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RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions JEE MAIN OFFICIAL ONLINE EXAM / 11 January19 Slot II / Solutions Date: 11 Jan 2019 Rao IIT Academy Website : www.raoiit.com 1

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Page 1: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

JEE ­ MAINOFFICIAL ONLINE

EXAM / 11 January­19Slot­ II / Solutions

Date: 11 Jan 2019

Rao IIT Academy Website : www.raoiit.com1

Page 2: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

1. Di�iculty : Easy

Topics :

Newton's Laws of motion,System of particles,

2. Di�iculty : Medium

Topics :

MAGNETISM,

W.D. by magnetic is zero

W.D. =  

3. Di�iculty : Easy

Topics :

Electromagnetic waves,

 = 

Rao IIT Academy Website : www.raoiit.com2

Page 3: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

4. Di�iculty : Easy

Topics :

Heat and thermodynamics,

                                        

                                 

5. Di�iculty : Easy

Topics :

Modern Physics,

From   to   :-

             ...........(1)

           ..........(2)

 

Rao IIT Academy Website : www.raoiit.com3

Page 4: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

6. Di�iculty : Medium

Topics :

Wave optics,

 single b/w first & second di�raction

  Aungular fringe width

No. of bringe = 

                                   = 4.81

7. Di�iculty : Easy

Topics :

Current electricity,

                   

     

     

     

Rao IIT Academy Website : www.raoiit.com4

Page 5: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

8. Di�iculty : Easy

Topics :

Capacitors,

9.Di�iculty : Easy

Topics :

Simple harmonic motion,

Rao IIT Academy Website : www.raoiit.com5

Page 6: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

10. Di�iculty : Medium

Topics :

Ray Optics,

11. Di�iculty : Easy

Topics :

Modern Physics,

Rao IIT Academy Website : www.raoiit.com6

Page 7: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

12. Di�iculty : Medium

Topics :

Heat and thermodynamics,

 condition :- 

 condition :-

  

   

13. Di�iculty : Medium

Topics :

Rotational Motion,

Taking torque about the point of contact

14. Di�iculty : Easy

Topics :

Electrostatics,

Rao IIT Academy Website : www.raoiit.com7

Page 8: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

15. Di�iculty : Medium

Topics :

Heat and thermodynamics,

% rise in temp =   

16. Di�iculty : Medium

Topics :

First law of thermodynamics,

 Constant

 For polytropic process

                                               

                                           

                                           

17. Di�iculty : Easy

Topics :

Units,Dimensions & Error analysis,

 

Rao IIT Academy Website : www.raoiit.com8

Page 9: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

18. Di�iculty : Easy

Topics :

Simple harmonic motion,

Max K.E. 

19. Di�iculty : Medium

Topics :

Current electricity,

N = Total turns

length of winding = (d) diameter (N)

Self inductance increased by 3 times 

20. Di�iculty : Medium

Topics :

Equivalent resistance,

Rao IIT Academy Website : www.raoiit.com9

Page 10: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

21. Di�iculty : Di�icult

Topics :

MAGNETISM,

(Bonus Question)

No option is correct

22. Di�iculty : Medium

Topics :

Simple harmonic motion,

Option (D) is correct

23. Di�iculty : Medium

Topics :

Current electricity,

Option (C) is correct

Rao IIT Academy Website : www.raoiit.com10

Page 11: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

24. Di�iculty : Medium

Topics :

Rotational Motion,

 (option A is correct)

25.Di�iculty : Easy

Topics :

Kinematics,

Option (C) is correct

26. Di�iculty : Easy

Topics :

Rotational Motion,

 (Option (C) is correct)

27. Di�iculty : Medium

Topics :

Heat and thermodynamics,

 

Rao IIT Academy Website : www.raoiit.com11

Page 12: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

28. Di�iculty : Easy

Topics :

MAGNETISM,

Option (A) is correct 

29. Di�iculty : Medium

Topics :

Communication systems,

Figure of merit 

Current senstivity = 

 

30. Di�iculty : Medium

Topics :

Communication systems,

Amplitude varies as 8 to 10  i.e. 9   1

time period as   (Sinusoidal wave)

AND   (carrier wave)

signal is 

Rao IIT Academy Website : www.raoiit.com12

Page 13: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

1. Di�iculty : Medium

Topics :

Atomic Structure,

We know   

 of photoelectron can be written as

2.Di�iculty : Easy

Topics :

Thermodynamics,

    

         

             

            

 

Rao IIT Academy Website : www.raoiit.com13

Page 14: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

3. Di�iculty : Easy

Topics :

BIOMOLECULES AMINOACIDS,

 gives phthalein dye test because of phenolic ring

gives ester test

 Gives carbolamine test because of   amine

4. Di�iculty : Easy

Topics :

CHEMISTRY IN EVERYDAY LIFE,

Taj Mahal is being slowly disfigured and discoloured due to acid rain.

Rao IIT Academy Website : www.raoiit.com14

Page 15: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

5.Di�iculty : Easy

Topics :

Volumetric analysis,

For   solution - 

For   solution-

             

              

     

            

Now for   solution-

                   

            

6. Di�iculty : Easy

Topics :

Periodic,

On going le� to right in a period electronegativity increases due to decrease in size and increase in e�ective nuclear charge.

Hence  is more electonegative than .

Rao IIT Academy Website : www.raoiit.com15

Page 16: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

7. Di�iculty : Easy

Topics :

Solid State,

As ball is placed at the edge of a B.C.C. cube.

              ......  (i)

             ...... (ii)               

        

8. Di�iculty : Easy

Topics :

GOC,

  

lone pair of  are not in resonance. Hence these are favorable sites for protonation.

9. Di�iculty : Easy

Topics :

d-block,

10. Di�iculty : Easy

Topics :

Polymers,

Rao IIT Academy Website : www.raoiit.com16

Page 17: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

11. Di�iculty : Easy

Topics :

Chemical equilibrium,

Vont Ho� factor 

                       

12. Di�iculty : Easy

Topics :

Thermodynamics,

We know

Given

 is 

Hence if   then endothermic 

         if   then exothermic

13. Di�iculty : Easy

Topics :

AMINES,

Rao IIT Academy Website : www.raoiit.com17

Page 18: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

14. Di�iculty : Easy

Topics :

Electrochemistry,

            

             

            

  

15. Di�iculty : Easy

Topics :

Acid base titration,

16. Di�iculty : Easy

Topics :

P-block,

Due to inert pair e�ect on moving down the relative stability of  oxidation state increases.

 

Rao IIT Academy Website : www.raoiit.com18

Page 19: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

17. Di�iculty : Easy

Topics :

Thermodynamics,

For feasible reaction 

18. Di�iculty : Easy

Topics :

Phenols,Alcohols,

   

 

decolourises   and also reacts with 

 

Rao IIT Academy Website : www.raoiit.com19

Page 20: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

19. Di�iculty : Medium

Topics :

Coordination Compounds,

 is

 is bidentate

 is monodentate.

The co-ordination number 

20. Di�iculty : Medium

Topics :

CHEMISTRY IN EVERYDAY LIFE,

Allosteric e�ect   Molecule binding to a site other than the active site of enzyme.

Competitive inhibitor     molecular binding to active site of enzyme

Receptor    Cruicila molecule for communication in the body.

 Poison   Molecule binding to enzyme covalently.

21. Di�iculty : Easy

Topics :

d-block,

It is a example of roasting because it is in the presence of 

22. Di�iculty : Easy

Topics :

Coordination Compounds,

No. of   bond 

 bonds 

Rao IIT Academy Website : www.raoiit.com20

Page 21: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

23. Di�iculty : Easy

Topics :

GOC,

24. Di�iculty : Medium

Topics :

Aromatic compounds,

25. Di�iculty : Easy

Topics :

Chemical Kinetics,

Zeroth order reaction.

The time taken in reaction of 

hence time required for the reaction of 

26. Di�iculty : Easy

Topics :

Aromatic compounds,

Rao IIT Academy Website : www.raoiit.com21

Page 22: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

27. Di�iculty : Easy

Topics :

Liquid Solutions,

Cheese is a colloid in which dispersed phase liquid and continuous phase is solid. In milk dispersion phase and continuousphase both are liquid. In smoke dispersion phase is solid and medium is gas

28. Di�iculty : Medium

Topics :

S-block,

 is obtained from solvay process

 is the reason of temperorary hardness

 is obtained by castner-kellner process

is a ingredient

29. Di�iculty : Di�icult

Topics :

Hydrogen,

 is a electron precise hydride

30.Di�iculty : Easy

Topics :

CHEMISTRY IN EVERYDAY LIFE,

 causes sti�ness of flower buds

Rao IIT Academy Website : www.raoiit.com22

Page 23: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

1. Di�iculty : Easy

Topics :

Area under curve,

equation of tanged : 

                              

Required area

                    

 

 

Rao IIT Academy Website : www.raoiit.com23

Page 24: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

2.Di�iculty : Easy

Topics :

Parabola,

                       

                       

Rao IIT Academy Website : www.raoiit.com24

Page 25: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

3. Di�iculty : Di�icult

Topics :

Indefinite integration,

Let 

Let

Rao IIT Academy Website : www.raoiit.com25

Page 26: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

4. Di�iculty : Medium

Topics :

Definite integration,

Let  

Rao IIT Academy Website : www.raoiit.com26

Page 27: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

5. Di�iculty : Easy

Topics :

Determinants & Matrices,

                          

                    

                       

          

Now,

                          

                         

                         

 

Rao IIT Academy Website : www.raoiit.com27

Page 28: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

6. Di�iculty : Medium

Topics :

Di�erential Equations,

Let 

7. Di�iculty : Easy

Topics :

Probability,

 No. of white balls drawn

                          

Rao IIT Academy Website : www.raoiit.com28

Page 29: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

8. Di�iculty : Easy

Topics :

Three Dimensional Geometry,Vectors,

Equation of a plane

Rao IIT Academy Website : www.raoiit.com29

Page 30: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

9. Di�iculty : Easy

Topics :

Functions,

                               

     

Now for   only

         

Now finally

       

Range   here codomain is subset of range so, question is wrong, but if we so; this is not one-one but codomain considercodomain as 

The range   codomain, so 

10. Di�iculty : Easy

Topics :

Number Systems,

If the squares of two numbers are equal, then the numbers are equal

Rao IIT Academy Website : www.raoiit.com30

Page 31: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

11. Di�iculty : Medium

Topics :

Quadratic Equations,Inverse Trigonometric Functions,

      or      

         

Rao IIT Academy Website : www.raoiit.com31

Page 32: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

12. Di�iculty : Medium

Topics :

Vectors,

Bisector of   and   is  

                                                                             

                                                                             

 

 

 

 

 

 

 

 

Then

Rao IIT Academy Website : www.raoiit.com32

Page 33: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

13. Di�iculty : Medium

Topics :

Functions,

Required answer

                         

14. Di�iculty : Easy

Topics :

Straight lines,

15. Di�iculty : Easy

Topics :

Hyperbola,

Rao IIT Academy Website : www.raoiit.com33

Page 34: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

16. Di�iculty : Medium

Topics :

Trigonometric Equations,

17. Di�iculty : Medium

Topics :

Introduction Determinants & Matrices,

Put 

So^, 

So^,

Rao IIT Academy Website : www.raoiit.com34

Page 35: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

18.Di�iculty : Medium

Topics :

Solutions of Triangle,

                             

                                                                               

                                                             

                     

19. Di�iculty : Medium

Topics :

Sequence & Series,

Rao IIT Academy Website : www.raoiit.com35

Page 36: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

20. Di�iculty : Medium

Topics :

Limits,

.

             

21. Di�iculty : Medium

Topics :

Sequence & Series,

22. Di�iculty : Medium

Topics :

Mathematics,

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RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

23. Di�iculty : Medium

Topics :

Functions,

 is increasing 

24. Di�iculty : Medium

Topics :

Limits,

R.H.D     

L.H.D     

L.H.D = R.H.D

 is di�esentiable at 

 is Every where di�erentiable

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Page 38: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

25. Di�iculty : Medium

Topics :

Conics,

This is parabola

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Page 39: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

26.Di�iculty : Medium

Topics :

Mathematics,

                                              

Now , 

         

        

     

     

   

    

27. Di�iculty : Medium

Topics :

Complex Numbers,

    

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Page 40: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

28. Di�iculty : Medium

Topics :

Probability,

Sum should be   So we don't want total   so;

we can select all except 

we can select all except 

we can select all except 

we can select all except

we can select all except  

Required probability

Total No. of subsets

29. Di�iculty : Medium

Topics :

Straight lines,

          

So point      

Reflection is 

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Page 41: JEE MAIN Date: 11 Jan 2019 OFFICIAL ONLINE EXAM / 11 ...€¦ · 01/11/2019  · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions 27. Diiculty

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 11 January-19 Slot- II / Solutions

30. Di�iculty : Medium

Topics :

Conics,

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