CBSE Class 12 Physics 2024 question paper (55/3)
Maximum marks 70 · Time 3 hours · 3 sets
Try each question first, then open its model answer. Where the paper offers a choice, both questions are shown with OR between them.
Section A
1 mark each
- Q.11 markConsider a group of charges , , … such that . Then equipotentials at a large distance, due to this group are approximately :
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- Q.21 markA proton is taken from point to point , both located in an electric field. The potentials at points and are V and V respectively. Assuming that kinetic energies of the proton at points and are zero, the work done on the proton is :
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- Q.31 markA cm segment of wire, carrying A current in positive y-direction lies along y-axis, as shown in the figure. The magnetic field at a point (3 m, 4 m, 0) due to this segment (part of a circuit) is :
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- Q.41 markA circular loop of wire, carrying a current 'I' is lying in xy-plane with its centre coinciding with the origin. It is subjected to a uniform magnetic field pointing along + z-axis. The loop will :
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- Q.51 markA current carrying circular loop of magnetic moment is suspended in a vertical plane in an external magnetic field such that its plane is normal to . The work done in rotating this loop by about an axis perpendicular to is closest to :
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- Q.61 markThe current in a coil of 15 mH increases uniformly from zero to 4 A in s. The emf induced in the coil will be :
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- Q.71 markConsider a solenoid of length and area of cross-section A with fixed number of turns. The self-inductance of the solenoid will increase if :
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- Q.81 markWhich one of the following has the highest frequency ?
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- Q.91 markA proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be :
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- Q.101 markWhich one of the following is the correct graph between the maximum kinetic energy of the emitted photoelectrons and the frequency of incident radiation for a given photosensitive surface ?
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- Q.111 markAn electron makes a transition from n = 2 level to n = 1 level in the Bohr model of a hydrogen atom. Its period of revolution :
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- Q.121 markSi is doped with a pentavalent element. The energy required to set the additional electron free is about :
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- Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.Q.131 markAssertion (A) : In a semiconductor, the electrons in the conduction band have lesser energy than those in the valence band. Reason (R) : Donor energy level is just above the valence band in a semiconductor.
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- Q.141 markAssertion (A) : Photoelectric effect demonstrates the particle nature of light. Reason (R) : Photoelectric current is proportional to frequency of incident radiation.
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- Q.151 markAssertion (A) : A proton and an electron enter a uniform magnetic field with the same momentum such that is perpendicular to . They describe circular paths of the same radius. Reason (R) : In a magnetic field, orbital radius r is equal to .
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- Q.161 markAssertion (A) : A convex lens, when immersed in a liquid, disappears. Reason (R) : The refractive indices of material of the lens and the liquid are equal.
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Section B
2 marks each
- Q.17 (a)2 marksWhat is meant by 'relaxation time' of free electrons in a conductor ? Show that the resistance of a conductor can be expressed by , where symbols have their usual meanings.
OR
Q.17 (b)2 marksDraw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flows through the galvanometer in it.- Q.182 marksThe magnifying power of an astronomical telescope is 24. In normal adjustment, distance between its two lenses is 150 cm. Find the focal length of the objective lens.
- Q.192 marksExplain the following : (a) For a simple microscope, the angular size of the object equals the angular size of the image. Yet it offers magnification. (b) Both plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances ?
- Q.202 marksThe minimum intensity of white light that our eyes can perceive is about nWm. Calculate the number of photons of this light entering our pupil (area cm) per second. (Take average wavelength of white light = 500 nm and Planck's constant = Js)
- Q.212 marksSuppose a pure Si crystal has atoms m. It is doped by 1 ppm concentration of boron. Calculate the concentration of holes and electrons, given that m. Is the doped crystal n-type or p-type ?
Section C
3 marks each
- Q.223 marksDetermine the current in branches AB, AC and BC of the network shown in figure.
- Q.233 marksTwo long straight parallel conductors carrying currents, exert a force on each other. Why ? Derive an expression for the force per unit length between two long straight parallel conductors carrying currents in opposite directions. Explain the nature of the force between these conductors.
- Q.243 marksA sinusoidal voltage is applied to an electric circuit containing a circuit element 'X' in which the current leads the voltage by . (a) Identify the circuit element 'X' in the circuit. (b) Write the formula for its reactance. (c) Show graphically the variation of this reactance with frequency of ac voltage. (d) Explain the behaviour of this element when it is used in (i) an ac circuit, and (ii) a dc circuit.
- Q.253 marksThe electric field in an electromagnetic wave in vacuum is given by : (a) Find the wavelength and frequency of the wave. (b) What is the amplitude of the magnetic field of the wave ? (c) Write an expression for the magnetic field of this wave.
- Q.263 marksState Bohr's first and second postulates. Use them to derive an expression for the radius of the orbit in a hydrogen atom.
- Q.273 marks(a) Define atomic mass unit (u). (b) Calculate the energy required to separate a deuteron into its constituent parts (a proton and a neutron). Given : m(D) = u u u
- Q.28 (a)3 marksDraw the circuit diagrams for obtaining the V – I characteristics of a p-n junction diode. Explain briefly the salient features of the V – I characteristics in (i) forward biasing, and (ii) reverse biasing.
OR
Q.28 (b)3 marksOn the basis of energy band diagrams, distinguish between (i) an insulator, (ii) a semiconductor, and (iii) a conductor.
Section D
1 mark each
- The figure shows four pairs of parallel identical conducting plates, separated by the same distance cm and arranged perpendicular to x-axis. The electric potential of each plate is mentioned. The electric field between a pair of plates is uniform and normal to the plates.Q.29 (i)1 markFor which pair of the plates is the electric field along ?
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- Q.29 (ii)1 markAn electron is released midway between the plates of pair IV. It will :
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- Q.29 (iii)1 markLet be the potential at the left plate of any set, taken to be at x = 0 m. Then potential V at any point between the plates of that set can be expressed as : where is a constant, positive or negative.
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- Q.29 (iv) (a)1 markLet , , and be the magnitudes of the electric field between the pairs of plates, I, II, III and IV respectively. Then :
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OR
Q.29 (iv) (b)1 markAn electron is projected from the right plate of set I directly towards its left plate. It just comes to rest at the plate. The speed with which it was projected is about : (Take (e/m) = C/kg)Tap an option to check your answer.
- Diffraction and interference are closely related phenomena that occur together. Diffraction is the phenomenon of bending of light around the edges of the obstacle, while interference is the combination of waves that results in a new wave pattern. In order to get interference, there must be at least two waves that are diffracting. So while diffraction can occur without interference, interference cannot occur without diffraction. Two slits of width 2 m each in an opaque material are separated by a distance of 6 m. Monochromatic light of wavelength 450 nm is incident normally on the slits. One finds a combined interference and diffraction pattern on the screen.Q.30 (i)1 markThe number of peaks of the interference fringes formed within the central peak of the envelope of the diffraction pattern will be :
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- Q.30 (ii)1 markThe number of peaks of the interference formed if the slit width is doubled while keeping the distance between the slits same will be :
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- Q.30 (iii) (a)1 markIf instead of 450 nm light, another light of wavelength 680 nm is used, number of peaks of the interference formed in the central peak of the envelope of the diffraction pattern will be :
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OR
Q.30 (iii) (b)1 markConsider the diffraction of light by a single slit described in this case study. The first minimum falls at an angle equal to :Tap an option to check your answer.
- Q.30 (iv)1 markThe number of bright fringes formed due to interference on 1 m of screen placed at m away from the slits is :
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Section E
5 marks each
- Q.31 (a)5 marks(i) Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates. (ii) A charge of 6 C is given to a hollow metallic sphere of radius m. Find the potential at (i) the surface and (ii) the centre of the sphere.
OR
Q.31 (b)5 marks(i) A charge + Q is placed on a thin conducting spherical shell of radius R. Use Gauss's theorem to derive an expression for the electric field at a point lying (i) inside and (ii) outside the shell. (ii) Show that the electric field for same charge density is twice in case of a conducting plate or surface than in a nonconducting sheet.- Q.32 (a)5 marks(i) (1) What is meant by current sensitivity of a galvanometer ? Mention the factors on which it depends. (2) A galvanometer of resistance G is converted into a voltmeter of range (0 – V) by using a resistance R. Find the resistance, in terms of R and G, required to convert it into a voltmeter of range . (ii) The magnetic flux through a coil of resistance 5 increases with time as : mWb Find the magnitude of induced current through the coil at t = 2 s.
OR
Q.32 (b)5 marks(i) A rectangular coil of N turns and area of cross-section A is rotated at a steady angular speed in a uniform magnetic field. Obtain an expression for the emf induced in the coil at any instant of time. (ii) Two coplanar and concentric circular loops and are placed coaxially with their centres coinciding. The radii of and are 1 cm and 100 cm respectively. Calculate the mutual inductance of the loops. (Take )- Q.33 (a)5 marks(i) Trace the path of a ray of light showing refraction through a triangular prism and hence obtain an expression for angle of deviation in terms of A, i and e, where symbols have their usual meanings. Draw a graph showing the variation of angle of deviation with the angle of incidence. (ii) In the figure, a ray of light is incident on a transparent liquid contained in a thin glass box at an angle of with its one face. The emergent ray passes along the face AB. Find the refractive index of the liquid.
OR
Q.33 (b)5 marks(i) The displacement of two light waves, each of amplitude 'a' and frequency , emanating from two coherent sources of light, are given by and . is the phase difference between the two waves. These light waves superpose at a point. Obtain the expression for the resultant intensity at that point. (ii) In Young's double slit experiment, find the ratio of intensities at two points on a screen when waves emanating from two slits reaching these points have path differences (i) and (ii) .
Section A
1 mark each
- Q.11 markAn isolated conductor, with a cavity, has a net charge +Q. A point charge +q is inside the cavity. The charges on the cavity wall and the outer surface are respectively :
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- Q.21 markA proton is taken from point to point , both located in an electric field. The potentials at points and are V and V respectively. Assuming that kinetic energies of the proton at points and are zero, the work done on the proton is :
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- Q.31 markA cm segment of wire, carrying A current in positive y-direction lies along y-axis, as shown in the figure. The magnetic field at a point (3 m, 4 m, 0) due to this segment (part of a circuit) is :
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- Q.41 markTwo thin long parallel wires separated by a distance 'a' carry current 'I' in opposite directions. The wires will :
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- Q.51 markA current carrying circular loop of magnetic moment is suspended in a vertical plane in an external magnetic field such that its plane is normal to . The work done in rotating this loop by about an axis perpendicular to is closest to :
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- Q.61 markThe mutual inductance of two coils and is 20 mH. In coil , the current changes from 4 A to zero in s. If the resistance of coil is 4 , then the charge that flows through it per second will be :
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- Q.71 markConsider a solenoid of length and area of cross-section A with fixed number of turns. The self-inductance of the solenoid will increase if :
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- Q.81 markElectromagnetic waves with frequency Hz are known as :
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- Q.91 markA proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be :
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- Q.101 markThe figure shows the variation of stopping potential with frequency of incident radiation, for three materials , and with work functions , and respectively. Then :
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- Q.111 markAn electron makes a transition from n = 2 level to n = 1 level in the Bohr model of a hydrogen atom. Its period of revolution :
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- Q.121 markSi is doped with a pentavalent element. The energy required to set the additional electron free is about :
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- Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.Q.131 markAssertion (A) : In a semiconductor, the electrons in the conduction band have lesser energy than those in the valence band. Reason (R) : Donor energy level is just above the valence band in a semiconductor.
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- Q.141 markAssertion (A) : Photoelectric effect demonstrates the particle nature of light. Reason (R) : Photoelectric current is proportional to frequency of incident radiation.
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- Q.151 markAssertion (A) : A proton and an electron enter a uniform magnetic field with the same momentum such that is perpendicular to . They describe circular paths of the same radius. Reason (R) : In a magnetic field, orbital radius r is equal to .
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- Q.161 markAssertion (A) : A convex lens, when immersed in a liquid, disappears. Reason (R) : The refractive indices of material of the lens and the liquid are equal.
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Section B
2 marks each
- Q.17 (a)2 marksWhat is meant by 'relaxation time' of free electrons in a conductor ? Show that the resistance of a conductor can be expressed by , where symbols have their usual meanings.
OR
Q.17 (b)2 marksDraw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flows through the galvanometer in it.- Q.182 marksThe magnifying power of an astronomical telescope is 24. In normal adjustment, distance between its two lenses is 150 cm. Find the focal length of the objective lens.
- Q.192 marksWrite two points of difference between interference and diffraction of light.
- Q.202 marksLight of wavelength 500 nm is incident on caesium metal (work function eV) and photoemission of electrons occurs. Calculate the (i) kinetic energy (in eV) of the fastest electrons and (ii) stopping potential for this situation. (Take hc = 1240 eV.nm)
- Q.212 marksSuppose a pure Si crystal has atoms m. It is doped by 1 ppm concentration of boron. Calculate the concentration of holes and electrons, given that m. Is the doped crystal n-type or p-type ?
Section C
3 marks each
- Q.223 marksA battery of unknown emf E and internal resistance r is connected in a circuit as shown in the figure. When the key (K) is open, the voltmeter reads V and ammeter reads 0 A. In the closed circuit, the voltmeter reads V and ammeter reads A. Calculate : (a) emf of the battery, (b) internal resistance of the battery (r), and (c) external resistance (R).
- Q.233 marksA rectangular loop of area , carrying current I, is placed in a uniform magnetic field . With the help of a suitable diagram, derive an expression, in vector form, for the torque acting on the loop.
- Q.243 marksDistinguish between reactance and impedance of an ac circuit. Show that an ideal inductor in an ac circuit does not dissipate any power.
- Q.253 marksThe electric field in an electromagnetic wave in vacuum is given by : (a) Find the wavelength and frequency of the wave. (b) What is the amplitude of the magnetic field of the wave ? (c) Write an expression for the magnetic field of this wave.
- Q.263 marksExplain the origin of the spectral lines of hydrogen atom using Bohr's theory. Draw the energy level diagram of hydrogen atom showing its various spectral series.
- Q.273 marks(a) Define atomic mass unit (u). (b) Calculate the energy required to separate a deuteron into its constituent parts (a proton and a neutron). Given : m(D) = u u u
- Q.28 (a)3 marksDraw the circuit diagrams for obtaining the V – I characteristics of a p-n junction diode. Explain briefly the salient features of the V – I characteristics in (i) forward biasing, and (ii) reverse biasing.
OR
Q.28 (b)3 marksOn the basis of energy band diagrams, distinguish between (i) an insulator, (ii) a semiconductor, and (iii) a conductor.
Section D
1 mark each
- The figure shows four pairs of parallel identical conducting plates, separated by the same distance cm and arranged perpendicular to x-axis. The electric potential of each plate is mentioned. The electric field between a pair of plates is uniform and normal to the plates.Q.29 (i)1 markFor which pair of the plates is the electric field along ?
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- Q.29 (ii)1 markAn electron is released midway between the plates of pair IV. It will :
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- Q.29 (iii)1 markLet be the potential at the left plate of any set, taken to be at x = 0 m. Then potential V at any point between the plates of that set can be expressed as : where is a constant, positive or negative.
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- Q.29 (iv) (a)1 markLet , , and be the magnitudes of the electric field between the pairs of plates, I, II, III and IV respectively. Then :
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OR
Q.29 (iv) (b)1 markAn electron is projected from the right plate of set I directly towards its left plate. It just comes to rest at the plate. The speed with which it was projected is about : (Take (e/m) = C/kg)Tap an option to check your answer.
- Diffraction and interference are closely related phenomena that occur together. Diffraction is the phenomenon of bending of light around the edges of the obstacle, while interference is the combination of waves that results in a new wave pattern. In order to get interference, there must be at least two waves that are diffracting. So while diffraction can occur without interference, interference cannot occur without diffraction. Two slits of width 2 m each in an opaque material are separated by a distance of 6 m. Monochromatic light of wavelength 450 nm is incident normally on the slits. One finds a combined interference and diffraction pattern on the screen.Q.30 (i)1 markThe number of peaks of the interference fringes formed within the central peak of the envelope of the diffraction pattern will be :
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- Q.30 (ii)1 markThe number of peaks of the interference formed if the slit width is doubled while keeping the distance between the slits same will be :
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- Q.30 (iii) (a)1 markIf instead of 450 nm light, another light of wavelength 680 nm is used, number of peaks of the interference formed in the central peak of the envelope of the diffraction pattern will be :
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OR
Q.30 (iii) (b)1 markConsider the diffraction of light by a single slit described in this case study. The first minimum falls at an angle equal to :Tap an option to check your answer.
- Q.30 (iv)1 markThe number of bright fringes formed due to interference on 1 m of screen placed at m away from the slits is :
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Section E
5 marks each
- Q.31 (a)5 marks(i) Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates. (ii) A charge of 6 C is given to a hollow metallic sphere of radius m. Find the potential at (i) the surface and (ii) the centre of the sphere.
OR
Q.31 (b)5 marks(i) A charge + Q is placed on a thin conducting spherical shell of radius R. Use Gauss's theorem to derive an expression for the electric field at a point lying (i) inside and (ii) outside the shell. (ii) Show that the electric field for same charge density is twice in case of a conducting plate or surface than in a nonconducting sheet.- Q.32 (a)5 marks(i) (1) What is meant by current sensitivity of a galvanometer ? Mention the factors on which it depends. (2) A galvanometer of resistance G is converted into a voltmeter of range (0 – V) by using a resistance R. Find the resistance, in terms of R and G, required to convert it into a voltmeter of range . (ii) The magnetic flux through a coil of resistance 5 increases with time as : mWb Find the magnitude of induced current through the coil at t = 2 s.
OR
Q.32 (b)5 marks(i) A rectangular coil of N turns and area of cross-section A is rotated at a steady angular speed in a uniform magnetic field. Obtain an expression for the emf induced in the coil at any instant of time. (ii) Two coplanar and concentric circular loops and are placed coaxially with their centres coinciding. The radii of and are 1 cm and 100 cm respectively. Calculate the mutual inductance of the loops. (Take )- Q.33 (a)5 marks(i) Trace the path of a ray of light showing refraction through a triangular prism and hence obtain an expression for angle of deviation in terms of A, i and e, where symbols have their usual meanings. Draw a graph showing the variation of angle of deviation with the angle of incidence. (ii) In the figure, a ray of light is incident on a transparent liquid contained in a thin glass box at an angle of with its one face. The emergent ray passes along the face AB. Find the refractive index of the liquid.
OR
Q.33 (b)5 marks(i) The displacement of two light waves, each of amplitude 'a' and frequency , emanating from two coherent sources of light, are given by and . is the phase difference between the two waves. These light waves superpose at a point. Obtain the expression for the resultant intensity at that point. (ii) In Young's double slit experiment, find the ratio of intensities at two points on a screen when waves emanating from two slits reaching these points have path differences (i) and (ii) .
Section A
1 mark each
- Q.11 markThe plates and of a 2 F capacitor are at potentials 25 V and V respectively. The charge on plate will be :
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- Q.21 markA proton is taken from point to point , both located in an electric field. The potentials at points and are V and V respectively. Assuming that kinetic energies of the proton at points and are zero, the work done on the proton is :
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- Q.31 markA cm segment of wire, carrying A current in positive y-direction lies along y-axis, as shown in the figure. The magnetic field at a point (3 m, 4 m, 0) due to this segment (part of a circuit) is :
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- Q.41 markWhich of the following is a diamagnetic substance ?
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- Q.51 markA current carrying circular loop of magnetic moment is suspended in a vertical plane in an external magnetic field such that its plane is normal to . The work done in rotating this loop by about an axis perpendicular to is closest to :
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- Q.61 markThe average value of the alternating voltage v = (157 V) sin over its first half-cycle is :
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- Q.71 markConsider a solenoid of length and area of cross-section A with fixed number of turns. The self-inductance of the solenoid will increase if :
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- Q.81 markA plane electromagnetic wave is travelling in air in + x direction. At a particular moment, its electric field is along + y direction. At that moment, the magnetic field is along :
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- Q.91 markA proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be :
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- Q.101 markThe wavelength of matter wave associated with an electron of kinetic energy K is . If the kinetic energy of the electron is doubled, the associated wavelength becomes :
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- Q.111 markAn electron makes a transition from n = 2 level to n = 1 level in the Bohr model of a hydrogen atom. Its period of revolution :
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- Q.121 markSi is doped with a pentavalent element. The energy required to set the additional electron free is about :
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- Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.Q.131 markAssertion (A) : In a semiconductor, the electrons in the conduction band have lesser energy than those in the valence band. Reason (R) : Donor energy level is just above the valence band in a semiconductor.
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- Q.141 markAssertion (A) : Photoelectric effect demonstrates the particle nature of light. Reason (R) : Photoelectric current is proportional to frequency of incident radiation.
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- Q.151 markAssertion (A) : A proton and an electron enter a uniform magnetic field with the same momentum such that is perpendicular to . They describe circular paths of the same radius. Reason (R) : In a magnetic field, orbital radius r is equal to .
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- Q.161 markAssertion (A) : A convex lens, when immersed in a liquid, disappears. Reason (R) : The refractive indices of material of the lens and the liquid are equal.
Tap an option to check your answer.
Section B
2 marks each
- Q.17 (a)2 marksWhat is meant by 'relaxation time' of free electrons in a conductor ? Show that the resistance of a conductor can be expressed by , where symbols have their usual meanings.
OR
Q.17 (b)2 marksDraw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flows through the galvanometer in it.- Q.182 marksThe magnifying power of an astronomical telescope is 24. In normal adjustment, distance between its two lenses is 150 cm. Find the focal length of the objective lens.
- Q.192 marksWhat is a sustained or stable interference pattern ? What are the conditions for obtaining such an interference pattern ?
- Q.202 marksLight of wavelength 600 nm is incident on potassium (work function eV). Will photoemission of electrons occur ? What is the longest wavelength that will cause photoemission of electrons ? (Take hc = 1240 eV. nm)
- Q.212 marksSuppose a pure Si crystal has atoms m. It is doped by 1 ppm concentration of boron. Calculate the concentration of holes and electrons, given that m. Is the doped crystal n-type or p-type ?
Section C
3 marks each
- Q.223 marksA current of A flows through a wire when a potential difference of V is applied across it. The length and cross-sectional area of the wire are m and m respectively. Calculate : (a) Electric field across the wire (b) Current density (c) Average relaxation time (Number density of free electrons in the wire is m)
- Q.233 marksAn electron (charge , mass m) is revolving around a nucleus, in a hydrogen atom, in a circle of radius r. Derive an expression, in vector form, for the magnetic dipole moment, in terms of its orbital angular momentum . What is gyromagnetic ratio ?
- Q.243 marksProve that induced charge depends on the net change in the magnetic flux and not on the time interval of the flux change.
- Q.253 marksThe electric field in an electromagnetic wave in vacuum is given by : (a) Find the wavelength and frequency of the wave. (b) What is the amplitude of the magnetic field of the wave ? (c) Write an expression for the magnetic field of this wave.
- Q.263 marksState Bohr's second postulate for his theory of hydrogen atom. Prove that the radius of Bohr's orbit of a hydrogen atom is directly proportional to , where n is the principal quantum number.
- Q.273 marks(a) Define atomic mass unit (u). (b) Calculate the energy required to separate a deuteron into its constituent parts (a proton and a neutron). Given : m(D) = u u u
- Q.28 (a)3 marksDraw the circuit diagrams for obtaining the V – I characteristics of a p-n junction diode. Explain briefly the salient features of the V – I characteristics in (i) forward biasing, and (ii) reverse biasing.
OR
Q.28 (b)3 marksOn the basis of energy band diagrams, distinguish between (i) an insulator, (ii) a semiconductor, and (iii) a conductor.
Section D
1 mark each
- The figure shows four pairs of parallel identical conducting plates, separated by the same distance cm and arranged perpendicular to x-axis. The electric potential of each plate is mentioned. The electric field between a pair of plates is uniform and normal to the plates.Q.29 (i)1 markFor which pair of the plates is the electric field along ?
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- Q.29 (ii)1 markAn electron is released midway between the plates of pair IV. It will :
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- Q.29 (iii)1 markLet be the potential at the left plate of any set, taken to be at x = 0 m. Then potential V at any point between the plates of that set can be expressed as : where is a constant, positive or negative.
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- Q.29 (iv) (a)1 markLet , , and be the magnitudes of the electric field between the pairs of plates, I, II, III and IV respectively. Then :
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OR
Q.29 (iv) (b)1 markAn electron is projected from the right plate of set I directly towards its left plate. It just comes to rest at the plate. The speed with which it was projected is about : (Take (e/m) = C/kg)Tap an option to check your answer.
- Diffraction and interference are closely related phenomena that occur together. Diffraction is the phenomenon of bending of light around the edges of the obstacle, while interference is the combination of waves that results in a new wave pattern. In order to get interference, there must be at least two waves that are diffracting. So while diffraction can occur without interference, interference cannot occur without diffraction. Two slits of width 2 m each in an opaque material are separated by a distance of 6 m. Monochromatic light of wavelength 450 nm is incident normally on the slits. One finds a combined interference and diffraction pattern on the screen.Q.30 (i)1 markThe number of peaks of the interference fringes formed within the central peak of the envelope of the diffraction pattern will be :
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- Q.30 (ii)1 markThe number of peaks of the interference formed if the slit width is doubled while keeping the distance between the slits same will be :
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- Q.30 (iii) (a)1 markIf instead of 450 nm light, another light of wavelength 680 nm is used, number of peaks of the interference formed in the central peak of the envelope of the diffraction pattern will be :
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OR
Q.30 (iii) (b)1 markConsider the diffraction of light by a single slit described in this case study. The first minimum falls at an angle equal to :Tap an option to check your answer.
- Q.30 (iv)1 markThe number of bright fringes formed due to interference on 1 m of screen placed at m away from the slits is :
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Section E
5 marks each
- Q.31 (a)5 marks(i) Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates. (ii) A charge of 6 C is given to a hollow metallic sphere of radius m. Find the potential at (i) the surface and (ii) the centre of the sphere.
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Q.31 (b)5 marks(i) A charge + Q is placed on a thin conducting spherical shell of radius R. Use Gauss's theorem to derive an expression for the electric field at a point lying (i) inside and (ii) outside the shell. (ii) Show that the electric field for same charge density is twice in case of a conducting plate or surface than in a nonconducting sheet.- Q.32 (a)5 marks(i) (1) What is meant by current sensitivity of a galvanometer ? Mention the factors on which it depends. (2) A galvanometer of resistance G is converted into a voltmeter of range (0 – V) by using a resistance R. Find the resistance, in terms of R and G, required to convert it into a voltmeter of range . (ii) The magnetic flux through a coil of resistance 5 increases with time as : mWb Find the magnitude of induced current through the coil at t = 2 s.
OR
Q.32 (b)5 marks(i) A rectangular coil of N turns and area of cross-section A is rotated at a steady angular speed in a uniform magnetic field. Obtain an expression for the emf induced in the coil at any instant of time. (ii) Two coplanar and concentric circular loops and are placed coaxially with their centres coinciding. The radii of and are 1 cm and 100 cm respectively. Calculate the mutual inductance of the loops. (Take )- Q.33 (a)5 marks(i) Trace the path of a ray of light showing refraction through a triangular prism and hence obtain an expression for angle of deviation in terms of A, i and e, where symbols have their usual meanings. Draw a graph showing the variation of angle of deviation with the angle of incidence. (ii) In the figure, a ray of light is incident on a transparent liquid contained in a thin glass box at an angle of with its one face. The emergent ray passes along the face AB. Find the refractive index of the liquid.
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Q.33 (b)5 marks(i) The displacement of two light waves, each of amplitude 'a' and frequency , emanating from two coherent sources of light, are given by and . is the phase difference between the two waves. These light waves superpose at a point. Obtain the expression for the resultant intensity at that point. (ii) In Young's double slit experiment, find the ratio of intensities at two points on a screen when waves emanating from two slits reaching these points have path differences (i) and (ii) .