FIITJEE – INTERNAL Phase Test

PHYSICS, CHEMISTRY & MATHEMATICS

QP CODE: 100654-0 PAPER - 1

BATCHES – Two Year CRP2325_Reshuffling Test

Time Allotted: 3 Hours Maximum Marks: 180

▪ 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.

INSTRUCTIONS
Caution: Question Paper CODE as given above MUST be correctly marked in the answer
OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.

A. General Instructions
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. All the section can be filled in PART-A & B of 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 Parts.

(i) PART–A (01–03) contains (3) Multiple Choice Questions which have One or More Than One 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 (04-07) – Contains Four (04) multiple choice questions which have ONLY ONE CORRECT answer
Each question carries +3 marks for correct answer and -1 marks for wrong answer.
(iii) Part-A (08-11) – This section contains Four (04) Matching List Sets. Each set has ONE Multiple Choice
Question. Each set has TWO lists: List-I and List-II. List-I has Four entries (P), (Q), (R) and (S) and List-II
has Five entries (1), (2), (3), (4) and (5). 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 answer and -1 marks for wrong answer.
(iii) Part-B (01-06) This section contains SIX (06) questions. The answer to each question is a NON-
NEGATIVE INTEGER. For each question, enter the correct integer corresponding to the answer. Each
question carries +4 marks for correct answer. There is no negative marking.

Name of the Candidate: ____________________________________________

Batch: ____________________ Date of Examination: ___________________

Enrolment Number: _______________________________________________

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 2 Two Year CRP2325_RT_Paper-1_Set-A

S
SEEC
CTTIIO
ONN –– II :: P
PHHY
YSSIIC
CSS
(PART – A)
(One or More Than One Options Correct Type)
This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

1. Two waves travelling in opposite directions produce a standing wave. The individual wave
functions are given by y1 = 4 sin(3x – 2t) and y2 = 4 sin(3x + 2t) cm, where x and y are in cm
3
(A) The maximum displacement of the motion at x = cm is 4 cm.
4

(B) The maximum displacement of the motion at t = sec is 4 2 cm .
6
(C) Nodes are formed at x values given by 0, /3, 2/3, , 4/3, ………..
(D) Antinodes are formed at x values given by /6, /2, 5/6, 7/6, ………….

2. A partition divides a container having insulated walls into two

compartments I and II. The same gas fills the two compartments
whose initial parameters are given. The partition is a conducing
wall which can move freely without friction. Which of the following
statement is/are correct, with reference to the final equilibrium
position?
(A) The pressure in the two compartments are equal.
3V
(B) Volume of compartment I is
5
12V
(C) Volume of compartment II is
5
5P
(D) Final pressure in compartment I is
3

3. A 100 cm long cylindrical flask with inner and outer diameter

2 cm and 4 cm respectively is completely filled with ice at 0°C
as shown in the figure. The constant temperature outside the
flask is 40°C. (thermal conductivity of the flask is 0.693 W/m°C,
Lice = 80 cal/gm, 1 cal = 4.2 Joule).
(A) Rate of heat flow form outside to the flask is 80 J/s

(B) The rate at which ice melts is Kg / s
4200
(C) The rate at which ice melts is 100  Kg/s
(D) Rate of heat flow from outside to flask is 40  J/s
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 3 Two Year CRP2325_RT_Paper-1_Set-A

(Single Correct Answer Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

4. A travelling wave is given by

0.8
y= 2
3x + 12xt + 12t 2 + 4
Where x and y are in m and t is in sec, then velocity and amplitude of wave will be
(A) 2 m/s, 0.2 m (B) 4 m/s, 0.2 m
(C) 2 m/s, 0.4 m (D) none of these

5. A cylindrical container of radius ‘R’ and height ‘h’ is completely filled with a liquid and is open
to atmosphere at top. Two horizontal L shaped pipes of small cross-section area ‘a’ are
connected to the cylinder as shown in the figure. Now the two pipes are opened and fluid
starts coming out of the pipes horizontally in opposite directions. Then the torque due to
ejected liquid on the system about central axis is:

(A) 4aghR (B) 8aghR (C) 2aghR (D) None of these

6. A man standing on a road hold his umbrella at 300 with the vertical to keep the rain away. He
throws the umbrella and starts running at 10 km/hr. He finds that raindrops are hitting his
head vertically, the speed of raindrops with respect to the road will be
(A) 10 km/hr (B) 20 km/hr (C) 30 km/hr (D) 40 km/hr
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 4 Two Year CRP2325_RT_Paper-1_Set-A

7 One mole of an ideal monoatomic gas is taken from A to C

along the path ABC. The temperature of the gas at A is T0.
For the process ABC (where R is gas constant). Which of 2P0 C
the following is incorrect,
11
(A) Heat absorbed by the gas is RT0
12
P0 B
(B) Work done by the gas = RT0 A
9
(C) Change in internal energy of gas is RT0
2
V0 2V0
(D) None of these

(Matching List Sets)

This section contains FOUR (04) Matching List Sets. Each set has ONE Multiple Choice Question. Each set
has TWO lists: List-I and List-II. List-I has Four entries (P), (Q), (R) and (S) and List-II has Five entries (1),
(2), (3), (4) and (5). 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.

8. A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per
unit length , 2, 3 and 4 respectively. The instrument is played by vibrating the strings by
varying the free length in between the range L0 and 2L0. It is found that in string-1.() at free
length L0 and tension T0 the fundamental mode frequency is f0.
List-I gives the above four strings while List-II lists the magnitude of some quantity.

List-I List-II
(P) String-1 () (1) 1
(Q) String-2 (2) (2) 1/ 2
(R) String-3 (3) (3) 1/ 2
(S) String-4 (4) (4) 1/ 3
(5) 3 / 16

If the tension in each string is T0 the correct match for the highest fundamental frequency in
f0 units will be.
(A) P → 1 ; Q → 3 ; R → 4 ; S → 2 (B) P → 2 ; Q → 4 ; R → 3 ; S → 1
(C) P → 1 ; Q → 2 ; R → 5 ; S → 4 (D) P → 2 ; Q → 1 ; R → 3 ; S → 5
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 5 Two Year CRP2325_RT_Paper-1_Set-A

9. A rectangular block of density , base area A and height h is kept on m

h
a spring. The lower end of spring is fixed on the bottom of an empty
vessel of base area 2A. The block compresses the spring by h/4 at
equilibrium. The vessel is then slowly filled by a liquid of density 2 till k
the spring becomes relaxed. The block is then slowly pushed inside
the liquid till it is immersed completely. Work done to slowly push the
block completely inside is W1, work done by gravity on the block is
W2, and work done by upthrust is W3.
Match the following based on the above statements.

List-I List-II
(P) | W1 | (1) 5gh2 A
8
(Q) | W2 | (2) gh2 A
−
4
(R) | W3 | (3) 3gh2 A
4
(S) W3 (4) gh2 A
4
(5) 3gh2 A
−
4
The correct option is:
(A) P → 1 ; Q → 3 ; R → 5 ; S → 2 (B) P → 1 ; Q → 4 ; R → 3 ; S → 5
(C) P → 1 ; Q → 4 ; R → 3 ; S → 3 (D) P → 2 ; Q → 3 ; R → 1 ; S → 5

10. The system shown below is initially in

Spring 1 C
equilibrium
mA = mB = 3kg
mC = mD = mE = 2kg B D

Spring 2

A E

List – I List – II
(P) Just after the spring 2 is cut the block D (1) Accelerates up
(Q) Just after the spring 2 is cut the block B (2) Accelerates down
(R) Just after the spring 1 is cut, the block A (3) Momentarily at rest
(S) Just after the spring 1 is cut, the block D (4) Has acceleration g upwards
(5) Has acceleration g downwards
(6) Has acceleration g/2 downwards

(A) P → 1, Q → 3, R → 4, S → 5 (B) P → 1, Q → 3, R → 2,5, S → 2

(C) P → 2, Q → 1, R → 3,4, S → 1,6 (D) P → 1, Q → 3, R → 2,6, S → 4

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 6 Two Year CRP2325_RT_Paper-1_Set-A

1 m/s

S C
11. Consider the system shown in the figure.
Here the pulleys can move in a vertical A
plane, point A and B are on the rope,
P B
point C is the centre of the indicated 2 m/s
pulley while point D is a point on the rope 1 m/s
R
near the bottom of the middle pulley. The
string are taut D

1 m/s
Q

List – I List – II
(P) 5 m/s (1) Speed of point A must be
(Q) 1.5 m/s (2) Speed of point B must be
(R) 3 m/s (3) Speed of point C must be
(S) 17 m/s (4) Speed of point D must be
(5) Speed of pulley S must be

(A) P → 2, Q → 3, R → 1, S → 4 (B) P → 2, Q → 4, R → 3, S → 1
(C) P → 1, Q → 2, R → 5, S → 4 (D) P → 2, Q → 1, R → 3, S → 5

(PART – B)
(Non – Negative Integer)

1. A large tank is filled with water to a height H. A small hole is made at the base of the tank.
It takes T1 time to decrease the height of water to H/ 9 and it takes T2 time to take out the
rest of water. Find T1 / T2.

2. A liquid X of density 3.36 g/cm3 is poured in a U-tube, which Y X

contains Hg. Another liquid Y is poured in left arm with height 8 cm 10 cm
8 cm. Upper levels of X and Y are same. The density of Y is
N
 5  gm/cc. Find the value of ‘N’.
 
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 7 Two Year CRP2325_RT_Paper-1_Set-A

3. A tuning fork of frequency 340 Hz is vibrated just above a cylindrical tube of length 130 cm.
Water is slowly poured in the tube. If the speed of sound is 340 ms–1 then the minimum
height of water required for resonance is (in mm).

4. In a room where temperature is 30oC a body cools from 61oC to 59oC is 4 minutes. Find the
time (in seconds) taken by the body to cool from 51oC to 49oC.

5. A variable force f acts on a body which is free to move. The displacement of the body is
proportional to t3, where t = time. The power delivered by f to the body will be proportional to
tn, find n.

6. 2 kg of ice at –22.50C is mixed with 2.5 kg of water at 250C in an insulating container. If the
specific heat of ice and water are 0.5 cal/gm°C and 1 cal/gm°C respectively. Latent heat of
fusion of ice = 80 cal/gm. Find the final amount of water present in the container (in kg).
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 8 Two Year CRP2325_RT_Paper-1_Set-A

S
SEEC
CTTIIO
ONN –– IIII :: C
CHHE
EMMIIS
STTR
RYY
(PART – A)
(One or More Than One Options Correct Type)
This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

1. Compounds fHo in kJ mol-1 Sof in JK–1 mol–1

A 40 120
B 80 50
C 50 100
Above data are given for the reaction A ( g) + 2B ( g) ⎯⎯→ C ( g) , choose correct
statement(s).
(A) The reaction is exothermic
(B) The reaction become spontaneous above 1250 K
(C) If the temperature of the surrounding becomes 500 K due to the reaction, the entropy
change of the surrounding becomes 300 J K–1 mol–1
(D) The entropy change of the system is zero when the reaction becomes spontaneous

2. The type of alkyl chlorosilanes which form different silicones upon hydrolysis are given
below:
Type of silicones Formula of alkyl chlorosilanes
Cyclic silicones (R)mSi(Cl)n
Linear silicones (R)pSi(Cl)q
Cross-linked silicones (R)aSi(Cl)b
Linear chain terminator (R)rSi(Cl)s
Choose correct statement(s)
(A) (m + n) = (p + q) = (a + b) = (r + s) (B) a + p = b
(C) r > s (D) r = b

3. Which of the following sets contain only isoelectronic ions?

(A) Zn2+, Ca2+, Ga3+, Al3+ (B) K+, Ca2+, Sc3+, Cl–
3– 2– – +
(C) P , S , Cl , K (D) Ti4+, Ar, Cr3+, V5+
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 9 Two Year CRP2325_RT_Paper-1_Set-A

(Single Correct Answer Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

4. CH3

CH3Cl (Monosubstitution )
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
Anhy AlCl
→P + Q
3

KMnO4/OH-
Heat

(R)
Select the correct statement:
(A) P and Q are less reactive than R toward electrophilic aromatic substitution reaction.
(B) R has highest acidic strength than P and Q
(C) oxidation of P and Q forms benzoic acid
(D) dipole moment of P and Q, both are zero

5. Which equilibrium shifts towards forward direction by increasing the concentration of NO 2(g)
at constant volume?
(A) N2 ( g) + O2 ( g) 2NO ( g) (B) 2NO ( g) + O2 ( g) 2NO2 ( g)
(C) NO ( g) + NO2 ( g) N2O3 ( ) (D) N2O5 ( g) NO2+ ( g) + NO3− ( g)

6. Which contains an asymmetric carbon atom?

H H H H H3C H H CH3
C C C C C C C C
(A) (B)
H CH H H CH H
Cl Cl
H H H CH3 H H H H
C C C C C C C C
(C) (D)
H3C CH H H3C CH CH3
Cl Cl

7. Which property is different between hydrogen peroxide and water?

(A) Boiling point (B) Thermal stability
Ka
(C) Acidic strength( p values) (D) All properties are different

Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 10 Two Year CRP2325_RT_Paper-1_Set-A

(Matching List Sets)

This section contains FOUR (04) Matching List Sets. Each set has ONE Multiple Choice Question. Each set
has TWO lists: List-I and List-II. List-I has Four entries (P), (Q), (R) and (S) and List-II has Five entries (1),
(2), (3), (4) and (5). 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.

8. Match the reactants from list-I with the reagent they need to give products by ring formation
mentioned in list-II.
List– I List – II
(P) CH 2CH 2CH 2COCl (1) HF

(Q) CH 2Br (2) BF3

Br

(R) CH 2CH 2CH 2CH 2OH (3) Na/dry ether

(S) CH3 (4) Anhy AlCl3

CH - CH 2 - CH 2 - CH = CH 2

(5) H2O/H+
(A) P → 4; Q → 2; R → 1; S → 3 (B) P → 1; Q → 2; R → 3; S → 4
(C) P → 4; Q → 3; R → 2; S → 1 (D) P → 2; Q → 3; R → 5; S → 4

9. Match the electronic configurations mentioned in List-I with their first ionization energy
mentioned in List-II.
List– I List – II
(Electronic configuration of elements) (First ionization enthalpy in kJ mol–1)
(P) 1s22s2 (1) 801
2 2 4
(Q) 1s 2s 2p (2) 899
(R) 1s22s22p3 (3) 1314
(S) 1s22s22p1 (4) 1402
(5) zero
(A) P → 2; Q → 4; R → 1; S → 3 (B) P → 3; Q → 2; R → 1; S → 4
(C) P → 3; Q → 2; R → 5; S → 1 (D) P → 2; Q → 3; R → 4; S → 1
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
11 Two Year CRP2325_RT_Paper-1_Set-A

10. Match the characteristics of gases as mentioned in list-I with their factors mentioned in list-II.
List– I List – II
(P) Liquification of gases (1) Only temperature
(Q) Root mean square velocity (2) Only molecular mass
(R) Vapour density (3) Temperature, pressure and molecular
mass
(S) Average kinetic energy (4) Temperature and molecular mass
(5) Temperature and pressure
(A) P → 4; Q → 3; R → 1; S → 2 (B) P → 1; Q → 3; R → 4; S → 2
(C) P → 3; Q → 4; R → 2; S → 1 (D) P → 2; Q → 4; R → 2; S → 1

11. Match the salts(consisting of cationic and anionic parts) mentioned in list-I with their
characteristics mentioned in list-II.
List– I List – II
(P) NH NO + − (1) Bond angle of cation is 180o
4 3
(Q) O2+BF4− (2) Both cation and anion are diamagnetic
(R)
(
N2O5 NO2+NO3− ) (3) Cation is paramagnetic and anion is
diamagnetic
(S) Na2C2 (4) Both cation and anion contain
coordinate-covalent bonds according to
valence bond theory
(5) Nitrogen undergoes same hybridization
in cation as well as anion
(A) P → 2; Q → 4; R → 3; S → 1 (B) P → 4; Q → 3; R → 1; S → 2
(C) P → 2; Q → 3; R → 5; S → 4 (D) P → 1; Q → 2; R → 5; S → 4
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 12 Two Year CRP2325_RT_Paper-1_Set-A

(PART – B)
(Non – Negative Integer)

1. Consider the reaction, N2O4 ( g) 2NO2 ( g) . The temperature at which Kc = 20.4 and
Kp = 600.1 is x Kelvin. What is the value of x (Round off to nearest integer) [Assume all
gases are ideal and R = 0.0831 L bar K–1 mol–1]

-1
in B(g)
0.06 m
k1 =
2. A(g) k2 =
0.00
93 m
in -1

C(g)
In above reaction, the half-life period of A(g) in minute unit is

3. How many maximum number of electron of iron should have s = +½?

4. How many maximum number of mono enol(s) including stereoisomer(s) is/are possible for
O CH3 O

CH 3 - C - CH 2 - CH - CH 2 - C - CH 2 - CH 3

5. What is the pH of 0.1 M aqueous solution of CH3COONa?

[Ka of CH3COOH = 10–5]

6.

, , , , , ,
N
How many antiaromatic compounds are there in above list?
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 13 Two Year CRP2325_RT_Paper-1_Set-A

S
SEEC
CTTIIO
ONN –– IIIIII :: M
MAAT
THHE
EMMA
ATTIIC
CSS
(PART – A)
(One or More Than One Options Correct Type)
This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

A circle S passes through the point (0, 1) and is orthogonal to the circles ( x − 1) + y 2 = 16
2
1.
and x2 + y2 = 1 Then
(A) radius of S is 8 (B) radius of S is 7
(C) centre of S is (–7, 1) (D) centre of S is (–8, 1)

(1 + x )
n
2. If Cr’s denotes the combinatorial coefficients in the expansion of ,n  N then
C + 3C + 5C ………….upto (n+1) terms, is equal to
2
0
2
1
2
2

(B) ( 2n + 1)
2n −1
(A) 2n
Cn + 2n.2n−1Cn−1 Cn
(C) 2 ( n + 1) Cn + (n + 1) .2n−1Cn−1
2n −1 2n−1
Cn−1 (D)

3. Let z, z and z + z represent three vertices of ABC where  is non real cube root of
– 1, then:
2 2
(A) centroid of ABC is ( z + z ) (B) orthocenter of ABC is ( z + z )
3 3
2 2
(C) circumcenter of ABC is ( z + z ) (D) incentre of ABC is ( z + z )
3 3

(Single Correct Answer Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

4. If a variable circle of radius 4 cuts the circle x2 + y2 = 1 orthogonally then locus of its
centre will be
(A) x2 + y2 = 16 (B) x2 + y2 =17
2 2
(C) x + y - 2x - 4y = 1 (D) 2x - 4y + 5 = 0

5. The values of   ( 0, 2) for which 2sin2  − 5sin  + 2  0 , are

    5    5 
(A)  0,    , 2  (B)  , 
 6  6  8 6 
     5    41 
(C)  0,    ,  (D)  , 
 8   6 6   48 
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 14 Two Year CRP2325_RT_Paper-1_Set-A

6. If 5 ( tan2 x − cos2 x ) = 2 cos 2x + 9 , then the value of cos 4x is

1 2
(A) (B)
3 9
7 3
(C) − (D) −
9 5

7. ABCD is a trapezium such that AB and CD are parallel and BC ⊥ CD . If ADB = , BC = p

and CD = q, then AB is equal to

(A) 2
p2 + q2
(B)
(p2 + q2 ) sin 
p cos  + q2 sin  (p cos  + q sin  )
2

(C)
(p 2
)
+ q2 sin 
(D)
p2 + q2 cos 
pcos  + qsin  pcos  + qsin 

(Matching List Sets)

This section contains FOUR (04) Matching List Sets. Each set has ONE Multiple Choice Question. Each set
has TWO lists: List-I and List-II. List-I has Four entries (P), (Q), (R) and (S) and List-II has Five entries (1),
(2), (3), (4) and (5). 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.

x2 y2
8. Let H : − = 1, where a  b  0 , be a hyperbola in the xy – plane whose conjugate axis
a2 b2
LM subtends an angle of 60o at one of its vertices. N. Let the area of the triangle LMN be
4 3.
LIST - I LIST – II
(P) The length of the conjugate axis of H is (1) 8
(Q) The eccentricity of H is (2) 4
3
(R) The distance between the foci of H is (3) 2
3
(S) The length of the latus rectum of H is (4) 4
(5) 3
The correct option is
(A) P → 4; Q → 2; R → 1; S → 3 (B) P → 4; Q → 3; R → 1; S → 2
(C) P → 4; Q → 1; R → 3; S → 2 (D) P → 3; Q → 4; R → 2; S → 5
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 15 Two Year CRP2325_RT_Paper-1_Set-A

9. Consider two circles C1 of radius a and C2 of radius b (b > a) both lying in the first quadrant
b
and touching the coordinate axes. In each of conditions listed in list– I, the ratio of is given
a
in list II
List – I List – II
(P) C1 and C2 touch each other. (1) 2+ 2
(Q) C1 and C2 are orthogonal (2) 3
(R) C1 and C2 intersect so that common chord is longest (3) 2+ 3
(S) C1 passes through center of C2 (4) 3+2 2
(5) 3−2 2
The correct option is
(A) P → 4; Q → 3; R → 1; S → 5 (B) P → 3; Q → 4; R → 1; S → 2
(C) P → 4; Q → 3; R → 2; S → 1 (D) P → 3; Q → 4; R → 2; S → 1

10.
List - I List – II
(P) The tangents drawn to the ellipse 3x2 + y2 = 3 , which (1) 4
are equally inclined to the coordinate axes, form a
quadrilateral of area equal to
(Q) The radius of the circle passing through both the focus (2) 2
x2 y2
of the ellipse + = 1 and having its centre at (0, 3)
16 9
is
(R) The number of integral points (both x and y integer) on (3) 8
x2
the ellipse + y 2 = 1 is
3
(S) The sum of all real x satisfying x2 + x − 1 = 1 (4) 1
(5) 5
(A) P → 3, Q →5, R →2, S →4 (B) P → 3, Q →1, R →2, S →4
(C) P → 2, Q →3, R →4, S →5 (D) P → 3, Q →2, R →1, S →4

11.
List – I List – II
(P) Let f ( x ) is a quadratic function such that f ( 6 ) = f ( 7 ) (1) 4
f ( 4 ) − f (1)
and = f ( 5 ) , then the value of f ( 8 ) is
f (3) − f ( 2)
(Q) The equation ax2 + bx + a = 0 (a  0 ) a,b  R and (2) 3
x3 − 2x 2 + 2x − 1 = 0 have two roots common, then the
value of a + b is
(R) x2 y2 (3) 2
Least distance between − = −1 and 3x − 4y = 0 is
4 3
5d
d then is
3
(S) Let a,b  R . If the equation x 4 − 4x3 + ax 2 + bx + 1 = 0 (4) 0
has four positive roots, then a + b is
(5) 1
(A) P → 2, Q →4, R →3, S →5 (B) P → 2, Q →4, R →3, S →3
(C) P → 2, Q →4, R →5, S →3 (D) P → 1, Q →2, R →4, S →3

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
 16 Two Year CRP2325_RT_Paper-1_Set-A

(PART – B)
(Non – Negative Integer)

1. Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the
ratio of the sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the
seventh term lies in between 130 and 140, then the common difference of this A.P. is

2. Let x be a non – negative real number. The minimum value of

 27  6 
f ( x ) =  2x + + 2  x + + 1 occurs at x = , then  is ____
 x +1  x +1 

3 5 7
3. + 2 + 2 + ...... to  is
1 1 + 2 1 + 22 + 32
2 2

x2 y2
4. If a tangent of slope 2 of the ellipse + = 1( a  b  0 ) is a normal to the circle
a2 b2
x2 + y2 + 4x + 1 = 0, then the maximum value of ab is

2
z + z3 − 2z1
5. If z1,z2,z3 are the vertices of an equilateral triangle, then 2 is
z 2 − z3

1/3
6. If z1 = 2, z2 = 3, z3 = 4 and 2z1 + 3z2 + 4z3 = 9, then value of 8z2 z3 + 27z3 z1 + 64z1z2
is
Space For Rough Work

FIITJEE Ltd., Punjabi Bagh Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
17 Two Year CRP2325_RT_Paper-1_Set-A

FIITJEE INTERNAL TEST

BATCHES: Two Year CRP2325
Reshuffling Test: PAPER-1
Code: 100654-0
JEE ADVANCED LEVEL
ANSWER KEY
ANSWER KEYS
Physics
PART – A
1. CD 2. ABCD 3. AB 4. A
5. A 6. B 7. A 8. A
9. B 10. B 11. A
PART – B
1. 2 2. 4 3. 50 4. 360
5. 3 6. 3

Chemistry
PART – A
1. ABC 2. ABCD 3. BC 4. B
5. C 6. C 7. D 8. C
9. D 10. C 11. B
PART – B
1. 354 2. 10 3. 15 4. 14
5. 9 6. 3

Mathematics
PART – A
1. BC 2. AC 3. ABCD 4. B
5. A 6. C 7. C 8. B
9. C 10. B 11. B
PART – B
1. 9 2. 2 3. 6 4. 4
5. 3 6. 6

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