CBSE Class 12 Physics 2026 question paper (55/1)
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 markIn a region, the electric potential varies as , where V is in volts and in meters. The electric field in the region is :
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- Q.21 markA conducting wire connects two charged metallic spheres A and B of radii and respectively. The distance between the spheres is very large compared to their radii. The ratio of electric fields, at the surfaces of spheres A and B will be
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- Q.31 markA long straight wire of circular cross-section (radius a) carries a steady current I. The current is uniformly distributed across this cross-section. The magnitude of the magnetic field produced at a point at a distance (a/2) from the axis of the wire will be
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- Q.41 markThe shape of the interference fringes in Young's double-slit experiment, when the distance between the slit and the screen is very large as compared to the slit-separation, is nearly
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- Q.51 markAn electromagnetic wave passes from vacuum into a dielectric medium with relative electrical permittivity (3/2) and relative magnetic permeability (8/3). Then, its
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- Q.61 markIn a series LCR circuit, the voltage across the resistor, capacitor and inductor is 10 V each. If the capacitor is short circuited, the voltage across the inductor will be
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- Q.71 markElectromagnetic waves used in a diagnostic tool in medicine have a wavelength range
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- Q.81 markThe 'distance of closest approach' of an alpha-particle is 'd' when it moves with a velocity head-on towards the target nucleus. If the velocity of alpha particle is halved, the new 'distance of closest approach' will be -
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- Q.91 markA concave lens of focal length 10 cm is cut into two identical plano-concave lenses. The focal length of each lens will be
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- Q.101 markFour independent waves are expressed as (i) (ii) (iii) (iv) The interference between two of these waves is possible in
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- Q.111 markTwo heaters rated as and are connected in series across a dc source of volt. The power consumed by the combination will be -
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- Q.121 markIn an unbiased p-n junction, at equilibrium, which of the following statements is true ?
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- For question number 13 to 16, two statements are given - one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer to these questions from the options (A), (B), (C) and (D) as given below :Q.131 markAssertion (A) : All atoms have a net magnetic moment. Reason (R) : A current loop does not always behave as a magnetic dipole.
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- Q.141 markAssertion (A) : If accelerated electrons are passed through a narrow slit, a diffraction pattern is observed. Reason (R) : Electrons behave as both particles and waves.
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- Q.151 markReason (A) : The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R) : Energy is absorbed when the nucleons are bound together to form a nucleus.
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- Q.161 markReason (A) : In Bohr model of hydrogen atom, the energy levels are discrete and quantised. Reason (R) : In a hydrogen atom, the electrostatic force on the electron provides the necessary centripetal force to it to revolve around the nucleus.
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Section B
2 marks each
- Q.172 marksIn a photoelectric experiment, the emitter plate is irradiated with radiation of 200 nm. The photocurrent becomes zero when the collector plate potential is - 0.80 V. Calculate the work function (in eV) of the emitter.
- Q.18 (a)2 marksA beam of light consisting of two wavelengths 400 nm and 600 nm is used to illuminate a single slit of width 1 mm. Find the least distance of the point from the central maximum where the dark fringes due to both wavelengths coincide on the screen placed 1.5 m from the slit.
OR
Q.18 (b)2 marksIn a Young's double-slit experimental set-up with slit separation 0.6 mm a beam of light consisting of two wavelengths 440 nm and 660 nm is used to obtain interference pattern on a screen kept 1.5 m in front of the slits. Find the least distance of the point from the central maximum where the bright fringes due to both the wavelengths coincide.- Q.192 marksA wire of length L is bent round into (i) a square coil having N turns and (ii) a circular coil having N turns. The coil in both cases is free to turn about a vertical axis coinciding with the plane of the coil, in a uniform, horizontal magnetic field and carry the same currents. Find the ratio of the maximum value of the torque acting on the square coil to that on the circular coil.
- Q.202 marksWhat is the order of magnitude of drift velocity of electrons in a conductor ? Deduce the relation between the current flowing through a conductor and drift velocity of electrons in it.
- Q.212 marksDraw the plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from this plot.
Section C
3 marks each
- Q.22 (a)3 marks(a) Using Gauss's law, deduce an experession for electric field at a point due to a uniformly charged infinite plane thin sheet. (b) Two large thin plane sheets, each having surface charge density , are held close and parallel to each other in air. What is the net electric field at a point (i) inside and (ii) outside, the sheets ?
OR
Q.22 (b)3 marks(a) Obtain the condition of balance of a Wheatstone bridge. (b) Find net resistance of the network of resistors connected between A and B, as shown in figure.- Q.233 marksA parallel plate capacitor of capacitance C has a dielectric slab between its plates. It is charged to a potential difference V by connecting it across a battery. The battery is then disconnected. If the dielectric slab is now withdrawn from the capacitor, how will the following be affected ? (a) Capacitance of the capacitor, (b) Energy stored in the capacitor, and (c) The potential difference between the plates of the capacitor. Justify your answer in each case.
- Q.243 marksFigure shows a narrow beam of electrons entering with a velocity of m/s, symmetrically through the space between two parallel horizontal plates and kept 2 cm apart. If each plate is 3 cm long, calculate the potential difference V applied between the plates so that the beam just strikes the end .
- Q.253 marksAn ac voltage V is applied between points A and B in a network of two ideal diodes and three resistors as shown in figure. During the positive half-cycle of the input voltage supplied to the network. (a) Identify which of the two diodes will conduct and why ? (b) Redraw an equivalent circuit diagram to show the flow of current. (c) Calculate the output voltage drops across the three resistors when the input voltage attains its peak value.
- Q.263 marksBriefly explain the two important processes that occur during the formation of a p-n junction.
- Q.273 marks(a) Draw the ray diagram to show the image formation by a refracting telescope and write the expression for angular magnification for the telescope in normal adjustment. (b) Give two reasons to explain why a reflecting telescope is preferred over a refracting telescope.
- Q.283 marks(a) State the two conditions under which total internal reflection occurs. (b) A transparent container contains layers of three immiscible transparent liquids A, B and C of refractive indices n, and , respectively. A laser beam is incident at the interface between A and B at an angle as shown in figure. Prove that the beam does not enter region C at all for .
Section D
1 mark each
- A galvanometer is used to detect or/and measure small currents in an electrical circuit. It essentially works on the fact that a current-carrying coil experiences a deflecting torque when placed in a magnetic field. This deflection in the coil can be measured and it is related to the current flowing in the coil, the number of turns in the coil, area of the coil and the magnetic field. A hair spring attached to the coil provides a counter torque and helps in measuring the deflection. A galvanometer can be converted to an ammeter or a voltmeter of desired range by using suitable resistances.Q.29 (I)1 markThe torque on the coil remains constant irrespective of the coil's orientation during rotation due to
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- Q.29 (II)1 markThe best way to increase current sensitivity of a galvanometer is by
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- Q.29 (III) (a)1 markA moving coil galvanometer has a coil with area of cross-section and number of turns 50. The coil is rotating in a magnetic field of 0.25 T. The torque acting on the coil when a current of 5 A passes through it is
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OR
Q.29 (III) (b)1 markA galvanometer coil has a resistance of 15 and the meter shows full scale deflection for a current of 3 mA. The value of resistance required to convert it into a voltmeter of range (0 – 12 V) isTap an option to check your answer.
- Q.29 (IV)1 markA galvanometer with coil of resistance 20 shows full scale deflection for a current of 5 mA. To convert it into an ammeter of range (0 – 10 A), a resistance of
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- A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corrosponding stopping potentials . The graph shows the variation of stopping potential with the frequency of incident radiation for metals A and B.Q.30 (I)1 markFrom the graph, the work functions of A and B are (h is Planck's constant and e value of charge on an electron)
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- Q.30 (II)1 markFor radiation of frequency incident on the surfaces of A and B, the maximum kinetic energy of ejected electron is
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- Q.30 (III)1 markIf the intensity of the incident radiation for both metals A and B, is doubled keeping its frequency constant, then
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- Q.30 (IV) (a)1 markThe threshold frequency for a metal surface is . If the radiation of frequency illuminates the surface, the maximum kinetic energy (KE) of photoelectrons is . If the frequency were increased to , the maximum KE of the photoelectrons becomes . Then equals
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OR
Q.30 (IV) (b)1 markLet m be the slope of the graph line for metal B. If e is the value of electron charge, then Planck's constant 'h' is given byTap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(a) An electric dipole consists of two point charges q and -q separated by a distance 2a. Derive an expression for the electric field due to this dipole at a point distant r from the centre of the dipole on the equatorial plane. Write the expression for the electric field at a far off point, i.e. r >> a. (b) A dipole is placed in x-y plane such that charges q and -q are located at and respectively. There exists an electric field in the region. Calculate the force and torque experienced by the dipole.
OR
Q.31 (b)5 marks(a) Two cells of emf and with internal resistances and respectively, are connected in parallel by connecting their positive terminals together and negative terminals together. Deduce an expression for equivalent emf and equivalent internal resistance of the combination. (b) A parallel combination, as stated in (a) above, of two cells of emfs E and 3E and internal resistances R each is connected across a resistance 2R. Find the current that flows through resistance 2R.- Q.32 (a)5 marks(a) Using the relation for refraction at a curved spherical surface, derive the expression for lens maker's formula. (b) Three lenses , and , each of focal length 40 cm, are placed coaxially. The distance between and and between and are 120 cm and 20 cm respectively. An object is kept at a distance of 80 cm to the left of lens . Find the distance of the final image formed from the object.
OR
Q.32 (b)5 marks(a) Draw a ray diagram to show the image formation by a concave mirror when the object is kept between its focus and the centre of curvature. Using this diagram, derive the mirror formula. (b) A concave mirror produces a two times magnified virtual image of an object kept 10 cm in front of it. Calculate the focal length of the mirror.- Q.33 (a)5 marks(a) State Faraday's law of electromagnetic induction. (b) Derive an expression for the self-inductance of an air-filled long solenoid of length and cross-sectional area A having N turns. (c) A conducting rod of length 50 cm, with one end pivoted, is rotated with angular speed of 60 rpm in a uniform magnetic field of 4.0 mT directed perpendicular to the plane of rotation of rod. Find the emf induced in the rod.
OR
Q.33 (b)5 marks(a) Draw a labelled diagram of a step-up transformer. State the principle on which it works and obtain the ratio of secondary voltage to primary voltage in terms of number of turns and currents in the two coils. (b) The ratio of the number of turns in the primary to the secondary of an ideal transformer is 1 : 5. If 5 kW power at 200 V is supplied to the primary, find (i) current in the primary, and (ii) output voltage.
Section A
1 mark each
- Q.11 markIn a region electric field is given by N/C. The potential difference between points A ( m) and B ( m), is
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- Q.21 markIn an unbiased p-n junction, at equilibrium, which of the following statements is true ?
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- Q.31 markA copper wire is stretched to increase its length by 1%. Then the change in its resistance is close to
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- Q.41 markFour independent waves are expressed as (i) (ii) (iii) (iv) The interference between two of these waves is possible in
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- Q.51 markA concave lens of focal length 40 cm is coaxially in contact with two convex lenses, each of focal length 20 cm, on each side. The focal length of the combination is
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- Q.61 markThe distance-of-closest-approach for an alpha particle is 'd' when it moves head-on with speed v towards a target nucleus. If the alpha particle is replaced by a proton moving with the same speed, the new distance-of-closest-approach will be
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- Q.71 markElectromagnetic waves used for purification of water are
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- Q.81 markA conducting wire connects two charged metallic spheres A and B of radii and respectively. The distance between the spheres is very large compared to their radii. The ratio of electric fields, at the surfaces of spheres A and B will be
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- Q.91 markA straight conductor lies along -axis. It carries a current of 10 A along direction. The magnetic field due to 1 cm segment of this conductor, centred at the origin, at a point (0, 1 m, 0) is
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- Q.101 markThe angular width of interference fringes in Young's double-slit experiment depends on
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- Q.111 markAn electromagnetic wave passes from vacuum into a dielectric medium with relative electrical permittivity (3/2) and relative magnetic permeability (8/3). Then, its
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- Q.121 markA resistor and an inductor of negligible resistance are connected in series to a 20 V ac source. If the voltage across the resistor is 12 V, the voltage across the inductor will be
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- For question number 13 to 16, two statements are given - one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer to these questions from the options (A), (B), (C) and (D) as given below :Q.131 markReason (A) : In Bohr model of hydrogen atom, the energy levels are discrete and quantised. Reason (R) : In a hydrogen atom, the electrostatic force on the electron provides the necessary centripetal force to it to revolve around the nucleus.
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- Q.141 markReason (A) : The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R) : Energy is absorbed when the nucleons are bound together to form a nucleus.
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- Q.151 markAssertion (A) : All atoms have a net magnetic moment. Reason (R) : A current loop does not always behave as a magnetic dipole.
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- Q.161 markAssertion (A) : If accelerated electrons are passed through a narrow slit, a diffraction pattern is observed. Reason (R) : Electrons behave as both particles and waves.
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Section B
2 marks each
- Q.17 (a)2 marksA beam of light consisting of two wavelengths 400 nm and 600 nm is used to illuminate a single slit of width 1 mm. Find the least distance of the point from the central maximum where the dark fringes due to both wavelengths coincide on the screen placed 1.5 m from the slit.
OR
Q.17 (b)2 marksIn a Young's double-slit experimental set-up with slit separation 0.6 mm a beam of light consisting of two wavelengths 440 nm and 660 nm is used to obtain interference pattern on a screen kept 1.5 m in front of the slits. Find the least distance of the point from the central maximum where the bright fringes due to both the wavelengths coincide.- Q.182 marksFind the ratio of de Broglie wavelength associated with an alpha particle to de Broglie wavelength associated with a proton if both are moving with the (a) same velocity (b) same kinetic energy.
- Q.192 marksWhat is the order of magnitude of drift velocity of electrons in a conductor ? Deduce the relation between the current flowing through a conductor and drift velocity of electrons in it.
- Q.202 marksA wire of length L is bent round into (i) a square coil having N turns and (ii) a circular coil having N turns. The coil in both cases is free to turn about a vertical axis coinciding with the plane of the coil, in a uniform, horizontal magnetic field and carry the same currents. Find the ratio of the maximum value of the torque acting on the square coil to that on the circular coil.
- Q.212 marksDraw a graph showing variation of binding energy per nucleon as a function of mass number A. The binding energy per nucleon for heavy nuclei (A > 170) decreases with increase in mass number. Explain its significance.
Section C
3 marks each
- Q.223 marksFigure shows a narrow beam of electrons entering with a velocity of m/s, symmetrically through the space between two parallel horizontal plates and kept 2 cm apart. If each plate is 3 cm long, calculate the potential difference V applied between the plates so that the beam just strikes the end .
- Q.233 marks(a) State the two conditions under which total internal reflection occurs. (b) A transparent container contains layers of three immiscible transparent liquids A, B and C of refractive indices n, and , respectively. A laser beam is incident at the interface between A and B at an angle as shown in figure. Prove that the beam does not enter region C at all for .
- Q.24 (a)3 marks(a) Using Gauss's law, deduce an experession for electric field at a point due to a uniformly charged infinite plane thin sheet. (b) Two large thin plane sheets, each having surface charge density , are held close and parallel to each other in air. What is the net electric field at a point (i) inside and (ii) outside, the sheets ?
OR
Q.24 (b)3 marks(a) Obtain the condition of balance of a Wheatstone bridge. (b) Find net resistance of the network of resistors connected between A and B, as shown in figure.- Q.253 marksAn ac voltage V is applied between points A and B in a network of two ideal diodes and three resistors as shown in figure. During the positive half-cycle of the input voltage supplied to the network. (a) Identify which of the two diodes will conduct and why ? (b) Redraw an equivalent circuit diagram to show the flow of current. (c) Calculate the output voltage drops across the three resistors when the input voltage attains its peak value.
- Q.263 marksA 12.0 capacitor is charged to a potential difference of 150 V. The terminals of the charged capacitor are then connected to those of an uncharged 6.0 capacitor. Calculate final potential difference across and charge on, each capacitor.
- Q.273 marksA semiconductor has equal electron and hole concentration of . On doping with a certain impurity, the hole concentration increases to . (a) What type of semiconductor is obtained on doping ? (b) Calculate the new electron concentration of the semiconductor. (c) How does the energy gap of semiconductor change with doping ? Draw the energy band diagram for it.
- Q.283 marksDraw a labelled ray diagram showing the formation of image by a compound microscope when final image is formed at least distance of distinct vision. Derive an expression for its magnifying power for this case.
Section D
1 mark each
- A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corrosponding stopping potentials . The graph shows the variation of stopping potential with the frequency of incident radiation for metals A and B.Q.29 (I)1 markFrom the graph, the work functions of A and B are (h is Planck's constant and e value of charge on an electron)
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- Q.29 (II)1 markFor radiation of frequency incident on the surfaces of A and B, the maximum kinetic energy of ejected electron is
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- Q.29 (III)1 markIf the intensity of the incident radiation for both metals A and B, is doubled keeping its frequency constant, then
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- Q.29 (IV) (a)1 markThe threshold frequency for a metal surface is . If the radiation of frequency illuminates the surface, the maximum kinetic energy (KE) of photoelectrons is . If the frequency were increased to , the maximum KE of the photoelectrons becomes . Then equals
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OR
Q.29 (IV) (b)1 markLet m be the slope of the graph line for metal B. If e is the value of electron charge, then Planck's constant 'h' is given byTap an option to check your answer.
- A galvanometer is used to detect or/and measure small currents in an electrical circuit. It essentially works on the fact that a current-carrying coil experiences a deflecting torque when placed in a magnetic field. This deflection in the coil can be measured and it is related to the current flowing in the coil, the number of turns in the coil, area of the coil and the magnetic field. A hair spring attached to the coil provides a counter torque and helps in measuring the deflection. A galvanometer can be converted to an ammeter or a voltmeter of desired range by using suitable resistances.Q.30 (I)1 markThe torque on the coil remains constant irrespective of the coil's orientation during rotation due to
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- Q.30 (II)1 markThe best way to increase current sensitivity of a galvanometer is by
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- Q.30 (III) (a)1 markA moving coil galvanometer has a coil with area of cross-section and number of turns 50. The coil is rotating in a magnetic field of 0.25 T. The torque acting on the coil when a current of 5 A passes through it is
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OR
Q.30 (III) (b)1 markA galvanometer coil has a resistance of 15 and the meter shows full scale deflection for a current of 3 mA. The value of resistance required to convert it into a voltmeter of range (0 – 12 V) isTap an option to check your answer.
- Q.30 (IV)1 markA galvanometer with coil of resistance 20 shows full scale deflection for a current of 5 mA. To convert it into an ammeter of range (0 – 10 A), a resistance of
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Section E
5 marks each
- Q.31 (a)5 marks(a) State Faraday's law of electromagnetic induction. (b) Derive an expression for the self-inductance of an air-filled long solenoid of length and cross-sectional area A having N turns. (c) A conducting rod of length 50 cm, with one end pivoted, is rotated with angular speed of 60 rpm in a uniform magnetic field of 4.0 mT directed perpendicular to the plane of rotation of rod. Find the emf induced in the rod.
OR
Q.31 (b)5 marks(a) Draw a labelled diagram of a step-up transformer. State the principle on which it works and obtain the ratio of secondary voltage to primary voltage in terms of number of turns and currents in the two coils. (b) The ratio of the number of turns in the primary to the secondary of an ideal transformer is 1 : 5. If 5 kW power at 200 V is supplied to the primary, find (i) current in the primary, and (ii) output voltage.- Q.32 (a)5 marks(a) An electric dipole consists of two point charges q and -q separated by a distance 2a. Derive an expression for the electric field due to this dipole at a point distant r from the centre of the dipole on the equatorial plane. Write the expression for the electric field at a far off point, i.e. r >> a. (b) A dipole is placed in x-y plane such that charges q and -q are located at and respectively. There exists an electric field in the region. Calculate the force and torque experienced by the dipole.
OR
Q.32 (b)5 marks(a) Two cells of emf and with internal resistances and respectively, are connected in parallel by connecting their positive terminals together and negative terminals together. Deduce an expression for equivalent emf and equivalent internal resistance of the combination. (b) A parallel combination, as stated in (a) above, of two cells of emfs E and 3E and internal resistances R each is connected across a resistance 2R. Find the current that flows through resistance 2R.- Q.33 (a)5 marks(a) Using the relation for refraction at a curved spherical surface, derive the expression for lens maker's formula. (b) Three lenses , and , each of focal length 40 cm, are placed coaxially. The distance between and and between and are 120 cm and 20 cm respectively. An object is kept at a distance of 80 cm to the left of lens . Find the distance of the final image formed from the object.
OR
Q.33 (b)5 marks(a) Draw a ray diagram to show the image formation by a concave mirror when the object is kept between its focus and the centre of curvature. Using this diagram, derive the mirror formula. (b) A concave mirror produces a two times magnified virtual image of an object kept 10 cm in front of it. Calculate the focal length of the mirror.
Section A
1 mark each
- Q.11 markFour independent waves are expressed as (i) (ii) (iii) (iv) The interference between two of these waves is possible in
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- Q.21 markAn electromagnetic wave passes from vacuum into a dielectric medium with relative electrical permittivity (3/2) and relative magnetic permeability (8/3). Then, its
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- Q.31 markIn an unbiased p-n junction, at equilibrium, which of the following statements is true ?
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- Q.41 markA conducting wire connects two charged metallic spheres A and B of radii and respectively. The distance between the spheres is very large compared to their radii. The ratio of electric fields, at the surfaces of spheres A and B will be
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- Q.51 markThe electric potential for various points in -y plane is given by , where V is in volts and , y are in metres. The angle that the electric field at point (2.0 m, 1.0 m) makes with the positive -axis is –
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- Q.61 markA current of 1.5 A is maintained in a copper wire of length 1 m with area of cross-section . The magnitude of electric field in the wire is [ m)
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- Q.71 markLight from a small object in air falls on a spherical glass surface (n = 1.5) of radius of curvature R. A real image of the object will be formed if the object distance u is related to R as :
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- Q.81 markThe ratio of the potential energy to the kinetic energy of an electron in orbit of Bohr model of hydrogen atom is
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- Q.91 markWelders wear special glass goggles or face masks with glass windows to protect their eyes from
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- Q.101 markA circular loop has radius R and carries current I as shown in figure. In order that the net magnetic field at the centre of the loop is zero, the current in wire AB should have magnitude
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- Q.111 markThe phenomenon of interference is shown by
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- Q.121 markA series LCR circuit with R = 3 , = 4 , = 8 is connected to a 220 V, 50 Hz ac source. The power factor for the circuit is
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- For question number 13 to 16, two statements are given - one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer to these questions from the options (A), (B), (C) and (D) as given below :Q.131 markReason (A) : The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R) : Energy is absorbed when the nucleons are bound together to form a nucleus.
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- Q.141 markAssertion (A) : All atoms have a net magnetic moment. Reason (R) : A current loop does not always behave as a magnetic dipole.
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- Q.151 markReason (A) : In Bohr model of hydrogen atom, the energy levels are discrete and quantised. Reason (R) : In a hydrogen atom, the electrostatic force on the electron provides the necessary centripetal force to it to revolve around the nucleus.
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- Q.161 markAssertion (A) : If accelerated electrons are passed through a narrow slit, a diffraction pattern is observed. Reason (R) : Electrons behave as both particles and waves.
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Section B
2 marks each
- Q.172 marksWhat is the order of magnitude of drift velocity of electrons in a conductor ? Deduce the relation between the current flowing through a conductor and drift velocity of electrons in it.
- Q.182 marksA wire of length L is bent round into (i) a square coil having N turns and (ii) a circular coil having N turns. The coil in both cases is free to turn about a vertical axis coinciding with the plane of the coil, in a uniform, horizontal magnetic field and carry the same currents. Find the ratio of the maximum value of the torque acting on the square coil to that on the circular coil.
- Q.19 (a)2 marksA beam of light consisting of two wavelengths 400 nm and 600 nm is used to illuminate a single slit of width 1 mm. Find the least distance of the point from the central maximum where the dark fringes due to both wavelengths coincide on the screen placed 1.5 m from the slit.
OR
Q.19 (b)2 marksIn a Young's double-slit experimental set-up with slit separation 0.6 mm a beam of light consisting of two wavelengths 440 nm and 660 nm is used to obtain interference pattern on a screen kept 1.5 m in front of the slits. Find the least distance of the point from the central maximum where the bright fringes due to both the wavelengths coincide.- Q.202 marksIn an electron microscope, accelerated electrons have wavelength of 0.011 nm. Calculate the voltage through which electrons were accelerated to attain this wavelength. (Take e = C, kg, h = J.s)
- Q.212 marksSuppose a nucleus with mass number A = 240 and MeV, breaks into two nuclei, each of mass number A = 120 with MeV. Calculate the energy released in the process.
Section C
3 marks each
- Q.223 marksAn ac voltage V is applied between points A and B in a network of two ideal diodes and three resistors as shown in figure. During the positive half-cycle of the input voltage supplied to the network. (a) Identify which of the two diodes will conduct and why ? (b) Redraw an equivalent circuit diagram to show the flow of current. (c) Calculate the output voltage drops across the three resistors when the input voltage attains its peak value.
- Q.233 marksFigure shows a narrow beam of electrons entering with a velocity of m/s, symmetrically through the space between two parallel horizontal plates and kept 2 cm apart. If each plate is 3 cm long, calculate the potential difference V applied between the plates so that the beam just strikes the end .
- Q.243 marks(a) State the two conditions under which total internal reflection occurs. (b) A transparent container contains layers of three immiscible transparent liquids A, B and C of refractive indices n, and , respectively. A laser beam is incident at the interface between A and B at an angle as shown in figure. Prove that the beam does not enter region C at all for .
- Q.25 (a)3 marks(a) Using Gauss's law, deduce an experession for electric field at a point due to a uniformly charged infinite plane thin sheet. (b) Two large thin plane sheets, each having surface charge density , are held close and parallel to each other in air. What is the net electric field at a point (i) inside and (ii) outside, the sheets ?
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Q.25 (b)3 marks(a) Obtain the condition of balance of a Wheatstone bridge. (b) Find net resistance of the network of resistors connected between A and B, as shown in figure.- Q.263 marksA parallel plate capacitor of capacitance C is charged to V volt by a battery. After sometime the battery is disconnected and the distance between the plates is doubled. A slab of dielectric constant k = 1.8 is then introduced to completely fill the space between the plates. How will the following be affected ? (a) The capacitance of the capacitor. (b) The electric field between the plates of the capacitor. (c) The energy stored in the capacitor. Justify your answer in each case.
- Q.273 marks(a) Draw the V-I characteristics of silicon diode. (b) Explain the following terms : (i) minority carrier injection in forward bias (ii) breakdown voltage in reverse bias
- Q.283 marks(a) Why does one prefer to view the image formed at infinity than that formed at near point in microscope/telescope ? (b) Consider lenses , and as specified in the following table. Which of them will you select as objective and eyepiece for constructing best possible (i) telescope (ii) compound microscope ? Give reason for your answer.
Lens Power 6 D 3 D 10 D Aperture 1 cm 8 cm 1 cm
Section D
1 mark each
- A galvanometer is used to detect or/and measure small currents in an electrical circuit. It essentially works on the fact that a current-carrying coil experiences a deflecting torque when placed in a magnetic field. This deflection in the coil can be measured and it is related to the current flowing in the coil, the number of turns in the coil, area of the coil and the magnetic field. A hair spring attached to the coil provides a counter torque and helps in measuring the deflection. A galvanometer can be converted to an ammeter or a voltmeter of desired range by using suitable resistances.Q.29 (I)1 markThe torque on the coil remains constant irrespective of the coil's orientation during rotation due to
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- Q.29 (II)1 markThe best way to increase current sensitivity of a galvanometer is by
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- Q.29 (III) (a)1 markA moving coil galvanometer has a coil with area of cross-section and number of turns 50. The coil is rotating in a magnetic field of 0.25 T. The torque acting on the coil when a current of 5 A passes through it is
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Q.29 (III) (b)1 markA galvanometer coil has a resistance of 15 and the meter shows full scale deflection for a current of 3 mA. The value of resistance required to convert it into a voltmeter of range (0 – 12 V) isTap an option to check your answer.
- Q.29 (IV)1 markA galvanometer with coil of resistance 20 shows full scale deflection for a current of 5 mA. To convert it into an ammeter of range (0 – 10 A), a resistance of
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- A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corrosponding stopping potentials . The graph shows the variation of stopping potential with the frequency of incident radiation for metals A and B.Q.30 (I)1 markFrom the graph, the work functions of A and B are (h is Planck's constant and e value of charge on an electron)
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- Q.30 (II)1 markFor radiation of frequency incident on the surfaces of A and B, the maximum kinetic energy of ejected electron is
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- Q.30 (III)1 markIf the intensity of the incident radiation for both metals A and B, is doubled keeping its frequency constant, then
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- Q.30 (IV) (a)1 markThe threshold frequency for a metal surface is . If the radiation of frequency illuminates the surface, the maximum kinetic energy (KE) of photoelectrons is . If the frequency were increased to , the maximum KE of the photoelectrons becomes . Then equals
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Q.30 (IV) (b)1 markLet m be the slope of the graph line for metal B. If e is the value of electron charge, then Planck's constant 'h' is given byTap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(a) Using the relation for refraction at a curved spherical surface, derive the expression for lens maker's formula. (b) Three lenses , and , each of focal length 40 cm, are placed coaxially. The distance between and and between and are 120 cm and 20 cm respectively. An object is kept at a distance of 80 cm to the left of lens . Find the distance of the final image formed from the object.
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Q.31 (b)5 marks(a) Draw a ray diagram to show the image formation by a concave mirror when the object is kept between its focus and the centre of curvature. Using this diagram, derive the mirror formula. (b) A concave mirror produces a two times magnified virtual image of an object kept 10 cm in front of it. Calculate the focal length of the mirror.- Q.32 (a)5 marks(a) State Faraday's law of electromagnetic induction. (b) Derive an expression for the self-inductance of an air-filled long solenoid of length and cross-sectional area A having N turns. (c) A conducting rod of length 50 cm, with one end pivoted, is rotated with angular speed of 60 rpm in a uniform magnetic field of 4.0 mT directed perpendicular to the plane of rotation of rod. Find the emf induced in the rod.
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Q.32 (b)5 marks(a) Draw a labelled diagram of a step-up transformer. State the principle on which it works and obtain the ratio of secondary voltage to primary voltage in terms of number of turns and currents in the two coils. (b) The ratio of the number of turns in the primary to the secondary of an ideal transformer is 1 : 5. If 5 kW power at 200 V is supplied to the primary, find (i) current in the primary, and (ii) output voltage.- Q.33 (a)5 marks(a) An electric dipole consists of two point charges q and -q separated by a distance 2a. Derive an expression for the electric field due to this dipole at a point distant r from the centre of the dipole on the equatorial plane. Write the expression for the electric field at a far off point, i.e. r >> a. (b) A dipole is placed in x-y plane such that charges q and -q are located at and respectively. There exists an electric field in the region. Calculate the force and torque experienced by the dipole.
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Q.33 (b)5 marks(a) Two cells of emf and with internal resistances and respectively, are connected in parallel by connecting their positive terminals together and negative terminals together. Deduce an expression for equivalent emf and equivalent internal resistance of the combination. (b) A parallel combination, as stated in (a) above, of two cells of emfs E and 3E and internal resistances R each is connected across a resistance 2R. Find the current that flows through resistance 2R.