Q1
mcq
The plates P1 and P2 of a 2 F capacitor are at potentials 25 V and 25 V respectively. The charge on plate P1 will be :
- A. 0.02 mC
- B. 0.1 mC
- C. 0.1 C
- D. 1 C
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Q2
mcq
A proton is taken from point P1 to point P2, both located in an electric field. The potentials at points P1 and P2 are 5 V and + 5 V respectively. Assuming that kinetic energies of the proton at points P1 and P2 are zero, the work done on the proton is :
- A. 1·6 10 18 J
- B. 1·6 10 18 J
- C. Zero
- D. 0·8 10 18 J
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Q3
mcq
A 2.0 cm segment of wire, carrying 5.0 A current in positive y-direction lies along y-axis, as shown in the figure. The magnetic field at a point (3 m, 4 m, 0) due to this segment (part of a circuit) is :
- A. (0.12 nT) ^j
- B. (0.10 nT) ^j
- C. (0.24 nT) ^k
- D. (0.24 nT) ^k
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Q4
mcq
Which of the following is a diamagnetic substance ?
- A. Gadolinium
- B. Sodium
- C. Copper chloride
- D. Sodium chloride
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Q5
mcq
A current carrying circular loop of magnetic moment M is suspended in a vertical plane in an external magnetic field B such that its plane is normal to B . The work done in rotating this loop by 45 about an axis perpendicular to B is closest to :
- A. 0.3 MB
- B. 0.3 MB
- C. 1.7 MB
- D. 1.7 MB
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Q6
mcq
The average value of the alternating voltage v = (157 V) sin t over its first half-cycle is :
- A. 157 V
- B. 2/157 V
- C. 78·5 V
- D. 100 V
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Q7
mcq
Consider a solenoid of length l and area of cross-section A with fixed number of turns. The self-inductance of the solenoid will increase if :
- A. both l and A are increased
- B. l is decreased and A is increased
- C. l is increased and A is decreased
- D. both l and A are decreased
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Q8
mcq
A plane electromagnetic wave is travelling in air in +x direction. At a particular moment, its electric field E is along + y direction. At that moment, the magnetic field B is along :
- A. + z direction and in phase with E
- B. - z direction and in phase with E
- C. + z direction and out of phase with E
- D. - z direction and out of phase with E
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Q9
mcq
A proton and an alpha particle having equal velocities approach a target nucleus. They come momentarily to rest and then reverse their directions. The ratio of the distance of closest approach of the proton to that of the alpha particle will be :
- A. 1/2
- B. 2
- C. 1/4
- D. 4
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Q10
mcq
The wavelength of matter wave associated with an electron of kinetic energy K is . If the kinetic energy of the electron is doubled, the associated wavelength becomes :
- A. 1/2
- B. 1/2^0.5
- C. 2
- D. 2^0.5
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Q11
mcq
An electron makes a transition from n = 2 level to n = 1 level in the Bohr model of a hydrogen atom. Its period of revolution :
- A. increases by 87.5%
- B. decreases by 87.5%
- C. increases by 43.75%
- D. decreases by 43.75%
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Q12
mcq
Si is doped with a pentavalent element. The energy required to set the additional electron free is about :
- A. 0.01 eV
- B. 0.05 eV
- C. 0.72 eV
- D. 1.1 eV
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Q13
mcq
Assertion (A) : In a semiconductor, the electrons in the conduction band have lesser energy than those in the valence band. Reason (R) : Donor energy level is just above the valence band in a semiconductor.
- A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C. Assertion (A) is true, but Reason (R) is false.
- D. Assertion (A) is false and Reason (R) is also false.
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Q14
mcq
Assertion (A) : Photoelectric effect demonstrates the particle nature of light. Reason (R) : Photoelectric current is proportional to frequency of incident radiation.
- A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C. Assertion (A) is true, but Reason (R) is false.
- D. Assertion (A) is false and Reason (R) is also false.
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Q15
mcq
Assertion (A) : A proton and an electron enter a uniform magnetic field B with the same momentum p such that p is perpendicular to B. They describe circular paths of the same radius. Reason (R) : In a magnetic field, orbital radius r is equal to p/qB.
- A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C. Assertion (A) is true, but Reason (R) is false.
- D. Assertion (A) is false and Reason (R) is also false.
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Q16
mcq
Assertion (A) : A convex lens, when immersed in a liquid, disappears. Reason (R) : The refractive indices of material of the lens and the liquid are equal.
- A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C. Assertion (A) is true, but Reason (R) is false.
- D. Assertion (A) is false and Reason (R) is also false.
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Q17
long answer
2 marks
(a) What is meant by relaxation time of free electrons in a conductor ? Show that the resistance of a conductor can be expressed by R = ml / ne^2τA, where symbols have their usual meanings. OR (b) Draw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flows through the galvanometer in it.
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Q18
short answer
2 marks
The magnifying power of an astronomical telescope is 24. In normal adjustment, distance between its two lenses is 150 cm. Find the focal length of the objective lens.
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Q19
long answer
2 marks
What is meant by relaxation time of free electrons in a conductor? Show that the resistance of a conductor can be expressed by R = ml/ne^2At, where symbols have their usual meanings.
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Q19
short answer
2 marks
What is a sustained or stable interference pattern? What are the conditions for obtaining such an interference pattern?
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Q20
long answer
2 marks
Draw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flows through the galvanometer in it.
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Q20
short answer
2 marks
Light of wavelength 600 nm is incident on potassium (work function 2.3 eV). Will photoemission of electrons occur? What is the longest wavelength that will cause photoemission of electrons? (Take hc = 1240 eV. nm)
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Q21
short answer
2 marks
Suppose a pure Si crystal has 5x10^28 atoms m^-3. It is doped by 1 ppm concentration of boron. Calculate the concentration of holes and electrons, given that ni = 1.5x10^16 m^-3. Is the doped crystal n-type or p-type?
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Q22
long answer
3 marks
A current of 1.6 A flows through a wire when a potential difference of 1.0 V is applied across it. The length and cross-sectional area of the wire are 1.0 m and 1.0x10^-7 m^2 respectively. Calculate: (a) Electric field across the wire (b) Current density (c) Average relaxation time (Number density of free electrons in the wire is 9.0x10^28 m^-3)
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Q23
long answer
3 marks
An electron (charge e, mass m) is revolving around a nucleus, in a hydrogen atom, in a circle of radius r. Derive an expression, in vector form, for the magnetic dipole moment, in terms of its orbital angular momentum L. What is gyromagnetic ratio?
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Q24
short answer
3 marks
Prove that induced charge depends on the net change in the magnetic flux and not on the time interval of the flux change.
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Q25
long answer
3 marks
The electric field in an electromagnetic wave in vacuum is given by: E = (6.3 N/C) [cos (1.5 rad/m) y + (4.5x10^8 rad/s) t]. (a) Find the wavelength and frequency of the wave. (b) What is the amplitude of the magnetic field of the wave? (c) Write an expression for the magnetic field of this wave.
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Q26
short answer
3 marks
second postulate for his theory of hydrogen atom. Prove that a hydrogen atom is directly proportional to n2, where n is the principal quantum number.
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Q29
short answer
3 marks
Calculate the energy required to separate a deuteron into its constituent parts (a proton and a neutron). Given: m(D) = 2.014102 u, mH = 1.007825 u, mn = 1.008665 u.
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Q31
long answer
3 marks
(a) Draw the circuit diagrams for obtaining the V I characteristics of a p-n junction diode. Explain briefly the salient features of the V I characteristics in (i) forward biasing, and (ii) reverse biasing.
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Q31
long answer
5 marks
(a) (i) Obtain the expression for the capacitance of a parallel plate capacitor with a dielectric medium between its plates. (ii) A charge of 6 C is given to a hollow metallic sphere of radius 0.2 m. Find the potential at (i) the surface and (ii) the centre of the sphere.
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Q31
long answer
5 marks
(b) (i) A charge + Q is placed on a thin conducting spherical shell. Derive an expression for the electric field at a point lying (i) inside and (ii) outside the shell. (ii) Show that the electric field for same charge density is twice in case of a conducting plate or surface than in a nonconducting sheet.
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Q32
long answer
3 marks
(b) On the basis of energy band diagrams, distinguish between (i) an insulator, (ii) a semiconductor, and (iii) a conductor.
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The figure shows four pairs of parallel identical conducting plates, separated by the same distance 2.0 cm and arranged perpendicular to x-axis. The electric potential of each plate is mentioned. The electric field between a pair of plates is uniform and normal to the plates.
Q33
mcq
1 mark
For which pair of the plates is the electric field E along i ?
- A. I
- B. II
- C. III
- D. IV
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Q34
mcq
1 mark
An electron is released midway between the plates of pair IV. It will :
- A. move along i at constant speed
- B. move along i at constant speed
- C. accelerate along i
- D. accelerate along i
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Q35
mcq
1 mark
Let V0 be the potential at the left plate of any set, taken to be at x = 0 m. Then potential V at any point (0 x 2 cm) between the plates of that set can be expressed as :
- A. V = V0 + x
- B. V = V0 + x2
- C. V = V0 + x1/2
- D. V = V0 + x3/2
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Q36
mcq
1 mark
Let E1, E2, E3 and E4 be the magnitudes of the electric field between the pairs of plates, I, II, III and IV respectively. Then :
- A. E1 > E2 > E3 > E4
- B. E3 > E4 > E1 > E2
- C. E4 > E3 > E2 > E1
- D. E2 > E3 > E4 > E1
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Q37
mcq
1 mark
An electron is projected from the right plate of set I directly towards its left plate. It just comes to rest at the plate. The speed with which it was projected is about : (Take (e/m) =1.76 10^11 C/kg)
- A. 1.3 10^5 m/s
- B. 2.6 10^6 m/s
- C. 6.5 10^5 m/s
- D. 5.2 10^7 m/s
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Diffraction and interference are closely related phenomena that occur together. Diffraction is the phenomenon of bending of light around the edges of the obstacle, while interference is the combination of waves that results in a new wave pattern. In order to get interference, there must be at least two waves that are diffracting. So while diffraction can occur without interference, interference cannot occur without diffraction. Two slits of width 2 m each in an opaque material are separated by a distance of 6 m. Monochromatic light of wavelength 450 nm is incident normally on the slits. One finds a combined interference and diffraction pattern on the screen.
Q38
mcq
1 mark
The number of peaks of the interference fringes formed within the central peak of the envelope of the diffraction pattern will be :
- A. 2
- B. 3
- C. 4
- D. 6
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Q39
mcq
1 mark
The number of peaks of the interference formed if the slit width is doubled while keeping the distance between the slits same will be :
- A. 1
- B. 2
- C. 3
- D. 4
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Q40
mcq
1 mark
If instead of 450 nm light, another light of wavelength 680 nm is used, number of peaks of the interference formed in the central peak of the envelope of the diffraction pattern will be :
- A. 2
- B. 4
- C. 6
- D. 9
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Q41
mcq
1 mark
Consider the diffraction of light by a single slit described in this case study. The first minimum falls at an angle equal to :
- A. sin-1 (0.12)
- B. sin-1 (0.225)
- C. sin-1 (0.32)
- D. sin-1 (0.45)
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Q42
mcq
1 mark
The number of bright fringes formed due to interference on 1 m of screen placed at 4/3 m away from the slits is :
- A. 2
- B. 3
- C. 6
- D. 10
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Q45
long answer
5 marks
(i) (1) What is meant by current sensitivity of a galvanometer ? Mention the factors on which it depends. (2) A galvanometer of resistance G is converted into a voltmeter of range (0 V) by using a resistance R. Find the resistance, in terms of R and G, required to convert it into a voltmeter of range 2 V0 . (ii) The magnetic flux through a coil of resistance 5 increases with time as : = (2.0 t3 + 5.0 t2 + 6.0 t) mWb Find the magnitude of induced current through the coil at t = 2 s.
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Q46
long answer
5 marks
(i) A rectangular coil of N turns and area of cross-section A is rotated at a steady angular speed in a uniform magnetic field. Obtain an expression for the emf induced in the coil at any instant of time. (ii) Two coplanar and concentric circular loops L1 and L2 are placed coaxially with their centres coinciding. The radii of L1 and L2 are 1 cm and 100 cm respectively. Calculate the mutual inductance of the loops. (Take 2 = 10)
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Q47
long answer
5 marks
(i) Trace the path of a ray of light showing refraction through a triangular prism and hence obtain an expression for angle of deviation in terms of A, i and e, where symbols have their usual meanings. Draw a graph showing the variation of angle of deviation with the angle of incidence.
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Q48
long answer
5 marks
In the figure, a ray of light is incident on a transparent liquid contained in a thin glass box at an angle of 45 with its one face. The emergent ray passes along the face AB. Find the refractive index of the liquid.
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Q49
long answer
5 marks
The displacement of two light waves, frequency , emanating from two coherent sources of light, are given by y1 = a cos t and y2 = a cos ( t + ). is the phase difference between the two waves. These light waves superpose at a point. Obtain the expression for the resultant intensity at that point.
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Q50
long answer
5 marks
Find the ratio of intensities at two points on a screen when waves emanating from two slits reaching these points have path differences (i) 6 and (ii) 12.
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