10-01-15 jr.iit-z (iz) co-spark jee-main (2013) q'paper

NARAYANA IIT ACADEMYINDIA

Jr. IIT-IZ3-SPARK JEE MAIN Dt:10-01-15Time : 3:00 2013 model Marks : 360

IMPORTANT INSTRUCTIONS: 1. The test Booklet consists of 90 questions. The maximum marks are 360.2. 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 each correct response.

3. Candidates will be awarded marks as stated above in instruction No. 5 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.

4. 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 6 above.

PHYSICSPHYSICS

1) The length of a rectangular plate is measured by a meter scale and is found to be 10.0cm. Its breadth is measured by vernier calipers as 1.00 cm. The least count of the meter scale and vernier calipers are 0.1 cm and 0.01cm respectively. Maximum permissible error in area measurement is A) B) C) D) zero

2) A cylinder of radius R made of material of thermal conductivity k1 is surrounded by a cylindrical shell of inner radius R and outer radius 3R made of material of thermal conductivity k2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat from the curved surface and the system is in steady state. The effective thermal conductivity of the system is

A) B) C) D)

3) An experiment measures quantities x,y,z and then t is calculated from the data as

. If percentage errors in x, y and z are respectively 1%, 3%, 2%, then percentage

error in t is:A) 10% B) 4% C) 7% D) 13%

4) For a cubical block, error in measurement of sides is and error in measurement of mass is , then maximum possible error in density is A) 1% B) 5% C) 3% D) 7%

Narayana IIT Academy 10-01-15_Jr.IIT-IZ3-SPARK_JEE-Main 2013

5) A black body radiates power P and maximum energy is radiated by it around a wavelengtho. The temperature of the black body is now changed such that it radiates maximum energy around the wavelength 3o/4. The power radiated by it now is A) 256P/81 B) 16P/9 C) 64P/27 D) 4P/3

6) A student performs an experiment for determination of acceleration due to gravity

, and he commits an error of . For T he takes the time of n

oscillations with the stop watch of least count and he commits a human error of 0.1 sec. For which of the following data, the measurement of g will be most accurate?A) B) C) D)

7) To estimate ‘g’ (from ), error in measurement of L is and error in

measurement of T is . The error in estimated ‘g’ will be A) B) C) D)

8) The dimensions of a rectangular block measured with a vernier calipers having least count of 0.1 mm is 5 mm × 10 mm × 5 mm. The maximum percentage error in measurement of volume of the block is A) 5% B) 10% C) 15% D) 20%

9) Four rods of the same material with different lengths (L), radii (r) and temperature difference across their ends () are shown below: a) L = 50 cm, r = 2 cm, = 100oC b) L = 100 cm, r = 3 cm, = 60oC c) L = 80 cm, r = 4 cm, = 50oC d) L = 75 cm, r = 5 cm, = 80oC The decreasing order of the rates of heat conducted is A) d, c, a, b B) a, b, c, d C) d, c, b, a D) b, a, c, d

10) Two resistor and are joined in series. The equivalent resistance is (use equivalent resistance ).A) B) C) D)

11) A wire has a mass (0.3 0.003)g, radius (0.5 0.005) mm and length (6 0.06) cm. The maximum percentage error in the measurement of its density is A) 1% B) 2 % C) 3% D) 4%

12) A Carnot engine whose efficiency is 40% receives heat at 500K. If the efficiency is to be 50%, the source temperature for the same sink temperature is A) 900K B) 600K C) 700K D) 800K


13) Using screw gauge, the observation of the diameter of a wire are 1.324, 1.326, 1.334, 1.336 cm respectively. The percentage of error is.A) 0.1% B) 0.2% C) 0.3% D) 0.4%

14) A body of surface area 5 cm2 and temperature 727oC emits 300 J of energy per minute. Then its emissivity will be ( = 5.5510-8 Wm-2K-4)A) 1 B) 0.81 C) 0.18 D) 0.48

15) Under steady state, the temperature at a cross-section of a body conducting heat,A) decreases with timeB) increase with timeC) does not change with time and is same at all cross-sections of the bodyD) does not change with time and is different at different cross-sections of the body

16) During severe winter at the low temperature zones of the world, the superficial parts of the lakes are frozen, leaving water below. The freezing at the bottom is prevented becauseA) the conductivity of ice is lowB) the water has large latent heat of fusionC) the water has large specific heatD) both options 1 and 2 are correct

17) The cooling curves 1 and 2 of two liquids of same mass, specific heats S 1 and S2, same initial temperatures are cooled under identical conditions are as shown in the graph. Then the most appropriate option is

A) S1 = S2 B) S1 < S2 C) S1 > S2 D) S1 S2

18) The temperature of a black body corresponding to which it emits energy at the rate of 1 W/cm2 will be nearly ( = 5.710-8 Wm-2K-4)A) 350 K B) 1000 K C) 250 K D) 650 K

19) A tungsten filament lamp of power 625 W is at 2227oC. The emissivity of the filament


is 0.96. If = 610-8 Wm-2K-4, the surface area of the filament isA) 2.7810-4 m2 B) 16.6710-8 m2 C) 16.6710-4 m2 D) 2.7810-8 m2

20) A body cools from 60oC to 50oC in 12 minutes and from 50oC to 40oC in 24 minutes. What further time it would take to cool from 40oC to 38oC?A) 9.6 min B) 4.8 min C) 2.4 min D) 12 min

21) A 2 cm thick brass plate (K = 105 W/Km) is sealed to a glass sheet (K = 0.8 W/Km) and both have the same area. The exposed face of the brass plate is at 80oC, while exposed face of the glass is at 20oC. If the interface is at 65oC, the thickness of glass sheet is A) 0.46 mm B) 0.23 mm C) 0.92 mm D) 1.84 mm

22) If is efficiency of a Carnot engine and is coefficient of performance of a refrigerator, then which of the following is wrong?A) B) C) D)

23) If rate of loss of heat (dQ/dt) of the two bodies of different masses are same, then theA) their rates of fall of temperature (dT/dt) will be sameB) rate of fall of temperature of the body having large thermal capacity will be largeC) rate of fall of temperature of the body having large thermal capacity will be small D) The rate of fall of temperature depends only on ratio of masses of the bodies.

24) A black body radiates power P and maximum energy is radiated by it around a wavelengtho. The temperature of the black body is now changed such that it radiates maximum energy around the wavelength 3o/4. The power radiated by it now is A) 256P/81 B) 16P/9 C) 64P/27 D) 4P/3

25) A black body is at a temperature of 2880 K. The energy of radiation emitted by this object with wavelengths between 499 nm and 500 nm is u1, between 999 nm and 1000 nm is u2 and between 1499 nm and 1500 nm is u3. If the Wien’s constant b = 2.88106 nmK, then A) u1 = 0 B) u3 = 0 C) u1 > u2 D) u2 > u1

26) 2 litre water at 27°C is heated by a 1 kW heater in an open container. On an average heat is lost to surroundings at the rate 160 J/s. The time required for the temperature to reach 77°C is [specific heat of water = 4200J/kg°C] A) 8 min 20 sec B)10min C)7min D)14min

27) An ideal gas heat engine operates in carnot cycle between 2270 C and 1270 C. It absorbs 6.0 x 104 cal at higher temperature. The amount of heat converted into work is equal to A) 4.8 x 104 cal B) 3.5 x 104 cal C) 1.5 x 104 cal D) 1.2 x 104 cal

28) A Carnot engine operating between temperatures T1 and T2 has efficiency 1 /6. When the sink temperature (T2) is lowered by 62 K, its efficiency increases to 1 /3. Then T1 and T2 are respectively


A) 372K and 310 K B) 372K and 330 KC) 330K and 268 K D) 310K and 248 K

29) Two cubes of sides 2 cm and 3 cm made of same material are at same temperature. The ratio of amounts of heat radiated per second by them isA) 9 : 4 B) 8 : 27 C) 4 : 9 D) 27 : 8

30) Three metal rods of same length and same cross-sectional area are connected in parallel. If their conductivities are 30 Wm-1K-1, 90 Wm-1K-1 and 180 Wm-1K-1

respectively, the effective conductivity of the combination isA) 150 Wm-1K-1 B) 100 Wm-1K-1 C) 300 Wm-1K-1 D) 20/3 Wm-1K-1

CHEMISTRY

31. xA + yB zC. If = = 1.5 = then x,y and z are :

(A) 1,1,1 (B) 3,2,3 (C) 3,3,2 (D) 2,2,3

32. A reaction follows the given concentration (M)–time graph. The rate for this reaction at 20 seconds will be:

0 .5

0 .4

0 .3

0 .2

0 .1

0 2 0 4 0 6 0 8 0 1 0 0

T im e /s e c o nd(A) 4 10–3 M s–1 (B) 8 10–2 M s–1

(C) 2 10–2 M s–1 (D) 7 10–3 M s–1

33. aA + bB Product, dx/dt = k [A]a [B]b . If concentration of A is doubled, rate becomes four times. If concentration of B is made four times, rate is doubled. What is the relation between rate of disappearance of A and that of B ?(A) – {d [A] / dt} = – {d [B] / dt} (B) – {d [A] / dt} = – {4 d [B] /dt}(C) – {4 d [A] / dt} = – {d [B]/ dt} (D) None of these


34. For a first order reaction, the plot of log C against ‘t’ (logC vs 't') gives a straight line with slope equal to :(A) (k / 2.303) (B) (– k / 2.303) (C) (ln k / 2.303) (D) – k.

35. In presence of HCl, sucrose gets hydrolysed into glucose and fructose. The concentration of sucrose was found to reduce from 0.4 M to 0.2 M in 1 hour and to 0.1 M in a total of 2 hours. The order of the reaction is :(A) zero (B) one (C) two (D) None of these

36. In the first order reactions (A) Product, (B) Product, the ratio k1 /k2 if

90% of (A) has been reacted in time 't' while 99% of (B) has been reacted in time 2t is : (A) 1 (B) 2 (C) 1/2 (D) None of these

37. In the reaction,

The time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is

(A)2 (B) 3 (C) 0 (D) 1

38. The data for the reaction A + B C isExp. [A]0 [B]0 initial rate

1 0.012 0.035 0.102 0.024 0.035 0.803 0.012 0.070 0.104 0.024 0.070 0.80

(A) r = k [B]3 (B) r = k [A]3 (C) r = k [A] [B]4 (D) r = k [A]2 [B]2

39. In a gaseous state reaction, A2 (g) B(g) + (1/2)C (g), The increase in pressure

from 100 mm to 120 mm is noticed in 5 minutes. The rate of disappearance of A2 in

mm min–1 is:(A) 4 (B) 8 (C) 16 (D) 2

40. In the reaction NH4NO2 (aq.) N2 (g) + 2 H2O (l), the volume of N2 after 20 min

and after a long time are 40 ml and 70 ml respectively. The value of rate constant is :


(A) (1/20) In (7/4) min–1 (B) (2.303 /1200) log (7/3) sec–1

(C) (1/20) log (7/3) min–1 (D) (2.303 / 20) log (11/7) min–1

41. The activation energy of the reactionA + B + C + D + 38 k.cal is 20 k.cal, What would be the activation energy of the reaction,C + D + A + B(A) 20 k.cal (B) –20 k.cal (C) 18 k.cal (D) 58 k.cal

42. The first order rate constant k is related to temp. as log k = 15.0 – (106 /T) Which of the following pair of value is correct ?

(A) A = 1015 and E = 1.9 104 KJ (B) A = 10–15 and E = 40 KJ

(C) A = 1015 and E = 40 KJ (D) A = 10–15 and E = 1.9 104 KJ

43. For the reaction, A Products

a

1

xa

1

t

1k

A graph between (a–x)–1 and time ‘t’ is of the type

(A)

p

t

1)xa(

(B)

p

t

1)xa(

(C)

p

t

1)xa(

(D)

p

t

1)xa(

44. The reaction, X + 2Y + Z N occurs by the following mechanism(i) X + Y M very rapid equilibrium(ii) M + Z P slow(iii) O + Y N very fastWhat is the rate law for this reaction

(A) Rate = k[Z] (B) Rate = k[X] [Y]2 [Z] (C) Rate = [N] (D) Rate = k[X] [Y] [Z]

45. At a given temperature, k1 = k2 for the reaction A + B C + D.


If = k1 [A] [B] – k2[C] [D] in which set of the concentration reaction ceases?

[A] [B] [C] [D] [A] [B] [C] [D](A) 0.1 M 0.2 M 0.3 M 0.4 M (B) 0.4 M 0.25 M 0.2 M 0.5 M(C) 0.2 M 0.2 M 0.3 M 0.2 M (D) 0.2 M 0.2 M 0.4 M 0.2 M

46. A substance undergoes first order decomposition. The decomposition follows two parallel first order reactions as :

K1 = 1.26 10–4 sec–1 and K2 = 3.8 10–5 sec–1

The percentage distribution of B and C(A) 80% B and 20% C (B) 76.83% B and 23.17%C(C) 90% B and 10% C (D) 60% B and 40% C

47. The rate constant for two parallel reactions were found to be 1.0 10–2dm3 mol-1 s–1

and 3.0 10–2 dm3 mol–1 s–1. If the corresponding energies of activation of the

parallel reactions are 60.0 kJ mol–1 and 70.0 kJ mol–1 respectively, what is the apparent overall energy of activation ?

(A) 130.0 kJ mol–1 (B) 67.5 kJ mol–1

(C) 100.0 kJ mol–1 (D) 65.0 kJ mol–1

48. At the point of intersection of two curves as shown, the concentration of B is given for the reaction as


(A) (B) (C) (D)

49. The inversion of cane sugar proceeds with half life of 50 minute at pH = 5 for any concentration of sugar. However if pH = 6, the half life changes to 500 minute of any concentration of sugar . The rate law expression for sugar inversion can be written as :

(A) r = K [sugar]2 [H+]0 (B) r = K [sugar]1 [H+]0

(C) r = K [sugar]1 [H+]1 (D) r = K [sugar]0 [H+]0

50. Two I-order reactions have half-lives in the ratio 3 : 2. Calculate the ratio of time intervals t1 : t2. Where t1 is the time period for 25% completion of the first reaction and

t2, for 75% completion of the second reaction.

(A) 0.311 : 1 (B) 0.420 : 1 (C) 0.273 : 1 (D) 0.199 : 1

51. For the following parallel chain reaction

What will be that value of overall half-life of A in minutes?

(A) 3.3 (B) 6.3 (C) 3.6 (D) None

52. Decomposition of A follows first order kinetics by the following equation.4A(g) B(g) + 2C(g)


If initially, total pressure was 800 mm of Hg and after 10 minutes it is found to be 650 mm of Hg. What is half-life of A ? (Assume only A is present initially)(A) 10 mins (B) 5 mins (C) 7.5 mins (D) 15 mins

53. At least how many half-lives should elapse for a 1st order reaction A products so that the reaction is at least 95% completed ? (log 2 = 0.3)(A) 4 (B) 5 (C) 6 (D) 7

54. The reaction is an elementary process. In an experiment, the

initial pressure of A and B are atm and . When the rate of the reaction relative to the initial rate is(A) 1/48 (B) 1/24

(C) 9/16 (D)

55. A reaction takes place in three steps ; the rate constants are k1, k2 and k3.The overall

rate constant k = . If energies of activation are 40 , 30 and 20 kJ, the overall energy

of activation is (assuming ‘A’ to be constant for all )(A) 10 (B) 15 (C) 30 (D) 60

56. The rate of certain hypothetical reaction A + B + C products, is given, by r = – =

K [A]½ [B]1/3 [C]1/4. The order of reaction is given by - (A) 1 (B) 1/2 (C) 2 (D) 13/12

57. In a certain reaction, 10% of the reactant decomposes in one hour, 20 % in two hours, 30% in three hours and so on the dimensions of the rate constant is :

(A) hour–1 (B) mole litre–1 sec–1 (C) litre mole–1 sec–1 (D) mole sec–1

58. The rate of a chemical reaction doubles for every 10° C rise of temperature. If the temperature is raised by 50° C, the rate of the reaction increases by about :(A) 10 times (B) 24 times (C) 32 times (D) 64 times

59. The concentration of R in the reaction R → P was measured as a function of time and the following data is obtained:

[R] (molar)

1.0 0.75 0.40 0.10

T (min.) 0.0 0.05 0.12 0.18


The order of the reaction is(A)2 (B) 3 (C) 0 (D) 1

60. The polarimeter readings in an experiment to measure the rate of inversion of cane sugar were as followstime (min) : 0 30 angle (degree) : 30 20 – 15Identify the incorrect statement (log 2 = 0.3, log 3 = 0.48, log 7 = 0.84)

(A) The half life of the reaction is 82.7 min (B) The solution is optically inactive at 131 min. (C) The equimolar mixture of the products is dextrorotatory (D) The angle would be 7.5° at half time

MATHEMATICS

61. An investigator interviewed 100 students to determine their preferences for the three drinks milk(M), coffee(c), and tea(T). He reported the following : 10 students had all the three drinks M,C,T ; 20 had M and C only ; 30 had C and T ; 25 had M and T ; 12 had M only ;5 had C only ; 8 had T only . Find how many did not take any of the three drinksA) 20 B) 3 C) 36 D) 42

62. In a class of 100 students , 55 students have passed in Mathematics and 67 students have passed in physics . Then the number of students who have passed in physics only is A) 22 B) 33 C) 10 D) 45

63. Let W denotes the words in the English dictionary .Define the relation R by R ={(x,y) W x W:the words x and y have at least one letter in common }, then R is

A) reflexive, symmetric and transitive B) reflexive, not symmetric and transitiveC) not reflexive, symmetric and transitive D) reflexive, symmetric and not transitive

64. Let N denote the set of all natural numbers and R be the relation on N x N defined by (a,b) R (c,d) if ad (b+c)=bc(a+d), then R isA) symmetric only B) reflexive only


C) transitive only D) an equivalence relation

65. Let R be the real line . Consider the following subsets of the plane R x R :S={(x,y) : y=x+1 and 0<x<2} ; T={(x,y) : x-y is an integer }. Which one of the following is true?A) Both S and T are equivalence relations on R

B) S is an equivalence relation on R but T is not

C) T is an equivalence relation on R but S is not

D) Neither S nor T is an equivalence relation on R

66. Consider the following relations:

R = {(x,y) \ x,y are real numbers and x=wy for some rational number w};

integers such that n,q 0 and qm = pn }. Then

A) R is an equivalence relation but S is not an equivalence relation B) S is an equivalence relation but R is not an equivalence relation C) R and S both are equivalence relationsD) neither R nor S is an equivalence relation

67. The condition that has no extreme value is A) B) C) D)

68. Given such that x=0 is the only real root of If p(-1)<p(1), then in the interval [ -1,1]A) P(-1) is not minimum but p(1) is the maximum of pB) P(-1) ) is minimum but p(1) is not the maximum of pC) neither P(-1) is minimum nor p(1) is the maximum of pD) p(-1) is minimum and p(1) is the maximum of p

69. The shortest distance between the line and the curve is

A) B) C) D)

70. The greatest area of a right angled triangle of given perimeter is

A) B) C) D)


71. A Triangular park is enclosed on two sides by a fence and on the third side by a straight river Bank. The two sides having fence are of same length x. The maximum area enclosed by the Park is

A) B) C) D)

72. A cylindrical gas container is closed at the top and open at the bottom . If the Iron plate of the top is 5/4 times as thick as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same capacity isA) 4 B) 5 C) 4/5 D) 20

73. A cylindrical vessel of volume cubic meters which is open at the top is to be

manufactured from a sheet of metal . The dimensions of the vessel so that the amount of sheet used in manufacturing it is least areA) radius = height = 4 mts B) radius = height = 5 mtsC) radius = height = 2 mts D) radius = height = 3 mts

74. Let . Then for to be a decreasing function in R, possible

values of ‘a’ are given byA) B) C) [-2,2] D)none of these

75. Divide 20 into two parts such that the product of one part and the cube of the other is maximum , then two partsA) (10,10) B) (12,8) C) (15,5) D) none of these

76. If then the maximum value of is

A) B) C) D)

77. The minimum value of is

A) 1 B) 2 C) D) none of these

78. An isosceles triangle of vertical angle is inscribed in a circle of radius a. Then area of the triangle is maximum when

A) B) C) D)

79. The largest term in the sequence is

A) B) C) D)

80. The minimum value of is

A) 1/243 B) -5 C) 1/5 D) none of these


81. A bird is sitting on the top of a vertical pole 20m high and its elevation from a point O on the ground is . It flies horizontally straight away from the point O . After one second , the elevation of the bird from O is reduced to . Then the speed (in m/s) of the bird is A) B) C) D)

82. In a triangular plot ABC with BC = 7m, CA = 8m and AB = 9m. A lamp post is situated at the middle point E of the side AC and subtends as angle at the point B, the height of the lamp post is A) 21m B) 24m C) 27m D) Can’t be determine

83. A tower AB leans towards west making an angle with the vertical . The angular elevation of B, the top most point of the tower , is , as observed from a point C due east of A at a distance d from A. If the angular elevation of B from a point due east of C is at a distance 2d from C is , thenA) B) C) D) None

84. Three poles of heights at the vertices A,B and C of a ABC subtend angles respectively at the circumcentre of the triangle . If

are in A.P. then are in A) A.P. B) G.P. C)H.P. D)none of these

85. The angle of elevation of the top of a tower from a point A due south of it , is and that from B due west of it, is . If h is the height of the tower , then , where

A) B) C) D) none of these

86. A ladder leans against a wall at an angle to the horizontal . Its foot is pulled away through a distance so that it slides a distance down the wall and rests inclined at an angle with the horizontal. Its foot is further pulled away through so that it slides a further distance down the wall and is now inclined at an angle . If

, thenA) B) C) D) nothing can be said about the sum

87. AB is a vertical pole with B at the ground level and A at the top .A man finds that the angle of elevation of the point A from a certain point C on the ground is . He moves away from the pole along the line BC to a point D such that CD = 7m. From D the angle of elevation of the point A is . Then the height of the pole is


A) B) C) D)

88. A vertical pole subtends an angle at a point P on the ground . If the angles

subtended by the upper half and the lower half of the pole at P are respectively , then

A) B) C) D)

89. A tower stands at the center of a circular park . A and B are two points on the boundary of the park such that AB(=a) subtends an angle of at the foot of the tower , and the angle of elevation of the top of the tower from A or B is . The height of the tower is A) B) C) D)

90. ABCD is a trapezium such that AB and CD are parallel and BC CD. If ADB = , BC = p and CD = q, then AB is equal to

A) B)

C) D)

Paper Setters Info-hyd-mdp-vagdevi

Subject Paper Setters Mobile No.

MATHS V SRINIVASA RAO 7731031500

PHYSICS V N M PRASAD 9440263456

CHEMISTRY J MAHESH KUMAR 9393707007

10-01-15 jr.iit-z (iz) co-spark jee-main (2013) q'paper

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