iit model paper.pdf

7/26/2019 iit model paper.pdf

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Time:3 Hrs

Max Marks:36

IMPORTANT INSTRUCTIONS:

1. The test is of 3 hours duration.

2. The Test Booklet consists of 90 questions. The maximum marks are 360.

3. 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 correct response.

4. Candidates will be awarded marks as stated above in instruction No. 4 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.

5. There is only one correct response for each question. Filling up more than one

response in any question

will be treated as wrong response and marks for wrong response will be deducted

accordingly as per instruction 4 above.

PHYSICS

1. The diagram shows part of the vernier scale on a pair of calipers.

Which reading is correct?

1) 2.74 cm 2) 3.10cm 3) 3.26cm 4) 3.64cm

2. Two block 1 2M and M rest upon each other on an inclined plane. Coefficient of friction

between surfaces are shown. If the angle is slowly increased, and 1 2M M then

1) Block A slips first 2) Block B slips first

3) both slip simultaneously 4) both remain at rest


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3. Two blocks 1 2m and m are connected with a compressed spring and placed on a smooth

horizontal surface as shown in figure.

Force constant of spring is k. Under the influence of forces 1 2F and F at an instant

blocks move with common acceleration 0a . At that instant force 2F is suddenly

withdrawn. Mark correct option.

1) Instantaneous acceleration of 2m is1

0

1

Fa

m

2) Instantaneous acceleration of 22 02

Fm is a

m

3) Instantaneous acceleration of 1m is 1 0a

4) Instantaneous acceleration of 2 2 0m is a 4. In the figure shown the cart of mass 6 m is initially at rest. A particle of mass m is

attached to the end of the light rod which can rotate freely about A. If the rod is

released from rest in a horizontal position shown, determine the velocity relV of the

particle with respect to the cart when the rod is vertical. Assume friction less surface.

1) 73

gl 2) 76

gl 3) 143

gl 4) 83

gl

5. In the figure shown a particle P strikes the inclined fixed smooth plane horizontally

and rebounds vertically. If the angle is 060 , then the coefficient of restitution is:

1) 1/3 2) 1/ 3 3) 1/ 2 4) 1

6. A uniform horizontal rod of length l falls vertically from height h on two identicalblocks placed symmetrically below the rod as shown in figure. The coefficients of

restitution are 1 2e and e . The maximum height through which the centre of mass of the

rod will rise after bouncing off the blocks is

1) 1 2

h

e e 2)

2

1 2

4

e e h3)

2

1 2

2

e e h4) 2 21 2

4h

e e

7. The displacement of a particle is represented by the equation 3y sin t. The motion is

1) Non-periodic 2) Periodic but not simple harmonic


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3) Simple harmonic with period 2 / 4) Simple harmonic with period /

8. Two satellites 1 2S and S revolve around a planet in coplanar circular orbits in the same

sense. Their periods of revolution are 1 hour and 8 hours respectively. The radius of

the orbit of 1S is4

10 km . When 1S is closest to 2S , the angular speed of 2S as observed

by an astronaut in 1S is

1) /rad hr 2) / 3 /rad hr 3) 2 /rad hr 4) / 2 /rad hr

9. A source and an observer are situated on two perpendicular tracks as shown in the

figure. The observer is at rest and source is moving with a speed 50 m/s. The source

emits sound waves of frequency 90 Hz which travel in the medium with velocity 200

m/s. The frequency of sound heard by observer when the source crosses the origin O is

1) 84 Hz 2) 88 Hz 3) 92 Hz 4) 96 Hz10. Water waves produced by a motor boat sailing in water are

1) Neither longitudinal nor transverse

2) Both longitudinal and transverse

3) Only longitudinal

4) Only transverse

11. 1 mole of an ideal gas is contained in a cubical volume V, ABCDEFGH at 300 K in

figure. One face of the cube (EFGH) is made up of a material which totally absorbs

any gas molecule incident on it. At any given time

1) The pressure on EFGH would be zero2) The pressure on all the faces will be equal

3) The pressure of EFGH would be double the pressure on ABCD

4) The pressure on EFGH would be half that on ABCD.

12. Volume versus temperature graphs for a given mass of an ideal gas are shown in

figure at two different values of constant pressure. What can be inferred about relation

between 1 2P & P ?


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1) 1 2P P 2) 1 2P P 3) 1 2P P 4) data is insufficient

13. One mole of diatomic gas is being heated in a closed tank from 300K up to 1000 K.

During the process part of the molecules dissociate. At 1000 K the energy of thediatomic molecules are only half of that of the whole gas. By what factor has the gas

pressure increased /final initialP P ? (The oscillation of the molecules are not to be taken

in account.)1)

160

332)

16

113)

3

24)

2

3

14. A positively charged particle is released from rest in an uniform electric field. The

electric potential energy of the charge

1) Remains a constant because the electric field is uniform

2) Increases because the charge moves along the electric field

3) Decreases because the charge moves along the electric field

4) Decreases because the charge moves opposite to the electric field

15. Four capacitors and two sources of e.m.f. are connected as shown in the figure. Thep.d. in volts between the points a and b is :

1) zero 2) 13 3) 17 4) 27

16. A hollow conducting sphere of inner radius R and outer radius 2R has resistivity afunction of the distance r from the centre of the sphere: 2kr /R. The inner and

outer surfaces are painted with a perfectly conducting paint and a potential difference

V is applied between the two surfaces. Then, as r increases from R to 2R, theelectric field inside the sphere

1) increases 2) decreases

3) remains constant 4) passes through a maxima17. A galvanometer shows a reading of 0.65mA. When a galvanometer is shunted with a

4 resistance, the deflection is reduced to 0.13mA. If the resistance of 2 is further

connected parallel to 4 resistance (i.e galvanometer is further shunted with a 2 wire)the new reading will be (Assume main current remains the same)1) 0.60mA 2) 0.08mA 3) 0.12mA 4) 0.05Ma


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18. The resistance of a circular coil of 50 turns & 10cm diameter is 5 . What must be thepotential difference across the ends of the coil so as to nullify the horizontal

component of the earths magnetic field 5

HB 10 T at the centre of the coil? How

should the coil be placed to achieve this result?

1) 0.5V with plane of coil normal to the magnetic meridian2) 0.5V with plane of coil in the magnetic meridian

3) 0.25V with plane of coil normal to the magnetic meridian

4) 0.25V with plane of the coil in the magnetic meridian19. The figure shows a uniform conducting loop ABCDA placed in a uniform magnetic

field perpendicular to its plane. The part ABC is the (3/4)th portion of the square of

side length l. The part ADC is a circular arc of radius R. The points A and C are

connected to a battery which supply a current I to the circuit. The magnetic force on

the loop due to the field B is

1) zero 2) BIl 3) 2BIR 4) BI R

l R

20. In the circuit shown, the capacitor is initially charged with a 12V battery, when switch

1S is open and switch 2S is closed. 1S is then closed and, at the same time, 2S is

opened. The maximum value of current in the circuit is

1) 0.38mA 2) 0.84mA 3) 0.72mA 4) 0.1mA

21. In the figure, if LI =0.8A, CI =0.6A, then I=?(given currents are rms values)

1) 0.4A 2) 0.2A 3)1.0A 4)1.4A

22. An insect of negligible mass is sitting on a block of mass M, tied with a spring of force

constant K. The block performs simple harmonic motion with amplitude A in front of

a plane mirror placed as shown. The maximum speed of insect relative to its image

will be


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1) K

AM

2) A K

M23)

KA 2

M4)

MA

K

23. A ray of light incident at an angle on a refracting face of a prism emerges from theother face normally. If the angle of the prism is 05 and the prism is made of a material

of refractive index 1.5 the angle of incidence is

1) 07.5 2) 05 3) 015 4) 02.5

24. If light of wavelength of maximum intensity emitted from surface at temperature 1T is

used to cause photoelectric emission from a metallic surface, the maximum kinetic

energy of the emitted electron is 6 ev, which is 3 times the work function of the

metallic surface. If light of wavelength of maximum intensity emitted from a surface

at temperature 2 2 1T T 2T is used, the maximum kinetic energy of the photoelectrons

emitted is

1) 2eV 2) 4eV 3) 14eV 4) 18eV

25. An x-ray tube has three main controls.

(i) the target material (its atomic number z) (ii) the filament current f(I )and(iii) the acceleration voltage (V)

Figure shows a typical intensity distribution against wavelength. Which of the

following is incorrect?

1) The limit min is proportional to 1V

2) The sharp peak shifts to the right as Z in increased3) The penetrating power of X ray increases if V increased

4) The intensity everywhere increases if filament current fI is increased

26. Which of the following statement is correct in connection with hydrogen spectrum

1) The longest wavelength in the Balmer series is longer than the longest wavelength

in Lyman series

2) The shortest wavelength in the Balmer series is shorter than the shortest wavelengthin the Lyman series

3) The longest wavelength in both Balmer and Lyman series are equal

4) The longest wavelength in Balmer series is shorter than the longest wavelength inthe Lyman series.

27 The conductivity of a semiconductor increases with increase in temperature because1) Number density of free current carriers increases


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2) Relaxation time increases

3) Both number density of carriers and relaxation time increase

4) Number density of current carriers increases, relaxation time decreases but effect of

decrease in relaxation time is much less than increase in number density

28 A 220 V A.C supply is connected between points A and B as shown in figure. Whatwill be potential difference V across the capacitor?

1) 220 V 2) 110 v 3) 0 V 4) 220 2V

29 The output of the given circuit in figure

1) Would be zero at all times

2) Would be like a half wave rectifier with positive cycles output3) Would be like a half wave rectifier with negative cycles output

4) Would be like that of a full wave rectifier30. Three waves A, B and C of frequencies 1600 kHz, 5 MHz AND 60 MHz, respectively

are to be transmitted from one place to another. Which of the following is the most

appropriate mode of communication:1) A is transmitted via space wave while B and C are transmitted via sky wave

2) A is transmitted via ground wave, B via sky wave and C via space wave

3) B and C are transmitted via ground wave while A is transmitted via sky wave

4) B is transmitted via ground wave while A and C are transmitted via space wave.

CHEMISTRY

31. When dry chlorine is passed through silver chlorate heated to 90C then the oxide of

chlorine obtained is

1) 2ClO 2) 2Cl O 3) 3ClO 4) 2 7Cl O

32. With limited supply of 3 2,NH F gives:

1) 2N 2) 2 4N H 3) 3NF 4) 3HN

33. Relation between given pair is:

OH

Cl H

H

H Cl

H

OH1) Enantiomer 2) Diastereomers 3) Identical 4) Structural isomer

34. When sulphur dioxide is passed into acidified 2 2 7K Cr O solution, the oxidation state of

sulphur changes from:


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1) +4 to +6 2) +6 to +4 3) +4 to 0 4) +4 to +2

35. A gas obeys the equation of state P(Vb) = RT, where b is a constant. The slope of

an isochore will be

1)ve 2) zero 3) R

V b-4) R /P

36. Which reaction can be used to prepare phosphoric acid?

1)020

2 3 2

CP O H O 2)

080

2 3 2

CP O H O

3)025

2 3 2

CP O H O 4) 4 3.P conc HNO

37. The correct order of stability of the following carbanions is

CH3

CH3

O CH3

CH3

CH3

NH CH3

CH3

CH3

S CH3

P Q R

1) R>Q>P 2) R>P>Q 3)Q>P>R 4) P>Q>R

38. The figure depicts, the unit cell for a compound containing atoms A (filled circles) and

B (open circles). The empirical formula of the compound is

1) AB 3) AB2 3) A2B 4) A6B

39. The stability of dihalides of , ,Si Ge Sn and Pb increases steadily in the sequence:

1) 2 2 2 2GeX SiX SnX PbX 2) 2 2 2 2SiX GeX PbX SnX

3) 2 2 2 2SiX GeX SnX PbX 4) 2 2 2 2PbX SnX GeX SiX

40. The order of acidity of positions X, Y and Z isF

F

OH

NO2

x y

z

1) x>y>z 2) y>x>z 3) z>x>y 4) x>z>y

41. The correct Lewis acid order for boron halides is:

1) 3 3 3 3BF BCl BBr BI 2) 3 3 3 3BCl BF BBr BI

3) 3 3 3 3BI BBr BCl BF 4) 3 3 3 3BBr BCl BI BF

42. The correct relationship between the pH of equimolar solutions of (a)sodium oxide,(b)sodium sulphide, (c)sodium selenide and (d)sodium telluride is

1) a >b >c >d 2) a


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53. The order of SN1

reactivity of the following halides,

(i) (CH3)3C Br (ii) (C6H5)2CH Br

(iii) (C6H5)2C (CH3) Br (iv) (CH3)2 CH Br

1) iv > i > ii > iii 2) ii > i> iii > iv 3) i> iii > ii > iv 4) iii > ii > i> iv

54. Cleaning action of soap occurs because:1) non-polar tails of soap molecules dissolve in grease

2) oil and grease dissolved into hydrophilic centres of soap micelles acid washed away

3) hydrophilic head dissolve in grease

4) grease dissolve in soap solution

55. Which of the following reagents converts both acetaldehyde and acetone to alkanes?

1) 2/Ni H 2) 4LiAlH 3) 2/I NaOH 4) /Zn Hg con HCl

56. The freezing point of aq. Solution which contains 5% by mass urea (60), 1% by mass

KCl (74.5) and 10% by mass of glucose (180). 2

11.86f H Ok K molal

1) 290.2 K 2) 285.5 K 3) 269.32 K 4) 250 K57. Which will give positive isocyanide test

1)

CH3

CH3

NH2

2)

CH3 NH

CH3 3)

CH3

NH CH3 4)

CH3 N

CH3

CH3

58. An ester used as medicine is

1) ethyl acetate 2) methyl acetate 3) methyl salicylate 4) ethyl benzoate

59. If Ksp of certain silver salts are as follows: AgI III 2) II > III > I 3) III > II >I 4) III > I > II

60. Terylene is a condensation polymer of ethylene glycol and

1) benzoic acid 2) acetic acid

3)terephthalic acid 4) salicylic acid

MATHEMATICS

61. The median of the set of observations 1,3,5,7,11,13,17 is

1) 1 2) 7 3) 9 4) 17

62. If the complex numbers 1 2 3, ,z z z are such that1 3

2 3

1 3,

2

z z i

z z

then 1 2 3, ,z z z form

1) equilateral triangle 2) isosceles and right angled triangle

3) right angled triangle 4) collinear points

63. If a = 7, b = 8, c = 9, then the length of the line joining B to the midpoint of AC, is

1)5 2)8 3)7 4)10


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64. If 1, 1, 1x y z are in GP, then1 1 1

, ,1 ln 1 ln 1 lnx y z

are in

1)AP 2)HP 3)GP 4)AGP

65. If 1 1 2 0 0f x f x f x and f , then ,f n n sN i

1) 1nf 2) 1 n

f 3)0 4) 1f

66. If c a b and b c a , then

1)2

.a b c 2)2

.c a b 3) a b c 4)a b c

67. If the coefficient of x in the quadratic equation 2 0x px q was taken as 17 in placeof 13, its roots were found to be -2 and -15, then the roots of the original equation are

1)4, 9 2) 4, 9 3)3, 10 4) 3, 10

68. Number of irrational terms in the expansion of 15

2 3 are

1)9 2)7 3)16 4)10

69. If

2

2 ,

2

a b c d ab cd

A a b c d a b c d ab c d cd a b

ab cd ab c d cd a b abcd

then A is

1) Orthogonal matrix 2) Idempotent matrix

3) Non-singular 4) Singular

70. 2 2 2 2 2 20, , , 2If x y z x cy bz y az cx and z bx ay then a b c abc

1)2 2) a b c 3)1 4)ab bc ca

71. Let 1,2,3A and 1,1 , 1,3 , 3,1 , 2,2 , 2 ,3,1 , 3R then the relation R on A, is

1)reflexive 2)symmetric 3)transitive 4)equivalence

72. The number of integral solutions to the system of equations

1 2 3 4 5 1 220 15 0kx x x x x and x x when x is

1)300 2)350 3)336 4)316


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73. A and B alternately throw a pair of symmetrical dice. A wins if he throws 6 before B

throws 7 and B wins if he throws 7 before A throws 6. If A begins the game, the

Probability of his winning is

1)11

362)

30

613)

31

614)

1

36

74. The range of a random variable X is {1, 2, 3, 4, ....} and the probabilities are given

by 3

; 1, 2,3, 4......,CK

X K KK

P

then the value of C is

1) log 3e 2) log 2e 3) 3log log 2e 4) 2log log 3e

75.3 3.5 3.5.7

....6 6.9 6.9.12

1)3 3 2)4

3 33

3) 3 3 4 4) 2 3

76. The slope of the straight line which is both tangent and normal to the curve3 2

4 27x y is

1) 1 2)1

2 3)

1

2 4) 2

77.3

32

1lim

1

n

nr

r

r

1)1 2)1

23)

3

24)2

78. maximum , ,Let f x x x x x where [x] is the greatest integer less than or equal

to x. Then 2

2

f x dx

1)1 2)3 3)5 4)7

79.1

1

sinn

n r

rLt

n n

is

1)1 2)3 3)4 4)2


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80. Letg(x) be the inverse of the functionf(x) and 1 31

1f x

x

. Then 1g x

1)

3

1

1 g x

2)

3

1

1 f x

3) 3

1 g x 4) 3

1 f x

81. 1/2

1 2 tan tan secx x x dx

1) logsec sec tanx x x C 2) log sec sec tanco x x x C

3) log sec sec tanx x x C 4) log sec tanx x C

82. If x denotes the greatest integer less than or equal to x, then0

2x

dxe

is equal to

1) log 2e 2)2

e 3)0 4)2

e

83. 1

sin , 0

0 , 0

px x

Let f x x

x

Then f(x) is continuous but not differentiable at x = 0, if

1) 0p 2) 0p 3) 0 1p 4) 1p

84. The range of values of ' 'a such that the angle between the pair of tangents drawnfrom ,0a to the circle 2 2 1x y satisfies

2

, is

1) 1,2 2) 1, 2 3) 2, 1 4) 2, 1 1, 2

85. If , are the eccentric angles of the ends of a focal chord of the ellipse2 2

2 21

x y

a b ,

then the eccentricity of the ellipse is

1)

sin sin

sin

2)

sin sin

sin

3)

cos

cos

cos

4)

cos

cos

cos

86. An ellipse has eccentricity1

2and one focus at

1,1

2S

. If one directrix is the common

tangent, (nearer to S) to the circle 2 2 1x y and 2 2 1x y . Then the equation of theellipse is

1) 2

219 12 1 1

3x y

2) 2

2112 9 1 1

3x y

3)

2

21

12 112 9

x

y

4)

2

213 4 1 12

x y 87. From a point T a tangent is drawn and it touches the parabola 2 16y x at 16,16P .

If S be the focus of the parabola, then TPS can be equal to


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1) 13

tan4

2) 11 1

tan2 4

3) 11

tan2

4)4

88. Area of the trapezium whose vertices lie on the parabola 2 4y x and its diagonals

pass through 1,0 and having length25

4 units each, is

1)75

4sq. units 2)

625

16sq. units 3)

25

4sq. units 4)

25

8sq. units

89. If 1 2,t t and 3t are distinct, and the points 3 31 1 1 2 2 2, 2 , ,2t at at t at at , 33 3 3,2t at at arecollinear, then 1 2 3t t t

1)0 2) 1 3)1 4)290. Consider the family of lines 15 3 2 3 4 0x y x y and

21 2 2 0x y x y , then the equation of a straight line that belongs to both the

families, is

1)25 62 86 0x y 2)62 25 86 0x y 3)25 62 86x y 4)5 2 7 0x y

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