Science Stream (Class - XII) Past Paper PDF

# **Science Stream (Class - XII)** ## **Part A** **Instructions:** 1. This question paper contains a total of 50 objective type questions in Part A. All questions are compulsory. 2. Question numbers are from 1 to 50 and each question carries 1 mark. 3. Carefully read each question, select the cor...

# **Science Stream (Class - XII)** ## **Part A** **Instructions:** 1. This question paper contains a total of 50 objective type questions in Part A. All questions are compulsory. 2. Question numbers are from 1 to 50 and each question carries 1 mark. 3. Carefully read each question, select the correct option and mark the answer on the OMR sheet. 4. In the OMR sheet, against each corresponding question number, there are four circles (A) O, (B) O, (C) O, (D) O. Darken the circle of the correct option with a ballpoint pen. 5. Use the space provided in the test booklet for rough work. 6. The question paper set number printed on the top right side of the question paper should be filled in at the designated space on the OMR sheet. 7. Students may use a simple calculator and logarithm tables, wherever required. 8. The symbols used in this question paper have their usual meaning. **Questions:** 1. The radius of the innermost electron orbit of the hydrogen atom is 5.3 × 10⁻¹¹ m. What will be the radius of the n = 2 orbit? - (A) 2.12 × 10⁻¹⁰ - (B) 3.12 × 10⁻¹⁰ - (C) 1.22 × 10⁻¹⁰ - (D) 4.12 × 10⁻¹⁰ 2. The energy of the ground state of the hydrogen atom is -13.6 eV. The potential energy of the electron in this state is _____ eV. - (A) -13.6 - (B) -23.6 - (C) -27.2 - (D) -31.6 3. In a scattering experiment, the angle of scattering for head-on collision is 0 = _____ °. - (A) 90° - (B) 60° - (C) 0° - (D) 180° 4. ²³⁸U and ²³²Th are _____. - (A) isobars - (B) isotones - (C) isotopes - (D) isomers 5. The ratio of the radii of the nucleus of the isotopes ²³⁸Am and ¹⁰⁷Ag will be _____. - (A) 1.23 - (B) 3.12 - (C) 2.13 - (D) 2.31 6. Complete the nuclear reaction: n + ²³⁶U → _____ + ⁹¹Nb + ______ - (A) ¹³⁶Xe; 2n - (B) ¹²⁶Sb; 4n - (C) ¹⁴⁴Ba; 3n - (D) ¹³⁰Sb; 2n 7. The density of the nucleus is proportional to its _____. - (A) inverse of the atomic mass. - (B) square of the atomic mass. - (C) atomic mass. - (D) It does not depend on the atomic mass. 8. In an unbiased p-n junction, holes diffuse from the p-region to the n-region because _____. - (A) The concentration of holes in the p-region is more than the concentration in the n-region. - (B) they diffuse due to the potential difference across the junction. - (C) free electrons in the n-region attract them. - (D) holes in the p-region repel them. 9. Carbon, silicon, and germanium, each have four valence electrons. The valence and conduction bands separated by energy band gaps Eg, Es, and Eg respectively. Which of the following statements is true? - (A) Eg > Es > Eg - (B) Eg < Es > Eg - (C) Es < Eg < Eg - (D) Eg = Es = Eg 10. Which of the following statements is correct for an n-type silicon? - (A) Holes are majority carriers and trivalent atoms are dopants. - (B) Electrons are minority carriers and pentavalent atoms are dopants. - (C) Electrons are majority carriers and trivalent atoms are dopants. - (D) Holes are minority carriers and pentavalent atoms are dopants. 11. Which of the following is an inorganic compound semiconductor? - (A) Ge - (B) Si - (C) GaAs - (D) C 12. The total electric flux associated with a cubical Gaussian surface is 1.9 × 10⁹ Nm²C⁻¹. The charge enclosed at the centre of the cube is ______μC. (Edge of the cube = 9.0 cm) - (A) 4 μC - (B) 2 mC - (C) 2 μC - (D) 4 mC 13. A long linear charge produces an electric field of 9 × 10⁴ NC⁻¹ at a distance of 2 cm. The linear charge density will be _____. - (A) 0.1 µCm⁻¹ - (B) 0.2 mCm⁻¹ - (C) 0.1 mCm⁻¹ - (D) 0.2 µCm⁻¹ 14. An object contains 10¹⁰ electrons and 10¹⁰ protons. What will be the net charge on the object? - (A)1.6×10¹⁷ C - (B) 1.58×10⁷ C - (C) 1.6×10⁻¹⁷ C - (D) 1.58×10⁻⁷ C 15. A dipole moment p is kept in a uniform electric field E, when it is parallel to E, the force on the dipole will be _____. - (A) in the decreasing field direction. - (B) perpendicular to E. - (C) zero. - (D) in the increasing field direction. 16. A regular hexagon has sides of 9 cm with a 5μC charge at each vertex. What is the electric potential at the center of the hexagon? (K = 9×10⁹ Nm²C⁻²) - (A) 3 × 10⁶ - (B) 3 × 10⁵ - (C) 3 × 10⁷ - (D) 3 × 10⁸ 17. A 12 pF capacitor is connected to a 50V battery. The electrical energy stored in the capacitor will be ______ J. - (A) 2.5 × 10⁻⁸ - (B) 1,5 × 10⁻¹⁰ - (C) 1.5 × 10⁻⁸ - (D) 2.5 × 10⁻¹⁰ 18. For a parallel plate capacitor with a limited area of plates, the electric field lines tend to be curved near the edges of the plates. This phenomenon is called _____. - (A) Polarization - (B) Fringing of the field - (C) Electrostatic shielding - (D) Diffraction 19. Calculate V₂ - V c in the given circuit.  - (A) 20 V - (B) 15 V - (C) 40 V - (D) 30 V 20. A wire of length 15 m and uniform cross-sectional area 6 × 10⁻⁷ m² has a resistance of 52 Ω when the current flows through it. What will be the resistivity of the material at this temperature? - (A) 2 × 10⁻⁷ Ωm - (B) 3 × 10⁻⁷ Ωm - (C) 2 × 10⁷ Ωm - (D) 3 × 10⁷ Ωm 21. Three cells with the same emf ε = 1.2V, ε = 1.4V, and ε = 1.5V and internal resistances r₁ = 0.12, r₂ = 0.22, and r₁ = 0.32 are connected in parallel. What is the equivalent emf and equivalent resistance of the combination? - (A) 2.4 V, 3.4 Ω - (B) 3.4 V, 2.4 Ω - (C) 34 V, 3.4 Ω - (D) 24 V, 3.4 Ω 22. If power P is transmitted through a transmission line with a voltage V with fixed resistance R, then the energy loss in transmission will be _____. - (A) PR²/V - (B) PR/V² - (C) PR²/V² - (D) P²R/V² 23. A circular coil of radius 8.0 cm has 200 turns and carries a current of 0.40 A. What is the value of the magnetic field at the center of the coil? - (A) 2π × 10⁻⁶ T - (B) π × 10⁻⁴ T - (C) 2π × 10⁻⁴ T - (D) π × 10⁻⁶ T 24. Two very long, straight and parallel conductors of negligible cross-sectional area carry the same current of 1 mA, one meter apart in vacuum. What will be the force per unit length experienced by these two conductors? (µ₀ = 4π × 10⁻⁷ TmA⁻¹) - (A) 2 × 10⁻¹³ N - (B) 2 × 10⁻¹⁰ N - (C) 2 × 10⁻⁷ N - (D) 2 × 10⁻⁴ N 25. A solenoid has 1000 turns and a cross-sectional area of 2 × 10⁻⁴ m². If the current flowing through the solenoid is 5.0 A, what will be the magnetic moment associated with the solenoid. - (A) 2 Am² - (B) 3 Am² - (C) 4 Am² - (D) 1 Am² 26. _____ is used to make a compass needle. - (A) Copper - (B) Lodestone - (C) Bismuth - (D) Aluminium 27. The complete diamagnetism observed in superconductors is called the _____. - (A) Meissner effect - (B) Lorenz effect - (C) Curie effect - (D) Crompton effect 28. The dimension of self-inductance is _____. - (A) ML⁻²T⁻²A⁻² - (B) ML⁻²T⁻²A² - (C) ML²T⁻²A⁻² - (D) ML²T⁻²A² 29. A metallic wheel with 10 spokes of 0.5m length is rotating at a constant speed of 120 rev/min in a plane perpendicular to the earth’s horizontal component of the magnetic field H. What will be the induced emf between the axle and the rim of the wheel at this location if H = 0.4G? (1G = 10⁻⁴T) - (A) 6.28×10⁻² mV - (B) 6.28×10⁻² μV - (C) 6.28×10⁻⁵ mV - (D) 6.28×10⁻⁵ μV 30. The given figure shows the variation of the uniform magnetic field going in and out of the plane of the loop. Which of the loops given in the figure will have induced current in the same direction?  - (A) Only loop (iii) - (B) Only loop (ii) - (C) Only loop (i) - (D) Loop (ii) and Loop (iii) 31. What will be the magnetic energy per unit volume stored in a solenoid in terms of magnetic field B? - (A) 1/2 B²/µ₀ - (B) B²/2µ₀ - (C) B²/µ₀ - (D) 1/2 B²/µ₀ 32. The current in a circuit falls from 5.0A to 0.0A in 0.15 s. If an average emf of 200V is induced, the self-inductance of the circuit will be ______ H - (A) 40 - (B) 4.0 - (C) 0.4 - (D) 0.004 33. A 60 μF capacitor is connected to a 110V, 60Hz source. The rms value of the current in the circuit will be ______ A. - (A) 2.49 A - (B) 4.29 A - (C) 1.94 A - (D) 9.24 A 34. Power dissipation occurs in an LCR circuit in _____. - (A) Resistor only - (B) Capacitor only - (C) Inductor only - (D) Resistor, capacitor and inductor all 35. A 15.0 μF capacitor is connected to a 220V, 50Hz source, the capacitive reactance of the circuit will be ______ Ω. - (A) 202 Ω - (B) 152 Ω - (C) 122 Ω - (D) 212 Ω 36. A 27 mH inductor is connected to a fully charged 30 μF capacitor. The frequency of oscillation in the circuit will be _____Hz. - (A) 267.4 Hz - (B) 176.9 Hz - (C) 111.1 Hz - (D) 613.8 Hz 37. The LASIK eye surgery uses ______ radiation. - (A) Radio - (B) Ultraviolet - (C) Infrared - (D) Gamma 38. A charged particle oscillates about its mean equilibrium position with a frequency of 10 Hz. The frequency of the electromagnetic waves produced will be ______ Hz - (A) 1/√2 × 10⁹ Hz - (B) 1/2 × 10⁹ Hz - (C) 2 × 10⁹ Hz - (D) 10⁹ Hz 39. The distance between the objective and the eyepiece of a compound microscope, if the image distance for the objective is v and object distance for the eyepiece is u is _____. - (A) |v| - |u| - (B) |v| + |u| - (C) |v| / |u| - (D) |v| × |u| 40. A 1 mm² square is viewed through a converging lens, and the area of its image is 6.25 mm². The magnification power of the lens will be ______. - (A) 2.5 - (B) 5.25 - (C) 6.25 - (D) 0 41. What is the focal length of a double convex lens made of glass with refractive index 1.5, if both the surfaces are of the same radius of curvature R? - (A) R = f - (B) R = 2f - (C) R = f/2 - (D) R = f/4 42. If a prism is used to invert an image without changing its size, the angle of the prism must be ______. - (A) π rad/2 - (B) π rad/4 - (C) π rad/3 - (D) π rad/4 43. When a plane wavefront is incident on a thin convex lens, the emerging wavefront is. _____. - (A) Spherical - (B) Cylindrical - (C) Plane - (D) None of the above 44. The angle of diffraction for the second minimum in a diffraction pattern due to a single slit, when the width of the slit is half the wavelength of the incident light, is approximately ______. - (A) 6° - (B) 5° - (C) 4° - (D) 8° 45. According to Huygens principle, the amplitude of the secondary wavelets in the forward direction is ______ while that in the backward direction is ______. - (A) Zero, Zero - (B) Maximum, Zero - (C) Zero, Maximum - (D) Maximum, Maximum 46. In a photoelectric experiment, the cut-off voltage is found to be 4V. What is the maximum kinetic energy of the emitted photoelectrons? - (A) 8.0 eV - (B) 3.2 eV - (C) 6.4 eV - (D) 4.0 eV 47. In a photoelectric effect experiment, the slope of the graph between the stopping potential and the frequency of the incident light is ______. (h = 6.625 × 10⁻³⁴ Js) - (A) 4.14 × 10⁻¹⁵ Vs - (B) 6.14 × 10⁻¹⁵ Vs - (C) 1.41 × 10⁻¹⁵ Vs - (D) 2.14 × 10⁻¹⁵ Vs 48. A photon of an electromagnetic radiation has wavelength λ₁ and its de-Broglie wavelength is λ₂ then, _____. - (A) λ₁ = λ₂/2 - (B) λ₁ = 2λ₂ - (C) λ₁ = λ₂ - (D) λ₁ = λ₂/√2 49. The momentum of a photon of frequency ν is ______. - (A) c/hv - (B) hv/c - (C) hcv - (D) hv/c 50. Units of which two of the following physical quantities are the same? - (A) Work function and stopping potential - (B) Planck's constant and angular momentum - (C) Planck's constant and angular velocity - (D) Work function and threshold frequency ## Part B **Instructions:** 1. Write in a legible handwriting. 2. This question paper contains three sections in Part B. There are 27 questions in total. 3. All questions are compulsory. Internal options have been provided. 4. Marks against a question indicate its weightage. 5. Start a new section on a new page. 6. Write the answers to the questions in order. 7. Students may use a simple calculator and logarithm tables, where required. **Section A ** **Instructions:** Answer any 8 out of the 12 questions given below. **Questions:** 1. Write any four important properties of electric field lines. [2] 2. Derive the relation between electric field and electric potential. Mention two important conclusions of this relation. [2] 3. Derive the balancing condition of a Wheatstone bridge. [2] 4. State two reasons why a galvanometer cannot be directly used as an ammeter in a circuit. Explain the necessary modifications required to convert a galvanometer into an ammeter. [2] 5. A small bar magnet has a magnetic moment of 0.50 JT⁻¹. Calculate the magnetic field produced at a point: [2] - a) at a distance of 10 cm along the axis of the magnet. - b) at a distance of 10 cm on the equator of the magnet. 6. Derive the formula for the magnetic force on a current-carrying conductor placed in a uniform magnetic field. [2] 7. A capacitor of capacitance 80pF is being charged. What will be the rate of change of potential difference across the plates of the capacitor when charging current is 0.15A? Also, calculate the displacement current between the plates. [2] 8. Derive the formula for the effective focal length of a combination of two thin lenses in contact. [2] 9. Light of frequency 9.21 × 10¹⁴ Hz is incident on a metal surface. Electrons are emitted with a maximum speed from the surface of 6.0 × 10⁵ ms⁻¹. Calculate the threshold frequency for photoelectric emission. (h = 6.625 × 10⁻³⁴ Js) [2] 10. A hydrogen atom, initially in the ground state, absorbs a photon and gets excited to the n=4 level. Determine the wavelength of the photon. (h = 6.625 × 10⁻³⁴ Js, c = 3 × 10⁸ ms⁻¹) [2] 11. Explain nuclear binding energy. [2] 12. Discuss the operation of a p-n junction diode under forward bias. [2] **Section B** **Instructions:** Answer any 6 out of the 9 questions given below. **Questions:** 13. Derive the formula for electric field intensity due to an electric dipole at a point on the axial line. Also, mention one case of this formula. [3] 14. Two point charges carrying charges 5 × 10⁻⁸ C and −3 × 10⁻⁸ C are placed at a distance of 20 cm apart. At what points on the line joining these two charges will the electric potential be zero? Consider the potential at infinity to be zero. [3] 15. Derive the formula for the drift velocity of free electrons in a conductor. [3] 16. Derive the formula for the magnetic field at a point on the axis of a circular current loop. [3] 17. An LCR series circuit is connected to a 283V sinusoidal ac source of frequency 50Hz. If the resistance of the circuit is 32Ω, inductance is 25.48mH and capacitance is 796μF. Calculate, [3] - a) Impedence of the circuit - b) Phase difference between the source voltage and current - c) Power loss in the circuit. 18. Derive the formula for refraction at a spherical surface. [3] 19. The work function of cesium is 2.14 eV. [3] - a) Determine the threshold frequency for cesium. - b) If the stopping potential is 0.60V, what is the wavelength of the incident light? (h = 6.625 × 10⁻³⁴ Js) 20. A coin has a mass of 3.0g. All the neutrons and protons in the coin are separated from each other. Assuming the coin is made up of ⁶³Cu atoms only, calculate the nuclear energy required to separate all the neutrons and protons from each other. (⁶³Cu = 62.92960 u) [3] 21. Explain the use of a junction diode as a full-wave rectifier. [3] ## Part C **Instructions:** Answer any 4 out of the 6 questions given below. **Questions:** 22. A cube encloses a region as shown below.  The components of the electric field are E = ax, E = 0, E = 0, where a = 800 NC⁻²m⁻¹ and a = 0.1 m.Calculate: - a) Total flux out of the cube. - b) Charge enclosed within the cube. [4] 23. A rectangular loop carrying current is kept in a uniform magnetic field. The plane of the loop makes an angle θ with the magnetic field. Find the torque on the loop. [4] 24. Explain an inductor circuit with AC source. [4] 25. Derive the formula ô = i + e – A for a prism. Also, drive the formula for the refractive index of the material of the prism. [4] 26. In a Young’s double-slit experiment, two beams of light with wavelengths 4500 Å and 6000 Å are used to obtain interference fringes. The distance between the slits is d = 0.15 cm and the distance between the slits and the screen is D = 90cm. [4] - a) Calculate the distance of the third dark fringe from the central maximum for the wavelength 4500 Å. - b) How far from the central maximum should the screen be located so that the bright fringe from the 4500 Å beam coincides with the dark fringe from the 6000 Å beam? 27. Explain the process of energy production in stars due to nuclear fusion. Discuss the proton-proton cycle occurring in the sun. [ 4]