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NARAYANA IIT ACADEMY INDIA SR IIT-IZ3-SPARK
JEE MAINS MODEL)
TIME : 3 HRS
DATE :10-1-2015
CTM-2
MARKS : 360
INSTRUCTIONS 1 2
3
The Test Booklet consists of 90 questions. The maximum marks are 360. There are three parts in the question paper A, B, C consisting of Physics,Chemistry and Maths, having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct response. Candidates will be awarded marks as stated above in instruction No.2 for correct response of each question. 1/4 (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. There is only one correct response for each question. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 3 above.
PHYSICS 01. A simple pendulum has length l, mass of bob m. The bob is given a charge q. The pendulum is suspended between the vertical plates of charged parallel plate capacitor. If E is the field strength between the plates, then time period T equals l 1) 2 g
2)
2
l
3)
qE g m + + + +X + + + +
2
l qE g m
4)
2
l qE g m 2
-
02. In the figure, the equivalent capacitance between A and B is F F
F
F
F
1) 3.75 F
2) 5.25 F
F
F
3) 6.5 F
4) 10.5 F
2
03. In the given circuit he steady state current through the 2 resistor is
1) 0.6A
2) 0.9A
3) 1.2A
4) 1.5A
04. A and B are two points on a uniform ring of resistance R. The ACB , where C is the centre of the ring. The equivalent reistance between A and B is
2
2) R 1 3) R 4) R 2 2 4 05. A conducting rod of length l and mass m is moving down a smooth inclined plane of inclination with constant velocity ,. A current I is flowing in the conductor in a direction perpendicular to paper inwards and a vertically upward magnetic r field B exists in space. Then.
1)
R (2 ) 4 2
r B
r mg | B | sin 1) Il
r mg | B | tan 2) Il
r mg cos | B | 3) Il
r | B | 4)
mg I l sin
06. A proton accelerated by a potential difference 500KV moves through a transverse magnetic field of 0.51T as shown in figure. The angle through which the proton deviates from the initial direction of its motion is
1) 15°
2) 30°
3) 45°
4) 60°
07. A circular loop of mass m and radius r lies on a horizontal table (x-y plane). A uniform magnetic field is applied parallel to the x-axis. The current I that should flow in the loop so that it just tilts about one point on the table is y I r x
r
rB mg mg 3) 4) mg 2 rB rB 08. Two resistors of 10 and 20 and an ideal inductor of 10H are connected to a 2V
1)
mg r2B
2)
battery as shown. They key K is inserted at time t = 0. The initial (at t = 0) and final (at t ) currents through the battery are
1)
1 1 A; A 15 10
2)
1 1 A; A 10 15
3)
2 1 A; A 25 10
4)
1 2 A; A 15 25
09. A uniform but time varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region
1) is zero
2) decreases as
1 r
3) increases as r 4) decreases as
1 r2
10. Shown in the figure is a circular loop of rdius r and resistance R. A variable magnetic field of induction B B0et is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch is equal to
1)
B02 r 2 R
2)
B010r 3 R
3)
B02 2 r 4 R 5
4)
B02 2 r 4 R
11. In the circuit shown in figure neglecting source resistance the voltmeter and ammeter reading will respectively, will be
1) 0 V, 3A 2) 150 V, 3A 3) 150 V, 6A 4) 0V, 8A 12. In a circuit given in figure 1 and 2 are ammeters. Just after key K is pressed to complete the circuit, the reading is
1) zero in both 1 and 2 3) zero in 1 and maximum in 2
2) maximum in both 1 and 2 4) maximum in 1 and zero in 2
13. The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300K are 6.211021 J and 484 ms-1 respectively. The corresponding values at 600K are nearly (assuming ideal gas behavior) 1) 12.42 1021 J ,968ms 1 2) 8.78 1021 J , 684ms 1 3) 6.211021 J ,968 ms 1 4) 12.42 1021 J , 684 ms 1
14. Two rods of length L2 and coefficient of linear expansion 2 are connected freely to a third rod of length L 1 of coefficient of linear expansion 1 to form an isosceles triangle. The arrangement is supported on the knife edge at the midpoint of L1 which is horizontal. The apex of the isosceles triangle is to remain at a constant distance from the knife edge if L1
2
L
L1
2
L
1) L 2) 1 2 3) L 2 4) 1 2 2 L2 1 L2 1 2 1 2 1 15. A source of sound and a listener are both moving in the same direction, the source following the listener. If the respective velocities of sound, source and listener are v, vs , v1 then the ratio of the actual frequency of the source and the apparent frequency as received by the listener is v vs
v v1
v v1
v vs
1) v v 2) v v 3) v v 4) v v s 1 s 1 16. A tuning fork, whose frequency as given by the manufacturer is 512 Hz, is being tested using an accurate oscillator. It is found that they produce 2 beats per second when the oscillator reads 514 Hz, and 6 beats second when it reads of 510 Hz. The actual frequency of the fork is 1) 508 Hz 2) 512 Hz 3) 516 Hz 4) 518 Hz 17. Two tuning forks A and B give 5 bps. A resonates with a column of air 15 cm long, closed at one end, and B with a column 30.5 cm long, open and B with a column 30.5 cm long, open at both ends. Neglecting end correction, the frequencies of A and B are respectively. 1) 300 Hz, 295 Hz 2)295 Hz, 300Hz 3) 305 Hz, 300 Hz 4) 300 Hz, 305 Hz 18. A glass prism of refractive index 1.5 is immersed in water (refractive index
3 ). A 4
light beam incident normally on the face AB is totally reflected to reach the face BC,if 1) sin
8 9
2) sin
2 3
3)
2 8 sin 3 9
4) none of these
19. A compound microscope has an objective of focal length 2.0 cm and an eye piece of focal length 6.25 cm separated by 15 cm. If the final image is formed at the least distance of distinct vision (25 cm), the distance of the object from the objective is 1) 1.5 cm 2) 2.5 cm 3) 3.0 cm 4) 4.0 cm 20. A stone lies at the bottom of stream. A boy wants to hit it with a stick. Taking aim the boy holds the stick in the air at an angle of 45°. At what distance from the 4 3
stone will the stick hit the bottom, if the depth is 32cm (given a w ) 1) 8 cm
2) 12 cm
3) 16 cm
4) 12 2cm
21. In an interference pattern produced by two indentical slits, the intensity at the site of the central maximum is I. The intensity at the same spot when either of two slits is closed is 1)
I 2
2)
I 4
3)
I 2 2
4)
I 2
22. A thin sheet of glass (refractive index 1.5) of thickness 6 micron, introduced in the path of one of the interfering beams in a double-slit experiment, shifts the central fringe to a position earlier occupied by the fifth bright fringe. The wavelength of light used is 1) 3000Å 2) 6000Å 3) 4500Å 4) 7000Å 23. The radioactivity of a sample is R1 at time t1 and R2 a time t2. If the half life of the sample be T, the number of atoms that have disintegrated in time (t 1 – t2) is proportional to 1) R1t1 R2t2
2) ( R1 R2 )1
3)
( R1 R2 ) T
4) ( R1 R2 )T
24. Energy levels A, B, C of a certain atom correspond to increasing values of energy ie.e. E A EB EC . If 1 , 2, 3 are the wavelengths of radiations corresponding to the transitions C to B, B to A and C to A respectively, which of the following statements is correct ?
1 2 2) 3 3) 1 2 2 0 4) 32 12 22 1 2 25. Two radioactive materials X1 and X2 have decay constants 10 and respectively. If initially they have th same number of nuclei,then the ratio of the number of nuclei of X1 to that of X2 will be 1/e after a time.
1) 3 1 2
1)
1 10
2)
1 11
3)
2( hc ) m
3)
11 10
4)
1 9
26. The maximum velocity of an electron emitted by light of wavelength incident on the surface of a metal of work-function is 1)
2(hc ) m
2)
2(hc ) m
4)
2(h ) m
27. The maximum kinetic energy (EK) of photoelectrons varies with the frequency (v) of the incident radiation as
28. An electron of mass m, when accelerated through a potential difference V has deBroglie wavelength . The de-Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will be 1) M m
2)
m M
3) m M
4)
M m
29. A parallel plate capacitor consists of two circular plates each of radius 2cm, separated by a distance of 0.1mm. If voltge across the plates is varying at the rate of 5 1013Vs 1 , then the value of displacement current is 1) 5.50A 2) 5.56 102 A 3) 5.56 103 A 4) 2.28 104 A 30. Two junction diodes one of germanium (Ge) and other of silicon (Si) are connected as shown in figure to a battery of emf 12V and a load resistance 10k . The germanium diode conducts at 0.3 V and silicon diode at 0.7V. When a current flows in the circuit, the potential of terminal Y will be
1) 12 V
2) 11V
3) 11.3 V
4) 11.7V
CHEMISTRY 31. n-factor of Ba(MnO4)2 in the acidic medium is 1) 2 2) 6 3) 10
4) none of these
32. For the reaction, Fe0.95 O (molar mass: M) Fe2O3 .What is the eq. wt. of Fe0.95 O ? 1)
M 0.85
2)
M 0.95
3)
M 0.8075
4) none of these
33. Two mole of an ideal gas is expanded irreversibly and isothermally at 37°C until its volume is doubled and 3.41 kJ heat is absorbed from surrounding. Stotal (system + surrounding) is 1) -0.52 J/K 2) 0.52 J/K 3) 22.52 J/K 4) 0 34. The molar heat capacities of iodine vapour and solid are 7.8 and 14 cal/mol respectively if enthalpy of sublimation of iodine is 6096 cal/mole at 200°C, then what is U (internal energy change) at 250°C in cal/mol 1) 5360 2) 4740 3) 6406 4) none of these 35. Two solid compounds X and Y dissociates at a certain temperature as follows X ( s ) ƒ
A( g ) 2 B ( g ); K p1 9 10 3 atm3
Y ( s ) ƒ
2 B( g ) C ( g ); K p 2 4.5 10 3 atm3
The total pressure of gases over a mixture of X and Y is 1) 4.5 atm 2) 0.45 atm 3) 0.6 atm
4) none of these
36. A solution is 0.01M KI and 0.1 M KCl. If solid AgNO3 is added to the solution, what is the [I-] when AgCl begins to precipitate ? [ K sp ( AgI ) 1.5 1016 ; K sp ( AgCl ) 1.8 10 10 ]
1) 3.5 107
2) 6.1108
3) 2.2 107
4) 8.3 108
37. Column-I Column-II A) pH of 0.1 MHA (pKb = 5) and 0.01 M NaA B) pH of 0.1 MBOH (pKb = 6) and 0.1 M BCl C) pH of 0.1 M salt of weak acid (pKa = 5) and week base (pKb = 7) D) pH of 500 litre of 0.02 M HNO3 and 500 litre 0.01 M Sr(OH)2 1) A-P, B-S, C-R, D-Q 3) A-P, B-S, C-Q, D-R
2)A-S, B-P, C-R, D-Q 4)A-R, B-Q, C-S, D-P
P) 4 Q) 7 R) 6 S) 8
38. Consider the plots for the types of reaction
1 [ A]
[A]
d [ A] dt
[A]
(i)
t
(ii)
t
(iii)
These plots respectively correspond to the reaction orders 1) 0,2,1 2) 0,1,2 3) 1,1,2
4) 1,0,2
39. For the first order reaction A B C , carried out at 27°C, if 3.8 1016% of the reactant molecules exists in the activated state, the E a (activation energy) of the reaction is 1) 12 kJ/mole 2) 831.4 kJ/mole 3) 100 kJ/mole 4) 88.57 kJ/mole 40. The activity of a radioactive nuclide (X100) is 6.023 curie at a certain time ‘t’. If its disintegration constant is 3.7 104 s 1 the mass of X after t sec is 1) 6.022 106 g 2) 1013 g 3) 1015 g 4) 1017 g 41. An analysis of the rock shows that the relative number of Sr87 and Rb87 (t1/2 4.7 1010 year ) atoms is 0.05. What is the age of the rock ? Assume all Sr87 to be formed from Rb87 only. 1) 7.62 109 year 2) 1.43 109 year 3) 3.28 109 year 4) 4.32 108 year 42. During electrolysis of H2SO4 (aq) with high charge density, H2S2O8 formed as by product. In such electrolysis 22.4 L H 2(g) and 8.4L O2(g) liberated at 1 atm and 273 K at electrode. The moles of H2S2O8 formed is 1) 0.25 2) 0.50 3) 0.75 4) 1.00
43. Zn( s ) | Zn(CN ) 24 (0.5M ), CN (0.01) | | Cu ( NH 3 ) 42 (0.5M ), NH 3 (1M ) | Cu ( s) 2 16 2 12 Given K f of Zn(CN )4 10 , K f of Cu ( NH 3 ) 4 10 , 0 EZn 0.76V ; Ecu0 2 / Cu 0.34V , / Zn 2
2.303RT 0.06 F
The emf of above cell is 1) 1.22V 2) 1.10V
3) 0.98V
4) None of the these
44. Density of Li atom is 0.53g/cm3. The edge length of Li is 3.5Å. Find out the number of Li atoms in a unit cell. ( N A 6.0 1023 mol 1 , M 6.94 g mol 1 ) 1) 1 2) 2 3) 3 4) 4 45. If edge fraction unoccupied in ideal anti-fluorite structure is x. Calculate the value of Z. Where Z 1) 1
x 0.097
2) 4
3) 2
4) 3
3) 0, 0, 0, 15
4)
46. Magnetic moment of complexes i) [Ni(CN)3 (H2O)3]1ii) [Co(H2O)3 F3]0 iii) [Fe(CN)3(H2O)3]1iv) [Cr(CN)3 (H2O)3]0 are respectively (in B.M units) 1)
8, 0, 0, 15
2) 0, 24, 24, 0
8, 24, 0, 15
47. Total possible geometrical isomers and optically active complexes respectively for [M(NH3)2 (py)2 (NO2)2] 1) 5, 2 2) 6, 3 3) 4, 2 4) 6, 4 48. Which of the following is incorrectly matched ? Name of the process Use A) cyanide process extraction of Ag, Au B) thermite process extraction of Al C) mond’s process extraction of Ni D) baeyer’s process leaching of red bauxite 1) A 2) B 3) C
4) D
49. For reactions of metals to form their oxides one gram mole O 2 molecule is used may be plotted graphically against temperature. CO CO2 C CO2
X G in kJ / mol
C CO 710° C
T
Select incorrect using given Ellingham diagram (given above) 1) At 710C 2CO( g ) O2 ( g ) 2CO2 ( g ). G 0 x kJ / mol 2) At 710C C ( s ) O2 ( g ) CO2 ( g ). G 0 x kJ / mol 3) At 710C 2C ( s ) O2 ( g ) 2CO( g ); G 0 x kJ / mol 4) At 710C CO2 ( g ) C ( s ) 2CO( g ); G 0 x kJ / mol 50. Green solution is not obtained when 1) Cr2(SO4)3 is treated with excess of KOH(aq.) 2) standing the solution of K2Cr2O7 with H2SO4 and H2O2 3) K2Cr2O7 is treated with H2SO3 4) chrome alum is treated with excess of NH3(aq) 51. Starch-iodate test of SO2 gas is based on 1) acidic nature of SO2 2) reducing nature of SO2 3) oxidizing nature of SO2 4) bleaching nature of SO2 52. Cyanogen (C2N2) gas is produced when excess of KCN reacts with aq. Solution of 1) CdSO4 2) CuSO4 3) AgNO3 4) Fe2(SO4)3 53. When CS2 layer containing both Br2 and I2 is shaken with excess of Cl2 water, the violet colour due to I2 disappears and orange colour due to Br2 appears. The disappearance of violet colour is due to the formation of 1) I 3 2) HIO3 3) ICl3 4) I54. In which of the following option product gas X and Y (other than water vapour ) are same ? 1) Mg 2C3 H 2O X ; Al4C3 H 2O Y X ; ( NH 4 ) 2 Cr 2O7 Y 2) NH 4 NO 3 NaOH ( aq.) X ; NaNO3 Al / NaOH ( aq.) Y 3) NH 4Cl 4) Zn dil.HNO3 X ; Ag dil.HNO3 Y
55. In the following sub questions, choose the correct answer from among the following possibilities and select correct code of your answers (answer of 1,2,3 and 4 respectively) 1) the most stable electrovalent halide (1) GeCl2 (2) SnCl2 (3) PbCl2 2) A non existing halide (1) SnCl4 (2) SnO2 (3) SiO2 3) A purely acidic oxide (1) PbO2 (2) SnO2 (3) SiO2 4) thermally most stable hydride (1) NH3 (2) PH3 (3)AsH3 1) 3,2,1,3 2) 1,3,3,1 3) 3,3,3,1 4) 1,1,1,3 56. Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of 1) NO 2) NO2 3) N2O 4) N2O4 57. Which of following compounds give paramagnetic gas on decomposition ? I) Pb(NO3)2 II) LiNO3 III) NaNO3 IV) NH4NO2 1) I, II, III 2) II, III 3) I, II 4) III, Iv 58. PCl5 is formed when A) white phosphorus reacts with limited dry chlorine B) white phosphorus reacts with excess of dry chlorine C) white phosphorus reacts with excess of SOCl2 D) white phosphorus reacts with excess of SO2Cl2 1) BD 2) AB 3) ABC 4) AC 59. How many of the following are homopolymers nylon-6,6; PVC, Teflon, Bakelite, PMMA, Perlon-L, LDP, HDP, dextron, starch, cellulose 1) 5 2) 8 3) 7 4) 4 60. IUPAC name of Aspirin is 1) methyl salicylaldehyde 2)ethyl salicylate 3) O-methoxy benzoic acid 4) ethyl salicylaldehyde
MATHS
61. A and B are two sets defined by A = {(x, y); |x-3| < 1 and |y - 3| < 1} B = {(x, y); (x - 3)2 + (y - 3)2 2 } then 2) B A
1) B C
3) A B
4) A B A
62. S be the relation over the set of all real numbers R given by (a, b) S ab 0 then S is 1) symmetric only 2) reflexive only 3) symmetric and transitive only 4) equivalance 63. Domain of the function f ( x) [ x] 1 x where [ . ] denotes greatest integer function is 1) [1, ) 2) (0, 1) 3) {1} 4) (, 1] 64. Set of values of ‘a’ for which the function f : R R , given by f(x) = x3 + (a + 2) x2 + 3ax + 10 is one-one is given by 1) (,1] [4, ) 2) [1, 4] 3) [1, ) 4) (, 4]
x
n 2 tan(log(sec )) then area bounded by y = f(x) ; x = 0, x = 1 and 65. Let f ( x) lim x 0 n x-axis. is 1) 1/2 2) 1/3 3) 1/6 4) 2/3 e x [ x ] 1 , x0 66. If f ( x) x [ x] then 1 , x0 1) lim f ( x) exists 2) lim f ( x) f (0) x0
x 0
3) f(x) is continuous at x = 0
4) f(x) is discontinuous at x = 0
67. lim 2 x x a a
x 2 a
tan
1) e 2) ea 3) e1/ 4) e2/ 68. If e f ( x ) log e x and g(x) is inverse function of f(x), then g1(x) = 1) ee x 2) e x x 3) ee .e x 4) ee x
x
x
x
69. The set of all points where the function f ( x) 1 | x | is differentiable is 1) (0, )
2) (, )
3) (, 0)
4) (, 0) (0, )
sin( [ x ]) where [ . ] denotes greatest integer function then f(x) is 1 [ x]2 1) one-one function 2) discontinuous x R
70. Let f ( x)
3) continuous every where but not differentiable 4) differentiable x R 71. The curve y = f(x) satisfies f11(x) = 6x – 4 and f(x) has a local minimum value 5 when x = 1 then f(0) = 1) -1 2) 0 3) 5 4) 7
72. If f 11 ( x) 0 x R and h( x) f (sin 2 x) f (cos 2 x) then in the interval 0, h( x) is 4
1) increasing 2) decreasing 3) h1 ( x) does not exists 4) neither increasing nor decreasing 73. If the tangent at any point P on the curve x 2/3 y 2/3 4 meets the coordinate axes at A and B then the minimum value of OA+OB is 1) 4 2 2) 8 2 3) 2 4) 2 2 74. Two equal sides of an isosceles triangle with fixed base ‘b’ are decreasing at a rate of 3 cm/s. When the two equal sides are equal to base then the area of triangle is 1) decreasing at the rate 3b 2) decreasing at the rate b / 2 3) increasing at the rate 3b 4) decreasing at the rate b / 2 75. If Roll’s theorem holds for the function f ( x) 2 x3 ax 2 bx on the interval [-1, 1] at the point c 1
1 then (a, b) = 2
1
1) , 2 2) (-1, -2) 3) 2, 4) (2, -1) 2 2 76. The vector i xj 3k is rotated through an angle and is doubled in magnitude. If the new vector is 4 i (4 x 2) j 2k , the values of x are 2 4 4) , 2 3 3 77. a 2 i j 2k , b i 2 j and projection of r on a is 1 unit. If r a b then 9 r 1) 2 i j 7k 2) 6 i 3 j 3k 3) 2 i j 11k 4) 2 i j 7k
1) 1,-2
2) 2,
1 3
3) 2,
78. Let P (3, 2,6) is a point in the space and Q is any point on the line r i j 2k s (3i j 5k ) . The value of S for which PQ is parallel to the plane x – 4y + 3z = 1 1 8 79. In an equilateral triangle ABC with side length ‘a’ units AB.BC BC.CA CA. AB 3a 2 2 2 1) -a 2) a 3) 4) 2a2 2 80. A unit vector parallel to the line of intersection of the planes r .( i j k ) 5 and r .(2 i j 3k ) 4 is
1)
1 4
2)
2 i 5 j 3k 38
2)
1 4
2 i 5 j 3k 38 x 1 81. If is the angle between the line 1 1 2 x y z 4 0 and sin then 3 5 4 1) 2) 3 5
1)
3)
1 8
4)
2 i 5 j 3k 2 i 5 j 3k 4) 38 38 y 1 z 2 and the plane 2 2
3)
3)
3 5
4)
3 4
17 1 2 1 82. The largest value of k for which the equation sin x 16 x cos (k ) has 2 2
two distinct solutions is
1) 1 83.
e
2) 2 x
log x
2 1 x x 2
3) 3
4) 4
dx dx
log x c1 x c2 1) x 3) x log x e x c1 x c2
1 x x 4) e log x c1 x c2
2) e x log x c1 x c2
3
3 r 84. If (log x) dx x Ar (log x) B, then r 0
3
A r 0
r
1) 1 2) -2 3) -1 4) 2 2 85. Let f(x) = x + ax – b and the only solution of the equation f(x) = minimum of f(x) is x =0 and , are roots of f ( x) 0, x3 dx 1) 0
4 4 2) 2
a 4 b4 3) 2
4)
a 2 b2 4
86. If f is a continuous function on [0, a] satisfying f(x) f(a-x) = 1 and a > 0 then a
dx
1 f ( x) 0
1) 0 2) a 3) a/2 4) 2a 2 87. The area enclosed by the curve 3x + 5y = 32 and y = |x - 2| is 1) 13/2 2) 17/2 3) 23/2 4) 33/2 2 2 2 88. The area bounded by the curve y = x (1-x ) is 1) 1 2) 1/2 3) 4/3 4) 2/3 89. Let f(x) be differentiable on the interval (0, ) such that f (1) 1 and t 2 f ( x) x 2 f (t ) 1 then f(x) = t x tx 1 2 2 1 4 x 1) 2) x 2 3x 3 3x 3 lim
3)
1 2 x x2
4)
1 x
90. Let y = f(x) be the orthogonal trajectory of the family of curves x 2 – y2 = a2 , a R , such that y(1) = 1 then y(2) = 1) 2 2) 1 3) 0 4) 1/2
PAPER SETTERS : HYD–MDP-SARASWATHINARSINGI Subjects Name Phone VENU MATHEMATICS 9704305913 PHYSICS CHEMISTRY
SUDHAKAR SIR AVINASH SIR SUNITHA TANNIRU MADAM
9676006655 8142759039
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