CBSE Class 12 Physics 2025 question paper (55/6)
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 markThe figure shows the voltage (V) versus the current (I) graphs for a wire at two temperatures and . One can conclude that :
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- Q.21 markIf and are the equivalent resistances of n resistors, each of value R, in series and parallel combinations respectively, then the value of is :
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- Q.31 markThe value of magnetic field at point O in the given figure is :
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- Q.41 markA piece of a diamagnetic material, free to move when placed in a uniform magnetic field :
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- Q.51 markA galvanometer can be converted into an ammeter of desired range by connecting a :
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- Q.61 markA proton and an -particle enter with the same velocity in a uniform magnetic field such that . The ratio of the radii of their paths is :
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- Q.71 markA vertically held bar magnet is dropped along the axis of a copper ring having a cut as shown in the diagram. The acceleration of the falling magnet is :
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- Q.81 markAn ac source is connected to a resistor and an inductor in series. The voltage across the resistor and inductor are 8 V and 6 V respectively. The voltage of the source is :
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- Q.91 markTwo coherent waves, each of intensity , produce interference pattern on a screen. The average intensity of light on the screen is :
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- Q.101 markThe work function of a material is eV. Which of the following cannot produce photoelectrons from it ?
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- Q.111 markThe momentum (in kg m/s) of a photon of frequency Hz is :
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- Q.121 markInside a nucleus, the nuclear forces between proton and proton, proton and neutron, neutron and neutron are , and respectively. Then :
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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 reflecting telescope, the image does not have chromatic aberration. Reason (R) : Chromatic aberration occurs only due to refraction of light through an optical medium.
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- Q.141 markAssertion (A) : A hole is an apparent free particle with effective positive electronic charge. Reason (R) : A hole is not necessarily a vacancy left behind by an electron in the valence band.
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- Q.151 markAssertion (A) : X-rays are produced when slow moving electrons are stopped by a metal target of high atomic number. Reason (R) : X-rays consist of low-energy photons.
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- Q.161 markAssertion (A) : The binding energy per nucleon is practically constant for mass number in the range . Reason (R) : Nuclear forces between the nucleons for mass numbers in the range are not short-range.
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Section B
2 marks each
- Q.172 marksFind the equivalent resistance between points A and B for the network shown in the figure.
- Q.18 (a)2 marksFind the intensity at a point on the screen in Young's double slit experiment, at which the interfering waves of intensity each, have a path difference of (i) , and (ii) .
OR
Q.18 (b)2 marksA point source of light in air is kept at a distance of 12 cm in front of a convex spherical surface of glass of refractive index and radius of curvature 30 cm. Find the nature and position of the image formed.- Q.192 marksA laser beam of frequency Hz produces average power of 9 mW. Find (i) the energy of photon of the beam, and (ii) the number of photons emitted per second on an average by the source.
- Q.202 marksA right angled isosceles glass prism ABC is kept in contact with an equilateral triangular prism DBC as shown in the figure. Both prisms are made of the same glass of refractive index . Trace the path of the ray MN incident normally on face AB as it passes through the combination.
- Q.212 marksIn an n-type semiconductor electron-hole combination is a continuous process at room temperature. Yet the electron concentration is always greater than the hole concentration in it. Explain.
Section C
3 marks each
- Q.223 marksWhat is the difference between 'emf' and 'terminal voltage' of a cell ? Two cells of emfs and and internal resistances and are connected in parallel. Derive an expression for the emf and internal resistance of the equivalent cell.
- Q.233 marksA rectangular loop carries a current of 1 A. A straight long wire carrying 2 A current is kept near the loop in the same plane as shown in the figure. Find : (i) the torque acting on the loop, and (ii) the magnitude and direction of the net force on the loop.
- Q.24 (a)3 marksState Lenz's law. A rod MN of length L is rotated about an axis passing through its end M perpendicular to its length, with a constant angular velocity in a uniform magnetic field parallel to the axis. Obtain an expression for emf induced between its ends.
OR
Q.24 (b)3 marksDefine 'self-inductance' of a coil. Derive an expression for self-inductance of a long solenoid of cross-sectional area A and length , having n turns per unit length.- Q.253 marksName the electromagnetic wave used (i) in radar, (ii) in eye surgery and (iii) as diagnostic tool in medicine. Write their wavelength range also.
- Q.263 marksDraw a ray diagram showing the image formation when a concave mirror produces a real, inverted and magnified image of an object and hence obtain the mirror formula.
- Q.273 marksHow is the necessary force provided to an electron to keep it moving in a circular orbit according to Bohr model of hydrogen atom ? Derive an expression for the total energy of an electron moving in an orbit of radius r in hydrogen atom. Give the significance of negative sign in this expression.
- Q.283 marks(a) Consider the so-called 'D-T reaction' (Deuterium-Tritium reaction). In a thermonuclear fusion reactor, the following nuclear reaction occurs : Find the amount of energy released in the reaction. Given : u u u u (b) Show that the nuclear density is independent of mass number.
Section D
1 mark each
- A capacitor is a system of two conductors separated by an insulator. In practice, the two conductors have charges Q and – Q with potential difference between them. The ratio is a constant, denoted by C and is called the capacitance of the capacitor. It is independent of Q or V. It depends only on the geometrical configuration (shape, size, separation) of the two conductors and the medium separating the conductors. When a parallel plate capacitor is charged, the electric field is localised between the plates and is uniform throughout. When a slab of a dielectric is inserted between the charged plates (charge density ), the dielectric is polarised by the field. Consequently opposite charges appear on the faces of the slab, near the plates, with surface charge density of magnitude . For a linear dielectric is proportional to . Introduction of a dielectric changes the electric field, and hence, the capacitance of a capacitor, and hence, the energy stored in the capacitor. Like resistors, capacitors can also be arranged in series or in parallel or in a combination of series and parallel.Q.29 (i)1 markConsider a capacitor of capacitance C, with plate area A and plate separation d, filled with air [Fig. (a)]. The distance between the plates is increased to 2d and one of the plates is shifted as shown in Fig. (b). The capacitance of the new system now is :
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- Q.29 (ii)1 markA slab (area A and thickness ) of a linear dielectric of dielectric constant K is inserted between charged plates (charge density ) of a parallel plate capacitor [plate area A and plate separation ] and opposite charges with charge density of magnitude appear on the faces of the slab. The dielectric constant K is given by :
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- Q.29 (iii)1 markAn electric field E is established between the plates of an air filled parallel plate capacitor, with charges Q and – Q. V is the volume of the space enclosed between the plates. The energy stored in the capacitor is :
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- Q.29 (iv) (a)1 markThree capacitors A, B and M, each of capacitance C are connected to a capacitor N of capacitance 2C and a battery as shown in the figure. If the charges on A and N are Q and respectively, then is :
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OR
Q.29 (iv) (b)1 markA slab (area A and thickness ) of dielectric constant K is inserted in a parallel plate capacitor of plate area A and plate separation d. If C and are the capacitances of the capacitors with and without the dielectric, then is :Tap an option to check your answer.
- Extrinsic semiconductors are made by doping pure or intrinsic semiconductors with suitable impurity. There are two type of dopants used in doping, Si or Ge, and using them p-type and n-type semiconductors can be obtained. A p-n junction is the basic building block of many semiconductor devices. Two important processes occur during the formation of a p-n junction : diffusion and drift. When such a junction is formed, a 'depletion layer' is created consisting of immobile ion-cores. This is responsible for a junction potential barrier. The width of a depletion layer and the height of potential barrier changes when a junction is forward-biased or reverse-biased. A semiconductor diode is basically a p-n junction with metallic contacts provided at the ends for application of an external voltage. Using diodes, alternating voltages can be rectified.Q.30 (i)1 markWhich of the following is a donor impurity atom for Ge ?
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- Q.30 (ii)1 markWhen a pentavalent atom occupies the position of an atom in the crystal lattice of Si, four of its electrons form covalent bonds with four silicon neighbours, while the fifth remains bound to the parent atom. The energy required to set this electron free is about :
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- Q.30 (iii)1 markDuring formation of a p-n junction :
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- Q.30 (iv) (a)1 markIn reverse-biased p-n junction :
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OR
Q.30 (iv) (b)1 markThe output frequency of a full-wave rectifier with 50 Hz as input frequency is :Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) Write the principle of working of an ac generator. Draw its labelled diagram and explain its working. (ii) A resistor of 400 , an inductor of H and a capacitor of are joined in series across an ac source V. Find the rms voltages across these three circuit elements. The algebraic sum of these voltages is more than the rms voltage of source. Explain.
OR
Q.31 (b)5 marks(i) Write the principle of working of a transformer. With the help of a labelled diagram, explain the working of a step-up transformer. (ii) An ideal transformer is designed to convert 50 V into 250 V. It draws 200 W power from an ac source whose instantaneous voltage is given by V. Find : (I) rms value of input current. (II) expression for instantaneous output voltage. (III) expression for instantaneous output current.- Q.32 (a)5 marks(i) Draw a ray diagram to show the image formation by a compound microscope. Obtain the expression for the total magnification of the microscope when the final image is formed at infinity. (ii) In a compound microscope, an object is placed at a distance of cm from the objective of focal length cm. The eyepiece has a focal length of 5 cm. The final image is formed at infinity. Calculate the distance between the objective and the eyepiece.
OR
Q.32 (b)5 marks(i) Using Huygens' principle, explain the refraction of a plane wavefront, propagating in air, at a plane interface between air and glass. Hence verify Snell's law. (ii) Use mirror formula to deduce that a convex mirror always produces a virtual image of an object kept in front of it.- Q.33 (a)5 marks(i) The electric field in a region is given by N/C. Find the amount of work done in taking a unit positive charge from a point (0, 3m) to the point (5m, 0). (ii) A charge Q is distributed over two concentric hollow spheres of radii r and R (> r) such that their surface charge densities are equal. Find : (I) the electric field, and (II) the potential at their common centre.
OR
Q.33 (b)5 marks(i) Obtain an expression for the electric field due to a dipole of dipole moment at a point on its equatorial plane and specify its direction. Hence, find the value of electric field : (I) at the centre of the dipole (r = 0), and (II) at a point r >> a, where 2a is the length of the dipole. (ii) An electric field N/C exists in a region in which a cube of side L is kept as shown in the figure. Here x and L are in metres. Calculate the net flux through the cube.
Section A
1 mark each
- Q.11 markA wire of resistance R, connected to an ideal battery consumes a power P. If the wire is gradually stretched to double its initial length, and connected across the same battery, the power consumed will be :
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- Q.21 markA vertically held bar magnet is dropped along the axis of a copper ring having a cut as shown in the diagram. The acceleration of the falling magnet is :
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- Q.31 markA straight conductor is carrying a current of 2 A in +x direction along it. A uniform magnetic field T is switched on, in the region. The force acting on 10 cm length of the conductor is :
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- Q.41 markAn ac source is connected to a resistor and an inductor in series. The voltage across the resistor and inductor are 8 V and 6 V respectively. The voltage of the source is :
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- Q.51 markA proton and an -particle enter with the same velocity in a uniform magnetic field such that . The ratio of the radii of their paths is :
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- Q.61 markTwo coherent waves, each of intensity , produce interference pattern on a screen. The average intensity of light on the screen is :
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- Q.71 markIf and are the equivalent resistances of n resistors, each of value R, in series and parallel combinations respectively, then the value of is :
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- Q.81 markA galvanometer can be converted into an ammeter of desired range by connecting a :
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- Q.91 markInside a nucleus, the nuclear forces between proton and proton, proton and neutron, neutron and neutron are , and respectively. Then :
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- Q.101 markThe de Broglie wavelength associated with an electron moving with energy 5 eV is :
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- Q.111 markA piece of a diamagnetic material, free to move when placed in a uniform magnetic field :
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- Q.121 markThe momentum (in kg m/s) of a photon of frequency Hz is :
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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) : A hole is an apparent free particle with effective positive electronic charge. Reason (R) : A hole is not necessarily a vacancy left behind by an electron in the valence band.
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- Q.141 markAssertion (A) : In a reflecting telescope, the image does not have chromatic aberration. Reason (R) : Chromatic aberration occurs only due to refraction of light through an optical medium.
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- Q.151 markAssertion (A) : The binding energy per nucleon is practically constant for mass number in the range . Reason (R) : Nuclear forces between the nucleons for mass numbers in the range are not short-range.
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- Q.161 markAssertion (A) : X-rays are produced when slow moving electrons are stopped by a metal target of high atomic number. Reason (R) : X-rays consist of low-energy photons.
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Section B
2 marks each
- Q.172 marksA cell of emf E and internal resistance r is connected to an external variable resistance R. Plot a graph showing the variation of terminal voltage V of the cell as a function of current I, supplied by the cell. Explain how the emf of the cell and its internal resistance can be found from it.
- Q.182 marksIn an n-type semiconductor electron-hole combination is a continuous process at room temperature. Yet the electron concentration is always greater than the hole concentration in it. Explain.
- Q.192 marksA laser beam of wavelength 500 nm and power 5 mW strikes normally on a perfectly reflecting surface of area of a body. It rebounds back from the surface. Find the force exerted by the laser beam on the body.
- Q.202 marksA ray of light is incident on face AB of a prism ABC with angle of prism A and emerges out from face AC. The prism is set in the position of minimum deviation with angle of deviation . Find (i) the angle of incidence and (ii) the angle of refraction on face AB.
- Q.21 (a)2 marksFind the intensity at a point on the screen in Young's double slit experiment, at which the interfering waves of intensity each, have a path difference of (i) , and (ii) .
OR
Q.21 (b)2 marksA point source of light in air is kept at a distance of 12 cm in front of a convex spherical surface of glass of refractive index and radius of curvature 30 cm. Find the nature and position of the image formed.
Section C
3 marks each
- Q.223 marks(a) Define the term 'drift velocity' of conduction electrons in a conductor. (b) A conductor of length and area of cross-section A is connected across an ideal battery of emf V. Derive the formula for the current density in terms of relaxation time .
- Q.23 (a)3 marksState Lenz's law. A rod MN of length L is rotated about an axis passing through its end M perpendicular to its length, with a constant angular velocity in a uniform magnetic field parallel to the axis. Obtain an expression for emf induced between its ends.
OR
Q.23 (b)3 marksDefine 'self-inductance' of a coil. Derive an expression for self-inductance of a long solenoid of cross-sectional area A and length , having n turns per unit length.- Q.243 marksA ray of light is incident at an angle i on a parallel sided glass slab of thickness 'd' and gets refracted into the slab at angle r. Draw a ray diagram to show its path as its emerges out of the slab. Hence, obtain an expression for the lateral shift of the ray. Under what condition will the shift be minimum ?
- Q.253 marksDescribe briefly Geiger-Marsden scattering experiment. Depict the graph showing the variation of number of scattered particles detected with the scattering angle. How did this graph lead to the discovery of the nucleus ?
- Q.263 marksFind the Q value of the following nuclear reaction : Is this reaction exothermic or endothermic ? Given : u u u
- Q.273 marksA rectangular loop carries a current of 1 A. A straight long wire carrying 2 A current is kept near the loop in the same plane as shown in the figure. Find : (i) the torque acting on the loop, and (ii) the magnitude and direction of the net force on the loop.
- Q.283 marksName the electromagnetic wave used (i) in radar, (ii) in eye surgery and (iii) as diagnostic tool in medicine. Write their wavelength range also.
Section D
1 mark each
- Extrinsic semiconductors are made by doping pure or intrinsic semiconductors with suitable impurity. There are two type of dopants used in doping, Si or Ge, and using them p-type and n-type semiconductors can be obtained. A p-n junction is the basic building block of many semiconductor devices. Two important processes occur during the formation of a p-n junction : diffusion and drift. When such a junction is formed, a 'depletion layer' is created consisting of immobile ion-cores. This is responsible for a junction potential barrier. The width of a depletion layer and the height of potential barrier changes when a junction is forward-biased or reverse-biased. A semiconductor diode is basically a p-n junction with metallic contacts provided at the ends for application of an external voltage. Using diodes, alternating voltages can be rectified.Q.29 (i)1 markWhich of the following is a donor impurity atom for Ge ?
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- Q.29 (ii)1 markWhen a pentavalent atom occupies the position of an atom in the crystal lattice of Si, four of its electrons form covalent bonds with four silicon neighbours, while the fifth remains bound to the parent atom. The energy required to set this electron free is about :
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- Q.29 (iii)1 markDuring formation of a p-n junction :
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- Q.29 (iv) (a)1 markIn reverse-biased p-n junction :
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OR
Q.29 (iv) (b)1 markThe output frequency of a full-wave rectifier with 50 Hz as input frequency is :Tap an option to check your answer.
- A capacitor is a system of two conductors separated by an insulator. In practice, the two conductors have charges Q and – Q with potential difference between them. The ratio is a constant, denoted by C and is called the capacitance of the capacitor. It is independent of Q or V. It depends only on the geometrical configuration (shape, size, separation) of the two conductors and the medium separating the conductors. When a parallel plate capacitor is charged, the electric field is localised between the plates and is uniform throughout. When a slab of a dielectric is inserted between the charged plates (charge density ), the dielectric is polarised by the field. Consequently opposite charges appear on the faces of the slab, near the plates, with surface charge density of magnitude . For a linear dielectric is proportional to . Introduction of a dielectric changes the electric field, and hence, the capacitance of a capacitor, and hence, the energy stored in the capacitor. Like resistors, capacitors can also be arranged in series or in parallel or in a combination of series and parallel.Q.30 (i)1 markConsider a capacitor of capacitance C, with plate area A and plate separation d, filled with air [Fig. (a)]. The distance between the plates is increased to 2d and one of the plates is shifted as shown in Fig. (b). The capacitance of the new system now is :
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- Q.30 (ii)1 markA slab (area A and thickness ) of a linear dielectric of dielectric constant K is inserted between charged plates (charge density ) of a parallel plate capacitor [plate area A and plate separation ] and opposite charges with charge density of magnitude appear on the faces of the slab. The dielectric constant K is given by :
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- Q.30 (iii)1 markAn electric field E is established between the plates of an air filled parallel plate capacitor, with charges Q and – Q. V is the volume of the space enclosed between the plates. The energy stored in the capacitor is :
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- Q.30 (iv) (a)1 markThree capacitors A, B and M, each of capacitance C are connected to a capacitor N of capacitance 2C and a battery as shown in the figure. If the charges on A and N are Q and respectively, then is :
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OR
Q.30 (iv) (b)1 markA slab (area A and thickness ) of dielectric constant K is inserted in a parallel plate capacitor of plate area A and plate separation d. If C and are the capacitances of the capacitors with and without the dielectric, then is :Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) Draw a ray diagram to show the image formation by a compound microscope. Obtain the expression for the total magnification of the microscope when the final image is formed at infinity. (ii) In a compound microscope, an object is placed at a distance of cm from the objective of focal length cm. The eyepiece has a focal length of 5 cm. The final image is formed at infinity. Calculate the distance between the objective and the eyepiece.
OR
Q.31 (b)5 marks(i) Using Huygens' principle, explain the refraction of a plane wavefront, propagating in air, at a plane interface between air and glass. Hence verify Snell's law. (ii) Use mirror formula to deduce that a convex mirror always produces a virtual image of an object kept in front of it.- Q.32 (a)5 marks(i) The electric field in a region is given by N/C. Find the amount of work done in taking a unit positive charge from a point (0, 3m) to the point (5m, 0). (ii) A charge Q is distributed over two concentric hollow spheres of radii r and R (> r) such that their surface charge densities are equal. Find : (I) the electric field, and (II) the potential at their common centre.
OR
Q.32 (b)5 marks(i) Obtain an expression for the electric field due to a dipole of dipole moment at a point on its equatorial plane and specify its direction. Hence, find the value of electric field : (I) at the centre of the dipole (r = 0), and (II) at a point r >> a, where 2a is the length of the dipole. (ii) An electric field N/C exists in a region in which a cube of side L is kept as shown in the figure. Here x and L are in metres. Calculate the net flux through the cube.- Q.33 (a)5 marks(i) Write the principle of working of an ac generator. Draw its labelled diagram and explain its working. (ii) A resistor of 400 , an inductor of H and a capacitor of are joined in series across an ac source V. Find the rms voltages across these three circuit elements. The algebraic sum of these voltages is more than the rms voltage of source. Explain.
OR
Q.33 (b)5 marks(i) Write the principle of working of a transformer. With the help of a labelled diagram, explain the working of a step-up transformer. (ii) An ideal transformer is designed to convert 50 V into 250 V. It draws 200 W power from an ac source whose instantaneous voltage is given by V. Find : (I) rms value of input current. (II) expression for instantaneous output voltage. (III) expression for instantaneous output current.
Section A
1 mark each
- Q.11 markThe ratio of potential difference across AB in the circuit shown for the case (i) when switch S is closed and (ii) when S is open is :
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- Q.21 markTwo coherent waves, each of intensity , produce interference pattern on a screen. The average intensity of light on the screen is :
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- Q.31 markA particle of mass m and charge q moving with velocity is subjected to a uniform electric field . The particle will initially have a tendency to move in a circle of radius :
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- Q.41 markA vertically held bar magnet is dropped along the axis of a copper ring having a cut as shown in the diagram. The acceleration of the falling magnet is :
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- Q.51 markInside a nucleus, the nuclear forces between proton and proton, proton and neutron, neutron and neutron are , and respectively. Then :
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- Q.61 markAn ac source is connected to a resistor and an inductor in series. The voltage across the resistor and inductor are 8 V and 6 V respectively. The voltage of the source is :
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- Q.71 markA proton and an -particle enter with the same velocity in a uniform magnetic field such that . The ratio of the radii of their paths is :
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- Q.81 markIf and are the equivalent resistances of n resistors, each of value R, in series and parallel combinations respectively, then the value of is :
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- Q.91 markA piece of a diamagnetic material, free to move when placed in a uniform magnetic field :
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- Q.101 markThe wavelength of a photon is equal to the wavelength associated with an electron. Both will have the same value of :
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- Q.111 markA galvanometer can be converted into an ammeter of desired range by connecting a :
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- Q.121 markThe momentum (in kg m/s) of a photon of frequency Hz is :
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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) : X-rays are produced when slow moving electrons are stopped by a metal target of high atomic number. Reason (R) : X-rays consist of low-energy photons.
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- Q.141 markAssertion (A) : The binding energy per nucleon is practically constant for mass number in the range . Reason (R) : Nuclear forces between the nucleons for mass numbers in the range are not short-range.
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- Q.151 markAssertion (A) : In a reflecting telescope, the image does not have chromatic aberration. Reason (R) : Chromatic aberration occurs only due to refraction of light through an optical medium.
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- Q.161 markAssertion (A) : A hole is an apparent free particle with effective positive electronic charge. Reason (R) : A hole is not necessarily a vacancy left behind by an electron in the valence band.
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Section B
2 marks each
- Q.172 marksIn an n-type semiconductor electron-hole combination is a continuous process at room temperature. Yet the electron concentration is always greater than the hole concentration in it. Explain.
- Q.182 marks(a) What is the difference between 'velocity' and 'drift velocity' of electrons in a current-carrying conductor. (b) A copper wire of uniform cross-sectional area carries a current of A. The drift velocity of conduction electrons is mm/s. If the number density of electrons in copper is m, find the area of cross-section of the wire.
- Q.19 (a)2 marksFind the intensity at a point on the screen in Young's double slit experiment, at which the interfering waves of intensity each, have a path difference of (i) , and (ii) .
OR
Q.19 (b)2 marksA point source of light in air is kept at a distance of 12 cm in front of a convex spherical surface of glass of refractive index and radius of curvature 30 cm. Find the nature and position of the image formed.- Q.202 marksAn alpha particle and a deuterium ion are accelerated through the same potential difference. These are then directed towards a target nucleus to make head-on collision. It is observed that their distance of closest approach is the same. Justify it theoretically.
- Q.212 marksA tank is filled with a liquid of refractive index , up to a height of 30 cm. A tiny bulb is glowing at the bottom of the tank. Calculate the diameter of an opaque disc floating symmetrically on the liquid surface that can cut off completely the light from the bulb that comes out of the liquid surface.
Section C
3 marks each
- Q.223 marksName the electromagnetic wave used (i) in radar, (ii) in eye surgery and (iii) as diagnostic tool in medicine. Write their wavelength range also.
- Q.233 marks(a) Differentiate between 'nuclear fission' and 'nuclear fusion'. Briefly discuss one example of each. (b) Draw a graph of potential energy between a pair of nucleons as a function of their separation.
- Q.243 marksA rectangular loop carries a current of 1 A. A straight long wire carrying 2 A current is kept near the loop in the same plane as shown in the figure. Find : (i) the torque acting on the loop, and (ii) the magnitude and direction of the net force on the loop.
- Q.253 marks(a) A concave mirror has radius of curvature 20 cm. Calculate the distance of an object from the mirror so as to form an image of magnification – 2. Also find the location of the image. (b) If the silver coating around the centre of a concave mirror is removed, will the mirror still form the image of an object ? Justify your answer.
- Q.263 marksState Kirchhoff's laws. Apply these laws to find the values of current flowing in the three branches of the given circuit.
- Q.273 marksIn Bohr model of hydrogen atom, an electron is revolving in second orbit. Find the value of : (i) angular momentum of electron, (ii) radius of the orbit, and (iii) kinetic energy of electron. Take radius of first orbit of hydrogen atom as .
- Q.28 (a)3 marksState Lenz's law. A rod MN of length L is rotated about an axis passing through its end M perpendicular to its length, with a constant angular velocity in a uniform magnetic field parallel to the axis. Obtain an expression for emf induced between its ends.
OR
Q.28 (b)3 marksDefine 'self-inductance' of a coil. Derive an expression for self-inductance of a long solenoid of cross-sectional area A and length , having n turns per unit length.
Section D
1 mark each
- A capacitor is a system of two conductors separated by an insulator. In practice, the two conductors have charges Q and – Q with potential difference between them. The ratio is a constant, denoted by C and is called the capacitance of the capacitor. It is independent of Q or V. It depends only on the geometrical configuration (shape, size, separation) of the two conductors and the medium separating the conductors. When a parallel plate capacitor is charged, the electric field is localised between the plates and is uniform throughout. When a slab of a dielectric is inserted between the charged plates (charge density ), the dielectric is polarised by the field. Consequently opposite charges appear on the faces of the slab, near the plates, with surface charge density of magnitude . For a linear dielectric is proportional to . Introduction of a dielectric changes the electric field, and hence, the capacitance of a capacitor, and hence, the energy stored in the capacitor. Like resistors, capacitors can also be arranged in series or in parallel or in a combination of series and parallel.Q.29 (i) (a)1 markThree capacitors A, B and M, each of capacitance C are connected to a capacitor N of capacitance 2C and a battery as shown in the figure. If the charges on A and N are Q and respectively, then is :
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OR
Q.29 (i) (b)1 markA slab (area A and thickness ) of dielectric constant K is inserted in a parallel plate capacitor of plate area A and plate separation d. If C and are the capacitances of the capacitors with and without the dielectric, then is :Tap an option to check your answer.
- Q.29 (ii)1 markAn electric field E is established between the plates of an air filled parallel plate capacitor, with charges Q and – Q. V is the volume of the space enclosed between the plates. The energy stored in the capacitor is :
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- Q.29 (iii)1 markA slab (area A and thickness ) of a linear dielectric of dielectric constant K is inserted between charged plates (charge density ) of a parallel plate capacitor [plate area A and plate separation ] and opposite charges with charge density of magnitude appear on the faces of the slab. The dielectric constant K is given by :
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- Q.29 (iv)1 markConsider a capacitor of capacitance C, with plate area A and plate separation d, filled with air [Fig. (a)]. The distance between the plates is increased to 2d and one of the plates is shifted as shown in Fig. (b). The capacitance of the new system now is :
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- Extrinsic semiconductors are made by doping pure or intrinsic semiconductors with suitable impurity. There are two type of dopants used in doping, Si or Ge, and using them p-type and n-type semiconductors can be obtained. A p-n junction is the basic building block of many semiconductor devices. Two important processes occur during the formation of a p-n junction : diffusion and drift. When such a junction is formed, a 'depletion layer' is created consisting of immobile ion-cores. This is responsible for a junction potential barrier. The width of a depletion layer and the height of potential barrier changes when a junction is forward-biased or reverse-biased. A semiconductor diode is basically a p-n junction with metallic contacts provided at the ends for application of an external voltage. Using diodes, alternating voltages can be rectified.Q.30 (i) (a)1 markIn reverse-biased p-n junction :
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OR
Q.30 (i) (b)1 markThe output frequency of a full-wave rectifier with 50 Hz as input frequency is :Tap an option to check your answer.
- Q.30 (ii)1 markDuring formation of a p-n junction :
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- Q.30 (iii)1 markWhen a pentavalent atom occupies the position of an atom in the crystal lattice of Si, four of its electrons form covalent bonds with four silicon neighbours, while the fifth remains bound to the parent atom. The energy required to set this electron free is about :
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- Q.30 (iv)1 markWhich of the following is a donor impurity atom for Ge ?
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Section E
5 marks each
- Q.31 (a)5 marks(i) The electric field in a region is given by N/C. Find the amount of work done in taking a unit positive charge from a point (0, 3m) to the point (5m, 0). (ii) A charge Q is distributed over two concentric hollow spheres of radii r and R (> r) such that their surface charge densities are equal. Find : (I) the electric field, and (II) the potential at their common centre.
OR
Q.31 (b)5 marks(i) Obtain an expression for the electric field due to a dipole of dipole moment at a point on its equatorial plane and specify its direction. Hence, find the value of electric field : (I) at the centre of the dipole (r = 0), and (II) at a point r >> a, where 2a is the length of the dipole. (ii) An electric field N/C exists in a region in which a cube of side L is kept as shown in the figure. Here x and L are in metres. Calculate the net flux through the cube.- Q.32 (a)5 marks(i) Write the principle of working of an ac generator. Draw its labelled diagram and explain its working. (ii) A resistor of 400 , an inductor of H and a capacitor of are joined in series across an ac source V. Find the rms voltages across these three circuit elements. The algebraic sum of these voltages is more than the rms voltage of source. Explain.
OR
Q.32 (b)5 marks(i) Write the principle of working of a transformer. With the help of a labelled diagram, explain the working of a step-up transformer. (ii) An ideal transformer is designed to convert 50 V into 250 V. It draws 200 W power from an ac source whose instantaneous voltage is given by V. Find : (I) rms value of input current. (II) expression for instantaneous output voltage. (III) expression for instantaneous output current.- Q.33 (a)5 marks(i) Draw a ray diagram to show the image formation by a compound microscope. Obtain the expression for the total magnification of the microscope when the final image is formed at infinity. (ii) In a compound microscope, an object is placed at a distance of cm from the objective of focal length cm. The eyepiece has a focal length of 5 cm. The final image is formed at infinity. Calculate the distance between the objective and the eyepiece.
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Q.33 (b)5 marks(i) Using Huygens' principle, explain the refraction of a plane wavefront, propagating in air, at a plane interface between air and glass. Hence verify Snell's law. (ii) Use mirror formula to deduce that a convex mirror always produces a virtual image of an object kept in front of it.