Iit jee Model Paper 5
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Transcript of 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