Physics Past Paper PDF

## SECTION -A 1. A battery supplies 0.9 A current through a 2 Ω resistor and 0.3 A current through a 7 Ω resistor when connected one by one. The internal resistance of the battery is: (A) 2 Ω (C) 1 Ω (B) 1.2 Ω (D) 0.5 Ω 2. A particle of mass *m* and charge *q* describes a circular path of radiu...

## SECTION -A 1. A battery supplies 0.9 A current through a 2 Ω resistor and 0.3 A current through a 7 Ω resistor when connected one by one. The internal resistance of the battery is: (A) 2 Ω (C) 1 Ω (B) 1.2 Ω (D) 0.5 Ω 2. A particle of mass *m* and charge *q* describes a circular path of radius *R* in a magnetic field. If its mass and charge were 2*m* and $q \over 2$ respectively, the radius of its path would be (A) *R* / 4 (C) 2*R* (B) *R* / 2 (D) 4*R* 3. Which of the following pairs is that of paramagnetic materials? (A) Copper and Aluminium (C) Lead and Iron (B) Sodium and Calcium (D) Nickel and Cobalt 4. A galvanometer of resistance 50 Ω is converted into a voltmeter of range (0-2V) using a resistor of 1.0 ΚΩ. If it is to be converted into a voltmeter of range (0-10 V), the resistance required will be (A) 4.8 ΚΩ (C) 5.2 ΚΩ (B) 5.0 ΚΩ (D) 5.4 ΚΩ 5. Two coils are placed near each other. When the current in one coil is changed at the rate of 5 A/s, an emf of 2 mV is induced in the other. The mutual inductance of the two coils is (A) 0.4 mH (C) 10 mH (B) 2.5 mH (D) 2.5 H 6. The electromagnetic waves used to purify water are (A) Infrared rays (C) X-rays (B) Ultraviolet rays (D) Gamma rays 7. The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm, the magnification obtained by the microscope for most suitable viewing by relaxed eye is: (A) 250 (C) 150 (B) 200 (D) 125 8. The variation of the stopping potential (*V*₀) with the frequency (*v*) of the incident radiation for four metals A, B, C and D is shown in the figure. For the same frequency of incident radiation producing photo-electrons in all metals, the kinetic energy of photo-electrons will be maximum for metal (A) A (C) C | (B) B (D) D 9. The energy of an electron in the ground state of hydrogen atom is -13.6 eV. The kinetic and potential energy of the electron in the first excited state will be (A) -13.6 eV, 27.2 eV (C) 3.4 eV, -6.8 eV (B) -6.8 eV, 13.6 eV (D) 6.8 eV, -3.4 eV 10. A Young's double-slit experimental set up is kept in a medium of refractive index $4 \over 3$. Which maximum in this case will coincide with the 6th maximum obtained if the medium is replaced by air? (A) 4th (C) 8th (B) 6th (D) 10th ## SECTION -B 11. The potential energy between two nucleons inside a nucleus is minimum at a distance of about (A) 0.8 fm (C) 2.0 fm (B) 1.6 fm (D) 2.8 fm 12. A pure Si crystal having 5 * 10²⁸ atoms m⁻³ is doped with 1 ppm concentration of antimony. If the concentration of holes in the doped crystal is found to be 4.5 * 10⁹ m⁻³, the concentration (in m⁻³) of intrinsic charge carriers in Si crystal is about (A) 12 * 10¹⁵ (C) 3.0 * 10¹⁵ (B) 1.5 * 10¹⁶ (D) 2.0 * 10¹⁶ **For Questions 13 to 16, two statements are given - one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the options as given below.** (A) If both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (B) If both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A). (C) If Assertion (A) is true but Reason (R) is false. (D) If both Assertion (A) and Reason (R) are false. 13. **Assertion (A):** Equal amount of positive and negative charges are distributed uniformly on two halves of a thin circular ring as shown in figure. The resultant electric field at the centre O of the ring is along OC. **Reason (R):** It is so because the net potential at O is not zero. 14. **Assertion (A):** The energy of a charged particle moving in a magnetic field does not change. **Reason (R):** It is because the work done by the magnetic force on the charge moving in a magnetic field is zero. 15. **Assertion (A):** In a Young's double-slit experiment, interference pattern is not observed when two coherent sources are infinitely close to each other. **Reason (R):** The fringe width is proportional to the separation between the two sources. 16. **Assertion (A):** An alpha particle is moving towards a gold nucleus. The impact parameter is maximum for the scattering angle of 180°. **Reason (R):** The impact parameter in an alpha particle scattering experiment does not depend upon the atomic number of the target nucleus. 17. **(a)** Four point charges of 1 µC, -2 µC, 1 µC and -2 µC are placed at the corners A, B, C and D respectively, of a square of side 30 cm. Find the net force acting on a charge of 4 µC placed at the centre of the square. **OR** **(b)** Three point charges, 1 pC each, are kept at the vertices of an equilateral triangle of side 10 cm. Find the net electric field at the centroid of triangle. 18. Derive an expression for magnetic force *F* acting on a straight conductor of length *L* carrying current *I* in an external magnetic field *B*. Is it valid when the conductor is in zig-zag form? Justify. 19. A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. Calculate its magnifying power in normal adjustment and the distance of the image formed by the objective. ## SECTION -C 20. **(a)** Two energy levels of an electron in hydrogen atom are separated by 2.55 eV. Find the wavelength of radiation emitted when the electron makes transition from the higher energy level to the lower energy level. **(b)** In which series of hydrogen spectrum this line shall fall? 21. The earth revolves around the sun in an orbit of radius 1.5 * 10¹¹ m with orbital speed 30 km/s. Find the quantum number that characterises its revolution using Bohr's model in this case (mass of earth = 6.0 * 10²⁴ kg). 22. **(a)** Write Einstein's photoelectric equation. How did Millikan prove the validity of this equation? **(b)** Explain the existence of threshold frequency of incident radiation for photoelectric emission from a given surface. 23. **(a)** Define the term 'electric flux' and write its dimensions. **(b)** A plane surface, in shape of a square of side 1 cm is placed in an electric field **E** = (100 i) such that the unit vector normal to the surface is given by **n** = 0.8 **i** + 0.6 **k**. Find the electric flux through the surface. 24. **(a)** (i) State Lenz's Law. In a closed circuit, the induced current opposes the change in magnetic flux that produced it as per the law of conservation of energy. Justify. (ii) A metal rod of length 2 m is rotated with a frequency 60 rev/s about an axis passing through its centre and perpendicular to its length. A uniform magnetic field of 2T perpendicular to its plane of rotation is switched-on in the region. Calculate the e.m.f. induced between the centre and the end of the rod. **OR** **(b)** (i) State and explain Ampere's circuital law. (ii) Two long straight parallel wires separated by 20 cm, carry 5 A and 10 A current respectively, in the same direction. Find the magnitude and direction of the net magnetic field at a point midway between them. ## SECTION -D 25. An electron moving with a velocity **v** = (1.0 * 10⁷ m/s) **i** + (0.5 * 10⁷ m/s) **j** enters a region of uniform magnetic field **B** = (0.5 mT) **j**. Find the radius of the circular path described by it. While rotating; does the electron trace a linear path too? If so, calculate the linear distance covered by it during the period of one revolution. 26. **(a)** Name the parts of the electromagnetic spectrum which are (i) also known as 'heat waves' and (ii) absorbed by ozone layer in the atmosphere. **(b)** Write briefly one method each, of the production and detection of these radiations. 27. **(a)** Explain the characteristics of a p-n junction diode that makes it suitable for its use as a rectifier. **(b)** With the help of a circuit diagram, explain the working of a full wave rectifier. 28. Explain the following, giving reasons: **(a)** A doped semiconductor is electrically neutral. **(b)** In a p-n junction under equilibrium, there is no net current. **(c)** In a diode, the reverse current is practically not dependent on the applied voltage. ## SECTION -D 29. Dielectrics play an important role in design of capacitors. The molecules of a dielectric may be polar or non-polar. When a dielectric slab is placed in an external electric field, opposite charges appear on the two surfaces of the slab perpendicular to electric field. Due to this an electric field is established inside the dielectric. The capacitance of a capacitor is determined by the dielectric constant of the material that fills the space between the plates. Consequently, the energy storage capacity of a capacitor is also affected. Like resistors, capacitors can also be arranged in series and/or parallel. (i) Which of the following is a polar molecule? (A) O₂ (C) N₂ (B) H₂ (D) HCl (ii) Which of the following statements about dielectrics is correct? (A) A polar dielectric has a net dipole moment in absence of an external electric field which gets modified due to the induced dipoles. (B) The net dipole moments of induced dipoles is along the direction of the applied electric field. (C) Dielectrics contain free charges. (D) The electric field produced due to induced surface charges inside a dielectric is along the external electric field. (iii) When a dielectric slab is inserted between the plates of an isolated charged capacitor, the energy stored in it: (A) increases and the electric field inside it also increases. (B) decreases and the electric field also decreases. (C) decreases and the electric field increases. (D) increases and the electric field decreases. (iv) **(a)** An air-filled capacitor with plate area *A* and plate separation *d* has capacitance *C*₀. A slab of dielectric constant *K*, area *A* and thickness $d \over 5$ is inserted between the plates. The capacitance of the capacitor will become (A) $4K \over 5K + 1$ *C*₀ (C) $4K \over 5K$ *C*₀ (B) $4K \over K + 5$ *C*₀ (D) $5K \over 5K+ 4$ *C*₀ **OR** **(b)** Two capacitors of capacitances 2*C*₀ and 6*C*₀ are first connected in series and then in parallel across the same battery. The ratio of energies stored in series combination to that in parallel is (A) 1/4 (C) 2/15 (B) 1/6 (D) 3/16 30. A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by μ = $sin(A + δm \over 2)$ / $sin(A \over 2)$. If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected. (i) The critical angle for glass is θ₁, and that for water is θ₂. The critical angle for glass-water surface would be (given *a*g = 1.5, *a*w = 1.33) (A) less than θ₂ (B) between θ₁ and θ₂ (C) greater than θ₂ (D) less than θ₁ (ii) When a ray of light of wavelength λ and frequency ν is refracted into a denser medium (A) λ and ν both increase. (B) λ increases but ν is unchanged. (C) λ decreases but ν is unchanged. (D) λ and ν both decrease. (iii) **(a)** The critical angle for a ray of light passing from glass to water is minimum for (A) red colour (C) yellow colour (B) blue colour (D) violet colour **OR** **(b)** Three beams of red, yellow and violet colours are passed through a prism, one by one under the same condition. When the prism is in the position of minimum deviation, the angles of refraction from the second surface are *r*r, *r*y and *r*v respectively. Then (A) *r*v < *r*y <*r*r (C) *r*r < *r*y < *r*v (B) *r*y < *r*r < *r*v (D) *r*r = *r*y = *r*v (iv) A ray of light is incident normally on a prism ABC of refractive index √2, as shown in figure. After it strikes face AC, it will (A) go straight undeviated (B) just graze along the face AC (C) refract and go out of the prism (D) undergo total internal reflection ## SECTION -E 31. **(a)** (i) Draw equipotential surfaces for an electric dipole. (ii) Two point charges q₁ and q₂ are located at r₁ and r₂ respectively in an external electric field E. Obtain an expression for the potential energy of the system. (iii) The dipole moment of a molecule is 10⁻³⁰ Cm. It is placed in an electric field *E* of 10⁵ V/m such that its axis is along the electric field. The direction of *E* is suddenly changed by 60° at an instant. Find the change in the potential energy of the dipole, at that instant. **OR** **(b)** (i) A thin spherical shell of radius *R* has a uniform surface charge density σ. Using Gauss' law, deduce an expression for electric field (i) outside and (ii) inside the shell. (ii) Two long straight thin wires AB and CD have linear charge densities 10 µC/m and -20 µC/m, respectively. They are kept parallel to each other at a distance 1 m. Find magnitude and direction of the net electric field at a point midway between them. 32. **(a)** (i) You are given three circuit elements *X*, *Y* and *Z*. They are connected one by one across a given ac source. It is found that *V* and *I* are in phase for element *X*. *V* leads *I* by π/4 for element *Y* while *I* leads *V* by π/4 for element *Z*. Identify elements *X*, *Y* and *Z*. (ii) Establish the expression for impedance of circuit when elements *X*, *Y* and *Z* are connected in series to an ac source. Show the variation of current in the circuit with the frequency of the applied ac source. (iii) In a series *LCR* circuit, obtain the conditions under which (i) impedance is minimum and (ii) wattless current flows in the circuit. **OR** **(b)** (i) Describe the construction and working of a transformer and hence obtain the relation for $U_s \over U_p$ in terms of number of turns of primary and secondary. (ii) Discuss four main causes of energy loss in a real transformer. 33. **(a)** (i) A plane light wave propagating from a rarer into a denser medium, is incident at an angle *i* on the surface separating two media. Using Huygen's principle, draw the refracted wave and hence verify Snell's law of refraction. (ii) In a Young's double slit experiment, the slits are separated by 0.30 mm and the screen is kept 1.5 m away. The wavelength of light used is 600 nm. Calculate the distance between the central bright fringe and the 4th dark fringe. **OR** **(b)** (i) Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern. (ii) An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.