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RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
1. Di�iculty : Medium
Topics :
Elasticity,
2. Di�iculty : Easy
Topics :
Kinematics,
Velocity becomes negative a�er same time and the negative slope is constant.
3.Di�iculty : Easy
Topics :
Work ,Energy and power,
Rao IIT Academy Website : www.raoiit.com2
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
4.Di�iculty : Easy
Topics :
Work ,Energy and power,
or
or
or
or At
5.Di�iculty : Easy
Topics :
Rotational Mechanics,
Rao IIT Academy Website : www.raoiit.com3
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
6.Di�iculty : Medium
Topics :
Rotational Mechanics,
Torque of gravity about
or
7. Di�iculty : Easy
Topics :
Gravitation,
The desired graph is
Rao IIT Academy Website : www.raoiit.com4
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
8. Di�iculty : Easy
Topics :
Caloriemetry,
Heat lost by ball = Heat gain by calmimetre and water
9.Di�iculty : Easy
Topics :
Elasticity,
and
or
10. Di�iculty : Easy
Topics :
Physics,Heat and thermodynamics,
for hydrogen
for nitrogen
Rao IIT Academy Website : www.raoiit.com5
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
11. Di�iculty : Easy
Topics :
Physics,Heat and thermodynamics,
12. Di�iculty : Easy
Topics :
Simple harmonic motion,
The period of K.E graph is half of the period of displacement graph.Comment :-The points on the graph on -axis should be di�erentiable.In all option mentioned, the graph has cusps at the points on -axis.
13. Di�iculty : Medium
Topics :
Wave optics,
Rao IIT Academy Website : www.raoiit.com6
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
14. Di�iculty : Medium
Topics :
Electrostatics,
Since dipole moment is in
planeConsider
According to the problem
15. Di�iculty : Easy
Topics :
Capacitors,
8 rows, then Get
So minimum of capacitors are
Rao IIT Academy Website : www.raoiit.com7
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
16. Di�iculty : Easy
Topics :
Current electricity,
By KVL : -
So charge on capacitor is
17. Di�iculty : Easy
Topics :
Current electricity,
P.d across each resistor is zero. Hence correct is zero in each resistor.
18. Di�iculty : Easy
Topics :
Physics,
Topic : Classical Magnetism
Time period
Rao IIT Academy Website : www.raoiit.com8
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
19. Di�iculty : Easy
Topics :
Current electricity,
or
or or or
20. Di�iculty : Easy
Topics :
Electromagnetic Induction( EMI ),
or
or
or
or
or
Rao IIT Academy Website : www.raoiit.com9
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
21. Di�iculty : Easy
Topics :
Modern Physics,
or
The graph of Vs is as follows
22.Di�iculty : Easy
Topics :
Ray Optics,
Diverging lens forms the image at its focus. The image formed by diverging lens in the object to converging lens. Distance of the object from converging lens is i.e., object is at double focal point.
Image forms at double focal point on the other side of the lens.
Rao IIT Academy Website : www.raoiit.com10
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
23.Di�iculty : Easy
Topics :
Wave optics,
4th Bright of will coincide with 5th bright of
24. Di�iculty : Easy
Topics :
Modern Physics,
Rao IIT Academy Website : www.raoiit.com11
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
25. Di�iculty : Easy
Topics :
Modern Physics,
26. Di�iculty : Easy
Topics :
Modern Physics,
no. of undecayed nucleus no. of decyaed nucleus is
27. Di�iculty : Easy
Topics :
Physics,
Topic - SemiconductorVoltage gain of the amplifier is
-Ve sign indicates phase di�erence is
Rao IIT Academy Website : www.raoiit.com12
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
28. Di�iculty : Easy
Topics :
Physics,
Topic - Communication System will not be there in the frequencies.
29.Di�iculty : Medium
Topics :
Current electricity,
Null point does not change
30. Di�iculty : Easy
Topics :
Surface tension,
Rao IIT Academy Website : www.raoiit.com13
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
31. Di�iculty : Easy
Topics :
Chemistry,
Topic : Thermochemistry .....(1)
....(2)
.....(3)(1)+2 (2) and +(3)
32. Di�iculty : Medium
Topics :
Chemistry,Mole concept,
33. Di�iculty : Easy
Topics :
Chemistry,Thermodynamics,
From First law of Thermodynamics
for an Adiabatic process
34. Di�iculty : Easy
Topics :
Chemistry,Surface Chemistry,
Tyndall e�ect is observed when (1) The diameter fo the dispersed particle is not much smaller than the wavelength of the light used.(2) The refractive indices of the dispersed phase and dispersion medium di�er greatly in magnitude.
Rao IIT Academy Website : www.raoiit.com14
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
35. Di�iculty : Medium
Topics :
Chemistry,Solid State,
Distance of closest approach
36.Di�iculty : Medium
Topics :
Chemistry,Electrochemistry,
,
Strongest reducing agent is the atom/ ion which is easily oxidised i.e. having the largest value of standard oxidation potential(SOP)
is the maximum value.
37. Di�iculty : Medium
Topics :
Chemistry,Solutions,
Since,
or
Rao IIT Academy Website : www.raoiit.com15
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
38. Di�iculty : Easy
Topics :
Chemistry,Atomic Structure,
; n = orbit number,
39. Di�iculty : Medium
Topics :
Chemistry,Chemical Kinetics,
(At 300K)
40.Di�iculty : Easy
Topics :
Chemistry,Ionic equilibrium,
For the hydrolysis of a salt of weak acid and weak base
41. Di�iculty : Di�icult
Topics :
Chemistry,S-block,
form basic carbonate while lithium from normal carbonate .
Rao IIT Academy Website : www.raoiit.com16
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
42. Di�iculty : Medium
Topics :
Chemistry,Chemical Bonding,
is diamagnetic only and has bond order 3.0. Rest all are paramagnetic
43. Di�iculty : Medium
Topics :
Chemistry,P-block,
44. Di�iculty : Medium
Topics :
Chemistry,
Topic : Environmental science ppm causes brown mottling of teeth
ppm causes laxative ppm causes blue baby syndrome.
45. Di�iculty : Easy
Topics :
Chemistry,
Topic : Periodic properties in each species (all are isoelectronic).
Rao IIT Academy Website : www.raoiit.com17
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
46. Di�iculty : Medium
Topics :
Chemistry,S-block,
cold - dil
47. Di�iculty : Medium
Topics :
Chemistry,d-block,
48.Di�iculty : Di�icult
Topics :
Chemistry,
Topic : Qualitative analysis
is responsible for decolourisation of acidic solution of .
49.Di�iculty : Medium
Topics :
Chemistry,Mole concept,
is by mass is kgs
It replaced by weight is doubled i.e., kg kg increase
Rao IIT Academy Website : www.raoiit.com18
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
50. Di�iculty : Di�icult
Topics :
Chemistry,
Topic : coordination
No of moles of ions
moles. moles of gives moles of ions
No. of outside the co - ordination sphere should be 2
51. Di�iculty : Medium
Topics :
Chemistry,
Topic - Nitrogen containing compoundsAniline undergoes protination in con , so it undergoes metanitration
52. Di�iculty : Medium
Topics :
Chemistry,
Topic - AlkylhalidesTo shown decolourisation compound must be unsaturated
Rao IIT Academy Website : www.raoiit.com19
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
53. Di�iculty : Medium
Topics :
Chemistry,Polymers,
Nylon - 6 is prepared from caprolactum,caprolactum on hydrolysis it gives aminocarboxylicacid it undergoes polymerisation toform Nylon - 6
54.Di�iculty : Easy
Topics :
Chemistry,GOC,
Non aromatic compunds are less stable than aromatic
Rao IIT Academy Website : www.raoiit.com20
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
55. Di�iculty : Easy
Topics :
Chemistry,
Topic - AlkylhalidesRate of stabiling
56. Di�iculty : Easy
Topics :
Chemistry,
Topic - Hydrocarbons
Rao IIT Academy Website : www.raoiit.com21
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
57. Di�iculty : Di�icult
Topics :
Chemistry,
Topic - Carbohydrates
Sugar with hemiacetal are reducing sugar.
58. Di�iculty : Easy
Topics :
Chemistry,
Topic - Hydrocarbons
Product contains two chiral carbons so, 4 S.I
Rao IIT Academy Website : www.raoiit.com22
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
59.Di�iculty : Di�icult
Topics :
Chemistry,CARBONYLS,
60. Di�iculty : Di�icult
Topics :
Chemistry,CARBONYLS,
DIBAL-H can reduce esters only, not carboxylicacids
Rao IIT Academy Website : www.raoiit.com23
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
61. Di�iculty : Medium
Topics :
Functions,One-One Function (Injection),Onto Function (Surjection),
is many one
Range = Co-domain
62. Di�iculty : Medium
Topics :
Quadratic Equations,
as
Rao IIT Academy Website : www.raoiit.com24
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
63. Di�iculty : Easy
Topics :
Complex Numbers,Cube roots of unity,
i.e. is non-real cube root of unity
and
64. Di�iculty : Easy
Topics :
Determinants & Matrices,Adjoint of square Matrix,
65.Di�iculty : Medium
Topics :
Determinants & Matrices,Cramer's Rule,
As system no solution then
when then both equation and obeserv that if then no solutionsif then infinite solutions
Rao IIT Academy Website : www.raoiit.com25
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
66. Di�iculty : Medium
Topics :
Permutations & Combinations,
67. Di�iculty : Easy
Topics :
Binomial Theorem,
68. Di�iculty : Medium
Topics :
Sequence & Series,
are in AP
Rao IIT Academy Website : www.raoiit.com26
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
69. Di�iculty : Medium
Topics :
Sequence & Series,Functions,
70.Di�iculty : Easy
Topics :
Limits,
Rao IIT Academy Website : www.raoiit.com27
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
71. Di�iculty : Medium
Topics :
Math,Di�erentiation of one function with respect to another function,
Put and
as
72. Di�iculty : Medium
Topics :
Application of derivatives,
Equation of normal at will be which is satisfied by only in the given options.
Rao IIT Academy Website : www.raoiit.com28
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
73. Di�iculty : Easy
Topics :
Application of derivatives,
74. Di�iculty : Easy
Topics :
Math,Indefinite integration,
(Put n = 4)
Rao IIT Academy Website : www.raoiit.com29
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
75. Di�iculty : Easy
Topics :
Math,Definite integration,
76. Di�iculty : Di�icult
Topics :
Math,Area under curve,
Required area
Rao IIT Academy Website : www.raoiit.com30
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
77.Di�iculty : Easy
Topics :
Di�erential Equations,
...(I)
I.F. of equation (I) is Hence answer is
As So
Now
78. Di�iculty : Easy
Topics :
Straight lines,
or as
Triangle has co-ordinates
As one side is horizontal one altitude will be vertical arthocentre
Rao IIT Academy Website : www.raoiit.com31
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
79. Di�iculty : Medium
Topics :
Circles,Conic Sections,
If the radius of circle is r, then its centre will be
In an isoscales right angled above,
80.Di�iculty : Easy
Topics :
Conic Sections,
and
Again
Hence equation of ellipse is
and equation of normal at point is:
Equation of normal at point
is
Rao IIT Academy Website : www.raoiit.com32
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
81.Di�iculty : Medium
Topics :
Math,Conic Sections,
Which is satisfied by
82.Di�iculty : Easy
Topics :
Math,Three Dimensional Geometry,
Normal perpendicular to both the lines
Normal vector parallel to perpendicular
where
Hence equation of plane is
Now distance from point (1, 3, -7) to the plane is
Rao IIT Academy Website : www.raoiit.com33
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
83. Di�iculty : Medium
Topics :
Math,Three Dimensional Geometry,
Line PQ parallel to
As point R lies on plane then
Hence point R is (2, 2, 8)
84. Di�iculty : Medium
Topics :
Math,Vectors,
Using (2) in (1) we have
Rao IIT Academy Website : www.raoiit.com34
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
85. Di�iculty : Easy
Topics :
Math,Probability,
n = number of trials = 10
p = probability of drawing green ball
= probability of success
q = probability of failure
As the trials are Bernoulli trials, variance = npq
86. Di�iculty : Medium
Topics :
Math,Probability,
P(Exactly one of A or B occurs)
Adding all three
P (Atleast one event occurs) =
Rao IIT Academy Website : www.raoiit.com35
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
87. Di�iculty : Medium
Topics :
Math,Probability,
Two di�erent numbers are taken from the set
Let x + y = 4m ......(II)x - y = 4n ............ (III), x > yNow x = 2(m+n) y = 2(m-n)Hence both x and y are even numbers Then x and y are both in form of 4k or 4k + 2So order pair of (x, y) are
So Probability
88. Di�iculty : Medium
Topics :
Math,Trigonometric Ratios & Identities,
Rao IIT Academy Website : www.raoiit.com36
RAO IIT ACADEMY / JEE - MAIN EXAM - 2017 / SOLUTIONS / CODE - A
89. Di�iculty : Easy
Topics :
Math,
Topic : Height & Distance
90.
T T T F T T TT F F F T F TF T T T T T TF F T T F T T
Di�iculty : Easy
Topics :
Math,
Topic : Mathematical Reasoning
Rao IIT Academy Website : www.raoiit.com37
Hence it is a Tautology
Alternate :