JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL...

46
RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions / JEE MAIN OFFICIAL ONLINE EXAM / 9 January19 Slot II / Solutions Date: 09 Jan 2019 Rao IIT Academy Website : www.raoiit.com 1

Transcript of JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL...

Page 1: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

/ JEE ­ MAINOFFICIAL ONLINE

EXAM / 9 January­19Slot­ II / Solutions

Date: 09 Jan 2019

Rao IIT Academy Website : www.raoiit.com1

Page 2: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

1. Di�iculty : Medium

Topics :

Simple harmonic motion,

Rao IIT Academy Website : www.raoiit.com2

Page 3: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

2. Di�iculty : Medium

Topics :

Modern Physics,

If particle making circular path in magnetic field. 

then                            ____________(I)

if particle path is straight line in magnetic and electric field. Only possible when magentic force is equal electric field force onthe particle

i.e                       _____________ (II)

          

From (I) and (II)

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Page 4: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

3.Di�iculty : Medium

Topics :

Modern Physics,

At   

4. Di�iculty : Easy

Topics :

Ray Optics,

 

 

Angle between two mirror will be 

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Page 5: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

5.Di�iculty : Medium

Topics :

Simple harmonic motion,

P.E = K.E

  or 

Position of the particle at

 

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Page 6: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

6.Di�iculty : Easy

Topics :

Kinematics,

 

           ___________ (I)

         ___________ (II)

    

    

    

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Page 7: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

7. Di�iculty : Medium

Topics :

Electrostatics,

 

Rao IIT Academy Website : www.raoiit.com7

Page 8: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

8. Di�iculty : Medium

Topics :

Physics,

 

As use know, 

9.Di�iculty : Easy

Topics :

ELECTROMAGNETISM,

Energy associated with electric field and with magnetic field is same for electromagnetic wave in free space.

Rao IIT Academy Website : www.raoiit.com8

Page 9: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

10.Di�iculty : Medium

Topics :

Semiconductors,

then, 

                   ________ (I) 

If   diode connect are reversed then

 

then  

                             __________ (II) 

Change in 

                

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Page 10: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

11.Di�iculty : Medium

Topics :

Gravitation,

Energy required to take a satellite to heigh 

          _______________ (I)

Kinetic energy required for the satellite to be in circular path is

       ________ ( II)

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Page 11: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

12. Di�iculty : Medium

Topics :

Communication systems,

Available 1% frequency as a signal band

No. of channels accomodated for transmitting TV signals

13. Di�iculty : Easy

Topics :

Thermodynamics,

Amount of heat transfer 

                                    

                                               

                                                

                                           

Rao IIT Academy Website : www.raoiit.com11

Page 12: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

14.Di�iculty : Medium

Topics :

Physics,

                             

Here, +ve zero error 

                              

  True reading  = (Main scale) + (Circular  L.C) - (+ve error) 

                         

                        

15. Di�iculty : Easy

Topics :

Units,Dimensions & Error analysis,

Units of 

             

By elimination method 

               

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Page 13: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

16. Di�iculty : Easy

Topics :

Current electricity,

       

Power

          

Power 

Heat energy 

                 

Rao IIT Academy Website : www.raoiit.com13

Page 14: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

17.Di�iculty : Easy

Topics :

Current electricity,

 current in CDEF branch is

  Voltage drop across    is

      

  Total potential drop across CF or DE is

  Potential drop across BC = 

  Total current 

       

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Page 15: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

18. Di�iculty : Easy

Topics :

Sound wave,

for given pipe, frequency for second harmonic, 

appearent frequency heard by running person

       

       

19. Di�iculty : Medium

Topics :

Wave optics,

Number of bright fringes   ( just above the C.M.)

                                     

                                      

Total no. of bright frings = 

                                    

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Page 16: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

20. Di�iculty : Easy

Topics :

Current electricity,

 

       

 

21.Di�iculty : Medium

Topics :

Current electricity,

BONUS

22.Di�iculty : Easy

Topics :

Current electricity,

Resistance

               

Rao IIT Academy Website : www.raoiit.com16

Page 17: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

23. Di�iculty : Easy

Topics :

Work ,Energy and power,

Let's findout acceleration is constant or variable.

              ...(a = const)

  displacement in 1st 5 sec

                    

24. Di�iculty : Di�icult

Topics :

Photoelectric e�ect,

          ....I

  work function = 4.7 = eV

for maximum K.E., 

We know, 

  for max. K.E. we will take 

                                

                                

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Page 18: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

25.Di�iculty : Di�icult

Topics :

Electrostatics,

       

        

       

Rao IIT Academy Website : www.raoiit.com18

Page 19: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

26. Di�iculty : Easy

Topics :

Newton's Laws of motion,

and 

      ... (for equilibrium)

                  ...(i)

      

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Page 20: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

27. Di�iculty : Medium

Topics :

Thermodynamics,

If    then

       

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Page 21: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

28. Di�iculty : Medium

Topics :

MAGNETISM,

(1) Circular loop : 

      

      

         

                                  ...(i)

(2) Circular coil :

     

 

        

                             ...(ii)

From (i) and (ii)

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Page 22: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

29.Di�iculty : Medium

Topics :

Simple harmonic motion,

As 

So 

As 

So 

30.Di�iculty : Medium

Topics :

Rotational Motion,

Rao IIT Academy Website : www.raoiit.com22

Page 23: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

1. Di�iculty : Easy

Topics :

Chemical Kinetics,

  Products

        ....(1)

both A and B doubled

      .....(2)

Only A is doubled

      ....(3)

from (1) and (3)

2. Di�iculty : Medium

Topics :

Aldehydes,Ketones,

3. Di�iculty : Easy

Topics :

d-block,F-block,

Zn has lowest enthalpy of atomisation due to very weak metallic bonding due to absence of unpaired d-electron.

Rao IIT Academy Website : www.raoiit.com23

CHEMISTRY

Page 24: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

4. Di�iculty : Medium

Topics :

AMINES,

pKa   Basicity

5. Di�iculty : Di�icult

Topics :

Nitrogen containing compounds,

6. Di�iculty : Medium

Topics :

Electrochemistry,

Rao IIT Academy Website : www.raoiit.com24

Page 25: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

7.Di�iculty : Easy

Topics :

PERIODIC PROPERTIES,

Second electron gain enthalpy is positive as energy needs to be applied to add    to a negatively charge ion.

8. Di�iculty : Medium

Topics :

Aldehydes,

9. Di�iculty : Medium

Topics :

Nitrogen containing compounds,

Rao IIT Academy Website : www.raoiit.com25

Page 26: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

10.Di�iculty : Easy

Topics :

GOC,

11. Di�iculty : Di�icult

Topics :

STRUCTURE OF ATOM,

Order of spread of orbitals

Same is order of decreasing orbital angular momentum.

Statement (A) is correct

for     distribution peak of orbitals shi�s towards le� / decreasing 

Statement (B) is correct. Hence option (1) is correct.

12. Di�iculty : Easy

Topics :

Environmental Chemistry,

pH of rain water is 5.6 due to formation of carbonic acid is atmosphere 

 

Rao IIT Academy Website : www.raoiit.com26

Page 27: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

13. Di�iculty : Easy

Topics :

Coordination Compounds,

Higher absorbed wavelength weaker the ligand.

14.Di�iculty : Di�icult

Topics :

Thermodynamics,

 

 

15.Di�iculty : Medium

Topics :

Solid State,

  density of copper crystal.

Edge length 

16. Di�iculty : Medium

Topics :

Coordination Compounds,

  is a strong field ligand hence will come higher splitting energy. 

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Page 28: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

17.Di�iculty : Di�icult

Topics :

Solutions,

 (Ice separated)

18.Di�iculty : Easy

Topics :

P-block-II,

  has tow    bonds

19. Di�iculty : Medium

Topics :

Chemical Bonding,

 bond order    paramagnetic

  bond order   diamagnetic.  

20. Di�iculty : Medium

Topics :

Aldehydes,Ketones,

(a) 2,4- DNP test : Coloured compound :   group may be aldehyde (or) ketone

(b) Iodoform test : Yellow precipitate   presence of methyl ketone

(c) Azodye test : No dye formation : Nitrogen of amine does not involve in diazotisation hence no dye formation.

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Page 29: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

21.Di�iculty : Easy

Topics :

S-block,

  is only group 1 element which forms nitrides.

22. Di�iculty : Medium

Topics :

BIOMOLECULES ,

23.Di�iculty : Medium

Topics :

Metallurgy,

Using given elignham diagram.

 can reduce  at all temperatures.

24. Di�iculty : Medium

Topics :

Environmental Chemistry,

Methemoglobinemia is caused by nitrates in water.

255. Di�iculty : Easy

Topics :

PRACTICAL ORGANIC CHEMISTRY,

Benzaldehyde -Absorbate 

Alumina - Adsorbent

Acetonitrile - Colourless liquid - Mobile phase in chromatography. It is simplest organic nitrile used as polar aprotic solvent.

Rao IIT Academy Website : www.raoiit.com29

Page 30: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

26.Di�iculty : Easy

Topics :

Chemical equilibrium,

27. Di�iculty : Easy

Topics :

Mole concept,

  is 

 moles produce  moles 

moles produce  moles 

28. Di�iculty : Easy

Topics :

Hydrogen & Its compound,

Temporary hardness is due to presence of bicarbonates of calcium and magnesium.

29. BDi�iculty : Easy

Topics :

Surface Chemistry,

 solution is negatively charged sol so by using hardy-Schulze rule large charge on cation is required for e�ectivecoagulation.   will be the answer.

Rao IIT Academy Website : www.raoiit.com30

Page 31: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

30. Di�iculty : Di�icult

Topics :

CARBOXYLIC ACIDS AND ITS DERIVATIVES,

In presence of lewis acid   electrophile attacks the benzene ring.

1.Di�iculty : Medium

Topics :

Straight lines,

Equation of              ...(i)

 is point of intersection of   and   and   and   ispoint of intersection   and  .

Find point   and  , then 

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MATHEMATICS

Page 32: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

2. Di�iculty : Medium

Topics :

Sequence & Series,

   

   

     

     

     

Rao IIT Academy Website : www.raoiit.com32

Page 33: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

3. Di�iculty : Medium

Topics :

Vectors,

              ...(i)

                                            

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Page 34: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

4.Di�iculty : Medium

Topics :

Indefinite integration,

            

            

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Page 35: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

5.Di�iculty : Medium

Topics :

ContinuityDi�erentiability & Derivatives,

 and 

when   point is 

Now eliminating 

again di�. :

6. Di�iculty : Easy

Topics :

Inverse Trigonometric Functions,

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Page 36: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

7. Di�iculty : Easy

Topics :

Hyperbola,

Hyperbola :               ...(i)

(i) contains 

8. Di�iculty : Easy

Topics :

Sequence & Series,

Let   be first term of A.P. and   be common di�erence.

                 ...(i)

             ...(ii)

             ...(iii)

 in G.P. 

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Page 37: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

9. Di�iculty : Medium

Topics :

Area bounded by the curves,

 (region above x-axis including x-axis)

             

10. Di�iculty : Medium

Topics :

Binomial Theorem,

Coe�. of   in 

 Coe�. of  in 

 Coe�. of  in

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RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

11. Di�iculty : Medium

Topics :

Complex Numbers,

 is root of   i.e   or 

12. Di�iculty : Medium

Topics :

MATRICES,

 

 

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RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

13.Di�iculty : Medium

Topics :

Trigonometric Equations,

then 

14.Di�iculty : Medium

Topics :

Three Dimensional Geometry,

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Page 40: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

15. Di�iculty : Medium

Topics :

Three Dimensional Geometry,

Plane containing 

                   --------- (1)

Required plane :        ------(2)

No. (2) contains 

(1) & (2) are 

16. Di�iculty : Medium

Topics :

PERMUTATION AND COMBINATION,

         

using symmetricity 

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RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

17. Di�iculty : Easy

Topics :

Quadratic Equations,

roots real & distined 

  ------(1)

considering roots lie in 

             -------- (2)

    ---- (3)

        ----(4)

using   & 

     

18. Di�iculty : Easy

Topics :

Quadratic Equations,

for roots to be rational, D should be non-negative perfect square and   given as positive integer.

but   does not give D as perfect square 

So, 

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Page 42: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

19.Di�iculty : Medium

Topics :

ContinuityDi�erentiability & Derivatives,Definite integration,

 is a constant function

as 

20.Di�iculty : Medium

Topics :

Application of derivatives,Conics,

 area

                       

       

Max. area

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Page 43: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

21.Di�iculty : Medium

Topics :

Probability,

Probability that IInd ball is red

22.Di�iculty : Medium

Topics :

Definite integration,

23. Di�iculty : Medium

Topics :

Di�erential Equations,

put   but 

 is constant

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Page 44: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

24. Di�iculty : Medium

Topics :

Limits,

25. Di�iculty : Medium

Topics :

Circles,

 : family of circle with centre at   & variable radius.

Distance between centre: 

26.Di�iculty : Medium

Topics :

Permutations & Combinations,

Number of natural numbers less than 7000 using 0,1,3,7,9 (rep. allowed)

Single digit : 4

 two digit  : 4.5 =20

Three digit : 4.5 .5 = 100

4 digit but less than 7000 : 2.5.5.5 =250 

So no. are : 250 +100 +20 +4=374. 

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Page 45: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

27.Di�iculty : Medium

Topics :

Determinants & Matrices,

        ---------(1)

     -------(2)

    -------(3)

System is consistent

28.Di�iculty : Easy

Topics :

STATISTICS,

   --------(1)

   -------(2)

                 

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Page 46: JEE MAIN Date: 09 Jan 2019 OFFICIAL ONLINE EXAM / 9 ... · RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions 2. Diiculty : Medium Topics : Modern

RAO IIT ACADEMY / JEE - MAIN OFFICIAL ONLINE EXAM / 9 January-19 Slot- II / Solutions

29.Di�iculty : Medium

Topics :

Functions,

Function is injective but not surjective.

30. Di�iculty : Medium

Topics :

Mathematical reasoning,

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