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Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
Target Eng-2018 Rao IIT Academy JEE ADVANCED
EXAM 2018 / PAPER - 2 Solutions
Date: 20 May 2018
1. Di�iculty : Medium
Topics :
Work ,Energy and power,
Speed is proportional to time
hence force is constant
Force is constant, hence conservative
Correct options are (ABD)
Rao IIT Academy Website : www.raoiit.com1
PHYSICS
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
2.Di�iculty : Easy
Topics :
Viscosity newton's law of viscosity,
hence correct options (ACD)
3. Di�iculty : Medium
Topics :
Electrostatics,
and its component along -axis will be zero
hence correct options (AB).
Rao IIT Academy Website : www.raoiit.com2
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
4. Di�iculty : Di�icult
Topics :
Ray Optics,
So option (D) is correct.
5. Di�iculty : Easy
Topics :
Modern Physics,
Hence correct options (A) and (C)
Rao IIT Academy Website : www.raoiit.com3
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
6.Di�iculty : Di�icult
Topics :
Sound wave,
subtracting two equations
Correct option (A) and (C)
7. Di�iculty : Medium
Topics :
System of particles,
Rao IIT Academy Website : www.raoiit.com4
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
8.Di�iculty : Medium
Topics :
Kinematics,
9.Di�iculty : Di�icult
Topics :
Kinematics,
Rao IIT Academy Website : www.raoiit.com5
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
10. Di�iculty : Medium
Topics :
Current electricity,
round o� two decimal
11. Di�iculty : Medium
Topics :
Experiments based on using verniercalipers and screw gauge ( micrometer ),
Rao IIT Academy Website : www.raoiit.com6
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
12. Di�iculty : Easy
Topics :
Thermodynamics,
13.Di�iculty : Medium
Topics :
Modern Physics,Photoelectric e�ect,
Rao IIT Academy Website : www.raoiit.com7
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
14. Di�iculty : Easy
Topics :
Bohr’s model of an atom,
15. Di�iculty : Easy
Topics :
Electrostatics,
(1) Point charge at origin
(2)
(3) Uniform line charge
(4)
(5) Infinite plane charge constant
Rao IIT Academy Website : www.raoiit.com8
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
16. Di�iculty : Medium
Topics :
Gravitation,
17. Di�iculty : Medium
Topics :
Thermodynamics,
Process (1) is adiabatic
Process (2) is isobaric
Process (3) is isochoric
Process (4) is isothermal
Rao IIT Academy Website : www.raoiit.com9
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
18.Di�iculty : Di�icult
Topics :
Rotational Mechanics,
(P)
hence all conserved
(S)
not conserved
is only conserved
(R)
conserved
(Q)
conserved
hnce option (A)
Rao IIT Academy Website : www.raoiit.com10
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
1.Di�iculty : Medium
Topics :
Coordination Compounds,
(A) has two geometrical isomers.
(B) If bidentate is replaced by two cyanide ligands.
(C)
In presence of
Therefore it is diamagnetic in nature.
(D) is weaker ligand than , so absorbs light at longer wavelength as compared
to .
2.Di�iculty : Di�icult
Topics :
Qualitative analysis,
(A) and both show characteristic green colour in the flame test, so can't be distinguished.
(B) Only can give precipitate of when passing in acidic medium.
(C) and both show precipitate by passing in faintly basic medium.
(D) From electrochemical series
Rao IIT Academy Website : www.raoiit.com11
CHEMISTRY
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
3. Di�iculty : Medium
Topics :
Aromatic compounds,
Rao IIT Academy Website : www.raoiit.com12
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
4. Di�iculty : Easy
Topics :
Polymers,BIOMOLECULES ,
glucopyranose
5.Di�iculty : Medium
Topics :
Chemical Kinetics,
or
Comparing with So it is a straight line with negative slope.
For _______
constant
rate constant does not depend on concentration
Rao IIT Academy Website : www.raoiit.com13
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
6. Di�iculty : Di�icult
Topics :
Chemical equilibrium,
That measn on increasing temperature reaction is shi�ing in backward direction, so it is exothermic reaction i.e.,
It is possible when because (given)
at equilibrium
Rao IIT Academy Website : www.raoiit.com14
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
7. Di�iculty : Medium
Topics :
P-block,
Therefore and have at least one bridging oxo group.Rao IIT Academy Website : www.raoiit.com15
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
8. Di�iculty : Di�icult
Topics :
Mole concept,Metallurgy,
Noumber of equivalents of
9. Di�iculty : Easy
Topics :
Volumetric analysis,
m.eq of
......... (1)
From given equation __________
.......... (2)
Because of is in both equations, so
10. Di�iculty : Di�icult
Topics :
Stereochemistry,
One meso compound and 7 optically active isomers formed.
Rao IIT Academy Website : www.raoiit.com16
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
11.Di�iculty : Medium
Topics :
Aromatic compounds,
12. Di�iculty : Medium
Topics :
Thermodynamics,
______________________________________________________________________________
To prevent this reaction,
......... ( considering equality for minimum )
Minimum
Rao IIT Academy Website : www.raoiit.com17
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
13. Di�iculty : Medium
Topics :
Chemical Kinetics,
......... (i)
......... (ii)
equation (i) - (ii)
absolute value is
Rao IIT Academy Website : www.raoiit.com18
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
14.Di�iculty : Medium
Topics :
Electrochemistry,
________________________________________
Rao IIT Academy Website : www.raoiit.com19
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
15. Di�iculty : Medium
Topics :
Coordination Compounds,
(1)
(2)
(3)
(4)
(5)
due to back pairing of takes place
(6)
Due to electron pairing takes place
Rao IIT Academy Website : www.raoiit.com20
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
16. Di�iculty : Medium
Topics :
Alcohols,Ethers,
Rao IIT Academy Website : www.raoiit.com21
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
17.Di�iculty : Medium
Topics :
Alkyl halides,
Rao IIT Academy Website : www.raoiit.com22
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
18. Di�iculty : Medium
Topics :
Ionic equilibrium,
P.
m. moles m. moles so a�er reaction, will existas an acidic bu�er and its or is independent of dilution.
Q. m. moles m. moles only (salt) exists in solution. From salthydrolysis concept ________
........ (for salt of weak acid and strong base)
changes to times
R. m. moles m. moles only (salt of w. base and st. acid) will exist in solution
......... (from salf hydrolysis)
......... (
S. Because remains constant, so solubility of salt will not be changed, hence or will not be changeda�er dilution.
Rao IIT Academy Website : www.raoiit.com23
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
MATHEMATICS
. .1.
Di�iculty : Easy
Topics :
Inverse Trigonometric Functions,Limits,
(A) Zero is not in domain
(B) Zero is not in domain
(C)
(C is incorrect)
(D)
(D is correct)
Rao IIT Academy Website : www.raoiit.com24
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
2.Di�iculty : Medium
Topics :
Circles,
Let
and
and
Also
Thus lies on circle with points and as diameter.
Locus of is
does not lie on (D is correct)
Let midpoint of chord of be
is
Equation of chord is
Locus of midpoint of such chords passing through is
lies on B is incorrect
does not lie on C is incorrect
does not lie on D is correct
Also A is incorrect
Rao IIT Academy Website : www.raoiit.com25
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
3.Di�iculty : Di�icult
Topics :
Determinants & Matrices,
...(i) ...(ii)
...(iii)
Eq. (ii) + 2 eq (i) gives
Eq (ii) - 2eq (iii) gives
original condition
(A) unique solution
(B) ...(i) ...(ii)
...(iii)
we get
for infinite solutions
which is not the original condition.
It does not have a solution.
(C) ...(i) ...(ii)
...(iii)
Clearly planes are parallel for infinite solution which can be true considering original condition.
(D)
It has a solution.
Rao IIT Academy Website : www.raoiit.com26
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
4.Di�iculty : Easy
Topics :
Circles,Ellipse,Conics,Area under curve,
Let equation of common tangent be
One of the lines is
For ellipse
Equation of ellipse is
also (A is correct) For Area bounded by and is
Area
C is correct.
Rao IIT Academy Website : www.raoiit.com27
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
5.Di�iculty : Di�icult
Topics :
Complex Numbers,
...eq (i)
...eq (ii)
(eq i) (eq ii) we get
(A) If i.e. It has unique solution A is correct
(B) may have infinite or no solution
(D) If has more than one solution then no solution and unique solutions are ruled out. It has infinite solution.
(C) is a circle.
If has infinite solution then it lies on the line line and circle may have atmost two solutions.
Rao IIT Academy Website : www.raoiit.com28
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
6.Di�iculty : Medium
Topics :
Limits,Application of derivatives,
Apply L'Hospital
A is incorrect.
(B) Cosider
is decreasing
is decreasing
B is correct
(C) Apply Rolle's theorem in
for some C is correct
(D)
D is correct
Rao IIT Academy Website : www.raoiit.com29
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
7 Di�iculty : Easy
Topics :
Definite integration,
Put
Rao IIT Academy Website : www.raoiit.com30
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
8.Di�iculty : Di�icult
Topics :
Definite integration,
where etc.
for max
i.e. but and are dependent there is no such combination of s.t. each
and each
Keeping symetrically, anwser is not possible
let us see whether is possible i.e.
or or
Rao IIT Academy Website : www.raoiit.com31
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
9. Di�iculty : Easy
Topics :
Permutations & Combinations,
number of one-one functions from X to Y
number of onto functions from Y to X.
We have to distribute 7 items to 5 children such that each gets atleast one item.
Possible cases are
Rao IIT Academy Website : www.raoiit.com32
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
10. Di�iculty : Easy
Topics :
Di�erential Equations,
Rao IIT Academy Website : www.raoiit.com33
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
11.Di�iculty : Easy
Topics :
Functions,Di�erential Equations,
Put
Put
Rao IIT Academy Website : www.raoiit.com34
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
12.Di�iculty : Easy
Topics :
Three Dimensional Geometry,
Let the image of P ie Q be
Image of Q about is P
distance of P from x axis
is in first octant
R is image of P about x - y plane.
Rao IIT Academy Website : www.raoiit.com35
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
13.Di�iculty : Easy
Topics :
Vectors,
Now
required value
Rao IIT Academy Website : www.raoiit.com36
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
14.Di�iculty : Easy
Topics :
Binomial Theorem,
Consider
eq (i)
eq (ii)
Di�erentiate equation (i) we get
eq (iii)
Required series is coe�icient of in the product of eq (ii) and eq (iii)
coe�icient of in
Rao IIT Academy Website : www.raoiit.com37
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
15. Di�iculty : Easy
Topics :
Functions,
As is negative
Also
Range of
Its range contains (0,1) as well as
Also domain of f contains
domain of g is
Rao IIT Academy Website : www.raoiit.com38
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
16.Di�iculty : Easy
Topics :
Permutations & Combinations,
6 Boys:
5 Girls :
(i) Committee of 5 has 3 boys and 2 girls
(ii) Atleast 2 members and equal boys and girls
(iii)
(iv) Total ways of forming comitte of 4 with atleast 2 girls
Total ways of forming comittee of 4 with atleast 2 girls with both included
Rao IIT Academy Website : www.raoiit.com39
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
17.Di�iculty : Easy
Topics :
Hyperbola,Conics,
distance between foci is
Rao IIT Academy Website : www.raoiit.com40
Rao IIT Academy / JEE - ADVANCED EXAM - 2018 / PAPER - 2 / Solutions
18 Di�iculty : Medium
Topics :
ContinuityDi�erentiability & Derivatives,
(i)
(both finite) continuous but non di�erentiable
at
(ii)
Limit does not exist as discontinuous at
(iii)
Hence it is di�erentiable and its derivatives is continuous at
(iv)
di�erentiable
Now
Clearly discontinuous at is oscillatory
Rao IIT Academy Website : www.raoiit.com41