target eng-2018 rao iit academy date: 20 may 2018 … advanced/2018/paper-2...rao iit academy / jee...

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


2.Di�iculty : Easy

Topics :

Viscosity newton's law of viscosity,

hence correct options (ACD)


Topics :

Electrostatics,

and its component along -axis will be zero

hence correct options (AB).



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)



6.Di�iculty : Di�icult

Topics :

Sound wave,

subtracting two equations

Correct option (A) and (C)


Topics :

System of particles,



8.Di�iculty : Medium

Topics :

Kinematics,


Topics :

Kinematics,




Topics :

Current electricity,

round o� two decimal


Topics :

Experiments based on using verniercalipers and screw gauge ( micrometer ),




Topics :

Thermodynamics,


Topics :

Modern Physics,Photoelectric e�ect,




Topics :

Bohr’s model of an atom,


Topics :

Electrostatics,

(1) Point charge at origin

(2)

(3) Uniform line charge

(4)

(5) Infinite plane charge constant




Topics :

Gravitation,


Topics :

Thermodynamics,

Process (1) is adiabatic

Process (2) is isobaric

Process (3) is isochoric

Process (4) is isothermal




Topics :

Rotational Mechanics,

(P)

hence all conserved

(S)

not conserved

is only conserved

(R)

conserved

(Q)

conserved

hnce option (A)




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 .


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


CHEMISTRY



Topics :

Aromatic compounds,




Topics :

Polymers,BIOMOLECULES ,

glucopyranose


Topics :

Chemical Kinetics,

or

Comparing with So it is a straight line with negative slope.

For _______

constant

rate constant does not depend on concentration




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




Topics :

P-block,

Therefore and have at least one bridging oxo group.Rao IIT Academy Website : www.raoiit.com15



Topics :

Mole concept,Metallurgy,

Noumber of equivalents of


Topics :

Volumetric analysis,

m.eq of

......... (1)

From given equation __________

.......... (2)

Because of is in both equations, so


Topics :

Stereochemistry,

One meso compound and 7 optically active isomers formed.




Topics :

Aromatic compounds,


Topics :

Thermodynamics,

______________________________________________________________________________

To prevent this reaction,

......... ( considering equality for minimum )

Minimum




Topics :

Chemical Kinetics,

......... (i)

......... (ii)

equation (i) - (ii)

absolute value is




Topics :

Electrochemistry,

________________________________________




Topics :

Coordination Compounds,

(1)

(2)

(3)

(4)

(5)

due to back pairing of takes place

(6)

Due to electron pairing takes place




Topics :

Alcohols,Ethers,




Topics :

Alkyl halides,




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.



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)




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




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.




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.




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.




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



7 Di�iculty : Easy

Topics :

Definite integration,

Put




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




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




Topics :

Di�erential Equations,




Topics :

Functions,Di�erential Equations,

Put

Put




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.




Topics :

Vectors,

Now

required value




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




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




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




Topics :

Hyperbola,Conics,

distance between foci is



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


target eng-2018 rao iit academy date: 20 may 2018 … advanced/2018/paper-2...rao iit academy / jee...

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