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

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1 . Section-A contains Multiple Choice Questions (MCQ). Each question has 4 choices,, and, for its answer, out of which ONLY ONE is correct. From Q. to Q. carries Marks and Q. to Q. carries Marks each.. Section-B contains Multiple Select Questions(MSQ). Each question has 4 choices,, and 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.4 to Q.5 carries Mark each and Q.5 to Q.6 carries Marks each. For each NAT tpe question, the value of answer in between to In all sections, questions not attempted will result in ero mark. In Section A (MCQ), wrong answer will result in negative marks. For all mark questions, / marks will be deducted for each wrong answer. For all marks questions, / 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. -5, Mall Road, G.T.B. Nagar, Opp. G.T.B. Nagar Metro Station Gate No., Delhi- 9 Delhi- 6 DOWNLOAD CAREER ENDEAVOUR APP: E : info@careerendeavour.in North Delhi : -5, Mall Road, G.T.B. w : ww Nagar w.careerendeavour.in (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, 6869

2 Section-A : Multiple Choice Questions (MCQ) Q. to Q.: Carr Mark each.. A cone at radius R and height H is placed in an uniform electric field as shown in figure. The flu through the curved surface S of the cone. S H R R R H E R R H R E ero. Three charges, each of value Q, are placed at the verte of an equilateral triangle. A forth charge q is placed at the centre of the triangle. If the charges remains stationar then q is Q Q Q Q. Charges q and q are placed at point A and B respectivel, which are a distance L apart, C is the midpoint between A and B. The workdone in moving a charge Q along the semicircle CRD, is R qq L qq 6 L A C B D qq 6 L qq 4 L 4. Two spherical conductors of radii r and r are at potentials V and V respectivel, then what will be the common potential when the two conductors are brought in contact r V r V r r r V r V r r r V r V r r None of these 5. Two long thin wires each having charge densit are placed along the lines a and a. Electric field at (,, ) is a a a 6. The work function of some metals are listed below: Metal ev Li K Ag Mg a When light of wavelength nm is incident of the each of the metal independentl, then which of the following metals will show photoelectric effect? K onl K and Li onl K, Li and Mg onl All metals 7. Let and denote, the normalied eigenstates of a aprticle with energ eigenvalues E and E respectivel. At time t =, the particle is prepared in a state, t It is observed that both, t T and are, t T orthogonal to, t value of T T, is. The minimum non-ero North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, 6869

3 E E E E E E 8. A particle is moving in a two-dimensional potential well described as following: V, for L, L L otherwise The ground state eigenfunction for the sstem, is sin sin L L L cos sin L L L sin cos L L L 4 E E cos cos L L L 9. Let ˆ and p ˆ denote the position and momentum operator of a particle. The commutator bracket pˆ m pˆ, m will be ero, if 4. For a particle of energ E in one-dimensional square well of depth -V, centered at the origin and width a, the bound state wave function for large negative is of the form ep me ep me sin me cos me Q. to Q.: Carr Marks each.. An infinitel long wire is placed at distance d from a large grounded conducting sheet. The wire carries uniform linear charge densit. Workdone per unit length in moving the wire to separation d keeping its orientation parallel to the sheet, is 4 d 4 ln. From a uniforml charged sphere of radius R and volume charge densit, two spherical portions of radii R/ are removed as shown in the figure. ln Magnitude of electric field at the centre of one of the cavities is R. An electric dipole of dipole moment ˆ integral E dl along semicircle C : R C p p 4 R R R 6 R 8 p i is placed at (,, ). If E be the field of dipole then value of line from ( R, ) to ( R, ) in anticlockwise sense is p R p 4 R North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, 6869

4 4. A sphere has uniform polariation P ˆ. Potential difference between centre of sphere and the point (,, R ) is (where R is radius of the sphere). P R P R 6 P R 8 P R 5. A long wire carring current I is placed along -ais with current flowing in +-direction. If B be the magnetic Q field of the wire, then value of line integral B dl along the curve C : = a from P to Q is [where P and Q have co-ordinates ( a, a, ) and ( a, a, ) respectivel]. I I I I 4 P 6. When a non relativistic charge particle of mass m, charge q and speed v is thrown into a uniform perpendicular magnetic field from outside, it comes out of the field in time T. When direction of initial velocit is changed b angle it comes out in time T. T T is equal to m qb m qb m qb m qb 7. A charge Q is uniforml distributed on annular ring of inner and outer radii R and R. If the ring is uniforml rotated about its ais with angular velocit, what will be magnetic field at its centre. Q ( b a) Q ( b a) Q ( b a) Q ( b a) 8. A thin conducting rod of length l is rotated with uniform angular velocit as shown in the figure in presence of a uniform magnetic field. Motional e.m.f. between centre and free end of the rod is B B B B B 4 Bl sin 8 Bl sin 8 Bl sin 8 Bl sin 8 9. A square loop of side a and resistance R is placed in uniform magnetic field perpendicular to its plane. If the loop is rotated with uniform angular velocit about its one side, heat generated during one complete rotation will be a B a B a B a B R R 4R R. For a certain medium, the relation between the refractive inde n and angular frequenec is given as B n ; B The ratio of c v g in the given medium, will be B n n B n n B n n B n n North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, 6869

5 . Which of the following statements is not true about binding energ per nucleon? It is maimum for iron Its average value is about 5 MeV It is almost constant for most of the nuclei It increases for low mass nuclei and then becomes almost constant. The ground state energ of a particle of mass m in a two dimensional isotropic harmonic oscillator potential, is not ero. This is because The ground state does not have an nodes. This is the most convenient choice of the ero level of potential energ. The potential is smmetric about the origin. Position and momentum of the particle cannot be measured simultaneousl accuratel.. The wavefunction of a particle moving in free space is given b, epik ep ik The probabilit current densit corresponding to the wave function, is 5 k iˆ m 5 k iˆ m k i m ˆ k iˆ m 4. Particles of energ E are incident on a rectangular potential barrier of height V E minimum value of the width L, for which there will be maimum reflection from the barrier is m E V m E V m E V 5 and width L. The 5. If N is the original mass of the substance of half-life period t ½ = 5 ears, then the amount of substance left after 5 ears N /8 N /6 N / N /4 6. An atom of mass M can be ecited to a state of mass M b photon capture. The fre quenc of the photon which can cause this transition is c h c Mh c M Mh c M 7. A rod of length l carries a total charge q distributed uniforml. If this is observed in a frame moving with a speed v along the rod, the charge per unit length measured b the moving observer will be q v l c q l v c 8. Electric field in a region is E iˆ kˆ l q v c h q v l c. The flu through a semicircular region is The binding energ of a light nucleus (Z, A) in MeV is given b the approimate formula: B Z A A A A 4 / /, 6 N Z where N A Z is the neutron number.the value of Z of the most stable isobar for a given A is A / A A 8 / A A 4/ A A North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, / A A 6

6 . A meson at rest decas into a µ + meson and a neutrino in.5 8 s. Assuming that the meson has kinetic energ equal to its rest energ. What distance would the meson travel before decaing as seen b an observer at rest m 6.5 m m 5 m 6 Section-B : Multiple Select Questions (MSQ) Q. to Q.4: Carr Marks each.. Electric potential inside a solid sphere of radius R at distance r from the centre is ( r) ( ar b), then the correct statement(s) is/are : Electric field at r R depends on onl a Electric field at r R depends on onl b Electric field at r R depends on both a and b Electric field at r R does not depend a and b. A plane electromagnetic wave E ˆj E cos ( t k) propagating in space. It E 4 V 5 and 6 rad sec. The correct statement(s) is/are : m The direction of the ponting vector will be along î. The magnetic field corresponding to electromagnetic wave is given b B.67 cos ( t k) kˆ. The amplitude of e.m.f. induced in the equilateral triangular loop of sides a 5 cm and the resistance of the each side is as shown in figure is 5.65 µ volt. The amplitude of induce above current in the above loop will be 8.8 na.. A sphere of radius R has uniform volume charge densit ( ). Choose the INCORRECT statement(s) : The ratio of potential at the centre and electric field at the surface of sphere is depends on onl radius of the sphere R. The ratio of potential at the centre and electric field at the surface of sphere is depends on onl the charge densit of the sphere ( ). The ratio of potential at the centre and electric field at the surface of sphere is depends on both radius R and charge densit ( ) of the sphere. The ratio of potential at the centre and electric field at the surface of sphere is independent of both radius R and charge densit ( ) of the sphere. 4. A rectangular loop of sides cm and 5 cm carring a current A is placed in the different orientations as shown in the figures below : (A) B (B) B (C) B (D) B It there is a uniform magnetic field. T in the positive -direction. The CORRECT statement(s) is/are : North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, 6869

7 Orientations the loop (A) would be stable and (C) will be unstable. Orientations the loop (B) would be stable and (D) will be unstable. Orientations the loop (B) would be stable and (C) will be unstable. Orientations the loop (D) would be stable and (C) will be unstable Suppose nlm be the eigenfunction of the Hamiltonian operator of the hdrogen atom where n, l, m are principal, orbital and magnetic quantum number respectivel. Which of the following wavefunctions is/are an eigenfunction of above mentioned Hamiltonian operator? (a,b,c are constants) a b c a 4 b 4 c 4 a b c 4 a b c 6. Consider a particle of mass m is moving under the following -D potential: V, m 9 Which of the following statements is/are CORRECT? The energ eigenvalues of the particle is given b n. The degenerac of the third ecited state is. The energ of the fourth ecited state is A current flows through along cable such that current densit is uniform at ever point on its cross section. Which of the following statements is/are correct? Magnetic field inside is proportional to distance from ais Magnetic field outside is inversel proportional to distance from ais Ponting vector is radiall inward at ever point inside the cable. Curl of magnetic field is non-ero inside the cable and ero outside the cable. m The wave function of the third ecited state will be ep 8. The filament of a light bulb is clindrical with length mm and radius.5 mm. The filament is maintained at a temperature 5 K b an electric current. Assume that the filament behaves approimatel as a black bod, emitting radiation isotropicall. At night, ou observe the light bulb from a distance km with the pupil of our ee full dilated to a radius mm. Which of the following statements is/are CORRECT? (Given: Stefan- 8 4 Boltman constant = 5.6 W. m. K, Wien s Law constant =.9 m. K ) Total power radiated b the filament, is W. The amount of radiation power that enters our ee, is 4.95 W. The wavelength at which the filament radiate the most power, is 58 nm. 7 The number of radiated photons enter our ee per second, is Dimension of acitivit of a sample is Time energ planck constant Force mass work done 4. Two particles are moving with relativistic velocit in directions at right angles, the have moments P and P and total energies E and E. If the are the sole products of disintegration of a heavier object, then which of the following statements about heavier object is true / Rest mass is c E E P P c Velocit is c P P / E E North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, 6869 /

8 8 / Rest mass is c E E P P c / Velocit c P P / E E Section-C : Numerical Answer Tpe (NAT) Q.4 to Q.5: Carr Mark each. 4. X-ras with an energ of kev undergo Compton scattering with a target. If the scattered X-ras are detected at relative to the incident X-ras, then energ of the scattered X-ra will be KeV. (Your answer should be an INTEGER). 4. To observe small objects, one measures the diffraction of particles whose de Broglie wavelength is approimatel equal to the object s sie. The kinetic energ required for electrons to resolve a large a nucleus of sie fm, will be MeV. (Your answer should be an INTEGER). 4. A quantum sstem with three orthonormal states, and is described b following hamiltonian : Hˆ i i The sum of energ eigenvalues of the sstem, is units. (Your answer should be an INTEGER) 44. A particle of mass m is moving under the following -D potential: V,, for a, a, a elsewhere If the particle is found to be in an eigenstate of energ 7, then degenerac of the eigenstate is ma (Your answer should be an INTEGER) 45. An electron is bound in an infinite square-well potential on the - ais. The width of the well is L and the well etends from = nm to = 4.5 nm. In a given state, the normalied wave function of the electron is given b: sin L L The probabilit of finding the electron at =.5 nm, is closest to (Your Answer should be upto ONE Decimal Places) 46. The masses of C and B are respectivel.4u and.9u. The maimum energ of a positron can have in the deca of C to B is KeV. 47. A circular loop of radius a and carring a current I is smmetricall kept inside the hollow cube of side 4a such that centre of loop coincides with the centre of the cube. Total magnetic flu through the cube is 48. Two semi-infinite grounded conducting planes meet at an angle º the number of image charges formed 49. the value of magnetic field required to maintain non-relativistic proton of energ MeV in a circular orbit 7 9 of radius mm is (Given : mp.67 kg, e.6 C ) Tesla. D iˆ 4j ˆ kcm ˆ, the total charge enclosed b the cube,, 5. If is C. North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, 6869

9 9 Q.5 to Q.6: Carr Marks each. 5. A parallel plate capacitor having plates of area S and plate separation d, has capacitance c in air. When two dielectrics of different relative permitivities ( and 4) are introduced between the two plates as shown in the figure, the capacitance becomes c, the ratio c c is. d/ S/ (Upto nd decimal place). d 5. Two equal charges Q are separated b a distance d. A grounded conducting sphere is placed midwa between them. The two charges eperience ero force for the radius of the sphere R ( d / ), then the value of is. 5. The normalied wavefunction of a particle in three dimensions is given b r a r,, ep a a The ratio of the most probable distance from the origin to the mean distance from the origin, is (Your answer should be upto TWO decimal places). 54. A quantum mechanical sstem consists of one-dimensional infinite bo of Length L. Five identical non-interacting spin / particles, are first placed in the bo and the ground state energ of the sstem is found to be ev. If eleven such identical particles are placed inside the bo, then the ground state energ of the sstem will be ev. (Your answer should be an INTEGER) 55. Electrons of energ 9 ev are sent from the negative side towards =, where the potential suddenl jumps from V = to V = 5 ev. Let be the periodicit of the wavefunction of the electron in the region where the potential is ero and be the periodicit of the wave function of the electron in the region where the potential is 5 ev. The ratio / will be (Your Answer should be upto TWO Decimal Places) 56. Hdrogen atom in states of high quantum number have been created in the laborator and oberved in space. If the radius of the atom is. mm, then the energ of the atom is 5 ev. (upto second decimal place) (Given Bohr s radius a = 5.9 m) 57. The energ of the He + in its first ecited state is ev. 58. An electromagnetic wave 8 i45 t E e kˆ V/m is travelling in isotropic linear non-magnetic dielectric medium. The dielectric constant of the dielectric medium is 59. A light beam emitted b a 5-watt laser has a uniform cross-section of.5 mm. The amplitude of electric field associated with the beam (in V/m) is 4 6. If a particle has kinetic energ equal to its rest mass energ then the velocit of the particle is c. r ***** END OF QUESTION PAPER ***** North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, 6869

10 Space for Rough Work North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, 6869

11 IIT-JAM PHYSICA-PH TEST SERIES - (Modern Phsics + Electricit & Magnetism) Date : --8 Booklet: B ANSWER KEY Section-A : Multiple Choice Questions (MCQ) Section-B : Multiple Select Questions (MSQ)..,,,.,, 4. 5.,, 6.,,, 7.,,, 8.,,, 9., 4., Section-C : Numerical Answer Tpe (NAT) 4. (77 to 79) 4. ( to 5) 4. () 44. (4) 45. () 46. (94 to 96) 47. () 48. () 49. (.44) 5. () 5. (.) 5. (8) 5. (.65 to.69) 54. (87 to 89) 55. (.65 to.69) 56. ( 7. to 7.5) 57. (.6) 58. (9) 59. (8.5 to 8.9) 6. (.84 to.88) North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: , South Delhi : 8-A/, Jia Sarai, Near-IIT Hau Khas, New Delhi-6, Ph : -6858, 6869

Regn. No. North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-09, Ph: ,

Regn. No. North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-09, Ph: , 1. Section-A contains Multiple Choice Questions (MCQ). Each question has 4 choices, (b), (c) and, for its answer, out of which ONLY ONE is correct. From Q.1 to Q.1 carries 1 Marks and Q.11 to Q. carries