Section B
[1 Marks]
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(A) T₁ < T₂
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(B) T₁ = T₂ / 3
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(C) T₂ = 2T₁
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(D) T₁ > T₂
Explanation: The graph indicates that at higher temperatures, the resistance of the conductor increases, leading to a higher voltage for the same current, thus suggesting that T₁ < T₂, which corresponds to the fact that as temperature increases, resistance also increases.
[1 Marks]
Explanation: In a series combination, the equivalent resistance Rₛ is given by Rₛ = nR, while in a parallel combination, the equivalent resistance Rₚ is given by Rₚ = R/n. Therefore, (Rₛ - Rₚ) = nR - (R/n) = nR - R/n = (n^2 - 1)R/n. This expression shows that Rₛ is always greater than Rₚ for n > 1, leading to a positive value for (Rₛ - Rₚ).
[1 Marks]
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(A) moves opposite to the field
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(B) does not move at all
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(C) moves perpendicular to the field
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(D) moves along the field
Explanation: The correct answer is 'does not move at all.' Diamagnetic materials develop a net magnetic moment in the direction opposite to that of the applied field, resulting in a repulsive force. Since this force does not provide the material any motion along the direction of the magnetic field, it tends to stay in place despite the presence of a uniform magnetic field.
[1 Marks]
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(A) 1/2
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(B) 1/4
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(C) 4
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(D) 2
Explanation: The radius r of the path of a charged particle moving perpendicular to a magnetic field is given by r = mv / (|q|B), where m is the particle's mass, v is its velocity, q is its charge, and B is the magnetic field. For a proton, m_p = mass of proton and q_p = +e. For an α-particle, m_α = 4m_p (since it has 2 protons and 2 neutrons), and q_α = 2e (charge twice that of proton). Since both enter with the same velocity v and experience the same magnetic field B, the ratio of the radii is r_p / r_α = (m_p v / eB) / (4m_p v / 2e B) = (m_p / e) * (2e / 4m_p) = 2 / 4 = 1/2. However, this calculation must be rechecked carefully: r_p = (m_p v) / (e B), and r_α = (4 m_p v) / (2 e B) = (2 m_p v) / (e B). Therefore, the ratio r_p / r_α = (m_p v / e B) / (2 m_p v / e B) = 1 / 2. Therefore the ratio of the radius of the proton path to the α-particle path is 1/2, implying the radius of the proton's path is half of the α-particle’s path radius. The question asks for the ratio of the radii of their paths, which is r_proton / r_alpha = 1/2. Therefore the correct option should be 1/2. Since 1/2 is also an option listed, the answer is 1/2. (Note: There may be confusion about which ratio is asked, but per standard convention, proton to alpha radius ratio is 1/2.)
[1 Marks]
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(A) Violet light
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(B) Green light
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(C) Blue light
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(D) Red light
Explanation: Red light cannot produce photoelectrons from the material because its energy is lower than the work function of 2.21 eV. The energy of photons is given by the equation E = hv, where h is Planck's constant and v is the frequency of the light. Red light has the lowest frequency and consequently the lowest energy among the options provided, therefore it fails to meet the threshold energy required to emit photoelectrons.
[1 Marks]
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(A) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
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(B) Both Assertion (A) and Reason (R) are false.
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(C) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
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(D) Assertion (A) is true, but Reason (R) is false.
Explanation: Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A). Chromatic aberration does not occur in reflecting telescopes because they use mirrors, which reflect light, rather than refracting it through lenses. Thus, the presence of chromatic aberration is related to refraction, confirming the reason as true, but it does not explain the assertion.
[1 Marks]
Explanation: Lenders require collateral to mitigate the risk of loan default. Collateral acts as a security for the lender, ensuring that if the borrower fails to repay the loan, the lender can recover some or all of the lost funds through the sale of the collateral.
[1 Marks]
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(A) small resistance in series
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(B) large resistance in series
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(C) large resistance in parallel
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(D) small resistance in parallel
Explanation: The correct option is 'small resistance in parallel'. A galvanometer is sensitive and has a high resistance, so to measure larger currents (as an ammeter), a small shunt resistance is placed in parallel. This allows most of the current to bypass the galvanometer, thus enabling it to measure larger currents without being damaged.
[1 Marks]
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(A) zero
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(B) g
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(C) greater than g
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(D) less than g
Explanation: The correct answer is 'less than g'. When the bar magnet falls into the copper ring, it induces an electric current in the ring due to electromagnetic induction. This current creates a magnetic field that opposes the motion of the falling magnet (as per Lenz's law), resulting in a damping force that reduces the acceleration of the magnet below gravitational acceleration (g).
[1 Marks]
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(A) 10 V
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(B) 12 V
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(C) 14 V
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(D) 16 V
Explanation: The total voltage from the source in a series circuit is the vector sum of the voltages across each component. Since the voltages across the resistor (8 V) and inductor (6 V) are out of phase, we can use the Pythagorean theorem to find the total voltage: V_source = √(V_R^2 + V_L^2) = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 V.
[1 Marks]
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(A) 𝐹ₚₚ = 𝐹ₚₙ = 𝐹ₙₙ
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(B) 𝐹ₚₚ > 𝐹ₚₙ > 𝐹ₙₙ
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(C) 𝐹ₚₙ > 𝐹ₙₙ > 𝐹ₚₚ
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(D) 𝐹ₙₙ > 𝐹ₚₚ > 𝐹ₚₙ
Explanation: According to the context provided, the nuclear force does not distinguish between different types of nucleons (protons and neutrons) and is approximately the same for all interactions (𝐹ₚₚ, 𝐹ₚₙ, and 𝐹ₙₙ). Therefore, the correct answer is 𝐹ₚₚ = 𝐹ₚₙ = 𝐹ₙₙ.
[1 Marks]
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(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
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(B) Assertion (A) is true, but Reason (R) is false.
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(C) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
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(D) Both Assertion (A) and Reason (R) are false.
Explanation: Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). The assertion correctly describes a hole as a positive charge carrier, while the reason highlights that not all holes are directly associated with vacancies left by electrons, making them somewhat independent concepts.
[1 Marks]
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(A) Both Assertion (A) and Reason (R) are false.
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(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
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(C) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
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(D) Assertion (A) is true, but Reason (R) is false.
Explanation: Assertion (A) is true because X-rays are indeed produced when high-energy electrons collide with a metal target, especially those with high atomic numbers due to their ability to decelerate the electrons and emit X-rays. However, Reason (R) is false; X-rays are actually high-energy photons, not low-energy ones. Therefore, the correct option is: Assertion (A) is true, but Reason (R) is false.
[1 Marks]
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(A) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
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(B) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
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(C) Assertion (A) is true, but Reason (R) is false.
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(D) Both Assertion (A) and Reason (R) are false.
Explanation: Assertion (A) is true because the binding energy per nucleon is approximately constant at 8 MeV for mass numbers between 30 and 170. However, Reason (R) is false; the constancy of binding energy in that range is due to the short-range nature of nuclear forces. Therefore, the correct answer is that Assertion (A) is true, but Reason (R) is false.
Section C
[2 Marks]
Answer: To find the equivalent resistance between points A and B, we apply the principles of series and parallel combinations of resistors. Considering the circuit, the two cells' internal resistances can be represented as a single equivalent resistance between points A and C. Using the formulas for series and parallel resistances, we can derive the equivalent resistance as req = r1 + r2 for resistors in series and 1/req = 1/r1 + 1/r2 for resistors in parallel.
[2 Marks]
Answer: The energy of a photon can be calculated using the equation E = hν, where 'h' (Planck's constant) is approximately 6.63 × 10⁻³⁴ J·s. Substituting ν = 3.0 × 10¹⁴ Hz, the energy of a single photon, E, is about 1.986 × 10⁻¹⁸ J. To find the number of photons emitted per second, we divide the total power (9 mW or 9 × 10⁻³ W) by the energy of each photon, yielding approximately 4.54 × 10¹⁶ photons/second.
[2 Marks]
Answer: When the ray MN strikes face AB of prism ABC normally, it will pass through without bending, maintaining its path. Upon reaching face AC, the ray will encounter refraction. Since both prisms have the same refractive index of 1.6, the ray will refract towards the normal. Following this, it will pass through prism DBC and exit through face BC. The path of the ray illustrates how it propagates through both prisms effectively.
[2 Marks]
Answer: In n-type semiconductors, electrons are the majority carriers due to doping with pentavalent impurities, which donate extra electrons. These electrons outnumber the holes, which are created when electrons move and leave behind vacancies. Although electron-hole pair recombination occurs continuously, the constant generation of more electrons than holes ensures that the electron concentration remains higher than the hole concentration at room temperature.
[2 Marks]
Answer: To find the nature and position of the image, we can use the formula for refraction at a spherical surface: n2/v - n1/u = (n2 - n1)/R. Here, n1 = 1 (air), n2 = 1.5 (glass), u = -12 cm, and R = 30 cm. After substituting the values, we can calculate v, which gives the image distance. The sign of v indicates the nature of the image: if positive, the image is real; if negative, virtual. The final calculations show that the image is real and located at approximately 10 cm from the surface of the glass.
Section D
[3 Marks]
Answer: The electromotive force (emf) of a cell is the maximum potential difference across its terminals when no current flows, while terminal voltage is the potential difference when the cell is supplying current. Terminal voltage is less than emf due to internal resistance (V = ε - I*r). For two cells E₁ and E₂ in parallel with internal resistances r₁ and r₂, the equivalent emf (E_eq) is found using ε_eq / r_eq = ε₁/r₁ + ε₂/r₂. The equivalent internal resistance (r_eq) is given by 1/r_eq = 1/r₁ + 1/r₂.
[3 Marks]
Answer: To find the torque acting on the rectangular loop and the net force, we first ascertain the magnetic field produced by the long wire. The magnetic field (B) at the distance 'd' from the wire is given by the formula B = (μ₀I)/(2πd), where I is the current in the wire. For the 1 A loop, the magnetic moment (m) is defined as m = I A, where A is the loop area. The torque (τ) is calculated as τ = mB sin(θ). The net force on the loop can be calculated based on the interaction between the current in the loop and the magnetic field produced by the wire, which can lead to forces acting perpendicular to the direction of the current in the loop. The direction follows the right-hand rule, confirming the resultant forces and torques.
[3 Marks]
Answer: The electromagnetic wave used in (i) radar is microwaves, which have a wavelength range of approximately 1 mm to 1 m. In (ii) eye surgery, particularly LASIK, the wave used is ultraviolet light, with a wavelength range of about 100 nm to 400 nm. Lastly, the electromagnetic wave used as a diagnostic tool in medicine is X-rays, which have a wavelength range from about 10 nm (10^-9 m) to 0.01 nm (10^-11 m). Each of these waves serves distinct purposes in their respective fields.
[3 Marks]
Answer: To draw the ray diagram for a concave mirror producing a real, inverted, and magnified image, first, position the object beyond the center of curvature (C). Draw three key rays: one parallel to the principal axis (which reflects through the focal point F), one passing through the focal point (which reflects parallel to the axis), and one passing through the center of curvature (which reflects back on itself). The intersection of these rays behind the mirror indicates the location of the image A’B’. This image is real, inverted, and larger than the object. The mirror formula is given by the equation 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
[3 Marks]
Answer: In the Bohr model, the necessary centripetal force for an electron in circular motion is provided by the electrostatic force of attraction between the negatively charged electron and the positively charged nucleus (proton). The expression for this force can be written as F = k * e^2 / r^2, where k is Coulomb's constant. For circular motion, this force must equal the required centripetal force: m * v^2 / r. Using the quantization of angular momentum, we derive the total energy of the electron as E = K + U, where K is kinetic energy and U is potential energy. K = (1/2)mv^2 and U = -ke^2/r, leading to E = -ke^2/(2r). The negative sign indicates that the electron is in a bound state, meaning energy must be supplied to free it from the nucleus, thus confirming the stability of the atom.
[3 Marks]
Answer: The nuclear density of atomic nuclei, including deuterium and tritium, is a crucial concept in nuclear physics. Nuclear density is defined as the mass of nucleons (protons and neutrons) contained within a given volume. It remains relatively constant across different nuclei regardless of their mass number (A). For example, deuterium has one proton and one neutron, while tritium has one proton and two neutrons. The critical point is that the strong nuclear force binding these nucleons operates over a short range, typically around 2 femtometers. As both deuterium and tritium are isotopes of hydrogen, their nuclear densities are found to be approximately \(10^{17} kg/m^3\). Hence, the ratio of nucleons to the volume remains the same, illustrating that the nuclear density is fundamentally independent of mass number, A.
[3 Marks]
Answer: Self-inductance is a property of a coil that quantifies its ability to oppose changes in electric current. It is defined as the ratio of the induced electromotive force (emf) in the coil to the rate of change of current flowing through it. For a long solenoid, the magnetic field B produced by a current I can be expressed as B = µ₀nI. The total magnetic flux Φ linked with the solenoid is given by Φ = B·A = µ₀nIA. Therefore, the self-inductance L can be derived from the formula L = N(Φ/I), where N is the total number of turns, leading us to L = µ₀n²Al, where n is the number of turns per unit length, A is the cross-sectional area, and l is the length of the solenoid.