JEE(MAIN) 2018 TEST PAPER WITH ANSWER (HELD ON SUNDAY 08 th APRIL, 2018) PART C PHYSICS. 64. The density of a material in the shape of a cube ALLEN

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1 6. The agula width of the cetal maximum i a sigle slit diffactio patte is 60. The width of the slit is mm. The slit is illumiated by moochomatic plae waves. If aothe slit of same width is made ea it, Youg s figes ca be obseved o a scee placed at a distace 50 cm fom the slits. If the obseved fige width is cm, what is slit sepaatio distace? (i.e. distace betwee the cetes of each slit.) As. () () 50 mm () 75 mm 00 mm () 5 mm 6. A electo fom vaious excited states of hydoge atom emit adiatio to come to the goud state. Let l, l g be the de Boglie wavelegth of the electo i the th state ad the goud state espectively. Let L be the wavelegth of the emitted photo i the tasitio fom the th state to the goud state. Fo lage, (A, B ae costats) As. () JEE(MAIN) 08 TEST PAPER WITH ANSWER (HELD ON SUNDAY 08 th APRIL, 08) PART C PHYSICS () L» A+ Bl () L» A+ Bl B L»l () L» A + l 6. The eadig of the ammete fo a silico diode i the give cicuit is :- 00W CODE-C 6. The desity of a mateial i the shape of a cube As. () is detemied by measuig thee sides of the cube ad its mass. If the elative eos i measuig the mass ad legth ae espectively.5% ad %, the maximum eo i detemiig the desity is :- ().5 % ().5 % 6 % ().5 % 65. A electo, a poto ad a alpha paticle havig the same kietic eegy ae movig i cicula obits of adii e, p, a espectively i a uifom magetic field B. The elatio betwee e, p, a is:- () e < p = a () e < p < a e < a < p () e > p = a 66. Thee cocetic metal shells A, B ad C of espective adii a, b ad c (a < b < c) have suface chage desities +s, s ad +s espectively. The potetial of shell B is :- () () s éa -b b s éb -c b + cú + aú V () 5 ma ().5 ma.5 ma () 0 As. () () s éb -c c s éa -b a + aú + cú

2 JEE(MAIN) Two masses m = 5kg ad m = 0kg, coected by a iextesible stig ove a fictioless pulley, ae movig as show i the figue. The coefficiet of fictio of hoizotal suface is 0.5. The miimum weight m that should be put o top of m to stop the motio is :- m m T m T () 7. kg (). kg 0. kg () 8. kg 68. A paticle is movig i a cicula path of adius a ude the actio of a attactive potetial k U =. Its total eegy is :- k () a () Zeo - k a () k - a As. () 69. A paallel plate capacito of capacitace 90 pf is coected to a battey of emf 0V. If a dielectic mateial of dielectic costat K = 5 is iseted betwee the plates, the magitude of the iduced chage will be :- () 0. C (). C 0.9 C (). C As. () 70. A silve atom i a solid oscillates i simple hamoic motio i some diectio with a fequecy of 0 /sec. What is the foce costat of the bods coectig oe atom with the othe? (Mole wt. of silve =08 ad Avagado umbe = gm mole ) () 7. N/m (). N/m 5.5 N/m () 6. N/m 7. It is foud that if a euto suffes a elastic colliea collisio with deuteium at est, factioal loss of its eegy is p d ; while fo its simila collisio with cabo ucleus at est, factioal loss of eegy is p c. The values of p d ad p c ae espectively : As. () () (. 8,. 89) () (0, 0) (0, ) () (. 89,. 8) 7. The dipole momet of a cicula loop cayig a cuet I, is m ad the magetic field at the cete of the loop is B. Whe the dipole momet is doubled by keepig the cuet costat, the magetic field at the cete of the loop is B. The atio B B is : () () As. () () 7. I a potetiomete expeimet, it is foud that o cuet passes though the galvaomete whe the temials of the cell ae coected acoss 5 cm of the potetiomete wie. If the cell is shuted by a esistace of 5 W, a balace is foud whe the cell is coected acoss 0 cm of the wie. Fid the iteal esistace of the cell. ().5 W () W.5 W () W 7. A telephoic commuicatio sevice is wokig at caie fequecy of 0 GHz. Oly 0% of it is utilized fo tasmissio. How may telephoic chaels ca be tasmitted simultaeously if each chael equies a badwidth of 5 khz? As. () () 0 () () 0

3 CODE-C 75. Upolaized light of itesity I passes though a ideal polaize A. Aothe idetical polaize B is placed behid A. The itesity of light As. () beyod B is foud to be. Now aothe idetical polaize C is placed betwee A ad B. The itesity beyod B is ow foud to be I. The agle betwee polaize A ad C is : 8 () 0º () 5º 60º () 0º 76. O itechagig the esistaces, the balace poit of a mete bidge shifts to the left by 0 cm. The esistace of thei seies combiatio is kw. How much was the esistace o the left slot befoe itechagig the esistaces? As. () () 505 kw () 550 kw 90 kw () 990 kw 77. Fom a uifom cicula disc of adius R ad mass 9M, a small disc of adius R is emoved as show i the figue. The momet of ietia of the emaiig disc about a axis pepedicula to the plae of the disc ad passig though cete of disc is : () As. () 0 MR 9 7 MR 9 R R () 0 MR () MR 78. I a colliea collisio, a paticle with a iitial speed stikes a statioay paticle of the same mass. If the fial total kietic eegy is 50 % geate tha the oigial kietic eegy, the magitude of the elative velocity betwee the two paticles, afte collisio, is : () v () 0 () 79. A EM wave fom ai etes a medium. The electic fields ae é æz ö E = E0xcos ˆ pç -t ú i ai ad èc ø E = E0ˆ x cos ék ( z -ct) i medium, whee the wave umbe k ad fequecy v efe to thei values i ai. The medium is o-magetic. If ad efe to elative pemittivities of ai ad medium espectively, which of the followig optios is coect? () = () = = () = As. () 80. Fo a RLC cicuit dive with voltage of As. () amplitude v m ad fequecy w 0 = LC the cuet exibits esoace. The quality facto, Q is give by : () w 0R L CR w0 () ( w RC 0 ) () w 0L R

4 JEE(MAIN) All the gaphs below ae iteded to epeset the same motio. Oe of them does it icoectly. Pick it up. distace 8. A paticle is movig with a uifom speed i a cicula obit of adius R i a cetal foce ivesely popotioal to the th powe of R. If the peiod of otatio of the paticle is T, the, () time positio () time velocity time velocity () positio 8. Two batteies with e.m.f V ad V ae coected i paallel acoss a load esisto of 0 W. The iteal esistaces of the two batteies ae W ad W espectively. The voltage acoss the load lies betwee. ().5 V ad.6 V (). V ad.5 V.7 V ad.8 V ().6 V ad.7 V () As. () + Tµ R () + Tµ R ( )/ T µ R / () T µ R / fo ay 8. If the seies limit fequecy of the Lyma seies is v L, the the seies limit fequecy of the Pfud seies is : As. () 6 v L () v L /6 v L /5 () 5 v L 85. I a a. c. cicuit, the istataeous e.m.f. ad cuet ae give by e = 00 si 0 t i = 0 si æ p ö ç 0t - è ø I oe cycle of a.c., the aveage powe cosumed by the cicuit ad the wattless cuet ae, espectively. () 000, 0 () 50, 0 50, 0 () 50, Two moles of a ideal mooatomic gas As. () occupies a volume V at 7 C. The gas expads adiabatically to a volume V. Calculate (a) the fial tempeatue of the gas ad (b) chage i its iteal eegy. () (a) 95 K (b).7 kj () (a) 89 K (b).7 kj (a) 95 K (b).7 kj () (a) 89 K (b).7 kj

5 CODE-C 87. A solid sphee of adius made of a soft mateial of bulk modulus K is suouded by a liquid i a cylidical cotaie. A massless pisto of aea a floats o the suface of the liquid, coveig etie coss sectio of cylidical cotaie. Whe a mass m is placed o the suface of the pisto to compess the liquid, the factioal decemet i the adius of the sphee, æ d ç ö, is : è ø () Ka Ka () Ka () Ka As. () 88. A gaite od of 60 cm legth is clamped at its middle poit ad is set ito logitudial vibatios. The desity of gaite is.7 0 kg/m ad its Youg's modulus is Pa. What will be the fudametal fequecy of the logitudial vibatios? ().5 khz () 0 khz 7.5 khz () 5 khz As. () 89. The mass of a hydoge molecule is. 0 7 kg. If 0 hydoge molecules stike, pe secod, a fixed wall of aea cm at a agle of 5 to the omal, ad eboud elastically with a speed of 0 m/s, the the pessue o the wall is ealy : ().70 0 N/m ().5 0 N/m.70 0 N/m ().5 0 N/m As. () 90. Seve idetical cicula plaa disks, each of mass M ad adius R ae welded symmetically as show. The momet of ietia of the aagemet about the axis omal to the plae ad passig though the poit P is : As. () 55 MR () 7 MR 8 MR () 9 MR O P 5