CBSE Class 12 Physics 2025 question paper (55/5)
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 markA metal sheet is inserted between the plates of a parallel plate capacitor of capacitance C. If the sheet partly occupies the space between the plates, the capacitance :
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- Q.21 markThe electric field at a point in a region is given by , where is a constant and r is the distance of the point from the origin. The magnitude of potential of the point is :
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- Q.31 markFour resistors, each of resistance R and a key K are connected as shown in the figure. The equivalent resistance between points A and B when key K is open, will be :
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- Q.41 markA charged particle gains a speed of , when accelerated from rest through a potential difference 10 kV. It enters a region of magnetic field of T such that . The radius of circular path described by it is :
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- Q.51 markA current of A is maintained in a circular loop of radius 14 cm. The value of dipole moment associated with the loop is :
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- Q.61 markThe magnetic flux linked with a coil changes with time t as , where t is in seconds and is in Wb. The value of emf induced in the coil at s is :
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- Q.71 markWhich of the following rays coming from the Sun plays an important role in maintaining the Earth's warmth ?
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- Q.81 markThe dimensions of , where is permittivity and is permeability of a medium, are :
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- Q.91 markWhich of the following electromagnetic waves has photons of largest momentum ?
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- Q.101 markA compound microscope has an objective and an eyepiece of focal lengths and , respectively. To obtain a large magnification of a small object, the microscope should have :
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- Q.111 markTwo coherent light waves, each having amplitude 'a', superpose to produce an interference pattern on a screen. The intensity of light as seen on the screen varies between :
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- Q.121 markThe kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio of de Broglie wavelengths associated with them will be :
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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) : The impurities in p-type Si are not pentavalent atoms. Reason (R) : The hole density in valance band in p-type semiconductor is almost equal to the acceptor density.
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- Q.141 markAssertion (A) : During formation of a nucleus, the mass defect produced is the source of the binding energy of the nucleus. Reason (R) : For all nuclei, the value of binding energy per nucleon increases with mass number.
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- Q.151 markAssertion (A) : The Balmer series in hydrogen atom spectrum is formed when the electron jumps from higher energy state to the ground state. Reason (R) : In Bohr's model of hydrogen atom, the electron can jump between successive orbits only.
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- Q.161 markAssertion (A) : In Rutherford's alpha particle scattering experiment, the presence of only few alpha particles at angle of scattering led him to the discovery of nucleus. Reason (R) : The size of nucleus is approximately times the size of an atom and therefore only few alpha particles are rebounded.
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Section B
2 marks each
- Q.172 marksThe threshold frequency for a given metal is Hz. If monochromatic radiations of frequency Hz are incident on this metal, find the cut-off potential for the photoelectrons.
- Q.18 (a)2 marksA point object is placed in air at a distance R/3 in front of a convex surface of radius of curvature R, separating air from a medium of refractive index n (< 4). Find the nature and position of the image formed.
OR
Q.18 (b)2 marksIn Young's double slit experimental set-up, the intensity of the central maximum is . Calculate the intensity at a point where the path difference between two interfering waves is .- Q.192 marksA voltmeter of resistance 1000 can measure up to 25 V. How will you convert it so that it can read up to 250 V ?
- Q.202 marksWhen a neutron collides with , the nucleus gives and as fission products and two neutrons are ejected. Calculate the mass defect and the energy released (in MeV) in the process. Given : u, u u, u u MeV/
- Q.212 marksThe resistance of a wire at C is . When heated to C, its resistance becomes . Find (i) the temperature coefficient of resistance of the wire, and (ii) the resistance of the wire at C.
Section C
3 marks each
- Q.223 marks(a) Draw the energy-band diagrams for conductors, semiconductors and insulators at K. How is an electron-hole pair formed in a semiconductor at room temperature ? (b) Carbon and silicon both, are members of IV group of periodic table and have the same lattice structure. Carbon is an insulator whereas silicon is a semiconductor. Explain.
- Q.233 marksA parallel plate capacitor has plate area A and plate separation d. Half of the space between the plates is filled with a material of dielectric constant K in two ways as shown in the figure. Find the values of the capacitance of the capacitors in the two cases.
- Q.243 marksIn Young's double slit experiment, the separation between the two slits is mm and the screen is m away from the slits. A beam of light consisting of two wavelengths 500 nm and 600 nm is used to obtain interference fringes. Calculate : (a) the distance between the first maxima for the two wavelengths. (b) the least distance from the central maximum, where the bright fringes due to both the wavelengths coincide.
- Q.253 marksDifferentiate between half-wave and full-wave rectification. With the help of a circuit diagram, explain the working of a full-wave rectifier.
- Q.263 marksAn electron of mass m and charge is revolving anticlockwise around the nucleus of an atom. (a) Obtain the expression for the magnetic dipole moment of the atom. (b) If is the angular momentum of electron, show that .
- Q.273 marksA rectangular glass slab ABCD (refractive index ) is surrounded by a transparent liquid (refractive index ) as shown in the figure. A ray of light is incident on face AB at an angle i such that it is refracted out grazing the face AD. Find the value of angle i.
- Q.28 (a)3 marksTwo small solid metal balls A and B of radii R and 2R having charge densities and respectively are kept far apart. Find the charge densities on A and B after they are connected by a conducting wire.
OR
Q.28 (b)3 marksTwo infinitely long straight wires '1' and '2' are placed d distance apart, parallel to each other, as shown in the figure. They are uniformly charged having charge densities and respectively. Locate the position of the point from wire '1' at which the net electric field is zero and identify the region in which it lies.
Section D
1 mark each
- A galvanometer is an instrument used to show the direction and strength of the current passing through it. In a galvanometer, a coil placed in a magnetic field experiences a torque and hence gets deflected when a current passes through it. The name is derived from the surname of Italian scientist L. Galvani, who in 1791 discovered that electric current makes a dead frog's leg jerk. A spring attached with the coil provides a counter torque. In equilibrium, the deflecting torque is balanced by the restoring torque of the spring and we have : where N is the total number of turns in the coil A is the area of cross-section of each turn B is the radial magnetic field k is the torsional constant of the spring is the angular deflection of the coil As the current which produces full scale deflection in the galvanometer is very small, the galvanometer cannot as such be used to measure current in electric circuits. A small resistance, called shunt, of a suitable value is connected with the galvanometer to convert it into an ammeter of desired range. By using a higher resistance, a galvanometer can also be converted into a voltmeter.Q.29 (i)1 markThe value of the current sensitivity of a galvanometer is given by :
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- Q.29 (ii)1 markA galvanometer of resistance 6 shows full scale deflection for a current of A. The value of shunt to be used with this galvanometer to convert it into an ammeter of range A is :
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- Q.29 (iii)1 markThe value of resistance of the ammeter in case (ii) will be :
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- Q.29 (iv) (a)1 markA galvanometer is converted into a voltmeter of range by connecting with it, a resistance . If is replaced by , the range becomes . The resistance of the galvanometer is :
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OR
Q.29 (iv) (b)1 markA current of 5 mA flows through a galvanometer. Its coil has 100 turns, each of area of cross-section and is suspended in a magnetic field T. The deflecting torque acting on the coil will be :Tap an option to check your answer.
- Einstein explained photoelectric effect on the basis of Planck's quantum theory, where light travels in the form of small bundles of energy called photons. The energy of each photon is , where is the frequency of incident light and h is Planck's constant. The number of photons in a beam of light determines the intensity of the incident light. A photon incident on a metal surface transfers its total energy to a free electron in the metal. A part of this energy is used in ejecting the electron from the metal and is called its work function. The rest of the energy is carried by the ejected electron as its kinetic energy.Q.30 (i)1 markWhich of the following graphs shows the variation of photoelectric current I with the intensity of light ?
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- Q.30 (ii)1 markWhen the frequency of the incident light is increased without changing its intensity, the saturation current :
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- Q.30 (iii)1 markWhich of the following graphs can be used to obtain the value of Planck's constant ?
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- Q.30 (iv) (a)1 markRed light, yellow light and blue light of the same intensity are incident on a metal surface successively. , and represent the maximum kinetic energy of photoelectrons respectively, then :
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OR
Q.30 (iv) (b)1 markWhich of the following metals exhibits photoelectric effect with visible light ?Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) Three batteries , and of emfs and internal resistances V, , V, and V, respectively are connected as shown in the figure. Find the values of the currents passing through batteries , and . (ii) The ends of six wires, each of resistance R are joined as shown in the figure. The points A and B of the arrangement are connected in a circuit. Find the value of the effective resistance offered by it to the circuit.
OR
Q.31 (b)5 marks(i) Current I A is passing through a copper rod of varying cross-sections as shown in the figure. The areas of cross-section at points A and B along its length are and respectively. Calculate : (I) the ratio of electric fields at points A and B. (II) the drift velocity of free electrons at point B. (ii) Two point charges and are placed at points m and m. Find the net electric field at point m m.- Q.32 (a)5 marks(i) Define self-inductance of a coil. Derive the expression for the energy required to build up a current I in a coil of self-inductance L. (ii) The currents passing through two inductors of self-inductances 10 mH and 20 mH increase with time at the same rate. Draw graphs showing the variation of : (I) the magnitude of emf induced with the rate of change of current in each inductor. (II) the energy stored in each inductor with the current flowing through it.
OR
Q.32 (b)5 marks(i) Define the term mutual inductance. Deduce the expression for the mutual inductance of two long coaxial solenoids of the same length having different radii and different number of turns. (ii) The current through an inductor is uniformly increased from zero to 2 A in 40 s. An emf of 5 mV is induced during this period. Find the flux linked with the inductor at s.- Q.33 (a)5 marks(i) Draw a ray diagram of a reflecting telescope (Cassegrain) and explain the formation of image. State two important advantages that a reflecting telescope has over a refracting telescope. (ii) In a refracting telescope, the focal length of the objective is 50 times the focal length of the eyepiece. When the final image is formed at infinity, the length of the tube is 102 cm. Find the focal lengths of the two lenses.
OR
Q.33 (b)5 marks(i) Write any two advantages of a compound microscope over a simple microscope. Draw a ray diagram for the image formation at the near point by a compound microscope and explain it. (ii) A thin planoconcave lens with its curved face of radius of curvature R is made of glass of refractive index . It is placed coaxially in contact with a thin equiconvex lens of same radius of curvature of refractive index . Obtain the power of the combination lens.
Section A
1 mark each
- Q.11 markWhich of the following rays coming from the Sun plays an important role in maintaining the Earth's warmth ?
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- Q.21 markThe effective capacitance of the network between points A and B shown in the figure is :
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- Q.31 markThe electric field at a point in a region is given by , where is a constant and r is the distance of the point from the origin. The magnitude of potential of the point is :
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- Q.41 markTwo coherent light waves, each having amplitude 'a', superpose to produce an interference pattern on a screen. The intensity of light as seen on the screen varies between :
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- Q.51 markA current of A is maintained in a circular loop of radius 14 cm. The value of dipole moment associated with the loop is :
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- Q.61 markA transformer is a device used for converting :
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- Q.71 markFour resistors, each of resistance R and a key K are connected as shown in the figure. The equivalent resistance between points A and B when key K is open, will be :
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- Q.81 markWhich of the following electromagnetic waves has photons of largest momentum ?
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- Q.91 markThe kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio of de Broglie wavelengths associated with them will be :
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- Q.101 markA glass slab () of thickness 6 cm is placed over a paper. The shift in the letters printed on the paper will be :
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- Q.111 markThe dimensions of , where is permittivity and is permeability of a medium, are :
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- Q.121 markA charged particle gains a speed of , when accelerated from rest through a potential difference 10 kV. It enters a region of magnetic field of T such that . The radius of circular path described by it 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) : In Rutherford's alpha particle scattering experiment, the presence of only few alpha particles at angle of scattering led him to the discovery of nucleus. Reason (R) : The size of nucleus is approximately times the size of an atom and therefore only few alpha particles are rebounded.
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- Q.141 markAssertion (A) : The Balmer series in hydrogen atom spectrum is formed when the electron jumps from higher energy state to the ground state. Reason (R) : In Bohr's model of hydrogen atom, the electron can jump between successive orbits only.
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- Q.151 markAssertion (A) : During formation of a nucleus, the mass defect produced is the source of the binding energy of the nucleus. Reason (R) : For all nuclei, the value of binding energy per nucleon increases with mass number.
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- Q.161 markAssertion (A) : The impurities in p-type Si are not pentavalent atoms. Reason (R) : The hole density in valance band in p-type semiconductor is almost equal to the acceptor density.
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Section B
2 marks each
- Q.17 (a)2 marksA point object is placed in air at a distance R/3 in front of a convex surface of radius of curvature R, separating air from a medium of refractive index n (< 4). Find the nature and position of the image formed.
OR
Q.17 (b)2 marksIn Young's double slit experimental set-up, the intensity of the central maximum is . Calculate the intensity at a point where the path difference between two interfering waves is .- Q.182 marksA wire of resistance X ohm is gradually stretched till its length becomes twice its original length. If its new resistance becomes 40 , find the value of X.
- Q.192 marksA circular coil of wire having 200 turns, each of radius cm is placed in a horizontal plane. It carries a current of A in clockwise direction. Find the magnitude and direction of the magnetic field at the centre of the coil.
- Q.202 marks(a) Why is the mass of a nucleus always less than the sum of the masses of its constituents, i.e. free neutrons and free protons ? (b) How is Coulomb repulsion between protons in a nucleus overcome ? Explain.
- Q.212 marksThe threshold frequency for a given metal is Hz. If monochromatic radiations of frequency Hz are incident on this metal, find the cut-off potential for the photoelectrons.
Section C
3 marks each
- Q.22 (a)3 marksTwo small solid metal balls A and B of radii R and 2R having charge densities and respectively are kept far apart. Find the charge densities on A and B after they are connected by a conducting wire.
OR
Q.22 (b)3 marksTwo infinitely long straight wires '1' and '2' are placed d distance apart, parallel to each other, as shown in the figure. They are uniformly charged having charge densities and respectively. Locate the position of the point from wire '1' at which the net electric field is zero and identify the region in which it lies.- Q.233 marks(a) Draw the energy-band diagrams for conductors, semiconductors and insulators at K. How is an electron-hole pair formed in a semiconductor at room temperature ? (b) Carbon and silicon both, are members of IV group of periodic table and have the same lattice structure. Carbon is an insulator whereas silicon is a semiconductor. Explain.
- Q.243 marksA capacitor of plate area A and plate separation d is charged by a battery to voltage V. The battery is disconnected and plates are slowly pulled apart till the separation becomes 2d. Find the value of : (a) potential difference between the plates, (b) electric field between the plates, (c) work done in pulling the plates apart.
- Q.253 marksUsing the Huygens' principle, briefly describe reflection of a plane wavefront from a reflecting surface. Hence, prove the laws of reflection.
- Q.263 marksAn air bubble is trapped at point P (CP = cm) in a spherical glass ball (n = ) of radius 7 cm as shown in the figure. Find the nature and position of the image when viewed from side B. Show the image formation by drawing a ray diagram.
- Q.273 marks(a) Use Ampere's law to derive the expression for the magnetic field due to a long straight current carrying wire of infinite length. (b) Why is Ampere's law used for the derivation in (a) above and not Biot-Savart's law ? Explain.
- Q.283 marksDifferentiate between half-wave and full-wave rectification. With the help of a circuit diagram, explain the working of a full-wave rectifier.
Section D
1 mark each
- Einstein explained photoelectric effect on the basis of Planck's quantum theory, where light travels in the form of small bundles of energy called photons. The energy of each photon is , where is the frequency of incident light and h is Planck's constant. The number of photons in a beam of light determines the intensity of the incident light. A photon incident on a metal surface transfers its total energy to a free electron in the metal. A part of this energy is used in ejecting the electron from the metal and is called its work function. The rest of the energy is carried by the ejected electron as its kinetic energy.Q.29 (i)1 markWhich of the following graphs shows the variation of photoelectric current I with the intensity of light ?
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- Q.29 (ii)1 markWhen the frequency of the incident light is increased without changing its intensity, the saturation current :
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- Q.29 (iii)1 markWhich of the following graphs can be used to obtain the value of Planck's constant ?
Tap an option to check your answer.
- Q.29 (iv) (a)1 markRed light, yellow light and blue light of the same intensity are incident on a metal surface successively. , and represent the maximum kinetic energy of photoelectrons respectively, then :
Tap an option to check your answer.
OR
Q.29 (iv) (b)1 markWhich of the following metals exhibits photoelectric effect with visible light ?Tap an option to check your answer.
- A galvanometer is an instrument used to show the direction and strength of the current passing through it. In a galvanometer, a coil placed in a magnetic field experiences a torque and hence gets deflected when a current passes through it. The name is derived from the surname of Italian scientist L. Galvani, who in 1791 discovered that electric current makes a dead frog's leg jerk. A spring attached with the coil provides a counter torque. In equilibrium, the deflecting torque is balanced by the restoring torque of the spring and we have : where N is the total number of turns in the coil A is the area of cross-section of each turn B is the radial magnetic field k is the torsional constant of the spring is the angular deflection of the coil As the current which produces full scale deflection in the galvanometer is very small, the galvanometer cannot as such be used to measure current in electric circuits. A small resistance, called shunt, of a suitable value is connected with the galvanometer to convert it into an ammeter of desired range. By using a higher resistance, a galvanometer can also be converted into a voltmeter.Q.30 (i)1 markThe value of the current sensitivity of a galvanometer is given by :
Tap an option to check your answer.
- Q.30 (ii)1 markA galvanometer of resistance 6 shows full scale deflection for a current of A. The value of shunt to be used with this galvanometer to convert it into an ammeter of range A is :
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- Q.30 (iii)1 markThe value of resistance of the ammeter in case (ii) will be :
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- Q.30 (iv) (a)1 markA galvanometer is converted into a voltmeter of range by connecting with it, a resistance . If is replaced by , the range becomes . The resistance of the galvanometer is :
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OR
Q.30 (iv) (b)1 markA current of 5 mA flows through a galvanometer. Its coil has 100 turns, each of area of cross-section and is suspended in a magnetic field T. The deflecting torque acting on the coil will be :Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) Define self-inductance of a coil. Derive the expression for the energy required to build up a current I in a coil of self-inductance L. (ii) The currents passing through two inductors of self-inductances 10 mH and 20 mH increase with time at the same rate. Draw graphs showing the variation of : (I) the magnitude of emf induced with the rate of change of current in each inductor. (II) the energy stored in each inductor with the current flowing through it.
OR
Q.31 (b)5 marks(i) Define the term mutual inductance. Deduce the expression for the mutual inductance of two long coaxial solenoids of the same length having different radii and different number of turns. (ii) The current through an inductor is uniformly increased from zero to 2 A in 40 s. An emf of 5 mV is induced during this period. Find the flux linked with the inductor at s.- Q.32 (a)5 marks(i) Draw a ray diagram of a reflecting telescope (Cassegrain) and explain the formation of image. State two important advantages that a reflecting telescope has over a refracting telescope. (ii) In a refracting telescope, the focal length of the objective is 50 times the focal length of the eyepiece. When the final image is formed at infinity, the length of the tube is 102 cm. Find the focal lengths of the two lenses.
OR
Q.32 (b)5 marks(i) Write any two advantages of a compound microscope over a simple microscope. Draw a ray diagram for the image formation at the near point by a compound microscope and explain it. (ii) A thin planoconcave lens with its curved face of radius of curvature R is made of glass of refractive index . It is placed coaxially in contact with a thin equiconvex lens of same radius of curvature of refractive index . Obtain the power of the combination lens.- Q.33 (a)5 marks(i) Three batteries , and of emfs and internal resistances V, , V, and V, respectively are connected as shown in the figure. Find the values of the currents passing through batteries , and . (ii) The ends of six wires, each of resistance R are joined as shown in the figure. The points A and B of the arrangement are connected in a circuit. Find the value of the effective resistance offered by it to the circuit.
OR
Q.33 (b)5 marks(i) Current I A is passing through a copper rod of varying cross-sections as shown in the figure. The areas of cross-section at points A and B along its length are and respectively. Calculate : (I) the ratio of electric fields at points A and B. (II) the drift velocity of free electrons at point B. (ii) Two point charges and are placed at points m and m. Find the net electric field at point m m.
Section A
1 mark each
- Q.11 markA beam of light of wavelength 720 nm in air enters water (refractive index = ). Its wavelength in water will be :
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- Q.21 markA capacitor of capacitance C has reactance X in an ac circuit. If the capacitance and the frequency of the applied voltage are doubled, the new reactance will become :
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- Q.31 markFour point charges Q each, are held at the four corners of a square of side . The amount of work done in bringing a charge Q from infinity to the centre of the square will be :
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- Q.41 markA metal sheet is inserted between the plates of a parallel plate capacitor of capacitance C. If the sheet partly occupies the space between the plates, the capacitance :
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- Q.51 markFour resistors, each of resistance R and a key K are connected as shown in the figure. The equivalent resistance between points A and B when key K is open, will be :
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- Q.61 markA charged particle gains a speed of , when accelerated from rest through a potential difference 10 kV. It enters a region of magnetic field of T such that . The radius of circular path described by it is :
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- Q.71 markA current of A is maintained in a circular loop of radius 14 cm. The value of dipole moment associated with the loop is :
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- Q.81 markWhich of the following rays coming from the Sun plays an important role in maintaining the Earth's warmth ?
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- Q.91 markThe dimensions of , where is permittivity and is permeability of a medium, are :
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- Q.101 markWhich of the following electromagnetic waves has photons of largest momentum ?
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- Q.111 markThe kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio of de Broglie wavelengths associated with them will be :
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- Q.121 markTwo coherent light waves, each having amplitude 'a', superpose to produce an interference pattern on a screen. The intensity of light as seen on the screen varies between :
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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) : During formation of a nucleus, the mass defect produced is the source of the binding energy of the nucleus. Reason (R) : For all nuclei, the value of binding energy per nucleon increases with mass number.
Tap an option to check your answer.
- Q.141 markAssertion (A) : In Rutherford's alpha particle scattering experiment, the presence of only few alpha particles at angle of scattering led him to the discovery of nucleus. Reason (R) : The size of nucleus is approximately times the size of an atom and therefore only few alpha particles are rebounded.
Tap an option to check your answer.
- Q.151 markAssertion (A) : The impurities in p-type Si are not pentavalent atoms. Reason (R) : The hole density in valance band in p-type semiconductor is almost equal to the acceptor density.
Tap an option to check your answer.
- Q.161 markAssertion (A) : The Balmer series in hydrogen atom spectrum is formed when the electron jumps from higher energy state to the ground state. Reason (R) : In Bohr's model of hydrogen atom, the electron can jump between successive orbits only.
Tap an option to check your answer.
Section B
2 marks each
- Q.172 marksFind the effective resistance of the network of resistors between points A and F as shown in the figure.
- Q.182 marksA current of 5 A is passing along +X direction through a wire lying along X-axis. Find the magnetic field at a point m due to 1 cm element of the wire, centered at origin.
- Q.192 marksDefine the term, 'distance of closest approach'. A proton of MeV energy approaches a target nucleus Z = 79 in head-on position. Calculate its distance of closest approach.
- Q.20 (a)2 marksA point object is placed in air at a distance R/3 in front of a convex surface of radius of curvature R, separating air from a medium of refractive index n (< 4). Find the nature and position of the image formed.
OR
Q.20 (b)2 marksIn Young's double slit experimental set-up, the intensity of the central maximum is . Calculate the intensity at a point where the path difference between two interfering waves is .- Q.212 marksThe threshold frequency for a given metal is Hz. If monochromatic radiations of frequency Hz are incident on this metal, find the cut-off potential for the photoelectrons.
Section C
3 marks each
- Q.223 marks(a) "There is a limit to the amount of charge that can be stored on a given capacitor." Explain. (b) A capacitor is charged by a battery to a potential difference V. It is disconnected from the battery and connected across another identical uncharged capacitor. Calculate the ratio of total energy stored in the combination to the initial energy stored in the capacitor.
- Q.233 marks(a) "You cannot see a person standing on the other side of a boundary wall but can hear him." Explain with reason. (b) Light of wavelength 750 nm is incident normally on a slit of width mm. Diffraction pattern is obtained on a screen m away from the slit. Find the distance of the nearest point from the central maxima at which the intensity is zero.
- Q.243 marksThe magnetic moment (5J/T) of a bar magnet points along a uniform magnetic field T. (a) Calculate (i) the potential energy of the bar magnet, and (ii) the work done in turning the magnet by . (b) In which case is the potential energy of the magnet minimum ?
- Q.253 marksA right-angled prism ABC (refractive index ) is kept on a plane mirror as shown in the figure. A ray of light is incident normally on the face AC. (a) Trace the path of the ray as it passes through the prism. (b) Find the angle of deviation produced by the prism.
- Q.26 (a)3 marksTwo small solid metal balls A and B of radii R and 2R having charge densities and respectively are kept far apart. Find the charge densities on A and B after they are connected by a conducting wire.
OR
Q.26 (b)3 marksTwo infinitely long straight wires '1' and '2' are placed d distance apart, parallel to each other, as shown in the figure. They are uniformly charged having charge densities and respectively. Locate the position of the point from wire '1' at which the net electric field is zero and identify the region in which it lies.- Q.273 marks(a) Draw the energy-band diagrams for conductors, semiconductors and insulators at K. How is an electron-hole pair formed in a semiconductor at room temperature ? (b) Carbon and silicon both, are members of IV group of periodic table and have the same lattice structure. Carbon is an insulator whereas silicon is a semiconductor. Explain.
- Q.283 marksDifferentiate between half-wave and full-wave rectification. With the help of a circuit diagram, explain the working of a full-wave rectifier.
Section D
1 mark each
- A galvanometer is an instrument used to show the direction and strength of the current passing through it. In a galvanometer, a coil placed in a magnetic field experiences a torque and hence gets deflected when a current passes through it. The name is derived from the surname of Italian scientist L. Galvani, who in 1791 discovered that electric current makes a dead frog's leg jerk. A spring attached with the coil provides a counter torque. In equilibrium, the deflecting torque is balanced by the restoring torque of the spring and we have : where N is the total number of turns in the coil A is the area of cross-section of each turn B is the radial magnetic field k is the torsional constant of the spring is the angular deflection of the coil As the current which produces full scale deflection in the galvanometer is very small, the galvanometer cannot as such be used to measure current in electric circuits. A small resistance, called shunt, of a suitable value is connected with the galvanometer to convert it into an ammeter of desired range. By using a higher resistance, a galvanometer can also be converted into a voltmeter.Q.29 (i) (a)1 markA galvanometer is converted into a voltmeter of range by connecting with it, a resistance . If is replaced by , the range becomes . The resistance of the galvanometer is :
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OR
Q.29 (i) (b)1 markA current of 5 mA flows through a galvanometer. Its coil has 100 turns, each of area of cross-section and is suspended in a magnetic field T. The deflecting torque acting on the coil will be :Tap an option to check your answer.
- Q.29 (ii)1 markThe value of resistance of the ammeter in case (ii) will be :
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- Q.29 (iii)1 markA galvanometer of resistance 6 shows full scale deflection for a current of A. The value of shunt to be used with this galvanometer to convert it into an ammeter of range A is :
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- Q.29 (iv)1 markThe value of the current sensitivity of a galvanometer is given by :
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- Einstein explained photoelectric effect on the basis of Planck's quantum theory, where light travels in the form of small bundles of energy called photons. The energy of each photon is , where is the frequency of incident light and h is Planck's constant. The number of photons in a beam of light determines the intensity of the incident light. A photon incident on a metal surface transfers its total energy to a free electron in the metal. A part of this energy is used in ejecting the electron from the metal and is called its work function. The rest of the energy is carried by the ejected electron as its kinetic energy.Q.30 (i)1 markWhich of the following graphs can be used to obtain the value of Planck's constant ?
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- Q.30 (ii) (a)1 markRed light, yellow light and blue light of the same intensity are incident on a metal surface successively. , and represent the maximum kinetic energy of photoelectrons respectively, then :
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OR
Q.30 (ii) (b)1 markWhich of the following metals exhibits photoelectric effect with visible light ?Tap an option to check your answer.
- Q.30 (iii)1 markWhen the frequency of the incident light is increased without changing its intensity, the saturation current :
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- Q.30 (iv)1 markWhich of the following graphs shows the variation of photoelectric current I with the intensity of light ?
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Section E
5 marks each
- Q.31 (a)5 marks(i) Draw a ray diagram of a reflecting telescope (Cassegrain) and explain the formation of image. State two important advantages that a reflecting telescope has over a refracting telescope. (ii) In a refracting telescope, the focal length of the objective is 50 times the focal length of the eyepiece. When the final image is formed at infinity, the length of the tube is 102 cm. Find the focal lengths of the two lenses.
OR
Q.31 (b)5 marks(i) Write any two advantages of a compound microscope over a simple microscope. Draw a ray diagram for the image formation at the near point by a compound microscope and explain it. (ii) A thin planoconcave lens with its curved face of radius of curvature R is made of glass of refractive index . It is placed coaxially in contact with a thin equiconvex lens of same radius of curvature of refractive index . Obtain the power of the combination lens.- Q.32 (a)5 marks(i) Three batteries , and of emfs and internal resistances V, , V, and V, respectively are connected as shown in the figure. Find the values of the currents passing through batteries , and . (ii) The ends of six wires, each of resistance R are joined as shown in the figure. The points A and B of the arrangement are connected in a circuit. Find the value of the effective resistance offered by it to the circuit.
OR
Q.32 (b)5 marks(i) Current I A is passing through a copper rod of varying cross-sections as shown in the figure. The areas of cross-section at points A and B along its length are and respectively. Calculate : (I) the ratio of electric fields at points A and B. (II) the drift velocity of free electrons at point B. (ii) Two point charges and are placed at points m and m. Find the net electric field at point m m.- Q.33 (a)5 marks(i) Define self-inductance of a coil. Derive the expression for the energy required to build up a current I in a coil of self-inductance L. (ii) The currents passing through two inductors of self-inductances 10 mH and 20 mH increase with time at the same rate. Draw graphs showing the variation of : (I) the magnitude of emf induced with the rate of change of current in each inductor. (II) the energy stored in each inductor with the current flowing through it.
OR
Q.33 (b)5 marks(i) Define the term mutual inductance. Deduce the expression for the mutual inductance of two long coaxial solenoids of the same length having different radii and different number of turns. (ii) The current through an inductor is uniformly increased from zero to 2 A in 40 s. An emf of 5 mV is induced during this period. Find the flux linked with the inductor at s.