ALLEN TM CAREER INSTITUTE Path to Success KOTA (RAJASTHAN) ALLEN JEE-MAIN SAMPLE PAPER # 02 TARGET - 2014 egRoiw . kZ lw p uk,¡ IMPORTANT INSTRUCTIONS Do not open this Test Booklet until you are asked to do so. bl ijh{kk iq fLrdk dks rc rd u [kksysa tc rd dgk u tk,A ijh{kk iqfLrdk ds bl i`"B ij vko';d fooj.k uhys@dkys ckWy ikbaV isu ls rRdky HkjsaA isfUly dk iz;ksx fcYdqy oftZr gaSA ijh{kkFkhZ viuk QkeZ ua- (fu/kkZfjr txg ds vfrfjä) ijh{kk iqfLrdk @ mÙkj i= ij dgha vkSj u fy[ksaA ijh{kk dh vof/k 3 ?ka V s gSA bl ijh{kk iqfLrdk esa 90 iz'u gaSA vf/kdre vad 360 gSaA 1. Immediately fill in the form number on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited. 1. 2. The candidates should not write their Form Number anywhere else (except in the specified space) on the Test Booklet/Answer Sheet. 2. 3. The test is of 3 hours duration. 3. 4. The Test Booklet consists of 90 questions. The maximum marks are 360. 4. 5. There are three parts in the question paper A,B,C consisting of Mathematics, Physics and Chemistry having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response. 5. bl ijh{kk iqfLrdk es a rhu Hkkx A, B, C gSa] ftlds izR;sd Hkkx esa xf.kr] HkkSfrd foKku ,oa jlk;u foKku ds 30 iz'u gaS vkSj lHkh iz'uksa ds vad leku gASa izR;sd iz'u ds lgh mÙkj ds fy, 4 (pkj)vad fuèkkZfjr fd;s x;s gAaS 6. One Fourth mark will be deducted for indicated incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the Answer Sheet. 6. 7. Use Blue/Black Ball Point Pen only for writting particulars/marking responses on Side–1 and Side–2 of the Answer Sheet. Use of pencil is strictly prohibited. 7. 8. No candidate is allowed to carry any textual material, printed or written, 8. izR;sd xyr mÙkj ds fy, ml iz'u ds dqy vad dk ,d pkSF kkbZ vad dkVk tk;sxkA mÙkj iqfLrdk esa dksbZ Hkh mÙkj ugha Hkjus ij dqy izkIrkad esa ls ½.kkRed vadu ugha gksxkA mÙkj i= ds i` " B&1 ,oa i` " B&2 ij okafNr fooj.k ,oa mÙkj vafdr djus gsrq dsoy uhys@ dkys ckWy ikba V isu dk gh iz;ksx djsaA isf Uly dk iz ;ksx fcYdqy oftZr gSA ijh{kkFkhZ }kjk ijh{kk d{k @ gkWy esa ifjp; i= ds vykok fdlh Hkh izdkj dh ikB~; lkexzh eqfær ;k gLrfyf[kr dkxt dh ifpZ;ksa] istj] eksckby Qksu ;k fdlh Hkh izdkj ds bysDVªkfud midj.kksa ;k fdlh vU; izdkj dh lkexzh dks ys tkus ;k mi;ksx djus dh vuqefr ugha gSaA bits of papers, pager, mobile phone any electronic device etc, except the Identity Card inside the examination hall/room. 9. jQ dk;Z ijh{kk iqfLrdk esa dsoy fu/kkZfjr txg ij gh dhft;sA 10. On completion of the test, the candidate must hand over the Answer Sheet to the invigilator on duty in the Room/Hall. However, the candidate are allowed to take away this Test Booklet with them. 10. 11. Do not fold or make any stray marks on the Answer Sheet. 11. ijh{kk lekIr gksus ij] ijh{kkFkhZ d{k@gkWy NksM+us ls iwoZ mÙkj i= d{k fujh{kd dks vo'; lkiSa nsAa ijh{kkFkhZ vius lkFk bl ijh{kk iq fLrdk dks ys tk ldrs gaS A mÙkj i= dks u eksMa+s ,oa u gh ml ij vU; fu'kku yxk,saA 9. Rough work is to be done on the space provided for this purpose in the Test Booklet only. Corporate Office ALLEN Career Institute, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005, Trin : +91 - 744 - 2436001 Fax : +91-744-2435003, E-Mail: [email protected] Website: www.allen.ac.in 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 HAVE CONTROL ¾® HAVE PATIENCE ¾® HAVE CONFIDENCE Þ 100% SUCCESS BEWARE OF NEGATIVE MARKING PART A - MATHEMATICS 1. A bag contains 3 white and 3 red balls, pairs 1. of balls are drawn without replacement until the bag is empty. The probability that each pair consists of one white and one red ball is3 4 5 6 (2) (3) (4) 10 10 10 10 In a test paper there are 10 true-false questions. If a student randomly answers all the questions, then the probability that atleast six answer are correct is p/q (where p & q are relatively prime), then (q – p) is (1) 319 (2) 273 (3) 353 (4) 407 A polynomial function satisfies 2. é pö Let ƒ : R ® ê0, ÷ ë 2ø –1 2 (1) 319 (3) 353 3. (2) 273 (4) 407 ;fn ,d cgqin Qyu] æ1ö æ1ö ƒ ( x ) ƒ ç ÷ = ƒ ( x ) + ƒ ç ÷ , x ¹ 0 dks larq"V èxø èxø djrk gS rFkk ƒ(3) = –26 gks] rks ƒ(4) dk eku gksxk& (1) –15 4. 2 ƒ(x) = tan (x + 6x + a – 2a) is an onto function, then product of r eal values of a will be(1) 2 (2) –19 (3) –9 (4) 12 SPACE FOR ROUGH WORK / ALLEN (2) ,d fo|kFkhZ lHkh iz'uksa ds ;kn`PN;k mÙkj djrk gks] rks de ls de N% mÙkj lgh gksus dh izkf;drk p/q gks (tgk¡ p rFkk q ijLij vHkkT; la[;k;sa g) S rc (q – p) dk eku gksxk& æ1ö æ1ö ƒ ( x ) ƒ ç ÷ = ƒ ( x ) + ƒ ç ÷ , x ¹ 0 and èxø èxø ƒ(3) = –26, then value of ƒ(4) is (1) –15 (2) –63 (3) –47 (4) –255 4. 3 10 A LL EN 3. 4 5 6 (3) (4) 10 10 10 ,d iz'u i= esa 10 lR;&vlR; okys iz'u gSA ;fn (1) (1) 2. ,d Fky S s esa 3 lQsn rFkk 3 yky xasnsa gaS] xsanksa dk ,d tksM+k rc rd fudkyk tkrk gS] tc rd fd Fky S k [kkyh uk gks tk;sA izkf;drk rkfd izR;sd tksM+s esa ,d lQsn rFkk ,d yky xsan gks] gksxh - (2) –63 (3) –47 (4) –255 é pö ekuk ƒ : R ® ê0, ÷ ë 2ø ƒ(x) = tan–1(x2 + 6x + a2 – 2a) vkPNknd Qyu gks] rks a ds okLrfod ekuksa dk xq.kuQy gksxk& (1) 2 (2) –19 (3) –9 (4) 12 jQ dk;Z ds fy;s txg H-1/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 6. 7. 8. If inequality (x – 2a) (x – a – 2) < 0 is satisfied 5. for all x Î (2,3), then number of integral values of 'a' will be(1) 2 (2) 3 (3) 1 (4) 0 4 ù é Value of ê lim 2 sin x 4x -p ú is êë x® p4 úû (where [.] denotes greatest integer function) (1) 0 (2) 1 (3) 2 (4) 7 If x + 6y + 6z = ax 4x – y + 4z = ay 2ax + 2ay + az = 5z has a non trivial solution, then value of a will be(1) 0 (2) –2 (3) –7 (4) –5 If 'X' is a five digit number abcde, then ( ) 6. (1) 2 é ê lim êë x® p4 (2) 3 ( 2 sin x ) 4 4x -p (3) 1 (4) 0 ù ú dk eku gksxk úû 8. (tgk¡ [.] egÙke iw.kk±d Qyu dks n'kkZrk g)S (1) 0 (2) 1 (3) 2 (4) 7 ;fn x + 6y + 6z = ax 4x – y + 4z = ay 2ax + 2ay + az = 5z dk vfujFkZd gy gks] rks a dk eku gksxk& (1) 0 (2) –2 (3) –7 (4) –5 ;fn 'X' ika p va d h; la [ ;k abcde gks ] rks X will be a+b+c+d+e (1) 10000 (2) 11000 (3) 9000 (4) 9999 xi(i = 1,2,3,......n) denotes a distribution whose variance is 10 then variance of a distribution 3x1 + 2, 3x2 +2, 3x3 + 2,........3xn + 2 will be(1) 10 (2) 30 9. X dk vf/kdre eku gksxk& a+b+c+d+e (1) 10000 (2) 11000 (3) 9000 (4) 9999 xi(i = 1,2,3,......n) foHkktu dks n'kkZrk gS ftldk 7. maximum value of 9. ;fn vlfedk (x – 2a) (x – a – 2) < 0 lHkh x Î (2,3) ds fy;s larq"V gksrh gks] rks 'a' ds iw.kk±d ekuksa dh la[;k gksxh& A LL EN 5. (3) 10 3 (4) 90 SPACE FOR ROUGH WORK / H-2/31 izlj.k 10 gks] rks foHkktu 3x1 + 2, 3x2 +2, 3x3 + 2,........3xn + 2 dk izlj.k gksxk& (1) 10 (2) 30 10 3 (4) 90 (3) jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 10. 11. Negation of statement "Rahul is rich or Priya is beautiful" is (1) Rahul is poor or Priya is ugly. (2) Rahul is poor and Priya is ugly. (3) Rahul is rich and Priya is beautiful. (4) Rahul is rich or Priya is ugly Given ƒ(x) = ax2 + bx + c. If lim ( ƒ ( x )) x ®0 1/ x 13. 14. dFku ^^jkgqy /kuh gS ;k fiz;k [kw- clwjr g*S * dk izfrokn gksxk(1) jkgqy xjhc gS ;k fiz;k cnlwjr gS (2) jkgqy xjhc gS rFkk fiz;k cnlwjr gS (3) jkgqy xjhc gS rFkk fiz;k [kw - clwjr gS (4) jkgqy xjhc gS ;k fiz;k cnlwjr gS 11. ekuk ƒ(x) = ax2 + bx + c gAS ;fn lim ( ƒ ( x )) x ®0 1/ x = e 3 , then ƒ'(0) will be- (1) 0 (2) 1 (3) 2 (4) 3 Four different integers are in increasing AP 12. such that one of them is sum of squares of others, then number of such AP(s) will be(1) 0 (2) 1 (3) 2 (4) 3 x1, x2 & x 3 when divided by 4 leaves a 13. remainder of 0,1 & 2 respectively find number of non-negative integral solution of the equation x1 + x2 + x3 = 35, is (1) 45 (2) 55 (3) 105 (4) 190 If |z – 3 – 2i| = |z + 2i|, where z is a complex 14. number, then minimum value of |z| will be 1 4 7 9 (2) (3) (4) 2 5 10 10 2 2 In a DABC if 2c + b – 2bc = 6ac – 9a2, (with usual notation), then value of cosB is (1) 15. (1) 0 (1) 1 2 (2) 1 3 (3) 1 4 (4) 1 6 SPACE FOR ROUGH WORK / ALLEN (3) 2 (4) 3 pkj fHkUu iw.kk±d o/kZeku lekUrj Js.kh esa bl izdkj gS fd buesa ls ,d vU; ds oxks± ds ;ksxQy ds cjkcj g]S rks bl izdkj dh lekUrj Js.kh;ksa dh la[;k gksxh& (1) 0 (2) 1 (3) 2 (4) 3 x1, x2 rFkk x3 dks 4 ls foHkkftr djus ij 'ks"kQy Øe'k% 0,1 rFkk 2 izkIr gksrs gAS lehdj.k x1 + x2 + x3 = 35 ds v½.kkRed iw.kk±d gyksa dh la[;k gksxh& (1) 45 (2) 55 (3) 105 (4) 190 ;fn |z – 3 – 2i| = |z + 2i|, tgk¡ z lfEeJ la[;k gks] rks |z| dk U;wure eku gksxk - (1) 15. = e 3 gks] rks ƒ'(0) dk eku gksxk& (2) 1 A LL EN 12. 10. 1 2 (2) 4 5 (3) 7 10 (4) 9 10 f=Hkqt ABC esa lkekU; ladsrksa ds lkFk ;fn 2c2 + b2 – 2bc = 6ac – 9a2 gks] rks cosB dk eku gksxk& (1) 1 2 (2) 1 3 (3) 1 4 (4) 1 6 jQ dk;Z ds fy;s txg H-3/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 15 16. Value å( 15 r =0 C r 40 C15 20 C r - 35 C15 15 C r 25 C r is(1) 0 40 (3) 35C15 – 17. 40 (2) C15 – C15 20. 21. C15 (2) 40C15 – 35C15 (3) 35 C15 – 40 C15 2 {ks=Qy gksxk& (1) 16 (2) 20 16 = 4 ,then minimum value of |z| will bez 5 -1 (3) 2 5 - 2 (1) 1 19. p (4) 32 p p 4 - x + ò dt ³ x ò sin 2 tdt gks] rks x ds 20 0 2 (2) 3 (3) 5 (4) 7 f=Hkqt ABC esa lkekU; ladsrksa ds lkFk a = 10, ÐA= p 6 rFkk H yEcdsUnz gks] rks H, B rFkk C }kjk fufeZr f=Hkqt dh ifjf=T;k gksxh- 20. (1) 5 (2) 10 (3) 20 (4) 40 ;fn 3x + 4y = 2 fdlh ijoy; ftldh ukfHk (1,1) g]S dh fu;rk dk lehdj.k gks] rks ukfHkyEc dh yEckbZ gksxh& (1) 1 21. (2) 0 (4) 5 + 1 SPACE FOR ROUGH WORK / H-4/31 ;fn (3) 24 iw.kk±d ekuksa dh la[;k gksxh& (4) 7 p & 6 H is orthocenter then circumradius of triangle formed by H, B & C is(1) 5 (2) 10 (3) 20 (4) 40 If 3x + 4y = 2 is directrix of parabola whose focus is (1,1), then length of latus rectum will be(1) 1 (2) 2 (3) 3 (4) 4 If z - 18. (4) 40C15 4y = |4 – x2|, |x| + y = 7 rFkk x > 0 }kjk ifjc¼ p p 4 - x + ò dt ³ x ò sin 2 tdt , then number 20 0 ) C r 40 C15 20 C r - 35 C15 15 C r 25 C r dk eku (1) 0 2 For an acute angle DABC, a = 10, ÐA = (1) 15 gksxk& (4) 40C15 of integral values of x will be(1) 1 (2) 3 (3) 5 19. å( A LL EN If 15 r =0 Area bounded by 4y = |4 – x |, |x| + y = 7 and 17. x > 0, is(1) 16 (2) 20 (3) 24 (4) 32 p 18. 35 ) 16. (2) 2 (3) 3 (4) 4 ;fn z - 16 = 4 gks ] rks |z| dk U;w u re eku z gksxk(1) 5 - 1 (2) 0 (3) 2 5 - 2 (4) 5 + 1 jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 23. 24. 25. Which of the following is false ? (1) Two vectors are always coplanar r r r are linearly independent then (2) If a, b, c r r r éa b c ù ¹ 0 ë û (3) Four points always lie in a plane r r (4) If a & b are linearly dependent then r r a´ b = 0 Tangents are drawn from every point on the 22. fuEu esa ls dkuS vlR; g?S (1) nks lfn'k lno S leryh; gksrs gSA r r r js[kh; Lora= gks] rks é ar br cr ù ¹ 0 (2) ;fn a, b, c ë û gksxkA (3) pkj fcUnq lno S ,d lery esa fLFkr gksrs gAS r r r (4) ;fn a rFkk b js[kh; ijra= gks] rks ar ´ b = 0 gksxkA 23. js[kk x + 9y = 4 ds lHkh fcUnq vks a ls nh?kZ o` Ù k A LL EN 22. x 2 9y 2 + = 1, line x + 9y = 4 to the ellipse 4 4 then the corresponding chords of contact always pass through (a,b), then value of (a + b) is(1) 0 (2) 2 (3) 5 (4) 7 A(3,6) is a point lying on parabola y2 = 4ax 24. such that chord AB subtends 90º at origin, then distance OB will, where O is origin- (1) 0 (2) 2 (3) 5 (4) 7 2 fcUnq A(3,6) ijoy; y = 4ax ij bl izdkj fLFkr g]S fd thok AB ewyfcUnq ij 90º dks.k varfjr djrh g]S rks nwjh OB gksxh, tgk¡ O ewyfcUnq g&S (1) 12 20 (1) 12 20 (2) 12 17 (3) 9 17 (4) 9 10 Normal at variable point P on ellipse 25. 2x2+y2= 1 meets the coordinate axes at Q & R, then eccentricity of locus of mid point of QR will be(1) 1 2 (2) 1 3 (3) 1 2 (4) 2 SPACE FOR ROUGH WORK / ALLEN x 2 9y 2 + = 1 ij Li'kZ js[kk;sa [khpha tkrh gS] rc 4 4 laxr Li'kZ thok lnSo (a,b) ls xqtjrh g]S rks (a + b) dk eku gksxk& (2) 12 17 (3) 9 17 (4) 9 10 fdlh nh?kZo`Ùk 2x +y = 1 ds pj fcUnq P ij [khapk x;k vfHkyEc funs'khZ v{kksa dks Q rFkk R ij feyrk g]S rc QR ds e/; fcUnq ds fcUnqi Fk dh mRdsUnzrk gksxh(1) 1 2 2 (2) 2 1 3 (3) 1 2 (4) 2 jQ dk;Z ds fy;s txg H-5/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 26. 26. If center of ellipse ( x + 3y - 5) 10 2 ( 3x - y - 5 ) + then 2a + b will be (1) 1 (2) 2 (3) 3 27. ( ( x + 3y - 5) 2 20 = 4 is (a,b), 10 (4) 5 ) 27. ( 3x - y - 5 ) + 20 =4 dk ds U nz (4) 5 fcUnq P (1, 2 2 ) vfrijoy; 9x2–y2 = 1 ij fLFkr A LL EN 3 1 1 (2) 3 (3) (4) 2 6 3 Statement-I : y = ea+bx is a general solution of 3 (2) 3 2 dFku -I : vody (1) 28. 2 differential equation y 2 gAS P ij [khap s h xbZ Li'kZ js[kk] vfrijoy; dh vuUr Li'khZ;ksa dks Q rFkk R ij dkVrh gS] rc f=Hkqt OQR dk {ks=Qy gksxk& Tangent at P on hyperbola cuts asymptotes of hyperbola at Q & R, then area of DOQR will be- 28. 2 (a,b) gks] rks 2a + b dk eku gksxk& (1) 1 (2) 2 (3) 3 P 1, 2 2 is a point on hyperbola 9x2–y2 = 1. (1) ;fn nh?kZo`Ùk d 2 y æ dy ö =ç ÷ . dx 2 è dx ø lehdj.k y (3) 1 6 (4) 1 3 2 d 2 y æ dy ö = ç ÷ dk gy y = ea+bx gSA dx 2 è dx ø 2 æ d 2 y ö æ dy ö Statement-II : Degree of y ç 2 ÷ = ç ÷ is è dx ø è dx ø two. (1) Statement-I is true, Statement-II is true; statement-II is a correct explanation for Statement-I. (2)Statement-I is true, Statement-II is true; statement-II is not a correct explanation for Statement-I. (3) Statement-I is true, Statement-II is false. (4) Statement-I is false, Statement-II is true. SPACE FOR ROUGH WORK / H-6/31 2 æ d 2 y ö æ dy ö dFku -II : y ç 2 ÷ = ç ÷ dh ?kkr nks gAS è dx ø è dx ø (1) dFku -I lR; g S _ dFku -II lR; g S _ dFku -II dFku-I dh lgh O;k[;k gSA (2) dFku -I lR; g S _ dFku -II lR; g S_ dFku -II dFku-I dh lgh O;k[;k ugha gSA (3) dFku-I lR; gS] dFku-II vlR; gSA (4) dFku-I vlR; gS] dFku-II lR; gSA jQ dk;Z ds fy;s txg ALLEN ALLEN JEE-MAIN SAMPLE PAPER # 02 30. Let 3a + 6c – 4b – 12d = 0. 29. Statement-I : Equation ax3 + bx2 + cx + d=0 will have atleast one root in (–1,0) Statement-II : ƒ(x) = ax3 + bx2 + cx + d is continuous in (–1,0). (1) Statement-I is true, Statement-II is true; statement-II is a correct explanation for Statement-I. (2)Statement-I is true, Statement-II is true; statement-II is not a correct explanation for Statement-I. (3) Statement-I is true, Statement-II is false. (4) Statement-I is false, Statement-II is true. S1 : x2 + y2 = 4 30. S2 : x2 + y2 – 4x = 0 Statement-I : Point of intersection of transverse common tangents of circles S1 & S2 is mid point of their centers. Statement-II : Point of intersection of transverse common tangents divides centers in ratio of their radii internally. (1) Statement-I is true, Statement-II is true; statement-II is a correct explanation for Statement-I. (2)Statement-I is true, Statement-II is true; statement-II is not a correct explanation for Statement-I. (3) Statement-I is true, Statement-II is false. (4) Statement-I is false, Statement-II is true. ekuk 3a + 6c – 4b – 12d = 0 gAS dFku -I : lehdj.k ax3 + bx2 + cx + d = 0 dk vUrjky (–1,0) eas de ls de ,d ewy gksxkA dFku -II : ƒ(x) = ax3 + bx2 + cx + d, vUrjky (–1,0) esa larr~ gAS (1) dFku -I lR; g S _ dFku -II lR; g S _ dFku -II dFku-I dh lgh O;k[;k gSA (2) dFku -I lR; g S _ dFku -II lR; g S _ dFku -II dFku-I dh lgh O;k[;k ugha gSA (3) dFku-I lR; gS] dFku -II vlR; gSA (4) dFku-I vlR; gS] dFku -II lR; gSA A LL EN 29. 2014 SPACE FOR ROUGH WORK / ALLEN S1 : x2 + y2 = 4 S2 : x2 + y2 – 4x = 0 dFku -I : o`Ùkksa S1 rFkk S2 dh f=;Zd mHk;fu"B Li'kZ js[kkvksa dk izfrPNsn fcUnq muds dsUnzksa dks feykus okyh js[kk dk e/; fcUnq gSA dFku -II : f=;Zd mHk;fu"B Li'kZ js[kkvksa dk izfrPNsn fcUnq] o`Ùkksa dsUnzksa dks feykus okyh js[kk dks mudh f=T;k ds vuqikr esa vUr% foHkkftr djrk gSA (1) dFku -I lR; g S _ dFku -II lR; g S _ dFku -II dFku-I dh lgh O;k[;k gSA (2) dFku -I lR; g S _ dFku -II lR; g S _ dFku -II dFku-I dh lgh O;k[;k ugha gSA (3) dFku-I lR; gS] dFku -II vlR; gSA (4) dFku-I vlR; gS] dFku -II lR; gSA jQ dk;Z ds fy;s txg H-7/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 PART B - PHYSICS 32. Figure A shows two identical plano-convex 31. lenses in contact as shown. The combination has focal length 24 cm. Figure B shows the same with a liquid introduced between them. If refractive index of glass of the lenses is 1.50 and that of the liquid is 1.60, the focal length of the system in figure B will be fp= A esa nks ,dleku leryksÙky ysal n'kkZ;s x;s gaS tks fd ,d&nwljs ds lkFk laidZ esa gAS bl la;kstu dh Qksdl nwjh 24 cm gAS fp= B esa bl la;kstu ds e/; esa ,d nzo Hkj fn;k x;k gAS ;fn ysalksa ds dk¡p dk viorZukad 1.50 rFkk nzo dk viorZukad 1.60 gks rks fp= B esa n'kkZ;s x;s la;kstu dh Qksdl nwjh gksxh (1) –120 cm (1) –120 cm (2) 120 cm (2) 120 cm A LL EN 31. (3) –24 cm (3) –24 cm (4) 24 cm (4) 24 cm A test tube of mass 2m closed with a cork of 32. mass m contains a drop of liquid of negligible mass. When the test tube is heated, the liquid evaporates and the cork flies off under the pressure of the gas. What must be the minimum velocity with which the cork must be ejected such that the test tube describes a full circle of radius R about the pivot ? (Assuming test tube as a point object) 2m nOz ;eku dh ,d ij[kuyh dks m nzO;eku ds dkWdZ ls cUn fd;k x;k g]S ftlesa ux.; nOz ;eku ds nzo dh ,d cwna gAS ;g uyh ds dsUæ ds Åij R yEckbZ dh ,d jLlh }kjk yVdh gqbZ gAS tc ij[kuyh dks xeZ fd;k tkrk gS rks noz ok"ihd`r gks tkrk gS rFkk xl S ds nkc ds dkj.k dkWdZ [kqy tkrk gAS dkWdZ fdl U;wure osx ls fudysxk rkfd ij[kuyh dhyd ds lkis{k R f=T;k dk iw.kZ o`Ùk cuk;s\ (ij[kuyh dks fcUnq nzO;eku ekfu;s) (1) (1) 5Rg 5Rg R (2) 2 5Rg 2m m (2) 2 5Rg (3) 2 3Rg (3) 2 3Rg (4) 2 4Rg (4) 2 4Rg SPACE FOR ROUGH WORK / H-8/31 R 2m m jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 A square conducting loop is placed in the time 33. ,d oxkZdkj pkyd ywi dks le; ifjorhZ pqEcdh; æ dB ö = + ve constant ÷ . varying magnetic field ç è dt ø {ks= ç The centre of square coincides with axis of cylindrical region of magnetic field. The directions of induced electric field at point a, b and c. dsUnz] pqEcdh; {ks= ds csyukdkj Hkkx dh v{k ds lkFk lEikrh gAS fcUnq a, b rFkk c ij izsfjr fo|qr {ks= dh fn'kk,¡ g%S & æ dB ö = +ve fu;rkad ÷ esa j[kk x;k gAS oxZ dk è dt ø A LL EN 33. a a b (1) b (3) a b b (3) (4) c c SPACE FOR ROUGH WORK / ALLEN a b a b (2) c c c a b (1) (2) c a a b (4) c c jQ dk;Z ds fy;s txg H-9/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 With reference to figure of a cube of edge a 34. and mass m, state whether the following (O is the centre of the cube.) option is CORRECT:- B z A fp= esa a Hkqtk rFkk m æO;eku okyk ,d ?ku n'kkZ;k x;k gS ftldk dsUnz O gAS lgh dFku pqfu;s%& B z A O O y A LL EN 34. y x x (a) The moment of inertia of cube about z-axis is Iz = Ix + Iy (b) The moment of inertia of cube about ma 2 A-axis is I A = I z + 2 (c) The moment of inertia of cube about B axis is IB = Iz + ma 2 2 (a) z-v{k ds lkis{k ?ku dk tM+Ro vk?kw.kZ Iz = Ix + Iy gSA (b) A- v{k ds lkis { k ?ku dk tM+ R o vk?kw . kZ IA = Iz + (c) B- v{k ds lkis { k ?ku dk tM+ R o vk?kw . kZ IB = I z + (d) Ix = Iz ma 2 gAS 2 ma 2 gAS 2 (d) Ix = Iz (1) b, c (2) a, b (1) b, c (2) a, b (3) b (4) d (3) b (4) d SPACE FOR ROUGH WORK / H-10/31 jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 35. The variation of lengths of two metal rods A and B with change in temperature are shown 35. aA in figure. The ratio of a is B nks /kkfRod NM+kas A rFkk B dh yEckbZ;ksa esa rki ds lkFk gksus okys ifjorZu dks fp= esa n'kkZ;k x;k gAS aA a B dk vuqikr gksxk%& 106 B 104 length(cm) length(cm) 106 A 100 0 0 3 2 4 3 (2) (3) (4) 2 3 3 4 In standard YDSE setup, a small transparent 36. slab containing material of m = 1.5 is placed along AS2 (figure). What will be the distance from O of the central maxima (PO = 1m) (S1S2 = d) 36. 2 4 3 (3) (4) 3 3 4 ,d ekud YDSE O;oLFkk esa m = 1.5 okys inkFkZ ls cuh ,d NksVh ikjn'khZ ifêdk dks fp=kuqlkj AS2 ds vuqfn'k j[kk tkrk gAS dsfUnz; mfPp"B dh O ls nwjh Kkr dhft,A (PO = 1m) (S1S2 = d) (1) 3 2 (2) S1 P A L= d/4 O S2 T temp. (°C) temp. (°C) (1) A 100 A LL EN T B 104 A L= d/4 S1 P O S2 Screen Screen (1) 0.125 m above O (2) 0.125 m below O (1) O ls 0.125 m Åij (2) O ls 0.125 m uhps (3) 0.25 m below O (4) 0.25 m above O (3) O ls 0.25 m uhps (4) O ls 0.25 m Åij SPACE FOR ROUGH WORK / jQ dk;Z ds fy;s txg ALLEN H-11/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 t=0 B A' D C C' x in m E fdlh ruh gq b Z jLlh ij le; ds nks {k.kks a (lhekUr] ekè;) ij vizxkeh rjaxks ds izfr:i dks fp= esa n'kkZ ; k x;k g SA vizxkeh rja x ks ds fuekZ. k ds fy;s vè;kjksf ir gksus okyh nks rjaxks dk osx 360 ms–1 rFkk vko`fr;k¡ 256 Hz gAS t dk laHkkfor eku (sec es)a ugha gksxk:A t=0 B A' x in m t=? D C C' A LL EN 38. A 37. displacement The pattern of standing waves formed on a stretched string at two instants of time (extreme, mean) are shown in figure. The velocity of two waves superimposing to form stationary waves is 360 ms–1 and their frequencies are 256 Hz. Which is not possible value of t (in sec) :- displacement 37. x in m E x in m t=? (1) 9.8 × 10–4 (2) 10–3 (1) 9.8 × 10–4 (2) 10–3 (3) 2.94 × 10–3 (4) 4.9 × 10–3 (3) 2.94 × 10–3 (4) 4.9 × 10–3 Three identical small electric dipoles are 38. arranged parallel to each other at equal separation a as shown in the figure. Their total interaction energy is U. Now one of the end dipole is gradually reversed, how much work is done by the electric forces. (1) (3) 17U 8 (2) 16U 8 (4) 16U 17 + + a + (1) a 18U 17 SPACE FOR ROUGH WORK / H-12/31 rhu loZle NksVs fo|qr f}/kzqoksa dks fp=kuqlkj ,d nwljs ls leku nwjh a ij ,d&nwljs ds lekUrj O;ofLFkr fd;k tkrk gAS budh dqy vU;ksU; ÅtkZ U gAS vc fljs ij j[ks fdlh ,d f}/kqzo dks /khjs&èkhjs O;qRØfer dj nsrs gaS rks fo|qr cyksa }kjk fd;k x;k dk;Z D;k gksxk\ (3) 17U 8 (2) 16U 8 (4) 16U 17 + + a + a 18U 17 jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 39. Even number of infinite +l 39. concentric circular arcs R –l of same angular span q carry uniform linear R +l charge densities +l and q –l alternatively as R shown in figure. Their radii are R, 2R, 3R....... respectively. The potential at their common centre is– (3) 40. lq ln2 (2) 4p Î0 lq ln 2 2p Î0 (1) lq ln2 4p Î0 A LL EN (1) +l le la[;k okys vuUr ladUs nzh ; o`Ù kkdkj pki ftudk dks. kh; R –l QSyko q leku g]S ij fp=kuqlkj R +l Øekxr :i ls +l rFkk –l q R le:i js[kh; vkos'k ?kuRo gaAS mudh f=T;k,a Øe'k% R, 2R, 3R... gSA muds mHk;fu"B dsUnz ij foHko gksxk% lq ln1 (3) lq ln1 (2) lq ln 2 2p Î0 (4) buesa ls dksbZ ugh (4) None of these 4p Î0 A current carrying wire in the form of 'V' 40. alphabet is kept as shown in the figure. Magnetic field intensity at point P which lies on the angular bisector of V is ,d /kkjkokgh rkj tks fd V vkÏfr esa eqM+k gqvk gS] fp=kuqlkj fLFkr gAS V ds dks.kh; yEc v¼Zd ij fLFkr fcUnq P ij pqEcdh; {ks= rhozrk gksxh %& m0i (1) 4 pr [1 - cos a ] 0 m0 i (2) 2pr [1 - cos a ] 0 m0i (1) 4 pr [1 - cos a ] 0 m0 i (2) 2pr [1 - cos a ] 0 m 0 i [1 - cos a] (3) 4 pr0 sin a m0 i [1 - cos a ] (4) 2pr sin a 0 m 0 i [1 - cos a] (3) 4 pr sin a 0 m0 i [1 - cos a ] (4) 2pr sin a 0 SPACE FOR ROUGH WORK / ALLEN 4p Î0 jQ dk;Z ds fy;s txg H-13/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 42. A prism is made of wire mesh with each side 41. having equal resistance R. A battery of 6 volt and zero resistance is connected across E and F as shown in the figure. The current in the branch AB, if R is equal to 5W, is :- fp= esa rkj ls cus ,d fizTe dh izR;sd Hkqtk dk izfrjksèk R gAS ,d 'kwU; izfrjks/k okyh 6 volt dh cVS jh dks fp=kuqlkj E o F ds e/; tksM+ fn;k tkrk gAS ;fn R dk eku 5W gks rks 'kk[kk AB esa /kkjk dk eku gksxk %& A LL EN 41. (1) 0.6 A (2) 0.8 A (3) 0.4 A (4) 2A (1) 0.6 A (2) 0.8 A (3) 0.4 A (4) 2A An electrical cable of copper has just one 42. wire of radius 9 mm. Its resistance is 5 W. This single copper wire of the cable is replaced by 7 different well insulated copper wires each of radius 3 mm and same length. The total resistance of the cable will now be equal to rkacs ls cuh ,d fo|qr dscy esa dsoy ,d rkj gS ftldh f=T;k 9 mm gS rFkk izfrjks/k 5 Ohm gAS bl vdsys rkacs ds rkj ds LFkku ij izR;sd 3mm f=T;k rFkk leku yEckbZ okys 7 vyx&vyx dqpkyd rkacs ds rkj izfrLFkkfir dj fn, tkrs gaSA vc bl dscy dk dqy izfrjks/k gksxk %& (1) 6.5 W (2) 45 W (1) 6.5 W (2) 45 W (3) 90 W (4) 270 W (3) 90 W (4) 270 W SPACE FOR ROUGH WORK / H-14/31 jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 44. A and C are concentric conducting spherical 43. shells of radius a and c respectively. A is surrounded by a concentric dielectric of inner radius a, outer radius b and dielectric constant k. If sphere A is given a charge Q, the potential at the outer surface of the dielectric is. fp= eas A rFkk C Øe'k% f=T;k a o c okys ladsUnzh; pkyd xksykdkj dks'k gaSA A ,d ladsUnzh ; ijko| S qr }kjk f?kjk gqvk gS] ftldh vkUrfjd f=T;k a, cká f=T;k b rFkk ijko| S qrkad k gAS A dks Q vkos'k nsus ij ijko| S qr dh ckgjh lrg ij foHko gksxk%& Q (1) 4pe kb 0 Q (1) 4pe kb 0 Q æ1 1 ö (2) 4pe ç + k(b - a) ÷ø 0 èa Q æ1 1 ö (2) 4pe ç + k(b - a) ÷ø 0 èa Q (3) 4pe b 0 Q (3) 4pe b 0 (4) None of these The magnetic force between wires as shown 44. in figure is :- (4) buesa ls dksbZ ugha A LL EN 43. i fp= esa n'kkZ;s x;s rkjksa ds chp pqEcdh; cy gksxk%& i l x l x I I (1) m 0 iI 2 æ x + l ö ln ç ÷ 2p è 2x ø m 0 iI æ x + l ö ln ç (3) ÷ 2p è x ø (2) m 0 iI 2 æ 2x + l ö ln ç ÷ 2p è 2x ø (4) None of these SPACE FOR ROUGH WORK / ALLEN m 0 iI 2 æ x + l ö ln ç (1) ÷ 2p è 2x ø (3) m 0 iI æ x + l ö ln ç ÷ 2p è x ø m 0 iI 2 æ 2x + l ö ln ç (2) ÷ 2p è 2x ø (4) buesa ls dksbZ ugha jQ dk;Z ds fy;s txg H-15/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 45. 46. Let np and ne be the numbers of holes and 45. conduction electrons in an extrinsic semiconductor :(1) np > ne (2) np = ne (3) np < ne (4) np ¹ ne A linearly polarized electromagnetic wave 46. r given as E = E 0 ˆi cos ( kz - wt ) is incident 47. (1) np > ne (2) np = ne (3) np < ne (4) np ¹ ne ,d j S f [kd /k z q f or fo|q r pq E cdh ; rja x r E = E 0 ˆi cos ( kz - wt ) fdlh iw . kZ r ;k ijkorZ d vuUr yEch nhokj ij z = a ij yEcor~ vkifrr gksrh gAS ekukfd bl nhokj dk inkFkZ izdkf'kd :i ls vfØ; gS rc ijkofrZr rjax dh lehdj.k gksxh %& A LL EN normally on a perfectly reflecting infinite wall at z = a. Assuming that the material of the wall is optically inactive, the reflected wave will be given as r (1) Er = - E0iˆ cos ( kz - wt ) r (2) Er = E0 iˆ cos ( kz + wt ) r (3) Er = - E0iˆ cos ( kz + wt ) r (4) Er = E0 iˆ sin ( kz - wt ) ekuk fdlh viæO;h v/kZpkyd esa fNæ rFkk pkyu bysDVªkWuksa dh la[;k Øe'k% np o ne g]S rc :- r (1) Er = - E0iˆ cos ( kz - wt ) r (2) Er = E0 iˆ cos ( kz + wt ) r (3) Er = - E0iˆ cos ( kz + wt ) r (4) Er = E0 iˆ sin ( kz - wt ) The energy spectrum of b-particles [number 47. N(E) as a function of b-energy E] emitted from a radioactive source is - ,d jsfM;kslfØ; òksr ls mRlftZr b-d.kksa dk ÅtkZ LisDVªe [la[;k N(E), b-ÅtkZ E ds Qyu ds :i esa g]S gS- (1) N(E) (1) N(E) (2) N(E) E0 E (3) N(E) E0 E E E0 E SPACE FOR ROUGH WORK / H-16/31 E (3) N(E) (4) N(E) E0 E0 (2) N(E) E0 E (4) N(E) E0 E E0 E jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 48. If the binding energy per nucleon in 37 Li and 4 2 He 48. ;fn 37 Li rFkk 24 He ukfHkdksa dh izfr U;wfDy;ksu cUèku ÅtkZ Øe'k% 5.70 MeV rFkk 7.06 MeV g]S rc nuclei are 5.70 MeV and 7.06 MeV vfHkfØ;k: respectively, then in the reaction : p + 37 Li ® 2 24 He p + 37 Li ® 2 24 He energy of proton must be- esa izkVs kWu dh ÅtkZ vo'; gksuh pkfg,- (1) 28.24 MeV (1) 28.24 MeV A LL EN (3) 1.46 MeV 49. (2) 17.28 MeV (4) 16.58 MeV A wooden cube (density of wood ' r ') of side 3 (3) 1.46 MeV 49. (2) 17.28 MeV (4) 16.58 MeV r 3 Hkqtk 'l' ds ,d ydM+h ds ?ku (ydM+h dk ?kuRo ' ') 'l' floats in a liquid of density 'r' with its upper dks ?kuRo 'r' ds ,d æo esa bl izdkj rjS k;k tkrk gS and lower surfaces horizontal. If the cube is fd mldk Åijh vkjS fupyk i`"B {kfS rt jgsA ;fn ?ku pushed slightly down and released, it performs dks FkksM+k lk nckdj NksM+ fn;k tk,] og vkorZ dky simple harmonic motion of period 'T'. Then, 'T' is equal to :3l (1) 2p 2g (3) 2p 3l g l (2) 2p 3g (1) 2p 3l 2g (2) 2p l 3g 2l g (3) 2p 3l g (4) 2p 2l g (4) 2p SPACE FOR ROUGH WORK / ALLEN 'T' ls ljy vkorZ xfr djrk gAS rc 'T' dk eku gS :- jQ dk;Z ds fy;s txg H-17/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 51. Two full turns of the circular scale of gauge 50. cover a distance of 1 mm on scale. The total number of divisions on circular scale is 50. Further, it is found that screw gauge has a zero error of -0.03 mm. While measuring the diameter of a thin wire a student notes the main scale reading of 4 mm and the number of circular scale division in line, with the main scale as 40. The diameter of the wire is (1) 4.42 mm (2) 4.83 mm (3) 4.77 mm (4) 4.88 mm A spherical solid ball of volume V is made of 51. a material of density r0. It is falling through a liquid of density r' (r' < r0). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v. i.e., Fviscous = –kv2, k > 0. The terminal speed of the ball is (1) 52. Vg(r0 - r ') k (2) Vgr0 k V(r0 - r ') Vgr0 (4) k k Two point white dots are 1 mm apart on a black 52. paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm] (1) 1 m (2) 3 m (3) 5 m (4) 7 m (3) fdlh LØwxst dk o`Ùkkdkj ieS kuk nks iw.kZ pDdjksa esa eq[; iSekus ij 1 mm nwjh r; djrk gAS o`Ùkkdkj ieS kus ds dqy Hkkxksa dh la[;k 50 gAS vkxs ;g Hkh izfs {kr gksrk gS fd LØw xst esa -0.03mm dh 'kwU; =qfV gAS ,d irys rkj dk O;kl ekis tkus ds nkSjku] ,d fo/kkFkhZ ;g izsf{kr djrk gS fd eq[; ieS kus dk ikB~;kad 4 mm gS rFkk o`Ùkkdkj iSekus ds 40 Hkkx eq[; ieS kus ds lkFk ,d js[kk esa gAS rkj dk O;kl gS (1) 4.42 mm (2) 4.83 mm (3) 4.77 mm (4) 4.88 mm ,d V vk;ru dh Bksl xksyh; xsan r0 ?kuRo ds inkFkZ ls cuh gqbZ gAS bls r' (r' < r0) ?kuRo ds nzo ls fxjk;k A LL EN 50. SPACE FOR ROUGH WORK / H-18/31 tkrk gAS eku yhft;s fd nzo] xsan ij ,d ';ku cy vkjksfir djrk gS tks fd bldh pky v ds oxZ ds lekuqikrh g]S vFkkZr~ Fviscous = –kv2, k > 0 gS rks xsan dh lhekUr pky gksxh(1) Vg(r0 - r ') k (2) Vgr0 k (3) Vgr0 k (4) V(r0 - r ') k fdlh dkys dkxt ij nks 'osr fcUnq ,d nwljs ls 1 mm nwjh ij vafdr gaSA bu fcUnqvksa dks fdlh us= ftldh iqryh dk O;kl 3 mm g]S }kjk ns[kk tkrk gAS og yxHkx vf/kdre nwjh D;k gS ftl ij us= }kjk bu fcUnqvksa dk foHksnu fd;k tk ldrk g\ S [izdk'k dh rjaxn/S ;Z = 500 nm yhft,A] (1) 1 m (2) 3 m (3) 5 m (4) 7 m jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 53. In which of the following cases, the transistor is operating in the active region ? 1V 2V (3) 0V (2) 1V 2V (1) 2V 1V 0V 2V 0V 2V (4) 1V (3) 1V 0V combination with the states of output X, Y and Z given for inputs P, Q, R and S all at state 1. When inputs P and R change to state 0 with inputs Q and S still at 1, the states of outputs X, Y and Z change to X(1) Z(0) Y(0) (1) 1, 0, 0 (2) 1, 1, 1 (3) 0, 1, 0 (4) 0, 0, 1 SPACE FOR ROUGH WORK / ALLEN 2V 0V The circuit diagram shows a logic 54. R(1) S(1) (2) 1V 1V P(1) Q(1) 0V 0V 2V 54. fuEu esa ls dkuS ls fodYi esa VªkaftLVj lfØ; {ks= esa dk;Zjr g\ S A LL EN (1) 53. (4) 1V 2V 0V fp= esa ,d rkfdZd }kjksa dh ,d O;oLFkk çnf'kZr dh xbZ gS] ftlesa voLFkk 1 ij fo|eku fuos'kh P, Q, R o S ds fy, fuxZr X, Y rFkk Z dh voLFkk n'kkZ;h x;h gAS tc fuos'kh P o R dh voLFkk ifjofrZr dj 0 dj nh tkrh gS tcfd Q o S vc Hkh voLFkk 1 ij gh gS rks fuxZr X, Y o Z dh voLFkk ifjofrZr gksdj D;k gks tk;sxh\ P(1) Q(1) R(1) S(1) (1) 1, 0, 0 (3) 0, 1, 0 X(1) Z(0) Y(0) (2) 1, 1, 1 (4) 0, 0, 1 jQ dk;Z ds fy;s txg H-19/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 55. The real time variation of input signals A and 55. B are as shown below. If the inputs are fed into NAND gate, then select the output signal from the following A fuos'kh ladrs ksa A rFkk B ds okLrfod le; ifjorZu dks uhps iznf'kZr fd;k x;k gAS ;fn bu fuos'kksa dks NAND }kj esa i; z qDr fd;k tk;s rks fuxZr ladsr D;k gksxk\ A B A B B Y A B A LL EN t(s) Y Y (1) 0 2 4 6 8 t(s) (3) Y 0 56. 6 8 t(s) 0 2 4 6 8 t(s) 0 0 2 4 6 8 (2) t(s) (3) Y 2 4 6 8 0 t(s) A certain radioactive sample is observed to undergo 10000 decays in 10 sec. In which of the following cases can we say that decay rate during this time interval is approximately constant and equal to 1000 dps. (1) t1/2 = 10 sec (2) tmean = 10 sec (3) t1/2 >> 10 sec (4) t1/2 << 10 sec 56. SPACE FOR ROUGH WORK / H-20/31 Y (1) (4) Y 2 4 t(s) Y (2) 2 4 Y 6 8 0 2 4 6 8 t(s) 2 4 6 8 t(s) (4) Y t(s) 0 fdlh jsfM;kslfØ; izfrn'kZ ds 10 sec esa 10000 fo?kVu gksrs gaSA fuEu esa ls dkuS lh fLFkfr esa ge dg ldrs gaS fd bl le;kUrjky esa fo?kVu nj fu;r rFkk 1000 fo?kVu izfr lsd.M ds cjkcj gS %& (1) t1/2 = 10 sec (3) t1/2 >> 10 sec (2) tmean = 10 sec (4) t1/2 << 10 sec jQ dk;Z ds fy;s txg ALLEN ALLEN JEE-MAIN SAMPLE PAPER # 02 57. Which one of the following statements is 57. wrong? (1) Radio waves in the frequency range 30 MHz to 60 MHz are called sky waves (2) Radio horizon of the transmitting antenna for space wave is dT = ( Rh T ) (3) Fiber optical communication is free from electrical disturbances 58. fuEu esa ls xyr dFku pqfu;s %& (1) vko`fÙk ijkl 30 MHz ls 60 MHz esa fo|eku jsfM;ks rjaxs] O;kse rjaxs gksrh gAS (2) vkdk'k rjaxksa ds fy;s lEisz"k.k ,afVuk dk jsfM;k f{kfrt dT = ( Rh T ) gksrk gSA (R = i`Foh dh f=T;k, hT = lEizs"k.k ,afVuk dh Å¡pkbZ) A LL EN (R = radius of earth, h T = height of transmitting antenna) 2014 (3) izdkf'kd rarq lapkj fo|qr fo{kksHkksa ls Lora= gksrk gSA (4) The principle of fibre optical communication is total internal reflection (4) izdkf'kd rarq lapkj dk fl¼kUr iw.kZ vkarfjd Electromagnetic waves with frequencies 58. greater than the critical frequency of ionosphere cannot be used for communication using sky wave propagation, because (1) the refractive index of the ionosphere becomes very high for f > fc (2) the refractive index of the ionosphere becomes very low for f > fc (3) the refractive index of the ionosphere becomes very high for f < fc (4) None of these vk;u e.My dh Økafrd vko`fr ls vf/kd vko`fr;ksa SPACE FOR ROUGH WORK / ALLEN ijkorZu gksrk gSA okyh o| S qr pqEcdh; rjaxkas dk mi;ksx O;kse rjax lapj.k }kjk lapkj ds fy;s ugh fd;k tk ldrk] D;ksafd%& (1) f > fc ds fy;s vk;u e.My dk viorZukad cgqr vf/kd gks tkrk gAS (2) f > fc ds fy;s vk;u e.My dk viorZukad cgqr de gks tkrk gAS (3) f < fc ds fy;s vk;u e.My dk viorZukad cgqr vf/kd gks tkrk gAS (4) buesa ls dksbZ ugha jQ dk;Z ds fy;s txg H-21/31 ALLEN JEE-MAIN SAMPLE PAPER # 02 60. Statement-1 : When ultraviolet light is 59. incident on a photocell, its stopping potential is V0 and the maximum kinetic energy of the photoelectrons is Kmax . When the ultraviolet light is replaced by X-rays, both V0 and Kmax increases. Statement-2 : Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light. (1) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1. (2) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (3) Statement-1 is true, statement-2 is false. (4) Statement-1 is false, statement-2 is true. Statement-1: In a resonance co lumn 60. apparatus, the displacement node is formed at the free surface of water. Statement-2 : The sound wave undergoes a phase change of p on reflection from a water surface. (1) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1. (2) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (3) Statement-1 is true, statement-2 is false. (4) Statement-1 is false, statement-2 is true. dFku -1 : tc fdlh QksVks lsy ij ijkcSaxuh izdk'k vkifrr gksrk gS rks bldk fujks/kh foHko V0 rFkk QksVks bysDVªkWuksa dh vf/kdre xfrt ÅtkZ K max gksrh gSA tc bl ijkcSaxuh izdk'k ds LFkku ij X-fdj.k iz;qä dh tkrh gS rks V0 o Kmax nksuksa c<+ tkrs gaSA dFku -2 : izdk'k bysDVªkWu 'kwU ; ls vf/kdre eku ijkl okyh pky ds lkFk mRlftZr gksrs gaSA ,slk vkifrr izdk'k esa fo|eku fofHkUu ijkl dh vko`fÙk;ksa ds dkj.k gksrk gAS (1) dFku –1 lR; gS] dFku –2 lR; g S; dFku –2 dFku–1 dh lgh O;k[;k djrk gAS (2) dFku –1 lR; gS] dFku –2 lR; g S; dFku –2 dFku–1 dh lgh O;k[;k ugha djrk gS (3) dFku–1 lR; g,S dFku–2 vlR; gAS (4) dFku–1 vlR; gS] dFku–2 lR; gAS dFku-1: vuqukn LrEHk midj.k esa ,d foLFkkiu fuLian ty dh eqä lrg ij curk gAS dFku -2: ty lrg ls ijkorZu gksus ij /ofu rjax esa p dykUrj mRiUu gks tkrk gAS (1) dFku –1 lR; gS] dFku –2 lR; g S; dFku –2 dFku–1 dh lgh O;k[;k djrk gAS (2) dFku –1 lR; gS] dFku –2 lR; g S; dFku –2 dFku–1 dh lgh O;k[;k ugha djrk gS (3) dFku–1 lR; g,S dFku–2 vlR; gAS (4) dFku–1 vlR; gS] dFku–2 lR; gAS A LL EN 59. 2014 SPACE FOR ROUGH WORK / H-22/31 jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 PART C - CHEMISTRY 62. 63. 64. Which among the following aqueous solution have highest boiling point (1) 1 molal KCl solution (2) 2 molal glucose (3) 1 molal Co(NO3)2 solution (4) 1 molal NaCl solution For a first order reaction choose the CORRECT statement :– (1) The degree of dissociation is equal to (1 – e–kT) (2) The pre-exponential factor in the arrhenius equation has the dimension of time–1 (3) A plot of reciprocal concentration of the reactant v/s time gives a straight line (4) (1) & (2) both The number of electrons of chlorine atom for which n + l + m = 1 is : (1) 4 (2) 2 (3) 3 (4) 5 61. fuEu tyh; foy;uks a es a ls fdldk DoFkuka d lokZf/kd gksxk (1) 1 eksy y KCl foy;u (2) 2 eksyy Xywdkst (3) 1 eksy y Co(NO3)2 foy;u (4) 1 eksyy NaCl foy;u 62. izFke dksfV vfHkfØ;k ds fy, lgh dFku dk p;u dhft, :– (1) fo;kstu dh ek=k (1 – e–kT) ds cjkcj gksrh gS (2) vkjfguh;l lehdj.k esa iwoZ ?kkrkadh xq.kkd –1 dh foek le; gksrh gS (3) fØ;kdkjdks dh lkUnzrk dk O;qRØe v/s le; dk oØ ,d lh/kh js[kk gksrh gS (4) (1) rFkk (2) nksuksa 63. Dyksfju ijek.kq ds ,sls byDS Vªkus ksa dh la[;k ftuds fy, n + l + m = 1 gksrk g]S gSa& A LL EN 61. How many grams of CaC2O4 will dissolve in 64. distilled water to make 1 lt. of sturated solution? (Ksp for CaC2O4 = 2.5 × 10–9 and its molecular wt. is 128) (1) 4 (3) 3 (2) 2 (4) 5 ,d yhVj lar`Ir foy;u cukus ds fy, vklqr ty esa CaC2 O 4 ds fdrus xz k e foys ; fd;s tk,s x s a ] (CaC2O4 ds fy, Ksp = 2.5 × 10–9 rFkk bldk vkf.od Hkkj 128 gksrk gS) (1) 0.0064 gm (2) 0.0128 gm (1) 0.0064 gm (2) 0.0128 gm (3) 0.0032 gm (4) 0.0640 gm (3) 0.0032 gm (4) 0.0640 gm SPACE FOR ROUGH WORK / ALLEN jQ dk;Z ds fy;s txg H-23/31 ALLEN JEE-MAIN SAMPLE PAPER # 02 66. 67. 68. Equivalent mass of oxidising agent in the reaction, SO2 + 2H2S ® 3S + 2H2O is (1) 32 (2) 64 (3) 16 (4) 8 DGº of the cell reaction AgCl(s) + ½ H2(g)Ag(s)+H+(aq.)+ Cl–(aq.) is –21.52 kJ. Calculate the EMF for the cell reaction 2AgCl(s)+H2(g)Ag(s)+2H+(aq.)+ 2Cl–(aq.) (1) 0.223 V (2) 0.446 V (3) 0.112 V (4) 0.337 V The aq.solutions of the following substances were electrolysed using inert electrodes. In which case, the pH of the solution does not change (1) AgNO3 (aq.) (2) CuSO4 (aq.) (3) dil.NaCl (aq.) (4) K2SO4 (aq.) Identify the correct statement regarding entropy. (1) At absolute zero temperature, the entropy of perfectly crystalline substance is +ve. (2) At absolute zero temp. entropy of perfectly crystalline substance is taken to be zero. (3) At 0 °C the entropy of a perfectly crystalline substance is taken to be zero. (4) At absolute zero temperature, the entropy of all crystalline substances is taken to be zero. 65. fuEu vfHkfØ;k esa vkWD lhdkjd dk rqY ;kad Hkkj gksxk SO2 + 2H2S ® 3S + 2H2O (1) 32 (2) 64 (3) 16 (4) 8 66. fuEu lSYk vfHkfØ;k dk AgCl(s) + ½ H2(g)Ag(s)+H+(aq.)+ Cl–(aq.) DGº = –21.52 kJ gS fuEu ly S vfHkfØ;k ds fy, EMF dh x.kuk dhft,A 2AgCl(s)+H2(g)Ag(s)+2H+(aq.)+ 2Cl–(aq.) (1) 0.223 V (2) 0.446 V (3) 0.112 V (4) 0.337 V A LL EN 65. 67. fuEu inkFkksZ ds tyh; foy;uksa dks OkS|qr vi?kfVr fd;k x;kA ;fn vfØ; bysDVªkM s +ks dk mi;ksx fd;k x;k gks] rks fdl fLFkfr esa] foy;u dh pH ifjofrZr ugha gksrh gS - (1) AgNO3 (aq.) (3) dil.NaCl (aq.) 68. SPACE FOR ROUGH WORK / H-24/31 2014 (2) CuSO4 (aq.) (4) K2SO4 (aq.) ,UVªkWih ds lanHkZ esa lgh dFku igpkfu, & (1) ije'kwU; rki ij iw.kZr% fØLVyh; inkFkZ dh ,UVªkWih /kukRed gksrh gSA (2) ije'kwU; rki ij iw.kZr% fØLVyh; inkFkZ dh ,UVªkWih 'kwU; ekuh tkrh gAS (3) 0°C ij iw.kZr% fØLVyh; inkFkZ dh ,UVªkWih 'kwU; ekuh tkrh gSA (4) ije'kwU; rki ij lHkh fØLVyh; inkFkks± dh ,UVªkWih 'kwU; ekuh tkrh gSA jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 70 The number of atoms per unit cell in a simple 69. cubic, face-centred cubic and body-centered cubic structure respectively are (1) 1, 4, 2 (2) 1, 2, 4 (3) 8, 14, 9 (4) 8, 4, 2 10 moles of SO3 gas is taken in 1 lt. closed 70 rigid container and allowed to attain equilibrium at 27ºC as 2SO3(g) 2SO2(g)+ O2(g) 2 moles of O2(g) is formed at equilibrium. If 10 moles of SO2(g) & 5 moles of O2(g) is taken in the same container at same temperature, then number of moles of SO 3(g ) formed at equilibrium is : (1) 4 mole (2) 8 mole (3) 2 mole (4) 6 mole Which of the following is not 71. disproportionation reaction. (1) Heating of H3PO3 ljy ?kuh;] Qyd dsfUnz r ?kuh; rFkk dk; dsfUnzr ?kuh; lajpukvksa esa izfr bdkbZ lSy esa ijek.kqvksa dh la[;k Øe'k% gS (1) 1, 4, 2 (2) 1, 2, 4 (3) 8, 14, 9 (4) 8, 4, 2 10 eksy SO3 xl S dks 1 yhVj ds can n`< ik= esa fy;k x;k rFkk 27ºC ij lkE; izkIr gksus fn;k x;k 2SO3(g) 2SO2(g)+ O2(g) lkE; ij 2 eksy O2(g) dk fuekZ.k gksrk gS A LL EN 69. ;fn 10 eksy SO2(g) rFkk 5 eksy O2(g) dks leku ik= esa leku rki ij fy;k x;k gks] rks lkE; ij cuus okys SO3(g) ds eksyksa dh la[;k gksxh : (1) 4 eksy (2) 8 eksy (3) 2 eksy (4) 6 eksy fuEu esa ls dkuS lh vfHkfØ;k fo"kekuqikru vfHkfØ;k ugha gS (1) H3PO3 dks xeZ djuk (2) XeF6 dk ty vi?kVu (2) Hydrolysis of XeF6 (3) NaOH ds lkFk P4 dks xeZ djuk (3) Heating of P4 with NaOH (4) NO2 dk ty vi?kVu (4) Hydrolysis of NO2 72. Which of the following metal does not evolve 72. fuEu esa ls dkSulh /kkrq viuh mi;qDr ifjfLFkfr ij H2O ds lkFk H2 xl S mRlftZr ugha djrh gS& H2 gas with H2O at their appropriate condition 71. (1) Cu (3) Mg (2) Na (4) Fe SPACE FOR ROUGH WORK / ALLEN (1) Cu (3) Mg (2) Na (4) Fe jQ dk;Z ds fy;s txg H-25/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 74. 75. 76. 77. 78. Which of the following metal is inert towards reaction with conc. nitric acid. (1) Cu (2) Zn (3) Ag (4) Pt Which of the following product is formed when S2O32– reacts with MnO4– in the presence of acidic medium. (1) SO42– (2) S4O62– (3) S (4) Both (1) & (3) Which of the following species is paramagnetic in nature(1) MnO42– (2) CrO42– (3) [Pt(NH3)4]2+ (4) All of these Which of the following molecule has S–O–S linkage (1) H2S 2O 8 (2) H2S2O5 (3) S3O 9 (4) H2S2O4 Which of the following lanthanide is man made and radioactive in nature (1) Ce (2) Pm (3) Nd (4) Gd Which of the following order is incorrect(1) F < Cl : Electron affinity + 2+ (2) Au > Hg : Ionic radius (3) B < Be : 1st Ionisation energy (4) Li < Cs : Electronegativity 73. fuEu esa ls dkSulh /kkrq lkUnz ukbfVªd vEy ds lkFk vfHkfØ;k ds izfr vfØ; gksrh gS (1) Cu (3) Ag 74. tc vEyh; ek/;e dh mifLFkfr esa S 2O3 2– dh MnO4– ds lkFk vfHkfØ;k djkrs gaS rc fuEu mRiknksa esa ls fdldk fuekZ.k gksrk gS& (1) SO42– (3) S 75. (2) Zn (4) Pt (2) S4O62– (4) nksuksa (1) rFkk (3) fuEu esa ls dkSulh Lih'kht vuqpqEcdh ; izd`fr dh gS - A LL EN 73. (1) MnO42– (3) [Pt(NH3)4]2+ 76. 77. fuEu esa ls dk S ulk y SU Fksu kbM ekuo fufeZ r rFkk jsfM;ks/kehZ izd`fr dk gAS (1) Ce (3) Nd 78. SPACE FOR ROUGH WORK / H-26/31 (2) CrO42– (4) mijksDr lHkh fuEu esa ls dkSuls v.kq esa S–O–S ca/ku mifLFkr gS (1) H2S 2O 8 (2) H2S2O5 (3) S3O 9 (4) H2S2O4 (2) Pm (4) Gd fuEu esa ls dkSulk Øe xyr gS (1) F < Cl : bySDVªkWu ca/kqrk + 2+ (2) Au > Hg : vk;fud f=T;k (3) B < Be : izFke vk;uu ÅtkZ (4) Li < Cs : fo|qr½.krk jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 80. 81. Which of the following complex is low spin as 79. well as paramagnetic in nature. (1) [Fe(NH3)6]2+ (2) [Mn(NH3)6]2+ (3) [Co(H2O)6]3+ (4) [Co(NH3)6]2+ Which of the following step is not involved in 80. the extraction of blister copper from copper pyrite. (1) Smelting (2) Roasting (3) Auto / Self reduction (4) Polling 81. Identify correct acidic strength order OH (I) 82. 83. fuEu esa ls dkuS lk ladqy U;wu pØ.k ds lkFk lkFk vuqpqEcdh; izd`fr dk gS - (1) [Fe(NH3)6]2+ (3) [Co(H2O)6]3+ COOH OH (II) OH (2) HktZu (3) Lor% vip;u (1) I > II > III (2) II > III > I (3) III > II > I (4) II > I > III dentify artificial sweetner (1) Alitame (2) Aspartame (3) Saccharine (4) All are correct Identify condensation copolymer (1) Natural rubber (2) Bakelite (3) PVC (4) Nylon-6 vEyh; lkeF;Z dk lgh Øe igpkfu;s - (I) 82. 83. SPACE FOR ROUGH WORK / ALLEN (4) ikWfyax OH NO2 (III) (2) [Mn(NH3)6]2+ (4) [Co(NH3)6]2+ fuEu esa ls dkSulk in dkWij ikbjkbV ls QQksysnkj dkWij ds fu"d"kZ.k esa lfEefyr ugha gS (1) izxyu A LL EN 79. COOH OH (II) OH NO2 (III) (1) I > II > III (2) II > III > I (3) III > II > I (4) II > I > III d`f=e feBkl (sweetner) dks igpkfu;s (1) ,fyVse (2) ,LikjVe (3) lsfØu (4) lHkh lgh gS la?kuu lgcgqyd dks igpkfu;s (1) izkd`frd jcj (2) cd S y s kbV (3) PVC (4) uk;ykWu-6 jQ dk;Z ds fy;s txg H-27/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 OH OH NaOH Br2 water 84. NaOH Br2 water 84. Major product is - SO3H SO3H OH OH OH Br Br (2) (1) Br OH SO3H (3) Br Br Br Br Mixture of alcohol and acetone is separated by 85. (1) Aq. NaHCO3 extraction (2) Aq. NaOH extraction (3) NaHSO3 test (4) Victor mayer test Identify total structural isomers for C6H14 86. molecular formula (1) 3 (2) 5 (3) 7 (4) 9 SPACE FOR ROUGH WORK / H-28/31 Br OH OH (4) Br 86. Br (2) SO3H Br OH 85. Br Br SO3H (3) OH Br Br A LL EN (1) eq[; mRikn gS - (4) Br Br Br SO3H ,YdksgkWy rFkk ,lhVksu ds feJ.k dks fdlds }kjk i`Fkd fd;k tk ldrk gS (1) tyh; NaHCO3 fu"d"kZ .k (2) tyh; NaOH fu"d"kZ.k (3) NaHSO3 ijh{k.k (4) foDVj es;j ijh{k.k vkf.od lw= C6H14 ds fy, lajpuk leko;fo;ksa dh dqy la[;k gS- (1) 3 (3) 7 (2) 5 (4) 9 jQ dk;Z ds fy;s txg ALLEN 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 87. Identify major product for following reaction 87. O O O pH 4 to 6 + NH2–NH2 ¾¾¾¾ ® major product (1) O N N N NH (2) (4) H2N N OH O (1) OH (3) N N N NH (2) (4) excess AC2O OH major product 88. OH O OH excess AC2O OH N eq[; mRikn N O O O O O C Me O C Me O C Me O C Me (1) COOH (2) (1) O C Me OH O C Me O OH (3) O (4) OH O OH (4) C Me OH O SPACE FOR ROUGH WORK / O C Me (3) C Me OH COOH (2) C Me ALLEN H2N N OH OH 88. pH 4 to 6 + NH2–NH 2 ¾¾¾¾ ® eq[ ; mRikn - A LL EN (3) fuEu vfHkfØ;k ds fy, eq[; mRikn crkb;s O jQ dk;Z ds fy;s txg H-29/31 2014 ALLEN JEE-MAIN SAMPLE PAPER # 02 89. Identify correct reactivity order for dehydration 89. of following compounds [Reaction with conc.H2SO4/D]- 90. OH (II) OH (I) OH (III) A LL EN OH (I) fuEu ;kfS xdksa ds futZyhdj.k ds fy, fØ;k'khyrk dk lgh Øe igpkfu;s [lkUnz H2SO4 /D ds lkFk vfHkfØ;k]- (1) I > II = III (1) I > II = III (2) I > III > II (2) I > III > II (3) III > II > I (3) III > II > I (4) II > I > III (4) II > I > III Identify correct reactivity order for the 90. following compounds on reaction with anhydrous PCl3 OH (I) (II) (1) I > II > III (2) II > I > III (3) III > II > I (4) III > I > II SPACE FOR ROUGH WORK / H-30/31 djkus ij fØ;k'khyrk dk lgh Øe crkb;sA OH (III) OH (III) fuEu ;kfS xdks dh futZyh; PCl3 ds lkFk vfHkfØ;k OH OH OH (II) (I) OH (II) OH (III) (1) I > II > III (2) II > I > III (3) III > II > I (4) III > I > II jQ dk;Z ds fy;s txg ALLEN ALLEN JEE-MAIN SAMPLE PAPER # 02 jQ dk;Z ds fy;s txg A LL EN SPACE FOR ROUGH WORK / 2014 SPACE FOR ROUGH WORK / ALLEN jQ dk;Z ds fy;s txg H-31/31
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