Regn. No. South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : ,

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1 1. Section-A contains 3 Multiple Choice Questions (MCQ). Each question has 4 choices (a), (b), (c) and (d), for its answer, out of which ONLY ONE is correct. From Q.1 to Q.1 carries 1 Marks and Q.11 to Q.3 carries Marks each. 3. Section-B contains 1 Multiple Select Questions(MSQ). Each question has 4 choices (a), (b), (c) and (d) for its answer, out of which ONE or MORE than ONE is/are correct. For each correct answer ou will be awarded marks. 4. Section -C contains Numerical Answer Tpe (NAT) questions. From Q.41 to Q.5 carries 1 Mark each and Q.51 to Q.6 carries Marks each. For each NAT tpe question, the value of answer can be an real number. 5. In all sections, questions not attempted will result in zero mark. In Section A (MCQ), wrong answer will result in negative marks. For all 1 mark questions, 1/3 marks will be deducted for each wrong answer. For all marks questions, /3 marks will be deducted for each wrong answer. In Section B (MSQ),there is no negative and no partial marking provision. There is no negative marking in Section C (NAT) as well. Regn. No , Mall Road, G.T.B. Nagar, Opp. G.T.B. Nagar Metro Station Gate No. 3, Delhi A/11, Jia Sarai, Near IIT Metro Station, Gate No. 3, New Delhi DOWNLOAD CAREER ENDEAVOUR APP South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: ,

2 Q.1 To Q.1 : Each carr ONE mark [PART-A : MULTIPLE CHOICE QUESTIONS (MCQ)] 1. If and are boolean variables, which one of the following is the equivalent of? (a) (b) (c) (d) 1. Radiation of angular frequenc is incident separatel on two metals A and B having work functions and 4, respectivel. The ratio of stopping potential for A to that of B is (a) /3 (b) 3/ (c) 1/ (d) /1 3. In -dimension, an ensemble of N classical particles has energ of the form p 1 1 p E k k m m The average internal energ of the sstem at temperature is (a) 3 1 N kbt (b) N kbt (c) N kbt (d) 5 N kbt 4. A parametric curve defined b cos ( n/), sin ( n/) in the range n 1 is rotated about the - ais b 36º. Area of the surface generated is (a) (b) (c) (d) 4 5. A particle moves in a plane with constant radial velocit r 4. The angular velocit is constant and has magnitude rad/s. When the particle is 3m from the origin, the magnitude of its acceleration is (a) (b) 15 (c) 1 (d) 7 6. A uniform rope of mass M and length L is pivoted at one end and whirls with uniform angular velocit. What is the tension in the rope at distance r from the pivot? (a) M r L (b) M r L (c) M L ( L r ) (d) M L ( L r ) 7. Oscillation of the particle under damping force is represented b the curve as shown below: I II III t Critical damping is represented b (a) Curve II (b) Curve III (c) Curve I (d) None of these A 8. A spherical shell of dielectric having inner radius a and outer radius b carries a polarization p rˆ, where A r is a constant and r is the distance from the centre ( a r b ). Then the potential at the centre will be (a) zero (b) A ln b a (c) A a b (d) A b a South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: ,

3 9. S 1 and S are two coherent sources as shown in figure. The interference fringes formed on the screen (- plane) will be S (a) strictl circular. 1 (b) strictl hperbola but approimatel straight lines. S (c) strictl straight lines. (d) strictl elliptical with major ais not equal to minor ais. 1. A circular loop carring current I placed at z = h, parallel to a uniform current sheet k k ˆ at z is shown below z I 3 Which of the following is correct? (a) Loop will have onl translation motion along z ˆ. (b) The loop will have onl rotational motion about it diameter. (c) The loop will have translation as well as rotational motion. (d) None of the above. Q.11 To Q.3 : Each carr TWO marks 11. In the voltage regulator (shown in the figure), the bad current var from 1 ma to 5 ma. Assuming that the zener diode is ideal (i.e., the zener knee current is negligibl small and zener resistance is zero in the break down region). The value of R is R 1 V 5 V Variable load 1 to 5 ma (a) 7 (b) 7 (c) 7 3 (d) The gain Vout V in for the circuit shown in figure, if the amplifier is ideal, is k k k V in 5 k V out (a) 48 (b) 8 (c) 36 (d) A particle of mass m is in a potential of the form 1 V ( r ) m ( 4 z ) [ is a real constant]. If the ground state energ of the particle is 7, its first ecited state energ E 1 and the value of is, 9 7 (a) 4, E1 (b) 16, E1 South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: ,

4 9 7 3 (c) 16, E1 (d) 4, E1 14. Consider the differential equation 3 3 d d d d. If (1), then ( ) is equal to (a) 4 (b) 1 (c) 1 (d) 1/ t [ t], t 15. Consider g( t). Here, [ t ] represents the largest integer less than or equal to t and { t} t { t}, t denotes the smallest integer greater than or equal to t. The coefficient of a in the Fourier epansion of g( t ), n t given b g( t) an sin is n 1 4 (a) 1 (b) 1 (c) (d) 16. A ring of mass m and radius r lies on a frictionless table. It is pivoted to the table at its rim. A bug of mass m walks on the ring with relative speed v starting from the pivot. Angular speed of the ring when bug has moved half wa around is v v v v (a) (b) (c) (d) r 3r 3r 4r 17. A uniform stick of mass M and length L is held in horizontal position with end B on edge of table and the other end A held at rest b hand. The vertical acceleration of centre of mass at the moment its end A is released, is (a) g (b) g (c) g 3 (d) 3g In spherical coordinate, the spherical EM wave is given b 1 ˆ V E sin cos ( t r) r m.65 ˆ A H sin cos ( t r) r m at a large distance r from a dipole antenna in free space. The time average power crossing the hemispherical shell r 1 km, is (a) 11.1 W (b) 44.4 W (c) 55.5 W (d) 66.6 W 19. A proton is fied in a position and an electron revolves about proton in a circular path of radius 1 r.35 1 m. The magnetic field at the position of proton will be (a) zero (b) 5 T (c) 35 T (d) 45 T. A clindrical conductor of radius 1 mm has an internal magnetic field 4 r r H ˆ A/ m.3 The total current in the conductor is (a) 5A (b) 1 A (c) A (d) 4 A 1. The wavelength associated with an electron having an energ equal to the Fermi energ is given b 1/3 (a) (b) (c) 3n 3n 3n (Where n is the electronic concentration per unit volume.) 1/3 South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: , /3 (d) 3n /3

5 5. The miller indices of a plane that makes intercepts of Å, 3Å, 4Å on the co-ordinate aes of an orthorhombic crstal with a : b : c = 4 : 3: are (a) (41) (b) (14) (c) (41) (d) (43) 3. If 3 e e is the solution of the initial value problem d d 4, () 4 and 1, where, R, then d d (a) 3 and 4 (b) 1 and (c) 3 and 4 (d) 1 and 4. One mole of a monatomic ideal gas at a temperature 5 K is compressed from 1 atm to atm pressure b a reversible isothermal path. Subsequentl, it is epanded back to 1 atm b a reversible adiabatic path. The volume of the final state (in litres) is approimatel (a) 15.6 (b).156 (c) 31.5 (d) If a gas obes the equation of state P( V nb) nrt, where b is some constant, the ratio ( C C ) P V ( C C ) P V Given gas Ideal gas is ( CP and CV are heat capacit at constant pressure and volume respectivel) (a) > 1 (b) < 1 (c) 1 (d) 1 b 6. A conical pendulum consists of a bob of mass m and inetensible string of length l and negligible mass. The bob revolves in horizontal circle with uniform angular velocit so that the string makes a constant angle with downward vertical. Rate of change of angular momentum of the bob about point of suspension is (a) ml cos (b) ml ml sin (c) sin (d) 7. Suppose q is charge is distributed on a small conducting sphere of radius a. Now, it is taken towards a large earthed conducting plane and placed at a distance d from the plane ( d a ). The potential of the sphere will be (a) zero (b) q 4 a (c) q a 1 4 a d (d) q 4 d 8. Ms. Radhika purchased a Jhumka (ear-ring) of gold which has a Jhalar (wire mesh) at lower end (shown in figure). If separation between primar maima in diffraction pattern is 5 cm, then total number of Jhalar (wire) in her Jhumka is (Jhumka) Screen 5cm = 5 nm Light 5mm Diffraction pattern (a) 1 (b) 5 (c) 5 (d) 1 9. Equation of standing wave in resonates with fork is 5 3sin cos l 1 m South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: ,

6 6 If length of the wire is 5 cm, the value of / is (velocit of wave is m/s in string) (a) Hz (b) 4 Hz (c) 1 Hz (d) 6 Hz 3. Two sources are said to be coherent when (a) Their phase difference is either or. (b) The are in phase. (c) Their phase difference remains constant with time. (d) Their phase difference depends on time..5 [PART-B : MULTIPLE SELECTIVE QUESTIONS (MSQ)] Q.31 To Q.4 : Each carr TWO marks 31. In an ideal op-amp circuit shown below R1 k and R 1 k and Vin sin t volt. Which of the following statement(s) is/are correct? (a) The current through R 1 the current through R 1 = k R. (b) The potential at N is V R R R. R = 1 k V in N V out o 1 (c) The amplitude of V is V. o (d) The output voltage V o is out of phase with V in. 3. A photon of energ mc scatters off an electron b an angle. Which of the following statement(s) is/are correct? [ m is electron mass] (a) The fractional loss in the energ of the photon is (1/). (b) The angle of deviation of the recoil electron is cot (). (c) The wavelength of the scattered photon will be h mc. (d) The de-broglie wavelength of the recoiled electron is h 5mc. 33. Consider the matri P Which one of the following statements about P is CORRECT? (a) Determinant of P is equal to 1. (b) The eigenvectors of P are orthogonal to each other. (c) Inverse of P is equal to its transpose. (d) All eigenvalues of P are real numbers. 34. In figure shown equal volume of two liquids are filled in a container. Small orifices of same areas are made at A and B. Which of the following statement(s) is/are correct? (a) Speed of liquid from orifice A is gh. (b) Speed of liquid from orifice B is 3gH. (c) Ratio of torque due to impulse of liquid flowing out about A and B is 3. (d) If pressure at 1 and be P 1 and P respectivel, then value of atmospheric pressure is 3P P 1. South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: , H P 1 P A B

7 35. Two equal and opposite charge particle enter in a semi-magnetic region with same speed as shown in figure, then 7 +q 3º q (a) the will spend same time in the magnetic field region. (b) the positive charge particle will spend longer time than negative charge particle. (c) the negative charge particle will spend longer time than the positive charge particle. (d) the will follow the same radius of the arc inside the magnetic field. 36. Choose the correct statement(s) from the following : (a) The interplanar spacing for (111) planes of simple cubic sstem is a 3 (b) The atomic planar densit of (11) plane on bod centered cubic lattice is a (c) The interplanar spacing for (1) planes of face-centered cubic lattice is a 3º (d) The atomic planar densit of (111) plane in face-centered cubic lattice is 4 3a 37. A one mole of an ideal gas undergoes two cclic processes ABCA and ABDA as shown in the figure below: P P A P B D C V V V If out of processes AC and AD, one is isothermal and other is adiabatic, which of the following is/are correct? (a) The volume at point C is greater than 1. V. (b) The volume at point C is less than 1. V. (c) The work done in the process AC is greater than.8 P V. (d) The work done in the process AD is less than.9 P V. 38. Consider a QWP with optical ais along -ais. Optical ais is parallel to the surface. If light beam E( z, t) E e iˆ E e ˆj i ( t kz ) i ( t kz) 1 is incident on the crstal from the left, then (a) Incident beam is ellipticall polarized, if 1 and E E. z (b) Incident beam is ellipticall polarized, if 1 and E E. I QWP : Optical ais (c) If incident wave is ellipticall polarized with major ais at 45º with -ais, emergent ras is linearl polarized. (d) If incident wave is ellipticall polarized with major ais along -ais, emergent light is linearl polarized. South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: ,

8 39. A light beam is incident on a sstem of HWP and polarizer as shown below. Optical ais and pass ais of HWP ( ) and polarizer is along -ais. If incident wave is given b ˆ ˆ i t kz E E( i i j) e, then 8 z Polarizer I HWP (a) incident wave is linearl polarized. (b) incident wave is circularl polarized. (c) light emerging out of HWP is circular. (d) intensit of light after polarizer is I. 4. A verticall polarized (-ais) light travelling along z-ais incident on a HWP with optical ais as shown in figure. HWP (a) Emergent light is also vertical polarized. E 45º (b) Emergent light is horizontal polarized. (c) Emergent light is linearl polarized at 45º with -ais. z (d) Emergent light is linearl polarized at 45º with -ais. Optical ais [PART-C : NUMERICAL ANSWER TYPE QUESTIONS (NAT)] Q.41 To Q.5 : Each carr ONE mark 41. p is an eigenstate of p ˆ with an eigenvalue. p is an eigenstate of [ ˆ, p ˆ ] with an eigenvalue (in units of i ). (specif our answer in integer) 4. A bo throws a stone upward with speed 1 m/s. The time of flight of the stone as seen b an observer moving with speed c/ along horizontal direction is seconds. [Consider Earth to be an inertial frame and g = 1 m/s ]. [Specif our answer upto two digits after the decimal point] ln (1 ) Consider the function f ( ). The coefficient of is in the Talor series epansion of f ( ) (1 ) about is. [Specif our answer upto two digits after the decimal point] 44. A block of mass kg is at rest on a horizontal rough surface. The co-efficient of friction between the floor and suface is.5. A horizontal force force F 4t is applied on it at t. Speed of the block at t 5 sec is m/s. (Take g = 1 m/s ). [Specif our answer upto two digits after the decimal point] 45. The piston of a spring gun has mass 48 gm and it is attached to one end of a spring with spring constant k 4 N/m. The projectile is a marble of mass 16 gm. The piston and marble are pulled back a distance 1cm from equilibrium position and suddenl released. Speed of the marble when it loses contact with the marble is m/s. [Specif our answer upto two digits after the decimal point] Fied Piston Marble South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: ,

9 46. Consider the interface z = between two dielectrics. The electric field in the region z and region z are E ˆ ˆ ˆ 1 5i j 3k and E ˆ ˆ ˆ 5i j 4k respectivel. If the k 1 and k are dielectric in region 1 and region, then the value of k k 1 is. [Specif our answer upto two digits after the decimal point] 47. Aluminium has an FCC structure. Its densit is kg/m 3. The unit cell dimension in units of Å is. [Specif our answer upto two digits after the decimal point] 48. The number of was, b which three identical bosons can be filled in two energ states E 1 and E, where the energ state E is doubl degenerate is given b. [Specifi our answer in integer] 49. In a single slit Fraunhofer diffraction pattern, the intensit of the central maimum is I. If the slit width is doubled, the intensit of the central maimum would be I [Specifi our answer in integer] 5. The binding energ per nucleon of deuteron ( 1 H ) and helium nucleus ( 4 He ) is 1.1 MeV and 7 MeV respectivel. If two deuteron nuclei react to form a single helium nucleus, then the energ released is MeV. [Specif our answer upto one digit after the decimal point] 9 Q.51 To Q.6 : Each carr TWO marks 51. For a BJT, the common-base current gain =.98 and the collector base junction reverse bias saturation current I CO.5 µa. This BJT is connected in the common emitter mode and operated in the active region with a base drive current I B µa. The collector current I C for this mode of operation is ma. [Specif our answer upto one digit after the decimal point] An electron is in the state 1, [ and 1 are the ground and first ecited states 3 9 of a 1-D infinite potential well of width 1 Å]. The average kinetic energ of the electron is 1 ev. [Specif our answer upto two digits after the decimal point] 53. Let D be the region bounded b the parabola.[specifi our answer in integer] 54. The flu of the vector and the line. Then 3 d d equals to ˆ ˆ A i j z k ˆ through the curved surface area of an open clinder with radius a, height h and centered at the origin, is ah. [Specifi our answer in integer] 55. A particle of unit mass is at rest at point (,, ). The particle starts moving along the square under a force ˆ F ( i ˆj ). On returning to the initial point its speed is. [Specifi our answer in integer] (,,) D (,,) South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: ,

10 56. Consider three wire carring current I are placed as shown in figure. (Two are ling in the -plane and third one is carring current in negative z-direction). The magnetic field at the point (, d, ) is I d. The value of is [Specif our answer upto two digits after the decimal point] 1 3º 3º 57. Two Carnot engines A and B are operated in series. First engine A absorbs heat at 11 K and rejects it to the sink at T K. Second engine B absorbs half amount of heat rejected b first engine and rejects heat to the sink at K. If the work performed b both engines are equal, the value of T is K. [Specifi our answer in integer] 58. A thermall insulated container of volume V has a partition which divides it into two chambers in the ratio 1:. Each chamber contains an ideal gas X at temperature T and pressure P. If the number of molecules in the chambers are in the ratio 1 :, the change in the entrop of the sstem on removing the partition is J/K. [Specifi our answer in integer] 59. Consider a grating with slit separation d = 3a, where a is slit width. The ratio of intensit of the 3 rd order principal maima to first order is [Specif our answer upto one digit after the decimal point] 6. A atomic power reactor furnace can deliver 3 MW. The energ released due to fission of each of uranium atom 38 U is 17 MeV. The number of uranium atoms fissioned per hour will be 1 1. [Specifi our answer in integer] ************************ South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: ,

11 11 Space for rough work South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: ,

12 1 IIT-JAM-PHYSICS-PH TEST SERIES - 4 Date : FULL LENGTH TEST - 1 ANSWER KEY [PART-A : MULTIPLE CHOICE QUESTIONS (MCQ)] 1. (b). (a) 3. (b) 4. (c) 5. (a) 6. (d) 7. (b) 8. (b) 9. (a) 1. (b) 11.(d) 1. (a) 13. (c) 14. (b) 15. (b) 16.(d) 17. (d) 18. (c) 19. (c). (a) 1.(a). (c) 3. (a) 4. (c) 5. (c) 6.(c) 7. (c) 8. (c) 9. (c) 3. (c) [PART-B : MULTIPLE SELECTIVE QUESTIONS (MSQ)] 31.(a),(d) 3.(a),(b),(c),(d) 33.(a),(b),(c) 34.(a),(b),(c),(d) 35.(b),(d) 36.(a),(b),(c),(d) 37. (a) 38.(a),(b),(d) 39.(b), (c), (d) 4. (b) [PART-C : NUMERICAL ANSWER TYPE QUESTIONS (NAT)] 41.(4 to 4) 4. (.5 to.35) 43. (.54 to.6) 44. (16. to 16.3) 45.(.45 to.55) 46. (.7 to.8) 47. (4. to 4.1) 48. (1 to 1) 49.( to ) 5. (3.5 to 3.7) 51. (1.) 5. (1.36 to 1.4) 53.( to ) 54. ( to ) 55. (4 to 4) 56. (.5 to.5) 57.(8 to 8) 58. ( to ) 59. () 6. (4 to 4) South Delhi : 8-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : , North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-9, Ph: ,