JEE Advanced Part Test 02A (10.05.2023) PDF

SCHOLAR’S ACADEMY
JEE ADVANCED
PART TEST – 02(A)
Dated: 10 / 05 / 2023
MAX. MARKS = 252 [TIME : 3:00 HRS]
PHYSICS : Simple Harmonic Motion, Waves, Wave Optics, Thermal Physics,

Fluid Mechanics, Gravitation.
CHEMISTRY: GOC-01, Thermo Chemistry, Atomic Structure, Group-13, 14, GOC-02,
Group-15, 16, Isomerism, Group-17, 18, Hydrocarbons, Periodic Properties.
MATHS : Quadratic Equation, Binomial Theorem, Progression, Trigonometry,
Complex Number, Function.
General Instruction :
(i) All questions are compulsory.
(ii) Use the optical Response Sheet (ORS) provided separately for answering the questions.
(iii) Blank spaces are provided within this booklet for rough work.
(iv) You are allowed to take away the Question Paper at the end of the examination.
(v) The question paper has three parts : Physics, Chemistry and Mathematics.
(vi) Use of calculator is not permitted.
PHYSICS
Section : A
“Single Correct Option Type Questions”
• This section contains Six (06) questions.

• Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is the correct answer.
• For each question, choose the option corresponding to the correct answer.
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct option is chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : 1 In all other cases.
01. The two planets with radii R1, R2 have densities �� and atmospheric pressures p1 and p2 , respectively. Therefore,
the ratio of masses of their atmospheres, neglecting variation of g and � within the limits of atmosphere, is
R1, R2 �� p1 , p 2
p1 R2 P1 p1R2 P2 p1 R1P1 p1 R1 P2
(A) p R p (B) p R p (C) p R p (D) p R p
2 1 2 2 1 1 2 2 2 2 2 1
02. The coefficient of linear expansion of glass is ag per °C and the cubical expansion of mercury is �m per °C. The
volume of the bulb of a mercury thermometer at 0° C is Vo and cross section of the capillary is A0. What is the
length of mercury column in capillary at T°C, if the mercury just fills the bulb at 0°C?
ag / °C �m / °C 0° C Vo
A0 T°C 0°C ?
VoT m 3 g VoT m –3 g VoT m –2 g VoT m –2 g

(A) (B) (C) (D)
A0 (1 2 gT ) A0 (1 2 gT ) A0 (1 3 g T ) A0 (1 3 g T )
Space for Rough Work
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03. An L shaped bar of mass M is pivoted at one of its end so that it can freely rotatein a vertical plane, as shown in
the Fig. Find the value of tan �� If system is in equlibrium.
L M
��
(A) 1/2 (B) 1/3 (C) 1/4 (D) 3

04. Tow simple harmonic motions are represented by the following equations
y1 = 10 sin(�/4) (12t + 1) y2 = 5sin(sin��t + 3 cos3�t) Here t is in seconds.
Find out the ratio of their amplitudes.
y1 = 10 sin(�/4) (12t + 1) y2 = 5sin(sin��t + 3 cos3�t) Here t is in seconds.
(A) 1 : 1 (B) 2 : 3 (C) 10 : 5 (D) 3 : 2

05. Two identical narrow slits S1 and S2 are illuminated by light of wavelength � from a point source P.
� P
(A) (l1 – l2) = (2n+1)�/2 (B) (l3 – l4) = (2n + 1)�/2

(C) (l1 + l2) – (l3 + l4) = n� (D) (l1 + l3) – (l2 + l4) = (2n + 1) �/2
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06. Two point monochromatic and coherent sources of light of wavelength � are placed on the dotted line in front
of a large screen. The source emit waves in phase with each other. The distance between S1 and S2 is 'd' while
their distance from the screen is much larger. Then,
�
'd'
(A) � If d = 7�/2, O will be a minima ( )

(B) � If d = 4.3�, there will be a total of 8 minima on y axis. ( )
(C) � If d = 7�/ O will be a maxima ( )
(D) � If d = ��there will be only one maxima on the screen. ( )
Which is the set of correct statement:
(A) 1,2 & 3 (B) 2,3 & 4 (C) 1, 2, 3 & 4 (D) 1, 3 & 4
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Section : B
“Paragraph Type Questions”
• This section contains Two (02) paragraphs. Based on each paragraph, there are TWO (02) questions.
• Each question has FOUR options. ONE OR MORE THAN ONE of these four option(s) is (are) correct answer(s).
• For each question, choose the option(s) corresponding to (all) the correct answer(s).
• Answer the each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (all the correct option(s) is (are) chosen;
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen;
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct;
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct
option;
Negative Marks : –2 In all other cases.
PassageI
The satellites when launched from the earth are not given the orbital velocity initially, a multistage rocket propeller
carries the spacecraft up to its orbit and during each stage rocket has been fired to increase the velocity to acquire
the desired velocity for a particular orbit. The last stage of the rocket bringes the satellite in circular/elliptical
(desired) orbit.
Consider a satellite of mass 150 kg in a low circular orbit. In this orbit, we cannot neglect the effect of air
drag. This air opposes the motion of satellite and hence the total mechanical energy of earth satellite system
decreases. That means the total energy becomes more negative and hence the orbital radius decreases which
causes the increase in KE. When the satellite comes in the low energy orbit. excessive thermal energy generation
due to air friction may cause the satellite to burn up. Based on the above information, answer the following
questinos.
07. It has been mentioned in the passage that as r decreases, E decreases but K increases. The increase in K = is kinetic
energy
r E K K
(A) due to increase in gravitiational PE ( )
(B) due to decrease in gravitational PE ( )
(C) due to work done by air force ( )
(D) both (2) and (3) ( )
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08. If due to air drag, the orbital radius of the earth decreases from R to R – �R, �R, << R, then the expression for
increase in the orbital velocity is
R R – �R, �R, << R,
R GM R GM GM GM
(A) (B) (C) R (D) R
2 R3 2 R3 R3 R3
PassageII
In an organ pipe (may be closed or open) of 99 cm length standing wave is set up, whose equation is given by
longitudinal displaacement.
2
(0.1mm) cos (y+1 cm) cos(400)t
0.8
where y is measured from the top of the tube in metres and t in seconds. Here 1 cm is the end correction
y
9. The upper end and the lower end of the tube are respectively.
(A) open closed (B) closed open

(C) open open (D) closed closed
10. The air column is vibrating in
(A) first overtone (B) second overtone

(C) third overtone (D)�fundamental mode
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Section : C
“Numerical Value Type Questions”
• This section contains SIX (06) questions.
• The answer to each question is a NUMERICAL VALUE.
• For each question, enter the correct numeric value of the answer using the mouse and the onscreen virtual
numeric keypad in the place designated to enter the answer. If the numerical value has more than two decimal
places, truncate/roundoff the value of TWO decimal places.
• Answer to each question will be evaluated according to the following marking scheme :
Full marks : +3 If ONLY the correct option is chosen;
11. A horizontal oriented tube AB of length � = 2.5 m rotates with a constant angular velocity � = 5 rad/s about a
stationary vertical axis OO' passing through the end A. Initially the tube is filled with an ideal fluid. The end A of the
tube is open, the closed end B has a very small orifice. Find the velocity of the fluid (in m/s) relativ to the tube when
the liquid column length in tube reduce to h = 1 m.
AB � = 2.5 � = 5 rad/s OO'
A B
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12. We would like to increse the length of a 15 cm long copper rod of cross section 4 mm2 by 1 mm. The energy absorbed
by the rod if it is heated is E1. The energy asorbed by the rod if it is stretched slowly is E2. Then find E1/E2
[Various parameters of copper are density = 9 × 103 kg/m3, thermal coefficient of linear expansion = 16 × 10–6 /k.
Young's modules = 1.35 × 109 Pa, specific heat = 400 J/kg–k]
4 mm2
E1 E2 E1/E2 9 × 103 kg/m3
= 16 × 10–6 /k = 1.35 × 109 Pa, = 400 J/kg–k]
13. The apparatus shown in the figure consists of four glass columns connected by horizontal sectins. The height of two
central columns B and C are 49 cm each The two outer column A and D are open to the atmosphere. A and C are
maintained at a temperature of 95°C. while the B and C maintained at 5°C The heights of the liquid A and D
measured from the base line are 52.8 cm and 51 cm respectively. Determine the coefficient of thermal expansion
of the liquid. (in × 10–4/ °C)
B C 49 cm
A D A C 95°C B D, 5° A D
52.8 cm 51 cm (in × 10–4/ °C)
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14. A uniform plank of mass m, free to move in the horizontal direction only, is placed at the top of a solid cylinder of
mass 2 m and radius R. The plank is attached to a fixed wall by means of a light spring of spring constant k There
is no slipping between the cylinder and the plank, and between the cylinder and teh ground. Find the time period
of small oscillations of the system. If k = �2 n/m, m = 7 kg.
m 2m R
k
k = � n/m, m = 7 kg.
2
15. AB is a cylinder of length 1.0 m fixed with a thin flexible diaphram C at the middle and two others thinflexible
diaphragms A and B at the ends. The portions AC and BC contains hydrogen and oxygen gases, respectively. The
diaphragms A and B are set into vibrations of same frequency. What is the minimum frequency of these vibrations
for which the diaphragm C is a node? Under the conditions of teh experiment, the velocity of sound in hydrogen
is 1100 m/s and in oxygen is 300 m/s.
AB 1.0 m C
A B AC BC A B
C 1100 m/s
300 m/s.
A C B
H2 O2
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16. A broad source of light of wavelength 680nm lilluminates normally two glass plates 120mm long that meet at
one end and are separated by a wire 0.048 mm in diameter atthe other end. Find the number of bright fringes
14456formed over the 120 mm distance
120mm 680 nm
0.048 mm 120 mm
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Section : D
“Matrix Type Questions”
• This section contains Four Matrix Match.
• Each Matrix match have FOUR Questions and carry total 8 Marks.
• Each question have four options. One or more options may be correct.
17. Match the statements of Column I with values of Column II

Column–I Column–II
�
(A) A cube of mass m and density � is pulled by a force Fx mgiˆ in (p)
in an accelerating liquid of density �, The value of ax/ay is

�
m �� Fx mgiˆ
�, ax/ay
(B) The sphere of mass m is pulled horizontally by a force (q) 1:1

Fx = mg in a nonaccelerating liquid. The value of ax/ay is
Fx = mg
ax/ay is
mg
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(C) A close tube of length x is placed in a rotaing liquid. The value (r)
of ax/g, where ax is the horizontal acceleration of the cube, is

x
ax/g ax
2
(D) The string of a pendulum makes an angle � with vertical when the cart (s)
2( )
moves with an acceleration a. If the cart is filled with liquid of density
� < � (density of the bob), the value of the angle of inclination with
tan
the vertical becomes �‘ Then is
tan '
�� a
�� <�( ),
tan
�‘
tan '
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(A) Hydrostatic force on the side wall of the cubical vessel, � = density of liquid (p) A�v2
�=
1
(B) Buoyant force on the cube, � = density of liquid (q) A v2
2
,�=
(C) Impact (reaction) force on the vessel by the liquid coming out of the (r) t
vessel, � = density of liquid
,�=
1
(D) Aerodynamci force acting on the flat roof surface of (s) ghA
2
area A, � = density of air
A ,�=
A v
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19. For a planet orbiting about the Sun in a elliptical orbit, some incomplete statements regarding physical quantities
are given in Column I, which can be completed by using the entries of Column II. Match the entries of Column I
with the entries of Column II.
(A) Maximum PE of the Sun planet system (p) is at perihelioin
(B) Maximum speed of planet (q) is at aphelion
(C) Minimum PE of Sun planet system (r) is independent of the mass of planet
(D) Minimum kinetic energy of planet (s) is independent of semimajor axis of orbit
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20. A cylindrical isotropic solid of coefficient of thermal expansion � and density � (at STP) floats in a liquid of coefficient
of volume expansion � and density d (at STP) as shown in the diagram. Match the following:
�� (at STP) � d (at STP)
(A) Volume of cylinder inside the liquid remains constnt (p) � = 0
(B) Volume of cylinder outside the liquid remains constant (q) � = 2�
d
(C) Height of cylinder outside the liquid remains constant (r) 3
p
d
(D) Height of cylinder inside the liquid remain constant (s) 2 t
p
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CHEMISTRY
Section : A
01. Consider the following changes :

(1) Sublimation energy of M = p
(2) Sublimation E + I.E.1 + I.E.2 of M = q
(3) I.E.1 of M = r
(4) I.E.2 of M = s
(5) I.E.1 + I.E.2 of M = t
2
The enthalpy changes for the reaction M(g) M(g) e2 could be calculated from the energy value associated
with :
(1) p = M
(2) M E + I.E.1 + I.E.2 = q
(3) M I.E.1 = r
(4) M I.E.2 = s
(5) M I.E.1 + I.E.2 = t
2
M(g) M(g) e2 :
(A) (p) + (r) + (s) (B) (q) – (p) + (r) (C) (p) + (t) (D) (t) – (r)
02. If C C 348 kJ mol 1 , C H 412 kJ mol 1
and H H 436 kJ mol 1 , the Pauling electronegativity of C is about:
(Given : electronegativity of H = 2.1, A B = Bond energy of AB bond).
1 1 1
C C 348 kJ mol , C H 412 kJ mol H H 436 kJ mol C :
( :H = 2.1, AB = A B
)
(A) 1.64 (B) 1.84 (C) 2.58 (D) 2.91
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03. An alkaline earth metal (M) gives a salt with chlorin, which is soluble in water at room temperature. It is also
forms an insoluble sulphate whose mixture with a sulphide of a transition metal is called ‘lithopone’–a white
pigment. Metal M is :
(M)
‘ ‘ M
(A) Ca (B) Mg (C) Ba (D) Sr
04. The following electronic transitions occur when Lithium atoms are sprayed into a hot flame;
I II III IV V
2s 2p 3d 3p 4s 3p,
Which of these transition would result in the emission of light ?
(A) I, II and IV (B) III and V (C) III, IV and V (D) all of these steps
(A) I, II IV (B) III V (C) III, IV V (D)

05. Compare the acids strength of both the structures.
H Cl Cl H
H Cl Cl H
COOH COOH
(a) (b)
(A) A is more acidic than B (B) B is more acidic than A
(C) Both are equally acidic (D) Can’t be predicted
(A) A, B (B) B, A
(C) (D)
06. The possible product of the reaction
(A) (B) (C) (D)
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Section : B
option;
Passage01
Ozone is an unstable, dark blue diamagnetic gas. It absorb strongly the UV radiation, thus protecting the
people on the earth from the harmful UV radiation from the sun. The use of chlorofluorocarbon (CFC) in
aerosols and refrigerator and thre subsequent escape into the atmosphere, is blamed for making holes in the
ozone layer over the Antarctic and Aretic.
Ozone acts as a strong oxidising agent in acidic and alkaline medium. For this property ozone is used as a
germicide and disinfectant for sterilizing water and improving the atmosphere of crowded places.
UV UV
(CFC)
07. Which one of the following property is correct for ozone ?

(A) It oxidises lead sulphide (B) It oxidises potassium iodide
(C) It oxidises hydrogen sulphide (D) It cannot act as bleaching agent in dry state
(A) (B)
(C) (D)
08. Which of the following solutions change its colour on passing ozone through it is :
(A) starch iodide solution (B) alcoholic solution of benzidine
(C) acidic solution of potassium dichromate (D) acidified solution of FeSO4
(A) (B)
(C) (D) FeSO4
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Passage02
All asymmetric compound and dissymmetric compounds are chiral. Compound with single chiral centre is
always chiral. Molecules with more than one chiral centre are usually chiral. The exceptions are meso comounds.
09. Choose the correctly matched pair(s) :

:
(A) and Diastereomers/
(B) and Geometrical isomers/
(C) and Chain isomers/
(D) and Identical/
10. Which of the following is/are chiral molecules?
(A) (B)
(C) (D)
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Section : C
numeric keypad in the place designated to enter the answer. If the numerical value has more than two
decimal places, truncate/roundoff the value of TWO decimal places.
11. The general formula for polythionic acid series is H2Sn–1O6 where n = 1 to 6. What is the value of n for pentathonic
acid ?
H2Sn–1O6 n=1 6 n
12. When K2Cr2O7 reacts with HCl in how many products chlorine exists as chloride ion.
K2Cr2O7 HCl
13. The heat evolved on combustion of 1 g of starch, (C6H10O5)x, into CO2(g) and H2O(l) is 4.6 kcal. Heat of formation
of CO2(g) and H2O(l) are – 94.2 and –68.4 kcal/mol, respectively. The magnitude of standard enthalpy of
formation of 1 g of starch (in kcal) is
1g (C6H10O5)x CO2(g) H2O(l) 4.6 kcal CO2(g) H2O(l)
– 94.2 –68.4 kcal/mol 1g
14. A volume of 1.642 1 sample of a mixture of methane gas and oxygen measured at 298 K and 1.192 atm, was
allowed to react at constant pressure in a calorimeter which together with its content had a heat capacity of
1260 cal/K. The complete combustion of methane to carbon dioxide and water caused a temperature rise in
calorimeter 0.667 K. the volume percent of methane in original mixture is (Given the heat of combustion of
methane is –210 kcal/mole)
298 K 1.192 atm 1.642 1
1260 cal/K
0.667 K –210 kcal/mole
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15. A solution of 6.3 g of haemoglobin (molar mass = 64,000 g/mol) in 25 ml of solution shows a temperature rise
of 0.03°C for complete oxygenation. Each mole of haemoglobin binds 4 moles of oxygen. If the heat capacity
of the solution is 4.2 J/Kml, the amount of heat released per mole of oxygen bound (in kJ) is
4.2 J/Kml
kJ
2x y
16. Among the following compounds aromatic are x, antiaromatic y and nonaromatic z, then find out ?
z
2x y
x y z
z
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
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Section : D
17. Match the following columns:

Column I (Atom) Column II (IUPAC group no. in periodic table)
(A) With atomic number = 29 (P) 1
(B) Having electronic configuration [Kr] 5s2 4d10 (Q) 11
(C) Which from ion with 3s2, 3p6, 3d10 (R) 2
configuration of outermost shell after the
removal of 3 electrons.
(D) In which last centered electron have (S) 12
n = 4, l = 0, m = 0. s 1 2 set of quantum
number? (T) 13
II II IUPAC
(A) = 29 (P) 1
(B) [Kr] 5s2 4d10 (Q) 11
(C) 3s2, 3p6, 3d10 (R) 2
(D) n = 4, l = 0, (S) 12
m = 0. s 1
2
(T) 13
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18. Match the items of column I to those of column II.
I II
Column I Column II
(A) B2H6 .2NH3 200 C
(P) H2
Red hot
(B) B2H6 (Q) B3N3H6
(C) B2H6 6H2O (R) H3BO3
(D) B2H6 HCl (S) B
19. Some thermochemical details are given as :
3A(g) � A3(g), �H300 = – 100 kJ

A(l) � A(g), �vapH300 = +25 kJ/mol
A3(l) � A3(g), �vapH400 = +40 kJ/mol
The standard boiling points of A(l) and A3(l) are 300 K and 400 K, respectively.
Molar heat capacities at constant pressure (in J/Kmol): A(l) = 40; A(g) = 20; A3(l) = 50; A3(g) = 30
Match the column on the basis of these details:
A(l) A3(l) 300 K 400 K J/Kmol A(l) = 40; A(g) = 20;
A3(l) = 50; A3(g) = 30
Column I Column II
(A) A(l) � A(g), �vapH400 (P) –103 kJ/mol
(B) A3(l) � A3(g), �vapH300 (Q) +23 kJ/mol
(C) 3A(l) � A3(l), �H300 (R) +52 kJ/mol
(D) 3A(l) � A3(l), �H400 (S) –77 kJ/mol
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20. ColumnI ColumnII
(Reaction) (Properties)
(A) (P) Hydrocarbon will obtain as a product
(B) (Q) Mechanism used is E1CB / E1CB
(C) (R) Second order kinetics involved
(D) (S) Mechanism used is E2/ E2
(T) Aldehyde is present in product
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MATHS
Section : A

r
4r 5 5
01. The value of is
r 1 r 5r 5
r
4r 5 5
r 1 r 5r 5
1 2 1 2
(A) (B) (C) (D)
5 5 25 125
02. Area bounded by the relation [2x] + [y] = 5, x, y > 0 is (where[.] represent greatest integer function)
[2x] + [y] = 5, x, y > 0 ( [.] )
(A) 2 (B) 3 (C) 4 (D) 5
1 1
03. If z 1 and a = z2017 2017 and b is the last digit of the number 22n 1 when the integer n > 1, the value of
z z
a2 + b2 is
1 1
z 1 a = z2017 b
2017
n
22 1 a 2 + b2 n>1
z z
(A) 23 (B) 24 (C) 26 (D) 27
n 101 2 100
04. If coefficient of x in the expansion of (1+x) (1 – x + x ) is nonzero, then n cannot be of the from
(1+x)101 (1 – x + x2)100 xn n
(A) 3�+1 (B) 3� (C) 3�+2 (D) 4�+1
33x–2 11x+2 22x+1
05. The sum of the roots of the equation 2 +2 =2 + 1 is
33x–2 11x+2 22x+1
2 +2 =2 +1
1 2 3 4
(A) (B) (C) (D)
11 11 11 11
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3
06. Let x 0, and log 24sinx
(24 cos x) then find the value of cosec2x.
2 2
3
x 0, log 24sinx (24 cos x) cosec2x
2 2
(A) 9 (B) 6 (C) 10 (D) 5
Section : B
option;
PassageI
Let w be nonreal fifth root of 3 and x = w3 + w4. If x5 = f(x), where f(x) is real quadratic polynomial with roots
� and �, (�� C) , then determine f(x) and answer the following questions.
w, 3 x = w3 + w4. x5 = f(x), f(x)
� �, (�� C) f(x)
07. Every term of the sequence {f(n)}, n � N is divisible by
{f(n)}, n � N
(A) 12 (B) 18 (C) 24 (D) 27
08. If � and � are represented by points A and B in argand plane, then circumradius of �OAB, where O is origin,
is
� �� argand A B �OAB O
(A) �� (B) 8/5 (C) 16/5 (D) 32/5
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PassageII
We are giving the concept of arithmetic mean of mth power. Let a1, a2, a3,....., an be n positive real numbers
(not all equal) and m be a real number. Then,
m a1, a2, a3,....., an , n
( ) m
m
a1m a2m a3m .... anm a1 a2 a3 .... an
n n
if m � R � [0, 1]
m � R � [0, 1]
However, if m � (0, 1), then
m � (0, 1),
m
a1m a2m a3m .... anm a1 a2 a3 .... an
n n
Obviously, if m = {0, 1}, then
m = {0, 1},
m
a1m a2m a3m .... anm a1 a2 a3 .... an
n n
x y z
09. If x > 0, y > 0, z > 0 and x + y + z = 1, the minimum value of is
2 x 2 y 2 z
x y z
x > 0, y > 0, z > 0 x + y + z = 1,
2 x 2 y 2 z
(A) 0.2 (B) 0.4 (C) 0.6 (D) 0.8
10. If sum of the mth powers of first n odd numbers is �, � m > 1, then
n m �� , � m > 1,
(A) � < n m
(B) � > n m
(C) ��< nm+1 (D)��> nm+1
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Section : C
numeric keypad in the place designated to enter the answer. If the numerical value has more than two
decimal places, truncate/roundoff the value of TWO decimal places.
11. If the roots of the equation 10x3 – cx2– 54x – 27 = 0 are in harmonic progression, the value of c is
10x3 – cx2– 54x – 27 = 0 c
n 100
n
ar 101 n
12. If (1 + x)n a r x r , br 1 and br then the value of is
r 0 ar 1 r 1 100! 20
n 100
n
r ar 101 n
(1 + x) n
a r x , br 1 br
r 0 ar 1 r 1 100! 20
117
1 p
13. Let S , where [.] denotes the greatest integer function and if S , when p and q are co
r 1 2 r 1 q
primes, the value of p + q is

117
1 p
S , [.] S , p q p+q
r 1 2 r 1 q
14. If 4 sin 2 x + cosec2 x, a, sin2y + 4 cosec2 y are in AP, then minimum value of (2a) is
4 sin2 x + cosec2 x, a, sin2y + 4 cosec2 y (2a)
15. The number of solutions of the equations |z – (4 + 8i)| = 10 and|z – (3+ 5i)|+| z – (5 + 11i) |= 4 5 , where
i 1
|z – (4 + 8i)| =
10 |z – (3+ 5i)|+| z – (5 + 11i) |= 4 5 , i 1
16. Let a function f be defined as f : {1, 2, 3, 4} � {1, 2, 3, 4}. If f satisfy f(f(x)) = f(x), � x � {1, 2, 3, 4}, then number
of such functions is
f f : {1, 2, 3, 4} � {1, 2, 3, 4}. f, f(f(x)) = f(x), � x � {1, 2, 3, 4},
(RBTS)- JEE-2023 28
Section : D

x 1, when x 0 x 3
(A) If f x then fof(x) for – 1 � x < 0 is (p)
x 2 1, when x 0 2
x 1, x 0
f x fof(x), – 1 � x < 0
x 2 1, x 0
2 tan x cos2 x 1 sec 2 x 2 tan x

(B) If f then f(x) is (q) x2 + 2x
1 tan 2 x 2
2 tan x cos2 x 1 sec 2 x 2 tan x
f f(x)
1 tan 2 x 2
2
(C) If f(x + y + 1) = f ( x) f ( y) for all x, y � R and f(0) = 1, then f(x) is (r) 1 + x
2
f(x + y + 1) = f ( x) f ( y) � x, y � R f(0) = 1, f(x)
x
(D) If 4 < x < 5 and f ( x ) 2 x 2 , where [y] is the greatest integer (s) (x + 1) 2
4
� y, then f –1 (x) is
x
4<x<5 f ( x) 2x 2 , [y] �y , f–1 (x)
4
(RBTS)- JEE-2023 29
1 30
(A) If a1, a2, a3, ...... are in AP and a1+a6+a10+a21 + a25+a 30 = 120, then . a is (p) 2
100 i 1 i
a1, a2, a3, ...... a1+a6+a10+a21 + a25+a30 = 120 ,
1 30
. a
100 i 1 i
(B) If a, b, c are positive, a + b + c = 1 and the minimum value of (q) 4
1 1 1
1 1 1 is
a b c
1 1 1
a, b, c a+b+c=1 1 1 1
a b c
(C) If a > 0, b > 0, c > 0, s = a + b + c and the minimum value of
2s 2s 2s
is (k – 1), then k is (r) 6
s a s b s c
2s 2s 2s
a > 0, b > 0, c > 0, s = a + b + c
s a s b s c
(k – 1) k
(D) If a > 0, b > 0, c > 0, a, b, c are in GP and the minimum value of
a c
is 2, then � is (s) 8
b b
a c
a > 0, b > 0, c > 0, a, b, c
b b
2 � (t) 10
(RBTS)- JEE-2023 30
19. Match the statement of column I with values of Column II
5
2
(A) The value of x n 1/ x n when x2 – x + 1 = 0, is (p) 2
n 1
5
2
x n 1/ x n x2 – x + 1 = 0
n 1
4
1 cos i sin
(B) If cos n + i sinn�, then n = (q) 4
sin i (1 cos )
4
1 cos i sin
cos n + i sinn�, n=
sin i (1 cos )
(C) The adjacent vertices of a regular polygon of n sides having center at (r) 9
origin are the points z and z . If Im(z)/Re(z) = 2 1 then the
value of n/4 is
n z
z Im(z)/Re(z) = 2 1 n/4
4
10
(D) If � is cube root of unity then (1 / 50)
2
r r (s) 8
r 1
10
��
2
(1 / 50) r r
r 1
(RBTS)- JEE-2023 31
20. Match the statement of column I with values of Column II
(A) If �� and � are four solutions of the equation tan 3 tan3�, no (p) 2
4
two of which have equal tangents, then the value of tan � + tan � + tan � + tan � is
�� tan 3 tan3�

4
tan � + tan � + tan � + tan �
cos cos
(B) If 1 2 3 4
0 then tan �1 tan �2 tan �3 tan �4 = (q) 3
cos 1 2 cos 3 4
cos cos
1 2 3 4
0 tan �1 tan �2 tan �3 tan �4 =
cos 1 2 cos 3 4
(C) If sec(�� –� �), sec � and sec(��) are in A.P. (with ��0), then cos sec (r) –1
2
sec(�� –� �), sec � sec(��) ( �� 0), cos sec

2
tan
2cos 1 2 is equal to
(D) If cos 0 , then (s) 0
2 cos tan
2
tan
2cos 1 2
cos 0 ,
2 cos tan
2
(RBTS)- JEE-2023 32

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SCHOLAR’S ACADEMY

MAX. MARKS = 252 [TIME : 3:00 HRS]

PHYSICS : Simple Harmonic Motion, Waves, Wave Optics, Thermal Physics,

• This section contains Six (06) questions.

VoT m 3 g VoT m –3 g VoT m –2 g VoT m –2 g

(A) 1/2 (B) 1/3 (C) 1/4 (D) 3

y1 = 10 sin(�/4) (12t + 1) y2 = 5sin(sin��t + 3 cos3�t) Here t is in seconds.

(A) 1 : 1 (B) 2 : 3 (C) 10 : 5 (D) 3 : 2

(A) (l1 – l2) = (2n+1)�/2 (B) (l3 – l4) = (2n + 1)�/2

(A) � If d = 7�/2, O will be a minima ( )

(A) open ­ closed (B) closed ­ open

(A) first overtone (B) second overtone

Space for Rough Work

Space for Rough Work

Space for Rough Work

Space for Rough Work

17. Match the statements of Column I with values of Column II

in an accelerating liquid of density �, The value of ax/ay is

(B) The sphere of mass m is pulled horizontally by a force (q) 1:1

Space for Rough Work

of ax/g, where ax is the horizontal acceleration of the cube, is

Space for Rough Work

(B) Maximum speed of planet (q) is at aphelion

Space for Rough Work

(B) Volume of cylinder outside the liquid remains constant (q) � = 2�

Space for Rough Work

01. Consider the following changes :

(A) I, II IV (B) III V (C) III, IV V (D)

06. The possible product of the reaction

(A) (B) (C) (D)

Space for Rough Work

07. Which one of the following property is correct for ozone ?

09. Choose the correctly matched pair(s) :

(A) and Diastereomers/

(B) and Geometrical isomers/

(C) and Chain isomers/

(D) and Identical/

10. Which of the following is/are chiral molecules?

Space for Rough Work

(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

Space for Rough Work

17. Match the following columns:

3A(g) � A3(g), �H300 = – 100 kJ

(A) (P) Hydrocarbon will obtain as a product

(B) (Q) Mechanism used is E1CB / E1CB

(C) (R) Second order kinetics involved

(D) (S) Mechanism used is E2/ E2

(T) Aldehyde is present in product

Space for Rough Work

• This section contains Six (06) questions.

(A) 9 (B) 6 (C) 10 (D) 5

primes, the value of p + q is

Space for Rough Work

17. Match the statements of Column I with values of Column II

2 tan x cos2 x 1 sec 2 x 2 tan x

Space for Rough Work

������� ��� � tan 3 tan3�

(A) open closed (B) closed open

�� tan 3 tan3�

sec(�� –� �), sec � sec(��) ( �� 0), cos sec