CBSE Class 12 Physics 2026 question paper (55/2)
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 markThree point charges 2q, and q are kept at the vertices of an equilateral triangle of side . The potential energy of the system is
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- Q.21 markTwo metal spheres of radii and having charges and respectively kept in air, are brought in contact. Which of the following statements is not correct ?
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- Q.31 markThe maximum kinetic energy of the electrons emitted from a photo sensitive surface depends on
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- Q.41 markIn Bohr model of hydrogen atom, for large values of n, the distance between the consecutive orbits is proportional to
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- Q.51 markA straight long wire lying along y-axis, carries a current of 1 A along direction. The magnetic field due to the conductor at a point (50 cm, 0, 0) will point along.
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- Q.61 markWhich of the following materials has positive and small value of magnetic susceptibility ?
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- Q.71 markA galvanometer of resistance 27 is converted into an ammeter of range (0 – 10 mA) using a resistance of 3 . The galvanometer will show full scale deflection for a current of about –
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- Q.81 markThe magnetic flux (in Wb) linked with a coil is related to time t (in s) as The SI units of A and B are respectively
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- Q.91 markThe figure shows the variation of capacitive reactance of two ideal capacitors of capacitances & with the reciprocal of angular frequency of ac source. The value of is
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- Q.101 markA magnet held vertically, with its north pole down is dropped along the axis of a closed solenoid placed vertically on a table. If the observer looks down from the top,
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- Q.111 markAn electromagnetic wave is propagating along x-axis. At any instant, the phase difference (in radian) between the electric field and the magnetic field associated with the wave is
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- Q.121 markIn Bohr model of hydrogen atom, the electron makes a transition from n = 5 to n = 1 state. As a result, a photon of wavelength is emitted in the process. The wavelength of the photon emitted when an electron makes a transition from energy level n = 5 to n = 2 will be
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- For question numbers 13 to 16, two statements are given – one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below :Q.131 markAssertion (A) : On increasing the intensity of incident light of frequency on a photosensitive surface, the photocurrent increases. Reason (R) : The stopping potential for a photosensitive surface increases with increase of frequency of incident light.
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- Q.141 markAssertion (A) : On forward biasing a p-n junction diode, the height of the barrier potential increases. Reason (R) : In forward biasing of a p-n junction diode, the direction of the applied voltage is in the same direction as the built-in potential.
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- Q.151 markAssertion (A) : Light added to light can produce darkness. Reason (R) : When two coherent light waves interfere, there is darkness at position of destructive interference.
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- Q.161 markAssertion (A) : Two electric heaters of power and are joined in series across a dc source of voltage V. The power consumed by the combination will be less than that consumed by when connected across the same source. Reason (R) : The power consumed by a electric device when connected to a dc source of voltage V is proportional to its resistance.
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Section B
2 marks each
- Q.172 marksWrite two points of difference between intrinsic and extrinsic semiconductors.
- Q.182 marksFind ratio of the de Broglie wavelength and associated respectively with an alpha particle and a proton, (i) if they are moving with the same kinetic energy. (ii) just after they are accelerated through the same potential difference.
- Q.192 marksA ray of light in air is incident at angle on a face of an equilateral glass prism and is refracted through the prism. As is varied, it is observed that the ray undergoes minimum deviation, when the is three-fourth of the angle of the prism. Calculate the speed of light in the prism.
- Q.202 marksA heating element using nichrome is connected to a 220 V supply. Initially it draws a current of 2.9 A. After some time, the current attains a steady value of 2.5 A. Find the steady temperature of the heating element if the room temperature is 27 C. The temperature coefficient of resistance of nichrome is C.
- Q.21 (a)2 marksA 5 cm long pencil is placed along the principal axis of a concave mirror of focal length 20 cm such that its nearest end is at a distance of 25 cm from the mirror. Calculate the length of the image of the pencil.
OR
Q.21 (b)2 marksIn a Young's double-slit experiment, a beam of light consisting of two wavelengths 500 nm and 600 nm is used. The interference fringes are observed at a screen placed 1.8 m away from the plane of slits (slit separation 0.3 mm). Calculate the least distance from the central maximum where the bright fringes due to both the wavelengths coincide.
Section C
3 marks each
- Q.223 marks(a) Consider the following nuclides : , , , Group them into isotopes and isotones. (b) How does the size of a nucleus depend on its mass number A ? Hence prove that the density of nucleus is a constant, independent of A, for all nuclei.
- Q.233 marks(a) An electric field exists in a region of space. Draw three equipotential surfaces in the region. (b) Two point charges and are located at points and respectively. Find the electrostatic potential at point where .
- Q.243 marksName the electromagnetic waves which are used for (i) detection of fractures in bones (ii) physiotherapy (iii) radar systems Also write their wavelength range.
- Q.25 (a)3 marks(i) Define mutual inductance of a pair of coils. Write its SI unit. (ii) A long solenoid of radius R and length L has n turns per unit length. A circular loop of radius r(<R) is placed inside at the centre of the solenoid such that its axis coincides with the axis of the solenoid. Obtain the mutual inductance of the solenoid and the loop.
OR
Q.25 (b)3 marksTwo long straight parallel conductors A and B carrying steady currents and in the same direction are separated by a distance d. Deduce the expressions for the force acting on length L of conductor B due to conductor A and show it in figure. Write the expression for the force acting on length L of conductor A due to conductor B and show that it follows Newton's third law.- Q.263 marks(a) State Bohr's second postulate and mention its significance. (b) Prove that, in Bohr model of hydrogen atom as principal quantum number n becomes large, the energy levels get closer and closer.
- Q.273 marks(a) Explain the statement : "Current is a scalar although we represent current with an arrow". (b) Use Kirchhoff's rules to find the current through 3 resistor in the circuit shown in the figure :
- Q.283 marksDerive an expression for the magnetic field , due to a circular coil of N turns, each of radius r carrying current I, at a distance '' from the centre along its axis.
Section D
1 mark each
- A p-type or n-type semiconductor can be converted into a p-n junction by doping it with suitable impurity. The motion of majority charge carriers causes diffusion current across the junction while the barrier electric field causes motion of minority carriers for drift current. In case of unbiased diode, the diffusion and drift currents are equal. This equilibrium is disturbed by the biasing batteries. Diodes, therefore, allow currents in one direction. This property of diode is used in making rectifiers.Q.29 (i)1 markSilicon is doped with which of the following to obtain p-type semiconductor ?
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- Q.29 (ii)1 markA semiconductor has an electron concentration of . The concentration of holes is (given )
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- Q.29 (iii)1 markDuring forward biasing of a p-n junction diode, the
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- Q.29 (iv) (a)1 markThe threshold voltage for silicon diode is about
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OR
Q.29 (iv) (b)1 markWhen we dope Ge with a pentavalent element, four of its electrons bond with four germanium neighbours but fifth electron remains weakly bound. The ionisation energy for this electron is aboutTap an option to check your answer.
- In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.Q.30 (i)1 markThe value of d is
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- Q.30 (ii)1 markCompared to the size of the object, the images formed in the two positions of the lens are respectively
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- Q.30 (iii)1 markIf the distance between object and screen is 80.00 cm and the lens forms sharp images at two positions separated by 20.00 cm., the focal length of convex lens is
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- Q.30 (iv) (a)1 markConsider a convex lens of focal length 15 cms. For which of the following values of object-screen distance, two positions of the object can be found to obtain sharp image on the screen ?
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OR
Q.30 (iv) (b)1 markA thin convex lens of focal length 10 cm and another thin lens of focal length 'f' are placed coaxially in contact. If the power of their combination is D, the value of 'f' isTap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(a) What are coherent sources ? Why they are necessary for observing stable interference pattern ? Draw a graph showing the variation of intensity of light with the position on the screen in Young's double-slit experiment. (b) Find the intensity of light at a point on the screen when two interfering waves of the same intensity have a path difference of (i) and (ii) .
OR
Q.31 (b)5 marks(a) Draw a labelled ray diagram of a refracting telescope when it forms image of a distant object at infinity. Derive expression for its magnifying power. (b) (i) In a telescope the objective has much larger aperture than the eye piece. Why ? (ii) Write two advantages of reflecting telescope over refracting telescope.- Q.32 (a)5 marks(a) Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates. (b) Two air-filled capacitors of capacitances and are connected in parallel with a dc battery. After the capacitors are fully charged, a slab of dielectric constant K is inserted between the plates of each capacitor. How will the (i) charge on each capacitor and (ii) energy stored in the capacitor affected after the slab is introduced.
OR
Q.32 (b)5 marks(a) An electric field is established across the ends of a cylindrical conductor of length L and area of cross-section A. Discuss how electrons attain an average velocity, independent of time. Hence, obtain a relation between current in the conductor and this 'average velocity' of electrons. (b) (i) This 'average velocity' is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ? (ii) Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.- Q.33 (a)5 marks(a) A series combination of L, C and R is connected to an a.c. source. Using a phasor diagram, derive an expression for the impedance of the circuit and phase difference between V and I. (b) Under what conditions the (i) impedance of the circuit is minimum ? (ii) Wattless current flows in the circuit ?
OR
Q.33 (b)5 marks(i) With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator. (ii) Deduce an expression for the induced emf in the coil of the generator. (iii) If T is the time period of the rotation of the coil, at what values of T in a cycle, the emf generator is maximum ?
Section A
1 mark each
- Q.11 markThree point charges +q, and +q are placed along -axis at points m, m and m respectively. The potential energy of the system is
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- Q.21 markA photosensitive surface is illuminated by radiations of wavelength , and one by one and photoemission is observed in each case. , lies in UV range and in visible range. If , and are stopping potential in these cases respectively, then
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- Q.31 markIn Bohr model of hydrogen atom, the value of potential energy of an electron in orbit varies with 'n' as
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- Q.41 markTwo metal spheres of radii and having charges and respectively kept in air, are brought in contact. Which of the following statements is not correct ?
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- Q.51 markIn Bohr model of hydrogen atom, an electron makes a transition from n = 4 state to n = 1 state and a photon of frequency is emitted. The frequency of photon emitted when an electron makes a transition from n = 4 state to n = 2 state in the same model is
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- Q.61 markFigure shows a magnet dropped through a small loop with a small cut. Which of the following statements is correct ?
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- Q.71 markThe expression of magnetic fields associated with four electromagnetic waves are given below : I. II. III. IV. Which wave is travelling in free space ?
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- Q.81 markWhich of the following substance has relative magnetic permeability ?
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- Q.91 markA straight conductor lies along -axis and carries a current of 2 A along direction. The magnetic field at a point (0, 40 cm, 0) due to 1 cm length of conductor centered at the origin points along.
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- Q.101 markA galvanometer of resistance 27 is converted into an ammeter of range (0 – 10 mA) using a resistance of 3 . The galvanometer will show full scale deflection for a current of about –
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- Q.111 markThe magnetic flux (in Wb) linked with a coil is related to time t (in s) as The SI units of A and B are respectively
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- Q.121 markThe figure shows the variation of capacitive reactance of two ideal capacitors of capacitances & with the reciprocal of angular frequency of ac source. The value of is
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- For question numbers 13 to 16, two statements are given – one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below :Q.131 markAssertion (A) : Light added to light can produce darkness. Reason (R) : When two coherent light waves interfere, there is darkness at position of destructive interference.
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- Q.141 markAssertion (A) : Two electric heaters of power and are joined in series across a dc source of voltage V. The power consumed by the combination will be less than that consumed by when connected across the same source. Reason (R) : The power consumed by a electric device when connected to a dc source of voltage V is proportional to its resistance.
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- Q.151 markAssertion (A) : On increasing the intensity of incident light of frequency on a photosensitive surface, the photocurrent increases. Reason (R) : The stopping potential for a photosensitive surface increases with increase of frequency of incident light.
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- Q.161 markAssertion (A) : On forward biasing a p-n junction diode, the height of the barrier potential increases. Reason (R) : In forward biasing of a p-n junction diode, the direction of the applied voltage is in the same direction as the built-in potential.
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Section B
2 marks each
- Q.17 (a)2 marksA 5 cm long pencil is placed along the principal axis of a concave mirror of focal length 20 cm such that its nearest end is at a distance of 25 cm from the mirror. Calculate the length of the image of the pencil.
OR
Q.17 (b)2 marksIn a Young's double-slit experiment, a beam of light consisting of two wavelengths 500 nm and 600 nm is used. The interference fringes are observed at a screen placed 1.8 m away from the plane of slits (slit separation 0.3 mm). Calculate the least distance from the central maximum where the bright fringes due to both the wavelengths coincide.- Q.182 marksCalculate the temperature at which the resistance of a conductor becomes 20% more than its resistance at 27 C. The value of the temperature coefficient of resistance of the material of conductor is C.
- Q.192 marksA ray of light is incident on the face of a triangular prism of refracting angle 60 and it just suffers total internal reflection at the other face. Find the angle of incidence for the ray if the refractive index of the material of the prism is .
- Q.202 marksWrite two points of difference between intrinsic and extrinsic semiconductors.
- Q.212 marksFind ratio of the de Broglie wavelength and associated respectively with an alpha particle and a proton, (i) if they are moving with the same kinetic energy. (ii) just after they are accelerated through the same potential difference.
Section C
3 marks each
- Q.22 (a)3 marks(i) Define mutual inductance of a pair of coils. Write its SI unit. (ii) A long solenoid of radius R and length L has n turns per unit length. A circular loop of radius r(<R) is placed inside at the centre of the solenoid such that its axis coincides with the axis of the solenoid. Obtain the mutual inductance of the solenoid and the loop.
OR
Q.22 (b)3 marksTwo long straight parallel conductors A and B carrying steady currents and in the same direction are separated by a distance d. Deduce the expressions for the force acting on length L of conductor B due to conductor A and show it in figure. Write the expression for the force acting on length L of conductor A due to conductor B and show that it follows Newton's third law.- Q.233 marksCalculate the de Broglie wavelength associated with an electron revolving in the second excited state of hydrogen atom. The ground state energy of the hydrogen atom is – 13.6 eV. Take kg, h = J.s.
- Q.243 marksName the electromagnetic waves which are used (i) as a diagnostic tool in medicine (ii) in remote switches for TV sets (iii) in water purifiers Also write their wavelength range.
- Q.253 marks(i) Draw electric field lines and equipotential surfaces for a system of two equal and opposite point charges separated by some distance. (ii) Why electric field at a point on an equipotential surface must be perpendicular to the surface at that point ?
- Q.263 marks(a) Consider the following nuclides : , , , Group them into isotopes and isotones. (b) How does the size of a nucleus depend on its mass number A ? Hence prove that the density of nucleus is a constant, independent of A, for all nuclei.
- Q.273 marksDerive an expression for the magnetic field , due to a circular coil of N turns, each of radius r carrying current I, at a distance '' from the centre along its axis.
- Q.283 marks(a) Explain the statement : "Current is a scalar although we represent current with an arrow". (b) Use Kirchhoff's rules to find the current through 3 resistor in the circuit shown in the figure :
Section D
1 mark each
- In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.Q.29 (i)1 markThe value of d is
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- Q.29 (ii)1 markCompared to the size of the object, the images formed in the two positions of the lens are respectively
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- Q.29 (iii)1 markIf the distance between object and screen is 80.00 cm and the lens forms sharp images at two positions separated by 20.00 cm., the focal length of convex lens is
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- Q.29 (iv) (a)1 markConsider a convex lens of focal length 15 cms. For which of the following values of object-screen distance, two positions of the object can be found to obtain sharp image on the screen ?
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OR
Q.29 (iv) (b)1 markA thin convex lens of focal length 10 cm and another thin lens of focal length 'f' are placed coaxially in contact. If the power of their combination is D, the value of 'f' isTap an option to check your answer.
- A p-type or n-type semiconductor can be converted into a p-n junction by doping it with suitable impurity. The motion of majority charge carriers causes diffusion current across the junction while the barrier electric field causes motion of minority carriers for drift current. In case of unbiased diode, the diffusion and drift currents are equal. This equilibrium is disturbed by the biasing batteries. Diodes, therefore, allow currents in one direction. This property of diode is used in making rectifiers.Q.30 (i)1 markSilicon is doped with which of the following to obtain p-type semiconductor ?
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- Q.30 (ii)1 markA semiconductor has an electron concentration of . The concentration of holes is (given )
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- Q.30 (iii)1 markDuring forward biasing of a p-n junction diode, the
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- Q.30 (iv) (a)1 markThe threshold voltage for silicon diode is about
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OR
Q.30 (iv) (b)1 markWhen we dope Ge with a pentavalent element, four of its electrons bond with four germanium neighbours but fifth electron remains weakly bound. The ionisation energy for this electron is aboutTap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(a) A series combination of L, C and R is connected to an a.c. source. Using a phasor diagram, derive an expression for the impedance of the circuit and phase difference between V and I. (b) Under what conditions the (i) impedance of the circuit is minimum ? (ii) Wattless current flows in the circuit ?
OR
Q.31 (b)5 marks(i) With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator. (ii) Deduce an expression for the induced emf in the coil of the generator. (iii) If T is the time period of the rotation of the coil, at what values of T in a cycle, the emf generator is maximum ?- Q.32 (a)5 marks(a) What are coherent sources ? Why they are necessary for observing stable interference pattern ? Draw a graph showing the variation of intensity of light with the position on the screen in Young's double-slit experiment. (b) Find the intensity of light at a point on the screen when two interfering waves of the same intensity have a path difference of (i) and (ii) .
OR
Q.32 (b)5 marks(a) Draw a labelled ray diagram of a refracting telescope when it forms image of a distant object at infinity. Derive expression for its magnifying power. (b) (i) In a telescope the objective has much larger aperture than the eye piece. Why ? (ii) Write two advantages of reflecting telescope over refracting telescope.- Q.33 (a)5 marks(a) Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates. (b) Two air-filled capacitors of capacitances and are connected in parallel with a dc battery. After the capacitors are fully charged, a slab of dielectric constant K is inserted between the plates of each capacitor. How will the (i) charge on each capacitor and (ii) energy stored in the capacitor affected after the slab is introduced.
OR
Q.33 (b)5 marks(a) An electric field is established across the ends of a cylindrical conductor of length L and area of cross-section A. Discuss how electrons attain an average velocity, independent of time. Hence, obtain a relation between current in the conductor and this 'average velocity' of electrons. (b) (i) This 'average velocity' is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ? (ii) Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.
Section A
1 mark each
- Q.11 markThe figure shows the variation of capacitive reactance of two ideal capacitors of capacitances & with the reciprocal of angular frequency of ac source. The value of is
Tap an option to check your answer.
- Q.21 markThe magnetic flux (in Wb) linked with a coil is related to time t (in s) as The SI units of A and B are respectively
Tap an option to check your answer.
- Q.31 markA galvanometer of resistance 27 is converted into an ammeter of range (0 – 10 mA) using a resistance of 3 . The galvanometer will show full scale deflection for a current of about –
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- Q.41 markTwo metal spheres of radii and having charges and respectively kept in air, are brought in contact. Which of the following statements is not correct ?
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- Q.51 markA person is standing facing geographic north and a vertical wire in front of him is carrying a current in downward direction. The direction of magnetic field at a point on the right side of wire is
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- Q.61 markWhich one of the following materials has magnetic susceptibility in the range ?
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- Q.71 markThe electric field and the magnetic field components of an electromagnetic wave travelling in vacuum are represented as where m, n, and are constants characterising the wave. Then
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- Q.81 markTwo identical circular loops A and B of metal wire are arranged on a table close to each other. Loop A is connected to a battery and the current in it increases with time. In response, the loop B
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- Q.91 markIn Bohr model of hydrogen atom, an electron is moving in an orbit, with total energy eV. Its angular momentum will be
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- Q.101 markAccording to Bohr model of hydrogen atom, the time period of an electron in its orbit is proportional to
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- Q.111 markThe equivalent mass of a photon of wavelength 100 nm is
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- Q.121 markA point charge of 5 is located at (1 cm, 1 cm) in -y plane. A second charge of 6 is brought from infinity to point cm, 4 cm). The work done in the process is
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- For question numbers 13 to 16, two statements are given – one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below :Q.131 markAssertion (A) : Two electric heaters of power and are joined in series across a dc source of voltage V. The power consumed by the combination will be less than that consumed by when connected across the same source. Reason (R) : The power consumed by a electric device when connected to a dc source of voltage V is proportional to its resistance.
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- Q.141 markAssertion (A) : Light added to light can produce darkness. Reason (R) : When two coherent light waves interfere, there is darkness at position of destructive interference.
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- Q.151 markAssertion (A) : On forward biasing a p-n junction diode, the height of the barrier potential increases. Reason (R) : In forward biasing of a p-n junction diode, the direction of the applied voltage is in the same direction as the built-in potential.
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- Q.161 markAssertion (A) : On increasing the intensity of incident light of frequency on a photosensitive surface, the photocurrent increases. Reason (R) : The stopping potential for a photosensitive surface increases with increase of frequency of incident light.
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Section B
2 marks each
- Q.172 marksFind ratio of the de Broglie wavelength and associated respectively with an alpha particle and a proton, (i) if they are moving with the same kinetic energy. (ii) just after they are accelerated through the same potential difference.
- Q.182 marksWrite two points of difference between intrinsic and extrinsic semiconductors.
- Q.19 (a)2 marksA 5 cm long pencil is placed along the principal axis of a concave mirror of focal length 20 cm such that its nearest end is at a distance of 25 cm from the mirror. Calculate the length of the image of the pencil.
OR
Q.19 (b)2 marksIn a Young's double-slit experiment, a beam of light consisting of two wavelengths 500 nm and 600 nm is used. The interference fringes are observed at a screen placed 1.8 m away from the plane of slits (slit separation 0.3 mm). Calculate the least distance from the central maximum where the bright fringes due to both the wavelengths coincide.- Q.202 marks(a) Why manganin is used in wire-wound standard resistors ? Calculate the temperature at which the resistance of a wire increases by 25% of its resistance at room temperature 27.5 ? The temperature coefficient of resistance of the material of the wire is 0.004 . (b) How does the resistivity of a semiconductor depend on temperature ? Show it on a plot.
- Q.212 marksA ray of light is incident at an angle 2A on one of the faces of a glass prism of refracting angle A. After refraction from this face, the ray strikes the opposite face which is silvered. The reflected ray from this face retraces on its path. Trace the ray diagram and find the relation between the refractive index of material of prism and the angle of prism.
Section C
3 marks each
- Q.22 (a)3 marks(i) Define mutual inductance of a pair of coils. Write its SI unit. (ii) A long solenoid of radius R and length L has n turns per unit length. A circular loop of radius r(<R) is placed inside at the centre of the solenoid such that its axis coincides with the axis of the solenoid. Obtain the mutual inductance of the solenoid and the loop.
OR
Q.22 (b)3 marksTwo long straight parallel conductors A and B carrying steady currents and in the same direction are separated by a distance d. Deduce the expressions for the force acting on length L of conductor B due to conductor A and show it in figure. Write the expression for the force acting on length L of conductor A due to conductor B and show that it follows Newton's third law.- Q.233 marksDerive an expression for the magnetic field , due to a circular coil of N turns, each of radius r carrying current I, at a distance '' from the centre along its axis.
- Q.243 marks(a) Consider the following nuclides : , , , Group them into isotopes and isotones. (b) How does the size of a nucleus depend on its mass number A ? Hence prove that the density of nucleus is a constant, independent of A, for all nuclei.
- Q.253 marks(a) Explain the statement : "Current is a scalar although we represent current with an arrow". (b) Use Kirchhoff's rules to find the current through 3 resistor in the circuit shown in the figure :
- Q.263 marks(a) Draw electric field lines and equipotential surfaces for a system of two equal positive charges separated by some distance. (b) Using the drawing in (a) above, explain that electric field need not be a constant over each point of an equipotential surface.
- Q.273 marksName the electromagnetic waves which are (i) also known as 'heat waves', (ii) used in LASIK eye surgery, (iii) used to destroy cancer cells. Also write their wavelength range.
- Q.283 marks(a) A particle of charge q and mass m is accelerated through a potential difference V. Deduce an expression for the de Broglie wavelength associated with the particle. (b) Plot a graph for a particle of charge q and mass m showing variation of de Broglie wavelength with , where V is the potential difference through which the particle is accelerated.
Section D
1 mark each
- A p-type or n-type semiconductor can be converted into a p-n junction by doping it with suitable impurity. The motion of majority charge carriers causes diffusion current across the junction while the barrier electric field causes motion of minority carriers for drift current. In case of unbiased diode, the diffusion and drift currents are equal. This equilibrium is disturbed by the biasing batteries. Diodes, therefore, allow currents in one direction. This property of diode is used in making rectifiers.Q.29 (i)1 markSilicon is doped with which of the following to obtain p-type semiconductor ?
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- Q.29 (ii)1 markA semiconductor has an electron concentration of . The concentration of holes is (given )
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- Q.29 (iii)1 markDuring forward biasing of a p-n junction diode, the
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- Q.29 (iv) (a)1 markThe threshold voltage for silicon diode is about
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OR
Q.29 (iv) (b)1 markWhen we dope Ge with a pentavalent element, four of its electrons bond with four germanium neighbours but fifth electron remains weakly bound. The ionisation energy for this electron is aboutTap an option to check your answer.
- In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.Q.30 (i)1 markThe value of d is
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- Q.30 (ii)1 markCompared to the size of the object, the images formed in the two positions of the lens are respectively
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- Q.30 (iii)1 markIf the distance between object and screen is 80.00 cm and the lens forms sharp images at two positions separated by 20.00 cm., the focal length of convex lens is
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- Q.30 (iv) (a)1 markConsider a convex lens of focal length 15 cms. For which of the following values of object-screen distance, two positions of the object can be found to obtain sharp image on the screen ?
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Q.30 (iv) (b)1 markA thin convex lens of focal length 10 cm and another thin lens of focal length 'f' are placed coaxially in contact. If the power of their combination is D, the value of 'f' isTap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(a) Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates. (b) Two air-filled capacitors of capacitances and are connected in parallel with a dc battery. After the capacitors are fully charged, a slab of dielectric constant K is inserted between the plates of each capacitor. How will the (i) charge on each capacitor and (ii) energy stored in the capacitor affected after the slab is introduced.
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Q.31 (b)5 marks(a) An electric field is established across the ends of a cylindrical conductor of length L and area of cross-section A. Discuss how electrons attain an average velocity, independent of time. Hence, obtain a relation between current in the conductor and this 'average velocity' of electrons. (b) (i) This 'average velocity' is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ? (ii) Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.- Q.32 (a)5 marks(a) A series combination of L, C and R is connected to an a.c. source. Using a phasor diagram, derive an expression for the impedance of the circuit and phase difference between V and I. (b) Under what conditions the (i) impedance of the circuit is minimum ? (ii) Wattless current flows in the circuit ?
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Q.32 (b)5 marks(i) With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator. (ii) Deduce an expression for the induced emf in the coil of the generator. (iii) If T is the time period of the rotation of the coil, at what values of T in a cycle, the emf generator is maximum ?- Q.33 (a)5 marks(a) What are coherent sources ? Why they are necessary for observing stable interference pattern ? Draw a graph showing the variation of intensity of light with the position on the screen in Young's double-slit experiment. (b) Find the intensity of light at a point on the screen when two interfering waves of the same intensity have a path difference of (i) and (ii) .
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Q.33 (b)5 marks(a) Draw a labelled ray diagram of a refracting telescope when it forms image of a distant object at infinity. Derive expression for its magnifying power. (b) (i) In a telescope the objective has much larger aperture than the eye piece. Why ? (ii) Write two advantages of reflecting telescope over refracting telescope.