RT(Main)

FIITJEE - JEE (Mains) 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 Allotted: 3 Hours

 

Maximum Marks: 360

Do not open open this Test Booklet until you you are asked to do do so. so. Please read the instructions instructions carefully. carefully. You are are allotted allotted 5 minutes specifically for this purpose. purpose.

Importa Important nt Ins truct ruc tions : 1.

Immediately fill fill in the particulars on on this page page of the Test Booklet Booklet with Blue / Black Ball Point Pen. Use of  pencil is strictly prohibited.

2.

The Answer Sheet is kept inside this Test Test Booklet. When you are directed to open open the Test Booklet, Booklet, take out the Answer Sheet and fill in the particulars carefully.

3.

The test is of 3 hours duration.

4.

The Test Booklet consists of 90 questions. The maximum marks are 360.

5.

There are three  parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct answer and  – 1 mark for wrong answer .

6.

There is only one correct response response for each question. Filling up more than one response response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction.

7.

Use B lue / B lack  for writing particulars / marking responses on S ide-1  and S ide-2  of the lack B all all Point P en only  for prohibited.  Answer Sheet. Us e of pencil is s trictly prohibited.

8.

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

9.

On completion of the test, the candidate must must hand over the Answer Sheet to the Invigilator Invigilator on duty in the candidates are all allowed owed to take take away away this Tes t B ooklet with them. them. Room / Hall. However , the candidates

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

Name of the Candidate (in Capital Letters) :_____________________________________ Enrolment Number :_________________________________________________________ Batch :________________________ :___________ _____________ Date of Examination Examinatio n : ___________________ ________________________  _____ 

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

-: 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  –3

0.1m. When the particle passes through the mean position, its K.E. is 8×10 J. 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 S1

4.

In the figure the intensity of waves arriving at D from two coherent sources S 1 and S 2 is I 0. The wave length of the wave is  = 4m. Resultant intensity at D will be (A) 4I0 (B) I0 (C) 2I0 (D) zero

4m

D

3m

S2

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 T

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 x t

(A) Ex

 Ey and a x  a y  

(B) Ex

 E y and a x  a y

(C) Ex

 E y and a x  a y  

(D) Ex

 Ey and a x  a y

 S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

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 M 1 to distance travelled by M 2? (A)

M1   M2

M2 M1 1 (D) 2 (B)

(C) 1 10.

The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is k A k A (A) 1   (B) 2 k2 k1 (C)

k1A k1  k 2

 

(D)

k2 A

k1

k2 P

M

k1  k 2

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

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

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

3 2 1

O

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) 2

(C) 2

R   g g R

(B) 

(D) 

 

R g g R P

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

1 2

V

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? er

er ar

ar

ut

ut

(A)

e

e

(B) p m

p m

e

e T

T

Heat supplied

Heat supplied

er

er ut

ut ra e

(C) m e

e p m e

T

T

Heat supplied

18.

ra

(D) p

Heat supplied

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 1 st harmonic (fundamental frequency) in AB is equal to 2 nd  harmonic frequency in CD. Then, length of BO is (A) L/5 (B) 4L/5 (C) 3L/4 (D) L/4

C

 A

D

B

L x

m

 S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

19.

Two SHM’s are represented by y 1 = 10 sin  3t   / 4   and y2 = 5 sin(3  t) + 53 cos(3t), the ratio of their amplitudes is (B) 5 : 7 (D) 1:1

(A) 1 : 2 (C) 2 : 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

r    20 r  (C)   10

r  15 r  (D) 5

(A)

(B)

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 T 0. While box B contains one mole of helium at temperature

7T0 . The boxes 3

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 T 0 is:

5T0   2 7T0 (C)   3 (A)

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) 2

(C)

24.

3T0 7 3T0 (D) 2

(B)

gR   Rx

gR Rx 1 2 

 gR  R x 2

(D) 

One mole of a gas expands with temperature according to the relation V = KT 2/3. What is the work done when the temperature changes by 30 0C? (A) 10 R (B) 20 R (C) 30 R (D) 40 R  S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

25.

A liquid takes 5 minutes to cool from 60 0C to 500C, when temperature of surrounding is 30 0C. How long will it take to cool fr om 50 0C to 400C? (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.

6

(A) y 

 

(B) y 

2

 

(D) y 

 x  4.5t   3 6

(C) y 

27.

2

 x  4.5t   3

2

 x  4.5t   3 6 2

 x  4.5t   3

A simple pendulum has time period T 1. The point of suspension is now moved upward according to the relation. y = Kt 2. (K = 1m/s2) where y is vertical displacement. The time period now become T 2. The

T12

ratio of

T22

 is (g = 10 m/s 2)

(A) 6/5 (C) 1 28.

6

(B) 5/6 (D) 4/5

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) V1  V2  V3  V4

 V3  V2  V1 (C) V1  V2 ;V3  V4 and V2  V3 (D) V1  V2 ,V3  V4 and V2  V3 (B) V4

4

P

2

3 1

T

29.

2

(A) zero (C) 30.

3

The slope of a graph plotted between T and r  for a planet, will be GM /4   2

(B)

4  GM 

(D)

42 / GM 

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

2T   

(A) (C)

3 2

T   

(B) (D)

T 

2 T 

3

 S pace for roug h work 

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

PART  – B (CHEMISTRY) 1.

CH 3CH 2CHCH 2Cl 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)

3.

(D)

Which of the following hydrocarbon is prepared by the following reaction? Dry ether   Products 2CH3 Cl  Na 

(A) CH4 4.

5.

(B) C2H4

(C) C2H6

Which of the following is the least pollutant gas? (A) CO2 (B) SO2 (C) N2

(D) C2H2

(D) CO

Which of the following is an electrophilic substitution reaction? CH 2Cl

CH3

(A)

Cl2 /h   

HCl

CH3

CH3

Cl

(B) Cl /Fe

2   

CCl 3

CH3

(C)

Cl Heat

2   

CHCl 2

CH3

(D)

Cl2 /h    

 S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

6.

Which of the following compound is most acidic in nature? (A) CH3CH2COOH (B) ClCH2CH2COOH (C)

CH 3CHCOOH

(D)

ClCH 2CHCOOH Cl

Cl

7.

Which functional group is present in the functional isomer of alcohols? (A)  – CHO (B) C=O

(C)

-O-

(D)

O -C-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. H 2SO4 and conc.HNO 3 are heated is 

(A) SO3 

(B) NO2

(C) NO+ 

(D) N2



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 K a? OH CH 2OH

(A)

(B)

CH3

CH 2CH 2OH

OCH 3

(C)

(D)

 S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

12.

Which of the following compound shows geometrical as well as optical isomerism? (A) CH  CH  CH  CH  CH  CH 2

2

2

3

CH3

(B)

CH3 – CH = CH – CH = CH – CH3

(C)

CH3  CH  CH  CH2  CH  CH3 Cl

(D)

CH2  CH  CH  CH  CH2 Cl

13.

Which of the following reaction produces ethane(C 2H6)? 2 4 (A) CH3CH2OH      Heat

(B) CH3CH2Cl     Heat

2 (C) HC  CH   

(D) ClCH2CH2Cl     Heat

Conc.H SO

 Alcohol/KOH

H /Ni

14.

Zn

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

CH3

(A)

(B)

CH 2OH

CCl 3

15.

16.

(C)

(D)

Acid rain contains (A) hydrides of sulphur and nitrogen (C) oxy-acids of sulphur and nitrogen

(B) oxides of sulphur and nitrogen (D) chlorides of sulphur and nitrogen

Which of the following carbonium ion is most stable? (A) (B) CH 3CH 2CH 2CH 2CH 2

C 2H5 CH 3  - C CH3

(C)

CH 3CHCHCH 3

(D) CH 3CHCH 2CH 2

CH3

CH3

 S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

17.

Which of the following substance is most basic in non-polar solvent? (A) CH3NH2 (B) CH3NHCH3 (C)

(D)

CH3 N H3C

CH3 CH 3 - N - CH 3

CH3

CH3

18.

Which is not an isomer of formula C4H8? (A)

(B)

(C)

(D)

19.

CH3 CH 3 - C - CH 2 - CH 3 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 H 2 in presence of Ni as catalyst? (A) CH3 – CH = CH2 (B) CH2 = CH2 (C) CH3CH = CHCH 3 (D) CH3CH2CH = CH 2

21.

CH3  CH  CH  CH2   Products

HCl

CH3

The major product of above reaction is: (A) CH3  CH  CH2  CH2Cl

(B)

CH3  CH  CH  CH3 CH3 Cl

CH3

(C)

(D)

Cl

CH3  CH  CH2  CH3

CH3  C  CH2  CH3

CH 2Cl

CH3

 S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

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 CH3

23.

NO2

4 3

1 2

 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)

 S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

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) NO 2Cl

28.

CH3CH = CH2 will produce only a secondary alcohol when treated with (A) H2O/H+ 

B2H6 ,THF

(C)

29.

(B)

Hg  OCOCH3 2 ,H2O NaBH4

(D) Cl2/H2O

NaOH,H2O2 OH

BrCl    Product

One of the products of above reaction is: OH

OH Br 

(A)

Cl

(B)

OH Cl

(C)

(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

 S pace for roug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

PART – C (MATHEMATICS) 1.

For the complex number z , if

1  iz z i

 1 , then

(A) z lies on the imaginary axis (C) z lies on the unit circle

(B) z lies on the real axis (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 (C) altitudes are in H.P

(B) sides are in A.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  2 (C)1 - 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 13Cr is denoted by Cr , then the value of C 1+C5+C7+C9+C11 is equal to (A) 212-287 (B) 212-165 (C) 212-C2-C13 (D) none of these

9.

In a  ABC, if c2 + a2 – b2 = ac, then  B = (A) (C)



6

 



3

(B)



4

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

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

10.

If arg  z 1   = arg(z2), then (A) z2 = k z1 –1 (k > 0) (C) |z2| = |  z 1|

11.

(B) z2 = kz1 (k > 0) (D) none of these

The general solution of the equation tan 2 + 23 tan = 1 is given by (A)  



2

(C) n 

 

(B)    n 

  

12

 

(D)

1  2

n 12

12.

If |z1| =|z2|=|z3| = 1 and z 1 z 2 z 3 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) z1z2 z3  = 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 =

15.

(B)

(C) 

(D) 2

   

If  cos x  2

1  =

non –real, is

2

  1  tan2 2y 3  sin 3z   4 , then cos x  1

2

(B) x can not be an even multiple of  (D) None of these

The number of ways of distributing 10 different books among 4 students (S 1, … S4) such that S 1 and S2 gets 2 books each and S 3 and S4 get 3 books each is (A) 12600 (B) 25200 (C)

17.

3



(A) 0

(A) x may be a multiple of  (C) z can be a multiple of  16

1  and  =

10C

4 

(D)



(A) even (C) neither

2n 1



Integral part of 5 5  11

10 ! 2 ! 2 ! 3 ! 3 !

 is (B) odd (D) can’t Say  S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

-: 15 :NWTR820A01-A04,B01, NWTW820G01,B01-B08,C01-C02 & PANINI820-G1,XI1-XI6, XIC_MAINS-PT3(PCM) 9

18.

 2 1 The coefficient of x in the expansion of  x    is x  (B) 1 (D) 0

(A) 1 (C) 48 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 (a 1/5 + b1/10)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 (A) z  3  3i   (C) z  3  3i  

24.



4

(D) x = n +



4

Number of ways in which four letter of the word ‘DEGREE’ can be selected is (A) 7 (B) 6 (C)

26.

(B) z  5  5i (D) z  1  i

The general solution of the equation cos 62 x = 1 + sin 4x is (A) x = 2n (B) x = n (C) x = n  –

25.

 2 is

6! 3!

(D) none of these.

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.  S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000

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

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 6

28.

The value of

k 1

(A) 1 (C) i 29.

2k 2k   icos   is 7 7  (B) 0 (D) i

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

30.



  sin

 9

 6

, ,

 4

 9

 

(B)

 

(D)

 3

 3

,

,

 9

 4

The number of 5-digit numbers in which no two consecutive digits are identical, is (A) 92  83 (B) 9  84 5 (C) 9 (D) none of these.  S pace for r oug h work

FIITJEE

, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000