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Fiitjee: Physics, Chemistry & Mathematics

This document appears to be an exam paper for Physics, Chemistry, and Mathematics. It provides instructions for taking the exam, which will last 3 hours and contain 186 total marks. The paper contains three sections - Section I is Physics, Section II is Chemistry, and Section III is Mathematics. Each section is further divided into two parts: Part A and Part B. Part A contains multiple choice questions with one or more correct answers, while Part B contains numerical questions. The document provides detailed instructions on how to fill out the answer sheet and the marking schemes for Parts A and B. It then begins the Physics section with the first multiple choice question.

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Harshul Singal
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© © All Rights Reserved
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100% found this document useful (1 vote)
191 views19 pages

Fiitjee: Physics, Chemistry & Mathematics

This document appears to be an exam paper for Physics, Chemistry, and Mathematics. It provides instructions for taking the exam, which will last 3 hours and contain 186 total marks. The paper contains three sections - Section I is Physics, Section II is Chemistry, and Section III is Mathematics. Each section is further divided into two parts: Part A and Part B. Part A contains multiple choice questions with one or more correct answers, while Part B contains numerical questions. The document provides detailed instructions on how to fill out the answer sheet and the marking schemes for Parts A and B. It then begins the Physics section with the first multiple choice question.

Uploaded by

Harshul Singal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 19

FIITJEE

PHYSICS, CHEMISTRY & MATHEMATICS


NWCM2022A5W, NWCM2022A6W, NWCM2022A7W, NWCM2022A8W, PANINI2022-G1, PANINI2022-XII 1, PANINI2022-XII 2,
NWCM2022B1R, NWCM2022B1W, NWCM2022G1, NWCM2022A1W, NWCM2022A2W, NWCM2022A3W, NWCM2022A4W,
BATCHES – NWCM822O1S, NWCM2022S1W, NWCM2022A1R, NWCM2022A2 R + DEHRADUN-2022R, NWCM2022A3R,

PANINI2022-XII 3, NWCM2022E1R+NWCM2022E1W, NWCM2022EW, RCM2022B1R, RCM 2022B1W, PANINI2022B01

QP CODE: RIT- 5

Time Allotted: 3 Hours Maximum Marks: 186

▪ Please read the instructions carefully. You are allotted 5 minutes specifically for
this purpose.
▪ You are not allowed to leave the Examination Hall before the end of the test.

1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Sections.
3. Section-I is Physics, Section-II is Chemistry and Section-III is Mathematics.
4. Each Section is further divided into Two Parts: Part-A & B in the OMR.
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be
provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic
devices, in any form, are not allowed.

B. Filling of OMR Sheet


1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on
OMR sheet.
2. On the OMR sheet, darken the appropriate bubble with Blue/Black Ball Point Pen for each
character of your Enrolment No. and write in ink your Name, Test Centre and other details at the
designated places.
3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Two Part.


(i) PART–A (01–08) contains (8) Multiple Choice Questions which have One or More Correct answer.
Full Marks: +4 If only the bubble(s) corresponding to all the correct options(s) is (are) darkened.
Partial Marks: +1 For darkening a bubble corresponding to each correct option, provided NO incorrect
option is darkened.
Zero Marks: 0 If none of the bubbles is darkened.
Negative Marks: −1 In all other cases.
For example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will result
in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will result in −1
marks, as a wrong option is also darkened.
(ii) Part-A (09-12) – This section contains Two (02) List-Match Sets, each List-Match set has Two (02) Multiple
Choice Questions. Each List-Match set has two lists: List-I and List-II. FOUR options are given in each
Multiple Choice Question based On List-I and List-II and ONLY ONE of these four options satisfies the
condition asked in the Multiple Choice Question. Each question carries +3 Marks for correct combination
chosen and -1 marks for wrong options chosen.
(iii) Part-B (01-06) contains six (06) Numerical based questions, the answer of which maybe positive or
negative numbers or decimals (e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) and each question carries +3
marks for correct answer. There is no negative marking.

Name of the Candidate :____________________________________________

Batch :____________________ Date of Examination :___________________

Enrolment Number :_______________________________________________


2 IT−2022 (RIT-5)-(PCM)

S
SEEC
CTTIIO
ONN –– II :: P
PHHY
YSSIIC
CSS
(PART – A)
(One or More Than One Options Correct Type)
This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

1. A bimetallic strip is formed by two identical strips, one of copper and the other of brass. The
coefficients of linear expansion of the two metals are C and  B . On heating, the
temperature of the strip goes up by T and the strip bends to from an arc of radius of
curvature R. Then R is
(A) proportional to T (B) inversely proportional to T
(C) proportional to B − C (D) inversely proportional to B − C

1. BD

2. A mixture of two diatomic gases X and Y is enclosed in a container at constant temperature.


The molecular weight of X is 16 times that of Y and mass of the gas X is 2 times that of Y.
Then
(A) The average molecular kinetic energy of X equals that of Y.
(B) The r.m.s. molecular speed of translation of X is 1/4th that of Y.
(C) The pressure exerted by X is 1/8th that by Y.
(D) The pressure exerted by X is 8 times that by Y.

2. ABC

3. Figure shows intensity vs wavelength graph of a T1


black body at temperatures T1, T2 & T3. Suppose T2
area under these graphs are A1, A2 and A3
respectively. Then we have T3
(A) T1 > T2 > T3 Intensity
(B) T1 < T2 < T3
(C) A1 : A2 : A3 = T12 : T22 : T32
(D) A1 : A2 : A3 = T14 : T24 : T34 

3. AD

4. In the arrangement shown in the figure, gas is thermally insulated.


An ideal gas is filled in the cylinder having pressure
P0(> atmospheric pressure Pa). The spring of force constant K is
initially unstretched. The piston of mass m and area S is
frictionless. In equilibrium, the piston rises up a distance x0, then
Kx K
mg
(A) final pressure of the gas is Pa + 0 +
S S
1 m, S
(B) work done by the gas is Kx02 + mgx 0
2 Po
1
(C) decrease in internal energy of the gas is Kx02 + mgx 0 + PaSx 0
2
(D) all of the above

4. AC
3 IT−2022 (RIT-5)-(PCM)

5. Which of the following are correct?


(A) For a very small deformation of a material, the ratio of stress and strain is constant as
deformation decreases.
(B) For a large deformation of a material, the ratio of stress and strain may decreases or
increases as deformation decreases.
(C) Two wires made of different materials, having the same diameter and length are
connected end to end. A force is applied which stretches their combined length by 2 mm.
Now the strain in same in both the wire but stress is different.
(D) None of these

5. AB

6. A particle of mass m moves in a straight line. If v is the velocity at a distance x from a fixed
point on the line and v 2 = a − bx 2 , where a and b are positive constant, then
(A) the motion continues along the positive x-direction only
(B) the motion is simple harmonic
b
(C) the particle oscillates with a frequency equal to
2
(D) the total energy of the particle is ma

6. BC

7. There is a uniform rod of mass m and length  as shown in figure. Cross sectional area and
Young’s modulus of rod are A and Y respectively. Two parallel forces F and 2F acts at ends
of rod A and B respectively along normal to cross sectional area as shown. Rod is placed on
smooth horizontal table. This situation is explained by Hooke’s Law which states that under
elastic limit, stress is directly proportional to strain. Young’s modulus is the ratio of stress
and strain. Here force does not cross the elastic limits of rod.
A M N B
F 2F

3 3 3

 1 in part MN is  2 and in part NB is  3 then which of the following is/are correct


F
(A) The magnitude of change in length in part AM is
AY 6
F
(B) The magnitude of change in length in part MN is
AY 6
F
(C) The magnitude of change in length in part NB is
AY 6
F
(D) The magnitude of change in length in part NB is
AY2

7. ABD

8. A monoatomic gas undergoes a process given by 2dU + 3dW = 0 (where dU = charge in


internal energy, dW = work done by the gas) then
(A) VT = constant (B) PV = constant
(C) PV2 = constant (D) PV5/3 = constant

8. AC
4 IT−2022 (RIT-5)-(PCM)

This section contains 2 List-Match Sets, each List-Match set has 2 Multiple Choice Questions. Each List-Match set has
two lists: List-I and List-II. Four options are given in each Multiple Choice Question based On List-I and List-II and ONLY
ONE of these four options satisfies the condition asked in the Multiple Choice Question.

Two particles start performing SHM along X-axis with origin as mean position with amplitude
A, angular frequency of SHM P and Q & starting from positions xP & xQ at t = 0. Their initial
velocities are directed towards each other. List-I contains the quantities to be calculated,
List-II contains their values in SI units.

List-I List-II
(I) The position where P & Q meet for the (P) 1
first time.
(II) Time at which P & Q meet for the first (Q) 11
time. 12
(III) Phase difference between P & Q. (R) 2
(IV) VP (S) 
Ratio of velocities just before
VQ
first collision.
(T) 6
(U) 7

− 3A A  
9. A = 4 m, XP = , XQ = , P = rad/ s , Q = rad/ s
2 2 2 12
(A) I → P, II → T, III → Q, IV → P (B) I → R, II → P, III → Q, IV → T
(C) I → R, II → U, III → S, IV → P (D) I → P, II → R, III → S, IV → U

9. B

− 3A A 3 7 
10. A = 2 m, XP = , XQ = , P = rad/ s , Q = rad/ s
2 2 24 24
(A) I → R, II → T, III → Q, IV → S (B) I → R, II → U, III → S, IV → R
(C) I → P, II → R, III → S, IV → U (D) I → P, II → Q, III → S, IV → R

10. C
5 IT−2022 (RIT-5)-(PCM)

Answer the following by appropriately matching the lists based on the information given in
the paragraph.
In the thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed
by the gas is given by TX. where T is temperature of the system and X is the infinitesimal
change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas
3  T   V 
X = R ln   + R ln   . Here R is gas constant. V is volume of gas. TA and VA are
2  TA   VA 
constants.

The List-I below gives some quantities involved in a process and List-II gives some possible
values of these quantities.

List – I List – II
(I) Work done by the system in process 1→2→3 (P) 1
RT0 ln 2
3
(II) Change in internal energy in process 1→2→3 (Q) 1
RT0
3
(III) Heat absorbed by the system in process 1→2→3 (R) RT0
(IV) Heat absorbed by the system in process 1→2 (S) 3
RT0
3
(T) 1
RT0 ( 3 + ln 2 )
3
(U) 5
RT0
6

11. If the process carried out on one mole of monatomic ideal gas is as shown in figure in the
1
PV-diagram with P0 V0 = RT0 , the correct match is.
3

(A) I→Q, II→R, III→S, IV→U (B) I→Q, II→S, III→R, IV→U
(C) I→Q, II→R, III→P, IV→U (D) I→S, II→R, III→Q, IV→T
11. A

12. If the process carried out on one mole of monatomic ideal gas is as shown in figure in the
1
PV-diagram with P0 V0 = RT0 , the correct match is.
3

(A) I→P, II→T, III→Q, IV→T (B) I→S, II→T, III→Q, IV→U
(C) I→P, II→R, III→T, IV→S (D) I→P, II→R, III→T, IV→P
12. D
6 IT−2022 (RIT-5)-(PCM)

(PART – B)
(Integer Type)
Part-C (01-06) contains six (06) Numerical based questions, the answer of which maybe positive or negative
numbers or decimals (e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) and each question carries +4 marks for correct
answer and there will be no negative marking.

1
13. A gas undergoes a process such that P  . If the molar heat capacity for this process
T
if C = 33.24 J/ mol- K. Find the degree of freedom of the molecules of the gas.

13. 4.00

14. A liquid cools from 700C to 600C in 5 minute. Calculate the time taken by the liquid to cool
from 600C to 500C, if the temperature of the surrounding is constant at 300C.

14. 7.00

15. 2 kg of ice at –20°C is mixed with 5 kg of water at 20°C in an insulating vessel having
negligible heat capacity. Calculate the final mass of water (in kg) remaining in the container.
It is given that the specific heats of water and ice are 1 kcal/kg/°C and 0.5 kcal/kg/°C
respectively, while the latent heat of fusion of ice is 80 kcal/kg.

15. 6.00

16. A particle of mass m is attached to three identical B


C
springs A, B and C each of force constant k as
shown in figure. If the particle of mass m pushed 90o
slightly against the spring A and released, if the FC FB
O
m
time period of oscillations is 2 , then find the
4nk FA
A
value of ‘n’.

16. 0.50

 = 0.6
17. What can be the maximum 1 kg
amplitude (in m) of the system  = 0.4
so that there is no slipping 2 kg
K = 24 N/m
between any of the blocks
3 kg

17. 1.00

18. An amount Q of heat is added to a monatomic ideal gas in a process in which the gas
performs a work Q/2 on its surrounding. The molar heat capacity for the process = 2nR.
Find ‘n’.

18. 1.50

Space For Rough Work


7 IT−2022 (RIT-5)-(PCM)

S
SEEC
CTTIIO
ONN -- IIII :: C
CHHE
EMMIIS
STTR
RYY
(PART – A)
(One or More Than One Options Correct Type)
This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

1. Which of the following species is/are aromatic in nature?

(A) (B)

(C) (D)

1. ABC

2. The correct statement(s) about the following species is(are)

(A) I and II are resonance structures (B) II and III are resonance structures
(C) II and III are diastereomers (D) III is a tautomer of I

2. CD

3. Which of the following represent the correct order of acidity?

(A)

(B)

(C)

(D)
8 IT−2022 (RIT-5)-(PCM)

3. ABD

4. Which of the following compound will not show enolisation?

(A) (B)

(C) (D)

4. ABCD

5. Identify the reaction(s) which is/are correct given:


O

Ph−C −Cl
⎯⎯⎯⎯⎯⎯ →
(A) AlCl3 CH3
S S
O

CH3

(B) Conc.H2SO4
⎯⎯⎯⎯⎯⎯⎯→

Ph
OH
CH3
(C) CH3 −C−CH3
⎯⎯⎯⎯⎯⎯⎯→ HO C OH
Conc.H2SO4
CH3
Cl HS

F F
(D) NaSH
⎯⎯⎯⎯→
DMF

NO2 NO2

5. ABC

6. Identify the correct statements


(A) Nucleophilic substitution on pyridine in more favoured at 2 and 4 positions than at 3rd
position.
(B) Electrophilic substitution is more favoured on pyridine at 3rd position than at 2 or 4
positions
(C) Thiophene is more aromatic than pyrrole
(D) Nucleophilicity of SH is more than OH–

6. ABCD
9 IT−2022 (RIT-5)-(PCM)

7. In which of the following reaction, tert-butyl benzene is formed as major product?

(A)

(B)

(C)

(D)

7. ABD

8. Which of the following reactions are least possible by Friedel-Craft acylation as per
expectation?

(A) (B)

(C) (D)

8. BD
10 IT−2022 (RIT-5)-(PCM)

This section contains 2 List-Match Sets, each List-Match set has 2 Multiple Choice Questions. Each List-Match set has
two lists: List-I and List-II. Four options are given in each Multiple Choice Question based On List-I and List-II and ONLY
ONE of these four options satisfies the condition asked in the Multiple Choice Question.

Match the following & answer accordingly:


List – I List– II
(I) OH (P) Less reactive than benzene
towards electrophilic methylation

(II) OCH 3 (Q) Forms tri-substituted product with


Br2 in presence of water

(III) Cl (R) Acidified permanganate oxidation


forms benzoic acid

(IV) CH3 (S) Reacts with HI

(T) Undergoes free-radical chlorination


(U) Forms salt with NaOH

9. Correct the correct combination between list-I and list-II is


(A) I → T (B) II → R
(C) III → P (D) IV → Q
9. C
11 IT−2022 (RIT-5)-(PCM)

Match the following & answer accordingly:


List – I List– II
(I) OH (P) Less reactive than benzene
towards electrophilic methylation

(II) OCH 3 (Q) Forms tri-substituted product with


Br2 in presence of water

(III) Cl (R) Acidified permanganate oxidation


forms benzoic acid

(IV) CH3 (S) Reacts with HI

(T) Undergoes free-radical chlorination


(U) Forms salt with NaOH

10. Correct the correct combination between list-I and list-II is


(A) I → U (B) II → Q
(C) III → S (D) IV → P

10. A
12 IT−2022 (RIT-5)-(PCM)

Match the following & answer accordingly:


List – I List– II
(A) OH (P) +I effect
CH3

(B) OH (Q) –I effect

CH3
(C) OH (R) +R

NO2
(D) OH (S) –R

NO2
(T) Hyperconjugation

(U) Both +R and –I effect

11. The correct matching is


(A) I → R (B) II → T
(C) III → S (D) IV → U

11. B
13 IT−2022 (RIT-5)-(PCM)

Match the following & answer accordingly:


List – I List– II
(A) OH (P) +I effect
CH3

(B) OH (Q) –I effect

CH3
(C) OH (R) +R

NO2
(D) OH (S) –R

NO2
(T) Hyperconjugation

(U) Both +R and –I effect

12. The correct matching is


(A) I → S (B) II → R
(C) III → P (D) IV → Q
12. D

(PART – B)
(Integer Type)
Part-C (01-06) contains six (06) Numerical based questions, the answer of which maybe positive or negative
numbers or decimals (e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) and each question carries +4 marks for correct
answer and there will be no negative marking.

13. Use the following data to answer the question below.


H2
⎯⎯⎯ → (H = -28.6 kcal mol–1)
Ni

excess H2
⎯⎯⎯⎯⎯⎯ → (H = -116.2 kcal mol–1)
(Ni)

Anthracene

Calculate the resonance energy of anthracene.

13. 84
14 IT−2022 (RIT-5)-(PCM)

14. How many double bond equivalents does amoxicillin possess?

14. 9

15. How many resonance structures are there for anthracene?

15. 4

16. Total number of -hydrogen in given compound is

16. 6

17. How many of the following halides give white precipitate with Aq. AgNO3 solution?
Cl Cl Cl Cl Cl Cl
HO Cl

CH2 = CH - Cl CH2 = CH - CH 2 - Cl Ph - CH 2 - Cl

17. 7

18. The possible number of stereoisomers formed in the following reaction would be :

18. 8

Space of Rough Work


15 IT−2022 (RIT-5)-(PCM)

S
SEEC
CTTIIO
ONN -- IIIIII :: M
MAAT
THHE
EMMA
ATTIIC
CSS
(PART – A)
(One or More Than One Options Correct Type)
This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

1. Consider the equation z 40 − z20 − a ( a + 1) = 0 ( a  R + ) . Which of the following are true,


where  is a root of the equation?
(A) Number of  ’s with Re (  )  0 is 20. (B) Number of  ’s with Re (  )  0 is 19.
(C) Number of  ’s with Re (  )  0 is 21. (D) Number of  ’s with Re (  )  0 is 20.

1. BC

2. If z = 1 and ‘a’ and ‘b’ respectively are the minimum and maximum values of
1 + z + 1 − z + z 2 , then
(A) a = 3 (B) a = 2 + 1
13
(C) b = 3 (D) b =
4
2. AD

n
3. Let Sn ( x ) =  nCk sin (kx ) cos (n − k ) x  , then
k =0

  
(A) S5   = 16 (B) S7   = −64
2 2
(C) S100 ( ) = 0 (D) S101 ( ) = 2100
3. ABC

4. Let n = 3100 , then for n:


(A) unit’s digit is 1 (B) ten’s digit is 0
(C) unit’s digit is 7 (D) ten’s digit is 2

4. AB

( )
10
5. If 1 + 2x + 3x 2 = a0 + a1x + a2 x 2 + ..... + a20 x 20 , then:
(A) a1 = 20 (B) a 2 = 210
(C) a 4 = 8085 (D) a20 = 22 = 22.37 .7

5. ABC

6. Which of the following is/are correct?


(A) 10150 − 9950  10050 (B) 10150 − 10050  9950
(C) (1000 )  (1001) (D) (1001)  (1000 )
1000 999 999 1000

6. BC
16 IT−2022 (RIT-5)-(PCM)

7. Let A ( z1 ) ,B ( z2 ) ,C ( z3 ) ,D ( z4 ) be four distinct points in complex plane such that


2 z4 − z1 = z4 − z2 + z4 − z3 , 2 z4 − z2 = z4 − z1 + z4 − z3
z4 − z1
2 z4 − z3 = z4 − z1 + z4 − z2 and is purely imaginary, then
z3 − z 2
z 4 − z2 z − z3
(A) is purely real (B) 4 is purely imaginary
z3 − z1 z2 − z1
(C) 3z4 = z1 + z2 + z3 (D) z4 − z1 = z4 − z2

7. BCD

8. Let points P ( z1 ) ,Q ( z2 ) and R ( z3 ) be three points in argand plane such that


z1 + z2 = z1 − z2 and (1 − i ) z1 + iz3 = z1 + z3 − z1 , then
(A) z2 − z3 = z2 + z3 − 2z1
(B) P, Q, R are vertices of right angled triangle
(C) P, Q, R are vertices of equilateral triangle
1
(D) P, Q, R lie on circle with radius z3 − z2
2

8. ABD

This section contains 2 List-Match Sets, each List-Match set has 2 Multiple Choice Questions. Each List-Match set has
two lists: List-I and List-II. Four options are given in each Multiple Choice Question based On List-I and List-II and ONLY
ONE of these four options satisfies the condition asked in the Multiple Choice Question.

Answer the following by appropriately matching the list


List - I List – II
(1) The least value of 8 z − 7 + 6 z − 5 ; z  C (P) 12
(2) z − 7 + 11i z +5−i z+4 (Q) 13
The least value of + + ; Z  C is
2 2 2
(3) Find the least value of (R) 24
z − 3 − 4i + z − i + z + z − 1; z  C
(4) 2 2
The least value of z − 3 + z − 5 + 2i + z − 1 + i is
2 (S) 10
(T) 5+ 2

9. Which of the following is the only correct combination?


(A) IV →P (B) II →S
(C) III →R (D) I →R

9. C

10. Which of the following is the only correct combination?


(A) IV →R (B) I →P
(C) III →P (D) II →S

10. B
17 IT−2022 (RIT-5)-(PCM)

(11 – 12)

Answer the following by appropriately matching the list


(Based on the information given in paragraph)
Given x = z 1 + z2 + z3 , y = z1 + z2 w + z3 w 2, z = z1 + z2 w 2 + z3 w; where w is cube root of
unity then
List – I List – II
(1) (P)
 z1 + z1 ( z2 w + z2 w ) + z2 ( z3 w + z1w ) + z3 ( z1w + z2w 2 )
2 2 2 2
x
(2) (Q)
 z1 + z1 ( z2 w 2 + z2 w ) + z2 ( z3 w 2 + z1w ) + z3 ( z1w 2 + z2w )
2 2
y
(3) (R)
3 z1
2 2
z
(4)
x (S)
 z1 + z1 ( z2 + z3 ) + z2 ( z3 + z1 ) + z3 ( z1 + z2 )
2 2

(T)
( z1 + z2 + z3 )
2

(U)
 z1
2

11. Which of the following is the only correct combination?


(A) IV →R (B) III →P
(C) II →U (D) I →T

11. A

12. Which of the following is the only correct combination?


(A) II →T (B) III →Q
(C) I →U (D) IV →P

12. B

(PART – B)
(Integer Type)
Part-C (01-06) contains six (06) Numerical based questions, the answer of which maybe positive or negative
numbers or decimals (e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) and each question carries +4 marks for correct
answer and there will be no negative marking.

1. Let z1 = 3 and z 2 = 7 represent two points A and B respectively on complex plane. Let the
2 2
curve C1 be the locus of point P(z) satisfying z − z1 + z − z2 = 10 and the curve C2 be the
2 2
locus of points P (z) satisfying z − z1 + z − z2 = 16 . Least distance between curves C1
and C2 is:

1. 1

2. Let q be a positive integer with q  50 . If the sum


98
C30 + 2. 97C30 + 3. 96C30 + ....... + 68. 31C30 = 100
Cq , then sum of digit of q is ________

2. 5

((1 + x )( 2 + x )(3 + x )) ( 2 + x )(3 + x )2


10
3. The coefficient of x 32 in the expansion of is  then
−8
will be
10
18 IT−2022 (RIT-5)-(PCM)

3. 8

4. Let n be an odd natural number greater than 1. Then the number of zeros at the end of the
sum 99n + 1 is _______

4. 2

5. Let ,  are real numbers, and


((cos  + isin ) + (cos  + isin )) + ((cos  − isin  ) + (cos  − isin ))
7 7

 −
= 2m cos7   cos (n (  +  ) ) , then m + 2n − 10 =
 2 

5. 5

6.    
The sets A = z z18 = 1 and B =  48 = 1 consider the set C = z z  A and  B . If n
be the number of distinct elements in C, then n −3

6. 9

Space For Rough Work


19 IT−2022 (RIT-5)-(PCM)

FIITJEE COMMON TEST


BATCHES:
PHASE TEST–2: PAPER-2
JEE ADVANCED LEVEL
ANSWER KEY
ANSWER KEYS
PHYSICS

CHEMISTRY

MATHEMATICS

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