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8/10/2019 JEE Advanced 2014_Test 2 (Paper II) Code B
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8/10/2019 JEE Advanced 2014_Test 2 (Paper II) Code B
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PART - I : PHYSICS
SECTION - 1
Only One Option Correct TypeThis section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY
ONE is correct.
1. A spring of spring constant kconnected to a block of mass m is placed on a rough horizontal surface having
coefficient of friction . The spring is given initial elongation3mg
kand the block is released from rest. For the
subsequent motion, the maximum speed of the block is
(A) m
gk
(B) 2 m
gk
m
3 mg
k
(C) 2 mgk
(D)2
mgk
2. As shown in figure mass of the block resting on the floor is 3 m while that of hanging block is m. The floor is
frictionless and horizontal and all pulleys ideal. The system is initially held stationary with the inclined thread making
an angle = 30 with the horizontal. The blocks are now released from rest and allowed to move. The hangingblock falls through a height hbefore hitting the floor and at this time the value of becomes 60. The speed withwhich the hanging block hits the floor is
3m
m
(A) 2
4
gh(B)
3
4
gh
(C) 2gh (D) 2
7
gh
TEST - 2 (Paper - II)Time : 3 Hrs. MM : 186
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3. Two steel spheres, having radii aand 2aare released from a height has shown in
figure. Assume that during motion the centres of the spheres lies on a vertical line.
Large sphere collides with the ground and recoils and collides with the small sphere.
Collisions are perfectly elastic. Velocity of small sphere just after its collision is
(A)9
2 ( 2 )5
g h a (B)9
2 ( 2 )23
g h a
a
h
2a
(C)5
2 ( 2 )9
g h a (D)23
2 ( 2 )9
g h a
4. As shown in figure a solid sphere is rolling without slipping on rough ground. It collides with an identical sphere at
rest elastically. Radius and mass of each sphere is Rand m. There is no friction between the two spheres. The
net angular impulse about its centre, imparted to second sphere after impact is
v
at rest
(A)5
7mRv (B)
3
7mRv
(C)2
7mRv (D)
4
7mRv
5. A uniform disc of radiusRlies in x-yplane with its centre at origin. Its moment of inertia about the axis17
2=y R
and z= 0 is equal to moment of inertia about the axis x= dand y= 0. The value of dis
R
(0 0)
y=172 R
d
x
y
(A) 3R (B) 4R
(C) R (D) 2R
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6. As shown in figure an object comprises of a uniform chordABand a ring of radius R(not necessarily both made
of the same material). Which of the following cannot be the centre of mass of object?
y
x
B
A(0, 0)
(A) ,4 4
R R
(B) ,3 3
R R
(C) ,3 3
R R
(D)2 2
,5 5
R R
SECTION - 2
One or More Options Correct Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE
OR MORE are correct.
7. A plank of length Land mass Mis placed at rest on a smooth horizontal surface. As shown in figure a small block
of mass mis projected with a velocity v0. The coefficient of friction between the block and the plank is , plank is
very long so that block eventually comes to rest on it.
m
M
v0
Smooth
(A) The final common velocity is 0mv
vM m
=
+
(B) The work done by friction on the plank is =
2
2
02
1
2( )+
m Mv
m M
(C) The work done by friction on the block is2
02
1 ( 2 )
2 ( )
+=
+
mM M mv
M m
(D) The net work done by friction is2
0
1
2=
+
mMv
M m
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8. A ball of mass mmoving at a speed vmakes a head on collision with an identical ball at rest. The kinetic energy
of the balls after the collision is3
4th of original. Choose the correct statements
m
v
m
v2
m
v1
(A) 1 1is2
ev v+
(B)2
1is2
ev v
(C) Coefficient of restitution is1
2(D) Coefficient of restitution is
1
2
9. A uniform slender rod of length Land mass Mis pivoted at one end. It is held horizontal and released. Given that
the pivot is frictionless, select the correct alternative(s).
L
M
(A) The angular acceleration of the stick immediately after it is released is
3
2
g
L
(B) The angular acceleration of the stick immediately after it is released is2
3
g
L
(C) The force F0exerted on the stick by the pivot immediately after release is
4
Mg
(D) The force F0exerted on the stick by the pivot immediately after release is
2
Mg
10. The net force (F) acting on a particle depends on its position (x) as shown in figure. Choose the correct statement.
F
A
B
C x
(A)Ais the point of stable equilibrium (B) Cis the point of unstable equilibrium
(C) Bis the point of neutral equilibrium (D) Bis the point of stable equilibrium
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11. A particle of mass mis suspended from a string of length Rand at the bottom it
is given velocity 3=u gR . Choose the correct velocity and tension for different
points given in the figure.
(A) Velocity at point B is 7gR (B) Tension at point B is 7mg
D B
C
u
R
(C) Velocity at point C is 5gR (D) Tension at point Cis 4mg
SECTION - 3
Paragraph Type
This section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs
with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices
(A), (B), (C) and (D).
Paragraph for Question Nos. 12 to 13
A constant horizontal force F= mgstarts acting on a suspended pendulum bob of mass m, initially at rest.
m F
12. The maximum angular deflection of the string
(A)3
(B)
6
(C)2
(D)
4
13. Tension is maximum at angular deflection of the string
(A)3
(B)
6
(C)2
(D)
4
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Paragraph for Question Nos. 14 to 15
Two smooth balls Aand B, each of mass mand radius Rhave their centres at (0, 0, R) and at (5R, R, R)
respectively, in a coordinate system as shown. Before collision, ballAis moving along positivex-axis with speed
of 4 m/s and ball Bis stationary. The collision between the balls is elastic.
x(m)
y
A
B
14. Velocity of the ballAjust after collision is
(A) 3i j (B) 3+i j
(C) 3 +i j (D) 3 i j
15. Impulse of the force exerted byAon Bduring collision is equal to
(A) 3 3mi mj (B) 3 3+mi mj
(C) 3 3+mi mj (D) 3 3mi mj
SECTION - 4
Matching Column Type
This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columns
have choices (A), (B), (C) and (D) out of which ONLY ONEis correct.
16. The figure shows a fixed hemisphere of radius R. A small ball of mass mis projected horizontally along the tangent
with a speed vfrom a point C. The centre O, lowest pointAand point Clie in same vertical plane.
Column I Column II
(P) Angular momentum about O (1) mvR
(Q) Angular momentum about C (2) 2mvRcos2
A
O
C
(R) Angular momentum aboutA (3) mvRsin
(S) Angular momentum about OA (4) Zero
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Codes :
P Q R S
(A) 1 3 4 2
(B) 3 2 1 4
(C) 1 4 2 3
(D) 4 2 1 3
17. When a wheel rolls without slipping on a horizontal surface, any point (B) on its circumference moves along a
curved path called cycloid. Consider a point Bon the circumference, initially in contact with the surface, consider
that point as origin. Match column I having coordinate of point Band velocity of point Bafter the time interval twith
the column II.
v
B
c
Column I Column II
(P) x-coordinate of point B (1) cos cv t
r rr
(Q)y-coordinate of point B (2) cos c
c c
v tv v
r
(R) Horizontal component of velocity of point B (3) sin
c
c
v tv t r
r
(S) Vertical component of velocity of point B (4) sin c
c
v tv
r
Codes :
P Q R S
(A) 1 3 2 4
(B) 3 1 2 4
(C) 3 2 1 4
(D) 4 2 3 1
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SECTION - 5
Integer Value Correct Type
This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The
appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,
if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of
bubbles will look like the following :
0
X
Y
Z 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
18. A uniform rod of mass mand length Iis free to rotate about hinge O. A slight disturbance causes the rod to rotate
freely about O. Horizontal force applied on rod by hinge just before the rod hits the surface is .xmg
yFind the value
ofx+ y.
O
l
19. The system of blocks must be released from >nmg
hk
with the spring unstretched so that after perfectly inelastic
collision (e= 0) with ground, Bmay be lifted off the ground. Find the least possible value of n. (kis spring constant).
m
2m
A
B
h
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25. The solubility of Ag2CO
3in presence of Na
2CO
3is expressed by
(A)sp
23
2K
CO (B)
sp
23
K1
2 [CO ]
(C)sp
1[Na ]
2K
+ (D) 2Ksp
[CO32]
26. The entropy change when 1 mole of ideal gas expands reversibly from an initial volume of 2 litres to final volume of
20 litres at 25C is
(A) 19.15 JK1mol1 (B) 4.6 JK1mol1
(C) 0.1914 JK1mol1 (D) 46.06 JK1mol1
SECTION - 2
One or More Options Correct Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE
OR MORE are correct.
27. Cp
Cv= R. This R is not equal to
(A) Change in KE
(B) Change in rotational energy
(C) Work done which system can do on expanding the gas per mol per degree increase in temperature
(D) Change in PE
28. Chemical equilibrium for a reversible change means for
(A) The forward reaction proceeds as fast as the backward reaction i.e. velocity of opposing reaction is equal
(B) No change in concentration of reaction species with time
(C) Dynamic equilibrium
(D) The concentration of reactant molecules must be equal to the concentration of product molecules
29. Which of the relationships is/are correct?
(A) av8RT
CM
=
(B) rms3RT
CM
=
(C) PM = dRT (D) Cav
= 0.816 Crms
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30. For which reactions given fact(s) is /are correct?
(A)2 2 3
H S H O H O HS+ + + : Kcis ionisation constant for acid
(B)2 2 3
H O H O H O OH+ + + : Kcis ionic product of water
(C)3 2 2 3 3
CH NH H O CH NH OH
++ + : Kcis ionisation constant of base
(D) 2 23 3 4
Cu 4NH [Cu(NH ) ]+ ++ : Kcis stability constant of complex
31. In the reaction2 4 2
Cl OH Cl ClO H O + + + ; Chlorine (Cl2) is
(A) Oxidised
(B) Reduced
(C) Disproportionated
(D) Neither oxidised nor reduced
SECTION - 3
Paragraph Type
This section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs
with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices
(A), (B), (C) and (D).
Paragraph for Question Nos. 32 to 33
The methods employed for the determination of equilibrium constant are different for different equilibria depending
on the nature of the system and the types of reaction. In simple gaseous dissociation such as
2 4 2N O (g) 2NO (g) ; 1 mole of N2O4(g) is decomposed under atmospheric condition at 25C.
32. Value of KPincreased by when degree of dissociation becomes equal to 50% at constant temperature
(A) 1.5 times (B) Remains constant
(C) 2 times (D) Decreases
33. If the degree of dissociation of the above equilibrium is 50%, then observed vapour density is
(A) 30.6 (B) 54.22
(C) 90.23 (D) 25.46
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Paragraph for Question Nos. 34 to 35
Iron metal is produced commercially by reducing iron (III) oxide into iron ore with carbon monoxide as follows
2 3 2Fe O (s) 3CO(g) 2Fe(s) 3CO (g)+ +
Fe O2 3
CO (g) Fe (s) CO (g)2
H (kJ/mol)f
S (J/mol K)824.0 110.5 0 393.587.5 197.5 27.0 213.5
34. The standard free energy change for the reaction at 25C is
(A) + 15.0 kJ (B) 29.3 kJ
(C) 15.0 kJ (D) 20 kJ
35. Choose the correct statement
(A) The reverse reaction becomes spontaneous at a lower temperature
(B) The reverse reaction becomes spontaneous at a higher temperature
(C) The reverse reaction is not spontaneous at any temperature
(D) The forward reaction is not spontaneous at any temperature
SECTION - 4
Matching Column Type
This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columns
have choices (A), (B), (C) and (D) out of which ONLY ONEis correct.
36. Match the following
Column I Column II
(Mixture) (pH values)(P) 0.1 M CH
3COOH + 0.1 M (1) 7.4
CH3COONa (pK
aof CH
3COOH = 4.74)
(Q) 100 ml of 0.1 M HCl + 100 ml of 0.1 M NaOH (2) 9.26
(R) 100 ml of 0.1 M NH4OH (3) 7.0
(pKb
= 4.74) + 50 ml of 0.1 M HCl
(S) Blood buffer (4) 4.74
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Codes :
P Q R S
(A) 1 2 3 4
(B) 2 3 4 1
(C) 4 3 2 1
(D) 4 2 3 1
37. Match the following
Column I Column II
(P) 2
Cu Cu Cu+ + + (1) Oxidation
(Q)3
ClO Cl (2) Reduction
(R) 24 4
MnO MnO (3) Disproportionation
(S) 2 22 7 4
Cr O CrO (4) Neither oxidation nor reduction
Codes :
P Q R S
(A) 3 2 1 4
(B) 2 3 1 4
(C) 3 2 4 1
(D) 3 1 2 4
SECTION - 5
Integer Value Correct Type
This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The
appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of
bubbles will look like the following :
0
X
Y
Z 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
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38. The n-factor of the underline compound is
4 3 2 2NH NO N O 3H O +
39. 100 ml of 0.75 N NH4OH is mixed with 100 ml of 0.50 N HCl. The K
bof NH
4OH is 2 105.Hence pOH of the
solution is _________.
40. The ratio of excluded volume and actual molecular volume of real gas is _________.
PART - III : MATHEMATICS
SECTION - 1
Only One Option Correct Type
This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY
ONE is correct.
41. Number of positive integers n2014 such that '6' is a factor of n2+ 3n+ 2 is
(A) 2014 (B) 1342
(C) 1343 (D) 1341
42. Sides of a triangle are distinct positive integers in an arithmetic progression. If the smallest side is 20 cm, then the
number of such triangles is
(A) 20 (B) 30
(C) 21 (D) 19
43. Let A= {1, 2, 3,.........., 12}, B= {101, 102,..........., 106}, number of functions defined from A to B such that
f(1) + f(2) +........ + f(12) is even is
(A) 612 (B) 3. 611
(C) 611 (D) 312 1
44. LetAdenote the matrix0
0
i
i
, i2= 1 and let Idenote the identity matrix1 0
0 1
, thenA+ A2+ ..... +A2020is
equal to
(A)0 0
0 0
(B)1
1
i
i
(C)0
0
i
i
(D)1 0
0 1
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45. A= {x1,x
2,x
3,.........., x
2n},x
iI, i= 1, 2, .............., 2n. Elements ofAare arranged along a circle in that order.
If each number is equal to average of its two adjacent numbers. If 21
n
m
m
x k
=
= , then sum of all numbers is
(A) 0 (B)2
2
k k+
(C) 2k (D) 4k
46. LetAbe n nmatrix such that it is idempotent matrix. The value of (I+ A)2nis equal to (where Iis the identity
matrix of order n)
(A) I+ A (B) I+ 2nA
(C) I+ 22nA (D) I+ (22n 1)A
SECTION - 2
One or More Options Correct Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE
OR MORE are correct.
47. 1 2 3 42 6 10 14
1 ....up to3 3 3 3
S = + + + + +
84 2 3
2 3 . 3 . 3 ....up toS = then
(A)S1> S
2(B)S
1< S
2
(C) Number of positive divisors of S1+ S
2is 6 (D) S
1= 2S
2
48. Letx1,x
2,x
3,......x
50be fifty nonzero numbers such thatx
i+ x
i+1= kfor all 1 i 49. Ifx
14= a,x
27= b, then
(A) x20
+ x37
= 3a+ 2b (B)x20
+x37
= 2k (a+ b)
(C) x20
+x37
= a+ b (D) x20
+x37
= 2k
49. Letx1 andx2be the roots of the equationx2 3x+ a= 0,x3 andx4 be roots of the equationx2 12x+ b= 0,x4,x
5be roots of equation ofx2+ cx+ d= 0, ifx
1< x
2< x
3< x
4< x
5< x
6are in G.P., then
(A)ab= 64 (B) c+ d= 564
(C) c +d = 560 (D) |c d| = 464
50. Let S3n
= 1 22+ 33+ 4 52+ 63+ .... up to 3n terms then
(A)S3n
is always divisible by 3 (B) S3n
is always divisible by 6
(C) S30
is divisible by 10 (D) S30
is not divisible by 10
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51. IfAis a square matrix of order 3 such that A3= Iand (A+ I)3+ (A I)3 6A= B,where Iis the identify matrix
of order 3, then
(A)B= 2I (B)B= 3I
(C) |B|= 2 (D) |B|= 8
SECTION - 3
Paragraph TypeThis section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs
with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices
(A), (B), (C) and (D).
Paragraph for Question Nos. 52 to 53
Let a1, a
2, a
3,......, a
nbe npositive real numbers then
1/1 2
1 2 3
...( . . ... ) nn
n
a a aa a a a
n
+ + + equality holds when
a1= a
2= .... = a
n.
52. For x > 3the minimum value of
22 12 26
( ) 3
x xf x
x
+ +
= + is
(A) 8 (B) 4
(C) 6 (D) 12
53. Ifx+ y+ z= 55,x, y, z> 0 thenx2y4z5will be maximum whenxis equal to
(A)55
3(B) 5
(C) 22 (D) 10
Paragraph for Question Nos. 54 to 55
Suppose that each term in the sequence x1,x
2,x
3,......x
n(nis even) is either 1 or 1 or 0. Let Srepresent sum
of product of terms taken two at a time i.e. all xix
j(0
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55. Maximum value of Sis
(A)2
1
2
n n +
(B)2
2
n
(C)2
2
n n+
(D)2
2
n n
SECTION - 4
Matching Column Type
This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columns
have choices (A), (B), (C) and (D) out of which ONLY ONEis correct.
56. LetA= {1, 3, 5}. A number is selected from set Awith replacement and this process is done 920 times for each
i= 1, 3, 5. Let f(i) represents the number of times the number ( i) is selected i.e. f(1) + f(3) + f(5) = 920, Let S
be sum of all 920 numbers selected. If S3= 405 f(1). f(3). f(5) then match the statement in column I with statement
in column II and select appropriate code.
Column I Column II
(P) f(1) (1) 120
(Q) f(3) (2) 200
(R) f(5) (3) 600
(S) Harmonic mean of f(1), f(3), f(5) is (4) 100Codes :
P Q R S
(A) 2 3 2 1
(B) 3 2 1 4
(C) 3 2 1 2
(D) 1 2 3 4
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57. Match the following
Column I Column II
(P) Letx 2y= 1,x y+ az= 2, ay+ 9z= b. (1) 6
Number of values ofafor which given system
of equations does not possess unique solution is
(Q) For above given equation(s) in part (P) number of (2) 2
ordered pair (a, b) for which given system of
equations have infinite solution is
(R) If5 2
2 1A
=
andA1= A+ Ithen is equal to (3) 12
(S) Let N= 253253, number of divisors of Nwhich are (4) 11
of the form 8+ 4, Nis
Codes :
P Q R S
(A) 2 2 1 4
(B) 2 2 1 3
(C) 1 1 2 3
(D) 2 1 3 4
SECTION - 5
Integer Value Correct Type
This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The
appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of
bubbles will look like the following :
0
X
Y
Z 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
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58. a, b, c, dbe positive real numbers such that a+ b+ c+ d= 12 and abcd= 27 + ab+ ac+ ad+ bc+ bd+ cd
then value of2( )
3
a d b c + + +is __________
59. If
4 4 4
24 4 4 1 2 3
1 1 11 3 .... (2 1)
14 4 4
1 1 1
2 4 .... (2 )4 4 4
n
k n k n k
n
+ + +
= + +
+ + +
then k1 k
2+ k
3 is equal to
60. Let
4 1 6
6 4 9
5 0 5
A
=
. If |adj adjA| = 5k, then kis equal to
8/10/2019 JEE Advanced 2014_Test 2 (Paper II) Code B
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8/10/2019 JEE Advanced 2014_Test 2 (Paper II) Code B
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8/10/2019 JEE Advanced 2014_Test 2 (Paper II) Code B
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Test - 1 (Paper - II) (Answers & Hints) All India Aakash Test Series for JEE (Advanced)-2014
TEST - 1 (Paper - II)
PHYSICS
1. (B)
2. (C)
3. (A)
4. (D)
5. (B)
6. (C)
7. (B, C)
8. (A, B)
9. (A, C)
10. (A, C, D)
11. (A, B, C, D)
12. (B)
13. (C)
14. (D)
15. (D)
16. (B)
17. (C)
18. (9)
19. (3)
20. (2)
CHEMISTRY
21. (C)
22. (D)
23. (B)
24. (D)
25. (B)
26. (A)
27. (A, B, D)
28. (A, C)
29. (A, D)
30. (A, C, D)
31. (C)
32. (A)
33. (B)
34. (D)
35. (D)
36. (B)
37. (A)
38. (5)
39. (9)
40. (4)
MATHEMATICS
41. (B)
42. (C)
43. (A)
44. (D)
45. (D)
46. (B)
47. (A, B)
48. (A, C)
49. (A, B)
50. (A, B)
51. (A, B, D)
52. (A)
53. (B)
54. (C)
55. (A)
56. (C)
57. (D)
58. (4)
59. (2)
60. (4)
ANSWERS