Test Booklet Code C Regd. Office : Aakash Tower, Plot No.-4, Sec-11, MLU, Dwarka, New Delhi-110075 Ph.: 011-47623456 Fax : 011-47623472 Time : 3 hrs. JEE (MAIN)-2015 M.M. : 360 (Mathematics, Physics and Chemistry) Important Instructions : 1. The test is of 3 hours duration. 2. The Test Booklet consists of 90 questions. The maximum marks are 360. 3. 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 each correct response. 4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each question. ¼ (one-fourth) marks will be deducted for indicating 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. 5. There is only one correct response for each question. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 4 above. 6. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side-1 and Side-2 of the Answer Sheet. Use of pencil is strictly prohibited. 7. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination room/hall. 8. The CODE for this Booklet is C. Make sure that the CODE printed on Side-2 of the Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet. JEE (MAIN)-2015 PART–A : MATHEMATICS 1. A complex number z is said to be unimodular if |z| = 1. Suppose z1 and z2 are complex numbers 1. z1 2 z2 such that is unimodular and z 2 is not 2 z1 z2 unimodular. Then the point z1 lies on a (1) Circle of radius 2 2 (1) (4) Circle of radius 2 2. (1) Meets the curve again in the fourth quadrant (2) Does not meet the curve again (3) Meets the curve again in the second quadrant (4) Meets the curve again in the third quadrant The sum of first 9 terms of the series 13 1 3 2 3 13 2 3 3 3 ........ is 1 1 3 135 3. z2 ,dekikadh ugha gS] rks (2) x-v{k ds lekarj ,d js[kk ijA (3) y-v{k ds lekarj ,d js[kk ijA okys o`Ùk ijA oØ x2 + 2xy – 3y2 = 0 (1) oØ dks nksckjk prqFkZ prqFkk±'k esa feyrk gS (2) oØ dks nksckjk ugha feyrk (3) oØ dks nksckjk f}rh; prqFkk±'k esa feyrk gS (4) oØ dks nksckjk r`rh; prqFkk±'k esa feyrk gS Js.kh z1 2 z2 2 z1 z2 fcUnq z1 f=kT;k okys o`Ùk ijA (4) 2 f=kT;k The normal to the curve, x2 + 2xy – 3y2 = 0 at (1,1) : |z| = 1 ,dekikadh dgykrh gS ;fn rFkk z2 ,slh lfEeJ la[;k,¡ gSa fd ,dekikadh gS rFkk fLFkr gS (3) Straight line parallel to y-axis 3. z1 gSA ekuk (2) Straight line parallel to x-axis 2. z ,d lfEeJ la[;k ds fcUnq (1,1) ij vfHkyEc 13 1 3 2 3 13 2 3 3 3 ........ 1 1 3 135 ds izFke 9 inksa dk ;ksx gS 4. (1) 192 (2) 71 (3) 96 (4) 142 Let f(x) be a polynomial of degree four having extreme 4. f (x) ⎤ ⎡ values at x = 1 and x = 2. If lim ⎢ 1 ⎥ 3 , then x 0 ⎣ x2 ⎦ f(2) is equal to (1) 192 (2) 71 (3) 96 (4) 142 ekuk f(x) x = 2 ij ?kkr 4 dk ,d cgq i n gS ftlds pje eku gSAa ;fn f (x) ⎤ ⎡ lim ⎢ 1 ⎥3 x 0 ⎣ x2 ⎦ x=1 rFkk gS] rks f(2) cjkcj gS 5. 6. (1) 4 (2) –8 (3) –4 (4) 0 The negation of ~ s (~ r s) is equivalent to (1) s r (2) s ~ r (3) s (r ~ s) (4) s (r ~ s) 5. ⎡1 2 2 ⎤ ⎢ ⎥ If A = ⎢ 2 1 2 ⎥ is a matrix satisfying the ⎢⎣ a 2 b ⎥⎦ equation AAT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to 6. (1) 4 (2) –8 (3) –4 (4) 0 ~ s (~ r s) dk fu"ks/ lerqY; gS (1) s r (2) s ~ r (3) s (r ~ s) (4) s (r ~ s) ;fn ⎡1 2 2 ⎤ A = ⎢⎢ 2 1 2 ⎥⎥ ⎢⎣ a 2 b ⎥⎦ ,d ,slk vkO;wg gS tks vkO;wg lehdj.k AAT = 9I, dks larq"V djrk gS] tgk¡ I, 3 × 3 dk rRled vkO;wg gS] rks Øfer ;qXe (a, b) dk eku gS (1) (–2, –1) (2) (2, –1) (1) (–2, –1) (2) (2, –1) (3) (–2, 1) (4) (2, 1) (3) (–2, 1) (4) (2, 1) 2 JEE (MAIN)-2015 7. The integral 1 4 ⎛ x 1⎞ (1) ⎜ 4 ⎟ c ⎝ x ⎠ 4 1 4 8. 1 ⎛ x4 1⎞ 4 (1) ⎜ 4 ⎟ c ⎝ x ⎠ 1 4 (3) ( x 4 1) 4 c 1 ⎛ x4 1⎞ 4 (2) ⎜ 4 ⎟ c ⎝ x ⎠ 1 1 8. (4) ( x 4 1) 4 c means between l and n, then G14 2G24 G34 equals. ;fn nks fofHk okLrfod la[;kvksa l rFkk n (l, n > 1) dk lekarj ekè; (A.M.) m gS vkSj l rFkk n ds chp rhu xq.kksÙkj ekè; (G.M.) G1, G2 rFkk G3 gSa] rks G14 2G24 G34 cjkcj gS (1) 4 l2m2n2 (1) 4 l2m2n2 (2) 4 l2mn (3) 4 lm2n (4) 4 lmn2 If m is the A.M. of two distinct real numbers l and n (l, n > 1) and G1, G2 and G3 are three geometric (3) 4 9. 4 lekdy ∫ 2 4dx 3/4 cjkcj gS x ( x 1) 1 4 ⎛ x 1⎞ (2) ⎜ 4 ⎟ c ⎝ x ⎠ 4 (4) ( x 1) c (3) ( x 1) c 4 7. dx ∫ x 2 (x 4 1)3/4 equals (2) 4 l2mn lm2n (4) 4 lmn2 Let y(x) be the solution of the differential equation x log x 9. dy y 2 x log x , ( x 1). dx ekuk vody lehdj.k x log x Then y(e) is equal to dy y 2 x log x , ( x 1) dx (1) 2e (2) e y(e) cjkcj (3) 0 (4) 2 (1) 2e (2) e (3) 0 (4) 2 10. The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is (1) 72 (3) 192 10. vadksa iz;ksx ls] fcuk nksgjk;s] cuus okys 6,000 ls cM+s iw.kk±dksa dh la[;k gS (2) 216 (4) 120 (3) 192 (4) 120 (1) 780 (2) 901 (3) 861 (4) 820 12. Let and be the roots of equation x2 – 6x – 2 = 0. If an = n – n, for n 1, then the value of 12. a10 – 2 a8 2 a9 f=kHkqt] ftlds 'kh"kZ (0, 0), (0, 41) rFkk (41, 0) gSa] ds vkUrfjd Hkkx esa fLFkr mu fcUnqvksa dh la[;k ftuds nksuska funsZ'kkad iw.kk±d gSa] gS (1) 780 (2) 901 (3) 861 (4) 820 ekuk rFkk f}?kkr lehdj.k ;fn is equal to n1 x2 – 6x – 2 = 0 ds fy,] an = n – n gS] rks eku gS (1) –3 (2) 6 (1) –3 (2) 6 (3) –6 (4) 3 (3) –6 (4) 3 ⎛ 2x ⎞ 13. Let tan 1 y tan 1 x tan 1 ⎜ ⎝ 1 x 2 ⎟⎠ where |x| 1 3 13. ekuk ⎛ 2x ⎞ tan 1 y tan 1 x tan 1 ⎜ ⎝ 1 x 2 ⎟⎠ tgk¡ |x| . Then a value of y is 1 3 gS] rks y dk ,d eku gS (1) 3x x 3 1 3x 2 (2) 3x x 3 1 3x 2 (1) 3x x 3 1 3x 2 (2) 3x x 3 1 3x 2 (3) 3x x 3 1 3x 2 (4) 3x x 3 1 3x 2 (3) 3x x 3 1 3x 2 (4) 3x x 3 1 3x 2 3 gS] rks 3, 5, 6, 7 rFkk 8 ds (1) 72 11. y(x) gS (2) 216 11. The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is dk gy ds ewy gSaA a10 – 2 a8 2 a9 dk JEE (MAIN)-2015 14. The distance of the point (1, 0, 2) from the point of 14. x2 y1 z2 intersection of the line and the 3 4 12 plane x – y + z = 16, is x2 y1 z2 3 4 12 js[kk ds izfrPNsn fcUnq dh] fcUnq rFkk lery (1, 0, 2) ls nwjh gS (1) 13 (1) 13 (2) 2 14 (2) 2 14 (3) 8 (4) 3 21 (3) 8 (4) 3 21 15. {(x, y) : y2 2x rFkk y 4x – 1} }kjk ifjHkkf"kr {ks=k dk {ks=kiQy (oxZ bdkb;ks)a esa gS 15. The area (in sq. units) of the region described by {(x, y) : y2 2x and y 4x – 1} is 9 (1) 32 7 (2) 32 (1) 9 32 (2) 7 32 5 (3) 64 15 (4) 64 (3) 5 64 (4) 15 64 16. 16. Let O be the vertex and Q be any point on the parabola, x2 = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is (1) x 2 2 y (2) x 2 y (3) y 2 x (4) y 2 2 x (1) 14.0 (2) 16.8 (3) 16.0 (4) 15.8 ekuk ijoy; x2 = 8y dk 'kh"kZ O rFkk ml ij dksbZ fcUnq Q gSA ;fn fcUnq P] js[kk[kaM OQ dks 1 : 3 ds vkarfjd vuqikr esa ck¡Vrk gS] rks P dk fcUnqiFk gS % (1) x 2 2 y (2) x 2 y (3) y 2 x (4) y 2 2 x 17. 16 iz{s k.kksa okys vk¡dM+kas dk ekè; 16 gSA;fn ,d iz{s k.k ftldk eku 16 gS] dks gVk dj] 3 u;s izs{k.k ftuds eku 3, 4 rFkk 5 gSa] vk¡dM+ksa esa feyk fn;s tkrs gSa] rks u;s vk¡dM+ksa dk ekè; gS 17. The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is 18. 18. The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to (1) 14.0 (2) 16.8 (3) 16.0 (4) 15.8 nh?kZo`Ùk x2 y2 1 9 5 ds ukfHkyEcksa ds fljksa ij [khaph xbZ Li'kZ js[kkvksa }kjk fufeZr prqHkqZt dk {ks=kiQy (oxZ bdkb;ksa es)a gSa x2 y2 1 , is the ellipse 9 5 (1) 27 (1) 27 27 4 (3) 18 (2) 27 (2) 4 (3) 18 (4) x – y + z = 16 (4) 27 2 19. 19. The equation of the plane containing the line 2x – 5y + z = 3; x + y + 4z = 5, and parallel to the plane, x + 3y + 6z = 1, is (1) 2 x 6 y 12 z 13 (2) 2 x 6 y 12 z 13 (3) x 3y 6 z 7 (4) x 3y 6 z 7 4 27 2 js[kk 2x – 5y + z = 3; x + y + 4z = 5 dks varfoZ"V djus okys lery] tks lery x + 3y + 6z = 1 ds lekarj gSa] dk lehdj.k gS (1) 2 x 6 y 12 z 13 (2) 2 x 6 y 12 z 13 (3) x 3y 6 z 7 (4) x 3y 6 z 7 JEE (MAIN)-2015 20. The number of common tangents to the circles x2 + y2 – 4x – 6y – 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0, is (1) 4 (2) 1 (3) 2 (4) 3 20. 21. The set of all values of for which the system of linear equations x2 + y2 – 4x – 6y – 12 = 0 rFkk x2 + y2 + 6x + 18y + 26 = 0 dh mHk;fu"B Li'kZ js[kkvksa dh la[;k gS (1) 4 (2) 1 (3) 2 (4) 3 21. ds lHkh ekuksa dk leqPp;] ftuds fy, jSf[kd lehdj.k fudk; 2x1 – 2x2 + x3 = x1 2x1 – 2x2 + x3 = x1 2x1 – 3x2 + 2x3 = x2 2x1 – 3x2 + 2x3 = x2 –x1 + 2x2 = x3 –x1 + 2x2 = x3 has a non-trivial solution dk ,d vrqPN gy gS] (1) Contains more than two elements (2) Is an empty set (3) Is a singleton (4) Contains two elements 11 (2) 55 ⎛ 2 ⎞ ⎜ ⎟ 3 ⎝3⎠ 22. 11 12 10 2 ⎛1⎞ (3) 55 ⎛⎜ ⎞⎟ (4) 220 ⎜ ⎟ ⎝3⎠ ⎝3⎠ 23. The sum of coefficients of integral powers of x in the binomial expansion of 1 2 x 50 (1) esa nks ls vf/d vo;o gSAa (2) ,d fjDr leqPp; gSA (3) ,d ,dy leqPp; gSA (4) 22. If 12 identical balls are to be placed in 3 identical boxes, then the probability that one the boxes contains exactly 3 balls is ⎛1⎞ (1) 22 ⎜ ⎟ ⎝3⎠ o`Ùkksa 23. is esa nks vo;o gSa ;fn 12 ,d tSlh xsans] 3 ,d tSls cDlksa esa j[kh tkrh gSa] rks buesa ls ,d cDls esa Bhd 3 xsna as gksus dh izkf;drk gS ⎛1⎞ (1) 22 ⎜ ⎟ ⎝3⎠ 11 2 (3) 55 ⎛⎜ ⎞⎟ ⎝3⎠ 10 1 2 x (2) 50 55 ⎛ 2 ⎞ ⎜ ⎟ 3 ⎝3⎠ 11 ⎛1⎞ (4) 220 ⎜ ⎟ ⎝3⎠ ds f}in izlkj esa x 12 dh iw.kk±dh; ?kkrksa ds xq.kkadksa dk ;ksx gS (1) 1 50 (2 1) 2 (2) 1 50 (3 1) 2 (1) 1 50 (2 1) 2 (2) 1 50 (3 1) 2 (3) 1 50 (3 ) 2 (4) 1 50 (3 1) 2 (3) 1 50 (3 ) 2 (4) 1 50 (3 1) 2 4 24. The integral to ∫ 2 log x log x 2 2 log(36 – 12 x x 2 ) (1) 6 (2) 2 (3) 4 (4) 1 4 dx is equal 24. 25. 25. If the function. (1) 4 (2) 2 16 (3) 5 10 (4) 3 dx cjkcj gS lekdy ∫ log x 2 log(36 – 12 x x 2 ) 2 (1) 6 (2) 2 (3) 4 (4) 1 ;fn iQyu ⎪⎧ k x 1 g( x ) ⎨ ⎪⎩ mx 2 ⎪⎧ k x 1 , 0 x 3 g( x ) ⎨ ⎪⎩ mx 2 , 3 x 5 is differentiable, the value of k + m is vodyuh; gS] rks (1) 4 (3) 5 log x 2 16 5 , 0x3 , 3x5 k + m dk eku gS (2) 2 (4) 10 3 JEE (MAIN)-2015 26. 26. Locus of the image of the point (2, 3) in the line (2x – 3y + 4) + k(x – 2y + 3) = 0, k R, is a (1) Circle of radius 3 (2, 3) 3 (1) (2) Straight line parallel to x-axis (3) Straight line parallel to y-axis (4) Circle of radius ds js[kk (2x – 3y + 4) + k(x – 2y + 3) = 0, k R esa izfrfcac dk fcUnqiFk ,d fcUnq (2) x-v{k ds lekarj js[kk gSAa (3) y-v{k ds lekarj js[kk gSAa 2 2 (4) 27. lim 1 cos 2 x 3 cos x x tan 4x x 0 is equal to 27. 1 2 (2) 4 (3) 3 (4) 2 (1) (1) 2 : 3 3 : (3) (2) 2 lim 28. 3 : 1 (4) 1 : (2) 219 (3) 256 (4) 275 1 cos 2 x 3 cos x x tan 4x 3 (2) 4 (3) 3 (4) 2 rhu lajs[k fcUnqvksa A, B rFkk C, ,d ,slh js[kk ij fLFkr gSa tks ,d ehukj ds ikn dh fn'kk esa ys tkrh gS] ls ,d ehukj ds f'k[kj ds mÂ;u dks.k Øe'k% 30º, 45º rFkk 60º gS]a rks AB : BC dk vuqikr gS 30. Let a , b and c be three non-zero vectors such that no two of them are collinear and 30. 1 ( a b ) c |b ||c | a . If is the angle between 3 vectors b and c , then a value of sin is (2) 3 : (3) 29. 3 : 1 (4) 1 : 2 3 ekuk A rFkk B nks leqPp; gSa ftuesa Øe'k% pkj rFkk nks vo;o gS]a rks leqPp; A × B ds mu mileqPp;ksa dh la[;k] ftuesa izR;sd esa de ls de rhu vo;o gS]a gS (1) 510 (2) 219 (3) 256 (4) 275 ekuk a, b rFkk c rhu 'kwU;srj ,sls lfn'k gSa fd muesa ls dksbZ nks laj[s k ugha gSa rFkk lfn'kksa eku gS b rFkk (1) 2 3 3 (1) 2 3 3 (2) 2 2 3 (2) 2 2 3 (3) 2 3 (3) 2 3 (4) 2 3 (4) 2 3 6 cjkcj gS 1 2 (1) 2 : 3 29. Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is (1) 510 f=kT;k dk o`Ùk gSA x 0 (1) 28. If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30º, 45º and 60º respectively, then the ratio, AB : BC, is f=kT;k dk o`Ùk gSA c 1 ( a b ) c |b ||c | a 3 ds chp dk dks.k gS] rks gSA ;fn sin dk ,d JEE (MAIN)-2015 PART–B : PHYSICS 31. In the circuit shown, the current in the 1 resistor is 6V 31. n'kkZ;s x;s ifjiFk esa 6V 2 P 1 3 1 izfrjksèkd 1 3 9V 3 Q Q (1) 0.13 A, P ls Q dh (1) 0.13 A, from P to Q (2) 1.3 A, from P to Q (3) 0 A (4) 0.13 A, from Q to P 32. Distance of the centre of mass of a solid uniform cone from its vertex is z0. If the radius of its base is R and its height is h then z0 is equal to (1) 3h 2 8R (2) h2 4R (3) 3h 4 (4) 5h 8 32. 33. Match List-I (Fundamental Experiment) with List-II (its conclusion) and select the correct option from the choices given below the list: List -I (A) Franck-Hertz experiment (B) Photo-electric experiment (C) Davison-Germer experiment 2 P 9V 3 (3) 0 A ls izokfgr èkkjk gksxh% 33. List-II Particle nature of light (ii) Discrete energy levels of atom (iii) Wave nature of electron (iv) Structure of atom vksj (2) 1.3 A, P ls Q dh (4) 0.13 A, Q ls P dh (1) 3h 2 8R (2) h2 4R (3) 3h 4 (4) 5h 8 lwph&I (ewy iz;ksx) dk lwph&II (mlds ifj.kke) ds lkFk lqesyu (eSp) dhft;s vkSj fuEukafdr fodYiksa esa ls lgh fodYi dk p;u dhft;s % (A) lwph -I izsaQd gV~Zl iz;ksx (i) (B) izdk'k fo|qr iz;ksx (ii) (C) Msohlu teZj iz;ksx (iii) lwph-II izdk'k dh df.kdk izÑfr v.kq ds fofoDr ÅtkZ Lrj bysDVªkWu dh rjax izÑfr ijek.kq dh lajpuk (1) (A) - (iv) (B) - (iii) (C) - (ii) (2) (A) - (i) (B) - (iv) (C) - (iii) (1) (A) - (iv) (B) - (iii) (C) - (ii) (3) (A) - (ii) (B) - (iv) (C) - (iii) (2) (A) - (i) (B) - (iv) (C) - (iii) (4) (A) - (ii) (B) - (i) (C) - (iii) (3) (A) - (ii) (B) - (iv) (C) - (iii) (4) (A) - (ii) (B) - (i) (C) - (iii) (iv) L g . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The accuracy in the determination of g is T 2 34. vksj fdlh ,dleku Bksl 'kadq ds nzO;eku dsUæ dh mlds 'kh"kZ ls nwjh z0 gSA ;fn 'kadq ds vkèkkj dh f=kT;k R rFkk 'kadq dh Å¡pkbZ h gks rks z0 dk eku fuEukafdr esa ls fdlds cjkcj gksxk\ (i) 34. The period of oscillation of a simple pendulum is vksj fdlh ljy yksyd dk vkorZ] T 2 L g gSA L dk ekfir eku 20.0 cm gS] ftldh ;FkkFkZrk 1 mm gSA bl yksyd ds 100 nksyuksa dk le; 90 s gS] ftls 1 s foHksnu dh ?kM+h ls ukik x;k gSA rks] g ds fuèkkZj.k esa ;FkkFkZrk gksxh % (1) 5% (2) 2% (1) 5% (2) 2% (3) 3% (4) 1% (3) 3% (4) 1% 7 JEE (MAIN)-2015 35. A red LED emits light at 0.1 watt uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is 35. ,d yky jax dk ,y-bZ-Mh- (izdk'k mRltZd Mk;ksM) 0.1 okV ij] ,dleku izdk'k mRlftZr djrk gSA Mk;ksM ls 1 m nwjh ij] bl izdk'k ds fo|qr {ks=k dk vk;ke gksxk % (1) 7.75 V/m (2) 1.73 V/m (1) 7.75 V/m (2) 1.73 V/m (3) 2.45 V/m (4) 5.48 V/m (3) 2.45 V/m (4) 5.48 V/m 36. In the given circuit, charge Q2 on the 2 F capacitor changes as C is varied from 1 F to 3 F. Q2 as a function of C is given properly by : (Figures are drawn schematically and are not to scale) 36. fn;s x;s ifjiFk esa] C ds eku ds 1F ls 3F ifjofrZr gksus ls] 2F laèkkfj=k ij vkos'k Q2 esa ifjorZu gksrk gSA 'C' ds iQyu ds :i esa Q2 dks dkSu lk vkys[k lgh n'kkZrk gS\ (vkys[k dsoy O;oLFkk vkjs[k gSa vkSj Ldsy ds vuqlkj ugha gSaA) 1 F 1 F C C 2 F 2 F E E Charge Charge Q2 Q2 (1) 1 F 3 F 1 F 3 F (1) C 1 F (3) C 1 F 3 F C 37. gL (2) sin cos 0 gL (3) 2 sin cos 0 (4) 2 I L (4) 3 F C 1 F gL tan 0 gL (2) sin cos 0 I gL (3) 2 sin cos 0 gL tan 0 (4) 2 8 C 3 F C nks irys yEcs rkjksa esa izR;sd ls I èkkjk izokfgr gks jgh gSA bUgsa L yEckbZ ds fo|qrjksèkh èkkxksa ls yVdk;k x;k gSA bu èkkxksa esa izR;sd ds }kjk ÅèokZèkj fn'kk ls dks.k cukus dh fLFkfr esa] ;s nksuksa rkj lkE;koLFkk esa jgrs gSaA ;fn bu rkjksa dh izfr bdkbZ yEckbZ nzO;eku gS rFkk g xq#Roh; Roj.k gS rks] I dk eku gksxk % (1) 3 F Q2 1 F (g = gravitational acceleration) gL tan 0 1 F vkos'k (3) 37. Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle with the vertical. If wires have mass per unit length then the value of I is (1) C Q2 (4) 3 F 3 F vkos'k Q2 Q2 1 F (2) Charge Charge Q2 Q2 (2) C vkos'k vkos'k gL tan 0 I L I JEE (MAIN)-2015 38. A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction wth speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to 39. 38. x–fn'kk esa 2v pky ls ls] y–fn'kk esa v osx pyrs gq, m æO;eku ds ,d d.k ls pyrk gqvk 2m æO;eku dk ,d d.k] Vdjkrk gSA ;fn ;g la?kV~V (VDdj) iw.kZr% vizR;kLFk gS rks] VDdj ds nkSjku ÅtkZ dk {k; (gkfu) gksxh% (1) 62% (2) 44% (1) 62% (2) 44% (3) 50% (4) 56% (3) 50% (4) 56% F F A B A B 39. ;gk¡ vkjs[k esa nks CykWd (xqVds) A vkSj B n'kkZ;s x;s gSa ftuds Hkkj Øe'k% 20 N rFkk 100 N gSaA bUgsa] ,d cy F }kjk fdlh nhokj ij nck;k tk jgk gSA ;fn ?k"kZ.k xq.kkad dk eku] A rFkk B ds chp 0.1 rFkk B vkSj nhokj ds chp 0.15 gS rks] nhokj }kjk CykWd B ij yxk cy gksxk % Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is (1) 150 N (2) 100 N (3) 80 N (4) 120 N 40. 40. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as Vq, where V is the volume of the gas. The value of q is (1) 150 N (2) 100 N (3) 80 N (4) 120 N ,d vkn'kZ xSl fdlh cUn (laor` )] fo;qDr (foyfxr) d{k esa lhfer (j[kh) gSA bl xSl esa #n~èkks"e izlkj gksus ij] blds v.kqvksa ds chp VDdj dk vkSlr dky (le;) V q ds vuqlkj c<+ tkrk gS] tgk¡ V xSl dk vk;ru gSA rks q dk eku gksxk % ⎛ CP ⎞ ⎜ ⎟ Cv ⎠ ⎝ ⎛ CP ⎞ ⎜ ⎟ Cv ⎠ ⎝ 1 (1) 2 3 5 (2) 6 (1) 1 2 (2) 3 5 6 3 5 (3) 6 1 (4) 2 (3) 3 5 6 (4) 1 2 41. 10 cm rFkk 5 cm Hkqtkvksa ds ,d vk;rkdkj ywi (ik'k) ls ,d fo|qr èkkjk] I = 12 A, izokfgr gks jgh gSA bl ik'k dks vkjs[k esa n'kkZ;s x;s vuqlkj fofHkUu vfHkfoU;klksa (fLFkfr;ks)a esa j[kk x;k gSA 41. A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below: z z I B I (a) y I x I y I x B z B I I x I (a) z (b) I B I I I (b) y x 9 I I I I y JEE (MAIN)-2015 z z I I I (c) x I B I x z (d) I I I x y I (1) (b) and (c), respectively (2) (a) and (b), respectively 42. (3) (a) and (c), respectively (4) (b) and (d), respectively 42. Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with U 4 internal energy per unit volume u T and V 1 U pressure P ⎛⎜ ⎞⎟ . If the shell now undergoes an 3⎝V ⎠ adiabatic expansion the relation between T and R is 1 R3 y I z I I I x If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium? (1) T B B B (d) I (c) y I y I ;fn ogk¡ 0.3 T rhozrk dk dksbZ ,dleku pqEcdh; {ks=k] èkukRed z fn'kk esa fo|eku gS rks] n'kkZ;s x;s fdl vfHkfoU;kl es]a ;g ik'k (ywi) (i) LFkk;h laryq u rFkk (ii) vLFkk;h laryq u es]a gksxk\ (1) Øe'k% (b) rFkk (c) esa (2) Øe'k% (a) rFkk (b) esa (3) Øe'k% (a) rFkk (c) esa (4) Øe'k% (b) rFkk (d) esa fdlh xksyh; dks'k ('kSy) dh f=kT;k R gS vkSj bldk rki T gSA blds Hkhrj Ñf".kdk fofdj.kksa dks iQksVkWuksa dh ,d ,slh vkn'kZ xSl ekuk tk ldrk gS ftldh izfr bdkbZ vk;ru vkUrfjd ÅtkZ ] 1⎛U ⎞ p ⎜ ⎟ gSA ;fn 3⎝V ⎠ rFkk R ds chp lacèa k (1) T 1 R3 (3) T e–3R (2) T e–R 43. 1 (3) T (4) T R 43. As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion e–3R (1) Kinetic energy and total energy decrease but potential energy increases (2) Its kinetic energy increases but potential energy and total energy decrease (3) Kinetic energy, potential energy and total energy decrease (4) Kinetic energy decreases, potential energy increases but total energy remains same 44. 44. On a hot summer night, the refractive index of air is smallest near the ground and increases with height form the ground. When a light beam is directed horizontally, the Huygen's principle leads us to conclude that as it travels, the light beam 10 u U T4 V rFkk nkc] bl dks'k esa #n~èkks"e izlkj gks rks] T gksxk % (2) T e–R (4) T 1 R tc dksbZ bysDVªkuW ] gkbMªkt s u tSls ijek.kq@vk;u dh mÙksftr voLFkk ls U;wure ÅtkZ voLFkk esa laØe.k djrk gS rks mldh% (1) xfrt ÅtkZ o dqy ÅtkZ de gks tkrh gSa fdUrq] fLFkfrt ÅtkZ c<+ tkrh gSA (2) xfrt ÅtkZ esa o`f¼ rFkk fLFkfrt ÅtkZ rFkk dqy ÅtkZ esa deh gksrh gSA (3) xfrt ÅtkZ] fLFkfrt ÅtkZ rFkk dqy ÅtkZ esa deh gks tkrh gSA (4) xfrt ÅtkZ de gksrh gS] fLFkfrt ÅtkZ c<+rh gS vkSj dqy ÅtkZ ogh jgrh gSA xzh"e ½rq dh xeZ jkf=k esa] Hkw&ry ds fudV] ok;q dk viorZukad U;wure gksrk gS vkSj Hkw&ry ls Å¡pkbZ ds lkFk c<+rk tkrk gSA ;fn] dksbZ izdk'k&fdj.k&iqat {kSfrt fn'kk esa tk jgk gks rks] gkbxsUl ds fl¼kUr ls ;g ifj.kke izkIr gksrk gS fd] pyrs gq, izdk'k&fdj.k iaqt % JEE (MAIN)-2015 (1) Bends upwards (1) (2) Becomes narrower (2) (3) Goes horizontally without any deflection (3) (4) Bends downwards (4) 45. From a solid sphere of mass M and radius R, a R spherical portion of radius is removed, as 2 shown in the figure. Taking gravitational potential V = 0 at r = , the potential at the centre of the cavity thus formed is 45. (3) 2GM R (2) GM R (4) ,d Bksl xksys dk nzO;eku rFkk f=kT;k GM 2R (1) (2) 2GM 3R 2GM R GM 2R (3) GM R (4) 2GM 3R 46. Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is , a ray, incident at an angle , on the face AB would get transmitted through the face AC of the prism provided. 46. R gSA blls R 2 dk¡p ds fdlh fizTe dk dks.k 'A' gSA bl ij ,do.khZ izdk'k vkifrr gksrk gSA ;fn] fizTe ds inkFkZ dk viorZukad gS rks] fizTe ds AB iQyd ij] dks.k vkifrr izdk'k dh fdj.k] fizTe ds iQyd AC ls ikjxr gksxh ;fn % A A B M f=kT;k dk ,d xksyh; Hkkx] vkjs[k esa n'kkZ;s x;s vuqlkj dkV fy;k tkrk gSA r = (vuUr) ij xq#Roh; foHko ds eku V dks 'kwU; (V = 0) ekurs gq,] bl izdkj cus dksVj (dSfoVh) ds dsUnz ij] xq#Roh; foHko dk eku gksxk% (G = xq#Roh; fLFkjk¡d gS) (G = gravitational constant) (1) Åij dh vksj >qd tk;sxkA ladfq pr (ladh.kZ) gks tk;sxkA fcuk fo{ksfir gq,] {kSfrt fn'kk esa pyrk jgsxkA uhps dh vksj >qd tk;sxkA C B C ⎡ ⎤ ⎛ 1 1 ⎛ 1 ⎞ ⎞ (1) cos ⎢ sin ⎜ A sin ⎜ ⎟ ⎟ ⎥ ⎢⎣ ⎝ ⎠ ⎠ ⎥⎦ ⎝ ⎡ ⎤ ⎛ 1 1 ⎛ 1 ⎞ ⎞ (1) cos ⎢ sin ⎜ A sin ⎜ ⎟ ⎟ ⎥ ⎢⎣ ⎝ ⎠ ⎠ ⎥⎦ ⎝ ⎡ ⎤ ⎛ 1 1 ⎛ 1 ⎞ ⎞ (2) sin ⎢ sin ⎜ A sin ⎜ ⎟ ⎟ ⎥ ⎝ ⎠ ⎠ ⎦⎥ ⎝ ⎣⎢ ⎡ ⎤ ⎛ 1 1 ⎛ 1 ⎞ ⎞ (2) sin ⎢ sin ⎜ A sin ⎜ ⎟ ⎟ ⎥ ⎝ ⎠ ⎠ ⎦⎥ ⎝ ⎣⎢ ⎡ ⎤ ⎛ 1 1 ⎛ 1 ⎞ ⎞ (3) sin ⎢ sin ⎜ A sin ⎜ ⎟ ⎟ ⎥ ⎝ ⎠ ⎠ ⎦⎥ ⎝ ⎣⎢ ⎡ ⎤ ⎛ 1 1 ⎛ 1 ⎞ ⎞ (3) sin ⎢ sin ⎜ A sin ⎜ ⎟ ⎟ ⎥ ⎢⎣ ⎝ ⎠ ⎠ ⎥⎦ ⎝ ⎡ ⎤ ⎛ 1 1 ⎛ 1 ⎞ ⎞ (4) cos ⎢ sin ⎜ A sin ⎜ ⎟ ⎟ ⎥ ⎝ ⎠ ⎠ ⎦⎥ ⎝ ⎣⎢ ⎡ ⎤ ⎛ 1 1 ⎛ 1 ⎞ ⎞ (4) cos ⎢ sin ⎜ A sin ⎜ ⎟ ⎟ ⎥ ⎢⎣ ⎝ ⎠ ⎠ ⎥⎦ ⎝ 47. 47. Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m/s2) 11 fdlh 240 m Å¡ph pksVh ds ,d fdukjs ls] nks iRFkjksa dks ,dlkFk Åij dh vksj isaQdk x;k gS] budh izkjafHkd pky Øe'k% 10 m/s rFkk 40 m/s gS] rks] fuEukafdr esa ls dkSulk xzkiQ (vkys[k) igys iRFkj ds lkis{k nwljs iRFkj dh fLFkfr ds le; fopj.k (ifjorZu) dks lokZfèkd lgh n'kkZrk gS\ (eku yhft, fd] iRFkj tehu ls Vdjkus ds i'pkr Åij dh vksj ugha mNyrs gSa rFkk ok;q dk izfrjksèk ux.; gS] fn;k gS g = 10 m/s2) JEE (MAIN)-2015 (The figures are schematic and not drawn to scale) 240 (;gk¡ xzkiQ dsoy O;oLFkk vkjs[k gSa vkSj Ldsy ds vuqlkj ugha gSa) (y2 – y1) m 240 (y2 – y1) m (1) 8 240 (1) t (s) 12 8 12 t 8 (y2 – y1) m 12 (y2 – y1) m 240 t (s) (y2 – y1) m (2) t 8 (y2 – y1) m (2) t (s) 12 240 t (s) 240 (3) 12 240 (3) t (s) t (s) 12 (y2 – y1) m 240 (y2 – y1) m (4) (4) t (s) 8 12 48. For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly? 8 48. (Graphs are schematic and not drawn to scale) E E KE PE (1) KE E KE E KE PE (2) d PE (2) d E (3) E PE KE (3) d 12 t (s) fdlh ljy yksyd ds fy;s] mlds foLFkkiu d rFkk mldh xfrt ÅtkZ ds chp vkSj foLFkkiu d rFkk mldh fLFkfrt ÅtkZ ds chp xzkiQ [khaps x;s gSaA fuEukafdr esa ls dkSu lk xzkiQ (vkys[k) lgh gS\ (;gk¡ xzkiQ dsoy O;oLFkk vkjs[k gSa vkSj Ldsy ds vuqlkj ugha g)aS PE (1) 12 PE KE d JEE (MAIN)-2015 E E KE d KE d (4) (4) PE PE 49. 49. A train is moving on a straight track with speed 20 ms–1. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 ms–1) close to (1) 24% (2) 6% (3) 12% (4) 18% ,d Vªsu (jsyxkM+h) lhèkh iVfj;ksa ij 20 ms–1 dh pky ls xfr dj jgh gSA bldh lhVh dh èofu dh vko`fÙk 1000 Hz gSA ;fn èofu dh ok;q esa pky 320 ms–1 gks rks] iVfj;ksa ds fudV [kM+s O;fDr ds ikl ls Vªsu ds xqtjus ij] ml O;fDr }kjk lquh xbZ lhVh dh èofu dh vko`fÙk esa izfr'kr ifjorZu gksxk yxHkx : (1) 24% (3) 12% (2) 6% (4) 18% 50. LCR (,y-lh-vkj) ifjiFk fdlh voeafnr yksyd ds rqY; gksrk gSA fdlh LCR ifjiFk esa laèkkfj=k dks Q0 rd vkosf'kr fd;k x;k gS] vkSj fiQj bls vkjs[k esa n'kkZ;s x;s vuqlkj L o R ls tksMk+ x;k gSA 50. An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q0 and then connected to the L and R as shown below : R L R L C C If a student plots graphs of the square of maximum 2 charge QMax on the capacitor with time (t) for two different values L1 and L2 (L1 > L2) of L then which of the following represents this graph correctly? (Plots are schematic and not drawn to scale) 2 QMax ;fn ,d fo|kFkhZ L ds] nks fofHkUu ekuksa] L1 rFkk L2 (L1 > L2) ds fy;s] le; t rFkk laèkkfj=k ij vfèkdre vkos'k ds 2 oxZ QMax ds chp nks xzkiQ cukrk gS rks fuEukafdr esa ls dkSu lk xzkiQ lgh gS\ (IykWV dsoy O;oLFkk IykWV gSa rFkk Ldsy ds vuqlkj ugha gSa) 2 QMax Q0 (For both L1 and L2) 2 QMax 2 (2) (1) L1 QMax L2 t t Q0 (L1 vkSj L2 nksuksa ds fy,) (1) (2) L2 t 2 t 2 QMax (3) L1 QMax L2 L1 (4) t L1 L2 2 2 QMax (3) t 51. A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways : 51. (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat. (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat. 13 QMax L2 L1 (4) t L1 L2 t ,d Bksl fiaM (oLrq) dh fLFkj Å"ek /kfjrk 1 J/°C gSA bldks Å"edksa (Å"ek HkaMkjks)a ds lEidZ esa j[kdj fuEu nks izdkj ls xeZ fd;k tkrk gS] (i) vuqØfed :i ls 2 Å"edksa ds lEidZ esa bl izdkj j[kdj fd izR;sd Å"ed leku ek=kk esa Å"ek nsrk gS] (ii) vuqØfed :i ls 8 Å"edksa ds lEidZ esa bl izdkj j[kdj fd izR;sd Å"ed leku ek=kk esa Å"ek nsrk gS] JEE (MAIN)-2015 In both the cases body is brought from initial temperature 100°C to final temperature 200°C. Entropy change of the body in the two cases respectively is nksuksa fLFkfr;ksa esa fiaM dk izkjafHkd rki 100°C rFkk vfUre rki 200°C gSA rks] bu nks fLFkfr;ksa esa fiaM dh ,UVªkWih esa ifjorZu gksxk] Øe'k% (1) 2ln 2, 8ln 2 (2) ln 2, 4ln 2 (1) 2ln 2, 8ln 2 (2) ln 2, 4ln 2 (3) ln 2, ln 2 (4) ln 2, 2ln 2 (3) ln 2, ln 2 (4) ln 2, 2ln 2 52. 52. An inductor (L = 0.03 H) and a resistor (R = 0.15 k) are connected in series to a battery of 15 V EMF in a circuit shown below. The key K1 has been kept closed for a long time. Then at t = 0, K1 is opened and key K2 is closed simultaneously. At t = 1 ms, the current in the circuit will be ( e 5 150) 0.03 H n'kkZ;s x;s ifjiFk esa] ,d izsjd (L = 0.03 H) rFkk ,d izfrjksèkd (R = 0.15 k) fdlh 15 V fo|qr okgd cy (bZ-,e-,iQ) dh cSVjh ls tqM+s gSaA dqath K1 dks cgqr le; rd cUn j[kk x;k gSA blds i'pkr~ le; t = 0 ij] K1 dks [kksy dj lkFk gh lkFk] K2 dks cUn fd;k tkrk gSA le; t = 1 ms ij] ifjiFk esa fo|qr èkkjk gksxh % ( e 5 150) 0.03H 0.15 k K2 K2 15 V K1 (1) 0.67 mA (2) 100 mA (3) 67 mA (4) 6.7 mA 0.15 k 15V K1 (1) 0.67 mA (2) 100 mA (3) 67 mA (4) 6.7 mA 53. R f=kT;k ds fdlh ,dleku vkosf'kr Bksl xksys ds i`"B dk foHko V0 gS (ds lkis{k ekik x;k)A bl xksys ds fy;s] 53. A uniformly charged solid sphere of radius R has potential V0 (measured with respect to ) on its surface. For this sphere the equipotential surfaces 3V0 5V0 3V0 V , , rFkk 0 foHkoksa okys lefoHkoh 2 4 4 4 f=kT;k;sa] Øe'k% R1, R2, R3 rFkk R4 gSaA rks] V 3V0 5V0 3V0 , , and 0 have radius 2 4 4 4 R1, R2, R3 and R4 respectively. Then with potentials (1) 2R < R4 (2) R1 = 0 rFkk R2 > (R4 – R3) (2) R1 = 0 and R2 > (R4 – R3) (3) R1 0 rFkk (R2 – R1) > (R4 – R3) (3) R1 0 and (R2 – R1) > (R4 – R3) (4) R1 = 0 rFkk R2 < (R4 – R3) (1) 2R < R4 (4) R1 = 0 and R2 < (R4 – R3) 54. 54. A long cylindrical shell carries positive surface charge in the upper half and negative surface charge – in the lower half. The electric field lines around the cylinder will look like figure given in fdlh yEcs csyukdkj dks'k ds Åijh Hkkx esa èkukRed i`"B vkos'k rFkk fupys Hkkx esa ½.kkRed i`"B vkos'k – gSaA bl csyu (flfyUMj) ds pkjksa vksj fo|qr {ks=k&js[kk;sa] ;gk¡ n'kkZ;s x;s vkjs[kksa esa ls fdl vkjs[k ds leku gksxa hA (;g vkjs[k dsoy O;oLFkk vkjs[k gS vkSj Ldsy ds vuqlkj ugha gS) (figures are schematic and not drawn to scale) (1) (1) ++++ + + –– –– –– –– (2) 14 ++++ + + –– –– –– –– (2) i`"Bksa dh JEE (MAIN)-2015 (3) (3) ++ ++ + + –– –– –– –– (4) ++ ++ + + –– –– –– –– (4) 55. Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects that human eye can resolve at 500 nm wavelength is 55. (1) 300 m ;fn ekuo us=k dh iqryh dh f=kT;k 0.25 cm, vkSj Li"V lqfoèkk tud ns[kus dh nwjh 25 cm gks rks] 500 nm rjaxnSè;Z ds izdk'k esa] nks oLrqvksa ds chp fdruh U;wure nwjh rd ekuo us=k mu nksuksa ds chp foHksnu dj ldsxk\ (2) 1 m (1) 300 m (2) 1 m (3) 30 m (3) 30 m (4) 100 m (4) 100 m 56. 56. A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is/are ds fdlh ladrs (flXuy) dk 2 MHz vko`fÙk dh okgd rjax ij vk;ke ekWMy q u fd;k x;k gSA rks] ifj.kkeh flXuy (ladrs ) dh vko`fÙk gksxh % 5 kHz vko`fÙk (1) 2000 kHz (1) 2000 kHz and 1995 kHz rFkk 1995 kHz (2) 2 MHz dsoy (2) 2 MHz only (3) 2005 kHz and 1995 kHz (3) 2005 kHz (4) 2005 kHz, 2000 kHz and 1995 kHz (4) 2005 kHz, 2000 kHz 57. Two coaxial solenoids of different radii carry current I in the same direction. Let F1 be the 57. magnetic force on the inner solenoid due to the outer one and F2 be the magnetic force on the outer rFkk 1995 kHz nks lek{kh ifjukfydkvksa esa] izR;sd ls I èkkjk ,d gh fn'kk esa izokfgr gks jgh gSA ;fn] ckgjh ifjukfydk ds dkj.k] Hkhrjh ifjukfydk ij pqEcdh; cy F1 rFkk Hkhrjh ifjukfydk ds dkj.k] ckgjh ifjukfydk ij pqEcdh; cy solenoid due to the inner one. Then (1) F1 (1) F1 is radially outwards and F2 = 0 ckgj dh vksj o vjh; gS rFkk F2 gks rks % F2 = 0 gSA (2) F1 = F2 = 0 (2) F1 = F2 = 0 (3) F1 is radially inwards and F2 rFkk 1995 kHz (3) F1 is radially Hkhrj dh vksj o vjh; (f=kT;) gS rFkk dh vksj o vjh; gSA outwards (4) F1 (4) F1 is radially inwards and F2 = 0 15 Hkhrj dh vksj o vjh; gS rFkk F2 = 0 gSA F2 ckgj JEE (MAIN)-2015 58. A pendulum made of a uniform wire of crosssectional area A has time period T. When an additional mass M is added to its bob, the time period changes to TM. If the Young's modulus of the material of the wire is Y then 58. 1 is equal to Y fdlh ,dleku rkj dh vuqizLFk dkV dk {ks=kiQy 'A' gSA blls cuk;s x;s ,d yksyd dk vkorZdky T gSA bl yksyd ds xksyd ls ,d vfrfjDr M nzO;eku tksM+ nsus ls yksyd dk vkorZdky ifjofrZr gksdj TM gks tkrk gSA ;fn bl rkj ds inkFkZ dk ;ax xq.kkad 'Y' gks rks (g = gravitational acceleration) (g = xq#Roh; ⎡ ⎛ T ⎞2 ⎤ A (1) ⎢1 ⎜ T ⎟ ⎥ Mg ⎢⎣ ⎝ M ⎠ ⎥⎦ dk eku gksxk% Roj.k) ⎡ ⎛ T ⎞2 ⎤ A (1) ⎢1 ⎜ T ⎟ ⎥ Mg ⎢⎣ ⎝ M ⎠ ⎥⎦ ⎡⎛ TM ⎞ 2 ⎤ A (2) ⎢⎜ T ⎟ 1⎥ Mg ⎠ ⎥⎦ ⎣⎢⎝ ⎡⎛ TM ⎞ 2 ⎤ A (2) ⎢⎜ T ⎟ 1⎥ Mg ⎠ ⎣⎢⎝ ⎦⎥ ⎡⎛ TM ⎞ 2 ⎤ Mg (3) ⎢⎜ T ⎟ 1⎥ A ⎠ ⎣⎢⎝ ⎦⎥ ⎡⎛ TM ⎞ 2 ⎤ Mg ⎢ (3) ⎜ T ⎟ 1⎥ A ⎠ ⎥⎦ ⎣⎢⎝ ⎡ ⎛ TM ⎞ 2 ⎤ A (4) ⎢1 ⎜ T ⎟ ⎥ Mg ⎠ ⎦⎥ ⎣⎢ ⎝ ⎡ ⎛ TM ⎞ 2 ⎤ A (4) ⎢1 ⎜ T ⎟ ⎥ Mg ⎠ ⎥⎦ ⎢⎣ ⎝ 59. 59. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is fdlh Bksl xksys dk nzO;eku M rFkk bldh f=kT;k R gSA blesa ls vfèkdre laHko vk;ru dk ,d D;wc (?ku) dkV fy;k tkrk gSA bl D;wc dk tM+Ro vk?kw.kZ fdruk gksxk] ;fn] bldh ?kw.kZu&v{k] blds dsUnz ls gksdj xqtjrh gS rFkk blds fdlh ,d iQyd ds yEcor~ gS\ 4 MR 2 3 3 (1) 4 MR 2 3 3 (2) MR 2 32 2 (2) MR 2 32 2 (3) MR 2 16 2 (3) MR 2 16 2 4 MR 2 (4) 9 3 (4) 4 MR 2 9 3 (1) 1 Y 60. 0.1 m yacs fdlh rkj ds fljksa ds chp 5 V foHkokarj vkjksfir djus ls bysDVªkWuksa dh viokg pky 2.5 × 10–4 ms–1 gksrh gSA ;fn bl rkj esa bysDVªkWu ?kuRo 8 × 1028 m–3 gks rks] bl ds inkFkZ dh izfrjksèkdrk gksxh] yxHkx% 60. When 5 V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons is 2.5 × 10–4 ms–1. If the electron density in the wire is 8 × 1028 m–3, the resistivity of the material is close to (1) 1.6 × 10–5 m (1) 1.6 × 10–5 m (2) 1.6 × 10–8 m (2) 1.6 × 10–8 m (3) 1.6 × 10–7 m (3) 1.6 × 10–7 m (4) 1.6 × 10–6 m (4) 1.6 × 10–6 m 16 JEE (MAIN)-2015 PART–C : CHEMISTRY 61. The vapour pressure of acetone at 20°C is 185 torr. When 1.2 g of a non-volatile substance was dissolved in 100 g of acetone at 20°C, its vapour pressure was 183 torr. The molar mass (g mol–1) of the substance is 61. 20°C ij ,sflVksu dh ok"i nkc 185 torr gSA tc 20°C ij] 1.2 g vok"i'khy inkFkZ dks 100 g ,sflVksu esa ?kksyk x;k] rc ok"i nkc 183 torr gks x;kA bl inkFkZ dk eksyj nzO;eku (g mol–1 es)a gS : (1) 488 (2) 32 (1) 488 (2) 32 (3) 64 (4) 128 (3) 64 (4) 128 62. 62. 3 g of activated charcoal was added to 50 mL of acetic acid solution (0.06N) in a flask. After an hour it was filtered and the strength of the filtrate was found to be 0.042 N. The amount of acetic acid adsorbed (per gram of charcoal) is (1) 54 mg (2) 18 mg (3) 36 mg (4) 42 mg 63. Which of the following is the energy of a possible excited state of hydrogen? (1) +6.8 eV (2) +13.6 eV (3) –6.8 eV (4) –3.4 eV 63. 64. Which among the following is the most reactive? (1) ICl (2) Cl2 (3) Br2 (4) I2 64. 65. Which polymer is used in the manufacture of paints and lacquers? (1) Poly vinyl chloride (2) Bakelite (3) Glyptal (4) Polypropene 65. 66. The molecular formula of a commercial resin used for exchanging ions in water softening is C8H 7SO 3Na (mol. wt. 206). What would be the maximum uptake of Ca2+ ions by the resin when expressed in mole per gram resin? 66. ,d ÝykLd esa 0.06N ,flfVd vEy ds 50 mL foy;u esa 3 g lfØ;r~ dk"B dks;yk feyk;k x;kA ,d ?kaVs ds i'pkr~ mls Nkuk x;k vkSj fuL;an dh izcyrk 0.042 N ikbZ xbZA vf/'kksf"kr ,flfVd vEy dh ek=kk (dk"B&dks;yk ds izfr xzke ij) gS: (1) 54 mg (2) 18 mg (3) 36 mg (4) 42 mg fuEufyf[kr esa ls gkbZMªkstu dh laHko mÙksftr voLFkk dh mQtkZ dkSulh gS\ (1) +6.8 eV (2) +13.6 eV (3) –6.8 eV (4) –3.4 eV fuEufyf[kr esa ls dkSu lokZf/d vfHkfØ;k'khy gS\ (1) ICl (2) Cl2 (3) Br2 (4) I2 fdl cgqyd dk mi;ksx izyis vkSj izyk{k cukus esa gksrk gS\ (1) ikWfy okbfuy DyksjkbM (2) csdsykbV (3) fXyIVky (4) ikWfyizksihu ,d okf.kT; jsft+u dk vkf.od lw=k C8H7SO3Na gS (vkf.od Hkkj = 206) bl js f t+ u dh Ca2+ vk;u dh vfèkdre varxzgZ .k {kerk (eksy izfr xzke jsft+u) D;k gS\ 1 (1) 412 1 (2) 103 (1) 1 412 (2) 1 103 1 (3) 206 2 (4) 309 (3) 1 206 (4) 2 309 67. 67. In Carius method of estimation of halogens, 250 mg of an organic compound gave 141 mg of AgBr. The percentage of bromine in the compound is gSykstu ds vkdyu dh dSfjvl fof/ esa 250 mg dkcZfud ;kSfxd 141 mg AgBr nsrk gSA ;kSfxd esa czksehu dh izfr'krrk gSS : Ag = 108; Br = 80) (At. mass Ag = 108; Br = 80) (ijekf.od (1) 60 (2) 24 (1) 60 (2) 24 (3) 36 (4) 48 (3) 36 (4) 48 17 nzO;eku JEE (MAIN)-2015 68. Assertion : Nitrogen and Oxygen are the main components in the atmosphere but these do not react to form oxides of nitrogen. Reason : 68. The reaction between nitrogen and oxygen requires high temperature. (1) Both the assertion and reason are incorrect (2) Both assertion and reason are correct, and the reason is the correct explanation for the assertion (3) Both assertion and reason are correct, but the reason is not the correct explanation for the assertion (4) The assertion is incorrect, but the reason is correct 69. The following reaction is performed at 298 K. 69. 2NO (g) 2NO(g) + O2(g) 2 2NO (g) 2NO(g) + O2(g) 2 The standard free energy of formation of NO(g) is 86.6 kJ/mol at 298 K. What is the standard free energy of formation of NO2(g) at 298 K? 298 K ij NO(g) ds la H kou dh ekud 86.6 kJ/mol gSA 298 K ij NO2(g) dh mQtkZ D;k gS\(Kp = 1.6 × 1012) (Kp = 1.6 × 1012) 12 (1) 0.5 ⎡⎣ 2 86, 600 R 298 ln 1.6 10 ⎤⎦ (3) 86600 + R(298) ln(1.6 × 1012) (4) 86600 R 298 (4) 86600 70. 70. Which one of the following alkaline earth metal sulphates has its hydration enthalpy greater than its lattice enthalpy? (1) SrSO4 (2) CaSO4 (3) BeSO4 (4) BaSO4 71. 71. The number of geometric isomers that can exist for square planar [Pt(Cl)(py)(NH 3 )(NH 2 OH)] + is (py = pyridine) (1) 6 (2) 2 (3) 3 (4) 4 eqDr mQtkZ ekud eqDr 12 (1) 0.5 ⎡⎣ 2 86, 600 R 298 ln 1.6 10 ⎤⎦ (2) R(298) ln(1.6 × 1012) – 86600 (3) 86600 + R(298) ln(1.6 × 1012) (2) R(298) ln(1.6 × 1012) – 86600 ln 1.6 1012 vfHkdFku : ukbVªkstu vkSj vkWDlhtu okrkoj.k ds eq[; ?kVd gSa ijUrq ;g fØ;k djds ukbVªkstu ds vkWDlkbM ugha cukrsA rdZ : ukbVªkt s u vkSj vkWDlhtu ds chp vfHkfØ;k ds fy, mPp rki dh vko';drk gS (1) vfHkdFku o rdZ nksuksa xyr gSAa (2) vfHkdFku vkSj rdZ nksuksa lgh gSa vkSj rdZ vfHkdFku dk lgh Li"Vhdj.k gSA (3) vfHkdFku vkSj rdZ nksuksa lgh gSa ijUrq rdZ vfHkdFku dk lgh Li"Vhdj.k ugha gSA (4) vfHkdFku xyr gS ijUrq rdZ lgh gSA fuEufyf[kr vfHkfØ;k dks 298 K ij fd;k x;kA ln 1.6 10 12 R 298 fuEufyf[kr esa ls dkSu ls {kkjh; e`nk /krq lYiQsV dh ty;kstu ,sUFkkYih mlds tkyd ,sUFkkYih ls vf/d gS\ (1) SrSO4 (2) CaSO4 (3) BeSO4 (4) BaSO4 oxZ leryh; [Pt (Cl) (py) (NH 3 )(NH 2 OH)] + (py = pyridine) 72. 72. The synthesis of alkyl fluorides is best accomplished by ds T;kferh; leko;fo;ksa dh la[;k gS : (1) 6 (2) 2 (3) 3 (4) 4 vYdkby ÝyksjkbM ds la'ys"k.k ds fy, lcls csgrjhu fofèk gS (1) LokVZl vfHkfØ;k (1) Swarts reaction (2) eqDr ewyd Ýyksfjus'ku (2) Free radical fluorination (3) lSUMek;j vfHkfØ;k (4) fiQadyLVkbu vfHkfØ;k (3) Sandmeyer's reaction (4) Finkelstein reaction 73. 73. The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is og varjk&v.kqd vU;ksU; fØ;k tks v.kqvksa ds chp dh nwjh ds izfrykse ?ku ij fuHkZj gS] gS : (1) gkbZMªkstu ca/d (2) Ion-ion interaction (2) vk;u&vk;u vU;ksU; (3) Ion-dipole interaction (3) vk;u&f}/zoq vU;ksU; (4) London force (4) yaMu cy (1) Hydrogen bond 18 JEE (MAIN)-2015 74. In the context of the Hall-Heroult process for the extraction of Al, which of the following statement is false? 74. gkWy&gsjkWYV izØe ls ,syqfefu;e ds fu"d"kZ.k ds lanHkZ esa dkSu lk dFku xyr gS\ (1) Na3AlF6 fo|qr (1) Na3AlF6 serves as the electrolyte (2) (2) CO and CO2 are produced in this process bl izØe esa vi?kV~; dk dke djrk gSA CO rFkk CO2 dk mRiknu gksrk gSA (3) CaF2 dks Al2O3 esa feykus ij feJ.k dk xyukad de gksrk gS vkSj mlesa pkydrk vkrh gSA (3) Al2O3 is mixed with CaF2 which lowers the melting point of the mixture and brings conductivity (4) (4) Al 3+ is reduced at the cathode to form Al 75. 75. Which of the following compounds will exhibit geometrical isomerism? dSFkksM ij Al3+ vipf;r gks dj Al cukrk gSA fuEufyf[kr esa ls dkSu lk ;kSfxd T;kferh; leko;ork n'kkZrk gS\ (1) 1, 1 - MkbZiQsfuy - 1 izksisu (1) 1, 1 - Diphenyl - 1 propane (2) 1 - iQsfuy - 2 - C;wVhu (2) 1 - Phenyl - 2 - butene (3) 3 - iQsfuy - 1 - C;wVhu (3) 3 - Phenyl - 1 - butene (4) 2 - iQsfuy - 1 - C;wVhu (4) 2 - Phenyl - 1 - butene 76. N3–, O2– rFkk F– dh 76. The ionic radii (in Å) of N 3– , O 2– and F – are respectively (1) 1.71, 1.36 and 1.40 (2) 1.36, 1.40 and 1.71 vk;fud f=kT;k;sa (1) 1.71, 1.36 rFkk 1.40 (2) 1.36, 1.40 rFkk 1.71 (3) 1.36, 1.71 rFkk 1.40 (4) 1.71, 1.40 rFkk 1.36 (Å esa) Øe'k% gSa : (3) 1.36, 1.71 and 1.40 (4) 1.71, 1.40 and 1.36 77. H2O2 77. From the following statement regarding H 2O 2, choose the incorrect statement ds lanHkZ esa] fuEufyf[kr dFkuksa esa ls xyr dFku pqfu, (1) bls /wy ls nwj j[kuk pkfg, (1) It has to be kept away from dust (2) ;g dsoy vkWDlhdkjd gS (2) It can act only as an oxidizing agent (3) izdk'k esa bldk vi?kVu gksrk gS (3) It decomposes on exposure to light (4) bls IykfLVd ;k eksevVs dkap cksryksa esa va/js s esa laxfz gr fd;k tkrk gS (4) It has to be stored in plastic or wax lined glass bottles in dark 78. 78. Higher order (>3) reactions are rare due to mPp dksfV vfHkfØ;k (>3) nqyHZ k gS D;ksfa d : (1) Vdjko ls lfØ; Lih'kht+ dk {k; gksrk gSA (2) izfrfØ;k esa lHkh iztkfr;ksa ds ,d lkFk VDdj dh laHkkouk de gksrh gSA (3) vf/d v.kqvksa ds 'kkfey gkssus ls ,aVªkih vkSj lafØ;.k mQtkZ esa o`f¼ gksrh gSA (4) ykspnkj Vdjko ds dkj.k vfHkdkjdksa dh fn'kk esa lkE; dk LFkkukarj.k gksrk gSA (1) Loss of active species on collision (2) Low probability of simultaneous collision of all the reacting species (3) Increase in entropy and activation energy as more molecules are involved (4) Shifting of equilibrium towards reactants due to elastic collisions 19 JEE (MAIN)-2015 79. Match the catalysts to the correct processes : Catalyst 79. fn;s x, mRisjz dksa dks lgh izØe ds lkFk lqefs yr djsa Process mRizsjd izØe a. TiCl3 (i) Wacker process a. TiCl3 (i) okWdj izØe b. PdCl2 (ii) Ziegler-Natta polymerization b. PbCl2 (ii) RlhXyj&uêðk cgqydhdj.k c. CuCl2 (iii) Contact process c. CuCl2 (iii) laLi'kZ izØe (iv) Deacon's process d. V2O5 (iv) Mhdu izØe d. V2O5 (1) a(iii), b(i), c(ii), d(iv) (2) a(iii), b(ii), c(iv), d(i) (1) a(iii), b(i), c(ii), d(iv) (2) a(iii), b(ii), c(iv), d(i) (3) a(ii), b(i), c(iv), d(iii) (4) a(ii), b(iii), c(iv), d(i) (3) a(ii), b(i), c(iv), d(iii) (4) a(ii), b(iii), c(iv), d(i) 80. Which one has the highest boiling point? 80. fuEufyf[kr esa ls lokZf/d DoFkukad fdldk gS\ (1) Xe (2) He (1) Xe (3) Ne (4) Kr (2) He 81. In the reaction (3) Ne NH2 (4) Kr NaNO2/HCl 0-5°C D CuCN/KCN 81. E + N2 , fn, x, vfHkfØ;k esa mRikn E gS NH2 CH3 NaNO2/HCl 0-5°C the product E is D CuCN/KCN E + N2 , CH3 CH3 CH3 (1) (1) COOH COOH (2) (2) CH3 (3) H3C CH3 CH3 (3) H3C CN CH3 CN (4) (4) CH3 CH3 82. Which of the following compounds is not colored yellow? 82. fn, x, ;kSfxdksa esa dkSuls ;kSfxd dk jax ihyk ugha gS\ (1) BaCrO4 (1) BaCrO4 (2) Zn2[Fe(CN)6] (2) Zn2[Fe(CN)6] (3) K3[Co(NO2)6] (3) K3[Co(NO2)6] (4) (NH4)3[As (Mo3O10)4] (4) (NH4)3[As (Mo3O10)4] 20 JEE (MAIN)-2015 83. 83. Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of 4.29 Å. The radius of sodium atom is approximately (1) 0.93 Å (2) 1.86 Å (3) 3.22 Å (4) 5.72 Å (2) 1.86 Å (3) 3.22 Å (4) 5.72 Å ij vfHkfØ;k 2A B + C dh ekud fxCt+ mQtkZ 2494.2 J gSA fn, x, le; esa vfHkfØ;k feJ.k dk reaction 2A B + C is 2494.2 J. At a given time, 1 1 , B 2 vkSj C gS A vfHkfØ;k 2 2 gS : [R = 8.314 J/K/mol, e = 2.718] la ? kVu A is 1 1 , B 2 and C . The reaction proceeds 2 2 in the : [R = 8.314 J/K/mol, e = 2.718] (1) Reverse direction because Q < KC (2) Forward direction because Q > KC (3) Reverse direction because Q > KC (4) Forward direction because Q < KC 85. Which compound would give 5-keto-2-methyl hexanal upon ozonolysis? CH3 CH3 A (1) (1) 0.93 Å 84. 300 K 84. The standard Gibbs energy change at 300 K for the the composition of the reaction mixture lksfM;e /krq ,d var%dsfUnzr ?kuh; tkyd esa fØLVfyr gksrk gS ftlds dksj dh yackbZ 4.29Å gSA lksfM;e ijek.kq dh f=kT;k yxHkx gS : 85. vxzflr gksrh (1) foijhr fn'kk eas D;ksfa d Q < KC (2) vxz fn'kk esa D;ksfa d Q > KC (3) foijhr fn'kk esa D;ksfa d Q > KC (4) vxz fn'kk esa D;ksfa d Q < KC vkst+ksuksfyfll djus ij dkSulk ;kSfxd 5-dhVks-2-esfFky gSDlkuSy nsrk gS\ CH3 H3C (2) CH3 (1) CH3 (3) CH3 CH3 CH3 H3C (2) CH3 CH3 (4) (3) CH3 CH3 CH3 86. Which of the following compounds is not an antacid? 86. (1) Ranitidine (2) Aluminium Hydroxide (3) Cimetidine (4) Phenelzine 87. In the following sequence of reactions : KMnO SOCl 87. H /Pd 4 2 2 Toluene A B C, BaSO (3) C6H5CH3 (4) C6H5CH2OH fuEufyf[kr esa ls dkSulk ;kSfxd izfrvEy ugha gS\ (1) jSfufVMhu (2) ,syfq efu;e gkbMªkDlkbM (3) flesfVMhu (4) fiQufYtu fn, x, vfHkfØ;k vuqØe esa mRikn C gS : KMnO SOCl H /Pd 4 the product C is (2) C6H5COOH CH3 4 2 2 Toluene A B C, BaSO 4 (1) C6H5CHO (4) 88. 88. Which of the vitamins given below is water soluble? (1) Vitamin K (1) C6H5CHO (2) C6H5COOH (3) C6H5CH3 (4) C6H5CH2OH fuEufyf[kr foVkfeuksa esa ty esa foys; gksus okyk gS (1) foVkfeu K (2) foVkfeu C (3) foVkfeu D (4) foVkfeu E (2) Vitamin C (3) Vitamin D (4) Vitamin E 21 : JEE (MAIN)-2015 89. The color of KMnO4 is due to 89. KMnO4 ds (1) - * transition jax dk dkj.k gS (1) - * laØe.k (2) M L charge transfer transition (2) M L vkos'k (3) d - d transition LFkkukarj.k laØe.k (3) d - d laØe.k (4) L M charge transfer transition (4) L M vkos'k (1) 127 g LFkkukarj.k laØe.k CuSO4 ds ,d foy;u esa] nks iQSjkMs fo|qr izokfgr dh xbZA dSFkksM ij fu{ksfir rkacs dk nzO;eku gS : (Cu dk ijekf.od nzO;eku = 63.5 amu) (2) 0 g (1) 127 g 90. Two faraday of electricity is passed through a solution of CuSO4. The mass of copper deposited at the cathode is (at. mass of Cu = 63.5 amu) 90. (2) 0 g (3) 63.5 g (3) 63.5 g (4) 2 g (4) 2 g 22
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