PHYSICS SECTION-A 1. म ट रक स. क) gjfef k;u (Hermitian) ख) Ld; wgjfef k;u (Skew Hermitian ) ग) सम मत घ) एक मक. (क) cosz (ख) Sinz ग) Coshz.

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1 i 0 1. The matrix 0 i is : a) Hermitian b) Skew Hermitian c) Symmetric d) Unitary 2. In spherical coordinates, the coordinate curve (φ curve) due to the intersection of r = c 1 and θ = c 2 is a a) straight line b) circle c) semi circle d) Curve PHYSICS SECTION-A i 0 1. म ट रक स 0 i ह : क) gjfef k;u (Hermitian) ख) Ld; wgjfef k;u (Skew Hermitian ) ग) सम मत घ) एक मक 2. ग ल क र नद श क म सम वय क अव थ (φ curve) आर = स 1 और θ = स 2 क buvjlsd ku क वजह स ह क) स ध प क त ख) सकर ल ग) अद धर सकर ल घ) वक र 3. Binomial distribution may be approximated by Poisson distribution if a) n is large, p is large b) n is small, p is large c) n is large, p is small d) n is small, p is small 3 z 5 z 4. The series z ! 5! represent the function (a) cos z (b) sin z (c) cosh z (d) sinh z 5. If y 1 & y 2 are the solutions of 2 nd order 1 1 differential equation and y 1 and y 2 are their derivatives, then the Wronskian is given by (a) y 1 y y 2 y 1 (b) y 1 y 2 y 1 1 y 1 2 (c) y 1 y y 2 y 2 (d) y 1 y 1 y 1 2 y वपद वतरण Poisson वतरण buvjlsd ku gks ldrk gs rks mldk vuqeku yxk;k tk ldrk gs ;fn क) n cmk gs p cmk gs ख) n NksVk gs p cmk gs ग) n cmk gs p NksVk gs घ) n ह छ ट ह, p छ ट ह z z 4. खल z ! 5! प र त न ध व (क) cosz (ख) Sinz ग) Coshz (घ) Sinh Z 3 5 सम र ह क 5. ;fn Y1 और y2 second order आद श अ तर सम करण क सम ध न कर रह ह और y और y 2 उनक ड रव टव ह, त Wronskian }kjk दय ज त ह (क) y 1 y y 2 y 1 (ख) y 1 y 2 y 1 1 y 1 2 (ग) y 1 y y 2 y 2 (घ) y 1 y 1 y 1 2 y 1 2

2 6. Which one of the following functions is odd and periodic? (a) cos x (b) cosh x (c) sin x (d) sinh x 7. The vector perpendicular to the surface (x,y,z)= c, where c is a constant is : (a) (b) ( ) (c) (d) d dt 8. What is trajectory of projectile motion? a) linear b) parabolic c) elliptic d) circular 9. Which one of the following is true for inertial frame of reference? a) non-uniform velocity b) Newton s laws holds c) uniform velocity d) both (b) & (c) 10. What will be the angle between two velocity vectors after elastic collision of two equal-mass particles? a) 45 0 b) c) 30 d) Which one of the following is true for the eccentricity (e) of an elliptic orbit? a) e > 0 b) e < 0 c) e = 0 d) e = 1 6. fueu esa ls dksu lk QaD ku fo"ke o ihjhvksfmd gs? (क) cos x (ख) coshx (ग) sinx (घ) Sinh x 7. व क टर सतह (x,y,z)= c, ij vfoyeo gs जह स थर ह (क) (ख) ( ) (ग) d dt (घ) 8. प रक ष य ग त क trajectory क य ह? क) र खक ख) isjkoksfyd ग) अ ड क र और) xksykdkj 9. न न ल खत म स क न जड़ व य फ र म क लए सच ह? क) ग र वद र व ग ख) य टन क नयम रखत ह ग) सम न व ग घ) द न (ख) और (ग) 10. द बर बर-जन क कण क ल चद र टक कर क ब द द व ग व क टर ब च क ण ह ग? क) 45 0 ख) 60 0 ग) 30 0 घ) न न ल खत म स क न एक अ ड क र कक ष क,lSUVjhflVh (ई eccentricity (e) क लए सच ह? क) ई > 0 ख) ई <0 ग) ई = 0 घ) ई = 1

3 12. Which one is the example of noncentral force? a) nuclear b) gravitation c) electrostatic d) all of these 13. What will be total area of closed surface? a) zero b) positive c) negative d) infinite 14. Homogeneity of time leads to conservation of. a) kinetic energy b) angular momentum c) linear momentum d) total energy 15. A spherical body cannot roll on a) a rough inclined surface b) a smooth horizontal surface c) a smooth inclined plane d) a rough horizontal plane. 12. ज एक ग र क द र य बल क उद हरण ह? क) परम ण ख) ग व कषर ण ग) इल क ट र ट टक घ) सभ 13. ब द सतह क क ल क ष त रफल क क य ह ग? क) श य ख) iksftfvo ग) usfxfvo घ) अन त 14. समय क एक पत क स रक षण क लए ह त ह क) ग तज ऊज र ख) क ण य ग त ग) र ख य ग त घ) क ल ऊज र 15. एक ग ल क र oksmh (body), र ल नह कर सकतh क) ;fn [kqjnjh >qdh gqbz lrg ख) एक चकन lery सतह ग) एक चकन >qdh gqbz lrg घ) [kqjnjh lery सतह

4 Section B 16. Light is incident on an air- glass interface at angle 30, with the electric field component normal to the plane of incidence. The reflection and transmission amplitudes are [the refractive index of glass is 1.5 ] a) 0.24, b) 0.76, c) 0.76, d) 0.24, An object positioned at 10 cm to the left of a positive lens is imaged 30 cm to the right of the lens. Where will the image appear and it s nature if the object is now moved so that it is 2.5 cm from the lens? a) Virtual, erect, magnified and located 3.75 cm in the front of the lens. b) Real, inverted, magnified and located 3.75 cm in the front of the lens. c) Virtual, inverted, de- magnified and located 3.75 cm at the back of the lens. d) Real, erect, magnified and located 3.75 cm in the back of the lens. 18. A double convex lens has radii of 5 cm and 20 cm, thickness of 2 cm and index of refraction 1.5. Find the two principal points and focal points respectively. a) 0.12 cm, -3.4 cm, 3.2 cm. b) 0.27 cm, -1.1 cm, 8.2 cm. c) 1.6 cm, 2.3 cm, 1.2 cm. d) 2.3 cm, 1.9 cm, 0.6 cm. 16 lery izdk k dh,d fdj.k,;j&dkap buvjqsl ij 30 fmxzh ls bulhmsav djrh gs ftldk bysfdvz~d QhYM?kVd Iysu vkq bulhmsal dk vfhkyec gs प र त ब ब reflection और प र षण transmission, आय म ह [ग ल स क अपवतर न क 1.5 ह ] क) 0.24, ख) 0.76, ग) 0.76, घ) 0.24, एक +ve ल स क ब ई ओर 10 स म पर त न त व त ल स क nkbz vksj rhl lsaeh ij Nfo cukrk gs ;fn clrq dks ysl ls 2.5 स म fgyk;k tkrk gs rks Nfo dgka fn[kkbz nsxh o bldk uspj D;k gksxk? क) आभ स, स ध, बढ़ य और ल स क स मन 3.75 स म थत ह ख) असल, myvk बढ़ य और ल स क स मन 3.75 स म थत ह ग) आभ स, myvk de c<k gqvk vksj ysl ds ihns, 3.75 स म पर थत ह घ) रयल, स ध, बढ़ य और ल स ds ihns म 3.75 स म थत ह 18. एक डबल उ तल ल स dh f=t;k 5 स म और 20 स म, o 2 स म क म ट ई ह और अपवतर न 1.5 क स चक क dk ह द प रम ख ब द ओ और फ कल व इ ट क रमश प र त कर क) 0.12 स म, -3.4 स म, 3.2 स म ख) 0.27 स म, -1.1 स म, 8.2 स म ग) 1.6 स म, 2.3 स म, 1.2 स म घ) 2.3 स म, 1.9 स म, 0.6 स म

5 19. Two sheets of flat glass plate of length 30 cm are separated at one end by a spacer of 0.3 mm, thus forming a wedge shaped thin film. How many fringes will be obtained under normal illumination with wave of wavelength 300nm? a) 20. b) 50 c) 1,000. d) 10, A Michelson interferometer is adjusted to give a fringe pattern of concentric circles when illuminated by a light of wavelength 700 nm. How much must the movable arm be moved if 100 fringes are to emerge from the center? a) mm. b) 0.07 mm. c) 0.14 mm. d) 0.7 mm. 21. Light of wavelength 500 is incident on a single slit of width 0.5. The ratio of intensities of the second secondary maxima to the central maximum is approximately a) 25 %. b) 12.5 %. c) 4.8 %. d) 1.6%. 22. A rectangular horizontal hole of size in an opaque screen is illuminated by a light of wavelength 500. The diffraction pattern is cast on a screen in the focal plane of a positive lens of focal length 2.5. The central maximum is a) a rectangle of size b) two squares each of size c) two rectangles of total area d) dark. 19 nks QySV Xykl IysVksa dh yeckbz 30 lseh0 gs,d Nksj vyx gksus ij 0-3 feyhehvj ds Lis kj ij,d ippkj ds vkdkj iryh fqye cu jgh gs blesa fdruh fqzaftt cusxh ;fn bls lkeku; jks kuh dh rjaxns/;z 300 feyhehvj ls izdkf kr fd;k tkrk gs क) 20 ख) 50 ग) 1,000 घ) 10, म इक सन य तकरणम प dh तर ग द यर 700nm (एनएम) क प रक श स प रक शत fd;k tkrk gs rks ;g dksulsavfjd ldzy vkdkj dh fqzaftt cukrkgs py vkez dks fdruk LFkkukarfjr fd;k tkuk pkfg, ;fn dsunz ls 100 fqazfatt dks blesa bejt djuk gsa क) मम ख) 0.07 मम ग) 0.14 मम घ) 0.7 मम 21. izdk k तर गद यर 500 nm dks 0 +5 fe0eh0 pksmkbz dh,d lfyv ij bulhmsav fd;k tkrk gs dsunzh; esdlheka ls lsdsm ldsmjh esdlheka dh buvsaflvh dk vuqikr yxhkx gs क 25 %. ख 12.5 %. ग 4.8 %. घ 1.6%. 22 एक अप रदश र क र न म vk;rkdkj vkdkj dk {ksfrt Nsn rjax}s/;z 500,u,e ds izdk k ls izdkf kr fd;k tkrk gs foorzu isvuz iksftfvo ysal ds Qksdy yeokbz 2 +5 Ldzhu ij dklv gksrk gs A rks dsunzh; vf/kdre gs A क) आक र क एक आयत ख) द च क आक र क प र य क ग) क ल क ष त रफल5 2.5 क द आयत घ) अ ध र

6 23. A human eye of aperture 4 and focal length 15 is looking at a star emitting light at wavelength 500. The angular resolving power is (in seco nds) a) 0. b) c) 0.5. d) The electrostatic force between two electrical charges is minimum when they are placed in: a) air. b) water. c) Vacuum d) Glass 25. Under which of the following conditions Coulomb s law is NOT applicable: a) When charges are static and placed in water. b) When charges are static and placed in magnetic field. c) When the charges are moving relative to each other. d) The Coulomb s law is applicable in every condition. 26. The electric current through a capacitor when connected to DC supply is: a) Zero always b) High initially and then decreases with time c) Low initially and then increases with time d) Negligible 27. The units of dielectric strength is: a) V m b) C m -1 c) V m -1 d) C m 23.,d ekuo vka[k dk,ipzj 4fe0eh0 vksj Qksdy yeokbz 15 fe0eh0,d flrkjs dks ns[k jgh gs tks 500,u,e dh rjax}s/;z izdk k mrltz dj jgk gs क ण य हल श क त ( angular resolving power) (स क ड म ) ह क) 0 ख) 0.05 ग) 0.5. घ) द बजल क आर प क ब च व य त बल य नतम ह, जब व म रख ज त ह : क) हव ख) प न ग) व क य म घ) गल स 25 न न थ तय म स ज तहत ह Coulomb dk क न न ल ग नह gksrk A क) जब आर प थर और प न म रख ज त ह ख) जब आर प थर और च बक य क ष त र म रख ज त ह ग) जब आर प एक द सर क स प क ष बढ़ रह ह घ) Coulomb ह क न न हर ह लत म ल ग ह 26. व य त प रव ह एक स ध रत र क म यम स जब ड स आप तर स ज ड़ ह : क) श य हम श ख) उ च श म और फर समय क स थ कम ह ज त ह ग) कम श म और फर समय क स थ बढ़ ज त ह घ) नग य 27. अच लक श क त क इक इय ह : क) व एम ख) स एम -1 ग) व एम -1 घ) स एम

7 28. The energy density associated with electric (u E ) and magnetic field (u M ) in an electromagnetic signal are related as: a) b) c) d) No such relation exist 29. As per Faraday s laws of electromagnetic induction, which of the following is essential condition to obtain induced e.m.f.? a) Relative motion of coil and magnet. b) Change in magnetic flux linked with the coil. c) Both of the above. d) None of the above. 30. The value of self inductance of a long solenoid: a) Depend upon its length. b) Depend upon its diameter. c) Depends upon both of above. d) Do not depend on length or diameter. 28. एक व य त च बक य स क त म बजल (u E ) और च बक य क ष त र (u M ) क स थ ज ड़ ऊज र घन व क प म ज ड़ ह ए ह : ए) ख) ग) घ) उपर क त म स क ई नह ह 29. व य त च बक य प र रण क फ र ड क क न न क अन स र, न न म स ई.एम.एफ़ izkir djus ds fy, dksu lh vko ;d krz izsfjr gs क) त र और च बक क स प क ष ग त ख) च बक य त र क स थ ज ड़ ह आ प रव ह म प रवतर न ग) ऊपर क द न घ) उपर क त म स क ई नह ह 30. एक ल ब solenoid क आ म अ ध ठ पन क म य: क) इसक ल ब ई पर नभर र करत ह ख) इसक य स पर नभर र करत ह ग) ऊपर क द न पर नभर र करत ह घ) ल ब ई य य स पर नभर र नह ह

8 Section C 31. An inertial frame is the one which is a) Accelerated b) Decelerated c) Moving with uniform velocity or at rest. d) May be accelerated, decelerated or moving with constant velocity 32. An object of rest mass of 1 kg is moving at 99% of the speed of light. It s measured mass is a) 10 kg b) 3.5 kg c) 7.1 kg d) 15.5 kg 33. In photoelectric effect, the energies of the electrons emitted from the metal surface are (a) independent of the intensity of the incident radiation (b) depends on the intensity of the incident radiation (c) independent of the frequency of the incident radiation (d) independent of the wavelength of the incident radiation 34. The de Broglie wavelength, λ is proportional to (a) E 1 1 (b) 2 E (c) E 1 (d) E 35. The minimum amount of energy required to ionize a Hydrogen atom in n = 2 state is (a) 13.6 ev (b) 3.4 ev (c) 1eV (d) 5.6 ev 31. एक जड़ व य फ र म म स एक ज ह क) व रत /स,DljysV ख) Mh,DljysV ग) सम न व ग क स थ य vflfkj घ) त ज स,DljysV ] Mh,DljysV ;k fujarj osx ds lkfk py jgk gs A fdyks dh clrq izdk k dh xfr ls 99 izfr kr ls py jgh gsa bldk Hkkj ekik tkuk gs क) 10 कल ख) 3.5 कल ग) 7.1 कल घ) 15.5 कल 33. photoelectric प रभ व म, ध त क सतह स उ स जर त इल क ट र न क ऊज र ह (क) घटन व करण क त त क वत त र (ख) घटन व करण क त त पर नभर र करत ह (ग) घटन व करण क आव त क वत त र (घ) घटन व करण क तर ग द यर क वत त र 34. ड Broglie तर गद यर, क लए आन प तक ह (a) E 1 1 (b) 2 E (c) E 1 (d) E 35. ऊज र क य नतम र श एक ह इड र जन परम ण य ण बन न करन क लए n = 2 state म आव यक ह (क) 13.6 ev (ख) 3.4 ev (ग) 1EV (घ) 5.6 ev

9 36. In the probabilistic interpretation of 2 wave function, ψ is (a) probability amplitude (b) average amplitude (c) probability density (d) one always 37. In quantum mechanics, the expectation value of a dynamical variable is defined as (a) Instantaneous measurement on a system (b) Mean of measurements on a system (c) Median of measurements on a system (d) Average of repeated measurements on an ensemble of identically prepared systems. 38. The expectation value x of a particle trapped in a 1D box, L wide, is (for n=1) (a) L/4 (b) L (c) 2L (d) L/2 39. Mass of electron is (A) MeV/c 2 (B) MeV/c 2 (C) kev/c 2 (D) None 40. Proton and neutron is made up of the following combination of quarks (A) uuu and ddd (B) uud and ddu (C) ddu and uup (D) none 41. The lifetimes of nuclear excited states are generally in the range of (A) s. (B) 10-3 to 10-8 s (C) to s (D) none 36. लहर सम र ह (क) स भ वन आय म (ख) औसत आय म (ग) प र यकत घन व (घ) हम श एक 2 ψ क स भ य य ख य म ह 37. क व टम य त रक म, एक dynamical चर क उ म द क म य क प म प रभ षत कय गय ह (क) एक प रण ल पर त क लक म प (ख) एक प रण ल पर म प क Mean (ग) एक प रण ल पर म प क Median (घ) ह बह त य र प रण लय क ट कड़ पर द हर य म प क औसत ड ब क स म एक कण क expectation value x उ म द क म य, य पक ह, (for n=1) (क) L / 4 (ख) L (ग) 2L (घ) L / 2 39 इल क ट र न dk Hkkj gs A (क) MeV/c 2 (ख) MeV/c 2 (ग) kev/c 2 (घ) क ई नह 40 प र ट न और य ट र न क व क क न न ल खत स य जन स बन ह (क) UUU और DDD (ख) uud और DDU (ग) DDU और UUP (घ) क ई नह 41. परम ण उ स हत states क ज वन क ल क स म म आम त र पर कर रह ह (क) s. (ख) 10-3 to 10-8 s (ग) to s (घ) क ई नह

10 C and 16 are 6 8O (A) isotopes (B) isobars (C) isotone (D) no relation between the two C और ह O (क) आइस ट प (ख) isobars (ग) isotone (घ) द न क ब च क ई स ब ध नह 43. Which of the following can be detected in a magnetic field (A) X-rays (B) β-rays (C) γ-rays (D) infra-red rays 44. The nucleonic interactions on the nuclear surface are (A) isotropic (B) anisotropic (C) homogeneous (D) none 45. Dead and recovery time of GM counter is of the order of (A) 100 μs (B) 100 ps (C) 100 ns (D) None 43 न न म स क न स एक च बक य क ष त र म पत लग य ज सकत ह (क) एक स र (ख) β-rays (ग) γ-rays (घ) इ फ र -र ड करण 44. परम ण सतह पर nucleonic interactions ह (क) isotropic ख) anisotropic (ग) सज त य (घ) क ई नह 45 ज एम क उ टर dk म त और वस ल समय क आद श क bdkbz ह (क) 100 μs ख) 100 ps (ग) 100 ns (घ) क ई नह

11 Section D 46. Which one of the following transition in hydrogen atom showing the emission of shortest wavelength of photons. a) n = 1 n = 6 b) n = 6 n = 1 c) n = 6 n = 3 d) n = 3 n = subshell contains only one orbital. a) 5d e) 6f f) 4s g) 1p 48. There are orbitals in the second shell. a) 1 b) 2 c) 4 d) Which one is the correct value for spin (g) factor? a) ½ b) 1 c) 2 d) The Lande factor (g) for the level 2S1/2 is. a) 0 b) 4/3 c) 2/3 d) Molecular rotational spectra lie in region. a) radiowave b) Visible c) IR d) Microwave 52. Which one of the following is true for Raman scattering process? a) inelastic scattering b) elastic scattering c) induced dipole moment d) both (a) & (c) 46. ह इड र जन एटम म न न ल खत स क रमण फ ट न क कम स कम तर ग द यर क उ सजर न क दख न क एक gs क) एन = 1 एन = 6 ख) एन = 6 एन = 1 ग) एन = 6 एन = 3 घ) एन = 3 एन = subshell क वल एक कक ष य श मल ह क) 5 ड ख) 6F ग) 4s घ) 1p 48. वह द सर ख ल म कक ष ओ कर रह ह क) 1 ख) 2 ग) 4 घ) ज एक पन (G) क रक क लए सह म य ह? क) आध ख) 1 ग) 2 घ) Lande क रक (G) तर 2 S 1/2 क लए ह क) 0 ख) 4/3 ग) 2/3 घ) आ वक क ष त र घ ण र प क ट र {ks= esa gs A क) radiowave ख) Visible ग) आईआर घ) म इक र व व 52. न न ल खत म स क न रमन scattering क प र क रय क लए सच ह? क) थर scattering ख) ल चद र scattering ग) प र रत वध र व य पल induced dipole moment घ) द न (क) और (ग)

12 53. Raman spectroscopy is applied to know of materials. a) chemical bonding b) conductivity c) doping d) all of these 54. Determine the output voltage of an opamp for the input voltage Vi1=150μV, Vi2=140μV. The amplifier has a differential gain of Ad= 4000 and the value of CMRR is 100. a) 145 V b) 45.8 V c) 4.58V d) 0.458V 53. रमन प क ट र क प स मग र क ब र म पत करन क लए ल ग कय ज त ह क) र स य नक स ब ध ख) च लकत ग) ड प ग घ) सभ 54. vkizs kuy,eiyhqk;j dh vkmviqv oksyvst buiqv oksyvst V i1 =150μV, V i2 =140μV. ij fu/kkzfjr djs A,EiyhQk;j dh fmqjsaf k;y xsu A d = 4000 vksj CMRR = 100 gs क) 145 व ख) 45.8 व ग) 4.58V घ) 0.458V 55.Which one of the following is not a strong bond? (a) Covalent bond (b) van der Waals bond (c) Ionic bond (d) All of these 56. Coordination number in Face centered cubic crystal structure is a) 4 b) 8 c) 12 d) Fermi energy level for n-type semiconductors lies (a) At middle of the band gap (b) Close to conduction band (c) Close to valence band (d) All of these 58. Which of the following are the properties of superconductors? a) They are diamagnetic in nature b) They have zero resistivity c) They have infinite conductivity d) All of the above 55. न न ल खत म स क न एक मजब त ब धन नह ह? (क) सहस य जक ब धन (ख) व न डर व स ब धन (ग) आय नक ब ड (घ) सब क सब 56. सम वय स ख य क द रत घन क र टल स रचन -- ह क) 4 ख) 8 ग) 12 घ) फम र ऊज र तर n-type semiconductors म न हत ह (क) ब ड अ तर ल क ब च म (ख) च लन ब ड क utnhd (ग) valence ब ड क utnhd (घ) उपर क त सभ 58. न न ल खत म स क न अ तच लक क ग ण ह? क) व Mk;eSxuSfVd gsa ख) व श य प र तर धकत ह ग) व अन त च लकत ह D) उपर क त सभ

13 59. The h+k+l value for BCC crystal structure is a) Even b) Odd c) Both (a) and (b) d) Unmixedhkl 60. The reciprocal lattice vector is inversely proportional to a) Lattice spacing b) Square of lattice spacing c) Lattice parameter d) All of these 59. ब स स क र टल स रचन क लए h + K + L म य ह क) le ख) fo"ke ग) द न (क) और (ख) घ) Unmixedhkl 60. प र प रक ysfvl व क टर क वपर त आन प तक ह क) ysfvl lisflax ख) क व यर ysfvl lisflax ग) ysfvl प र म टर घ) उपर क त सभ

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