2. SECTION – I Single Correct Answer Type Select the correct answer from among those provided for the following and write in your answer book the corresponding letter (a), (b), (c) or (d) given in brackets.
3. 01 Problem Two bodies M and N of equal mass are suspended from two separate mass less springs of spring constants k1 and k2 respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of M to that of N is a. b. c. d.
4. Problem 02 A boat which has a speed of 5 km/h in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in kilometers per hour is 1 4 3 d.
5. Problem 03 A wave represented by the equation is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is a. b. c. d.
6. Problem 04 If one mole of a monatomic gas is mixed with one mole of a diatomic gas ( =7/5), the value of for the mixture is 1.40 1.50 1.53 3.07
7. Problem 05 Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are 5I and I 5I and 3I 9I and I 9I and 3I
8. Problem 06 A piece of copper and another of germanium are cooled from room temperature to 80 K. The resistance of Each of them increases Each of them decreases Copper increases and germanium decreases Copper decreases and germanium increases
9. Problem 07 Photoelectric effect supports quantum nature of light because: There is a minimum frequency of light below which no photoelectrons are emitted. The maximum kinetic energy of photoelectrons depends only on the frequency of light and not on its intensity Evan when the metal surface is faintly illuminated, the Photoelectrons leave the surface immediately Electric charge of the photoelectrons is unitized
10. Problem 08 During a negative beta decay: An atomic electron is ejected An electron which is already present within the nucleus is ejected A neutron in the nucleus decays emitting an electron A part of the binding energy of the nucleus is converted into an electron
11. Problem 09 During a nuclear fusion reaction: A heavy nucleus breaks into two fragments by itself. A light nucleus bombarded by thermal neutrons breaks up. A heavy nucleus bombarded by thermal neutrons breaks up. Two light nuclei combine to give a heaver nucleus and possibly other products
12. SECTION – II Fill in the Blanks In each of the statement given below, several alternatives are given. In some cases more than one alternative is correct, Select the correct alternative(s) in each case and write down the corresponding letter(s) (a), (b), (c) or (d) in your answer-book. For each part, marks will be awarded only if all the correct alternatives are written.
13. 01 Problem A vessel contains oil (density = 0.8g/cm3) over mercury (density = 13.6 g/cm3). A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of the sphere in g/cm3 is 3.3 6.4 7.2 12.8
14. Problem 02 An organ pipe P1, closed at one end and vibrating in its third harmonic, and another pipe P2, open both ends and vibrating in its fourth harmonic, are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is 8/3 3/8 ½ 1/3
15. Problem 03 A cylinder of radius R made of a material of thermal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in a steady state. The effective thermal conductivity of the system is K1 + K2 K1K22/( K1 + K2) (K1 + 3K2)/4 (3K1 + K2)/4
16. Problem 04 Two particles X and Y having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii R1 and R2, respectively. The ratio of the mass of X to the of Y is (R1/R2)1/2 R2/R1 (R1/R2)2 R1/R2
17. Problem 05 A short linear object length b lies along the axis of a concave mirror of focal length f at a distance u from the pole of the mirror. The size of the image approximately equal to a. b. c. d.
18. Problem 06 A potential difference applied to an X-ray tube is increased. As a result, in the emitted radiation, The intensity radiation, The minimum wavelength increases The intensity remains unchanged The minimum wavelength decreases
19. Problem 07 A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is 6 h 12 h 24 h 128 h
20. Problem 08 The impurity atoms with which pure silicon would be doped to make a p-type semiconductor are those of Phosphorus Boron Antimony Aluminum
21. SECTION – III Fill in the balks Read the following statements carefully, Indicate the subdivision number and write down your answer corresponding to each blank strictly in the order in which it appears in the statement.
22. 01 Problem In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are _______________.
23. Problem 02 The masses and radii on the earth and the moon are M1, R1 and M2, R2 respectively. Their centers are a distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway between the two centers so as escape to infinity is _______________.
24. Problem 03 A smooth uniform rod of length L and mass M has two identical beads of negligible size, each of mass m, which can slide freely along the rod. Initially, the two beads are at the center of the rod and the system is rotating with an angular velocity about an axis perpendicular to the rod and passing through the midpoint of rod (see Fig. 1988.1). There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is _____________.
25. Problem 04 A cylinder of mass M and radius R is resting on a horizontal platform (Which is parallel to the x-y plane) with its axis fixed along the y-axis and free to rotate about its axis . The platform is given a motion in the x-direction given as . There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is _____________.
26. Problem 05 A solid sphere of radius R made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere, , is ________________.
27. Problem 06 Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V. The battery is then disconnected and the region between the plates of the capacitor C completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes ____________.
28. Problem 07 In a hydrogen atom, the electron moves in an orbit of radius 0.5Å making 1016 revolutions per second. The magnetic moment associated with the orbital motion of the electron is ________________.
29. Problem 08 The wire loop PQRSP formed by joining two semicircular wires of radii R1 and R2 carries a current I as shown. The magnitude of the magnetic induction at the center C is ______________.
30. Problem 09 The binding energies per nucleon for deuteron ( ) and helium ( He) are 1.1 MeV and 7.0 MeV, respectively. The energy released when two deuterons fuse to form a helium nucleus ( He) is _________________.
31. Problem 10 In the forward bias arrangement of a p-n junction rectifier, the p end is connected to the __________ terminal of the battery and the direction of the current its from ____________ to ____________ in the rectifier.
32. SECTION – IV Each of which either true or False State whether the following statements are true or false. Given very brief reasons in support of your answers. Marks will be awarded only if correct reasons are also given.
33. 01 Problem Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively. The energy radiated per second by the first sphere is greater than that by the second
34. Problem 02 An electric line of force in the x-y plane is given by the equation A particle with unit positive charge, initially at rest at the point x = 1, y = 0 in the x-y plane, will move along the circular line of force.
35. Problem 03 A ring of radius R carries a uniformly distributed charge +Q. A point charge – q is placed on the axis of the ring at a distance 2R from the center of the ring released from rest. The particle executes a simple harmonic motion along the axis of the ring.
36. Problem 04 A parallel beam of white light falls on a combination of a concave and a convex lens, both of the same material. Their focal lengths are 15 cm and 30 cm respectively for the mean wavelength in white light. On the other side of the lens system, one sees colored patterns with violet at the outer edge.
