ENGLISH Form Number : Paper Code : 0000CT103116001 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 : 29 - 01 - 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)/29-01-2017 HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING PART A - PHYSICS 1. A compass needle is free to rotate in a horizontal plane. It’s magnetic moment is 60Am2. When it is pointing geographical (1) (2) north, it experiences a torque of 1.2 × 10–3 Nm due to earth’s magnetic field. If earth’s magnetic field in horizontal direction is 40 × 10–6 T, what is declination at that place ? (2) 45° (3) (4) (1) 60° (4) 0° (3) 30° 2. An unpolarized light passes through three 4. A steady force of 120 N is required to push polarizing sheets whose polariging a boat of mass 700 kg through water at a directions make an angle of 30°, 60° and constant speed of 1 m/s. If the boat is 30° with y axis in same sense. What fraction fastened by a spring and held at 2m from of initial intensity is transmitted by the the equilibrium position by a force of system ? 450 N, find the angular frequency of damped 1 9 3 9 SHM :- (1) 2 (2) 32 (3) 32 (4) 64 3. Assume that a block of very low shear (1) 0.56 rad/s modulus is fixed on an inclined plane as shown. Due to elastic forces it will deform. What will be the shape of the block ? (2) 0.21 rad/s fixed (3) 1.35 rad/s (4) Motion is overdamped SPACE FOR ROUGH WORK 0000CT103116001 E-1/17
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 5. Consider a gas for which diameter of 8. Government has divided the frequency molecules is , the gas is at a pressure P range from 30Mhz to 60 Mhz between 20 and temperature T and Na = avagodro’s stations which are independently beaming number. The mean free path along x axis their signals. Which of the signals can be is :- beamed by each of the stations :- (1) Voice signals only RT RT (2) Music signals and voice signals only (1) 2PNa2 (2) 3PNa2 (3) TV Signals, Music Signals as well as RT RT 9. voice signals (3) 6PNa2 (4) PNa2 (4) None of these A uniform solid cylinder of mass m and 6. Which of the following is heavily doped ? radius r is set in rotation about its axis with an angular velocity 0, then lowered (a) Photo diode with its lateral surface onto a horizontal plane and released. The coefficient of (b) Light emitting diode friction between the cylinder and plane is equal to µ. The time after which the (c) Zener diode cylinder starts rolling without slipping is :- (d) Solar cell 0 m (1) All four (2) (a), (b) & (c) O (3) (b) & (c) (4) c only 7. Match the column :- (A) Hallwachs & Lenard (P) Transformers (B) Franck-Hertz (Q) Microwave (C) Klystron valve (R) Quantization of energy levels (D) Nicola Tesla (S) Photoelectric 0R 20R g 3g effect (1) (2) (1) A S, B Q, C P, D R (2) A R, B S, C P, D Q 0R 30R 3g 4g (3) A S, B R, C Q, D P (3) (4) (4) A Q, B P, C S, D R SPACE FOR ROUGH WORK E-2/17 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 10. In the transistor circuit shown, assume A Y that the voltage drop between the base and Y the emitter is 0.5 V. What will be the ratio (1) B of the voltage across resistances R2 & R1 in C order to make this circuit function as a source of constant current, I = 1mA ? A B R2 LOAD (2) C Input 7.5 v A R1 2k B (3) Y C (1) 4.5 (2) 3.0 (3) 2.5 (4) 2.0 A Y 11. In a digital circuit for three input signals (4) B (A, B and C) the final output (Y) should be C such that for inputs 12. We use a simple microscope to magnify an A BC object. The microscope has a numerical 0 00 0 01 aperture of sin = 0.24. The object is so 010 small that the resolving power of the the output (Y) should be 0 and for all other cases it should be 1. Which of the following microscope is totally employed. If the digital circuits will give such output ? diameter of the eye's pupil is d = 4.0 mm, what is the minimum magnifying power of the microscope? (1)30 (2)20 (3)15 (4)10 SPACE FOR ROUGH WORK 0000CT103116001 E-3/17
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 13. An LC circuit consists of a capacitor and a 15. A wheel is rotating about an axis through coil with a large number of turns. Suppose its centre at 720 revolutions per minute. all the linear dimensions of all elements of the circuit are increased by a factor of 2 It is acted on by constant torque opposing while keeping the number of turns on the its motion for 8 seconds till it comes to rest. coil constant. How much does the resonant The number of revolutions made by the frequency of the circuit change? (1) becomes two times wheel in the 8 seconds is :- (2) becomes half (3) becomes one fourth (1) 48 (2) 72 (4) becomes four times (3) 96 (4) 120 14. In an experiment to study standing waves, you use a string whose mass per length is 16. A balloon of total mass ‘M’ and a fixed size µ = (1.0 ± 0.1) × 10–4 kg/m. You look at the starts coming down with an acceleration fundamental mode, whose frequency f is f(f < g). The fraction of the total mass of related to the length L and tension T of the string by the following equation the balloon which must be dropped from L 1 T it so that it starts going up with an 2f acceleration of ‘f’ (assuming negligible air You make a plot with L on the y-axis and resistance) is :- T on the x-axis, and find that the best fitting line is f 2f y = (8.0 ± 0.3) × 10–3 x + (0.2 ± 0.04) (1) g f (2) g f in SI units. What is the value of the 2f frequency of the wave (including the (4) g 2f error)? Express your result in SI unit (Hz). gf (1) 6250 ± 859.8 Hz (2) 1250 ± 32.3 Hz (3) f (3) 6250 ± 546.9 Hz (4) 4875 ± 287 Hz SPACE FOR ROUGH WORK E-4/17 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 17. Two men ‘A’ and ‘B’ are standing on a 19. Figure shows a cross-section of a large- plank. ‘B’ is at the middle of the plank and section of an infinite metal sheet carrying ‘A’ is at the left end of the plank. System is an electric current along its surface. The initially at rest and masses are as shown current per unit length is J. A current in figure. ‘A’ and ‘B’ starts moving such that carrying square loop is placed nearby the the position of ‘B’ remains fixed with metal sheet such that the plane of square respect to ground till ‘A’ meets ‘B’. Then is perpendicular to the plane of sheet the point where A meets B is located at :- then :- i0 40 kg 60 kg A B smooth (1) Square loop will be attracted towards the sheet 40kg 120cm (2) Square loop will be repelled away from the sheet (1) The middle of the plank (3) Square loop will remain in translational (2) 30 cm from the left end of the plank equilibrium (3) The right end of the plank (4) Square loop will remain in rotational (4) None of these equilibrium 18. The average density of Earth’s crust 10 km 20. When an electron in a hydrogen atom makes a transition from 2nd excited state beneath the surface is 2.7 gm/cm3. The to ground state, it emits a photon of speed of longitudinal seismic waves at that frequency f. The frequency of photon depth is 5.4 km/s. The bulk modulus of emitted when an electron of Li++ makes a Earth’s crust considering its behaviour as transition from 1st excited state to ground fluid at that depth is :- state is :- (1) 7.9 × 1010 Pa (2) 5.6 × 1010 Pa (1) 243 f (2) 81 f (3) 243 f (4) 27 f (3) 7.9 × 107 Pa (4) 1.46 × 107 Pa 32 32 8 8 SPACE FOR ROUGH WORK 0000CT103116001 E-5/17
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 21. The ratio Cp/Cv for a gas mixture consisting 24. Nine point charges are placed on a cube as shown in the figure. The charge q is placed of 8g of helium and 16 g of oxygen is :- at the body centre whereas all other charges are at the vertices. The electrostatic 23 15 potential energy of the system will be :- (1) 15 (2) 23 –Q +Q +Q +Q 27 17 –Q q (3) (4) –Q 17 27 22. Characteristic X-rays :- +Q +Q (1) Positive (1) Have only discrete wavelength which (2) Negative are characteristic of the target (3) Zero (4) Depends on sign and value of q (2) Have all the possible wavelength 25. ABCDE is a regular pentagon of uniform wire. The rate of heat entering at A and (3) Are characteristic of speed of projectile leaving at C is equal. TB and TD are electrons temperature of B and D. Find the temperature TC :- (4) None of these TB B 23. A parallel beam of white light falls on a convex lens. Images of blue, red and green AC light are formed on other side of the lens E D TD at distances x, y and z respectively from the pole of the lens. Then :- (1) 3TB 2TD 5 (1) x > y > z (2) x > z > y (2) 3TD – 2TB (3) y > z > x (4) None (3) 3TD + 2TB (4) Can have any value SPACE FOR ROUGH WORK E-6/17 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 26. A galvanometer gives full scale reading of 29. In an ac circuit, the instantaneous voltage e(t) and current I(t) are given 50 mA, when a p.d., across its terminals is by e(t) = 5[cos t + 3 sin t] volt 0.15 V. It can be used as an ammeter of range 0 - 100 A by connecting a shunt resistance of :- (1) 0.00075 (2) 0.00045 sin 4 (3) 0.0015 (4) 3 i (t) = 5 t amp then :- 27. An electrostatic field in a region is radially outward with magnitude E = r, where is a constant and r is radial distance. The (1) Current leads voltage by 4 charge contained in a sphere of radius R in this region (centred at the origin) is :- (1) 2 0 R3 (2) 4R3 3 (2) Voltage leads current by 3 (3) 8R2 (4) 0 (3) Voltage leads current by 6 28. By which of the following single load resistance the load bridge should be replaced so that the power to the load (4) Current leads voltage by remains unchanged :- 12 Supply line I load line r 30. A charged particle enters a uniform r magnetic field with velocity vector making r an angle of 30° with the magnetic field. The r particle describes a helical trajectory of pitch x. The radius of the helix is :- rr rr battery with r r x x internal resistance r = 3 (1) 2 (2) 2 2 (1) 1.1 (2) 2.4 x 3x (3) 3.0 (4) 3.3 (3) 2 3 (4) 2 SPACE FOR ROUGH WORK 0000CT103116001 E-7/17
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 PART B - CHEMISTRY 31. Uavg speed of O2 at × 10 bar pressure in 34. In a crystalline compound 'A' atoms occupy a 8 m3 container containing 2 moles is all corners, B occupy all face centered (1) 20 m/sec (2) 2 103 m/sec positions, 'C' occupy all edge centres and (3) 103 m/sec (4) 109 m/sec 'D' occupy all tetrahedral voids formed by A and B atoms find formula of compound. 32. Select the correct statement - (1) Entropy change of all the elementry (1) A4B3C6D2 (2) A4B3C6D4 reactions increases with increases in (3) AB3C3D8 (4) AB3C6D8 temperature 35. Solubility of B(OH)2 in water at 25ºC is (2) Enthalpy change of all the elementry 10–7 M. The value nearest to Ksp is - reactions increases with increase in temperature (1) 4 × 10–21 M3 (2) 9 × 10–21 M3 (3) Rate constant of all the elementry (3) 2 × 10–21 M3 (4) 6 × 10–21 M3 reaction increases with increase in temperature 36. Angular part of wave function for an orbital (4) Activation energy of all the elementry is reaction increases with increase in 15 1/2 temperature. 33. Select the correct statement- (1) Both chemical and physical adsorption = 4 sin cos sin increases with increase in pressure where = angle from z-axis Angular node(s) are - (2) Both chemical and physical adsorption (1) XY plane only increases with increase of temperature (2) YZ plane only (3) Both have high activation energy (3) XY & XZ plane only (4) Multilayers may form in both chemical and physical adsorption (4) XY, YZ & ZX plane SPACE FOR ROUGH WORK E-8/17 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 37. During dischargning of lead storage cell A blue whales gain 75 kg of mass per day concentration H2SO4 reduces from 40% w/w by feeding on krill. The whale must to 30% w/w. Find the total charged consume ten times this mass of krill each produced. Given volume of solution 4.9 litre day. The krill must consume 10.0 kg of and density = 1.2 gm/ml [Assuming volume diatoms to produce 1.0 kg of krill. and density remain constant] Assuming that the mass gain of a whale's (1) 6 faraday (2) 12 faraday life is due to the consumption of (3) 3 faraday (4) 18 faraday carbohydrates (C6H12O6), calculate the 38. Calculate the amount of water evaporated moles of CO2 that must be used by the if 2.8kg of 2m CaBr2 solution is heated to diatoms to produce the carbohydrates 110ºC at 1 atm. consumed by a blue whale in a day. (Given : Kb of water = 0.5 Kkg/mol. ; Atomic (1) 2.5 × 105 mol mass of Ca = 40, Br = 80) (2) 2.5 × 104 mol (1) 1400 gm (2) 300 gm (3) 2.5 × 107 mol (3) 1700 gm (4) 600 gm (4) 2.5 × 108 mol 39. Ratio of time taken to complete 60% and 41. Which of the following statement is 20% of first order reaction [A product] CORRECT is : (log2 = 0.3) (1) Li is harder than the other alkali metals (1) 3 (2) 2 (2) In Solvay process NH3 is recovered (3) 1 (4) 4 when the solution containing NH4Cl is 40. Diatoms, microscopic organisms, are an treated with H2O abundant food source in the oceans (3) Na2CO3 is pearl ash producing carbohydrates from carbon (4) Beryllium and aluminium ions do not dioxide and water by photosynthesis: have strong tendency to form complexes 6CO2 + 6H2O + solar energy C6H12O6+6O2 like BeF4–2, AlF6–3 SPACE FOR ROUGH WORK 0000CT103116001 E-9/17
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 42. Which of the following complex has 46. Which of the following compound is soluble highest C–O bond length ? in aqua regia :- (1) [Ni(CO)3(PF3)] (2) [Ni(CO)4] (1) HgS (2) NiS (3) [Ni(CO)3(PMe3)] (4) None (3) CoS (4) All of these 43. In the series Sc(Z = 21) to Zn(Z = 30), the 47. Hydrogenperoxide converts manganese(II) enthalpy of atomization of _____ is the hydroxide rapidly into '________' in lowest :- alkaline medium (1) Sc (2) Cr (3) Mn (4) Zn Which of the following compound is 44. Which of the following order is suitable for fill in the blank :- CORRECT :- (1) MnO(OH)2 (2) Mn3O4 (1) VO2+ < Cr2O7–2 < MnO4– (Oxidation state (3) Mn2O7 (4) MnO3 of central atom ) 48. Which of the following compound is diamagnetic :- (2) BeSO4 < MgSO4 < BaSO4 (Solubility) II (3) NaHCO3 > KHCO3 > RbHCO3 (Thermal (1) K4[Fe(CN)5(O2 )] (2) [NiF6]–2 stability) (3) [Fe(H2O)5(NO)]+2 (4) All of these (4) BeCl2 > MgCl2 > CaCl2 (Melting point) 49. Which of the following compound may 45. Which of method is used for purification show optical activity :- of Ni :- (1) Trans [CoCl2(en)2]+ (1) Monds process (2) Van-Arkel process (2) [Pt(NH2CH(CH3)COO)2–] (3) Zone refining (4) None of these (3) [Co(H2O)3F3] (4) All are optically active SPACE FOR ROUGH WORK E-10/17 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 50. Which of the following have same type of 54. Final product of following reaction contain hybridization but different shape :- CH3–C C–CH2–C–Cl H2–Pd BaSO4 (1) H2O, NH3 O (2) Ni(CO)4 , [Ni(CN)4]–4 (3) XeF4 , [Fe(CO)4]–2 (1) Only aldehyde groups (4) SF4 , CF4 51. Compound which can show stereisomerism (2) Triple bond & alcohol (1) 2-Chloro propane (2) 2-Chloro-3-methyl but-2-ene (3) Double bond & alcohol (3) 3-Ethyl pent-2-ene (4) Double bond & aldehyde 55. In Aniline & water mixture, Aniline can be seperate by : (1) Steam distillation (2) Fractional distillation (3) Simple distillation (4) 1-Chloro but-1-ene (4) Distillation under reduced pressure 52. Which of the following is cationic detergent 56. Arrange the following polymers in their (1) Sodium louryl sulphate (2) Glyceryl oleate intermolecular forces ? (3) Cetyltrimethyl ammonium bromide Nylon-6,6 Buna-S Polythene (4) Sodium stearate 53. Compound which decarboxylate on gentle (P) (Q) (R) heating : (1) Q > R > P (2) P > R > Q (3) Q > P > R (4) P > Q > R COOH COOH 57. Nitriles are reduced to corresponding (1) HOOC (2) H OH imine with stannous chloride in presence of hydrochloric acid, which on hydrolysis CH3 give corresponding aldehyde, this reaction is called : COOH COOH (1) Rosenmund reaction (2) Reimer-Tiemann reaction (3) (4) (3) Stephen reaction (4) Gabriel phthalimide synthesis SPACE FOR ROUGH WORK 0000CT103116001 E-11/17
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 58. A compound having molecular formula 59. Which of the following carbide will produce O propyne on hydrolysis ? C3H6O, on reaction with NH2–NH–C–NH2 produces mainly P (shows (1) CaC2 stereoisomerism) which on reaction with (2) Al4C3 KOH / ethylene glycol, produces propane (3) Mg2C3 then (P) is : (1) N NH–NH2 (4) Be2C O 60. A hydrocarbon C5H12 does not react with O chlorine in dark but gives six monochloro compound in bright sunlight. Then (2) NH–C–NH2 hydrocarbon is : N (1) N–NH–C–NH2 (2) (3) (3) (4) O O (4) N–C–NH–NH2 SPACE FOR ROUGH WORK E-12/17 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 PART C - MATHEMATICS 1 65. If cos4 sin4 1 , then the value of cos2 sin2 61. The value of 3 2x3 3x2 x 1 dx is - 0 (1) –1 (2) 0 cos4 sin4 (3) 1 (4) 2 is (where [.] denotes 62. Let cos2 sin2 greatest integer function) (1) 0 (2) 1 E 1 cos 61 1 cos 62 ....1 cos119 , (3) 2 (4) depends only on cos1 cos 2 cos 59 then E is equal to - 66. If cosec2x dx (cosecx cot x)9 / 2 1 (2) 1 (3) 2 3 1 (cosecx cot x)2 (1) 2 (4) 2 11 (cosecx cot x )7 / 2 C 63. The numbers of solution(s) of the equation 1 2 1 x cos2 2x 2 sin x 3 1 x (where C is constant of integration and sin sin N), then is - in [0, 4] is - (1) 5 7 (3) 10 (4) 7 (1) 0 (2) 2 (2) 2 67. Consider all possible permutations of the letters of the word EARTHQUAKE, then (3) 4 (4) more than 4 the number of permutation containing the word RAHU is - 64. 2 sin2 x dx is - The value of 1 (2017)x 2 7! 7! (1) 2!2! (2) 2! (3) (4) 0 (3) 7! (4) None of these (1) 4 (2) 2 SPACE FOR ROUGH WORK 0000CT103116001 E-13/17
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 68. Coefficient of t20 in the expansion of 73. If A is an idempotent matrix, then (I + A)4 (1 + t2)10(1 + t10)(1 + t20) is - is (where I is identity matrix of order same as A) - (1) 10C5 + 2 (2) 10C5 (1) I + 11A (2) I + 8A (3) 10C5 + 1 (4) None of these 69. A six faced fair dice is thrown until 2 (3) I + 17A (4) I + 15A comes, then the probability that 2 comes 74. If z 1 2 and w4 2 , then the value in even number of trials is (dice having six z4 w 1 faces numbered 1, 2, 3, 4, 5 and 6) - of |z – w|max + |z – w|min is - 1 5 6 5 (1) 8 (2) 9 (1) 6 (2) 6 (3) 11 (4) 11 (3) 10 (4) 11 70. For any integer k, let wk cos k i sin k , 75. In a ABC, the value of 11 11 sinA cos Bcos C + sinB cosC cosA + sinC cosA cosB where i 1 . The value of the expression is 8 (1) 0 (2) 1 |w2k1 w2k | (3) 3 3 (4) sinA sinB sinC 8 k1 is 76. The number of solution(s) of the equation 4 |w3k1 w3k2 | k 1 (1) 1 (2) 2 (3) 3 (4) 4 2x = x2 is - n is equal to (1) 1 (2) 2 (3) 3 (4) 4 71. The value of n2 1 n2(n2 2) 5 51 (1) 4 (2) 1 (3) 16 (4) 4 77. If the equation 1 1 1 3x3 has k 72. Let E = x2017 + y2017 + z2017 – 2017xyz x x 1 x 2 (where x, y, z > 0), then the least value of E real roots, then k is equal to - is - (1) 2 (2) 3 (1) 0 (2) –2014 (3) –2017 (4) 2017 (3) 4 (4) 6 SPACE FOR ROUGH WORK E-14/17 0000CT103116001
78. If the equation ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 81. Length of latusrectum of curve xy = 7x + 5y is sin1 x cos1 x2 1 tan1(tan y) a (1) 280 (2) 225 has at least one solution, then number of (3) 180 (4) 325 integral values of a is - (1) 1 (2) 2 82. If R = {(6, 6), (9, 9), (6, 12), (12, 12), (12,6)} is a relation on set A = {3, 6, 9, 12}, then (3) 3 (4) 4 relation R is - 79. Let the line y 3x 3 0 cuts the parabola (1) Only reflexive 2y2 = 2x + 3 at A and B. If P( 3,0) , then (2) Only symmetric value of |PA – PB| is [where PA denotes (3) Symmetric and transitive but not distance between points P and A] - reflexive (1) 6 4 3 2 (4) An equivalence relation 3 (2) 83. If x1, x2,.....xn are n observations such that 3 nn x 2 (3) 76 48 3 (4) 76 48 3 i 400 and xi 100 , then possible 3 3 i1 i1 80. If tangents are drawn from point value of n among the following is - P(3sin + 4cos, 3cos – 4sin), (1) 18 (2) 20 (3) 24 (4) 27 8 1 0 1 0 to the ellipse x2 y2 1 , then angle 84. If A 1 1 and I 0 , then which of 16 9 1 between the tangents is - the following holds for all n > 2, n N ? (1) An = 2n–1A + (n – 1)I (1) 8 (2) 4 (2) An = nA + (n – 1)I 3 (3) An = 2n–1A – (n – 1)I (3) 8 (4) 2 (4) An = nA – (n – 1)I SPACE FOR ROUGH WORK 0000CT103116001 E-15/17
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 85. If p : 5 is not greater than 2 88. If lines x 3 y1 z a and q : Jaipur is capital of Rajasthan, 2 3 p are two statements. Then negation of x2 y4 z5 statement p q is the statement and 2 4 2 (1) 5 is not greater than 2 or Jaipur is not capitalof Rajasthan are perpendicular coplanar lines, then value of a + p is - (2) 5 is not greater than 2 and Jaipur is not 3 2 capital of Rajasthan (1) 5 (2) 7 (3) 5 is greater than 2 and Jaipur is capital 4 3 of Rajasthan (3) 7 (4) 5 (4) 5 is greater than 2 and Jaipur is not capital of Rajasthan 89. Let ƒ(x) xe3x , x0 x3 , x2 1 3x2 cos(x x, x 0 86. lim sin2 x cos x 2) cos2 ( x 1) is - then complete values of x for which ƒ'(x) is x 1 1 increasing function is (2) cos1 (1) 0 2 3 2 1 (1) , 2 (2) (–1, 1) (3) (4) 6 1 sin 2 2 cos1 9 87. If the vectors (1 x)ˆi ˆj kˆ , iˆ (1 y)ˆj kˆ (3) , (4) none of these and ˆi ˆj (1 z)kˆ are coplanar vectors, then 90. 6 different letters of an alphabet are given. Words with four letters are formed from value of 1 1 1 is (x, y, z are non zero these given letters. Then the number of xyz words which have atleast one letter repeated and no two same letters are numbers) together, is (1) 0 (2) 3 1 (4) 1 (1) 390 (2) 360 (3) 3 (3) 240 (4) 150 SPACE FOR ROUGH WORK E-16/17 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 SPACE FOR ROUGH WORK SPACE FOR ROUGH WORK 0000CT103116001 E-17/17
Form Number : Paper Code : 0000CT103116001 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 : 29 - 01 - 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)/29-01-2017 HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS BEWARE OF NEGATIVE MARKING PART A - PHYSICS 1. A compass needle is free to rotate in a 1. horizontal plane. It’s magnetic moment is 60Am2 60Am2. When it is pointing geographical north, it experiences a torque of 1.2×10–3 Nm 1.2 × 10–3 Nm due to earth’s magnetic field. If earth’s magnetic field in horizontal 40 × 10–6 T direction is 40 × 10–6 T, what is declination at that place ? (1) 60° (2) 45° (1) 60° (2) 45° (3) 30° (4) 0° (3) 30° (4) 0° 2. An unpolarized light passes through three 2. polarizing sheets whose polariging y directions make an angle of 30°, 60° and 30° with y axis in same sense. What fraction 30°, 60° 30 ° of initial intensity is transmitted by the system ? 1 9 1 9 (1) 2 (2) 32 (1) (2) 2 32 3 9 3 9 (3) 32 (4) 64 (3) (4) 32 64 0000CT103116001 H-1/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 3. Assume that a block of very low shear 3. modulus is fixed on an inclined plane as shown. Due to elastic forces it will deform. What will be the shape of the block ? fixed fixed (1) (2) (1) (2) (3) (4) (3) (4) 4. A steady force of 120 N is required to push a 4. 700 kg 1m/s boat of mass 700 kg through water at a 120N constant speed of 1 m/s. If the boat is fastened by a spring and held at 2m from the 450 N equilibrium position by a force of 450 N, find 2m the angular frequency of damped SHM :- (1) 0.56 rad/s (1) 0.56 rad/s (2) 0.21 rad/s (2) 0.21 rad/s (3) 1.35 rad/s (3) 1.35 rad/s (4) Motion is overdamped (4) H-2/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 5. Consider a gas for which diameter of molecules 5. is , the gas is at a pressure P and temperature T and Na = avagodro’s number. The mean PTNa = free path along x axis is :- x RT RT RT (2) RT (1) 2PNa2 (2) (1) 3PN a 2 3PN a 2 2PN a 2 RT RT RT RT (3) 6PNa2 (4) PNa2 (3) 6PNa2 (4) PNa2 6. Which of the following is heavily doped ? 6. (a) (b) (a) Photo diode (b) Light emitting diode (c) Zener diode (d) Solar cell (c) (d) (1) All four (2) (a), (b) & (c) (1) (2) (a), (b) (c) (3) (b) & (c) (4) c only (3) (b) (c) (4) c 7. Match the column :- 7. (A) Hallwachs & Lenard (P) Transformers (A) (P) (B) (B) (C) Franck-Hertz (Q) Microwave - (Q) Klystron valve (R) Quantization of energy levels (C) (R) (D) Nicola Tesla (S) Photoelectric effect (D) (S) (1) A S, B Q, C P, D R (1) A S, B Q, C P, D R (2) A R, B S, C P, D Q (2) A R, B S, C P, D Q (3) A S, B R, C Q, D P (3) A S, B R, C Q, D P (4) A Q, B P, C S, D R (4) A Q, B P, C S, D R 8. Government has divided the frequency 8. 3 0Mhz 60 Mhz 20 range from 30Mhz to 60 Mhz between 20 stations which are independently beaming their signals. Which of the signals can be beamed by each of the stations :- (1) Voice signals only (1) (2) Music signals and voice signals only (2) (3) TV Signals, Music Signals as well as (3) TV voice signals (4) None of these (4) 0000CT103116001 H-3/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 9. A uniform solid cylinder of mass m and 9. m r radius r is set in rotation about its axis 0 with an angular velocity 0, then lowered with its lateral surface onto a horizontal plane and released. The coefficient of friction between the cylinder and plane is µ equal to µ. The time after which the cylinder starts rolling without slipping is :- 0 0 m m O O (1) 0R (2) 20R (3) 0R (4) 30R (1) 0R (2) 20R (3) 0R (4) 30R g 3g 3g 4g g 3g 3g 4g 10. In the transistor circuit shown, assume 10. that the voltage drop between the base and the emitter is 0.5 V. What will be the ratio 0.5 V R2R1 of the voltage across resistances R2 & R1 in order to make this circuit function as a I= 1mA source of constant current, I = 1mA ? R2 LOAD R2 LOAD 7.5 v 7.5 v R1 2k R1 2k Input Input (1) 4.5 (2) 3.0 (3) 2.5 (4) 2.0 (1) 4.5 (2) 3.0 (3) 2.5 (4) 2.0 H-4/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 11. In a digital circuit for three input signals 11. (A, BC) (A, B and C) the final output (Y) should be (Y) such that for inputs A BC A BC 0 00 0 00 0 01 0 01 010 010 the output (Y) should be 0 and for all other (Y) cases it should be 1. Which of the following 1 digital circuits will give such output ? AY AY (1) B (1) B C C A Y A Y B B (2) (2) C C A Y A Y B Y B Y (3) (3) C C A A (4) B (4) B C C 0000CT103116001 H-5/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 12. We use a simple microscope to magnify an 12. object. The microscope has a numerical aperture of sin = 0.24. The object is so sin = 0.24 small that the resolving power of the microscope is totally employed. If the diameter of the eye's pupil is d = 4.0 mm, d= 4.0 mm what is the minimum magnifying power of the microscope? (1)30 (2)20 (1)30 (2)20 (3)15 (4)10 (3)15 (4)10 13. An LC circuit consists of a capacitor and a 13. LC coil with a large number of turns. Suppose all the linear dimensions of all elements of the circuit are increased by a factor of 2 while keeping the number of turns on the coil constant. How much does the resonant frequency of the circuit change? (1) (1) becomes two times (2) (2) becomes half (3) (3) becomes one fourth (4) becomes four times (4) H-6/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 14. In an experiment to study standing waves, 14. you use a string whose mass per length is µ = (1.0 ± 0.1) × 10–4 kg/m µ = (1.0 ± 0.1) × 10–4 kg/m. You look at the fundamental mode, whose frequency f is f; LT related to the length L and tension T of the string by the following equation L 1 T L 1 T 2f 2f You make a plot with L on the y-axis and L y- T x- T on the x-axis, and find that the best fitting line is y = (8.0 ± 0.3) × 10–3 x + (0.2 ± 0.04) in SI units. What is the value of the y = (8.0 ± 0.3) × 10–3 x + (0.2 ± 0.04) SI frequency of the wave (including the SI error)? Express your result in SI unit (Hz). (Hz ) (2) 1250 ± 32.3 Hz (1) 6250 ± 859.8 Hz (2) 1250 ± 32.3 Hz (4) 4875 ± 287 Hz (3) 6250 ± 546.9 Hz (4) 4875 ± 287 Hz (1) 6250 ± 859.8 Hz (3) 6250 ± 546.9 Hz 15. A wheel is rotating about an axis through 15. its centre at 720 revolutions per minute. 720 It is acted on by constant torque opposing its motion for 8 seconds till it comes to rest. The number of revolutions made by the wheel in the 8 seconds is :- 8 8 (1) 48 (2) 72 (3) 96 (4) 120 (1) 48 (2) 72 (3) 96 (4) 120 0000CT103116001 H-7/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 16. A balloon of total mass ‘M’ and a fixed size 16. ‘M ’ starts coming down with an acceleration f(f < g) f(f < g). The fraction of the total mass of ‘f’ the balloon which must be dropped from it so that it starts going up with an acceleration of ‘f’ (assuming negligible air ( resistance) is :- ) f 2f g f 2f f 2f g f 2f (1) g f (2) g f (3) f (4) g 2f (1) g f (2) g f (3) f (4) g 2f 17. Two men ‘A’ and ‘B’ are standing on a 17. ‘A’‘B’ plank. ‘B’ is at the middle of the plank and ‘B’ ‘A’ ‘A’ is at the left end of the plank. System is initially at rest and masses are as shown ‘A’‘B’ in figure. ‘A’ and ‘B’ starts moving such that 'A' ‘B’ the position of ‘B’ remains fixed with respect to ground till ‘A’ meets ‘B’. Then ‘B’ the point where A meets B is located at :- A, B 40 kg 60 kg 40 kg 60 kg A B A B smooth smooth 40kg 40kg 120cm 120cm (1) The middle of the plank (1) (2) 30 cm from the left end of the plank (2) 30cm (3) The right end of the plank (3) (4) None of these (4) H-8/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 18. The average density of Earth’s crust 10 km 18. 10 km beneath the surface is 2.7 gm/cm3. The 2.7gm/cm3 speed of longitudinal seismic waves at that 5.4km/s depth is 5.4 km/s. The bulk modulus of Earth’s crust considering its behaviour as fluid at that depth is :- :- (1) 7.9 × 1010 Pa (2) 5.6 × 1010 Pa (1) 7.9 × 1010 Pa (2) 5.6 × 1010 Pa (3) 7.9 × 107 Pa (4) 1.46 × 107 Pa (3) 7.9 × 107 Pa (4) 1.46 × 107 Pa 19. Figure shows a cross-section of a large- 19. section of an infinite metal sheet carrying an electric current along its surface. The J current per unit length is J. A current carrying square loop is placed nearby the metal sheet such that the plane of square is perpendicular to the plane of sheet then :- i0 i0 (1) Square loop will be attracted towards (1) the sheet (2) (3) (2) Square loop will be repelled away from (4) the sheet (3) Square loop will remain in translational equilibrium (4) Square loop will remain in rotational equilibrium 0000CT103116001 H-9/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 20. When an electron in a hydrogen atom makes 20. a transition from 2nd excited state to ground f state, it emits a photon of frequency f. The Li++ frequency of photon emitted when an electron of Li++ makes a transition from 1st excited state to ground state is :- (1) 243 f (2) 81 f (3) 243 f (4) 27 f (1) 243 f (2) 81 f (3) 243 f (4) 27 f 32 32 8 8 32 32 88 21. The ratio Cp/Cv for a gas mixture consisting 21. 8g 16g of 8g of helium and 16 g of oxygen is :- Cp/Cv 23 15 27 17 23 15 27 17 (1) 15 (2) 23 (3) 17 (4) 27 (1) 15 (2) 23 (3) 17 (4) 27 22. Characteristic X-rays :- 22. X- (1) Have only discrete wavelength which (1) are characteristic of the target (2) Have all the possible wavelength (2) (3) Are characteristic of speed of projectile (3) electrons (4) None of these (4) 23. A parallel beam of white light falls on a 23. convex lens. Images of blue, red and green light are formed on other side of the lens x,yz at distances x, y and z respectively from the pole of the lens. Then :- (1) x > y > z (2) x > z > y (1) x > y > z (2) x > z > y (3) y > z > x (4) None (3) y > z > x (4) H-10/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 24. Nine point charges are placed on a cube as 24. shown in the figure. The charge q is placed at the body centre whereas all other charges q are at the vertices. The electrostatic potential energy of the system will be :- –Q +Q –Q +Q +Q +Q +Q +Q –Q q –Q q –Q +Q –Q +Q +Q +Q (1) Positive (1) (2) (2) Negative (3) Zero (3) (4) Depends on sign and value of q (4) q 25. ABCDE is a regular pentagon of uniform 25. ABC DE wire. The rate of heat entering at A and AC TBTD B leaving at C is equal. TB and TD are temperature of B and D. Find the D TC temperature TC :- TB TB BB AC AC E D TD E D TD (1) 3TB 2TD (1) 3TB 2TD 5 5 (2) 3TD – 2TB (2) 3TD – 2TB (3) 3TD + 2TB (3) 3TD + 2TB (4) Can have any value (4) 0000CT103116001 H-11/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 26. A galvanometer gives full scale reading of 26. 50mA 50 mA, when a p.d., across its terminals is 0.15 V. It can be used as an ammeter of 0.15V range 0 - 100 A by connecting a shunt 0 - 100 A resistance of :- (1) 0.00075 (2) 0.00045 (1) 0.00075 (2) 0.00045 (3) 0.0015 (4) 3 (3) 0.0015 (4) 3 27. An electrostatic field in a region is radially 27. outward with magnitude E = r, where is a constant and r is radial distance. The E= r r charge contained in a sphere of radius R R in this region (centred at the origin) is :- (1) 2 0 R3 (2) 4R3 (1) 2 0 R3 (2) 4R3 3 3 (3) 8R2 (4) 0 (3) 8R2 (4) 0 28. By which of the following single load 28. resistance the load bridge should be replaced so that the power to the load remains unchanged :- Supply line I load line r Supply line I load line r r r r r r r rr rr rr rr battery with r r battery with r r internal resistance r = 3 internal resistance r = 3 (1) 1.1 (2) 2.4 (1) 1.1 (2) 2.4 (3) 3.0 (4) 3.3 (3) 3.0 (4) 3.3 H-12/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 29. In an ac circuit, the instantaneous 29. ac e(t) voltage e(t) and current I(t) are given I(t) e(t) = 5[cos t + 3 sin t] by e(t) = 5[cos t + 3 sin t] volt sin i(t) = 5 sin t amp 4 4 i (t) = 5 t amp then :- (1) 4 (1) Current leads voltage by 4 (2) (2) Voltage leads current by 3 3 (3) 6 (3) Voltage leads current by 6 (4) 12 (4) Current leads voltage by 12 30. A charged particle enters a uniform 30. magnetic field with velocity vector making an angle of 30° with the magnetic field. The 30° x particle describes a helical trajectory of pitch x. The radius of the helix is :- x x x x (1) 2 (2) 2 2 (1) (2) 2 2 2 x 3x x (4) 3x (3) 2 3 (4) (3) 2 2 2 3 0000CT103116001 H-13/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 PART B - CHEMISTRY 31. Uavg speed of O2 at × 10 bar pressure in a 31. 2 8m 3 × 10 bar 8 m3 container containing 2 moles is O2 Uavg (1) 20 m/sec (2) 2 103 m/sec (1) 20 m/sec (2) 2 103 m/sec (3) 103 m/sec (4) 109 m/sec (3) 103 m/sec (4) 109 m/sec 32. Select the correct statement - 32. - (1) Entropy change of all the elementry (1) reactions increases with increases in temperature (2) Enthalpy change of all the elementry (2) reactions increases with increase in temperature (3) Rate constant of all the elementry (3) reaction increases with increase in temperature (4) Activation energy of all the elementry (4) reaction increases with increase in temperature. 33. Select the correct statement- 33. - (1) Both chemical and physical adsorption (1) increases with increase in pressure (2) Both chemical and physical adsorption (2) increases with increase of temperature (3) Both have high activation energy (3) (4) Multilayers may form in both chemical (4) and physical adsorption H-14/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 34. In a crystalline compound 'A' atoms occupy 34. 'A' all corners, B occupy all face centered B'C' positions, 'C' occupy all edge centres and 'D' 'D'AB occupy all tetrahedral voids formed by A and B atoms find formula of compound. (1) A4B3C6D2 (2) A4B3C6D4 (1) A4B3C6D2 (2) A4B3C6D4 (3) AB3C3D8 (4) AB3C6D8 (3) AB3C3D8 (4) AB3C6D8 35. Solubility of B(OH)2 in water at 25ºC is 35. 25ºC B(OH)2 10–7 M 10–7 M. The value nearest to Ksp is - Ksp - (1) 4 × 10–21 M3 (2) 9 × 10–21 M3 (1) 4 × 10–21 M3 (2) 9 × 10–21 M3 (3) 2 × 10–21 M3 (4) 6 × 10–21 M3 (3) 2 × 10–21 M3 (4) 6 × 10–21 M3 36. Angular part of wave function for an orbital 36. is 15 1/2 = 4 sin cos sin 15 1/2 = 4 sin cos sin = z- where = angle from z-axis (s) - Angular node(s) are - (1) XY (1) XY plane only (2) YZ plane only (2) YZ (3) XY & XZ plane only (3) XY XZ (4) XY, YZ ZX (4) XY, YZ & ZX plane 0000CT103116001 H-15/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 37. During dischargning of lead storage cell 37. H2SO4 concentration H2SO4 reduces from 40% w/w 40% w/w 30% w/w to 30% w/w. Find the total charged produced. Given volume of solution 4.9 litre and 4.9 =1.2g m/ml [ density = 1.2 gm/ml [Assuming volume and density remain constant] ] (1) 6 faraday (2) 12 faraday (1) 6 (2) 12 (3) 3 faraday (4) 18 faraday (3) 3 (4) 18 38. Calculate the amount of water evaporated 38. 1 atm 2.8kg 2m CaBr2 if 2.8kg of 2m CaBr2 solution is heated to 110ºC 110ºC at 1 atm. (Given : Kb of water = 0.5 Kkg/mol. ; Atomic ( : Kb = 0.5 Kkg/mol. ; Ca mass of Ca = 40, Br = 80) =40, Br = 80) (1) 1400 gm (2) 300 gm (1) 1400 gm (2) 300 gm (3) 1700 gm (4) 600 gm (3) 1700 gm (4) 600 gm 39. Ratio of time taken to complete 60% and 39. [A]6 0% 20% 20% of first order reaction [A product] is : (log2 = 0.3) (log2 = 0.3) (1) 3 (2) 2 (1) 3 (2) 2 (3) 1 (4) 4 (3) 1 (4) 4 H-16/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 40. Diatoms, microscopic organisms, are an 40. Diatoms abundant food source in the oceans producing carbohydrates from carbon dioxide and water by photosynthesis: 6CO2 + 6H2O + C6H12O6+6O2 6CO2 + 6H2O + solar energy C6H12O6+6O2 75kg A blue whales gain 75 kg of mass per day by feeding on krill. The whale must consume ten times this mass of krill each 1.0kg day. The krill must consume 10.0 kg of 10.0 kg diatoms to produce 1.0 kg of krill. Assuming that the mass gain of a whale's (C6H12O6) life is due to the consumption of CO2 carbohydrates (C6H12O6), calculate the moles of CO2 that must be used by the diatoms to produce the carbohydrates consumed by a blue whale in a day. (1) 2.5 × 105 mol (1) 2.5 × 105 mol (2) 2.5 × 104 mol (2) 2.5 × 104 mol (3) 2.5 × 107 mol (3) 2.5 × 107 mol (4) 2.5 × 108 mol (4) 2.5 × 108 mol 0000CT103116001 H-17/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 41. Which of the following statement is CORRECT 41. ? (1) Li is harder than the other alkali metals (1) Li (2) In Solvay process NH3 is recovered when the (2) NH4Cl H2O solution containing NH4Cl is treated NH with H O 3 2 (3) Na2CO3 is pearl ash (3) Na2CO3 (4) Beryllium and aluminium ions do not have strong tendency to form complexes like (4) BeF–2, AlF –3 46 BeF4–2, AlF6–3 42. Which of the following complex has highest 42. C–O C–O bond length ? ? (1) [Ni(CO) (PF )] (2) [Ni(CO) ] (1) [Ni(CO)3(PF3)] (2) [Ni(CO)4] 33 4 (3) [Ni(CO)3(PMe3)] (4) None (3) [Ni(CO) (PMe )] (4) 33 43. In the series Sc(Z = 21) to Zn(Z = 30), the 43. Sc(Z = 21) Zn(Z = 30) ______ enthalpy of atomization of _____ is the lowest :- :- (1) Sc (2) Cr (3) Mn (4) Zn (1) Sc (2) Cr (3) Mn (4) Zn 44. Which of the following order is CORRECT :- 44. :- (1) VO2+ < Cr2O7–2 < MnO4– (Oxidation state (1) VO2+ < Cr2O7–2 < MnO4– ( of central atom ) ) (2) BeSO < MgSO < BaSO (Solubility) (2) BeSO < MgSO < BaSO () 4 44 4 44 (3) NaHCO3 > KHCO3 > RbHCO3 (Thermal (3) NaHCO3 > KHCO3 > RbHCO3 ( stability) ) (4) BeCl2 > MgCl2 > CaCl2 (Melting point) (4) BeCl2 > MgCl2 > CaCl2 () H-18/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 45. Which of method is used for purification of Ni:- 45. Ni :- (1) Monds process (2) Van-Arkel process (1) (2) (3) Zone refining (4) None of these (3) (4) 46. Which of the following compound is soluble 46. :- in aqua regia :- (2) NiS (1) HgS (2) NiS (1) HgS (4) All of these (3) CoS (3) CoS (4) 47. Hydrogenperoxide converts manganese(II) 47. (II) hydroxide rapidly into '________' in alkaline '________' medium Which of the following compound is suitable :- for fill in the blank :- (1) MnO(OH)2 (2) Mn3O4 (1) MnO(OH)2 (2) Mn3O4 (3) Mn O (4) MnO (3) Mn2O7 (4) MnO3 27 3 48. Which of the following compound is 48. :- diamagnetic :- II (2) [NiF ]–2 6 II (1) K4[Fe(CN)5(O2 )] (1) K4[Fe(CN)5(O2 )] (2) [NiF6]–2 (3) [Fe(H2O)5(NO)]+2 (4) (3) [Fe(H2O)5(NO)]+2 (4) All of these 49. Which of the following compound may show 49. optical activity :- :- (1) Trans [CoCl (en) ]+ (1) [CoCl (en) ]+ 22 22 (2) [Pt(NH2CH(CH3)COO)2–] (2) [Pt(NH2CH(CH3)COO)2–] (3) [Co(H O) F ] (3) [Co(H O) F ] 2 33 2 33 (4) All are optically active (4) 0000CT103116001 H-19/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 50. Which of the following have same type of 50. hybridization but different shape :- :- (1) H O, NH (1) H2O, NH3 23 (2) Ni(CO)4 , [Ni(CN)4]–4 (2) Ni(CO) , [Ni(CN) ]–4 44 (3) XeF , [Fe(CO) ]–2 (3) XeF , [Fe(CO) ]–2 44 44 (4) SF , CF (4) SF4 , CF4 44 51. Compound which can show 51. stereisomerism (1) 2-Chloro propane (1) 2- (2) 2-Chloro-3-methyl but-2-ene (2) 2--3- -2- (3) 3-Ethyl pent-2-ene (3) 3- -2- (4) 1-Chloro but-1-ene (4) 1--1- 52. Which of the following is cationic detergent 52. detergent (1) Sodium louryl sulphate (1) (2) Glyceryl oleate (2) (3) Cetyltrimethyl ammonium bromide (3) (4) Sodium stearate (4) 53. Compound which decarboxylate on gentle 53. heating : COOH COOH COOH COOH (1) HOOC (2) H (1) HOOC (2) H OH OH COOH CH3 COOH CH3 COOH COOH (3) (3) (4) (4) H-20/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 54. Final product of following reaction contain 54. CH3–C C–CH2–C–Cl H2–Pd CH3–C C–CH2–C–Cl H2–Pd BaSO4 BaSO4 O O (1) Only aldehyde groups (1) (2) Triple bond & alcohol (2) (3) Double bond & alcohol (3) (4) Double bond & aldehyde (4) 55. In Aniline & water mixture, Aniline can be 55. seperate by : (1) Steam distillation (1) (2) Fractional distillation (2) (3) Simple distillation (3) (4) Distillation under reduced pressure (4) 56. Arrange the following polymers in their 56. intermolecular forces ? Nylon-6,6 Buna-S Polythene -6,6 -S (P) (Q) (R) (P) (Q) (R) (1) Q > R > P (2) P > R > Q (1) Q > R > P (2) P > R > Q (3) Q > P > R (4) P > Q > R (3) Q > P > R (4) P > Q > R 0000CT103116001 H-21/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 57. Nitriles are reduced to corresponding imine 57. with stannous chloride in presence of hydrochloric acid, which on hydrolysis give corresponding aldehyde, this reaction is called : (1) (1) Rosenmund reaction (2) (2) Reimer-Tiemann reaction (3) (3) Stephen reaction (4) (4) Gabriel phthalimide synthesis 58. A compound having molecular formula 58. C3H6O OO C3H6O, on reaction with NH2–NH–C–NH2 NH2–NH–C–NH2 produces mainly P (shows P stereoisomerism) which on reaction with KOH / KOH / ethylene glycol, produces propane (P) then (P) is : (1) N NH–NH2 O (1) N NH–NH2 O O O NH–C–NH2 NH–C–NH2 (2) N N (2) N–NH–C–NH2 (3) N–NH–C–NH2 (3) O O O O (4) N–C–NH–NH2 (4) N–C–NH–NH2 H-22/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 59. Which of the following carbide will produce 59. propyne on hydrolysis ? (1) CaC2 (1) CaC2 (2) Al4C3 (2) Al4C3 (3) Mg2C3 (3) Mg2C3 (4) Be2C (4) Be2C 60. A hydrocarbon C5H12 does not react with 60. C5H12 chlorine in dark but gives six monochloro compound in bright sunlight. Then hydrocarbon is : (1) (1) (2) (2) (3) (3) (4) (4) 0000CT103116001 H-23/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 PART C - MATHEMATICS 1 1 61. The value of 3 2x3 3x2 x 1 dx is - 61. 3 2x3 3x2 x 1 dx - 0 0 (1) –1 (2) 0 (1) –1 (2) 0 (3) 1 (4) 2 (4) 2 62. Let (3) 1 62. E 1 cos 61 1 cos 62 ....1 cos119 , E 1 cos 61 1 cos 62 .... 1 cos119 cos1 cos 2 cos 59 cos1 cos 2 cos 59 then E is equal to - E- 1 (2) 1 (3) 2 3 1 (2) 1 (3) 2 3 (1) 2 (4) 2 (1) 2 (4) 2 63. The numbers of solution(s) of the equation 63. [0, 4] 1 2 1 x cos2 2x 2 sin x 3 1 x 1 2 1 x cos2 2x 2 sin x 3 1 x sin sin sin sin in [0, 4] is - (1) 0 (2) 2 (1) 0 (2) 2 (3) 4 (4) more than 4 (3) 4 (4) 4 64. 2 sin2 x dx is - 2 sin2 x dx - The value of (2017)x 64. 1 1 (2017)x 2 2 (3) (4) 0 (3) (4) 0 (1) (2) (1) 4 (2) 2 4 2 H-24/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 65. If cos4 sin4 1 , then the value of 65. cos4 sin4 1 cos2 sin2 cos2 sin2 cos4 sin4 cos4 sin4 is (where [.] denotes cos2 sin2 cos2 sin2 greatest integer function) ([.] ) (1) 0 (2) 1 (1) 0 (2) 1 (3) 2 (4) depends only on (3) 2 (4) 66. If cosec2x dx 66. cosec2x dx (cosecx cot (cosecx cot x)9 / 2 x)9 / 2 x )7 / 2 1 (cosecx cot x )2 (cosecx cot x )7 / 2 1 (cosecx cot x )2 C 11 11 (cosecx cot C (where C is constant of integration and (C N) N), then is - - (1) 5 7 (1) 5 7 (3) 10 (2) 2 (2) (4) 7 2 (3) 10 (4) 7 67. Consider all possible permutations of the 67. EARTHQUAKE letters of the word EARTHQUAKE, then the number of permutation containing the word RAHU is - RAHU - 7! 7! 7! 7! (1) 2!2! (2) 2! (1) 2!2! (2) 2! (3) 7! (4) None of these (3) 7! (4) 0000CT103116001 H-25/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 68. Coefficient of t20 in the expansion of 68. (1 + t2)10(1 + t10)(1 + t20) t20 (1 + t2)10(1 + t10)(1 + t20) is - - (1) 10C5 + 2 (2) 10C5 (1) 10C5 + 2 (2) 10C5 (3) 10C5 + 1 (4) None of these (3) 10C5 + 1 (4) 69. A six faced fair dice is thrown until 2 69. comes, then the probability that 2 comes 2 2 in even number of trials is (dice having six ( faces numbered 1, 2, 3, 4, 5 and 6) - 1, 2, 3, 4, 5 6 )- 1 5 6 5 1 5 6 5 (1) (2) (3) (4) (1) (2) (3) (4) 6 6 11 11 6 6 11 11 70. For any integer k, let wk cos k i sin k , 70. k 11 11 where i 1 . The value of the expression wk cos k i sin k i 1 11 11 8 8 |w2k1 w2k | |w2k1 w2k | k1 k1 is 4 4 |w3k1 w3k2 | k 1 |w3k1 w3k2 | k 1 (1) 1 (2) 2 (3) 3 (4) 4 (1) 1 (2) 2 (3) 3 (4) 4 n is equal to 71. n 71. The value of n2 1 n2 (n2 2) n2 1 n2(n2 2) 5 (2) 1 5 1 5 (2) 1 5 1 (1) 4 (3) 16 (4) 4 (1) 4 (3) 16 (4) 4 72. Let E = x2017 + y2017 + z2017 – 2017xyz 72. E = x2017 + y2017 + z2017 – 2017xyz (where x, y, z > 0), then the least value of E (x, y, z > 0) E- is - (1) 0 (2) –2014 (1) 0 (2) –2014 (3) –2017 (4) 2017 (3) –2017 (4) 2017 H-26/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 73. If A is an idempotent matrix, then (I + A)4 is 73. A (I+A)4(I, A (where I is identity matrix of order same as ) - A) - (2) I + 8A (1) I + 11A (2) I + 8A (1) I + 11A (3) I + 17A (4) I + 15A (3) I + 17A (4) I + 15A 74. If z 1 2 and w4 2 , then the value 74. z 1 2 w 4 2 z4 w 1 z4 w 1 of |z – w|max + |z – w|min is - |z – w|max + |z – w|min - (1) 8 (2) 9 (1) 8 (2) 9 (3) 10 (4) 11 (3) 10 (4) 11 75. In a ABC, the value of 75. ABC , sinA cos Bcos C + sinB cosC cosA + sinC cosA cosB sinA cos Bcos C + sinB cosC cosA + sinC cosA cosB is (1) 0 (2) 1 (1) 0 (2) 1 33 (4) sinA sinB sinC (3) 3 3 (4) sinA sinB sinC (3) 8 8 76. The number of solution(s) of the equation 76. 2x = x2 - 2x = x2 is - (1) 1 (2) 2 (1) 1 (2) 2 (3) 3 (4) 4 (3) 3 (4) 4 77. If the equation 1 1 1 3x3 has k 77. 1 1 1 3x3 k x x 1 x 2 x x 1 x 2 real roots, then k is equal to - k (1) 2 (2) 3 (1) 2 (2) 3 (3) 4 (4) 6 (3) 4 (4) 6 0000CT103116001 H-27/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 78. If the equation 78. sin1 x cos1 x2 1 tan1(tan y) a sin1 x cos1 x2 1 tan1(tan y) a has at least one solution, then number of a - integral values of a is - (1) 1 (2) 2 (1) 1 (2) 2 (3) 3 (4) 4 (3) 3 (4) 4 79. Let the line y 3x 3 0 cuts the parabola 79. y 3x 3 0 , 2y2 = 2x + 3 2y2 = 2x + 3 at A and B. If P( 3,0) , then A B P(3,0) value of |PA – PB| is [where PA denotes |PA – PB| [PA, PA distance between points P and A] - ] - (1) 6 4 3 2 (1) 6 4 3 2 3 (2) 3 3 (2) 3 (3) 76 48 3 (4) 76 48 3 (3) 76 48 3 (4) 76 48 3 3 3 3 3 80. If tangents are drawn from point 80. P(3sin + 4cos, 3cos – 4sin), P(3sin + 4cos, 3cos – 4sin), 8 8 to the ellipse x2 y2 1 , then angle x2 y2 1 16 9 16 9 between the tangents is - - (1) 8 (2) 4 (1) (2) 8 4 3 3 (3) 8 (4) 2 (3) 8 (4) 2 H-28/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 81. Length of latusrectum of curve xy = 7x + 5y is 81. xy = 7x + 5y (1) 280 (2) 225 (1) 280 (2) 225 (3) 180 (4) 325 (3) 180 (4) 325 82. If R = {(6, 6), (9, 9), (6, 12), (12, 12), (12,6)} is 82. R = {(6, 6), (9, 9), (6, 12), (12, 12), (12,6)} a relation on set A = {3, 6, 9, 12}, then A = {3, 6, 9, 12} relation R is - R - (1) Only reflexive (1) (2) Only symmetric (2) (3) Symmetric and transitive but not (3) reflexive (4) An equivalence relation (4) 83. If x1, x2,.....xn are n observations such that 83. x1, x2,.....xn, n nn nn 2 xi n x2i 400 and xi 100 , then possible x i 400 100 i1 i1 i1 i1 value of n among the following is - - (4) 27 (1) 18 (2) 20 (3) 24 (4) 27 (1) 18 (2) 20 (3) 24 84. If A 1 0 and I 1 0 , then which of 84. A 1 0 I 1 0 n>2, 1 1 0 1 1 1 0 1 the following holds for all n > 2, n N ? n N (1) An = 2n–1A + (n – 1)I (1) An = 2n–1A + (n – 1)I (2) An = nA + (n – 1)I (2) An = nA + (n – 1)I (3) An = 2n–1A – (n – 1)I (3) An = 2n–1A – (n – 1)I (4) An = nA – (n – 1)I (4) An = nA – (n – 1)I 0000CT103116001 H-29/32
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 85. If p : 5 is not greater than 2 85. p: 5, 2 and q : Jaipur is capital of Rajasthan, q : pq are two statements. Then negation of statement p q is the statement (1) 5, 2 (1) 5 is not greater than 2 or Jaipur is not capitalof Rajasthan (2) 5, 2 (2) 5 is not greater than 2 and Jaipur is not capital of Rajasthan (3) 5, 2 (3) 5 is greater than 2 and Jaipur is capital (4) 5, 2 of Rajasthan (4) 5 is greater than 2 and Jaipur is not capital of Rajasthan 86. lim x2 1 is - 86. lim x2 1 - x1 sin2 x cos x cos(x 2) cos2(x 1) x1 sin2 x cos x cos(x 2) cos2(x 1) (1) 0 1 (1) 0 1 (2) cos1 (2) cos1 2 1 2 1 (3) sin 2 (4) 2 cos1 (3) sin 2 (4) 2 cos1 87. If the vectors (1 x)ˆi ˆj kˆ , iˆ (1 y)ˆj kˆ 87. (1 x)ˆi ˆj kˆ , iˆ (1 y)ˆj kˆ and ˆi ˆj (1 z)kˆ are coplanar vectors, then ˆi ˆj (1 z)kˆ 1x 1 1 y z 111 value of is (x, y, z are non zero xyz (x,y, z ) numbers) (1) 0 (2) 3 1 (4) 1 (1) 0 (2) 3 1 (4) 1 (3) 3 (3) 3 H-30/32 0000CT103116001
ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/29-01-2017 88. If lines x 3 y 1 za 88. x23 y 1 z a 2 3 p 3 p and x 2 y 4 z 5 x 2 y 4 z 5 242 2 4 2 are perpendicular coplanar lines, then a+p- value of a + p is - 3 2 3 2 (1) 5 (1) 5 (2) (2) 7 7 4 3 4 (4) 3 (3) 7 (4) (3) 7 5 5 89. Let ƒ(x) xe3x , 3x2 x0 89. ƒ(x) xe3x , 3x2 x0 x x3 , x3 x, x 0 x, x 0 then complete values of x for which ƒ'(x) is ƒ'(x) increasing function is (1) 2 , 2 (2) (–1, 1) (1) 2 , 2 (2) (–1, 1) 3 3 (3) 6 , 1 (4) none of these (3) 6 , 1 (4) 9 9 90. 6 different letters of an alphabet are given. 90. 6 Words with four letters are formed from these given letters. Then the number of words which have atleast one letter repeated and no two same letters are together, is (1) 390 (2) 360 (1) 390 (2) 360 (3) 240 (4) 150 (3) 240 (4) 150 0000CT103116001 H-31/32
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