iit model paper 3

8/20/2019 Iit Model Paper 3

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IMPORTANT INSTRUCTIONS

There are three parts in the question paper A, B, C consisting of Physics, Mathematics and

Chemistry 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 for correct response of each

question. 1/4 (one fourth) marks will be deducted for indicating incorrect response of eachquestion. 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

PHYSICS

1. Two long thin parallel wires and a square loop of side L are coplanar. The currents in the two wiresA and B are 2 A and 1 A and total flux through the loop is zero. Nearer side of the loop is at a

distance L from wire A. The separation between the wires is

A) L/3 B) L/2 C) 2L/3 D) 3L/4

2. Which of the following curves represent the speed of the electron in a hydrogen atom as a function of

the principal quantum number n ?

A) a B) b C) c D) d

3. Heat flows radially outward through a spherical shell of outside radius R2 and inner radius R1. The

temperature of inner surface of shell is q1 and that of outer is q2. The radial distance from centre of

shell where the temperature is just half way between q1 and q2 is :

A) 1 2R +R

2B) 1 2

1 2

R R

R +RC) 1 2

1 2

2R R

R +RD) R1 +

2

2

R


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4. Given X - ray spectrum is for a Coolidge tube having accelerating potential V. If accelerating

potential is decreased to4

V , then ( )cλ λ λ becomes four times with change in anode element

atomic no. from (neglect screening effect).

A) Z B) Z/2 C) 2Z D) Z/3

5. A rod AB of length L and mass M is free to move on a frictionless horizontal surface is moving with

a velocity v as shown in fig. End B of rod AB strikes end of wall. Assuming elastic impact, angular

velocity of rod AB just after impact is

A) v

2LB)

3v

LC)

3v

2LD)

v

L

6. A monatomic ideal gas sample is given heat Q. One half of this heat is used as work done by the gas

and rest is used for increasing its internal energy. The equation of process in terms of volume andtemperature is

A)2

3

V

T= constant B)

2V

T= constant

C) 3VT = constant D)2V T = constant

7. In the isolated long cylindrical region (shaded), having inner radius r and outer radius 2r, magnetic

field varies with time as B = a + b t, where a & b are positive constants and reference of time is

arbitrary. OPQ is a triangular loop made of wire having resistance per unit length and R is a pointon PQ.

Induced current in the loop is

A)

rb

2 3 3

B)

rb

4 3 3

C)

rb

6 3 3

D)

rb

8 3 3

8. Two moles of an ideal gas undergoes the process shown in figure. AB and CD are reversible

adiabatic process.


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Which of the following shows above process on V-T diagram?

A) B) C) D)

T

V

A

B

C

D

9. An undeformed spring of spring constant k is connected to a bead of mass m as shown in figure.

Bead can move along long rigid rod without friction. A particle of mass m moving with velocity v inthe vertical plane containing spring and rod strikes bead at an angle

045 with horizontal and sticks tobead. Choose correct alternative representing maximum elongation of spring is, all particles are in

same horizontal plane.

A) m

v

k

B)1

2

mv

k

C) 2 m

v

k

D

10. An engine whistling at a constant frequency 0n and moving with a constant velocity goes past a

stationary observer. As the engine crosses him, the frequency of the sound heard by him changes by

a factor f. The actual difference in the frequencies of sound heard by him before and after the engine

crosses him is

A) 0 21

12

n f B)0

21 1

2

f n

f

C)0

1

1

f n

f

D)0

1 1

2 1

f n

f

11. The potential energy in joule of a particle of mass 1 kg moving in X-Y plane obeys the law3 4 x y . Here x and y are in meters. If the particle is at rest at (6m, 8m) at time 0t , then the

work done by conservative force on the particle from initial position to the instant when it crosses theX – axis is

A) 50 J B) – 50 J C) 25 J D) – 25 J

12. A body of mass 0M

is placed on a smooth horizontal surface. The mass of body is decreasing

exponentially with disintegration constant λ . Assuming that the mass is ejected backward with a

relative velocity u , and initially the body was at rest, find the velocity of body after time t.(assume

the decay of mass is similar to that of natural radio activity)

A) λtue B) uλ t C) u ln 2 λ

tD)

e

ln 2u t

λt

13. Light of two different wavelengths 0 01 2λ = 4000 and λ = 6000 A A is incident on two identical slits

of YDSE as shown, the separation being 0.1 mm. A screen is kept at a distance of D. (Answer the

following question)


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O(Screen)

[O is equidistant from ]1 2

S and S

D = 2m

d = 0.1mm

1S 2S

B A

The ratio of intensities of individual wavelengths 1 2&λ λ at point P, which is 4 mm distant from O.

(on the screen along OA or OB).

A) Zero B) 4:1 C) Infinity D) 3:1

14. Three concentric wires of radii a, b and c respectively are arranged concentrically on a horizontalplane as shown in figure. The outer, inner wires are fixed and the space between inner and middle

wire is filled with a liquid of surface tension 2T . Space between middle and outer wires is filled with

a liquid of surface tension 1T . Tension in the middle wire is 1 2T T

A) 1 2( )T T T b B) 1 2( )T T T b C) 1 22( )T T T b D) 1 22( )T T T b 15. An object having uniform linear mass density is in equilibrium as shown in the diagram. The value

of / rl is

string

r

l

A) 1 B) 2 C) 3 D) 4

16. Two very long wires parallel to the z-axis and a distance 4a apart carry equal currents I in apposite

directions as shown in the figure. A cylinder of radius a and length L has its axis on the z-axis

midway between the wires. Calculate the net upward magnetic flux through half of the curved


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cylindrical surface above the xz plane.

2 , 0, 0a

2 , 0, 0a

z

L

y

A)0 IL

B)

0 ln3 IL

C)

0 ln 2 IL

D)

0

2

IL

17. What should be value of E for which galvanometer shows no deflection:

G20V

5

20

5

5

1010

5

10V E

O

10

O

A) 10V B) 5V C) 15V D) 20V

18. An ideal string is wrapped several times on a solid cylinder of mass 4 kg and radius 1 m. The pulleys

are ideal and the surface between block and ground is smooth. If the torque acting on the cylinder is

10x

9N-m, then find the value of x.

RF = 40 N

4 kgSolid cylinder

Block

Smooth

8 kg

A) 80/9 N B) 80/3 N C) 90/7 N D) 100/9 N

19. An electron is moving on a circular path around a stationary neutron under gravitational interaction.

Masses of the neutron and electron are M and m respectively. If Bohr’s quantum condition holds

here the minimum permissible de Broglie wavelength associated with the electron will be

A)

2

h2 GMm

B)

2

2h2 GMm

C)

2

2h2 GM m

D)

2

2h4 GM m

20. The energy of a particle executing SHM is given by E = Ax2

+ BV2

where x is displacement from

mean position and V is velocity. Then

A) time period of motion isA

2B

B) amplitude of SHM isE

2A

C) maximum velocity of particle during motion isE

B

D) dimension formula for 0 0 1A

is [M L T ]B


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21. Three sources of emf, V0sint, V0cost and V0 are connected in series as shown. RMS value of current in the circuit is

~ ~

R

V0V sin t0

V cos t0

A) 0V

R 2B) 0

V

RC) 0

V 2

RD) 0

2V

R

22. An equilateral prism produces a deviation of 60º. If prism is rotated in the plane of incident and

refracted ray by an angle 30º, deviation remains same. Possible values of angle of incidence are

A) 45º and 75º B) 15º and 45º C) 30º and 60º D) 35º and 80º

23. An ice cube is floating in water above which a layer of a lighter oil is poured. As the ice melts,

interface and the uppermost level of oil will respectively

Ice

Oil

Water

Interface

A) rise and fall B) fall and rise

C) not change and not change D) no change and fall

24. One end of a long cylindrical bar is kept at 0200 C and the other end is maintained at 040 C . In the

steady state the graph of temperature of bar against distance from hot end is shown here. From the

graph which of the following statements can be concluded incorrect?

Distance from hot end

T e m p e r a t u r e

A) The quantity of heat entering the hot end per second is equal to that leaving the other end per

second

B) The quantity of heat entering the hot end per second is greater than that reaching the other end persecond.

C) No heat is absorbed by any part of the bar

D) Heat is lost from the curved surface of the bar.

25. A hemispherical tank of diameter 4m is filled with water. A very small hole is punched at 1m above

bottom as shown. Centre of hemispherical tank is considered as origin, find x-co-ordinate, when

water strike the horizontal surface. (g = 10 m/s2)

C(0,0)

1m

xA) 3.4 m B) 2.2 m C) 2.8 m D) 1.7 m


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26. A block of mass m = 2kg is placed on a plank of mass M=10kg, which is placed on a smooth

horizontal plane. The coefficient of friction between the block and the plank is1

μ =3

. If a horizontal

force F is applied on the plank, then the maximum value of F for which the block and the plank

move together is 2g = 10m/s

mh

M F

h

4

A) 40 N B) 30 N C) 120 N D) 100 N

27. For a man walking horizontally with speed u, rain appears to hit him vertically down. When he

makes his speed ‘n’ times, rain appears to hit him making an angle to the ver tical. The original

speed of rain is

A)

2 2

u 1+ (n -1)cot θ B)

2 2

u 1+ (n -1)tan θ C)

2 2

u 1+ (n -1) tan θ D)

2 2

u 1+ (n -1) cot θ28. A glass hemisphere of refractive index 4/3 and of radius 4 cm is placed on a plane mirror. A point

object is placed at distance d on axis of this sphere as shown. If the final image is at infinity, the find

the value of d in cm.

A) 1 B) 3 C) 2 D) 4

29. The circuit shown in the figure consists of a battery of emf E, resistances R1 and R2, inductance L

and a two way switch ABC. First A is connected to B for a long time and then A is connected to C.

The total heat produced in R2 is

ABC

E R1

R2

L

A)

2

2

1

E L

RB)

2

2

22

LE

RC)

2

2

12

LE

RD)

2

1 22

LE

R R

30. A square loop of side l containing a resistance R, and a capacitance C is placed near an infinitely

long 0

0

ii t

t

current carrying wire as shown in figure. The current in the wire varies with time as

The charge stored in the capacitor at any time t equals


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1

1

1CRi

A) / 0 0

0

ln 2(1 )

2

t CRli C e

t

µ

π

B) / 0 00

ln 4(1 )

2

t CRli C e

t

µ

π

C) / 0 0

0

ln 4(1 )

4

t CRli C e

t

µ

π

D) Zero

MATHEMATICS

31. The number of different ways in which 8 persons can stand in a row so that between two particular

persons A and B there are always two persons is

A) 60 x 5! B) 15 x 51 x 5! C) 4! x 5! D) 15 x 5! x 4!

32. If the ratio of the roots of the equation x

2

+px+q=0 be equal to the ratio of the roots of x

2

+lx+m=0.Then

A) p2

m = q2

l B) pm2

= q2

l C) p2

l = q2

m D) p2

m = l2

q

33. If cos is a root of 25x2 + 5x – 12 = 0, (-1 < x < 0). Then a possible value of sin (2α) is

A)12

25B) -

12

25C) –

24

25D)

20

25

34. / 6

3sin 3 cos

6 x

x x Lt

xπ π

=

A) 3 B) 1/ 3 C) – 3 D) – 1/ 3

35. If : f , is a function such that f (1) = 2, f (2) = 6 and f (x + y) = f (x) + k xy – 2y2, for all, x y , then

A) f x = f (x) B) f x = 6 f (x) C) f x = 6 D) 8

3 f x x

36. If , are the roots of the quadratic equation 0)1a(x)2a(x2 , where ‘a’ is a variable then

the least value of 22 A) 3 B) 5 C) 7 D) 9

37. ( )1

dx log f x1 cos x sin x

e c= +

+ +ò then xf

A) 2

x

tan2 B) 2x

tan1 C) 2x

tan2 D) 2x

tan1

38. If a > 1,

dxbxcose

0

ax

A)22 ba

a

B)

22 ba

a

C)

22 ba

b

D)

22 ba

b

39. If

2x1if x

1x0if xxf

2

then dxxf 2

0

A) 3

124

B) 3

124

C) 1 D) 0

40. The change in y, when 2 2 y x x , x = 3 and δx = 0.01 isA) 3.6 B) 2 C) 0.08 D) 0.3

41. If x + 3y = 16 is the perpendicular bisector of AB and A = (5, 7) then B =


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A) (2, 1) B) (3, 1) C) (9, 1) D) (-2, - 3)

42. The equation of the bisector of the obtuse angle between the lines x – y+2 = 0,

7x+y+1 = 0 is

A) 2x – 6y + 9 =0 B) 8x – 4y + 11 = 0

C) 2x + 6y – 9 = 0 D) 8x + 4y – 11 = 0

43. Let A be the centre of the circle x2

+ y2

-2x – 4y – 20 = 0. The tangents at B (1, 7) and D (4, -2) on

the circle meet at the point C. The area of the quadrilateral ABCD is

A) 8 sq.unit B) 16 sq.unit C) 24 sq.unit D) 75 sq.unit44. The point on the curve, y2

= 2x, the tangent at which makes an angle of 45° with

x-axis will be given by

A) (2, 4) B) (1/2, 1/2) C) (1/2, 1) D) (1/4, 1/2)

45. The equation to the common tangent of y2

= 2x and x2

= 16y is

A) x + 2 y - 2 = 0 B) x + 2 y + 2 = 0 C) x + 2 y = 0 D) 2 x + y - 4 = 0

46. The point

4

πP lies on the ellipse 1

24

22

y x

whose foci S, S1. The equation of external angular

bisector of 1SPS of triangle 1SPS is

A) 2x 3 3y 12 B) 3x – 4y 12 2 0

C) x 2y 2 2 D) x y 12 2 47. cot16 cot44 + cot44 cot 76 - cot76 cot16 =

A) 0 B) 1 C) 3 D) 4

48. In triangle ABC, if cosAcosBcosC = 1/3 then the value of tanAtanB + tanBtanC + tanCtanA is

A) 1 B) 4/3 C) 3 D) 4

49. If sin 3, 4sin 2 3 1r r θ θ , and 0 2, then =

A)2

, , ,

4 3 6 3

π π π πB)

5 2, , ,

6 3 6 3

π π π πC)

5, , ,

3 3 2 5

π π π πD) none of these

50. If 1

12

x , then2

1 1 3 3cos cos

2 2

x x x

=

A) /2 B) /4 C) /3 D) 12cos3

x π

51. In a ∆ABC,2

π B , s – a = 3 and s – c = 2 then (a, c) =

A) (2, 3) B) (3, 4) C) (1, 2) D) (4, 3)

52. In a triangle ABC if r1 = 10, r2 = 15 then the length of the altitude from vertex C to the side AB is

A) 25 B) 12 C) 16 D) 20

53. 2,,1 are the cube roots of unity then the roots of 081x 3

A) 221,21,1 B) 221,21,1

C) 22,2,2 D) 22,2,2 54. If z1, z2, and z3 are two non-zero complex numbers such that |z1| = 1, |z2| = 5 and

|z3| = 6 and |z1 + z2 + z3| = 2, then the value of |36z1z2 + 25z1z3 + z2z3| is

A) 2 B) 60 C) 30 D) 1

55. If the system of equations x + 2y + 3 = 0, 2x – y – 4 = 0, 3x + ky – 5 = 0 has unique solution, then k

=

A) 1 B) -1 C) 2 D) -256. If P is a point on the line passing through A (3i+j-k) and parallel to 2i-j+2k such that AP = 15 then

the position vector of P is

A) 13i-4j+9k B) 13i+4j+9k C) 13i+4j-9k D) 13i-4j-9k


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57. The volume of the tetrahedron formed by the points whose position vectors are 4i+5j+k, -j+k,

3i+9j+4k and

4(-i+j+k) is

A) 7 B) 9 C) 11 D) 13

58. If f: R→R, g: R→R are defined by f(x)=5x-3, g(x)= 32 x , then (go 1 f )(3) =

A)9

25B)

25

111C)

25

9D)

111

25

59. If f: R→R and g: R→R are given by x x f and x xg for each xR, where [ ] denotes thegreatest integer function then the set {xR: g [f(x)] ≤ f [g(x)]}A) ,0 B) ,0 C) D)

60. If : f

, is a function satisfying the property that 1 100 10, f x f x x , then the

period of f x isA) 98 B) 99 C) 100 D) 198

CHEMISTRY

61. Terylene is a condensation polymer of ethylene glycol and

A) Phthalic acid B) m-Benzene dicarboxylic acidC) p-Benzene dicarboxylic acid D) Hexandioic acid

62. Which of the following reaction can produce aniline as the main product?

A) C6H5NO2 + Zn/KOH B) C6H5NO2 + Zn/NH4Cl

C) C6H5NO2 + Li Al H4 D) C6H5NO2 + Sn/HCl

63 The oxidative cleavage of compounds Glucose (A) and Fructose (B) with 4HIO leads to the

formation of acids and aldehydes. The ratio of formic acid to formaldehyde for (A) and (B)

respectively are

A) 5/1, 3/2 B) 5/2, 3/1 C) 3/2, 5/2 D) 4/2, 5/1

64. Bauxite is purified by

A) Hall’s process B) Bayer’s processC) Serpeck’s process D) All of the above

65. The equivalent weight of 32CO Na , when it is titrated against HCl in the presence of methyl orange,

is

A) 5.3 B) 53 C) 10.6 D) 106

66. In a reversible adiabatic change S is

A) Infinity B) Zero C) vC dT D)1

2lnV

V nR

67. Which of the following salt gives white precipitate with ammonium carbonate?

A) 2 BaCl B) 3FeCl C) 2 NiCl D) 4FeSO

68. The PH at which an acid indicator with Kacid(indicator) = 10-5 changes colour when the Conc. of the

indicator is 10-3

M.

A) 5 B) 11 C) 3 D) 8

69. S-S bond is not present in

A) H2S2O4 B) H2S2O5 C) H2S2O7 D) H2S2O3

70. Which of the following has minimum bond length ?

A) B2 B) C 2 C) F 2 D) 2O

71. A vol. V of a gas at a temp. T1 & a pressure ‘ p’ is enclosed in a sphere. Its connected to another

sphere of vol. V/2 by a tube & stopcock. The second sphere is initially evacuated and

the stopcock is closed. If the stopcock is opened the temp. of the gas in the 2nd

sphere becomes T2.the first sphere is maintained at T1. Then the final pressure in the apparatus is

A)12

2

2

2

T T

pT

B)

12

2

2

2

T T

pT

C)

12

2

2 T T

pT

D)

21

22

T T

pT


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72. The correct order of reactivity of alkalimetals towards H2 is

A) Cs RbK Na Li B) Cs RbK Na Li C) Cs RbK Li Na D) Cs RbK Li Na

73. For a reaction completed in 3 steps, the overal rate constant is given by2

2

3

3

1 .3K

K K K , where K1,K2

and K3 are the rate constants, for the 3 steps respectively. Then the overall E a of

the reaction is ( if E1,E2 &E3 are the Ea for the 3 steps respectively)

A)2

2

3

3

1 .

E

E E B)

2

2

3

3

1 .3 E

E E C) 3

2

2

3

1 E E E D) 321 23 E E E

74. When BaCl2 is heated with K2Cr2O7 in the presence of H2SO4, a red gas (A) is evolved. The gas

when passed through aqueous NaOH. solution turns it yellow(B), which gives yellow ppt.(C) with

(CH3COO)2Pb. Then which of the following is correct ?

A) C is PbO2 B) A is CrO2Cl2 C) B is Cr2O3 D) C is PbCrO275. The heat capacity of a bomb calorimeter is 500 J/

0C. When 0.1 g of methane was burnt in this

calorimeter, the temperature raised by 20C. The value of E per mole will be

A) +10 KJ B) -10 KJ C) +160 KJ D) -160 KJ

76. Which of the following does not exist?

A) 2 3KI I KI B) 2 3KF F KF C) KBr ICl K BrICl D) 3 4KF BrF K BrF

77. 2,3-pentadiene exhibits optical isomerism. Since it

A) contains one chiral carbon

B) contains two chiral carbons but the molecule as a whole is achiral

C) does not contain any chiral carbon but the molecule as a whole is chiral

D) 2,3-pentadiene does not exhibit optical isomerism

78. The ‘E’ isomer is

A)

C =

F

Cl

C

H

Br B)

C =

CH3

H

C

CH3

H

C)

C =

CH3

H

C

C2H5

CH(CH3)2 D)

C C =

F H

Cl I

79. The intermediate during the addition of HCl to propene in presence of peroxide is

A)

+

23 2CH CH CH B)

+

33CH CH CH C) 2 23CH CH CH

D) 33CH CH CH

80. In a trisubstituted benzene, if two groups are same and the other is different, the number of possible

structural isomers are

A)3 B)6 C)10 D)5

81. Aryl halides are less reactive towards nucleophili substitution reaction in comparison to alkyl halides

because

A) of the formation of less stable carbonium ion

B) C-X bond is longer

C)of positive I- effect of benzene ring

D) of sp2 hybridised carbon and stabilisation of C - X bond by resonance

82. An SN2 reaction at an asymmetric carbon of a compound always gives :

A)an enantiomer of the substrate B) a product with opposite optical rotation

C)a mixture of diastereomers D) a single stereoisomer.


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83. B

' Lindlar s catalyst

R – C C – R3 / Na Liq NH

A

A) A is trans, B is cis B) A and B both are cis

C) A and B both are trans D) A is cis, B is trans

84 Major Product in the following reaction is,

KOHCHCl3

A) B) C) D)

85. Chloroform, on heating with zinc dust and steam, formsA) CH4 B) C2H2 C) C2H4 D) CH2Cl2

86. Product of the following reaction : 3(1)

3 2 3 (2 ).....

O

HydrolysisCH C CCH CH are :

A) 3 2CH COOH CO B)3 2 3CH COOH HOOCCH CH

C) 3 3 2CH CHO CH CH CHO

D) 3 3 3CH COOH CH COCH

87. Which of the following structures represents an L-amino acid

A)

H

R

COOH

2 NH B) H

R COOH

2 NH

C) H

R

COOH2 H N

D)

H

R

COOH

2 NH

88. How many moles of Zn2+

carry a charge of C 5102 ?A) 410 B) 10104 C) 5104 D) 101.03 10-´

89. On hydrolysis, diborane produces

A) H3BO2 + H2O2 B) H3BO3 + H2C) B2O3 + O2 D) H3BO3 + H2O2

90. Which of the following is an ionic compound ?A) NI3 B) NF3 C) NCl3 D) BiF3

iit model paper 3

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