ENGLISH Form Number : Paper Code : 0000CT103116004 CLASSROOM CONTACT PROGRAMME (Academic Session : 2016 - 2017) LEADER & ENTHUSIAST COURSE TARGET : JEE (MAIN) 2017 Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Main TEST DATE : 19 - 03 - 2017 Important Instructions Do not open this Test Booklet until you are asked to do so. 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. 2. The candidates should not write their Form Number anywhere else (except in the specified space) on the Test Booklet/Answer Sheet. 3. The test is of 3 hours duration. 4. The Test Booklet consists of 90 questions. The maximum marks are 360. 5. There are three parts in the question paper A,B,C consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response. 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. 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. 8. No candidate is allowed to carry any textual material, printed or written, bits of papers, mobile phone any electronic device etc, except the Identity Card inside the examination hall/room. 9. Rough work is to be done on the space provided for this purpose in the Test Booklet only. 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. 11. Do not fold or make any stray marks on the Answer Sheet. Your Target is to secure Good Rank in JEE (Main) 2017 Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005 +91-744-5156100 [email protected] www.allen.ac.in
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING PART A - PHYSICS 1. A charge particle q0 of mass m0 is projected 3. A particle moves along a circle with a constant angular speed . Its displacement, along the y-axis at t = 0 from origin with a with respect to this position of the particle velocity V0. If a uniform electron field E0 also at time t = 0 is plotted against time. The exists along the x-axis, then the time at graph would look like : which de-broglie wavelength of the particle SS circular circular becomes half of the initial value is :- (1) (2) (1) m0 v0 (2) 2 m0v0 / t 2/ t q0E0 q0E0 S S sine curve (3) 3 m0v0 (4) 3 m0v0 (3) (4) q0E0 q0E0 2/ t / 2/ t 2. The charge flowing through a resistor R 4. A metallic rod is placed in a uniform electric field. Select the correct option. varies with time t as Q = 3t – 6t2. The heat E0 produced in R till the current in it becomes AB zero is :- (1) Inside the rod there will be an induced 3R 3R electric field from B to A. (1) 4 (2) 2 (2) Free electrons will accumulate at the end B of the rod. (3) The potential of the end A will be more than that at B. 4R 9R (4) The electric field outside the rod will (3) 2 (4) 2 not change due to the induced charged in the rod. SPACE FOR ROUGH WORK 0000CT103116004 E-1/18
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 5. Calculate energy needed for moving a mass 7. A particle is acted upon by a force whose of 4kg from the centre of the earth to its component's variations with time are surface (in joule), if radius of the earth is shown in diagrams. Then the magnitude of 6400 km and acceleration due to gravity at change in momentum of the particle in the surface of the earth is g = 10 m/sec2. 0.1sec will be :- (1) 1.28 × 108 J (2) 1.28 × 106 J Fz (3) 2.56 × 108 J Fx Fy (2) 2.56 × 1010 J 30N 80N 6. A ball of mass 'm' is released from the top t=0.1 sec of a smooth movable wedge of mass 'm'. 0 When the ball collides with the floor, 0 t=0.1 sec 0 t=0.1 sec –50N velocity of the wedge is 'v'. Then the maximum height attained by the ball after (1) 2 kg m (2) 10 kg m an elastic collision with the floor is : sec sec (Neglect any edge at the lower end of the wedge). (3) 12 kg m (4) 5 2 kg m sec sec m 8. A steel rod is projecting out m of rigid wall. The shearing AB smooth strength of steelis345 MN/m2. D The dimensions AB = 5 cm, 45° BC = BE = 2 cm. The CE maximum load that can be F put on the face ABCD is 2v2 v2 (neglect bending of the rod) (1) g (2) 4g 4v2 v2 (g = 10 m/s2) (2) 1380 kg (3) g (4) 2g (1) 3450 kg (4) 345 kg (3) 13800 kg SPACE FOR ROUGH WORK E-2/18 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 9. In a cylindrical container open to the atmosphere from the top a liquid is filled upto 10 m depth. Density of the liquid 12 varies with depth from the surface as (h) = 100 + 6h2 where h is in meter and is in kg/m3. The pressure at the bottom of the container will be : (atmosphere pressure 10 = 105 Pa, g = 10 m/sec2) (1) 1.7 × 105 Pa (2) 1.4 × 105 Pa (3) 1.6 × 105 Pa (4) 1.3 × 105 Pa 10. A plane electromagnetic wave of angular (1) –0.16 mm (2) +0.16 mm frequency propagates in a poorly (3) +0.14 mm (4) –0.14 mm conducting medium of conductivity and 12. A transistor is operating in the active mode. v1 is potential barrier across base relative permittivity . Find the ratio of emitter junction and v2 is potential barrier conduction current density and across collector base junction. b1 is width displacement current density in the of depletion layer of base emitter junction medium. and b2 is width of collector base junction. (1) 0 (1) v1 > v2, b1 > b2 (2) v1 < v2, b1 < b2 (2) 0 (3) v1 > v2, b1 < b2 (4) v1 < v2, b1 > b2 13. Inside a closed furnace held at a temperature (3) 0 (4) 0 of 400 K, we have a black body. A hole of area 10 cm2 is opened in the furnace so that 11. A screw gauge has some zero error but its sunlight starts falling on black body. The value is unknown. We have two identical intensity of sunlight is 2000 W/m2. In the rods. When the first rod is inserted in the steady state screw, the state of the instrument is shown (1) The black body and furnace can't be by diagram (I). When both the rods are inserted together in series then the state distinguished. is shown by the diagram (II). What is the (2) The black body will appear darker than zero error of the instrument ? 1 msd = 100 csd = 1 mm :- the furnace (3) The black body will appear brighter than the furnace (4) Information insufficient SPACE FOR ROUGH WORK 0000CT103116004 E-3/18
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 14. A thin rectangular magnet suspended freely 16. Identify the terminals on this BJT, and also the has a period of oscillation equal to T. Now it type of BJT it is (NPN or PNP): (Starting from is broken into two equal halves (each having left). The multimeter reads resistance and the half of the original length) and one piece is black terminal is connected to the negative made to oscillate freely in the same field. terminal of the battery :- If its period of oscillation is T', the ratio 0.623 0.625 T'/T is :- 1 A A (1) 2 2 V V 1 V OFF A V OFF A (2) 2 com com (3) 2 1 Black Black (4) 4 Red Red 15. For a GPS navigation to track a mobile (1) Emitter base collector NPN device, we use :- (2) Emitter base collector PNP (1) 3-satellites one for latitude, another for (3) Collector base emitter NPN (4) Collector base emitter PNP longitude and third for altitude 17. A physical quantity A is dependent on (2) 4-satellites one for altitude and 3 for other four physical quantities p, q, r and s position on ground. pq as given below A r2s3 . The percentage (3) 2-satellites one for position on ground on for altitude error of measurement in p, q, r and s 1%, 3%, 0.5% and 0.33% respectively, then the (4) 1 satellite only. maximum percentage error in A is : (1) 2% (2) 0% (3) 4% (4) 3% SPACE FOR ROUGH WORK E-4/18 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 18. Three rods AB, BC and AC having thermal 20. There is a long cylindrical pipe wire of resistances of 10 units, 10 units and 20 units, internal radius r and external radius R respectively, are connected as shown in the carrying current i along its length. The figure. Ends A and C are maintained at variation of magnetic field with distance constant temperatures of 100°C and 0°C, from the axis of the wire can be represented respectively. The rate at which the heat is by the :- crossing junction B is : B y-axis y-axis (1) (2) C r R x-axis R r x-axis A (1) 5 units (2) 10 units y-axis y-axis (3) 20 unites (4) 7.5 units B B 19. A wire carrying a current I is placed inside (3) (4) a uniform magnetic field B B0kˆ . The rR R r x-axis shape of the wire is parabolic and has x-axis equation Y = 2x – x2. The force on the wire will be : 21. In a series R-L-C AC circuit, for a Y particular value of R, L and C power ×××××× supplied by the source is P at resonance. If ××× the value of inductance is halved, then the power from the source again at resonance ii is P'. Then : O ××× A ×××××× y z (1) F = 2B0i, upwards (1) P P' (2) P = 2P' (2) F = 2B0i, downwards 2 (4) P = P' (3) F = 4B0i, upwards (4) F = 4B0i, downwards (3) P = 4P' SPACE FOR ROUGH WORK 0000CT103116004 E-5/18
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 22. Carefully analyses the diagram and choose 25. A hollow conducting sphere of inner radius the correct option : R and outer radius 2R is given a charge Q Spherical Spherical as shown in the figure, then the : wave wave (i) Focus (ii) Focus +Q B A Plane Thin Plane Thin OC Wave lens Wave lens R Spherical Spherical 2R wave wave (iii) Focus (iv) Focus (1) potential at A and B is different (2) potential at O and B is different Plane Thin Plane Thin Wave lens Wave lens (1) i and ii are true (2) i and iii are true (3) potential at O and C is different (3) i and iv are true (4) ii and iv are true (4) potential at A, B, C and O is same 23. A point source of light is placed at a depth h = 0.5 m below the surface of a liquid 26. A liquid is kept in a cylindrical vessel. When the vessel is rotated about its axis, 5 Then, the fraction of light energy the liquid rises at its sides. If the radius of 4 . the vessel is 0.05 m and the speed of rotation is 2 revolutions per second, the that escape directly from the liquid surface difference in the heights of the liquid at the is :- (1) 0.1 (2) 0.2 (3) 0.3 (4) 0.4 centre and at the sides of the vessels will 24. Two radioactive elements R and S be (take g = 10 ms–2 and 2 = 10) disintegrate as (1) 2 cm (2) 4 cm R P + ; R = 4.5 × 10–3 years–1 (3) 1 cm (4) 8 cm S P + ; S = 3 × 10–3 years–1 27. A uniform narrow 1.95 m long pipe is open at both ends. It resonates at two successive Starting with number of atoms of R and S harmonic of frequency 275 Hz and 330 Hz. in the ratio of 2 : 1, this ratio after the lapse The speed of sound in the tube is : of three half lives of R will be : (1) 200 m/s (2) 205 m/s (1) 3 : 2 (2) 1 : 3 (3) 1 : 1 (4) 2 : 1 (3) 210 m/s (4) 214.5 m/s SPACE FOR ROUGH WORK E-6/18 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 28. In the given figure a ring of mass m is kept 29. A ladder AP of length 5 m is inclined to a on a horizontal surface while a body of vertical wall is slipping over a horizontal equal mass 'm' attached through a string, surface with velocity of 2 m/s, when A is at which is wounded on the ring. When the a distance 3m from ground what is the velocity of C.M. at this moment : system is released the ring rolls without slipping. Consider the following statements and choose the correct option. m (1) 1.25 m/s (2) 0 m/s m (3) 1 m/s (4) 2 m/s 30. Two identical adiabatic vessels are filled (i) acceleration of the centre of mass of ring with oxygen at pressure P1 and P2 (P1 > P2). The vessels are interconnected with each g other by a nonconducting pipe. If U01 and is 3 U02 denote initial internal energy of oxygen (ii) acceleration of the hanging particle is in first and second vessel respectively and Uf1 and Uf2 denote final internal energy 2g values, than : 3 (1) U01 P1 , Uf1 Uf2 (iii) frictional force (on the ring) acts along U02 P2 forward direction (2) U01 P2 , Uf1 Uf2 (iv) frictional force (on the ring) acts along U02 P1 backward direction (3) U01 P2 , Uf1 Uf2 (1) statement (i) and (ii) only U02 P1 (2) statement (ii) and (iii) only (3) statement (iii) and (iv) only (4) U01 P1 , Uf1 Uf2 (4) none of these U02 P2 SPACE FOR ROUGH WORK 0000CT103116004 E-7/18
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 PART B - CHEMISTRY 31. A solid element, (metal) crystallises in 35. For a first order reaction, the rate constant ABABAB........type packing in three is 0.04 min–1 at 27ºC and 0.08min–1 at 37ºC. dimension. If the density of the element and The activation energy of reaction is its atomic radius are 5.0 gm/cm3 and (ln2 = 0.7) 100 2pm , the atomic mass of the element (1) 13.02 kcal /mol (2) 139.86 kcal /mol is (N = 6 × 1023) (3) 54.12 kcal /mol (4) 13020 kcal /mol A (1) 48 (2) 72 (3) 96 (4) 32 36. 20 gm iron pyrite, FeS , is roasted 2 32. In 20 ml 0.4 M-HA solution, 80 ml water is completely and SO gas produced is absorbed 2 added. Assuming volume to be additive, the completely in 400 ml NaOH solution. If only pH of final solution is 50% NaOH is used in the reaction, the (K of HA = 4 × 10–7 , log2 = 0.3) molarity of NaOH solution was a (1) 5M (2) 10 M (1) 4.30 (2) 3.75 (3) 3.40 (4) 3.70 3 3 33. Which of the following aqueous solution has highest freezing point ? (1) 0.2 m-urea solution (3) 5 M (4) 20 M (2) 0.15 m-NaCl solution 6 3 (3) 0.1 m CH COOH solution 37. Fe(OH) sol is prepared by the hydrolysis of 3 (4) 0.12 m-Ca(NO ) solution 3 3 2 FeCl in a hot water. If the sol is electrolysed 34. 5 moles of an ideal gas is expanded from 3 (10L, 300K) to (20L, 300K) against a using inert electrodes, the only correct constant external pressure of 1.0 bar. The statement is - only incorrect value of physical quantities (1) Coagulation will occur near anode for this change in state of the system, is- (2) Cl gas may be cathode product 2 (1) U = 0 (2) H = 0 (3) H gas may be anode product 2 (3) S = 0 (4) T = 0 (4) O gas may be anode product 2 SPACE FOR ROUGH WORK E-8/18 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 38. Certain mass of an ideal gas is heated at 41. An octahedral complex with no chelate ring constant volume. Which of the following of M+3 with NH3 and NO2 ligands only have parameter of gas will increase ? four M–N linkage and two M–O linkage, then (1) Density such complex will show :- (2) Mean free path (1) Geometrical isomerism (3) Collision frequency (2) Linkage isomerism (4) Molar mass of gas (3) Optical isomerism 39. Eº for the cell : (4) Both (1) and (2) cell Pt(s) |H (g)|HCOOH(aq.)||CH COOH(aq.)|H (g)|Pt(s) 42. 2 32 at 25ºC is (K of HCOOH = 2.4 × 10–4, K aa of CH COOH = 1.8 × 10–5, log2 = 0.3, log 0.48, 3 2.303 298 R 0.06 ) F (1) 0.0672V (2) –0.0672V yellow (3) –0.1344 V (4) –0.0336 V solution 40. The standard enthalpies of formation of 1, 3-butadiene (g), CO (g) and H O(g) at 22 298K are –30, –94 and –68 kcal/ mol, respectively. If the magnitude of resonance Identify (B), and F respectively :- enthalpies of 1,3-butadiene and CO are (1) AgCl , Cl2 (2) NH4Cl , NH3 2 10 and 20 kcal/mol, respectively, the enthalpy of combustion of 1, 3-butadiene(g) (3) Hg2Cl2 , NH3 (4) CHCl3 , NH3 at 298K, is (enthalpy of vaporisation of 43. KMnO4 is the oxo-salt of the acid of following H O(l) at 298K = 10 kcal/mol) oxide :- (2) Mn2O7 2 (1) MnO (1) –650 kcal / mol (2) +650 kcal / mol (3) –680 kcal / mol (4) –620 kcal / mol (3) MnO3 (4) MnO2 SPACE FOR ROUGH WORK 0000CT103116004 E-9/18
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 44. E° for the conversion of Ce+4 into Ce+3 is 48. Which set of quantum numbers is not 1.74V. It suggest that :- possible for last electron of 'Al' (Z = 13) :- (1) Ce+4 is more stable as compare to Ce+3 nl ms (2) Ce+4 will tend to change into Ce+3 although (1) 3 1 –1 – 1 Ce+4 have inert gas configuration 2 (3) Ce+4 compounds are neither good 1 (2) 3 0 0 2 oxidising nor good reducing agents (3) 3 1 0 1 (4) Ce+3 will tend to change into Ce+4 because 2 Ce+4 have inert gas configuration (4) 3 1 1 –1 45. Which of the following is mixed anhydride :- 49. An ore of metal 'M' Roasting 2 Metal oxide (1) ClO2 (2) NO2 (After crushing Carbon Reduction and grinding) (3) ClO3 (4) All of these 'M' 'M' may be :- 46. Which of the following reaction represent the redox reaction involving water :- (1) Al (2) Zn (1) SiCl4(l) + 2H2O(l) SiO2(s) + 4HCl(aq.) (3) Hg (4) All of these (2) H2O(l) + NH3(aq.) NH4+(aq.) + OH–(aq.) 50. If X(OH) > Y(OH) (acidic strength) (3) 2F2(g) + 2H2O(l) 4H+(aq.) + 4F–(aq.) 'X' and 'Y' both belong to same group then + O2(g) select the CORRECT statement :- (4) P4O10(s) + 6H2O(l) 4H3PO4(aq.) (1) Electron gain enthalpy of 'Y' must be 47. Which of the following species have all the greater than 'X' bond angles of X° and all the bond length of (2) Atomic size of 'X' must be greater than 'Y' (3) O-H bond will be easily broken in case of 'Y' Å :- hydroxide of 'X' (1) S2O32– (2) HCO3 (4) O-H bond will be easily broken in case of (3) CO32– (4) N2O5 hydroxide of 'Y' SPACE FOR ROUGH WORK E-10/18 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 51. Which of the following reaction will produces 54. Major product (R) of following reaction is : primary alcohol ? NH2 (1) Hydration of propene in the presence of CH3COCl P Br2 Q dilute sulphuric acid Pyridine CH3COOH (2) Reaction of propene with borane followed H3O+ by water R (3) Reaction of propanone with methyl Br Br NH2 magnesium bromide followed by NH2 Br hydrolysis (2) (1) (4) Catalylic reduction of butanal Br 52. Which of the following is not used as NH2 NH2 antispetic ? (2) Furacine (3) (4) (1) Soframicine (4) Prontosil (3) Iodoform Br Br 53. Which of the following is incorrectly 55. Major product (Q) of following reaction is matched ? used to form : (Formation of) (Best synthesis by) O (1) Alkyl fluoride Swarts reaction KMnO4 P dil. H2SO4 Q (2) Alkyl chloride Darzen process KOH (3) Alkyl ether Williamson synthesis (4) Alkyl iodide Wurtz reaction (1) Terylene (2) Bakelite (3) Glyptal (4) Nylon-6,6 SPACE FOR ROUGH WORK 0000CT103116004 E-11/18
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 56. Which of the following reaction will not 59. Major product obtained in following produce \"Aniline\" reaction is : NO2 COOH CH2–CH3 (1) H2 / Pd (2) HN3 O2N Br2 ethanol H2SO4 hv CN O C NH2 Br Br (1) (2) (3) Na(Hg) (4) Br2/NaOH C2H5OH O NO2 NO2 57. Compound CH3–C–CH2–OH reduces : (1) Tollen's reagent (2) NaOH / I2 solution Br (4) (3) Fehling solution (3) Br (4) All of these 58. By passing vapours of phenol over heated NO2 NO2 zinc dust will produce : 60. Which of the following pyrimidine base (1) Benzoic acid present in RNA ? (2) Quinone (3) Benzene (1) Ademine (2) Guanine (3) Uracil (4) All of these (4) Malic acid SPACE FOR ROUGH WORK E-12/18 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 PART C - MATHEMATICS 61. If area of quadrilateral formed by tangents 64. If n be the number of values of x for which drawn at ends of latus rectum of hyperbola x2 y2 x x 2 a2 b2 1 is equal to square of distance matrix (x) = 2 x x will be singular, x 2 x between centre and one focus of hyperbola, then e3 is (e is eccentricity of hyperbola) then det((n)) is (where det(B) denotes (1) 2 2 (2) 2 determinant of Matrix B) - (3) 3 (4) 8 (1) –8 (2) –6 (3) 0 (4) 10 62. Area bounded by curves x y 1 and y = x + 1 is- 65. A tetrahedron of volume 5 has three of its vertices at the points A(2,1,–1), B(3,0,1) and 1 8 C(2,–1,3). If the fourth vertex D lies on the (1) 3 sq. unit (2) 3 sq. unit y-axis, then sum of ordinates of all possible 1 2 points D is- (3) 1 (4) 2 (3) sq. unit (4) sq. unit (1) –1 (2) 0 6 3 63. Solution of differential equation dy x sin2 y sin y cos y is- 66. If be a non-real cube root of unity, then dx the value of (1) tany = (x – 1) + Ce–x {(1 (2) coty = (x – 1) + Ce–x 2017 (3) tany = (x – 1)ex + C is-cos 2 2 2 (4) coty = (x – 1)ex + C )(1 ) (2 )(2 ) .... (2017 )(2017 )}. (where C is an arbitrary constant) (1) –1 (2) 0 (3) 1 (4) 3 2 SPACE FOR ROUGH WORK 0000CT103116004 E-13/18
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 67. Let N be the set of natural numbers greater than 100. Define the relation R by : b cos x2 a is non-zero 70. If L lim R = {(x,y) N × N : the numbers x and y x2a x2 a sin cx2 a have atleast two common divisors}. Then R finite (a > 0), then- is- (1) L = 2, b = 1, c = 1 (1) Reflexive, Symmetric and transitive relation (2) L 1 ,b 1,c 1 (2) Symmetric, transitive and NOT 2 Reflexive relation (3) L 4,b 1,c 1 (3) Reflexive, transitive and NOT Symmetric relation (4) L 1 , b 1,c 1 (4) Reflexive, Symmetric and NOT 4 transitive relation 68. If 2017C0 + 2017C1 + 2017C2+......+ 2017C1008 71. The solution of = 2 ( > 0), then remainder when is divided 1 by 33 is- 2 +cosx + cos2x + cos3x + cos4x = 0 is- (1) 8 (2) 13 2n 9 (3) 17 (4) 25 (1) x ,n I,n 9m , m I 69. Let distinct lines L1,L2 belong to family of (2) x 2n ,n I,n 9m , m I lines (x – 2y – 3) + (x + 3y + 2) = 0 and B1 is 9 angle bisector of L1 and L2 which passes through point A(2,3), then equation of other (3) x n ,n I 9 2 bisector of L1 and L2 is ( is a parameter) (1) x + 4y + 3 = 0 (2) 4x + y – 3 = 0 (4) x 2n ,n I 3 6 (3) x + y = 5 (4) 2x – y = 1 SPACE FOR ROUGH WORK E-14/18 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 72. If tan1 x 2 tan1 x 2 tan 1 1 , 76. p q q ~ p is- 2 (1) equivalent to p q then sum of value(s) of x is equal to- (2) Tautology (3) Fallacy (1) 1 (2) –5 (3) –4 1 (4) Neither tautology nor fallacy (4) 77. Minimum distance between parabola 2 73. x1,x2........x34 are numbers such that y2 = 8x and its image with respect to line xi = xi+1 = 150 i {1,2,3,......9} and x + y + 4 = 0 is- xi+1 – xi + 2 = 0 i {10,11,12,......33}, then (1) 2 2 (2) 3 2 median of xi,x2,......x34 is- (3) 4 2 (4) 5 2 (1) 150 (2) 140 (3) 135 (4) 137 78. Two numbers x and y are chosen at random 74. Let A,B and C are three points on ellipse from the set of integers {1,2,3,4......15}. The x2 y2 1 where line joing A & C is parallel probability that point (x,y) lies on a line 25 16 2 to the x-axis and B is end point of minor axis through (0,0) having slope 3 is- whose ordinate is positive then maximum area of ABC, is- 1 1 1 1 (1) 3 (2) 15 (3) 21 (4) 42 (1) 12 3 (2) 20 79. The value of (3) 15 3 (4) 20 3 1 tan 1 tan 1 tan ..... terms 4 8 8 16 16 32 75. If () be intersection point of lines x – 3y + 2z + 4 = 0 = 2x + y + 4z + 1 and is equal to- 1 51 31 x 3 (1) (2) 2 y z 2 , then ) is- 41 8 3 6 (4) 21 (1) –2 (2) –1 (3) 0 (4) 2 (3) 4 2 SPACE FOR ROUGH WORK 0000CT103116004 E-15/18
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 80. Tangent to a non linear curve y = ƒ(x), at any 84. Two parallel towers A and B of different point P intersects x-axis and y-axis at A and heights are at some distance on same level B respectively. If normal to the curve ground. If angle of elevation of a point P at y = ƒ(x) at P intersects y-axis at C such that 20m height on tower B from a point Q at AC = BC, ƒ(2) = 3, then equation of curve is- 10m height on tower A is and is equal to (1) y 6 (2) x2 + y2 = 13 half the angle of elevation of point R at 50m x height on A from point P on B, then is- (3) 2y2 = 9x (4) 2y = 3x (1) 30º (2) 45º (3) 15º (4) 60º n n pm 81. If r3 1 80 , then possible value 85. Radius of circle touching y-axis at point r1 p1 m1 r1 P(0,2) and circle x2 + y2 = 16 internally- of n can be- 5 3 5 (1) 2 (2) 2 (3) 4 (1) 3 (2) 4 (3) 5 (4) 6 (4) 2 82. If in ABC, AB = 4, BC = 6 and AC = 5, h1,h2,h3 be the length of altitude of from 86. AB,BC are diagonals of adjacent faces of a vertices A,B,C respectively, then value of rectangular box with its centre at the origin, 1 1 1 its edges parallel to the co-ordiantes axes. is equal to- If the angles BOC, COA and AOB are and h1 h2 h3 respectively, then cos + cos + cos is- (1) 7 (2) 2 7 (3) 4 7 (4) 8 7 (1) –1 (2) 0 15 15 15 15 4 x2 6 2 3 (4) data insufficient (3) 2 83. 6 9 x2 3 ; (x 0) is not divisible 87. Number of solutions of the equation 2 3 1 x2 x by- 6 t2 1 nt dt 5|x|, x R0 is- 0 (1) x (2) x3 (3) 14+ x2 (4) x5 (1) 5 (2) 4 (3) 2 (4) 3 SPACE FOR ROUGH WORK E-16/18 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 88. The shaded region in given figure is- 90. If 3iˆ 2ˆj 5kˆ , 2ˆi ˆj kˆ , iˆ 3ˆj 2kˆ A r a b b and 2iˆ ˆj 3kˆ such that r a c , c then - (1) , , are in A.P 2 B C (2) 2 are in A.P (1) A B C (2) C A B (3) C B C (4) C A B (3) are in A.P 89. The number of numbers between 1 and 1010 (4) , , are in G.P which contains digit 1, is- 3 (1) 1010 – 910 (2) 1010 – 910 + 1 (3) 109 10 (4) 10 Cr 9r r0 SPACE FOR ROUGH WORK 0000CT103116004 E-17/18
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 SPACE FOR ROUGH WORK SPACE FOR ROUGH WORK E-18/18 0000CT103116004
Form Number : Paper Code : 0000CT103116004 HINDI CLASSROOM CONTACT PROGRAMME (Academic Session : 2016 - 2017) LEADER & ENTHUSIAST COURSE TARGET : JEE (MAIN) 2017 Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Main TEST DATE : 19 - 03 - 2017 Important Instructions Do not open this Test Booklet until you are asked to do so. 1. Immediately fill in the form number on this page of the 1. Test Booklet with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited. 2. 2. The candidates should not write their Form Number anywhere else (except in the specified space) on the Test Booklet/Answer Sheet. 3. 3 4. 90 360 3. The test is of 3 hours duration. 4. The Test Booklet consists of 90 questions. The maximum 5. A,B,C 30 marks are 360. 4 5. There are three parts in the question paper A,B,C consisting of Physics, Chemistry and Mathematics 6. having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response. 7. 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. 8. 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. 9. 8. No candidate is allowed to carry any textual material, 10. printed or written, bits of papers, mobile phone any electronic device etc, except the Identity Card inside the examination hall/room. 11. 9. Rough work is to be done on the space provided for this purpose in the Test Booklet only. 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. 11. Do not fold or make any stray marks on the Answer Sheet. Your Target is to secure Good Rank in JEE (Main) 2017 Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005 +91-744-5156100 [email protected] www.allen.ac.in
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING PART A - PHYSICS 1. A charge particle q0 of mass m0 is projected 1. q0 m0 y along the y-axis at t = 0 from origin with a t= 0 V0 velocity V0. If a uniform electron field E0 also exists along the x-axis, then the time at which de-broglie wavelength of the particle E0 x- becomes half of the initial value is :- m0 v0 2 m0v0 q0E0 q0E0 (1) (2) m0 v0 2 m0v0 q0E0 q0E0 (1) (2) (3) 3 m0v0 (4) 3 m0v0 (3) 3 m0v0 (4) 3 m0v0 q0E0 q0E0 q0E0 q0E0 2. The charge flowing through a resistor R 2. Rt varies with time t as Q = 3t – 6t2. The heat Q = 3t – 6t2 R produced in R till the current in it becomes zero is :- 3R 3R 3R 3R (1) 4 (2) 2 (1) 4 (2) 2 4R 9R 4R 9R (3) (4) (3) 2 (4) 2 2 2 0000CT103116004 H-1/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 3. A particle moves along a circle with a 3. constant angular speed . Its displacement, with respect to this position of the particle t= 0 at time t = 0 is plotted against time. The graph would look like : S S S S circular circular circular circular (1) (2) (1) (2) / t 2/ t / t 2/ t S S S S sine curve sine curve (3) (4) (3) (4) 2/ t / 2/ t 2/ t / 2/ t 4. A metallic rod is placed in a uniform 4. electric field. Select the correct option. E0 E0 AB AB (1) BA (1) Inside the rod there will be an induced electric field from B to A. (2) Free electrons will accumulate at the end B of the rod. (2) B (3) A B (3) The potential of the end A will be more (4) than that at B. (4) The electric field outside the rod will not change due to the induced charged in the rod. H-2/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 5. Calculate energy needed for moving a mass 5. 4kg of 4kg from the centre of the earth to its surface (in joule), if radius of the earth is 6400 km 6400 km and acceleration due to gravity at g=10 m/sec2 the surface of the earth is g = 10 m/sec2. (1) 1.28 × 108 J (1) 1.28 × 108 J (2) 1.28 × 106 J (2) 1.28 × 106 J (3) 2.56 × 108 J (3) 2.56 × 108 J (4) 2.56 × 1010 J (4) 2.56 × 1010 J 6. A ball of mass 'm' is released from the top 6. 'm' 'm' of a smooth movable wedge of mass 'm'. When the ball collides with the floor, 'v' velocity of the wedge is 'v'. Then the maximum height attained by the ball after an elastic collision with the floor is : ( (Neglect any edge at the lower end of the ) wedge). mm m m smooth smooth 45° 45° 2v2 v2 2v2 v2 (1) g (2) 4g (1) g (2) 4g 4v2 v2 4v2 v2 (3) g (4) 2g (3) g (4) 2g 0000CT103116004 H-3/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 7. A particle is acted upon by a force whose 7. component's variations with time are 0.1sec shown in diagrams. Then the magnitude of change in momentum of the particle in 0.1sec will be :- Fx Fy Fz Fx Fy Fz 30N 80N 30N 80N 0 0 0 t=0.1 sec 0 t=0.1 sec t=0.1 sec –50N t=0.1 sec –50N t=0.1 sec 0 t=0.1 sec 0 (1) 2 kg m (2) 10 kg m (1) 2 kg m (2) 10 kg m sec sec sec sec (3) 12 kg m (4) 5 2 kg m (3) 12 kg m (4) 5 2 kg m sec sec sec sec 8. A steel rod is projecting out 8. of rigid wall. The shearing strength of steelis345 MN/m2. AB A B The dimensions AB = 5 cm, D BC = BE = 2 cm. The 345 MN/m2 D C E maximum load that can be CE F AB = 5 cm, BC = BE = 2 cm F put on the face ABCD is ABCD (neglect bending of the rod) (g = 10 m/s2) () (1) 3450 kg (2) 1380 kg (g = 10 m/s2) (3) 13800 kg (4) 345 kg (1) 3450 kg (2) 1380 kg (3) 13800 kg (4) 345 kg H-4/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 9. In a cylindrical container open to the 9. atmosphere from the top a liquid is filled 10 m upto 10 m depth. Density of the liquid (h) =100 + 6h2 varies with depth from the surface as (h) = 100 + 6h2 where h is in meter and h, kg/m3 is in kg/m3. The pressure at the bottom of ( the container will be : (atmosphere pressure = 105 Pa, g = 10 m/sec2) = 105 Pa, g = 10 m/sec2) (1) 1.7 × 105 Pa (1) 1.7 × 105 Pa (2) 1.4 × 105 Pa (2) 1.4 × 105 Pa (3) 1.6 × 105 Pa (3) 1.6 × 105 Pa (4) 1.3 × 105 Pa (4) 1.3 × 105 Pa 10. A plane electromagnetic wave of angular 10. frequency propagates in a poorly conducting medium of conductivity and relative permittivity . Find the ratio of conduction current density and displacement current density in the medium. (1) 0 (1) 0 (2) 0 (2) 0 (3) 0 (4) 0 (3) 0 (4) 0 0000CT103116004 H-5/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 11. A screw gauge has some zero error but its 11. value is unknown. We have two identical rods. When the first rod is inserted in the screw, the state of the instrument is shown by diagram (I). When both the rods are (I) inserted together in series then the state is shown by the diagram (II). What is the (II) zero error of the instrument ? 1msd = 100 csd = 1 mm :- 1 msd = 100 csd = 1 mm :- 12 12 10 10 (1) –0.16 mm (2) +0.16 mm (1) –0.16 mm (2) +0.16 mm (3) +0.14 mm (4) –0.14 mm (3) +0.14 mm (4) –0.14 mm 12. A transistor is operating in the active 12. v1 mode. v1 is potential barrier across base v2 emitter junction and v2 is potential barrier b1 b2 across collector base junction. b1 is width of depletion layer of base emitter junction and b2 is width of collector base junction. (1) v1 > v2, b1 > b2 (2) v1 < v2, b1 < b2 (1) v1 > v2, b1 > b2 (3) v1 > v2, b1 < b2 (2) v1 < v2, b1 < b2 (4) v1 < v2, b1 > b2 (3) v1 > v2, b1 < b2 (4) v1 < v2, b1 > b2 H-6/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 13. Inside a closed furnace held at a 13. 400 K temperature of 400 K, we have a black body. 10cm2 A hole of area 10 cm2 is opened in the furnace so that sunlight starts falling on black body. The intensity of sunlight is 2000 W/m2. In the steady state 2000 W/m2 (1) The black body and furnace can't be (1) distinguished. (2) (2) The black body will appear darker than the furnace (3) (3) The black body will appear brighter than the furnace (4) Information insufficient (4) 14. A thin rectangular magnet suspended 14. freely has a period of oscillation equal to T T. Now it is broken into two equal halves (each having half of the original length) and T' one piece is made to oscillate freely in the same field. If its period of oscillation is T', T'/T the ratio T'/T is :- 1 1 1 1 (1) 2 2 (2) 2 (1) 2 2 (2) 2 1 (3) 2 1 (4) (4) (3) 2 4 4 0000CT103116004 H-7/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 15. For a GPS navigation to track a mobile 15. device, we use :- GPS navigation (1) 3-satellites one for latitude, another for (1) 3- longitude and third for altitude (2) 4-satellites one for altitude and 3 for position on ground. (2) 4- (3) 2-satellites one for position on ground on for altitude (3) 2- (4) 1 satellite only. (4) 16. Identify the terminals on this BJT, and also 16. BJT the type of BJT it is (NPN or PNP): (Starting from left). The multimeter reads resistance BJT (N PN PNP) and the black terminal is connected to the negative terminal of the battery :- 0.623 0.625 0.623 0.625 A A V V V V A A V OFF A V OFF A V OFF A V OFF A com com com com Black Black Black Black Red Red Red Red (1) Emitter base collector NPN (1) NPN (2) Emitter base collector PNP (2) PNP (3) Collector base emitter NPN (3) NPN (4) Collector base emitter PNP (4) PNP H-8/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 17. A physical quantity A is dependent on 17. Ap,q,rs other four physical quantities p, q, r and s pq A pq as given below A r2s3 . The percentage r 2s3 p, q, r s 1%, 3%, error of measurement in p, q, r and s 1%, 0.5% 0.33% A 3%, 0.5% and 0.33% respectively, then the maximum percentage error in A is : (1) 2% (2) 0% (1) 2% (2) 0% (3) 4% (4) 3% (3) 4% (4) 3% 18. Three rods AB, BC and AC having thermal 18. AB,BC AC resistances of 10 units, 10 units and 20 units, 10 1020 respectively, are connected as shown in the AC100°C 0°C figure. Ends A and C are maintained at B constant temperatures of 100°C and 0°C, respectively. The rate at which the heat is crossing junction B is : B B A CA C (1) 5 units (2) 10 units (1) 5 units (2) 10 units (3) 20 unites (4) 7.5 units (3) 20 unites (4) 7.5 units 0000CT103116004 H-9/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 19. A wire carrying a current I is placed inside 19. IBB0kˆ a uniform magnetic field B B0kˆ . The shape of the wire is parabolic and has Y= 2x – x2 equation Y = 2x – x2. The force on the wire will be : Y Y ×××××× ××× ×××××× ××× ii ii O ××× A O ××× A ×××××× y ×××××× y z z (1) F = 2B0i, 20. (1) F = 2B0i, upwards 20. (2) F = 2B0i, (2) F = 2B0i, downwards (3) F = 4B0i, (3) F = 4B0i, upwards (4) F = 4B0i, (4) F = 4B0i, downwards There is a long cylindrical pipe wire of r R internal radius r and external radius R i carrying current i along its length. The variation of magnetic field with distance from the axis of the wire can be represented by the :- y-axis y-axis y-axis y-axis (1) (2) (1) (2) r R x-axis R r x-axis r R x-axis R r x-axis y-axis y-axis y-axis y-axis B B B B (3) (4) (3) (4) rR R r x-axis rR R r x-axis x-axis x-axis H-10/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 21. In a series R-L-C AC circuit, for a 21. R -L-C AC R,L C particular value of R, L and C power supplied by the source is P at resonance. If P the value of inductance is halved, then the P' power from the source again at resonance is P'. Then : (1) P P' (2) P = 2P' (1) P P' (2) P = 2P' 2 2 (3) P = 4P' (4) P = P' (3) P = 4P' (4) P = P' 22. Carefully analyses the diagram and choose 22. the correct option : Spherical Spherical Spherical Spherical wave wave wave wave (i) Focus (ii) Focus (i) Focus (ii) Focus Plane Thin Plane Thin Plane Thin Plane Thin Wave lens Wave lens Wave lens Wave lens Spherical Spherical Spherical Spherical wave wave wave wave (iii) Focus (iv) Focus (iii) Focus (iv) Focus Plane Thin Wave lens Plane Thin Plane Thin Plane Thin Wave lens Wave lens Wave lens (1) i and ii are true (1) i ii (2) i and iii are true (2) i iii (3) i and iv are true (3) i iv (4) ii and iv are true (4) ii iv 0000CT103116004 H-11/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 23. A point source of light is placed at a depth 45 h = 0.5 m below the surface of a liquid 23. 5 . Then, the fraction of light energy that h = 0.5m 4 escape directly from the liquid surface is :- (1) 0.1 (2) 0.2 (1) 0.1 (2) 0.2 (3) 0.3 (4) 0.4 (3) 0.3 (4) 0.4 24. Two radioactive elements R and S 24. RS disintegrate as R P + ; R = 4.5 × 10–3 years–1 R P + ; R = 4.5 × 10–3 years–1 S P + ; S = 3 × 10–3 years–1 S P + ; S = 3 × 10–3 years–1 RS2: 1 Starting with number of atoms of R and S R in the ratio of 2 : 1, this ratio after the lapse of three half lives of R will be : (1) 3 : 2 (2) 1 : 3 (3) 1 : 1 (4) 2 : 1 (1) 3 : 2 (2) 1 : 3 (3) 1 : 1 (4) 2 : 1 25. A hollow conducting sphere of inner radius 25. R 2R R and outer radius 2R is given a charge Q Q as shown in the figure, then the : +Q B +Q B A A OC OC R R 2R 2R (1) potential at A and B is different (1) A B (2) potential at O and B is different (2) O B (3) potential at O and C is different (3) O C (4) potential at A, B, C and O is same (4) A, B, C O H-12/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 26. A liquid is kept in a cylindrical vessel. 26. When the vessel is rotated about its axis, the liquid rises at its sides. If the radius of 0.05m the vessel is 0.05 m and the speed of rotation is 2 revolutions per second, the 2 difference in the heights of the liquid at the centre and at the sides of the vessels will be (take g = 10 ms–2 and 2 = 10) (g = 10 ms–2 2 = 10) (1) 2 cm (1) 2 cm (2) 4 cm (2) 4 cm (3) 1 cm (3) 1 cm (4) 8 cm (4) 8 cm 27. A uniform narrow 1.95 m long pipe is open 27. 1.95 m at both ends. It resonates at two successive 275Hz 330 Hz harmonic of frequency 275 Hz and 330 Hz. The speed of sound in the tube is : (1) 200 m/s (1) 200 m/s (2) 205 m/s (2) 205 m/s (3) 210 m/s (3) 210 m/s (4) 214.5 m/s (4) 214.5 m/s 0000CT103116004 H-13/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 28. In the given figure a ring of mass m is kept 28. m on a horizontal surface while a body of m equal mass 'm' attached through a string, which is wounded on the ring. When the system is released the ring rolls without slipping. Consider the following statements and choose the correct option. mm mm (i) acceleration of the centre of mass of ring (i) 3g g (ii) 2g is 3 3 (ii) acceleration of the hanging particle is (iii) ( ) 2g 3 (iv) ( ) (iii) frictional force (on the ring) acts along forward direction (1) (i) (ii) (iv) frictional force (on the ring) acts along (2) (ii) (iii) backward direction (3) (iii) (iv) (4) (1) statement (i) and (ii) only (2) statement (ii) and (iii) only (3) statement (iii) and (iv) only (4) none of these H-14/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 29. A ladder AP of length 5 m is inclined to a 29. 5m vertical wall is slipping over a horizontal surface with velocity of 2 m/s, when A is at AP 2 m/s a distance 3m from ground what is the A 3m velocity of C.M. at this moment : (1) 1.25 m/s (2) 0 m/s (1) 1.25 m/s (2) 0 m/s (3) 1 m/s (4) 2 m/s (3) 1 m/s (4) 2 m/s 30. Two identical adiabatic vessels are filled 30. P1 with oxygen at pressure P1 and P2 (P1 > P2). P2 (P1 > P2) The vessels are interconnected with each other by a nonconducting pipe. If U01 and U02 denote initial internal energy of oxygen in first and second vessel respectively and U01 U02 Uf1 and Uf2 denote final internal energy Uf1 Uf2 values, than : U01 P1 , U02 P2 U01 P1 , Uf1 Uf2 (1) Uf1 Uf2 U02 P2 (1) U01 P2 , Uf1 Uf2 (2) U01 P2 , Uf1 Uf2 U02 P1 U02 P1 (2) U01 P2 , Uf1 Uf2 (3) U01 P2 , Uf1 Uf2 U02 P1 U02 P1 (3) U01 P1 , Uf1 Uf2 (4) U01 P1 , Uf1 Uf2 U02 P2 U02 P2 (4) 0000CT103116004 H-15/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 PART B - CHEMISTRY 31. A solid element, (metal) crystallises in 31. ( )ABA BAB........ ABABAB........type packing in three dimension. If the density of the element and 5.0gm /cm3 its atomic radius are 5.0 gm/cm3 and 100 2pm , the atomic mass of the element 100 2pm , is (N = 6 × 1023) (3) 96 (4) 32 (N = 6 × 1023) (3) 96 (4) 32 A A (1) 48 (2) 72 (1) 48 (2) 72 32. In 20 ml 0.4 M-HA solution, 80 ml water is 32. 20 ml 0.4 M-HA 80 ml added. Assuming volume to be additive, the pH (H A K = 4 × 10–7 , log2 = 0.3) pH of final solution is (K of HA = 4 × 10–7 , log2 = 0.3) a a (1) 4.30 (2) 3.75 (3) 3.40 (4) 3.70 (1) 4.30 (2) 3.75 (3) 3.40 (4) 3.70 33. Which of the following aqueous solution has 33. highest freezing point ? ? (1) 0.2 m-urea solution (1) 0.2 m- (2) 0.15 m-NaCl solution (2) 0.15 m-NaCl (3) 0.1 m CH COOH solution (3) 0.1 m CH COOH 3 3 (4) 0.12 m-Ca(NO ) solution (4) 0.12 m-Ca(NO ) 32 32 34. 5 moles of an ideal gas is expanded from 34. 51.0 bar (10L, 300K) to (20L, 300K) against a (10L, 300K) (20L, 300K) constant external pressure of 1.0 bar. The only incorrect value of physical quantities for this change in state of the system, is- - (1) U = 0 (2) H = 0 (1) U = 0 (2) H = 0 (3) S = 0 (4) T = 0 (3) S = 0 (4) T = 0 H-16/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 35. For a first order reaction, the rate constant 35. 27ºC is 0.04 min–1 at 27ºC and 0.08min–1 at 37ºC. 0.04 min–1 37ºC 0.08min–1 The activation energy of reaction is (ln2 = 0.7) (ln2 = 0.7) (1) 13.02 kcal /mol (2) 139.86 kcal /mol (1) 13.02 kcal /mol (2) 139.86 kcal /mol (3) 54.12 kcal /mol (4) 13020 kcal /mol (3) 54.12 kcal /mol (4) 13020 kcal /mol 36. 20 gm iron pyrite, FeS , is roasted 36. 20 gm Fe S 2 2 completely and SO gas produced is absorbed SO 4 00 ml NaOH 2 2 completely in 400 ml NaOH solution. If only 50% NaOH is used in the reaction, the 50% NaOH NaOH molarity of NaOH solution was - (1) 5M (2) 10 M (1) 5M (2) 10 M 3 3 3 3 (3) 5M (4) 20 M (3) 5 M (4) 20 M 6 3 6 3 37. Fe(OH) sol is prepared by the hydrolysis of 37. Fe(OH) FeCl 3 33 FeCl in a hot water. If the sol is electrolysed 3 using inert electrodes, the only correct statement is - - (1) Coagulation will occur near anode (1) (2) Cl gas may be cathode product (2) Cl 2 2 (3) H gas may be anode product (3) H 2 2 (4) O gas may be anode product (4) O 2 2 0000CT103116004 H-17/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 38. Certain mass of an ideal gas is heated at 38. constant volume. Which of the following parameter of gas will increase ? (parameter) ? (1) Density (1) (2) Mean free path (2) (3) Collision frequency (3) (4) Molar mass of gas (4) 39. Eº for the cell : 39. 25ºC cell Pt(s) |H (g)|HCOOH(aq.)||CH COOH(aq.)|H (g)|Pt(s) Pt(s) |H (g)|HCOOH(aq.)||CH COOH(aq.)|H (g)|Pt(s) 2 32 2 32 at 25ºC is (K of HCOOH = 2.4 × 10–4, K E º (H COOH K = 2.4 × 10–4, aa cell a of CH COOH = 1.8 × 10–5, log2 = 0.3, log 0.48, 3 CH COOH K = 1.8 × 10–5, log2 = 0.3, 2.303 298 R 0.06 ) 3a F log 0.48, 2.303 298 R 0.06 ) F (1) 0.0672V (2) –0.0672V (1) 0.0672V (2) –0.0672V (3) –0.1344 V (4) –0.0336 V (3) –0.1344 V (4) –0.0336 V 40. The standard enthalpies of formation of 40. 298K 1, 3-(g), CO(g) HO(g) 22 1, 3-butadiene (g), CO (g) and H O(g) at –30,–94 22 298K are –30, –94 and –68 kcal/ mol, –68 kcal/ mol1,3-CO respectively. If the magnitude of resonance 2 enthalpies of 1,3-butadiene and CO are 10 2 20 kcal/mol 298K 1, 3- 10 and 20 kcal/mol, respectively, the enthalpy of combustion of 1, 3-butadiene(g) (g) (298K H O(l) at 298K, is (enthalpy of vaporisation of 2 H O(l) at 298K = 10 kcal/mol) =10kcal/mol ) 2 (1) –650 kcal / mol (2) +650 kcal / mol (1) –650 kcal / mol (2) +650 kcal / mol (3) –680 kcal / mol (4) –620 kcal / mol (3) –680 kcal / mol (4) –620 kcal / mol H-18/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 41. An octahedral complex with no chelate ring 41. NH3 NO2 M+3 of M+3 with NH3 and NO2 ligands only have four M–N linkage and two M–O linkage, then M–N M–O such complex will show :- :- (1) Geometrical isomerism (1) (2) Linkage isomerism (2) (3) Optical isomerism (3) (4) Both (1) and (2) (4) (1) (2) 42. 42. yellow solution (HCl ) Identify (B), and F respectively :- (B) F :- (1) AgCl , Cl2 (2) NH4Cl , NH3 (1) AgCl , Cl2 (2) NH4Cl , NH3 (3) Hg2Cl2 , NH3 (4) CHCl3 , NH3 (3) Hg2Cl2 , NH3 (4) CHCl3 , NH3 43. KMnO4 is the oxo-salt of the acid of following 43. KMnO4 , oxide :- :- (1) MnO (2) Mn2O7 (1) MnO (2) Mn2O7 (3) MnO3 (4) MnO2 (3) MnO3 (4) MnO2 0000CT103116004 H-19/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 44. E° for the conversion of Ce+4 into Ce+3 is 44. Ce+4 Ce+3 E°, 1.74V 1.74V. It suggest that :- :- (1) Ce+4 is more stable as compare to Ce+3 (1) Ce+3 Ce+4 (2) Ce+4 will tend to change into Ce+3 although (2) Ce+4 Ce+4, Ce+3 Ce+4 have inert gas configuration (3) Ce+4 compounds are neither good (3) Ce+4 oxidising nor good reducing agents (4) Ce+3 will tend to change into Ce+4 because (4) Ce+3Ce+4 Ce+4 Ce+4 have inert gas configuration 45. Which of the following is mixed anhydride :- 45. :- (1) ClO2 (2) NO2 (1) ClO2 (2) NO2 (3) ClO3 (4) All of these (3) ClO3 (4) 46. Which of the following reaction represent the 46. redox reaction involving water :- :- (1) SiCl4(l) + 2H2O(l) SiO2(s) + 4HCl(aq.) (1) SiCl4(l) + 2H2O(l) SiO2(s) + 4HCl(aq.) (2) H2O(l) + NH3(aq.) NH4+(aq.) + OH–(aq.) (2) H2O(l) + NH3(aq.) NH4+(aq.) + OH–(aq.) (3) 2F2(g) + 2H2O(l) 4H+(aq.) + 4F–(aq.) (3) 2F2(g) + 2H2O(l) 4H+(aq.) + 4F–(aq.) + O2(g) + O2(g) (4) P4O10(s) + 6H2O(l) 4H3PO4(aq.) (4) P4O10(s) + 6H2O(l) 4H3PO4(aq.) 47. Which of the following species have all the 47. X° bond angles of X° and all the bond length of 'Y' Å:- 'Y' Å :- (1) S2O32– (2) HCO3 (1) S2O32– (2) HCO3 (3) CO32– (4) N2O5 (3) CO32– (4) N2O5 H-20/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 48. Which set of quantum numbers is not 48. 'Al' (Z = 13) possible for last electron of 'Al' (Z = 13) :- :- nl ms nl ms (1) 3 1 –1 – 1 (1) 3 1 –1 – 1 2 2 1 1 (2) 3 0 0 (2) 3 0 0 2 2 (3) 3 1 0 1 (3) 3 1 0 1 2 2 (4) 3 1 1 – 1 (4) 3 1 1 – 1 2 2 49. An ore of metal 'M' Roasting Metal oxide 49. 'M' (After crushing Carbon Reduction ( and grinding) ) 'M' may be :- 'M' 'M' :- 'M' (1) Al (3) Hg (2) Zn (1) Al (2) Zn (4) All of these (3) Hg (4) 50. If X(OH) > Y(OH) (acidic strength) 50. X(OH) > Y(OH) () 'X' and 'Y' both belong to same group then 'X' 'Y' select the CORRECT statement :- (1) Electron gain enthalpy of 'Y' must be :- (1) 'Y' 'X' greater than 'X' (2) Atomic size of 'X' must be greater than 'Y' (3) O-H bond will be easily broken in case of (2) 'X' 'Y' hydroxide of 'X' (3) 'X' O-H (4) 'Y' O-H (4) O-H bond will be easily broken in case of hydroxide of 'Y' 0000CT103116004 H-21/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 51. Which of the following reaction will produces 51. primary alcohol ? (1) Hydration of propene in the presence of (1) dilute sulphuric acid (2) Reaction of propene with borane followed (2) by water (3) Reaction of propanone with methyl (3) magnesium bromide followed by hydrolysis (4) (4) Catalylic reduction of butanal 52. Which of the following is not used as 52. antispetic ? (1) Soframicine (2) Furacine (1) (2) (3) Iodoform (4) Prontosil (3) (4) 53. Which of the following is incorrectly 53. matched ? (Formation of) (Best synthesis by) (1) (1) Alkyl fluoride Swarts reaction (2) Alkyl chloride Darzen process (2) (3) Alkyl ether Williamson synthesis (3) (4) Alkyl iodide Wurtz reaction (4) H-22/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 54. Major product (R) of following reaction is : 54. (R) NH2 NH2 CH3COCl P Br2 Q CH3COCl P Br2 Q Pyridine CH3COOH Pyridine CH3COOH H3O+ H3O+ R R Br Br NH2 Br Br NH2 NH2 Br NH2 Br (2) (2) (1) (1) Br Br NH2 NH2 NH2 NH2 (3) (3) (4) (4) Br Br Br Br 55. Major product (Q) of following reaction is 55. (Q) used to form : OO KMnO4 P dil. H2SO4 Q KMnO4 P dil. H2SO4 Q KOH KOH (1) Terylene (2) Bakelite (1) (2) (3) Glyptal (4) Nylon-6,6 (3) (4) -6,6 0000CT103116004 H-23/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 56. Which of the following reaction will not 56. \" \" produce \"Aniline\" NO2 COOH NO2 COOH (1) H2 / Pd (2) HN3 (1) H2 / Pd (2) HN3 ethanol H2SO4 ethanol H2SO4 CN O C NH2 O NH2 C (3) Na(Hg) (4) Br2/NaOH CN (4) Br2/NaOH C2H5OH (3) Na(Hg) C2H5OH O O 57. Compound CH3–C–CH2–OH reduces : 57. CH3–C–CH2–OH (1) Tollen's reagent (1) (2) NaOH / I2 solution (2) NaOH / I2 (3) Fehling solution (3) (4) All of these (4) 58. By passing vapours of phenol over heated 58. zinc dust will produce : (1) Benzoic acid (1) (2) (2) Quinone (3) (3) Benzene (4) (4) Malic acid H-24/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 59. Major product obtained in following 59. reaction is : CH2–CH3 CH2–CH3 Br2 O2N hv Br2 O2N hv Br Br Br Br (1) (2) (1) (2) NO2 NO2 NO2 NO2 Br (4) Br (4) (3) Br (3) Br NO2 NO2 NO2 NO2 60. Which of the following pyrimidine base 60. RNA present in RNA ? (1) Ademine (2) Guanine (1) (2) (3) Uracil (4) All of these (3) (4) 0000CT103116004 H-25/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 PART C - MATHEMATICS 61. If area of quadrilateral formed by tangents x2 y2 drawn at ends of latus rectum of hyperbola a2 b2 61. 1 x2 y2 1 is equal to square of distance a2 b2 e3(e ) between centre and one focus of hyperbola, then e3 is (e is eccentricity of hyperbola) (1) 2 2 (2) 2 (3) 3 (4) 8 (1) 2 2 (2) 2 (3) 3 (4) 8 62. Area bounded by curves x y 1 and 62. x y 1 y= x + 1 y = x + 1 is- - 1 8 (1) 1 (2) 8 (1) 3 sq. unit (2) 3 sq. unit 3 3 1 2 (3) 1 (4) 2 (3) sq. unit (4) sq. unit 6 3 6 3 63. Solution of differential equation 63. dy x sin2 y sin y cos y is- dy x sin2 y sin y cos y - dx dx (1) tany = (x – 1) + Ce–x (2) coty = (x – 1) + Ce–x (1) tany = (x – 1) + Ce–x (3) tany = (x – 1)ex + C (2) coty = (x – 1) + Ce–x (4) coty = (x – 1)ex + C (3) tany = (x – 1)ex + C (where C is an arbitrary constant) (4) coty = (x – 1)ex + C (C ) H-26/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 64. If n be the number of values of x for which 64. n, x (x) x x 2 x x 2 matrix (x) = 2 x x will be singular, = 2 x x det((n)) x 2 x x 2 x then det((n)) is (where det(B) denotes (det(B),B) - determinant of Matrix B) - (1) –8 (2) –6 (3) 0 (4) 10 (1) –8 (2) –6 (3) 0 (4) 10 65. A tetrahedron of volume 5 has three of its 65. 5 vertices at the points A(2,1,–1), B(3,0,1) and A(2,1,–1), B(3,0,1) C(2,–1,3) C(2,–1,3). If the fourth vertex D lies on the y-axis, then sum of ordinates of all possible D,y- points D is- D - (1) –1 (2) 0 (1) –1 (2) 0 (3) 1 (4) 2 (3) 1 (4) 2 66. If be a non-real cube root of unity, then 66. the value of {(1 cos ) (1 2 ) (2 )(2 2 ) .... (2017 )(2017 2 )}. 2017 cos {(1 ) (1 2 ) (2 )(2 2 ) .... (2017 )(2017 2 )}. 2017 - is- (1) –1 (2) 0 (1) –1 (2) 0 3 (3) 1 (4) 3 (4) 2 (3) 1 2 0000CT103116004 H-27/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 67. Let N be the set of natural numbers greater 67. N, 100 : than 100. Define the relation R by : R = {(x,y) N × N : xy R = {(x,y) N × N : the numbers x and y } RR have atleast two common divisors}. Then R is- (1) (1) Reflexive, Symmetric and transitive relation (2) (2) Symmetric, transitive and NOT Reflexive relation (3) Reflexive, transitive and NOT (3) Symmetric relation (4) Reflexive, Symmetric and NOT (4) transitive relation 68. If 2017C0 + 2017C1 + 2017C2+......+ 2017C1008 68. 2017C0 + 2017C1 + 2017C2+......+ 2017C1008 = 2 ( > 0), then remainder when is divided = 2 ( > 0) 33 by 33 is- - (1) 8 (2) 13 (1) 8 (2) 13 (3) 17 (4) 25 (3) 17 (4) 25 69. Let distinct lines L1,L2 belong to family of 69. L1,L2 (x– 2y – 3) + (x + 3y + 2) = 0 B1 L1 lines (x – 2y – 3) + (x + 3y + 2) = 0 and B1 is L2 A(2,3) angle bisector of L1 and L2 which passes L1 L2 through point A(2,3), then equation of other bisector of L1 and L2 is ( is a parameter) ( ) (1) x + 4y + 3 = 0 (1) x + 4y + 3 = 0 (2) 4x + y – 3 = 0 (2) 4x + y – 3 = 0 (3) x + y = 5 (3) x + y = 5 (4) 2x – y = 1 (4) 2x – y = 1 H-28/35 0000CT103116004
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 b cos x2 a 70. If L lim is non-zero 70. L lim b cos x2 a x2a x2 a sin cx2 a x2a x2 a sin cx2 a finite (a > 0), then- (a > 0) (1) L = 2, b = 1, c = 1 (1) L = 2, b = 1, c = 1 (2) L 1 ,b 1,c 1 (2) L 1 ,b 1,c 1 2 2 (3) L 4,b 1,c 1 (3) L 4,b 1,c 1 (4) L 1 , b 1,c 1 (4) L 1 , b 1,c 1 4 4 71. The solution of 1 1 71. 2 +cosx + cos2x + cos3x + cos4x = 0 2 +cosx + cos2x + cos3x + cos4x = 0 is- - 2n ,n (1) x 2n ,n I,n 9m , m I 9 9 (1) x I,n 9m , m I (2) x 2n ,n I,n 9m , m I (2) x 2n ,n I,n 9m , m I 9 9 n (3) x n ,n I 9 2 9 2 (3) x ,n I 2n ,nI (4) x 2n ,n I 3 6 3 6 (4) x 0000CT103116004 H-29/35
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 72. If tan1 x 2 tan1 x 2 tan 1 1 , 72. tan 1 x 2 tan1 x 2 tan 1 1 2 2 then sum of value(s) of x is equal to- x (1) 1 (2) –5 (3) –4 1 (1) 1 (2) –5 (3) –4 1 (4) (4) 2 2 73. x1,x2........x34 are numbers such that 73. x1,x2........x34 xi = xi+1 = 150 i {1,2,3,......9} and xi = xi+1 = 150 i {1,2,3,......9} xi+1 – xi + 2 = 0 i {10,11,12,......33}, then xi+1 – xi + 2 = 0 i {10,11,12,......33} median of xi,x2,......x34 is- xi,x2,......x34 (1) 150 (2) 140 (3) 135 (4) 137 (1) 150 (2) 140 (3) 135 (4) 137 74. Let A,B and C are three points on ellipse 74. A,B C x2 y2 1 where line joing A & C is parallel x2 y2 1 AC 25 16 25 16 to the x-axis and B is end point of minor axis whose ordinate is positive then maximum xB area of ABC, is- ABC - (1) 12 3 (2) 20 (1) 12 3 (2) 20 (3) 15 3 (4) 20 3 (3) 15 3 (4) 20 3 75. If () be intersection point of lines 75. () x –3y + 2z + 4 = 0 x – 3y + 2z + 4 = 0 = 2x + y + 4z + 1 and x 1 3 1 = 2x + y + 4z + 1 y z 3 x y z 8 3 6 , then ) is- ) - 8 3 6 (1) –2 (2) –1 (3) 0 (4) 2 (1) –2 (2) –1 (3) 0 (4) 2 H-30/35 0000CT103116004
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