RT(Main)

(1)

Batches: NWTR820A01-A04, B01, NWTW820G01,

B01-B08, C01-C02 & PANINI820-G1, XI1-XI6, XIC

PHYSICS, CHEMISTRY & MATHEMATICS

JEE

_–

MAINS- 2020

PHASE

_–

III

CODE: 119572

Time

Time Allotted:

Allotted: 3

3 Hours

Hours

Maximum

Maximum Marks:

Marks: 360

360



 Do Do not opnot open this en this Test Test Booklet Booklet until yuntil you are ou are asked asked to dto do so so.o. 

 Please Please read the read the instructioninstructions cas carefully. refully. You aYou are allottere allotted 5 d 5 minutes minutes specifically specifically for for this purthis purpose.pose.

Impo

Importa

rtant

nt Ins

Ins ttruc

ructtions

ions ::

1.

1. Immediately fImmediately fill in the ill in the particulars oparticulars on this pan this page of the ge of the Test BookTest Booklet withlet withBlue / Black Ball Point Pen. Use ofBlue / Black Ball Point Pen. Use of pencil is strictly prohibited.

pencil is strictly prohibited.

2.

2. The Answer The Answer Sheet is kept Sheet is kept inside this Tesinside this Test Booklet. t Booklet. When you are When you are directed to opedirected to open the Test Bn the Test Booklet, take ooklet, take outout the Answer Sheet and fill

the Answer Sheet and fill in the particulars carefully.in the particulars carefully. 3.

3. The The test test is is ofof3 hours3 hours duration. duration. 4.

4. The The Test Test Booklet Booklet consists consists ofof9090questions. The maximum marks arequestions. The maximum marks are360360.. 5.

5. There There areare threethree parts in the question paper A, B, C consisting of parts in the question paper A, B, C consisting of Physics, ChemistryPhysics, Chemistry andand MathematicsMathematics

having 30 questions in each part of equal weightage. Each question is allotted

having 30 questions in each part of equal weightage. Each question is allotted4 (four)4 (four) marksmarks for correctfor correct answer and

answer and – – 1 mark 1 mark for wrong answer for wrong answer .. 6.

6. There is only There is only one correct resone correct response for each ponse for each question. Filling up question. Filling up more than one rmore than one response in any esponse in any question willquestion will be treated as wrong response and marks for wrong response will be

be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction.deducted accordingly as per instruction. 7. Use

7. UseBB lue / lue / BB lalack ck BB alall Point Pl Point P en only en only for writing particulars / marking responses on for writing particulars / marking responses on S S ide-1ide-1 and and S S ide-2ide-2 of the of the Answer Sheet.

Answer Sheet.UsUs e of e of pencil is spencil is s trictly ptrictly prohibited.rohibited.

8.

8. No candidate is No candidate is allowed to callowed to carry any arry any textual material, prtextual material, printed or written, bits inted or written, bits of papers, pager, of papers, pager, mobile phone,mobile phone, any electronic device, etc. except the Admit Card inside the examination hall

any electronic device, etc. except the Admit Card inside the examination hall / room./ room. 9.

9. On completion On completion of the test, of the test, the candidate mthe candidate must hand over ust hand over the Answer the Answer Sheet to the InvigilSheet to the Invigilator on duty ator on duty in thein the Room / Hall.

Room / Hall.HoweverHowever , the candidat, the candidates es are aare allllowed to towed to take aake away this way this TesTes t Bt B ooklet with themooklet with them..

10.

10. Do not fold or make any stray marks on the Answer Sheet.Do not fold or make any stray marks on the Answer Sheet.

Name of the Candidate (in Capital Letters) :_____________________________________

FIITJEE

(2)

NWTR820A01-A04,B01, NWTW820G01,B01-B08,C01-C02 & PANINI820-G1,XI1-XI6, XIC_MAINS-PT3(PCM)

PART

_–

A (PHYSICS)

1. A satellite of mass m, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required- is

(A) mgR/4 (B) 2mgR

(C) mgR/2 (D) 3mgR/4

2. A satellite S is moving in an “elliptical” orbit around the earth. The mass of the satellite is very small compared to the mass of the earth

(A) the acceleration of S is always directed towards the centre of the earth

(B) the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant

(C) the total mechanical energy of S varies periodically with time (D) the linear momentum of S remains constant in magnitude

3. A point particle of mass 0.1kg (attached to a horizontal spring) is executing SHM with amplitude of 0.1m. When the particle passes through the mean position, its K.E. is 8×10 –3J. What is the value of spring constant k?

(A) 1.6 N/m (B) 0.4 N/m

(C) 3.2 N/m (D) 4 N/m

4. In the figure the intensity of waves arriving at D from two coherent sources S1 and S2 is I0. The wave length of the wave is

 = 4m. Resultant intensity at D will be

(A) 4I0 (B) I0 (C) 2I0 (D) zero S1 S2 4m 3m D

5. Two pendulums of length 121 cm and 100cm start vibrating. At some instant the two are in the mean position in the same phase. After how many vibration of the short pendulum the two will be in phase in the mean position?

(A) 10 (B) 11

(C) 20 (D) 21

6. The graph, shown in the diagram, represents the variation of temperature (T) of the bodies, x and y having same surface area, with time (t) due to the emission of radiation. Find the correct relation between the emissivity and absorptivity power of the two bodies

y

t T

x

(A)

E E and a a

_x



_y _x



_y (B)

E E and a a

_x



_y _x



_y

(C)

E E and a a

_x



_y _x



_y (D)

E E and a a

_x



_y _x



_y

(3)

7. A person carrying a whistle emitting continuously a note of 272 Hz is running towards a reflecting surface with a speed 18 km/ hr. The speed of sound in air is 345 m/s. The number of beats heard by him is

(A) 4 (B) 6

(C) 8 (D) 3

8. A closed gas cylinder is divided into two parts by a piston held tight. The pressure and volume of gas in two parts respectively are (P, 5V) and (10P,V). If now the piston is left free and the system undergoes isothermal process, then the volume of the gas in two parts respectively are

(A) 2V, 4V (B) 3V, 3V

(C) 5V, V (D) 4V, 2V

9. Two bodies of mass M1 and M2 are initially at rest and a distance R apart. They the move directly

towards one another under the influence of their mutual gravitational attraction. What is the ratio of distance travelled by M1 to distance travelled by M2?

(A) 1 2

M

(B) 2 1

M

(C) 1 (D)

1

2

10. The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

(A) 1 2 k A k (B) 2 1 k A k (C) 1 1 2 k A k k (D) 2 1 2 k A k k k1 k2 P M

11. A cylindrical tube, open at both ends, has a fundamental frequency f in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now

(A) f/2 (B) 3f/4

(C) f (D) 2f

12. A wave represented by the equation y = acos(kx - t) is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for other wave is

(A) a sin (kx + t) (B) – a cos (kx - t)

(C) – a cos(kx + t) (D) – a sin (kx - t) 13. Which of the following process does not occur through convection?

(A) Boiling of water (B) Land breeze and Sea breeze

(C) Circulation of air around furnace (D) Heating of glass bulb through filament S pace for r oug h work

(4)

14. The graph shown in the figure represents energy density E

versus  for three sources sun, welding arc, tungsten filament. (A) 1 –Tungsten, 2 –Welding arc, 3 –Sun

(B) 1 –Sun, 2 – Tungsten, 3 –Welding arc (C) 1 –Sun, 2 –Welding arc, 3 – Tungsten (D) 1 – Welding arc, 2 – Sun, 3 – Tungsten

E

O 

1 2 3

15. If a tunnel is dug along the diameter of the earth and a body is dropped into it, them the time taken by it to cross the tunnel once is (R = radius of earth)

(A)

g

R

2

 _(B)

g

R

 (C)

R

g

2

 _(D)

R

g



16. P –V plots for two gases during adiabatic processes are shown in the figure. Plots 1 and 2 should correspond respectively to

(A) He and O2 (B) O2 and He

(C) He and Ar (D) O2 and N2

P

V 2 1

17. A block of ice at –10°C is slowly heated and converted to steam at 100°C. Which of the following curves represent the phenomenon qualitatively?

(A) T e m p e ra tu re Heat supplied (B) T e m p e ra tu re Heat supplied (C) T e m p e ra tu re Heat supplied (D) T e m p e ra tu re Heat supplied

18. A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that BO is equal to ‘x’. Further, it is observed that the frequency of 1st

harmonic (fundamental frequency) in AB is equal to 2nd_harmonic

frequency in CD. Then, length of BO is

(A) L/5 (B) 4L/5 (C) 3L/4 (D) L/4 A B C D m L x

(5)

19. Two SHM’s are represented by y1 = 10 sin



3 t

  

/ 4



and y2 = 5 sin(3 t) + 53 cos(3t), the ratio of

their amplitudes is

(A) 1 : 2 (B) 5 :

7

(C) 2 : 1 (D) 1:1

20. A rocket is fired form the earth to the moon. The distance between the earth and the moon is r and the mass of the earth is 81 times the mass of the moon. The gravitational force on the rocket will be zero, when its distance from the moon is

(A)

r

20

(B)

r

15

(C)

r

10

(D)

r

5

21. In a resonance tube experiment, the first resonance is observed when the length of the air column is 14.2 cm and the second resonance when the length of the air column is 46.2 cm. Which of the following is correct choice? (Velocity of sound = 320 m/s)

(A) The wavelength of the vibration set up in the air column is 64 cm. (B) The diameter of the tube is 3 cm.

(C) The frequency of the tuning fork with which the air column is in resonance is 400 Hz. (D) The tube will be again in resonance when the length of the air column is 78.6 cm.

22. Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of Nitrogen at temperature T0. While box B contains one mole of helium at temperature 0

7T

3

. The boxes

are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature. (Ignore the heat capacity of boxes). Then the final temperature of the gases in terms of T0 is:

(A)

5T

0

2

(B) 0

3T

7

(C)

7T

0

3

(D) 0

3T

2

23. A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is acceleration due to gravity at surface then orbital speed is

(A) gx (B)

gR

R x



(C) 2

gR

R x



(D) 1 2 ₂

gR

R x







_







24. One mole of a gas expands with temperature according to the relation V = KT2/3_{. What is the work}

done when the temperature changes by 300_C?

(A) 10 R (B) 20 R

(C) 30 R (D) 40 R

(6)

25. A liquid takes 5 minutes to cool from 600_{C to 50}0_{C, when temperature of surrounding is 30}0_{C. How}

long will it take to cool fr om 500_{C to 40}0_{C? (nearly)}

(A) 5 minute (B) 4 minute

(C) 9 minute (D) 10 minute

26. At t = 0, a transverse wave pulse in a wire is described by the function y = 6/(x² – 3) where x and y are in metres. The function y(x, t) that describes this wave equation if it is travelling in the positive x direction with a speed of 4.5 m/s.

(A)





2

6 y

x 4.5t

3 





(B)

_

_

2

6 y

x 4.5t

3 





(C)





2

6 y

x 4.5t

3 



(D)

_

_

2

6 y

x 4.5t

3 



27. A simple pendulum has time period T1. The point of suspension is now moved upward according to the

relation. y = Kt2_{. (K = 1m/s}2_{) where y is vertical displacement. The time period now become T}₂_{. The}

ratio of 2 1 2 2

T

is (g = 10 m/s 2₎ (A) 6/5 (B) 5/6 (C) 1 (D) 4/5

28. Pressure versus temperature graph of an ideal gas to equal number of moles of different volumes are plotted as shown in figure. Choose the correct alternative

(A)

V V V V

₁



₂



₃



₄ (B)

V V V V

₄



₃



₂



₁ (C)

V V ;V

₁



₂ ₃



V and V

₄ ₂



V

₃ (D)

V V ,V

₁



₂ ₃



V and V

₄ ₂



V

₃ P T 1 2 3 4

29. The slope of a graph plotted between T 2

and

r 3_{for a planet, will be}

(A) zero (B)

4 

GM

(C) GM

/4



2 _(D)

_{4 /}



2 GM

30. The period of a simple pendulum inside a stationary lift is T. The lift accelerates upwards with an acceleration of g/3. The time period of pendulum will be

(A)

2

T _(B) 2 T (C) 3 2 T _(D) 3 T

(7)

PART

_–

B (CHEMISTRY)

1. CH₃CH₂CHCH₂Cl CH₃

Which of the following electronic effect is observed in the above molecule?

(A) +R effect (B) –R effect (C) +I and – I effect (D) Hyperconjugation 2. Which of the following is not an isomer of n-hexane?

(A) (B)

(C) (D)

3. Which of the following hydrocarbon is prepared by the following reaction?

Dry ether 3

2CH Cl Na





Products

(A) CH4 (B) C2H4 (C) C2H6 (D) C2H2

4. Which of the following is the least pollutant gas?

(A) CO2 (B) SO2 (C) N2 (D) CO

5. Which of the following is an electrophilic substitution reaction?

(A) CH₃ 2 Cl /h  CH₂Cl HCl (B) 2 Cl /Fe  CH₃ CH₃ Cl (C) 2 Cl Heat  CH₃ CCl₃ (D) CH₃ 2 Cl /h  CHCl ₂

(8)

6. Which of the following compound is most acidic in nature?

(A) CH3CH2COOH (B) ClCH2CH2COOH

(C) CH₃CHCOOH

Cl

(D) ClCH₂CHCOOH

Cl

7. Which functional group is present in the functional isomer of alcohols?

(A) – CHO (B)

C = O

(C) - O - _(D)

C O

-O

8. Which of the following hydrocarbon cannot decolourise bromine water?

(A) 2-butene (B) 2-pentyne

(C) 2-methyl butane (D) 2-methylbutene

9. The electrophile formed when a mixture of conc. H2SO4 and conc.HNO3 are heated is

(A) SO3 (B)

NO

₂

(C) NO+ _(D)

2

N



10. Which of the following gas is not formed by combustion of coal?

(A) CO2 (B) SO2

(C) CH4 (D) CO

11. Which of the following compound has the highest value of Ka?

(A) CH₂OH (B) OH CH₃ (C) OCH₃ (D) CH₂CH₂OH

(9)

12. Which of the following compound shows geometrical as well as optical isomerism? (A) 2 2 2 3

CH CH CH CH CH CH

 

 



CH₃ (B) CH3 – CH = CH – CH = CH – CH3 (C) 3 2 3

CH CH CH CH CH CH

  

 

Cl (D) 2 2

CH

   

CH CH CH CH

Cl

13. Which of the following reaction produces ethane(C2H6)?

(A) Conc.H SO2 4 3 2 Heat

CH CH OH





(B)

CH CH Cl

₃ ₂



Alcohol/KOH_Heat



(C)

HC CH





H /Ni2 _(D) Zn 2 2 Heat

ClCH CH Cl





14. Which of the following compound is most reactive towards Friedel Craft methylation reaction?

(A) Cl (B) CH₃ (C) CCl₃ (D) CH₂OH

15. Acid rain contains

(A) hydrides of sulphur and nitrogen (B) oxides of sulphur and nitrogen (C) oxy-acids of sulphur and nitrogen (D) chlorides of sulphur and nitrogen 16. Which of the following carbonium ion is most stable?

(A) CH₃CH₂CH₂CH₂CH₂ (B) CH₃ - C CH₃ C₂H₅ (C) CH₃CHCHCH ₃ CH₃ (D) CH₃CHCH₂CH₂ CH₃

(10)

17. Which of the following substance is most basic in non-polar solvent?

(A) CH3NH2 (B) CH3NHCH3 (C) N C H₃ CH₃ CH₃ (D) CH₃ - N - CH₃ CH₃ CH₃

18. Which is not an isomer of formula C4H8?

(A) (B) (C) (D) 19. CH₃ - C - CH₂ - CH₃ CH₃ CH₃

How many monochloro product(s) is/are formed by the above compound? (Do not consider stereoisomers)

(A) 1 (B) 2

(C) 3 (D) 4

20. Which of the following compound will produce maximum heat, when reacts with H2 in presence of Ni

as catalyst? (A) CH3 – CH = CH2 (B) CH2 = CH2 (C) CH3CH = CHCH3 (D) CH3CH2CH = CH2 21. 3 2 HCl

CH CH CH CH







Products

CH₃

The major product of above reaction is: (A) 3 2 2

CH CH CH CH Cl



CH₃ (B) 3 3

CH CH CH CH



CH₃ Cl (C) 3 2 3

CH C CH CH

 



CH₃ Cl (D) 3 2 3

CH CH CH CH



CH₂Cl

(11)

22. CH3 – CH = CH – CH3 and CH3 – CH2 – C  CH can be distinguished by using

(A) Br 2/H2O (B) H2/Ni (C) AgNO3/NH4OH (D) HCl 23. CH₃ NO₂ 1 2 3 4

Above compound will be favourably attacked by electrophiles at positions

(A) 1 and 2 (B) 2 and 3

(C) 3 and 4 (D) 2 and 4

24. The most stable free radical out of the following is:

(A) (B)

(C) (D)

25. Which of the following reaction intermediate is not an electron deficient species?

(A) Carbocation (B) Carbanion

(C) Free radical (D) Carbene

26. Which of the following compound has the highest melting point?

(A) (B)

(C) (D)

(12)

27. Addition of which of the following substance to an unsymmetrical alkene does not follow Markownikoff’s rule?

(A) Cl2/CCl4 (B) Br 2/H2O

(C) HCl (D) NO2Cl

28. CH3CH = CH2 will produce only a secondary alcohol when treated with

(A) H2O/H+ (B)



3



₂ 2 4

Hg OCOCH ,H O

NaBH

(C) 2 6 2 2

B H ,THF

NaOH,H O

(D) Cl2/H2O 29. OH BrCl

Product





One of the products of above reaction is:

(A) OH Br (B) OH Cl (C) OH Cl (D) Cl

30. CH3 – CH = CH2 will produce a racemic mixture when reacts with

(A) HCl (B) Cl2/CCl4

(C) H2O/H+ (D) H2/Ni

(13)

PART

_–

C (MATHEMATICS)

1. For the complex number z , if

1 iz

1 z i

 

 , then

(A) z lies on the imaginary axis (B) z lies on the real axis (C) z lies on the unit circle (D) None of these

2. The number of diagonals that can be drawn by joining the vertices of an octagon is

(A) 28 (B) 48

(C) 20 (D) None of these

3. O(0, 0) , A (z) and B (22 , 0) are the vertices of a right angle triangle at A . If |z| = 1 + 3 , then arg(z) is

(A) /12 (B) /6

(C) /3 (D) /2

4. sin A, sin B, sin C are in A.P for the  ABC then

(A) altitudes are in A.P (B) sides are in A.P (C) altitudes are in H.P (D) medians are in A.P

5. A point ‘z’ moves on the curve |z – 4 – 3i| = 2 in an argand plane. The maximum & minimum value of |z| are

(A) 2, 1 (B) 6, 5

(C) 4, 3 (D) 7, 3

6. Let x be a non real complex number satisfying (x – 1)3_{+ 8 = 0 , then x is}

(A) 1 + 2 (B) 1 – 8 

(C)1 - 22 _{(D) 1 + 2}2

7. The number of triangles which can be formed from 12 points out of which 7 are collinear is

(A) 105 (B) 210

(C) 175 (D) 185

8. If 13_C

ris denoted by Cr , then the value of C1+C5+C7+C9+C11 is equal to

(A) 212_-287 _{(B) 2}12_-165

(C) 212_-C₂_-C₁₃ _{(D) none of these}

9. In a  ABC, if c2_{+ a}2_– b2_{= ac, then  B =}

(A)

6

 (B)

4

 (C)

3

 (D) none of these S pace for r oug h work

(14)

10. If arg

 

z ₁ = arg(z2), then

(A) z2 = k z1 –1 (k > 0) (B) z2 = kz1 (k > 0)

(C) |z2| = | z1| (D) none of these

11. The general solution of the equation tan2 + 23 tan = 1 is given by

(A)

2

   _(B)

_n

1

2 



   

_

_





(C)

n

12

   _(D)

n

12



12. If |z1| =|z2|=|z3| = 1 and z1 z2 z3 are represented by the vertex of an equilateral triangle, then which of

the following is NOT true.

(A) z1 + z2 + z3 = 0 (B) z1 z2 z3 = 1

(C) z1 z2 + z2 z3 + z3 z1= 0 (D)

z z z

_{1 2 3} = 0

13. Four different persons have got four different rooms in a hotel. Number of ways that no- one will go to his own room.

(A) 9 (B) 12

(C) 16 (D) 4

14. The value of amp (i) + amp (i2_{), where i =}



₁_{and  =} 3₁_{= non –real, is}

(A) 0 (B) 2  (C)  (D) 2 15. If



1 tan

2 y





3 sin

3 z



4 x

cos

1 x

cos

2 ₂





2

















, then

(A) x may be a multiple of  (B) x can not be an even multiple of  (C) z can be a multiple of  (D) None of these

16 The number of ways of distributing 10 different books among 4 students (S1, … S4) such that S1 and

S2 gets 2 books each and S3 and S4 get 3 books each is

(A) 12600 (B) 25200 (C)10_C 4 (D)

10 !

2 ! 2 ! 3 ! 3 !

17. Integral part of



5 5 11



2n 1 



is

(A) even (B) odd

(C) neither (D) can’t Say

(15)

18. The coefficient of x in the expansion of

9 2

1 x

x















is (A) 1 (B) 1 (C) 48 (D) 0

19. If the data given to construct a triangle ABC is a = 5, b = 7, sin A = 3/4, then it is possible to construct

(A) only one triangle (B) two triangles

(C) infinitely many triangles (D) no triangle 20. If tan a - tan b = 0, then the values of  form a series in

(A) A.P. (B) G.P.

(C) H.P. (D) None of these

21. The number of terms which are free from radicals in the expansion of (a1/5_{+ b}1/10₎55_.

(A) 6 (B) 7

(C) 5 (D) 4

22. The number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the sides of the octagon is

(A) 24 (B) 52

(C) 48 (D) 16

23. The complex number z, the least in the absolute value, which satisfies the condition

z 4 4i

 



2

is

(A)

z 3 3i

 

(B)

z 5 5i

 

(C)

z 3 3i

 

(D)

z 1 i

 

24. The general solution of the equation cos6_{2 x = 1 + sin}4_{x is}

(A) x = 2n (B) x = n (C) x = n –

4

 (D) x = n +

4



25. Number of ways in which four letter of the word ‘DEGREE’ can be selected is

(A) 7 (B) 6

(C)

6!

3!

(D) none of these.

26. The number of ways in which a mixed double game can be arranged amongst 9 married couples if no husband and wife play in the same game is

(A) 756 (B) 1512

(C) 3024 (D) none of these.

(16)

27. The number of ways of selecting 10 balls out of an unlimited number of white, red, blue and green balls is (A) 270 (B) 84 (C) 286 (D) 86 28. The value of 6 k 1

2 k

sin

icos

7





















is (A) 1 (B) 0 (C) i (D) i

29. The values of  satisfying sin7 + sin = sin4 and 0 <  < /2 are (A)

,

9

4 



(B)

,

3

9 



(C)

,

6

9 



(D)

,

3

4 



30. The number of 5-digit numbers in which no two consecutive digits are identical, is

(A) 92 83 _{(B) 9  8}4

(C) 95 _{(D) none of these.}