iit jee model paper 5

8/20/2019 Iit jee Model Paper 5

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Max Marks:360

JEE-MAIN_2011 MODEL

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 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 marksfor wrong response will be deducted accordingly as per instruction

PHYSICS1. TV s and computer monitors are made up of pixels, which are colored dots very closely

spaced together. For someone with a near point of ‘D’, how close does the Rayleigh

criterion predict that the dots need to be in order to make viewing individual pixels

completely impossible without the aid of a magnifying device? Assume a maximum

pupil diameter of ‘d’ and a minimum visible wavelength of l .

1)1.22 / D d l 2) 0.61 / D d l 3) 0.61 / d Dl 4) 1.22 / d Dl

2. An LC circuit contains inductance 1 L H m= and capacitance 0.01C F m= .The wavelength

of electromagnetic wave generated is nearly

1) 0.5m 2) 5m 3) 190m 4) 30m

3. A sphere of brass released in a long liquid column attains a terminal speed v0. If the

terminal speed attained by the sphere of marble of the same radius and released in the

same liquid is nv0, then the value of n will be. Given: The specific gravities of brass,

marble and the liquid are 8.5, 2.5 and 0.8 respectively.

1)5

172)

17

773)

11

314)

17

5

4. In an electron gun, emission current from the cathode is given by the equation,( )( )2 B KT

I AT e-= [K = Boltzmann constant, A = constant] The dimensional formula for

2 AB is same as

1) KT 2) 2 IT 3) 2 IK 4)2

IK

T 5. On a T-P diagram, two moles of ideal gas performs process AB and CD. If the

work done by the gas in the process AB is two times the work done in the

process CD, then what is the value of 1 2 / T T ?


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12. In a particular fission process of a uranium atom at rest, fragments with mass numbers

1 A and 2 A are produced. A good estimate of the ratio of kinetic energies of the fragments,

1 2 / K K is :

1) 2 1A / A 2)2

2 1(A / A ) 3) 1 2 / A A 4)( )2

1 2 / A A

13. Which of these nuclear reactions is possible?

1)

23 1 20 4

11 1 10 2 Na H Ne He+ ® + 2)

10 4 13 1

5 2 7 1 B He N H + ® +3) 10 1 115 0 5 ¯ B n B vb+ ® + + 4)

14 1 12

7 1 6 ¯ N H C vb+ ® + +

14. A pn junction gemanium diode is shown here. The current in excess of 10mA throughthe diode produces a large Joule-heating which damages (burns) the diode. If we want

to use a 1.5V battery to forward bias the diode, what should be the value of resistor used

in series with the diode, so that the maximum current does not exceed 6mA? (For 6mA

current potential a cross diode is 0.6V)

1.5V

1) 150 2) 200W 3) 250W 4) 300W15. A thin uniform ring of mass m and electric charge Q uniformly distributed rotates

around an axis perpendicular to its plane and going through its center. The angular

momentum of the ring is 7.5 × 10 – 4 kg-m2 /s. The ring is in a homogeneous magnetic

field of a field strength of 0.1 T and the lines of the magnetic induction are parallel with

the plane of the ring. Torque exerted on the ring is? [The specific charge (charge-mass

ratio) of the ring is Q/m=10 – 5 C/kg].

x

y

1) 3.75 × 10 – 10 (N-m) along +y axis 2) 3.75 × 10 – 10 (N-m) along -y axis

3) 7.5 × 10 – 10 (N-m) along +y axis 4) none of these

16. A balloon has a volume of 0.09 m3 below the surface of the water (density = 3 310 kg / m )

at a depth of 40 m. If the temperature remains constant, what is its volume in m3 whenit is at the surface where the pressure is 5 21 10 N / m´ ?1) 0.43 2) 0.45 3) 0.36 4) 0.51

17. At 2 ‘O clock in the afternoon, the hour hand of the clock has a mechanism failure

because of which its hour hand (length =0.5m) falls under gravity with its one end being

attached to the clock centre, Calculate the angular velocity of the hand as it goes past

the 6 ‘O clock mark. ( 210 / g m s= )

1) 10 / rad s 2) 2 10 / rad s 3) 3 10 / rad s 4) 5 10 / rad s

18. 10 gm of ice at 0°C is mixed with ‘m’ gm of water at 50°C. What is minimum value of

m so that ice melts completely. (Lf = 80 cal/gm and sw = 1 cal/gm-°C)

1) 32 gm 2) 20 gm 3) 40 gm 4) 16 gm


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19. A sound source is emitting waves of wavelength 40cm from a tuning fork. A sonometer

of length 100 cm and mass 10g is in resonance with the fork. If tension in the sonometer

wire is 100 N then the number of loops formed in sonometer is ( speed of sound in air is320m/s)

1) 2.5 2) 16 3) 5 4) 8

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

1) The longest wavelength is the Balmer series is longer than the longest wavelength inLyman series2) The shortest wavelength in the Balmer series is shorter than the shortest wavelength

in the Lyman series

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

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

Lyman series.21. A glass lens has power of +5 dioptres in air. What will be it’s power if it is completely

immersed in water.4

3

a wm = and3

2

a gm =

1)40

9 D 2) 1.25D 3)

45

8 D 4)

10

3 D

22. A rectangular bar of soap has density 800 kg/m3 floats in water of density 1000 kg/m3.

Oil of density 300 kg/m3 is slowly added, forming a layer that does not mix with the

water. When the top surface of the oil is at the same level as the top surface of the soap.

What is the ratio of the oil layer thickness to the soap’s thickness, x/L ?

1)2

102)

2

73)

3

104)

3

8

23. Vernier callipers has 20 divisions on its vernier scale which coincide with 19 divisions

on the main scale. Least count of the instrument is 0.1 mm. The main scale division is :

1) 0.5mm 2) 1mm 3) 2mm 4) 0.25 mm

24. A circular loop wire of radius r rotates about the z-axis with angular velocity w . Thenormal to the loop is always perpendicular to the z-axis. At time t = 0, the normal is

parallel to the y-axis. An external magnetic field ˆˆ y z B B j B k = + is applied. The EMF ( )t

induced in the loop is :


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1) r2 By sin t 2) r2 Bz cos t 3) r2 Bz sin t 4) r2By cos 25. A solid conducting sphere having net charge Q and radius ‘3a’ contains a hollowed

spherical region of radius ‘2a’. A point charge +Q is placed at a position a distance ‘a’

from the common center of the spheres. What is the magnitude of the electric field atthe position ‘r=4a’from the center of the spheres as marked in the figure by P?

0

1

4K

π

1)216

kQ

a2)

2

3

16

kQ

a3)

28

kQ

a4) can't be determined

26. A galvanometer of resistance 100 W contains 100 division. It gives a deflection of onedivision on passing a current of –410 A. Find the resistance in ohms to be connected to it,

so that it becomes a voltmeter of range 10V.

1)500

9W 500 W 3) 100

9W 4)900 W

27. The combination of gates shown below yields

1) NAND gate 2) OR gate 3) NOT gate 4) XOR gate

28. Zener diodes have higher dopant densities as compared to ordinary p-n junction diodes.

This

1) Decreases the width of depletion layer as well as junction field

2) Increases the width of depletion layer as well as junction field

3) Decreases the width of depletion layer but increases the junction field4) Increases the width of depletion layer but decreases the junction field


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29. If the Young’s modulus of material of rod is 11 22 10 / N m´ and density is 38000 / kg m ,

what is the time taken by sound wave to travel 1m of the rod ?

1) 410 sec- 2) 210 sec- 3) 42 10 sec-´ 4) 22 10 sec-´30. A carnot engine operates at an efficiency of 30%, If the temperature of the sink

increases by 1%, the efficiency should (approx)1) Increase by 1% 2) Decrease by 1% 3) Decrease by 2% 4) Increase by 2%

CHEMISTRY

31. The major product for the reaction,3

3

2 2 2 2

H O

CH

CH C CH CH CH CH

|

O

will be

1)

CH2OH

CH3OH

2)

CH2OH

CH3

3)

3

3 2 2 2

|

|

CH

CH C CH CH CH CH

OH

O

4)

CH3

CH3

OH

32. Which of the following statement is correct ?

1) C-F bond is stronger than Si-F bond because C-F bond length is shorter than that of

Si-F

2) C-F bond is weaker than Si-F bond because of less difference in electronegativity

3) Si-F bond is stronger than C-F bond because of double bond character due to back bonding from F to Si

4) Si-F bond is stronger than C-F bond due to more difference in electro negativities

33. 173.42 0.56 97.1152´ = . The correct answer to this problem in proper number of significant digits is1) 97.1152 2) 97.115 3) 97 4) 97.12

34. The correct acidic order of the following isOH

(I)

OH

(II)

CH3

OH

(III)

NO2

1) I > II > III 2) III > I > II 3) II > III > I 4) I > III > II

35. Carborundum on heating with caustic soda in presence of air produces

1) 2 3 2 Na SiO H + 2) 2 3 2 3 Na SiO Na CO+

3) 2 2 2 Na SiO H + 4) 2 4 2 Na SiO H +

36. The degeneracy of hydrogen atom that has the energy equal to9

H R is (where H R is

Rydberg constant )

1) 4 2) 6 3) 9 4) 12


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37. Identify the major product, (Z) in the following reaction.

Cl

Br

Mg

1 mole

THF(X)

CO2 (Y)H+ (Z)

1)

Cl

COOH

2)

COOH

COOH

3)

COOH

4)

COOH

Br

38. The standard oxidation potential value of lithium is greater than that of potassium. Yet

potassium is more reactive towards water than lithium because,

1) The m.pt of K is less than Li and the heat of the reaction is sufficient to melt K. Sothe molten metal spreads out and exposes a larger surface to water

2)The m.pt of Li is less than K and the heat of reaction is sufficient to melt Li. So the

molten metal spreads out, and expose a larger surface to the water

3) The 0 E value is more negative and GD is more positive for Li e Li+ -+ ®

4) The 0 E value is more positive and GD is more negative for K e K + -+ ®39. The van der waals coefficient of the inert gases He, Ar and Xe are given below

Inert gas a ( )6 2. .atm dm mol- ( )2 3 110b dm mol- -

He 0.34 2.38

Ar 1.337 3.20

Xe 4.137 5.16

Choose the appropriate pair to complete the following statement.“The increase in the value of a signifies the increasing importance of _____ interaction

while increase in value in b is due to ______”

1) Ion-ion; increases atomic volume

2) Induced dipole- induced dipole; increased atomic volume

3) Induced dipole- dipole; dipole- dipole interaction

4) Dipole- dipole ; decreasing ionization energies

40.

3 HNO

2 4 H SO B A

2 Br

3FeBr

The compound B is

1)

NO2

Br

2)

NO2Br

3)

NO2

Br

4)

NO2

Br Br


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41. An alkali metal hydride NaH reacts with diborane in solvent Y to give a tetrahedral

compound Z which is extensively used as reducing agent in organic synthesis . The Y

and Z in the above reactions are

1) 2 6 2 5,C H C H Na 2) 2 5 2 5 4,C H OC H NaBH

3) 3 3 3 6, NH B N H 4) 3 8 3 7,C H C H Na

42. The equivalent weight of HCl in the given reaction is :

2 2 7 3 2 214 2 2 7 3K Cr O HCl KCl CrCl H ClO+ ® + + +1) 16.25 2) 85.1 3) 73 4) 36.5

43.

41% Hg So

0

2 44% ,60 H So C CH CH A B

Dilute

NaOH . The compound B is

1)

3 2

|

CH CH CH CHO

OH

- - -

2)

3 2

|

CH CH CH COONa

OH

- - -

3) 3 2 3

||

|

O

CH CH CH C CH

OH

- - - - 4) 3 2 3

3

OH O

CH C CH C CH

CH

| ||

|

44. Sodium carbonate solution on adding to magnesium sulphate solution forms

1) Soluble magnesium bicarbonate2) insoluble magnesium bicarbonate

3) insoluble basic magnesium carbonate

4)insoluble basic magnesium bicarbonate45. An ideal solution contains two volatile liquids ( )0 100 A A P torr = and B ( )0 200 B B P torr = .If mixture contains 1 mole of A and 4 moles of B, then total vapour pressure of the

distillate is

1) 150 torr 2) 180 torr 3) 188.88 torr 4) 198.88 torr

46. Among the following the least stable resonance structure is

1)N

O

O

2) N

O

O

3)N

O

O

4) N

O

O

47. The species present in solution when 2CO is dissolved in water are

1) only 2 3 H CO 2) only 2 3 3, H CO HCO

3) only 2 2 3,CO H CO 4) only2

2 2 3 3 3, , ,CO H CO HCO CO

48. For a hypothetical elementary reaction ,


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A

2B

2C

1k

2k

Where 1

2

1

2

k

k =

Initially only 2 moles of A are present. The total no. of moles of A,B and C at the end

of 75% reaction are :

1) 2 2) 3 3) 4 4) 3.5

49. Acid strength of the conjugate acids of the following are(I) (II) (III) (IV)

N NHN

HN NH

N

1) II > III > I > IV 2) II > IV > I > III 3) II > I > III > IV 4) II > IV > III > I

50. Liquid oxygen and liquid nitrogen are allowed to flow between the poles of an

electromagnet. Choose the correct observation .

1) Both will be attracted but to opposing poles

2) Both will be attracted to the same poles

3) Liquid oxygen will be attracted and liquid nitrogen will be repelled

4) Liquid oxygen will be attracted but liquid nitrogen is unaffected51. Solubility of AgCN is maximum in :

1) acidic buffer solution 2) basic buffer solution

3) in pure water 4) equal in all solution52. Acyclic stereoisomers having the molecular formula C4H7Cl are classified and

tabulated. Find out the correct set of numbers.Geometrical Optical

1) 6 2

2) 4 2

3) 6 0

4) 4 053. Which of the following pairs is expected to exhibit the same colour

1)3 3

58 69,Ce Ho+ +

2)3 3

60 68, Nd Er + +

3)3 3

61 69,Pm Tm+ +

4)3 3

63 70,Sm Yb+ +

54. When two mole on an ideal gas ,5

2 p mC R

æ ö÷ç = ÷ç ÷çè øheated from 300 K to 600 K at constant

pressure. The change in entropy of gas ( )S D is :

1)3

ln 22

R 2)3

ln 22

R- 3) 5R ln 2 4)5

ln 22

R

55. Identify the end product “B” here

2 / NaNo HCl

2 NH 0 00 5 C -

A BD

1) phenanthrene 2) benzene


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3) naphthalene 4) anthracene

56. In which of the following pairs find the pair in which first compound do not form

complex with 3 NH and second give coloured complex with 3 NH

1) 2 4,CoCl ZnSO 2) 4, AgI CuSO 3) 3 4, AlCl ZnSO 4) ( )3 42 ,Cd NO ZnSO

57. In which of the following pairs of structures, tetrahedral as well as octahedral holes are

found

1) bcc and fcc 2) hcp and simple cubic3) hcp and ccp 4) bcc and hcp

58. In the following reaction

Cellulose 2i CS NaOH

ii HCl HOH P

( ) /

( ) /

Here the product [P] is

1) Rayon 2) Cellulose acetate3) Gun cotton 4) Cellulose xanthate

59. Pure zirconium is obtained by1) chromatographic method 2) Cupellation

3) Zone refining 4) Van arkel method

60. A graph was plotted between molar conductivity of various electrolytes (NaCl, HCl

and 4 NH OH ) and C (in mol1

L- ). Identify the Correct setting .

I

IIIII

C

1) I(NaCl), II(HCl), III( 4 NH OH ) 2) ( ) ( ) ( )4, , I HCl II NaCl III NH OH

3) ( ) ( ) ( )4 , , I NH OH II NaCl III HCl 4) ( ) ( ) ( )4 , , I NH OH II HCl III NaCl

MATHEMATICS

61. In triangle ABC, R(b c) a bc where R is the circum radius of the triangle. Then thetriangle is

1) isosceles but not right angled 2) right angled but not isosceles

3) isosceles 4) equilateral62. Let , &a b c

be non coplanar unit vectors equally inclined to one another at an acute

angle . Then a b c

in terms of is equal to

1) 1 cos cos2 2) 1 cos 1 2cos2

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

63. If , ,a b c

are unit vectors equally inclined to each other at an angle 0 , then

the angle between a b

and the plane containing b

and c

is

1) 1sin tan cot2

. 2) 1 tan cot

2cos .

3) 1 cot tan2

cos . 4) 1 cot tan

2sin .

64. Statement 1: The shortest distance between the skew lines


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3 6

4 3 2

x y z

and

2 7

4 1 1

x y z

is 9

Statement 2: Two lines are said to be skew lines to each other if there exists no plane

passing through them

1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct Explanation For

Statement-1

2) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanationfor Statement-1

3) Statement-1 is True, Statement-2 is False 4) Statement-1 is False, Statement-2 is True

65. The number of distinct rational numbers of the form p

q, where , {1,2,3,4,5,6} p q is

1) 23 2)32 3) 36 4) 2866. Statement-1: Number of ways in which 10 identical toys can be distributed among three

students if each receives atleast two toys is 92C

Statement-2: Number of positive integral solutions of 7 x y z w is 63C .

1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct

Explanation For Statement-1

2) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct

explanation for Statement-1

3) Statement-1 is True, Statement-2 is False

4) Statement-1 is False, Statement-2 is True

67. A pair of unbiased dice are rolled together till a sum of either 5 or 7 is obtained.

Probability that 5 comes before 7 is

1)1

5

2)2

5

3)3

5

4)4

568. Team A plays with 5 other teams exactly once. Assuming that for each match the

probabilities of a win, draw and loss are equal, then

1) the probability that A wins and loses equal number of matches is34

81

2) the probability that A wins and loses equal number of matches is17

81

3) the probability that A wins more number of matches than it loses is17

81

4) the probability that A loses more number of matches than it wins is

16

81

69. Let f be a continuous function satisfying

, ,

2 2

f x f y x y f x y

If 10 1, 0 1 f f then

0

2

21

f

f

f xdx

x

1)4

π2)

2

π3) π 4) 0

70. Let ,α β be the roots of the equation 2 1 0 x x . Let n nnS α β for 1n . Evaluate

the determinant

1 2

1 2 3

2 3 4

3 1 1

1 1 11 1 1

S S

S S S S S S

1) 6 2) 7 3) 5 4) 0


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71. Variable circles which always touches the line 2 3 0 x y at (1 , 1), cuts the circle2 2 4 2 1 0 x y x y . Then all common chords of circles pass through a fixed point,

the co-ordinate of the point is

1)1 5

,2 6

2)1 17

,6 12

3)2 1

,3 5

4) (3,2)

72. A set of consecutive positive integers starting with one is written on blackboard one

number erased and thus the A.M of the remaining numbers is found to be7

3517

. The

erased number is

1) 6 2) 7 3) 8 4) 9

73. Let A = {1,2,3,4,5} and B={0,1,2,3,4,5}. How many one-one function : f A B can

be defined so that i ; i=2,3,4,5 and f 1 0 1 f i or

1)265 2)256 3)88 4)0

74. A tangent to the ellipse 2 24 9 36 x y is cut by the tangent at the extremities of the major

axes at T and T1

. The circle on TT1

as diameter always passes through the point1) 5,1 2) 5, 0 3) (0,0) 4)(3,2)

75. The expression 20

2 x y contain two terms a bkx y and 1 1a bkx y then a is

1) 8 2)5 3) 7 4) 6

76. If a,b,c are in G.P then the equations 2 2 0ax bx c and 2 2 0dx ex f have a

common root then

1) , , are in A.Pa b c

d e f 2) , , are in G.P

a b c

d e f

3) , , are in A.Pd e f

a b c 4) , , are in G.Pd e f

a b c

77. The maximum area of the rectangle whose sides passes through the angular points of agiven rectangle of sides ‘a’ and ‘b’ is

1) 21

2ab 2)

1

2a b 3)

21

2a b 4)

1

2ab

78. A curve 6

27 2 21 6 5 4g x x x x x x dx is passing through (0,0) then

1) 7

31

7g 2)

72

17

g 3) 1 2 / 7g 4) 7

31

14g

79. The number of solutions of the equation sin100

x x is

1)63 2)32 3)33 4)0

80. The number of real roots of the equation 3 3 1 0 x x is1) 0 2)1 3)2 4)3

81. Let

1, x 1For

x

2 , For x 1ax b

f x

If f(x) is continuous and differentiable every where then

1) 1 32 2

a b= = - 2) 1 32 2

a b= - =

3)a=1,b= -1 4)a=b=1


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82. The area bounded by the curve f(x) = x + sinx and its inverse between the ordinates

x = 0 to x π is 2 ,K K N then K= ––

1)3 2)4 3)5 4)6

83. If the tangent at 1 1, x y to the curve3 3 3

x y a meets the curve again at 2 2, x y then

1) 2 2

1 1

1 x y

x y 2) 2 1

1 2

1 x x

y y 3) 1 1

2 2

1 x y

x y 4) 2 2

1 1

1 x y

x y

84. Let cos cos cosa b g + = and sin sin sina b g + = then the value of ( )sin

sin 2

a b

g

+is

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

85. The value of 404

C4 – 4C1

303C4 +

4C2

202C4 –

4C3

101C4 =

1) (404)4

2) (101)4

3)0 4)1

86. Let a relation R in the set N of natural numbers be defined as ( ) 2 2, 4 3 0 x y x xy yÛ - + =

for all , x y N Î . The relation R is

1) Reflexive but not symmetric and not transitive

2) Symmetric but not reflexive and not transitive3) Transitive but not reflexive and not symmetric 4) Equivalence relation

87. Lines 1 x 4 y 2 0 and 4 x 1 y 6 3 0 are concurrent at

points A and B respectively and intersect at C, then equation of the locus of centroid

of ABC is

1)2 2

3 7 17x y

2 10 50

2)2 2

3 7 17x y

2 10 50

3)2 2

3 7 34x y

2 10 900

4) none of these

88. Let 3 2 4 z i , then the absolute difference between the maximum and minimum

values of z is

1) 2 11 2) 3 11 3) 2 13 4) 4 1389. The contra positive of the inverse of p qÞ : is

1) q pÞ: 2) p qÞ 3) q pÞ: : 4) p qÞ: : .

90. If in a frequency distribution, the mean and median are 21 and 22 respectively, then its

mode approximately is

1) 22. 0 2) 20.5 3) 25.5 4) 24.0

iit jee model paper 5

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