• SI unit of resistance: ohm (Ω).
• Ohm’s Law: $V = IR$, where $V$ is voltage, $I$ is current, and $R$ is resistance.
• Resistance of a conductor depends on its length, cross-sectional area, material, and temperature.

Answer: (B) Above the centre of gravity

Explanation

For a floating body to remain in stable equilibrium, the centre of buoyancy should lie above the centre of gravity, so that a restoring couple is produced when the body is slightly tilted. In rigorous physics, however, the actual condition is that the metacentre must lie above the centre of gravity.

Exam Facts

• Archimedes’ Principle: Buoyant force equals the weight of the displaced liquid.
• Centre of buoyancy (B): Centre of gravity of the displaced fluid.
• Metacentre (M): Point where the new line of action of buoyancy intersects the original vertical after a slight tilt.
• Actual condition for stable floating equilibrium: Metacentre (M) is above the centre of gravity (G).
• Unstable equilibrium: Metacentre lies below the centre of gravity.
• Neutral equilibrium: Metacentre coincides with the centre of gravity.

Answer: (B) Its volume increases.

Explanation

When a metallic ball is heated, every linear dimension of the ball expands uniformly, including the inner surface of the cavity. The cavity behaves as if it were filled with the same metal, so it also undergoes thermal expansion. Hence, the volume of the cavity increases.

Exam Facts

• A hole or cavity in a solid expands on heating and contracts on cooling.
• Thermal expansion occurs because the average separation between atoms increases with temperature.
• Cubical expansion: $\Delta V = \gamma V \Delta T$, where $\gamma$γ is the coefficient of cubical expansion.
• For isotropic solids, γ≈3α, where $\alpha$α is the coefficient of linear expansion.
• Metals generally expand on heating and contract on cooling.
• The ball-and-ring experiment demonstrates thermal expansion of solids.

Answer: (C) W₁ = W₂

Explanation

When the bird flies inside the closed cage, it pushes air downward with its wings. This downward force is transmitted through the air to the cage, so the spring balance still supports the combined weight of the cage and the bird. Therefore, the average reading of the spring balance remains unchanged.

Exam Facts

• A spring balance measures weight (force), not mass.
• Weight = mg, where $m$m is mass and $g$g is acceleration due to gravity.
• When a bird flies inside a closed cage, the downward force exerted on the air is transferred to the cage.
• By Newton’s Third Law, the bird pushes air downward, and the air exerts an equal upward force on the bird.
• In a closed system, the total external force on the spring balance remains equal to the combined weight of the cage and bird.
• If the bird were outside the cage, the spring balance reading would decrease by the bird’s weight.
• SI unit of force (weight): Newton (N).

Answer: (C) 40%

Explanation

The efficiency of a Carnot engine is given by:$$\eta = 1 – \frac{T_C}{T_H}$$

where temperatures are in Kelvin.

• Hot reservoir: $227^\circ\text{C} = 500\,\text{K}$
• Cold reservoir: $27^\circ\text{C} = 300\,\text{K}$

$$\eta = 1 – \frac{300}{500} = \frac{200}{500} = 0.4 = 40\%$$

Hence, the correct answer is (C) 40%.

Exam Facts

• Carnot efficiency: $\eta = 1 – \dfrac{T_C}{T_H}$​​, where temperatures must be in Kelvin.
• Temperature conversion: $K = {}^\circ C + 273$.
• A Carnot engine is an ideal reversible heat engine with the maximum possible efficiency.
• No heat engine can have 100% efficiency because some heat must always be rejected to the sink (Second Law of Thermodynamics).
• Efficiency increases when the temperature of the hot reservoir increases or the temperature of the cold reservoir decreases.
• Sadi Carnot is known as the “Father of Thermodynamics.”
• The efficiency of a Carnot engine depends only on the temperatures of the heat source and sink, not on the working substance.

Answer: (D) Volume

Explanation

When a solid is heated, all its dimensions expand. If the coefficient of linear expansion is α, then:

• Linear (diameter) expansion ≈ α
• Superficial (surface area) expansion ≈ 2α
• Cubical (volume) expansion ≈ 3α

Since 3α > 2α > α, the percentage increase in volume is the greatest.

Exam Facts

• Linear expansion: $\Delta L = \alpha L \Delta T$
• Superficial expansion: $\beta \approx 2\alpha$
• Cubical expansion: $\gamma \approx 3\alpha$
• For isotropic solids, γ>β>α, so volume expands the most.
• Density decreases on heating because mass remains constant while volume increases.
• Coefficient of linear expansion (α): SI unit is K⁻¹ (or °C⁻¹).
• The ball-and-ring experiment demonstrates thermal expansion of solids.

Answer: (B) $3 \times 10^{-4}\ \mathrm{°C^{-1}}$

Explanation

Since the mass remains constant, density is inversely proportional to volume:

For small changes,$$\beta=\frac{\Delta V}{V\Delta T} =\frac{\rho_1-\rho_2}{\rho_2\,\Delta T}$$

Here,

• $\rho_1 = 998\ \mathrm{kg\,m^{-3}}$
• $\rho_2 = 992\ \mathrm{kg\,m^{-3}}$
• $\Delta T = 40-20 = 20^\circ\mathrm{C}$

$$\beta=\frac{998-992}{992\times20} =\frac{6}{19840} \approx 3.0\times10^{-4}\ \mathrm{°C^{-1}}$$

Hence, the correct answer is (B) 3×10−4 °C−1

Exam Facts

• Coefficient of cubical expansion (β) is the fractional increase in volume per unit rise in temperature.
• For solids, β≈3α, where $\alpha$α is the coefficient of linear expansion.
• Density decreases with increase in temperature because volume increases while mass remains constant.
• Density = Mass ÷ Volume (ρ=m/V).
• Water has maximum density at 4°C (1000 kg m⁻³ approximately).
• The anomalous expansion of water occurs between 0°C and 4°C.
• SI unit of the coefficient of cubical expansion is K⁻¹ (or °C⁻¹).

Answer: (C) Plutonium

Explanation

Earlier generations of nuclear-powered cardiac pacemakers used the radioisotope Plutonium-238 (Pu-238) as a long-lasting power source. The heat released during its radioactive decay was converted into electricity using a thermoelectric generator. Modern pacemakers, however, use lithium-iodine batteries instead of radioactive materials.

Exam Facts

• Plutonium-238 (Pu-238) is an alpha-emitting radioactive isotope with a half-life of about 87.7 years.
• Early nuclear pacemakers were introduced in the 1970s and were designed to last for decades.
• Modern heart pacemakers are battery-operated, mainly using lithium-iodide cells.
• Plutonium (Pu) has atomic number 94 and is a man-made radioactive element.
• Deuterium is a stable isotope of hydrogen and is not radioactive.
• Radium (Ra), discovered by Marie and Pierre Curie, was historically used in medicine but not in pacemakers.
• Uranium (U) is primarily used as a nuclear fuel, not for powering pacemakers.

Answer: (B) 32°F

Explanation

The freezing point of pure water at standard atmospheric pressure (1 atm) is 0°C, which is equivalent to 32°F or 273.15 K. Therefore, the correct answer is 32°F.

Exam Facts

• Freezing point of pure water: 0°C = 32°F = 273.15 K.
• Boiling point of pure water: 100°C = 212°F = 373.15 K (at 1 atm).
• Temperature conversion formula: $$F=\frac{9}{5}C+32$$
• The Kelvin scale is the SI unit of thermodynamic temperature and begins at absolute zero (0 K = -273.15°C).
• The freezing and boiling points of water are the lower and upper fixed points used in the Celsius scale.
• The freezing point of water decreases when impurities (e.g., salt) are added (freezing point depression).
• Water shows anomalous expansion between 0°C and 4°C and has maximum density at 4°C.

Answer: (A) Radioactivity

Explanation

The Curie (Ci) is a non-SI unit used to measure the activity (radioactivity) of a radioactive substance. One curie is defined as the activity of a sample undergoing 3.7×10¹⁰ radioactive disintegrations per second. The SI unit of radioactivity is the Becquerel (Bq).

Exam Facts

• Curie (Ci) is a unit of radioactivity (activity).
• 1 Curie (Ci) = 3.7 × 10¹⁰ disintegrations per second = 3.7 × 10¹⁰ Bq.
• SI unit of radioactivity: Becquerel (Bq).
• 1 Becquerel (Bq) = 1 disintegration per second.
• The unit Curie is named after Marie Curie and Pierre Curie, pioneers in radioactivity.
• Henri Becquerel discovered natural radioactivity in 1896.
• Marie Curie discovered the radioactive elements Polonium and Radium and won two Nobel Prizes (Physics in 1903, Chemistry in 1911).

Answer: (B) Gamma rays

Explanation

The energy of electromagnetic radiation is directly proportional to its frequency:$$E = hf$$E=hf

Gamma rays have the highest frequency and the shortest wavelength in the electromagnetic spectrum. Therefore, they carry the maximum energy among the given options.

Exam Facts

• Order of electromagnetic waves (increasing energy): Radio < Microwave < Infrared < Visible < Ultraviolet < X-rays < Gamma rays.
• Gamma rays have the highest frequency, shortest wavelength, and maximum penetrating power.
• Gamma rays are emitted during nuclear transitions and radioactive decay.
• X-rays are mainly produced by the sudden deceleration of high-speed electrons or inner-shell electronic transitions.
• Ultraviolet (UV) rays are used for sterilization and help in the formation of Vitamin D in the skin.
• Infrared (IR) rays are associated with heat radiation and are used in remote controls, thermal imaging, and night vision.
• Gamma rays are used in cancer treatment (radiotherapy) and sterilization of medical instruments.

Answer: (D) Chlorofluorocarbon (CFC)

Explanation

Traditionally, Chlorofluorocarbons (CFCs) such as Freon-12 (CCl₂F₂) were widely used as refrigerants in refrigerators because they are chemically stable and non-flammable. However, due to their harmful effect on the ozone layer, CFCs have largely been replaced by environmentally safer refrigerants such as HFCs and hydrocarbons.

Exam Facts

• CFCs (Chlorofluorocarbons) were widely used as refrigerants, aerosol propellants, and foam-blowing agents.
• Freon-12 (CCl₂F₂) is a well-known CFC refrigerant.
• CFCs cause ozone layer depletion by releasing chlorine atoms in the stratosphere.
• The Montreal Protocol was signed in 1987 to phase out ozone-depleting substances like CFCs.
• World Ozone Day: 16 September (commemorates the Montreal Protocol).
• Modern refrigerators commonly use HFC-134a (R-134a), R-600a (Isobutane), or other eco-friendly refrigerants instead of CFCs.
• Ozone layer is located mainly in the stratosphere (about 15–35 km above Earth’s surface) and protects life by absorbing harmful ultraviolet (UV-B) radiation.

Answer: (B) Current

Explanation

A step-down transformer decreases the voltage from the primary to the secondary coil. Since an ideal transformer conserves power ($P = VI$), a decrease in voltage is accompanied by an increase in current, while the frequency remains unchanged.

Exam Facts

• An ideal transformer obeys: $$\frac{V_s}{V_p}=\frac{N_s}{N_p}$$where $V$ is voltage and $N$ is the number of turns.
• A step-down transformer has fewer turns in the secondary coil than in the primary coil ($N_s < N_p$​).
• In an ideal transformer, power is conserved: $V_pI_p = V_sI_s$.
• Voltage decreases and current increases in a step-down transformer.
• The frequency of AC remains unchanged during transformation.
• Transformers work only with alternating current (AC) because they operate on the principle of mutual induction.
• Michael Faraday discovered electromagnetic induction in 1831.

Answer: (D) $\mathbf{V^2/r}$

Explanation

In uniform circular motion, the speed remains constant, but the direction of velocity changes continuously. Hence, the particle has a centripetal acceleration directed towards the centre of the circle.$$a_c=\frac{V^2}{r}$$

Therefore, the correct answer is (D) V2/r.

Exam Facts

• Centripetal acceleration: $\displaystyle a_c=\frac{V^2}{r}=\omega^2r$
• Centripetal force: $\displaystyle F=\frac{mV^2}{r}$​.
• In uniform circular motion, speed is constant but velocity changes because its direction changes continuously.
• The centripetal acceleration is always directed towards the centre of the circular path.
• Tangential acceleration is zero in uniform circular motion since the speed remains constant.
• Angular velocity: $\omega=\dfrac{V}{r}$.
• Time period: $\displaystyle T=\frac{2\pi r}{V}=\frac{2\pi}{\omega}$​.

Answer: (C) √3 : √2

Explanation

For an ideal gas:

• Most probable speed: $\displaystyle v_{mp}=\sqrt{\frac{2RT}{M}}$​​
• RMS speed: $\displaystyle v_{rms}=\sqrt{\frac{3RT}{M}}$​​

Therefore,$$\frac{v_{rms}}{v_{mp}} = \sqrt{\frac{3RT/M}{2RT/M}} = \sqrt{\frac{3}{2}} = \frac{\sqrt{3}}{\sqrt{2}}$$

Hence, the correct answer is (C) √3 : √2

Exam Facts

• Most probable speed: $\displaystyle v_{mp}=\sqrt{\frac{2RT}{M}}$
• Average speed: $\displaystyle v_{avg}=\sqrt{\frac{8RT}{\pi M}}$​​
• RMS speed: $\displaystyle v_{rms}=\sqrt{\frac{3RT}{M}}$​​
• The order of molecular speeds is: $$v_{rms} > v_{avg} > v_{mp}$$
• RMS speed is the root mean square of the speeds of gas molecules.
• Molecular speeds increase with temperature and decrease with molar mass.
• These expressions are derived from the Maxwell–Boltzmann distribution of molecular speeds.

Answer: (C) Insulator

Explanation

Silicon is intrinsically a semiconductor at ordinary temperatures. However, at 0 K (absolute zero), all the valence electrons remain bound in covalent bonds, and there are no free charge carriers available for conduction. Hence, pure silicon behaves as an insulator at 0 K.

Exam Facts

• Silicon (Si) is an intrinsic semiconductor with atomic number 14.
• At 0 K, intrinsic semiconductors behave as insulators because the conduction band is empty.
• As temperature increases, some electrons gain enough energy to move to the conduction band, increasing conductivity.
• Unlike metals, the electrical conductivity of semiconductors increases with temperature.
• Band gap of silicon: approximately 1.1 eV at room temperature.
• n-type semiconductor: Formed by doping silicon with pentavalent impurities (e.g., phosphorus, arsenic).
• p-type semiconductor: Formed by doping silicon with trivalent impurities (e.g., boron, aluminium).

Answer: (B) 50 cm, convex

Explanation

The power of a lens is related to its focal length by:$$P=\frac{1}{f}$$

where $P$ is in dioptres (D), and $f$ is in metres.

Given $P = +2$ D,$$f=\frac{1}{2}=0.5\ \text{m}=50\ \text{cm}$$

The positive sign indicates a convex (converging) lens.

Exam Facts

• Power of a lens: $P=\dfrac{1}{f}$​ (with $f$ in metres).
• SI unit of power: Dioptre (D).
• 1 Dioptre = 1 m⁻¹.
• A convex lens has positive focal length and positive power.
• A concave lens has negative focal length and negative power.
• A convex lens is also called a converging lens, while a concave lens is called a diverging lens.
• Convex lenses are used in magnifying glasses, cameras, microscopes, and correcting hypermetropia.

Answer: (C) Diffraction

Explanation

A Compact Disc (CD) has thousands of closely spaced spiral tracks that act as a diffraction grating. When white light falls on the CD, different wavelengths are diffracted at different angles, producing the characteristic rainbow-like spectrum.

Exam Facts

• A CD acts as a reflection diffraction grating due to its closely spaced spiral grooves.
• Diffraction is the bending and spreading of light around obstacles or through narrow openings.
• Diffraction is most noticeable when the size of the obstacle or slit is comparable to the wavelength of light.
• Interference of the diffracted light produces the visible spectrum of colours on a CD.
• Refraction is the bending of light when it passes from one medium to another.
• Reflection is the bouncing back of light from a surface.
• Polarization is the phenomenon in which light vibrations are restricted to one plane; only transverse waves can be polarized.

Answer: (B) High k and low σ

Explanation

Diamond is an excellent conductor of heat because lattice vibrations (phonons) transfer thermal energy very efficiently through its strong covalent crystal structure. However, it has almost no free electrons, making it an electrical insulator with very low electrical conductivity.

Exam Facts

• Diamond is one of the best thermal conductors known.
• Diamond is an electrical insulator due to the absence of free electrons.
• Diamond is an allotrope of carbon with a three-dimensional tetrahedral covalent network (sp³ hybridization).
• Graphite, another allotrope of carbon, is a good conductor of electricity because it has delocalized (free) electrons.
• Thermal conductivity (k) is measured in W m⁻¹ K⁻¹.
• Electrical conductivity (σ) is the reciprocal of resistivity: $\sigma = \frac{1}{\rho}$​.
• Diamond is the hardest naturally occurring substance and has a hardness of 10 on the Mohs scale.

Answer: (B) 6 V

Explanation

In a series connection, the emfs of cells add up. If 2 cells are wrongly connected, their emfs oppose the others.

Total emf:$$E = (8 \times 1) – (2 \times 1) = 6\ \text{V}$$

Alternatively,$$E = (10 – 2 \times 2)\times 1 = 6\ \text{V}$$

Hence, the effective emf of the battery is 6 V.

Exam Facts

• In a series connection, the total emf is the sum of individual emfs.
• A wrongly connected (reversed) cell subtracts its emf from the total emf.
• If n cells of emf E are connected in series, the total emf is nE.
• If m cells are reversed, the effective emf is: $$E_{\text{net}}=(n-2m)E$$
• EMF (Electromotive Force) is the energy supplied per unit charge by a source.
• SI unit of EMF: Volt (V).
• A cell converts chemical energy into electrical energy.

Answer: (B) Pascal’s law

Explanation

A hydraulic press works on Pascal’s law, which states that pressure applied to an enclosed fluid is transmitted equally and undiminished in all directions. This allows a small force applied on a small piston to produce a much larger force on a larger piston.

Exam Facts

• Pascal’s Law: Pressure applied to a confined fluid is transmitted equally in all directions.
• Pressure: $P=\dfrac{F}{A}$.
• In a hydraulic press: $$\frac{F_1}{A_1}=\frac{F_2}{A_2}$$
• Hydraulic press, hydraulic lift, hydraulic jack, and hydraulic brakes all work on Pascal’s law.
• SI unit of pressure: Pascal (Pa), where 1 Pa = 1 N/m².
• Archimedes’ Principle deals with buoyancy, not hydraulic machines.
• Bernoulli’s Principle explains the relation between pressure and fluid speed in flowing fluids (used in airplane wings, atomizers, Venturi meter).

Answer: (C) Decreases

Explanation

A swing behaves like a simple pendulum, whose time period is:$$T = 2\pi\sqrt{\frac{L}{g}}$$

When the person stands up, the centre of gravity moves upward, reducing the effective length (L) of the pendulum. Since the time period is proportional to $\sqrt{L}$​, the time period decreases.

Exam Facts

• Time period of a simple pendulum: $T = 2\pi\sqrt{\frac{L}{g}}$​​.
• The time period increases with length and decreases when the length decreases.
• The time period is independent of the mass of the bob.
• For small oscillations, the time period is independent of amplitude (isochronism).
• Effective length is the distance from the point of suspension to the centre of gravity of the oscillating system.
• The acceleration due to gravity (g) is approximately 9.8 m/s² on Earth.
• A seconds pendulum has a time period of 2 seconds.

Answer: (D) Convection currents are set up.

Explanation

The freezer is placed at the top because cold air is denser and sinks, while warm air is lighter and rises. This establishes natural convection currents, which cool the entire refrigerator efficiently without requiring additional energy.

Exam Facts

• Heat transfer occurs by three modes: conduction, convection, and radiation.
• Convection is the transfer of heat through the actual movement of fluids (liquids and gases).
• Cold air is denser and sinks; warm air is less dense and rises.
• Refrigerators cool the lower compartments mainly by natural convection.
• Conduction is the transfer of heat without bulk movement of matter and is predominant in solids.
• Radiation does not require a material medium and can occur through a vacuum.
• Refrigerators work on the vapour compression refrigeration cycle, using refrigerants such as R-134a or R-600a in modern systems.

Answer: (C) Longitudinal and transverse

Explanation

The waves produced on the surface of water are surface waves, in which water particles move in both vertical and horizontal directions (approximately circular or elliptical paths). Therefore, these waves possess the characteristics of both transverse and longitudinal waves.

Exam Facts

• Water surface waves are a combination of transverse and longitudinal waves.
• In transverse waves, particles vibrate perpendicular to the direction of wave propagation.
• In longitudinal waves, particles vibrate parallel to the direction of wave propagation.
• Sound waves in air are longitudinal waves.
• Light (electromagnetic) waves are transverse waves and do not require a material medium.
• Stationary (standing) waves are formed by the superposition of two waves of the same frequency and amplitude traveling in opposite directions.
• Surface water waves transport energy, while the water particles mainly oscillate about their mean positions rather than moving with the wave.

Answer: (C) Greenhouse

Explanation

A solar cooker works on the greenhouse effect. The transparent glass cover allows short-wave solar radiation to enter but traps the long-wave infrared radiation emitted by the heated objects inside, thereby increasing the temperature and cooking the food.

Exam Facts

• A solar cooker works on the greenhouse effect.
• Black-painted interiors absorb maximum solar radiation and enhance heating.
• A glass cover allows sunlight to enter but reduces heat loss by trapping infrared radiation.
• Plane mirrors or reflectors are often used to concentrate more sunlight into the cooker.
• A bolometer measures electromagnetic radiation, especially infrared radiation.
• A pyrometer measures very high temperatures without direct contact.
• A solar photovoltaic (PV) cell converts solar energy directly into electrical energy using the photovoltaic effect.

Answer: (B) Increase by about 11%

Explanation

The resistance of the heater filament is directly proportional to its length:$$R=\frac{\rho L}{A}$$

If the length is reduced by 10%, then$$R’ = 0.9R$$

Since the heater is connected to a constant voltage supply,$$P=\frac{V^2}{R}$$

Therefore,$$P’=\frac{V^2}{0.9R}=\frac{P}{0.9}=1.11P$$

Hence, the power increases by about 11%.

Exam Facts

• Resistance of a wire: $\displaystyle R=\frac{\rho L}{A}$​.
• At constant voltage, Power: $\displaystyle P=\frac{V^2}{R}$.
• At constant current, Power: $\displaystyle P=I^2R$.
• Reducing the length of a wire decreases its resistance.
• Increasing the cross-sectional area also decreases the resistance.
• The SI unit of resistance is ohm (Ω).
• The SI unit of power is watt (W).
• Heating elements are commonly made of nichrome because of its high resistivity, high melting point, and resistance to oxidation.

Answer: (D) It will remain same.

Explanation

When passengers drink water from the tank, the mass of water in the tank decreases, but the mass of the boat (with passengers) increases by the same amount. As a result, the boat sinks slightly deeper and displaces an additional volume of water exactly equal to the volume of water consumed. Hence, the water level remains unchanged.

Exam Facts

• A floating body displaces a volume of liquid whose weight equals the weight of the body (Archimedes’ Principle).
• Buoyant force is equal to the weight of the displaced liquid.
• For floating bodies: $$\text{Weight of body} = \text{Buoyant force}$$
• If an object is transferred from the tank to the boat, the water level generally remains unchanged if the object floats.
• If a floating object sinks after being thrown into the water (e.g., a stone from a boat), the water level decreases—a frequently asked conceptual question.
• Density of pure water: approximately 1000 kg/m³ at 4°C.
• Archimedes’ Principle was discovered by Archimedes of Syracuse.

Answer: (D) √6 times slower

Explanation

The time period of a simple pendulum is:$$T = 2\pi\sqrt{\frac{L}{g}}$$

On the Moon, the acceleration due to gravity is about g/6. Therefore,$$T_{\text{Moon}} = 2\pi\sqrt{\frac{L}{g/6}} = \sqrt{6}\,T_{\text{Earth}}$$

Thus, the time period increases by √6 times, so the pendulum oscillates more slowly and the clock loses time, i.e., it runs √6 times slower.

Exam Facts

• Time period of a simple pendulum: $T = 2\pi\sqrt{\dfrac{L}{g}}$​​.
• The time period is inversely proportional to $\sqrt{g}$
• Gravity on the Moon ≈ $\dfrac{1}{6}$ of Earth’s gravity (≈ 1.62 m/s²).
• A pendulum clock runs slower where the value of g is smaller (e.g., on the Moon or at higher altitudes).
• The time period is independent of the mass of the bob.
• The time period is approximately independent of amplitude for small oscillations.
• A seconds pendulum has a time period of 2 seconds on Earth.

Answer: (C) $2k$

Explanation

The spring constant is inversely proportional to the length of the spring:$$k \propto \frac{1}{L}$$

When the spring is cut into two equal halves, the length becomes L/2. Therefore, the spring constant of each half becomes:$$k’ = \frac{kL}{L/2} = 2k$$

Hence, each half is twice as stiff as the original spring.

Exam Facts

• Hooke’s Law: $F = kx$, where $k$k is the spring constant.
• The spring constant is inversely proportional to the length of a uniform spring $(k \propto 1/L)$.
• If the spring is cut into n equal parts, the spring constant of each part becomes nk.
• The SI unit of spring constant is N/m.
• A larger spring constant means a stiffer spring.
• In series combination of springs, the equivalent spring constant decreases: $$\frac{1}{k_{\text{eq}}}=\frac{1}{k_1}+\frac{1}{k_2}$$
• In parallel combination of springs: $$k_{\text{eq}}=k_1+k_2$$

Answer: (D) $\dfrac{2v_1v_2}{v_1+v_2}$

Explanation

When equal distances are covered at different speeds, the average speed is the harmonic mean of the two speeds.

Let the total distance be $2d$. Then,

• Time for first half $= \dfrac{d}{v_1}$​
• Time for second half $= \dfrac{d}{v_2}$

Therefore,$$v_{\text{avg}} = \frac{2d}{\frac{d}{v_1}+\frac{d}{v_2}} = \frac{2v_1v_2}{v_1+v_2}$$

Hence, the correct answer is (D).

Exam Facts

• Average speed = Total distance ÷ Total time.
• For equal distances, average speed is the harmonic mean: $$v_{\text{avg}}=\frac{2v_1v_2}{v_1+v_2}$$
• For equal time intervals, average speed is the arithmetic mean: $$v_{\text{avg}}=\frac{v_1+v_2}{2}$$
• Average speed is a scalar quantity.
• Average velocity = Total displacement ÷ Total time.
• Average speed is always greater than or equal to the magnitude of average velocity.
• SI unit of speed: metre per second (m/s).

Answer: (A) Heavy body has greater momentum.

Explanation

The relation between kinetic energy and momentum is:$$KE=\frac{p^2}{2m}$$

For equal kinetic energy,$$p=\sqrt{2m\,KE}$$

Thus, momentum is proportional to the square root of mass $(p \propto \sqrt{m})$. Therefore, the heavier body has greater momentum.

Exam Facts

• Kinetic energy: $$KE=\frac{1}{2}mv^2$$
• Momentum: $$p=mv$$
• Relation between kinetic energy and momentum: $$KE=\frac{p^2}{2m}$$
• For equal kinetic energy, momentum is proportional to m\sqrt{m}m​.
• For equal momentum, kinetic energy is inversely proportional to mass: $$KE=\frac{p^2}{2m}$$
  Hence, the lighter body has greater kinetic energy.
• SI unit of momentum: kg·m/s (or N·s).
• Momentum is a vector quantity, while kinetic energy is a scalar quantity.

Answer: (D) Jiffy

Explanation

A jiffy is a unit of time, not distance. A light-year, parsec, and furlong are all units used to measure distance, with light-year and parsec being astronomical units.

Exam Facts

• Light-year (ly): Distance travelled by light in one year in vacuum.
  • 1 ly ≈ 9.46 × 10¹⁵ m
• Parsec (pc): Astronomical unit of distance.
  • 1 parsec ≈ 3.26 light-years ≈ 3.086 × 10¹⁶ m
• Furlong: Traditional unit of length.
  • 1 furlong = 220 yards = 201.168 m
• Jiffy is an informal unit of time; in physics/electronics, its exact value depends on the context.
• Astronomical Unit (AU): Average distance between the Earth and the Sun.
  • 1 AU ≈ 1.496 × 10¹¹ m
• SI unit of length: metre (m).
• Speed of light in vacuum (c): 3 × 10⁸ m/s.

Answer: (C) Dimensional change in material

Explanation

A dilatometer is an instrument used to measure the change in dimensions (length or volume) of a material due to changes in temperature. It is commonly used to determine the coefficient of thermal expansion of solids and liquids.

Exam Facts

• A dilatometer measures the thermal expansion (dimensional change) of materials.
• It is used to determine the coefficient of linear, superficial, or cubical expansion.
• Thermal expansion occurs because the intermolecular distance increases with rise in temperature.
• Coefficient of linear expansion (α\alphaα) has SI unit K⁻¹ (or °C⁻¹).
• Instruments often confused in exams:
  • Calorimeter → Measures heat.
  • Pyrometer → Measures very high temperature.
  • Thermometer → Measures temperature.
  • Bolometer → Measures electromagnetic (especially infrared) radiation.
• Thermal expansion is utilized in bimetallic strips, thermostats, and expansion joints in bridges and railway tracks.

Answer: (A) Scattering

Explanation

Sir C. V. Raman received the 1930 Nobel Prize in Physics for the discovery of the Raman Effect, which is based on the inelastic scattering of light. When light passes through a transparent medium, a small fraction of the scattered light changes its wavelength due to interaction with the molecules of the medium.

Exam Facts

• Raman Effect is based on the scattering of light.
• The Raman Effect was discovered by Sir C. V. Raman on 28 February 1928.
• Sir C. V. Raman received the Nobel Prize in Physics in 1930, becoming the first Asian to win a Nobel Prize in Physics.
• National Science Day is celebrated in India on 28 February to commemorate the discovery of the Raman Effect.
• Raman spectroscopy is widely used to identify the molecular structure and chemical composition of substances.
• Rayleigh scattering is elastic scattering, whereas the Raman Effect involves inelastic scattering with a change in wavelength.
• Diffraction is the bending of light around obstacles; interference is due to superposition of waves; polarization is the restriction of light vibrations to one plane.

Answer: (B) Angular momentum

Explanation

Angular momentum is a vector quantity because it has both magnitude and direction, determined by the right-hand rule. In contrast, heat, time, and work have only magnitude and are therefore scalar quantities.

Exam Facts

• Angular momentum: $\vec{L} = \vec{r} \times \vec{p}$​, where $\vec{p}=m\vec{v}$.
• The direction of angular momentum is determined by the right-hand thumb rule.
• Angular momentum is conserved when no external torque acts on a system.
• Scalar quantities: Mass, time, distance, speed, work, energy, power, heat, temperature.
• Vector quantities: Displacement, velocity, acceleration, force, momentum, angular momentum, torque.
• Work is a scalar quantity given by: $$W = \vec{F}\cdot\vec{s}$$W=F⋅s (dot product of two vectors).
• SI unit of angular momentum: kg·m²/s.

Answer: (B) 8 minutes

Explanation

Light travels at a speed of approximately 3 × 10⁸ m/s in vacuum. The average distance between the Earth and the Sun is about 1 Astronomical Unit (AU) = 1.496 × 10¹¹ m. Therefore, sunlight takes about 499 seconds, or 8 minutes 20 seconds, to reach the Earth.

Exam Facts

• Speed of light in vacuum (c): 3 × 10⁸ m/s.
• Average Earth–Sun distance: 1 AU = 1.496 × 10¹¹ m (≈ 149.6 million km).
• Time taken by sunlight to reach Earth: ≈ 8 minutes 20 seconds (commonly rounded to 8 minutes in exams).
• Light-year is the distance travelled by light in one year:
  • 1 light-year ≈ 9.46 × 10¹⁵ m.
• Sunlight takes about 1.3 seconds to reach the Moon from Earth.
• The Sun is the nearest star to Earth.
• Sunlight is a form of electromagnetic radiation and can travel through the vacuum of space.

Answer: (A) Fermi

Explanation

The size of an atomic nucleus is extremely small and is measured in fermi (fm). One fermi is equal to 10⁻¹⁵ metre, which is also known as one femtometre. Typical nuclear radii are of the order of 1–10 fm.

Exam Facts

• 1 fermi (fm) = 10⁻¹⁵ m (1 femtometre).
• The radius of a nucleus is approximately given by:
  $$R = R_0A^{1/3}$$where R0≈1.2×10⁻¹⁵
  
• Angstrom (Å) = 10⁻¹⁰ m, used for measuring atomic and molecular dimensions.
• Newton (N) is the SI unit of force.
• Tesla (T) is the SI unit of magnetic flux density (magnetic field).
• Typical atomic size is about 10⁻¹⁰ m, whereas nuclear size is about 10⁻¹⁵ m.
• The atomic nucleus consists of protons and neutrons (nucleons).

Answer: (C) Offer no resistance to the flow of current.

Explanation

A superconductor is a material whose electrical resistance becomes exactly zero when cooled below a certain critical temperature (Tc). In the superconducting state, electric current can flow without any loss of energy.

Exam Facts

• Superconductivity is the phenomenon of zero electrical resistance below a critical temperature (Tc).
• Superconductors also exhibit the Meissner Effect, i.e., they expel magnetic fields from their interior.
• Superconductivity was discovered by Heike Kamerlingh Onnes in 1911 using mercury.
• The SI unit of electrical resistance is ohm (Ω).
• Superconductors are used in MRI machines, maglev (magnetic levitation) trains, particle accelerators, and high-field electromagnets.
• Examples of superconducting materials include mercury (Hg), lead (Pb), niobium-titanium (Nb-Ti), and YBCO (a high-temperature superconductor).
• High-temperature superconductors operate at temperatures much higher than conventional superconductors, though still far below room temperature.

Answer: (D) Solids

Explanation

The speed of sound depends on the elasticity and density of the medium. Solids have very high elasticity, allowing sound to travel much faster than in liquids or gases. Sound cannot travel in a vacuum because there is no material medium.

Exam Facts

• Order of speed of sound: Solids > Liquids > Gases > Vacuum (no propagation).
• Sound is a mechanical wave and requires a material medium to travel.
• Approximate speeds of sound:
  • Air (20°C): 343 m/s
  • Water: ≈1500 m/s
  • Steel: ≈5000 m/s
• In gases, the speed of sound increases with temperature.
• The speed of sound is given by: $$v=\sqrt{\frac{E}{\rho}}$$where EEE is the modulus of elasticity and ρ\rhoρ is the density of the medium.
  
• Light can travel through a vacuum, but sound cannot.
• Sound waves in air are longitudinal waves.

Answer: (B) Capillary action

Explanation

Blotting paper contains numerous tiny pores that act as capillary tubes. When ink comes into contact with the paper, it is drawn into these pores by capillary action, which results from the combined effects of adhesion (between ink and paper) and cohesion (between ink molecules).

Exam Facts

• Capillary action is the rise or fall of a liquid in a narrow tube or porous material due to surface tension.
• It occurs because of the combined effects of adhesion and cohesion.
• Examples of capillary action:
  • Blotting paper absorbing ink.
  • Kerosene rising in the wick of a lamp.
  • Water rising in plant xylem vessels.
  • Absorption of water by a sponge or paper towel.
• Surface tension is responsible for many capillary phenomena.
• Viscosity is the resistance offered by a fluid to its flow.
• Diffusion is the movement of particles from a region of higher concentration to lower concentration.
• A siphon transfers liquid from a higher level to a lower level through a bent tube.

Answer: (B) Nuclear fusion

Explanation

A hydrogen bomb (thermonuclear bomb) works on the principle of nuclear fusion, in which light nuclei (such as isotopes of hydrogen) combine to form a heavier nucleus, releasing an enormous amount of energy. A nuclear fission bomb is used as the trigger to create the extremely high temperature and pressure required for the fusion reaction.

Exam Facts

• Hydrogen bomb is based on nuclear fusion.
• Atomic bomb is based on nuclear fission of heavy elements like Uranium-235 or Plutonium-239.
• In nuclear fusion, isotopes of hydrogen such as deuterium (²H) and tritium (³H) combine to form helium, releasing huge energy.
• Fusion powers the Sun and other stars.
• Nuclear fission was discovered by Otto Hahn and Fritz Strassmann (1938), and explained by Lise Meitner and Otto Frisch.
• Controlled nuclear fission is used in nuclear reactors to generate electricity.
• Fusion releases more energy per unit mass than fission but requires extremely high temperature and pressure.

Answer: (A) Nitrogen

Explanation

Ordinary incandescent electric bulbs are filled with nitrogen (often mixed with argon) to prevent the tungsten filament from oxidizing and to reduce its rate of evaporation. This increases the life of the filament and improves the bulb’s efficiency.

Exam Facts

• Nitrogen (often with argon) is used in incandescent electric bulbs.
• The filament of an incandescent bulb is made of tungsten because of its very high melting point (≈ 3422°C).
• An inert gas inside the bulb reduces the evaporation of the tungsten filament.
• Oxygen is not used because it would oxidize (burn) the hot tungsten filament.
• Argon is the most commonly used inert gas in modern incandescent bulbs, usually mixed with nitrogen.
• LED bulbs do not contain a tungsten filament and are much more energy-efficient than incandescent bulbs.
• Nitrogen constitutes about 78% of Earth’s atmosphere.

Answer: (A) Infrared frequency

Explanation

A TV remote control transmits signals using infrared (IR) radiation, which is invisible to the human eye. The remote contains an infrared LED that emits coded IR pulses, which are detected by an infrared sensor in the television.

Exam Facts

• TV remote controls use infrared (IR) waves for communication.
• Infrared radiation has a longer wavelength than visible light and a shorter wavelength than microwaves.
• IR radiation requires a line-of-sight between the remote and the TV receiver.
• Radio frequency (RF) remotes can work without direct line-of-sight (e.g., some smart TV and car key remotes).
• Infrared radiation is widely used in remote controls, thermal imaging cameras, and night vision devices.
• Visible light has wavelengths of approximately 400–700 nm.
• Ultraviolet (UV) radiation has a shorter wavelength than visible light and is used for sterilization and fluorescence.