Physics Sample Paper PDF

# SAMPLE PAPER ## [Average Concept] **Time Allowed:** 3 Hours **Maximum Marks:** 70 ## General Instructions: 1. There are 33 questions in all. All questions are compulsory. 2. This question paper has five sections: Section A, Section B, Section C, Section D and Section E. 3. All the sections are...

# SAMPLE PAPER ## [Average Concept] **Time Allowed:** 3 Hours **Maximum Marks:** 70 ## General Instructions: 1. There are 33 questions in all. All questions are compulsory. 2. This question paper has five sections: Section A, Section B, Section C, Section D and Section E. 3. All the sections are compulsory. 4. Section A contains sixteen questions, twelve MCQ and four Assertion Reasoning based of 1 mark each, Section B contains five questions of two marks each, Section C contains seven questions of three marks each, Section D contains two case study-based questions of four marks each and Section E contains three long answer questions of five marks each. 5. There is no overall choice. However, an internal choice has been provided in one question in Section B, one question in Section C, one question in each CBQ in Section D and all three questions in Section E. You have to attempt only one of the choices in such questions. 6. Use of calculators is not allowed. 7. You may use the following values of physical constants where ever necessary. * c = 3 × 10⁸ m/s * m_e = 9.1 × 10^-31 kg * m_p = 1.7 × 10^-27 kg * e = 1.6 × 10^-19 C * μ_o = 4π × 10^-7 Tm A^-1 * h = 6.63 × 10^-34 Js * ε_o = 8.854 × 10^-12 C² N^-1 m^-2 * Avogadro's number = 6.023 × 10²³ per gram mole ## Section A 1. At an axial point, distance r away from the centre of an electric dipole, the electric potential is proportional to: * (a) r^-1 * (b) r * (c) r^-3 * (d) r^-2 2. The resistance of a tungsten wire is 133 ohm at 150 °C. Find its resistance at 500 °C. Given that the temperature coefficient of resistance of tungsten is 0.0045 per °C. * (a) 158 Ω * (b) 258 Ω * (c) 528 Ω * (d) 825 Ω 3. A small magnetic dipole of dipole moment M is placed in a magnetic field of intensity B. The total work done in deflecting the dipole through an angle θ is: * (a) MB * (b) 2MB * (c) MB(1 − cos θ) * (d) MB sin θ 4. In an ammeter, 5% of the main current is passing through the galvanometer. If the resistance of the galvanometer is G, then find the shunt resistance. * (a) 19 G * (b) 20 G * (c) G/19 * (d) G/20 5. A cube of side l is situated in a uniform electric field as shown. Find the total electric flux through the cube. * (a) 2l²E * (b) 4l²E * (c) 6l²E * (d) Zero 6. A magnet is moved away with velocity 'v' along the axis of a circular coil as shown in the diagram. The induced current produced in the coil is * (a) clockwise. * (b) anticlockwise. * (c) zero. * (d) cannot be estimated. 7. The current lags behind the voltage by π / 2 in an a.c. circuit having * (a) L only. * (b) R only. * (c) C only. * (d) L, R circuit. 8. A convex lens forms a real image of a point object kept 0.5 m away from it, on the other side of the lens 0.5 m away from it. A convex mirror is now placed on the mid - point between the lens and the image. If the image formed now concides with the object then the focal length of the mirror is: * (a) 1 m * (b) 50 cm * (c) 0.125 m * (d) 25 cm 9. A proton and a deuteron are accelerated through the same accelerating potential. If λ and p represent their wavelengths and momenta, then: * (a) λ_p > λ_d * (b) p_p > p_d * (c) p_p < p_d * (d) None 10. The wavelength of the first line of Balmer series is 6563 Å. What is the wavelength of the first line of Lyman series? * (a) 4861 Å * (b) 1216 Å * (c) 4101 Å * (d) Data insufficient 11. In the nuclear reaction, * n + ²³²₉₂U → ^a₅₄X + ¹⁴⁸₅₈Sr + 2n * What are the values of a and b? * (a) a = 140; b = 38 * (b) a = 148; b = 30 * (c) a = 152; b = 26 * (d) None of the above 12. Applying forward bias in p-n junction, the potential barrier * (a) decreases. * (b) increases. * (c) becomes zero. * (d) remains unchanged. **For Q.13 to Q.16, two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b),(c) and (d) as given below.** * (a) If both Assertion and Reason are true and Reason is correct explanation of Assertion. * (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. * (c) If Assertion is true but Reason is false. * (d) If both Assertion and Reason are false. 13. Assertion (A): The electrostatic force between the plates of a charged isolated capacitor decreases when dielectric fills whole space between plates. Reason (R): The electric field between the plates of a charged isolated capacitance increases when dielectric fills whole space between plates. 14. Assertion (A): In a series LCR resonant circuit the impedance is equal to the ohmic resistance. Reason (R): At resonance the inductive reactance exceeds the capacitive reactance. 15. Assertion (A): The maximum possible angle of a refracting prism, A = 2C, where C is the critical angle for the material of the prism. Reason (R): The ray of light suffers grazing incidence and grazing emergence in this case. 16. Assertion (A): At higher temperatures, the effect of decrease in n_i is overcome by a higher number of electrons in conduction band and holes in valence band released at higher temperature. Reason (R): In semiconductors, we have almost an empty conduction band and almost filled valence band with a narrow forbidden energy gap ≈ 1 eV in between the bands. ## SECTION B 17. Show that the force of attraction between the plates of a parallel plate capacitor of capacitance C and distance of separation between the plates d, with a potential difference between the plates is CV²/2d. 18. Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A. 19. A ray of light falls on a transparent sphere with centre C as shown in the figure. The ray emerges from the sphere parallel to the line AB. Find the angle of refraction at A if refractive index of the material of the sphere is √3. 20. The energy levels of a hypothetical hydrogen - like atom are shown in the figure. Find out the transition, from the ones shown in the figure, which will result in the emission of a photon of wavelength 275 nm. **Or** Calculate the energy in fusion reaction: H + H → He + n, where BE of H = 2.23 MeV and BE of He = 7.73 MeV. ## SECTION C 21. Draw the circuit diagrams showing how a p - n junction diode is * (a) forward biased. * (b) reverse biased. * How is the width of depletion layer affected in the two cases? 22. A small compass needle of magnetic moment m is free to turn about an axis perpendicular to the direction of uniform magnetic field B. The moment of inertia of the needle about the axis is I. The needle is slightly disturbed from its stable position and then released. Prove that it executes simple harmonic motion. Hence, deduce the expression for its time period. 23. (a) State Faraday's law of electromagnetic induction. * (b) The magnetic field through a circular loop of wire 12 cm in radius and 8.5 Ω resistance, changes with time as shown in the figure. The magnetic field is perpendicular to the plane of the loop. Calculate the induced current in the loop and plot it as a function of time. 24. How are electromagnetic waves produced? What is the source of energy of these waves? Write mathematical expression for electric and magnetic fields of an electromagnetic wave propagating along the z-axis. Write any two important properties of electromagnetic waves. 25. A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept at 15 cm from each other. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed. **Or** A convex lens of focal length 20 cm is placed coaxially with a concave mirror of focal length 10 cm at a distance of 50 cm apart from each other. A beam of light coming parallel to the principal axis is incident on the convex lens. Find the position of the final image formed by this combination. Draw the ray diagram showing the formation of the image. 26. Two coherent light waves of intensity 5 × 10^-2 Wm² each superimpose and produce the interference pattern on a screen. At a point where the path difference between the waves is λ/6, λ being wavelength of the wave, find the * (a) phase difference between the waves. * (b) resultant intensity at the point. * (c) resultant intensity in terms of the intensity at the maximum. 27. In an experiment on a-particle scattering by a thin foil of gold, draw a plot showing the number of particles scattered versus the scattering angle θ. Why is it that a very small fraction of the particles are scattered at θ > 90°? Write two important conclusions that can be drawn regarding the structure of the atom from the study of this experiment. 28. (a) Distinguish between an intrinsic semiconductor and a p-type semiconductor. Give reason why a p-type semiconductor is electrically neutral, although n_i >> n_h * (b) Explain, how the heavy doping of both p-side and n-side of a p-n junction diode results in the electric field of the junction being extremely high even with a reverse bias voltage of a few volts. ## SECTION D ## Case Study Based Questions 29. Read the following paragraph and answer the questions that follow. A voltmeter is an instrument which measures the potential difference across any two points of a circuit directly in volts. It is connected in parallel with the part of the circuit across which the potential difference is to be measured. It must have high resistance so that it may not draw appreciable current through it, otherwise the current in the main circuit will decrease resulting in the fall of potential difference to be increased. If R is the resistance connected in series with the galvanometer, G is resistance of the galvanometer and i_g is the current that gives full scale deflection with galvanometer, then- **(i) We use high internal resistance in series of a voltmeter, so that** * (a) it will draw a high amount of current. * (b) its sensitivity is decreased. * (c) it becomes short circuited. * (d) it will not draw appreciable amount of current. **(ii) To convert the galvanometer into a voltmeter the resistance is** * (a) low and connected in series. * (b) high and connected in parallel. * (c) low and connected in parallel. * (d) high and connected in series. **(iii) A sinusoidal waveform is applied to a galvanometer, the reading shown by the galvanometer is** * (a) zero * (b) unity * (c) 1/√2 * (d) none of these **(iv) What will be the value of series resistance to convert the galvanometer into a voltmeter from 0 to V volt? (Where, G is galvanometer resistance and I_g is the current when full scale deflection of galvanometer).** * (a) V/I_g + G = R * (b) V/I_g - G = R * (c) I_g/V - G = R * (d) I_g/V + G = R **(iv) What will be the value of voltage drop across the series resistance 'R', when galvanometer is connected into voltmeter from 0 - V volt?** * (a) R/(R+G) V * (b) G/(R+G) V * (c) R/G V * (d) Data insufficient 30. Read the following paragraph and answer the questions that follow. The kinetic energy of liberated photoelectrons depends on the energy level from where they come out. They have different kinetic energies depending on the different energy levels. The intensity of light controls the number of photons in the incident beam and hence the number of photoelectrons ejected by the cathode. There is one to one correspondence between the incident photon and the emitted photoelectron. **(i) As the intensity of incident light increases** * (a) kinetic energy of emitted photoelectrons increases. * (b) photoelectric current decreases. * (c) photoelectric current increases. * (d) kinetic energy of emitted photoelectrons decreases. **(ii) When ultraviolet rays are incident on metal plates then photoelectric effect does not occur. It occurs by incidence of** * (a) infrared rays * (b) X-rays * (c) radio waves * (d) microwaves **(iii) According to Einstein's photoelectric equation, the graph between the kinetic energy of photoelectron ejected and the frequency of incident radiation is** **(iv) The figure shows a plot of photocurrent versus anode potential for a photosensitive surface for three radiation. Which one of the following is a correct statement?** **Or** **(iv) When photons of energy, hv fall on an aluminium plate (of work function E_o), photoelectrons of maximum kinetic energy K are ejected. If the frequency of radiation is doubled, the maximum kinetic energy of the ejected photoelectrons will be** * (a) K + hv * (b) K + E_o * (c) 2K * (d) K . E_o ## SECTION E 31. (a) State Gauss's law in electrostatics. Show, with the help of a suitable example along with the figure, that the outward flux due to a point charge q, in vacuum within a closed surface, is independent of its size or shape and is given by q/ε_o. **(b) Two parallel uniformly charge infinite plane sheets, 1 and 2, have charge densities + σ and -2σ respectively. Give the magnitude and direction of the net electric field at a point** * (i) in between the two sheets. * (ii) outside near the sheet 1. **Or** **(a) A parallel plate capacitor is charged by a battery to a potential. The battery is disconnected and a dielectric slab is inserted to completely fill the space between the plates. How will** * (i) its capacitance, (ii) electric field between the plates and (iii) energy stored in the capacitor be affected? Justify your answer giving necessary mathematical expressions for each case. * (b) Sketch the pattern of electric field lines due to (i) a conducting sphere having negative charge in it, (ii) an electric dipole. 32. (a) Define relaxation time of the free electrons drifting in a conductor. How is it related to the drift velocity of free electrons? Use this relation to deduce the expression for the electrical resistivity of the material. **(b) Calculate the value of the resistance R in the circuit shown in the figure so that the current in the circuit is 0.2 A. What would be the potential difference between points A and D?** **Or** **(a) Define the term 'drift velocity' of charge carriers in a conductor. Obtain the expression for the current density in terms of relaxation time.** **(b) A 100 V battery is connected to the electric network as shown. If the power consumed in the 2 Ω resistor is 200 W, determine the power dissipated in the 5 Ω resistor.** **(c) The circuit shown in the given figure shows that, the galvanometer 'G' gives zero deflection. If the batteries A and B have negligible internal resistance, find the value of the resistor R.** 33. (a) Draw a ray diagram to show image formation when the concave mirror produces a real, inverted and magnified image of the object. **(b) Obtain the mirror formula and write the expression for the linear magnification.** **(c) Explain two advantages of a reflecting telescope over a refracting telescope.** **Or** * State Huygens's principle. Show, with the help of a suitable diagram, how this principle is used to obtain the diffraction pattern by a single slit. * Draw a plot of intensity distribution and explain clearly why the secondary maxima become weaker with increasing order (n) of the secondary maxima.