20 Engg Test 2016

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INSTRUCTIONS FOR STUDENTS

1. Read each question carefully.

2. It is mandatory to use Blue/BlackBall Point Pen to darken the

appropriate circle in the answer sheet.

3. Mark should be dark and shouldcomplete fill the circle.

4. Rough work must be done on theQuestion Paper, no additional sheetwill be provided for this purpose.

5. Do not use white-fluid or any other rubbing material on answer sheet.No change in the answer oncemarked.

6. Student cannot use log tables andcalculators or any other material inthe examination hall.

7. Before attempting the question paper,student should ensure that the testpaper contains all pages and no page

is missing.8. Each correct answer carries four

marks. One mark will be deducted for each incorrect answer from the totalscore.

9. Before handing over the answer sheet to the invigilator, candidateshould check the particulars havebeen filled and marked correctly.

10. Immediately after the prescribedexamination time is over, the answer sheet to be returned to the invigilator.

11. Use of Calcu lator and other Electronic device is not permitted.

Time : 3 Hrs. M.M. : 360

[Test No. 20]

Engineering

Entrance Exam.

2016 H

O R I Z

O N TE S T S E R

I E

S

(Divisions of Horizon Study Circle Pvt. Ltd.)

Medical IIT-JEE Foundations| |HORIZON ACADEMY

R

Since 2003

Name.:

Test No.:

Subject Code.:

Date :

2

1

0

1 1

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Topics of The Test

Test No. 20

H 2 HORIZON ACADEMY :- B-3/41 A, YAMUNA VIHAR, WAZIRABAD ROAD, DELHI-53, (M) 9811139323, (O) 22922012

Maths 3 D Geometry

Physics

Chemistry

Thermodynamics

Isomerism and structures.

Test-20 (Objective) Horizon Test Series for Engineering-2016

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Space for Rough Work



Test No. 20

[PHYSICS]

1. Two non-reactive monoatomic ideal gases have theiratomic masses in the ratio 2 : 3. The ratio of their partialpressures, when enclosed in a vessel kept at a constanttemperature, is 4 : 3. The ratio of their densities is

(A) 1 : 4 (B) 1 : 2

(C) 6 : 9 (D) 8 : 9

2. Two rectangular blocks, having identical dimensions,can be arranged either in configuration I or inconfiguration II as shown in the figure. One of the

blocks has thermal conductivity and the other 2 .The temperature difference between the ends alongthe x-axis is the same in both the configurations. Ittakes 9 s to transport a certain amount of heat from thehot end to the cold end in the configuration I. The timeto transport the same amount of heat in theconfiguration II is

(A) 2.0 s (B) 3.0 s

(C) 4.5 s (D) 6.0 s3. A real gas behaves like an ideal gas if its

(A) pressure and temperature are both high

(B) pressure and temperature are both low

(C) pressure is high and temperature is low

(D) pressure is low and temperature is high

4. Calorie is defined as the amount of heat required toraise temperature of 1 g of water by 1°C and it is definedunder which of the following conditions ?

(A) From 14.5 °C to 15.5 °C at 760 mm of Hg(B) From 98.5 °C to 99.5 °C at 760 mm of Hg

(C) From 13.5 °C to 14.5 °C at 76 mm of Hg(D) From 3.5 °C to 4.5 °C at 76 mm of Hg

5. Variation of radiant energy emitted by sun, filamentof tungsten lamp and welding arc as a function of itswavelength is shown in figure.

Which of the following option is the correct match ?

(A) Sun-3T , tungsten filament- 1T , welding arc- 2T

(B) Sun-2,T tungsten filament-

1T , welding arc-

3T

(C) Sun-3,T tungsten filament-

2,T welding arc-

1T

(D) Sun-1

T , tungsten filament-2

T , welding arc-3

T

6. Two identical rods are connected between twocontainers. One of them is at 100°C containing waterand another is at 0°C containing ice. If rods areconnected in parallel then the rate of melting of ice is

1q g/s. If they are connected in series then the rate is

2q g/s. The ratio

2 1/q q is

(A) 2 (B) 4

(C) 1/2 (D) 1/4

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7. If liquefied oxygen at 1 atmospheric pressure is heatedfrom 50 K to 300 K by supplying heat at constant rate,the graph of temperature vs time will be

(A) (B)

(C) (D)

8. 2 kg of ice at –20°C is mixed with 5 kg of water at 20°Cin an insulating vessel having a negligible heatcapacity. Calculate the final mass of water remainingin the container. It is given that the specific heats ofwater and ice are 1 kcal/kg°C and 0.5 kcal/kg°C whilethe latent heat of fusion of ice is 80 kcal/kg

(A) 7 kg (B) 6 kg

(C) 4 kg (D) 2 kg

9. The PT diagram for an ideal gas is shown in the figure,where AC is an adiabatic process. Find thecorresponding PV diagram.

(A) (B)

(C) (D)

10. The graph, shown in the adjacent diagram, representsthe variation of temperature (T) of two bodies, x and yhaving same surface area, with time (t) due to theemission of radiation.

Find the correct relation between the emissivity andabsorptivity powers of the two bodies

(A) x yE E and x ya a

(B) x yE E and x ya a

(C) x yE E and x ya a

(D) x yE E

and x ya a

11. An ideal black-body at room temperature is throwninto a furnace. It is observed that

(A) initially it is the darkest body and at later timesthe brightest

(B) it is the darkest body at all times

(C) it cannot be distinguished at all times

(D) initially it is the darkest body and at later times itcannot be distinguished.

12. Three rods made of same material and having the samecross-section have been joined as shown in the figure.

Each rod is of the same length. The left and right endsare kept at 0°C and 90°C respectively. The temperatureof the junction of the three rods will be

(A) 45°C (B) 60°C

(C) 30°C (D) 20°C

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13. Starting with the same initial conditions, an ideal gas

expands from volume1

V to2

V in three different ways.

The work done by the gas is1W if the process is purely

isothermal,2

W if purely isobaric and3

W if purely

adiabatic. Then

(A)2 1 3

W W W (B)2 3 1

W W W

(C)1 2 3

W W W (D)1 3 2

W W W

14. An ideal gas is initially at temperatureT and volume

V . Its volume is increased by V due to an increase in

temperature T , pressure remaining constant. The

quantityV

V T

varies with temperature as

(A) (B)

(C) (D)

15. A monoatomic ideal gas, initially at temperature1

T ,

is enclosed in a cylinder fitted with a frictionlesspiston. The gas is allowed to expand adiabatically to

a temperature2

T by releasing the piston suddenly. If

1L and 2L are the lengths of the gas column before

and after expansion respectively, then1 2/T T is given

by

(A)

2/ 3

1

2

L

L

(B)1

2

L

L

(C)2

1

L

L (D)

2/ 3

2

1

L

L

16. A given quantity of an ideal gas is at pressure P andabsolute temperature ‘T’. The isothermal bulkmodulus of the gas is

(A)2

3P (B) P

(C)3

2P (D) 2P

17. One mole of a monoatomic gas is heated at a constantpressure of 1 atmosphere from 0 K to 100 K. If the gas

constant R = 8.32 J/mol K, the change in internal energyof the gas is approximately

(A) 2.3 J (B) 46 J

(C) 8.67×103 J (D) 1.25×103 J

18. A vessel contains 1 mole of O2 gas (molar mass 32) at

a temperature T . The pressure of the gas is P. Anidentical vessel containing one mole of He gas (relativemolar mass 4) at a temperature 2 T has a pressure of

(A) /8P (B) P

(C) 2P (D) 8P

19. The average translational kinetic energy and the rootmean square speed of molecules in a sample of oxygengas at 300 K are 6.21×10–21 J and 484 m/s respectively.The corresponding values at 600 K are nearly(assuming ideal gas behaviour)

(A) 12.42 × 10–21 J, 968 m/s

(B) 8.78 × 10–21 J, 684 m/s

(C) 6.21 × 10–21 J, 968 m/s

(D) 12.42 × 10–21 J, 684 m/s

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20. An ideal monoatomic gas is taken round the cycleABCDA as shown in the P-V diagram (see figure). Thework done during the cycle is

(A) PV (B) 2 PV

(C)2

PV (D) zero

21. The p diagram represents the thermodynamic

cycle of an engine, operating with an idealmonoatomic gas. The amount of heat, extracted from

the source in a single cycle is

(A) 0 04 p (B) 0 0 p

(C) 0 013

2 p

(D) 0 011

2 p

22. Helium gas goes through a cycle ABCDA (consistingof two isochoric and two isobaric lines) as shown infigure. Efficiency of this cycle is nearly (Assume thegas to be close to ideal gas )

(A) 9.1% (B) 10.5%

(C) 12.5% (D) 15.4%

23. Three perfect gases at absolute temperatures1 2,T T and

3T are mixed. The masses of molecules are 1 2,m m and

3m and the number of molecules are

1 2,n n and

3n respectively. Assuming no loss of energy, the final

temperature of the mixture is

(A) 1 2 3( )

3

T T T (B)1 1 2 2 3 3

1 2 3

n T n T n T

n n n

(C)

2 2 2

1 1 2 2 3 3

1 1 2 2 3 3

n T n T n T

n T n T n T

(D)

2 2 2 2 2 2

1 1 2 2 3 3

1 1 2 2 3 3

n T n T n T

n T n T n T

24. A thermally insulated vessel contains an ideal gas of

molecular mass M and ratio of specific heats . It is

moving with speed and is suddenly brought to rest.Assuming no heat is lost to the surroundings, itstemperature increases by

(A) 2( 1)

2( 1)K

R

(B)

2( 1)

2 M K

R

(C)2

2

M K

R

(D)

2( 1)

2K

R

25. A diatomic ideal gas is used in a Carnot engine as theworking substance. If during the adiabatic expansionpart of the cycle the volume of the gas increases from Vto 32 V, the efficiency of the engine is

(A) 0.25 (B) 0.5

(C) 0.75 (D) 0.99

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26. An insulated container of gas has two chambersseparated by an insulating partition. One of the

chambers has volume1

V and contains ideal gas at

pressure1P and temperature 1T . The other chamber

has volume2

V and contains ideal gas at pressure2

P

and temperature2T . If the partition is removed without

doing any work on the gas, the final equilibriumtemperature of the gas in the container will be

(A) 1 2 1 1 2 2

1 1 1 2 2 2

( )T T PV PV

PV T PV T

(B)

1 2 1 1 2 2

1 1 2 2 2 1

( )T T PV PV

PV T PV T

(C)1 1 1 2 2 2

1 1 2 2

PV T PV T

PV PV

(D)1 1 2 2 2 1

1 1 2 2

PV T PV T

PV PV

27. A system goes from A to B via two processes I and II as

shown in figure. If1

U and2

U are the changes in

internal energies in the processes I and II respectively,then

(A)2 1

U U

(B)2 2U U

(C) 1 2U U

(D) relation between1

U and2

U cannot be

determined

28. A Carnot engine takes 3×106 cal of heat from a reservoirat 627°C, and gives it to a sink at 27°C. The work doneby the engine is

(A) 4.2 × 106 J (B) 8.4 × 106 J

(C) 16.8 ×106 J (D) zero

29. 1 mole of a gas with 7 /5 is mixed with 1 mole of a

gas with 5/3 , then the value of for the resultingmixture is

(A) 7/5 (B) 2/5

(C) 24/16 (D) 12/7

30. Cooking gas containers are kept in a lorry moving withuniform speed. The temperature of the gas moleculesinside will

(A) increase

(B) decrease

(C) remain same

(D) decrease for some, while increase for others.

[CHEMISTRY]

31. The maximum number of isomers (includingstereoisomers) that are possible on monochlorinationof the following compound, is

(A) 2 (B) 4

(C) 6 (D) 832. The maximum number of possible optical isomers in

1-bromo-2-methyl cyclobutane is

(A) 4 (B) 2

(C) 8 (D) 16

33. Angle strain in cyclopropane is

(A) 24°44’ (B) 9°44’

(C) 44’ (D) –5°16’

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34. Which of the following is the correct order of priorityof groups in D-glyceraldehyde ?

(A) OH (1), CHO (2), CH2OH (3) and H (4)

(B) OH (1), CH2OH (2), CHO (3) and H (4)

(C) CH2OH (1), CHO (2), OH (3) and H (4)

(D) CHO (1), OH (2), CH2OH (3) and H (4)

35. The number of stereoisomers possible for a compoundof the molecular formula

3( ) MeCH CH CH CH OH is

(A) 3 (B) 2

(C) 4 (D) 6

36. Racemic compound has

(A) equimolar mixture of enantiomers

(B) 1 : 1 mixture of enantiomer and diastereomer

(C) 1 : 1 mixture of diastereomers

(D) 1 : 2 mixture of enantiomers

37. What is the structural formula of fumaric acid ?

(A)

(B)

(C)

(D)

38. The absolute configuration of the following

(A) 2 ,3S R (B) 2 ,3S S

(C) 2 ,3R S (D) 2 ,3R R

39. Which of the following compound (s) has ‘Z’configuration ?

(A) (i) only (B) (ii) only

(C) (iii) only (D) (i) and (iii)

40. Which of the following does not exhibit tautomerism?

(A) (B)

(C) (D)

41. Which one of the following compound will showoptical isomerism ?

(A)3 2

( )CH 2CH CH 3CH

(B)3

CH CHOH 3

CH

(C)3

CH 2

CHCl CH 3

CH

(D)3

CH 2

CCl2

CH 3

CH

42. In this reaction,

3 3( )CH CHO HCN CH CH OH CN

H OH3

( )CH CH OH COOH

an asymmetric centre is generated. The acid obtainedwould be

(A) 50% D + 50% L-isomer

(B) 20% D+80% L-isomer

(C) D-isomer

(D) L-isomer

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43. Metamers of ethyl propionate are

(A) C4H

9COOH and HCOOC

4H

9

(B) C4H

9COOH and CH

3COOC

3H

7

(C) CH3COOCH

3 and CH

3COOC

3H

7

(D) CH3COOC

3H

7 and C

3H

7COOCH

3

44. Which of the following compounds is optically active?

(A) (CH3)2CHCH2OH(B) CH

3CH

2OH

(C) CCl2F

2

(D) CH3CHOHC

2H

5

45. Identify, which of the below does not possess anyelement of symmetry ?

(A) (+) (–) tartaric acid

(B) Carbon tetrachloride

(C) Methane

(D) Meso-tartaric acid

46. One of the following compounds exhibit geometricalisomerism

(A) 3 2 2 3CH CH CH CH

(B)3

CH 3

( )HC CH 3

( )H C CH 3

CH

(C)3

CH 3

( )HC CH 3

CH

(D)3CH CH CH 3CH

47. Increasing order of stability among the three mainconformations (i.e., Eclipse, Anti, Gauche) of2-fluoroethanol is

(A) Eclipse, Gauche, Anti(B) Gauche, Eclipse, Anti

(C) Eclipse, Anti, Gauche

(D) Anti, Gauche, Eclipse

48. Which of the following is a pair of functional isomers?

(A) CH3COCH

3, CH

3CHO

(B) C2H

5CO

2H, CH

3CO

2CH

3

(C) C2H

5CO

2H, CHCO

2C

2H

5

(D) CH3CO

2H, CH

3CHO

49. Nitroethane can exhibit one of the following kind ofisomerism

(A) metamerism (B) optical activity

(C) tautomerism (D) position isomerism

50.

C2 is rotated anticlockwise 120°C about

2C

3C bond.

The resulting conformer is

(A) partially eclipsed(B) eclipsed

(C) gauche (D) staggered

51. The number of isomeric alkenes with molecularformula C

6H

12 are

(A) 8 (B) 10(C) 11 (D) 13

52. Ethyl acetoacetate shows, which type of isomerism?

(A) Chain (B) Optical

(C) Metamerism (D) Tautomerism

53. Which of the following compounds exhibitstereoisomerism ?

(A) 3-methyl butyne-1

(B) 2-methyl butene-1

(C) 2-methyl butanoic acid

(D) 3-methyl butanoic acid

54. Tautomerism is not exhibited by

(A) (B)

(C) (D)

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55. The total number of acyclic isomers including thestereoisomers with the molecular formula C

4H

7Cl

(A) 11 (B) 12

(C) 9 (D) 10

56. Ethylene dichloride and ethylidine chloride areisomeric compounds. The false statement about theseisomers is that they.

(A) react with alcoholic potash and give the sameproduct

(B) are position isomers

(C) contain the same percentage of chlorine

(D) are both hydrolysed to the same product

57. The number of isomeric hexanes is

(A) 5 (B) 2

(C) 3 (D) 4

58. Cis-trans isomers generally(A) contain an asymmetric carbon atom

(B) rotate the plane of polarized light

(C) are enantiomorphs

(D) contain double bonded carbon atoms

59. The optical isomers, which are not enantiomers, arecalled

(A) conformer (B) diastereomer

(C) mirror images (D) None of these

60. The (R) and (S) enantiomers of an optically activecompound differ in

(A) their reactivity

(B) their optical rotation of plane polarised light

(C) their melting point

(D) their solubility in achiral reagents

[MATHEMATICS]

61. Perpendiculars are drawn from points on the line

12

2 1 3

yx z

to the plane 3.x y z The feet of

perpendiculars lie on the line

(A)

1 2

5 8 13

yx z

(B)

1 2

2 3 5

yx z

(C)1 2

4 3 7

yx z

(D)

1 2

2 7 5

yx z

62. The equation of a plane passing through the line of

intersection of the planes 2 3 2x y z and

3x y z and at a distance2

3from the point

(3,1,–1) is

(A) 5 11 17x y z (B) 2 3 2 1x y

(C) 3x y z (D) 2 1 2x y

63. If the distance of the point (1, 2,1)P from the plane

2 2 ,x y z where 0, is 5, then the foot of the

perpendicular from P to the plane is

(A)8 4 7

, ,3 3 3

(B)

4 4 1, ,

3 3 3

(C)1 2 10

, ,3 3 3

(D)2 1 5

, ,3 3 3

64. Equation of the plane containing the straight line

2 3 4

yx z and perpendicular to the plane containing

the straight lines3 4 2

yx z and

4 2 3

yx z is

(A) 2 2 0x y z (B) 3 2 2 0x y z

(C) 2 0x y z (D) 5 2 4 0x y z

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65. The edges of a parallelopiped are of unit length and

are parallel to non-coplanar unit vectors ˆˆ ˆ, ,a b c

1ˆ ˆˆ ˆ ˆ ˆ2

a b b c a a

Then, the volume of the parallelopiped is

(A)

1

2 (B)

1

2 2

(C)3

2(D)

1

3

66. A plane which is perpendicular to two planes

2 2 0x y z and 2 4,x y z passes through

(1, 2 ,1) . The distance of the plane from the point

(1,2,2) is(A) 0 (B) 1

(C) 2 (D) 2 2

67. A variable plane at a distance of 1 unit from the origincuts the co-ordinate axes at A, B and C . If the centroid

( , , )D x y z of triangle ABC satisfies the relation

2 2 2

1 1 1,k

x y z then the value of k is

(A) 9 (B)1

3

(C) 1 (D) 3

68. The number of all possible triplets1 2 3

( , , )a a a such that

2

1 2 3cos(2 ) sin 0a a x a x x

is(A) zero (B) one(C) three (D) infinite

69. The image of the line31 4

3 1 5

yx z

in the plane

2 3 0x y z is the line

(A)53 2

3 1 5

yx z

(B)53 2

3 1 5

yx z

(C)53 2

3 1 5

yx z

(D)53 2

3 1 5

yx z

70. Distance between two parallel planes 2 2 8x y z

and 4 2 4 5 0x y z

is

(A)5

2(B)

7

2

(C)9

2(D)

3

2

71. An equation of a plane parallel to the plane

2 2 5 0x y z and at a unit distance from the

origin is

(A) 2 2 1 0x y z

(B) 2 2 5 0x y z

(C) 2 2 3 0x y z

(D) 2 2 1 0x y z

72. If the lines11 1

2 3 4

yx z and

3

1 2 1

y kx z

intersect, then k is equal to

(A) 9/2 (B) 0(C) –1 (D) 2/9

73. If the angle between the line1 3

2

y zx

and the

plane 2 3 4x y z is1 5cos

14

then equals

(A) 2/5 (B) 5/3(C) 2/3 (D) 3/2

74. A line AB in three-dimensional space makes angles45° and 120° with the positive x-axis and the positive

y-axis respectively. If AB makes an acute angle with

the positive z-axis, then equals

(A) 30° (B) 45°(C) 60° (D) 75°

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75. Let the line12 2

3 5 2

yx z

lie in the plane

3 0.x y z Then ( , ) equals

(A) (–6, 7) (B) (5, –15)

(C) (–5, 5) (D) (6, –17)

76. The projections of a vector on the three coordinate axisare 6, –3, 2 respectively. The direction cosines of thevector are

(A)6 3 2

, ,5 5 5

(B)

6 3 2, ,

7 7 7

(C)6 3 2

, ,7 7 7

(D) 6, 3,2

77. The line passing through the points (5, 1, a) and

(3, b, 1) crosses the yz-plane at the point17 13

0, ,

2 2

.

Then

(A) 8, 2a b (B) 2, 8a b

(C) 4, 6a b (D) 6, 4a b

78. Let L be the line of intersection of the planes

2 3 1x y z and 3 2 2.x y z If L makes an angle

with the positive x-axis, then cos equals

(A) 1 (B)1

2

(C)1

3(D)

1

2

79. If (2, 3, 5) is one end of a diameter of the sphere2 2 2 6 12 2 20 0,x y z x y z then the

coordinates of the other end of the diameter are

(A) (4, 3, 5) (B) (4, 3, –3)

(C) (4, 9, –3) (D) (4, –3, 3)

80. If a line makes an angle of /4 with the positive

directions of each of x-axis and y-axis, then the anglethat the line makes with the positive direction of thez-axis is

(A)4

(B)

2

(C)6

(D)

3

81. T he t wo lines ,x ay b z cy d and

,x a y b z c y d are perpendicular to each other

if

(A) 1aa cc (B) 1aa cc

(C) 1a c

a c

(D) 1a c

a c

82. The angle between the lines 2 3x y z and

6 4x y z is

(A) 90° (B) 0°

(C) 30° (D) 45°

83. If the angle between the line11 2

1 2 2

yx z

and the plane 2 4 0x y z is such that

1sin ,3

the value of is

(A)3

5 (B)

5

3

(C)4

3

(D)

3

4

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84. The distance between the line

ˆ ˆˆ ˆ ˆ ˆ2 2 3 ( 4 )r i j k i j k

and the plane

ˆˆ ˆ( 5 ) 5r i j k

is

(A)10

3 3(B)

10

9

(C)10

3(D)

3

10

85. If the plane 2 3 4 6 0ax ay az passes through

the midpoint of the line joining the centres

of the spheres 2 2 2 6 8 2 13x y z x y z and

2 2 2 10 4 2 8x y z x y z then a equals

(A) 1 (B) –1

(C) 2 (D) –2

86. A line with direction cosines proportional to 2, 1, 2

meets each of the linesx y a z

and2 2 .x a y z The co-ordinates of each of the points

of intersection are given by

(A) (3 ,2 ,3 ),( , ,2 )a a a a a a

(B) (3 ,2 ,3 ),( , , )a a a a a a

(C) (3 ,3 ,3 ),( , , )a a a a a a

(D) (2 ,3 ,3 ),(2 , , )a a a a a a

87. A line makes the same angle , with each of the x and

z axis. If the angle , which it makes with y-axis, is

such that 2 2sin 3sin , then2cos equals

(A) 3/5 (B) 1/5

(C) 2/3 (D) 2/5

88. The Lines32 4

1 1

yx z

k

and

41 5

2 1

yx z

k

are coplanar if

(A) k = 1 or –1 (B) k = 0 or –3

(C) k = 3 or –3 (D) k = 0 or –1

89. A tetrahedron has vertices at O (0, 0, 0), A (1, 2, 1),B (2, 1, 3) and C (–1, 1, 2). Then the angle between thefaces OAB and ABC will be

(A) 1cos (17/31) (B) 30

(C) 90 (D)1cos (19/35)

90. Two systems of rectangular axes have the same origin.

If a plane cuts them at distance , ,a b c and , ,a b c

from the origin, then

(A) 2 2 2 2 2 21 1 1 1 1 1

0a b c a b c

(B) 2 2 2 2 2 21 1 1 1 1 1

0a b c a b c

(C) 2 2 2 2 2 21 1 1 1 1 1

0a b c a b c

(D) 2 2 2 2 2 21 1 1 1 1 1

0a b c a b c

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20 Engg Test 2016