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Space for Rough Work
Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014
1/19
PART - I : PHYSICS
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.
1. In the given graph Kα line is drawn for square root of frequency and atomic number. Then choose the Kβ line graph
in figure shown.
( )a
( )b
( )c
( )dKα
z
v
(A) a (B) b
(C) c (D) d
2. The angle of incidence i for an equilateral prism of refractive index 3 so that the ray suffers minimum deviation is
(A) 30° (B) 60°
(C) 45° (D) Either 30° or 60°
3. A vessel is half filled with a liquid of refractive index μ. The other half of the vessel is filled with immiscible liquid of
refractive index 1.5 μ. The apparent depth of the vessel is 50% of the actual depth, then μ is
(A) 1.6 (B) 1.67
(C) 1.5 (D) 1.4
4. Monochromatic light strikes normally on two thin different films,
which are in air as shown. If t denotes the film thickness and λdenotes the wavelength of light in the film, which film(s) will produce
constructive interference as seen by observer?
(A) I only t
μt = 54λ
(I)
μt = λ2
(II)
eye
eye
t
(B) II only
(C) I and II both
(D) None of these
TEST - 7 (Paper - II)Time : 3 Hrs. MM : 186
Space for Rough Work
All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II)
2/19
5. In YDSE, one of the slits is wider than the other, so that, the amplitude of the light from one slit is double that from
the other slit. If Im
be the maximum intensity, the resultant intensity when they interfere at a phase difference φ is
given by
(A)2
1 2cos3 2
mI φ⎛ ⎞+⎜ ⎟
⎝ ⎠(B)
21 4cos
5 2
mI φ⎛ ⎞+⎜ ⎟
⎝ ⎠
(C)2
1 8cos9 2
mI φ⎛ ⎞+⎜ ⎟
⎝ ⎠(D)
28 cos
9 2
mI φ⎛ ⎞+⎜ ⎟
⎝ ⎠
6. The ratio of time period of revolution of 2nd orbit electron in He+ ion and 3rd excited state electron in Le++ is
(A)9
32(B)
32
9
(C)4
37(D)
37
4
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 equi-biconvex length of focal length 10 cm is silvered as shown in figure. Refractive index of glass is equal to 3.
2
(A) Focal length of mirror would be equal to –5 cm
(B) Focal length of mirror would be equal to –2.5 cm
(C) An object is placed at point on axis such that its image is also formed at same point, the distance of that
point from lens would be 10 cm
(D) An object is placed at point on axis such that its image is also formed at same point, the distance of that
point from lens would be 5 cm
Space for Rough Work
Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014
3/19
8. A beam of white light incident on a combination of thin prisms with equal angles. In the outgoing beam, the rainbow
colours are observed as shown. μ stands for refractive index and θ for angle of dispersion. Then
R
Y
V
White light
μ1
μ2
(A) μ1
< μ2
(B) μ2
= μ1
(C) μ1
> μ2
(D) θ1
> θ2
9. Two coherent monochromatic sources A and B emit light of wavelength λ. The distance between A and B is integral
multiple of λ. If a light detector is moved along a line CD, parallel to AB, from –∞ to +∞, 8 minimas are observed.
Choose the correct options.
Y
B
A
D
C
X
x = 0
(A) The distance between AB is 4λ
(B) If the detector is moved along X-axis from B to ∞, then 5 maximas will be observed
(C) At a distance of 15
24x
λ= first minima will be observed
(D) At a distance of 15
28x
λ= first minima will be observed
Space for Rough Work
All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II)
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10. ABC is a right angled prism having other angles of 30° and 60° as shown. Two rays 1, 2 are incident on prism such
that ray 1 just suffers TIR on second face. Ray 2 is incident on one face and emerges perpendicular to the other
face. If light incident has same wavelength, choose correct options.
30°
60°C
1
2
B
A
(A) Refractive index of the prism is 2
(B) Deviation suffered by ray 2 is 60°
(C) Angle of deviation suffered by ray 2 is 30°
(D) The refractive index of the prism is 2
11. A gas of hydrogen like atoms has some atoms in the lowest ground energy level A and some atoms in a particular
upper excited energy level B and there are no atoms in any other energy level. The atoms of gas make transition
to higher energy level by absorbing monochromatic light of photon energy 2.7 eV. Subsequently the atoms emit
radiation of only six different energy photons. Some of the emitted photons have an energy 2.7 eV, some have
more and some less than 2.7 eV.
(A) The principal quantum number of initially excited level B is 2
(B) The ionisation energy of gas atoms is 14.4 eV
(C) Maximum emitted energy of photon is 13.5 eV
(D) Minimum emitted photon has energy 0.7 eV
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
Consider a neutron and an electron bound to each other due to gravitational force. Assume that the electron orbits
around the neutron in circular path. Bohr's quantization rule for angular momentum is applicable in this case. Take
mass of neutron as m1
and mass of electron as m2. (assume m
1>>>m
2)
Space for Rough Work
Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014
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12. Radius of orbit of electron for nth quantum number is
(A)
2 2
2 2
1 2
n h
Gmmπ (B)
2 2
2 2
1 22
n h
Gmmπ
(C)
2 2
2
1 22
n h
Gm mπ (D)
2 2
2 2
1 24
n h
Gmmπ
13. Speed of electron in nth orbit is
(A)1 2
2 Gmm
nh
π(B)
1 2Gmm
nh
π
(C)1 2
Gmm
nh(D)
1 24 Gmm
nh
π
Paragraph for Question Nos. 14 to 15
A cylinder of height h and radius R is kept in the path of a parallel beam of light of large aperture. If beam carries
an intensity I.
14. If surface of cylinder is perfectly reflecting, the force on cylinder would be
(A)8
3
IhR
C(B)
IhR
C
π
(C)2IhR
C(D)
2
3
IhR
C
15. Let the surface of cylinder has reflection co-efficient 0.8, then force on cylinder would be
(A)8
3
IhR
C(B)
38
15
IRh
C
(C)2
15
IhR
C(D)
64
15
IRh
C
Space for Rough Work
All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II)
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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 ONE is correct.
16. In YDSE as shown in figure, θ is the angular position of any point on screen. Both the slabs are of same thickness
= 10 μm.
Match column-I with column-II in the codes given below the columns.
μ1
μ2
slab1
slab2
θαO
Screen
Column I Column II
(P) Central maxima must be above O (1) If α > 37° and μ1
≥ μ2
(Q) Central maxima must be below O (2) If α = 37°, μ1
= 1.25, μ2
= 1.5
(R) Central maxima must be at O (3) If α = 0 and μ1
= μ2
(S) Central maxima may be below O (4) If α = 0 and μ1
< μ2
Codes :
P Q R S
(A) 1 4 2 3
(B) 1 4 3 2
(C) 4 1 2 3
(D) 4 1 3 2
Space for Rough Work
Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014
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17. An electron is orbiting around the nucleus in nth orbit, of a hydrogen like atom. Assuming Bohr's model to be true,
match the physical quantities given in column-I with their dependence on the principal quantum number in
column-II, in the codes given below the columns.
Column I Column II
(P) Magnetic field at the site of nucleus (1)4
1
n
∝
(Q) Magnetic dipole moment (2)5
1
n
∝
(R) de-Broglie wavelength (3) ∝ n
(S) Centripetal acceleration (4) ∝ n3
Codes :
P Q R S
(A) 2 3 4 1
(B) 3 2 3 4
(C) 2 3 3 1
(D) 3 2 4 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
18. A radioactive sample contains two radioactive nuclides A and B having decay constant λ hr–1 and 2λ hr–1. Initially
25% of total decay comes from A. How long (in hr) will it take before 75% of total decay comes from A ? [Take λ = ln 3]
19. A light of wavelength λ is incident on a metal sheet of work function 2 eV. The wavelength varies with time as λ =3000 + 40t, where λ is in Å and t is in second. The time (second) after which the photoelectric emission will stop
to the nearest integer is 16n, find n. [Take hc = 12400 eV Å]
20. To measure the volume of the blood of an animal, the following experiment was done. A 10 ml sample of solution
containing radioactive element (t1/2
= 40 min) with an activity of 450 dps was injected into the animals blood stream.
20 min required for complete circulatory mixing. After 80 min, a 4.0 ml sample was withdrawn and found to have an
activity of 5 dps. If the volume of the blood in animal is 10 n (in ml), then find n.
Space for Rough Work
All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II)
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PART - II : CHEMISTRY
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.
21. Which of the following statement is incorrect ?
(A) Cyclopentanone undergoes faster nucleophilic addition reaction than cyclohexanone
(B) In water, HCHO exists majorly as geminal diol
(C) In CH2Cl
2, aldehydes and ketone can never form diol hence are not oxidized by PCC in CH
2Cl
2
(D) Chloral majorly exists in form of dihydrate
22. In the reaction sequence
O
NH2
P O2 5
ΔP Q
(i) CH MgBr 3
(Dry ether)
(ii) H O3+
I2
Ca(OH)2
R + yellow ppt
'R' is taken out from solution and dry heated which produces 'S'.
P and S respectively are
(A) NH2
NH2
and
O
(B)
N
and
O
(C) NH2and (D) andC N≡
23.
NH2
AB
CD
NaNO2
HClyellow oily liquid
(M = 113 g/mol)
Which of the following is incorrect for above reaction?
(A) "D" is having molecular formula C7H
15N (B) Reagent "C" can be H
2/Ni or LiAlH
4
(C) "B" has a characteristic smell (D) Reagent "A" is present in acidic medium
Space for Rough Work
Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014
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24.
O
20
OH
6
5
17
4
3
2
1CH3
CH3
2
NaOD
D O/ THF
When the above reaction takes place several hydrogens are readily exchanged by deuterium. The readily exchangeable
hydrogens are on atoms numbered
(A) 2 and 20 only
(B) 2, 4 and 17 only
(C) 2, 4 and 20 only
(D) 1, 2, 17 and 20
25.
O
Cl+
NH2
The major product in above reaction is
(A)
O
Cl
NHCH CH2 3
(B)
O
NHCH CH2 3
(C)
O
NH2
(D)Cl
NHCH CH2 3
26. Which of the following reactions would not be an acceptable method for the preparation of methyl benzoate?
(A)
O
C — ClCH OH
3
O
C OCH3 (B)
O
C O NaCH I
3
O
C OCH3
(C)
O
C O NaCH OH
3
O
C OCH3 (D)
O
C —O C — —CH OH
3
O
C OCH3
O
Space for Rough Work
All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II)
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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. Which of the following give single organic product on treatment with KOH ?
(A) PhCOCOPh (B) OHCCHO
(C) OHC(CH2)5CHO (D)
O
CHO
28. Which is true about the following reaction sequence ?
(C H ) N : + : CCl A C H + B2 5 3 2 2 4
C
H O/OH2
–
Δ
(A) CCl2
..
is acting as nucleophile (B) Compound "B" is N – CHCl2
(C) "A" to "B" is effective in polar aprotic solvent (D) Compound "C" is N – CHO
29. The type of possible interaction/s in Nylon-6, 6 is/are
(A) Hydrogen bonding (B) Diple-dipole interaction
(C) van der Waal interaction (D) Induced dipole - Induced dipole interaction
30.CO
CuCl, HCl
AlCl3
AHCHO
conc. KOHB + C
(major products)(major product)
Which of following is true for above reaction sequence?
(A) B = COOK (B) C = CH3OH
(C) C = CH OH2 (D) B = HCOOK
Space for Rough Work
Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014
11/19
31. In which of the following reaction/s cyclic intermediate / transition state is involved?
(A) Perkin reaction (B) Wittig reaction
(C) Decomposition of β -keto acid (D) Heating of α-hydroxy acid
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
An ordinary D-(+)-glucose has melting point 146ºC and specific rotation [α] = + 112°. One another form of D - (+)-
glucose has melting point 150°C and specific rotation [α] = 18.7°. The form of low melting point for glucose is
known as α form and other form as β-form.
When any of the pure form is allowed to stand in acidic solution then optical rotation changes till reaches to fix
value 52.7°. This change in optical rotation towards an equilibrium value is called mutarotation.
32. Mutarotation is the characteristic feature of
(A) Enantiomer (B) Anomer
(C) Epimer (D) Ring chain isomers
33. What percentage of β-(D) (+) glucopyranose is found at equilibrium in aqueous solution?
(A) 50% (B) 74%
(C) 36% (D) 64%
Paragraph for Question Nos. 34 to 35
A well known aromatic compound (A) is put up in following sequence of reaction
CABr
2
B(C H )
10 18
hν(mono
bromination)
(C H O)10 18
ZnCl
(–H O)2
2
D(i) O
3
(i) DMSE
Na CO ,2 3
ΔF
(i)
(i) aq.KOH
H /Pd2
(Major product)
34. What is the double bond equivalence of "F"?
(A) 3 (B) 2
(C) 4 (D) 5
Space for Rough Work
All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II)
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35. If "F" is put up in reductive ozonolysis then formed product is
(A)
O
O
(B)
OO
O
(C)
O
OO
(D)
O
O
O
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 ONE is correct.
36. In column (I) acids are given their respective acidic strength order is given from right to left in column (II).
Column I Column II
(P) CH2F COOH, Cl
2CH COOH, Cl
3CCOOH (1) Increases, Increases
(Q) NCH COOH2
+Me
3, O
2NCH
2COOH, NCCH
2COOH (2) Decreases, Decreases
(R) m-hydroxy benzoic acid, o-hydroxy benzoic acid, (3) Decreases, Increases
p-hydroxy benzoic acid
(S) Oxalic acid, Succinic acid, Propanedioic acid (4) Increases, Decreases
Codes :
P Q R S
(A) 1 2 3 4
(B) 2 1 4 3
(C) 3 1 2 3
(D) 2 3 1 4
Space for Rough Work
Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014
13/19
37. Compounds given in column (I) are treated with CH3MgBr (excess) in dry ether followed by addition of H
2O and
qualitative test on formed products are given in column II.
Column I Column II
(P)3
CH – C – Cl||
O
(1) Positive DNP
(Q) CH3 – C ≡ N (2) Gas is insoluble in H
2O
(R)3 2
CH – C–NH||
O
(3) Blue colour in Victor Meyer test
(S)3
H– C – OCH||
O
(4) Instantaneous white turbidity with Lucas reagent
Codes :
P Q R S
(A) 4 1 2 3
(B) 3 1 2 4
(C) 1 3 4 2
(D) 1 4 3 2
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
38. Succinaldehyde on reaction with P2O
5 produces organic compound 'X'. How many π electrons are there in 'X' in π
electron cloud?
39. Phthalic anhydride is treated with phenol in acidic medium. How many aromatic rings are there in one molecule of
product?
40. How many functionality are present in monomer of Nylon-6?
Space for Rough Work
All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II)
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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. If xdy = y(dx + ydy), y ≠ 0, y(1) = 1 and y(β) = – 3, then 'β' is equal to
(A) – 5 (B) 5
(C) 15 (D) – 15
42. A term is selected from the expansion of (x + y + z)10 at random. The probability that two variables out of x, y and
z have the same power is
(A)5
22(B)
3
11
(C)3
22(D)
9
22
43. Let ( )sin ( )cos 2( )r a b x b c y c a= × + × + ×� �
� � � � �
, where , ,a b c
�� �
are non-zero and non-coplanar vectors. If r�
is orthogonal
to a b c+ +�
� �
, then find the minimum value of
2 2
99
x y+
(A)25
4π (B)
25
99π
(C)5
4 99π (D)
25
4 99π
44. Two urns contains, respectively m1 and m
2 white balls and n
1 and n
2 black balls. One ball is drawn at random
from each urn and then from the two drawn balls one is taken at random. The probability that the drawn ball is white
(A)1 1 2 2
1 1 2 2
1
2
m n m n
m n m n
⎛ ⎞+⎜ ⎟+ +⎝ ⎠(B)
1 2
1 1 2 2
1
2
m m
m n m n
⎛ ⎞+⎜ ⎟+ +⎝ ⎠
(C)1 2 2 1
1 1 1 1
1
2
m n m n
m n m n
⎛ ⎞+⎜ ⎟+ +⎝ ⎠(D)
1 1
1 1 1 1
1
2
n m
m n m n
⎛ ⎞+⎜ ⎟+ +⎝ ⎠
Space for Rough Work
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45. Let ( )3
ˆ ˆ ˆlog 2a x i j k= λ + +�
( )3 3
ˆ ˆ ˆlog ( log )�
b x i x j k= + λ −
Given angle between a�
and b�
lies in the range ,2
π⎡ ⎤π⎢ ⎥⎣ ⎦ for every x ∈(0, ∞). Then λ belongs to
(A) [0, 1] (B) [–1, 0]
(C) [–1, 1] (D) [0, 2]
46. If , ,u v w
� � �
are non-zero and non-coplanar vectors, then find the number of ordered pairs (p, q) so that
[ ]3u pv pw
� � �
– [ ]pv w qu� � �
– [ ]2w qv qu
� � �
= 0
∀ p, q, ∈ R
(A) 1 (B) 2
(C) 3 (D) More than 3
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. Which of the following statement(s) is/are true for any two events A and B ?
(A) Suppose that P(A/B) = P(B/A), P(A ∪ B) = 1 and P(A ∩ B) > 0 then P(A) > 1
2
(B) If P(BC) = 1
4 and P(A/B) =
1
2 then maximum value of P(A) =
5
8
(C) If P(A) = 1
2 and P(B) =
1
3, then P(AC ∩ BC)C + P(AC ∪ BC)C =
2
3
(D) If A is subset of B, then P(B/A) is 1, where P(A) ≠ 0
48. Let first and second row vectors of matrix A be 1r
�
= [1 1 3] and 2r
�
= [2 1 1] and let the third row vector be in the
plane of 1r
�
and 2r
�
and perpendicular to 2r
�
with magnitude 5 , then which of the following is /are true ?
(A) Tr (A) = 3
(B) Volume of parallelopiped formed by 2r
�
, 3r
�
and 2 3r r� �
equals 30
(C) Row vectors are linearly dependent
(D) [ ]1 2 2 3 3 10r r r r r r× × × =
� � � � � �
Space for Rough Work
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49. If g(x) be a function defined on [–1, 1]. If the area of the equilateral triangle with two of its vertices at (0, 0) and (x,
g(x)) is 3
4, then the function is
(A) 2( ) – – 1g x x= (B) 2( ) 1g x x= − −
(C) 2( ) 1g x x= − (D) 2( ) – 1g x x=
50. The chance of occurrence of an event A is the square of the chance of occurrence of event B but the odds against
the event A are the cube of the odds against the event B. The chances of the events are
(A) ( ) 1
9P A = (B) ( ) 1
8P A =
(C) ( ) 1
3P B = (D) ( ) 1
2P B =
51. The solution of dy ax h
dx by k
+=+ represents a parabola when
(A) a = 0, b ≠ 0 (B) a ≠ 0, b ≠ 0
(C) b = 0, a ≠ 0 (D) a = 0, b ∈ R
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. 52 to 53
Let ( ) ( )1
ˆ ˆ ˆ ˆ ˆ ˆ: 2 2L r i j k i j k= + − + λ − +�
and 2
ˆ8 ˆ ˆ ˆ ˆ ˆ: 3 (2 )3
iL r j k i j k
⎛ ⎞= − + + μ − +⎜ ⎟⎝ ⎠
�
where λ and μ ∈ R be two lines in
space. A line L from origin meets the line L1 and L
2 at P and Q respectively.
52. The equation of the plane passing through the points P and Q and perpendicular to the plane ˆ ˆ ˆ.( ) 1 0r i j k− + + =�
is
(A) ˆ ˆ.(2 3 ) 0r i j− =�
(B) ˆ ˆ.(3 2 ) 0r i j+ =�
(C) ˆ ˆ.( ) 0r i j− =�
(D) ˆ ˆ.( ) 0r i j+ =�
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53. The volume of the tetrahedron OPAB where 'O' is the origin and A(0, –1, 3) and B(2, 0, 5) is equal to
(A)32
3(B)
51
2
(C)17
2(D)
13
3
Paragraph for Question Nos. 54 to 55
The probability that a family has exactly 'n' children is αpn, n ≥ 1. All sex distributions of n children in a family have
the same probability.
54. The probability that a family contains exactly 'k' boys is (where k ≥ 1)
(A) αpk (1 – p)–k–1 (B) 2αpk (2 – p)–k–1
(C) 2αp (2 – p)–k (D) 2αpk–1 (2 – p)–k–1
55. Given that a family includes at least one boy, show that the probability that there are two or more boys is
(A)(2 )
p
p− (B)1
p
p−
(C) 2(2 )
p
p− (D) 2(1 )
p
p−
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 ONE is correct.
56. For the non-zero vectors a�
and b�
, match the following.
Column I Column II
(P) If . .a b a c=�
� � �
⇒ b c=�
�
(1) Always true
(Q). .a b a c=�
� � �
and a b a c× = ×�
� � �
⇒ b c=�
�
(2) Always false
(R) a b a c× = ×�
� � �
and b c≠�
�
, then a�
is (3) May be true, may be false it will depends
perpendicular to –b c
��
upon andb c�
�
(S) a b a b+ = −� �
� �
⇒ . 0a b =�
�
(4) True only for unit vector andb c�
�
Space for Rough Work
All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II)
18/19
Codes :
P Q R S
(A) 3 1 2 1
(B) 3 1 3 4
(C) 2 3 1 4
(D) 2 1 4 3
57. Match the following :
Column I Column II
(P) If the function y = e4x + 2e–x is a solution of the differential equation (1) 3
3
313
d y dy
dxdxk
y
−= then the value of
3
k is
(Q) Number of straight lines which satisfy the differential equation (2) 4
2
0dy dy
x ydx dx
⎛ ⎞+ − =⎜ ⎟⎝ ⎠
is
(R) If real value of 'm' for which the substitution, y = um will transform (3) 2
the differential equation, 4 4 6
2 4dy
x y y xdx
+ = into a homogeneous
equation then the value of 2m is
(S) If the solution of differential equation
2
2
22 12
d y dyx x y
dxdx+ = is (4) 1
y = Axm + Bx–n then number of possible non-zero values of
|m + n| are
Codes :
P Q R S
(A) 2 1 3 4
(B) 2 3 1 4
(C) 1 2 3 4
(D) 1 3 2 4
Space for Rough Work
Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014
19/19
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
58. A six digit number is selected at random the probability that sum of square of its digit is 9 is 1
900000
k + then sum
of digits of k is
59. If 2xy dy = (x2 + y2 + 1)dx, y(1) = 0 and y(x0) = 3 , then sum of all possible values of x
0 is
60. Let ˆ ˆ ˆ3 2 4a i j k= + +�
; ˆ ˆ2( )b i k= +�
and ˆ ˆ ˆ4 2 3c i j k= + +�
. If the equation
�� �
xa yb zc+ + = ˆ ˆ ˆ( )xi yj zkα + + has a non-
trivial solution, then find the sum of all distinct possible values of α.
� � �
TEST - 6 (Paper - II)
PHYSICS
1. (B)
2. (D)
3. (B)
4. (D)
5. (D)
6. (B)
7. (A,B,C)
8. (B,C,D)
9. (A,C)
10. (B,C)
11. (A, C)
12. (B)
13. (D)
14. (B)
15. (B)
16. (C)
17. (B)
18. (1)
19. (2)
20. (4)
CHEMISTRY
21. (B)
22. (D)
23. (A)
24. (B)
25. (B)
26. (D)
27. (A, B)
28. (B, C)
29. (A, B, C)
30. (B, C, D)
31. (A, B, D)
32. (D)
33. (A)
34. (C)
35. (D)
36. (A)
37. (C)
38. (7)
39. (4)
40. (4)
MATHEMATICS
41. (B)
42. (B)
43. (A)
44. (D)
45. (C)
46. (B)
47. (B, D)
48. (A, B)
49. (A, B)
50. (A, B)
51. (A, C)
52. (B)
53. (D)
54. (A)
55. (B)
56. (B)
57. (A)
58. (2)
59. (0)
60. (3)
ANSWERS
Test - 6 (Paper - II) (Answers & Hints) All India Aakash Test Series for JEE (Advanced)-2014
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