Date : 08-05-2014RIIT JEE-ADVANCED
TEST [6][ Paper - 1 ]
JEE | MEDICAL-UG | BOARDS | KVPY | NTSE | OLYMPIADS
Target : JEE 2014
ANSWER KEY
MATHEMATICS
1. (C) 2. (B) 3. (C) 4. (B) 5. (C)6. (A) 7. (C) 8. (B) 9. (D) 10. (B)11. (A,B,D) 12. (C,D) 13. (A,C,D) 14. (A,C) 15. (A,D)16. (8) 17. (3) 18. (1) 19. (7) 20. (8)
PHYSICS
21. (D) 22. (C) 23. (D) 24. (A) 25. (B)
26. (A) 27. (C) 28. (D) 29. (B) 30. (B)
31. (ABC) 32. (ABCD) 33. (ACD) 34. (ACD) 35. (AC)
36. (2) 37. (1) 38. (6) 39. (3) 40. (4)
CHEMISTRY
41. (B) 42. (D) 43. (A) 44. (D) 45. (D)
46. (B) 47. (B) 48. (C) 49. (B) 50. (A)
51. (A,B,D) 52. (AD) 53. (AB) 54. (ABCD) 55. (ABCD)
56. (2) 57. (4) 58. (9) 59. (4) 60. (4)
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
2
PART-I: MATHEMATICS
= = = = = = = = = = = = = = = = = = = = == = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =1. (C)
1! 2! 3! 4! 33 Topic :- Number System / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir
2. (B)
22 2sin & 0 sin 1
4x y
xy
Topic :- Trigonometrical Ratios and Identities / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir3. (C)
Homogenise & checkTopic :- Pair of straight - lines / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir
4. (B)
tan tan 0A A Topic :-Properties and Solutions of triangle / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir
5. (C)
Equation of the tangent to the curve 2 5 6x x from origin at point 2, 5 6 is
2 5 6 2 5y x (putting 0x y ) 6
Slope of tangent at point 62 5 5 2 6x
Now take help of the graphTopic :- Application of Derivatives / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir
6. (A)
3 2
3 2
d x n n xx x n x
Topic :- Indefinite Integration / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir7. (C)
Use property IV of definite IntegrationTopic :- Definite Integration / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir
8. (B)
2 2 2
4
.2 2 2x xy e dx e ydy dx
y
2 2
2 22 2 0x xe ed d x x c
y y
Topic :- Differential equation / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
3
9. (D)Length of diagonals of the parallelogram are equalTopic :- Complex Number / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir
10. (B)
1x y z
Topic :- Inverse Trigonometric function / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir11. (A,B,D)
Replace sin x with cosecx sin cosecx x 2sin 1x
Topic :- Functions / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir12. (C,D)
Period of f x can be 2 is a b
when ,a b f x has period . Let us consider the domain 0,
Case -I 0, ,2
f x 2 2sin cos sina b x a b x
where 2 2
sin ba b
and 2 2
cos aa b
is an a cute angle
Clearly maximum value will occur when 2
x
and minimum value at 0x or 2
x
Similarly Case - II ,2
x
Topic :- Functions / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir13. (A,C,D)
Analyse case by caseTopic :- Functions / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir
14. (A,C)
xx
etc.
2 2 2
2a b c
a b b c c a
x
q r b cr p c ap q a b
Topic :-Determinants and matrices / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
4
15. (A,D)Given equation can be written as
22
tan 1sec dy yydx x x
Put 2tan sec dy dty t ydx dx
2
1 1dt tdx x x
which is a linear equations
1
.dx
xI F e x
2
1tx xdx cx
tanx y n x c Topic :- Differential Equations / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir
16. (8)
10 sin cosOA OB
10 2 sin4
max10 2OA OB
Also OA OB AB Topic :- Straight line / Level :- 2 / (Adv. -1) Test - 6 / KGm Sir
17. (3)Clearly the given fixed point is focus of the parabola and the locus is directrix.Topic :- Parabola / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir
18. (1)20112011' ' 1P Q P P Q P
Topic :- Matrix and determinant / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir19. (7)
ˆˆ ˆ3 7A B i j k
Now max
ˆˆ ˆˆ ˆ3 7A B C i j k C
59 1 59 Topic :- Vector / Level :- 1 / (Adv. -1) Test - 6 / KGm Sir
20. (8)Let first term is a and common difference is d.
12a d sum of first nine terms 12 9 27d Hence 200 12 9 27 220d
89 109 427 27
d d
Topic :- Sequence and series / Level :- II / (Adv. -1) Test - 6 / KGm Sir
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
5
PART-II: PHYSICS= = = = = = = = = = = = = = = = = = = = == = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =21. (D)
a
A1 2A
V
V
v sin n
nv cos
2 /n
Length of the side of the regular polygon is decreasing from a to zero at the rates 2cosV Vn
the
time after which the particles meet,
2cos
atv v
n
22 sin
a
vn
the distance covered by each particle = vt
22sin
a
n
Topic: Kinematic_L-2_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
22. (C)
1 12 22 2 2
m mTk k
112
mk
2 12mk
Topic: SHM_L-2__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
6
23. (D)
6V
2V
1
1
The part of the circuit shown can be replaced by a single battery of emf
1 2 2 1
1 2
6 1 2 1 22
E r E rE vr r
Internal resistance 1 2
1 2
12
r rrr r
Hence original circuit diagram can be replaced by
2A BV V V Topic: Current Electricity_L-2__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
24. (A)For real object convex mirror always forms a virtual image
Using 1 1 1f v u we get , 1 1 1
v f u
For ,u f V is ve image is real
For ,u f V is ve image is virtual
option (A) is correctTopic: Optics_L-2_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
25. (B)Since temperature remains unchanged therefore , .Uf Ui So Q W In the first step which is isochoric,
0.W In second step, pressure pn
. Volume V is increased from V to nV
1p nW nV V PVn n
12 1RTn
Topic: Thermodynamic_L-I_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
7
26. (A)Distance between plates on left hund side is d whereas on the right hand side is
sind t d l is small Mean distance between plates
12
d d l
12
d l
then using 0 ,ACd
we get
12 20 0 111 22
l l lCd dd lx
20 1
2l l
d d
Topic: Capacitors_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir27. (C)
Current in left network 6 29 3
A
Current in right network 12 49 3
A
2 4 43 5 2 5 103 3 3XYV
83
V
Topic: Current Electricity_L-I__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir28. (D)
By law of refraction sin constantn we get sin 90 sin 90n ( where is the angle of indinationof ray at B)
Then it implies that 1cosn
and 2tan 1n 3/ 2 3/ 41 1y y
or 3/ 4 3/ 4dy y or dx y dydx
or
3 14
1/ 443 14
yx y
or 4 256x yTopic: Optics_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
8
29. (B)(B) Explanation
The equation of straight line AB passsing through two point, 0 0 0 0,3 & 3 ,V P V P is
0 00 0
0 0
3 33
P PP P V VV V
0 0 0
0
4PV PVPV
From ideal gas equation PV = nRT
0 0 0
0
4PV PVPV VTnR V nR
-----------------(1)
or2
0 0 0
0
4PV V PVTnRV
---------------------------(i)
For temperature to be maximum
0 0 00 4 2 0dT PV PVdV
Using the value of volume in equation (i)
we get 2
0 0 0 0 0max
0
4 2 2PV V P VT
nRV
2 20 0 0 0 0 0 0 0
max0 0
8 4 4 4PV PV PV PVTnRV nRV nR
choices (A), (C) & (D) are wrongTopic: Thermodynamics_L-II__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
30. (B)Using Fleming’s left hand rule, the Alpha particles, being positively charged and heavier, will be deflected tothe left but not large amount. Similarly electrons being negatively charged and lighter are deflected to theright.Topic: Magnetics_L-I_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
31. (ABC)
[sin sin ]XGIR
[cos cos ]YGIR
Now If then 2 sinxGlR
0YI so, choice (A) is correct and choice (D) is wrong.
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
9
If 2 ( If length of rod is infinite )
2sin sin2 2X
G GIr r
So, choice (B) is correct.
0YI
Relation between gravitational field intensity and gravitational potential,
dvIdr
0 2v
r
GdV drr
0 2 log loge eV G r
2 log loge eV G r
2 logerV G
loger
is undefined
i.e., choice (C) is correctTopic: Gravitation_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
32. (ABCD)ExplanationAngular momentum = Linear momentum x Perpendicular distance from the point of rotationL Jl
Also 2
3mlI
L I
2
3 3L Jl JI ml ml
Kinetic energy 2 2 2 2
23
22 23
L J l JKmlI m
3
2 2Cl JV
m
So. choices (A) , (B) , (C) and (D) are correct.Topic: Rotational_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
10
33. (ACD)Explanation:
Epoch = Initial phase 2
( obvious )
velocity of wave 2 110 5
VK
units
velocity of particle 2(3.5)sin 2 102P
dyV t xdt
units are to be observed carefully.So choices (A), (C) and (D) are correct.Topic: Waves_L-I_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
34. (ACD)
pLi
7
O
O
O
Q value of reaction is
2 4 7.06 7 5.6Q MeV
Q = 17.28 MeVHence choice (A) is correct and choice (B) is wrong
Applying energy conservation
2pK Q K ----------------------(1)
where pK and K are the kinetic energies of proton and -particle respectively
From conservation of linear momentum,
2 2 2 cosp pm k m k ------------(2)
Squaring both sides
22 4 2 4 cosp p pm k m k
11616pk k
i.e, pK K --------------------------(3)
Solving (1) and (3) with Q = 17.28 MeVHence choice (c) and (d) are correct,Topic: Modern Physcis_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
11
35. (AC)On contact , the net excess presure is given by
4 4 4 1 1 1r a b r a b
on merging 3 3 3
0 0 04 4 4 4 4 4
3 3 3P r P a P b
r a b
3 3 3 2 2 20 4P r a b a b r
r depends on 0P and
So, (a) and (c) are correct and (b) and (d) are incorrect.Topic: Properties of Matter_L-II__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
36. (2)
4 1 cos 2U x
duFdx
8sin 2x
8 2 .....x x is small
16x 16K
2 mTk
1216
sec2
2n Topic: SHM_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
37. (1)When shells are connected, charge on inner shell will be transferred to the outer shell
22 2i
K QKQVR R
i.e., 032KQVR
0V
1n Topic: Electrostatics_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
12
38. (6)
V LVB= (1) (2) (3)= 6V
6R C LV V V V ( All are in parallel)
LdiV Ldt
6 2 didt
3 /di A Sdt
at 2 sec , 3 6I ATopic: EMI_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
39. (3)Blocks A & C both move due to friction. But less friction is available to A as compared to C. Becausenormal reaction between A and B is is less. Maximum friction between A and B can be
sf , max Am g
12
mg
maximum acceleration of A can be, maxmax
2sf gam
Also, max 3D
D
m gam m
3Dm m
3n Topic: NLM and Friction_L-II__Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
40. (4)Mechanical energy is conserved in both the cases
22 2
0 01 5 1 12 4 2 2
m V mV I
i.e., 2
2 2 00 0
2516
VIV Vm R
i.e., 2
2
25 116
mKmR
i.e., 34RK
4n Topic: Rotational dynamics_L-II_Target-14_JEE-Advanced Test -6_Paper-1_Physics_SPp Sir
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
13
PART-III: CHEMISTRY= = = = = = = = = = = = = = = = = = = = == = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =41. (B)
Structure with octet complete (I and III) are more stable than structure with incomplete octet (II and IV).(Most Important point to decide the stability of resonating structures )Negative charge on more electronegative atom is more stable.Topic:Concept of Resonance_L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
42. (D)1·5 0.0821 223
1mixdRTM
P
= 33.61
2
1mix CO COM M x M x
33.61 44 28 1x x
0.35x 1 0.65x (mole fraction of CO)Topic: Gaseous State _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
43. (A)
Topic: Chemical Bonding _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.44. (D)
In B-D glucose all OH & CH2OH at equatorial position (B-D glucose is more stable than D glucose)Topic: Carbohydrates _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
45. (D)Si does not disproportionate because it cannot take negative oxidation state.Topic: P-Block _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
46. (B)
Topic:Chemical Kinetices _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.47. (B)
2 388 802
gm gmFeS Fe O
Let FeS is x gm in 100 gm of ore. x gm FeS produces 80x/88 gm of Fe2O3.
80488
100 100
x x 44x
Topic: Mole Concept - 1 _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
14
48. (C)H E nRT H E RT H E
Topic: Thermodynamics - 1 _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.49. (B)
both 3
||&
O
H C CH group are presentTopic: Carbonyl Compound - 1 _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
50. (A)
Topic: Alcohol, Alkene, Carbonyl (Mixed)_ L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
51. (A,B,D)
2 33 42B OH H O B OH H O
3 4B OH NaOH Na B OH
Topic: P-Block _ Sub Topic _ Boron Group _ L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
52. (AD)(A) 10–2M HCl will neutralise 10–2 M NaOH 7pH
(B) 1 410 10M HCl M HCl Resultant conc. = 5.05×10–3 M 2.3pH (C) NaCN will hydrolyse to give pH more than 7
(D) As 7a bpK pK pH
Topic: Inoic Equilibrium_ L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.53. (AB)
4 3 2 4312 4 3Al C H O Al OH CH
2 2 424 2Be C H O Be OH CH
Topic: Metal Carbides _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
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54. (ABCD)101
A
A
V litreP atm
isothermal
1
10
B
A AB
B
V litreP VP atmV
B C adiabatic process
PV K
B B C CP V P V
BC B
C
VP PV
For Monoatomic Gas 52
5 /3110
10CP
5 213 310 10
For Diatomic Gas 7 215 57 10 10
5 CP
As the curve for compression (AB) is higher than the cruve for expansion (BC) thre network in done on thesystem .Topic: Cycloalkanes _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
55. (ABCD)
(A)
O
O
H C3
H
(1) LiAlH4 (excess)
(2) H O2
OH
OH
H C3
H
opticallyin active
(B)
O
O
H C3
H
(1) CH MgBr3 (excess)(2) H O2
OH
OH
H C3
H
opticallyin active
(C)
(D)
Topic: Stereo Isomerism_L- 2_Target-14_Advanced Test [6]_P-1_KRch sir.
RIIT JEE Advanced Test- 6/ Paper - 1 (Solutions)/ Target JEE-2014
16
56. (2)
2
4
85
n factor of Cu S isn factor of KMnO is
8 1.25 5 ? ? 2Topic: Mole _L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
57. (4)2 13.6IE Z eV
4 13.6 54.4IE of He eV 3 16 13.6 217.6IE of M eV
2 16Z 4Z Topic: Atomic Structure_L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
58. (9)Topic: Stereo Isomerism_L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.
59. (4)
ElcB Mech occurs when
(1) Acidic H is present
(2) Poor leaving group is presentTopic: Elimination Reations_L- 2_Target-14_Advanced Test [6]_P-1_KRch sir.
60. (4)Topic: Carbon Family_ Sub Topic : Silicates _ L- 1_Target-14_Advanced Test [6]_P-1_KRch sir.