JEE Advanced – 2 | Paper – 2 | JEE 2025

Date: 29th September 2024 Maximum Marks: 180

Timing: 2:00 PM to 5:00 PM Duration: 3.0 Hours

General Instructions
1. The question paper consists of 3 Subject (Subject I: Physics, Subject II: Chemistry, Subject III: Mathematics).
Each Part has four sections (Section 1, Section 2, Section 3 and Section 4).
2. Section 1 contains 4 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which
ONLY ONE CHOICE is correct.

Section 2 contains 3 Multiple Correct Answers Type Questions. Each question has 4 choices (A), (B), (C) and (D),
out of which ONE OR MORE THAN ONE CHOICE is correct.

Section 3 contains 6 Non-Negative Integer Type Questions. The answer to each question is a NON-NEGATIVE
INTEGER. For each question, enter the correct integer corresponding to the answer using the mouse and the
onscreen virtual numeric keypad in the place designated to enter the answer.

Section 4 contains TWO (02) paragraphs. Based on each paragraph, there are TWO (02) questions. The answer
to each question is a NUMERICAL VALUE. If the numerical value has more than two decimal places,
truncate/round-off the value to TWO decimal places.

3. For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your Test Code, Roll
No. and Group properly in the space given in the ANSWER SHEET.

SYLLABUS
Physics: Electrostatics, DC Circuits, Capacitors, Magnetism, EMI, AC Circuits and EM Waves, Ray Optics
Chemistry: Liquid Solutions, Chemical Kinetics, Electrochemistry, Organic Concepts – I, Halogen Containing Organic
Compound, Organic Concepts II, OCOC - I
Mathematics: Functions, Inverse Trigonometry, DC – I, DC – II, IC – I, IC – II, Differential Equation
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MARKING SCHEME

SECTION – 1 | (Maximum Marks: 12)

➢ This section contains Four (04) Multiple Choice 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.

SECTION – 2 | (Maximum Marks: 12)

➢ This section consists of Three (03) Questions. Each question has FOUR options. ONE OR MORE THAN
ONE of these four option(s) is(are) correct answer(s).
➢ Answer to 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 and
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
Zero Mark: 0 if none of the options is chosen (i.e. the question is unanswered)
Negative Marks: –2 In all other cases.

SECTION – 3 | (Maximum Marks: 24)

➢ 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 using the mouse and the
onscreen virtual numeric keypad in the place designated to enter the answer.
➢ Answer to each question will be evaluated according to the following marking scheme.
Full Marks : +4 If ONLY the correct integer is entered;
Zero Marks : 0 In all other cases.

SECTION – 4 | (Maximum Marks: 12)

➢ This section consists TWO (02) paragraphs. Based on each paragraph, there are TWO (02) questions.
The answer to each question is a NUMERICAL VALUE.
➢ If the numerical value has more than two decimal places, truncate/round-off the value to 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.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).

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SUBJECT I: PHYSICS 60 MARKS

SECTION-1
This section consists of 4 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which
ONLY ONE CHOICE is correct.
3Q
1. A solid sphere has a uniform volume charge density  = , where Q is the total charge and R is its
4R 3
radius. Consider a concentric spherical Gaussian surface with a radius r that increases at a constant rate as
r = kt , where k is a positive constant and t is time. Let  represents the total electric flux through the
Gaussian surface at any instant t. The plot between  and t will look like:

(A) (B)

(C) (D)

2. A thin wire with resistance R is bent into a large circular loop of radius a.
A capacitor C with a small gap between its plates is placed in the loop
without altering its shape. An AC voltage V = V0 sin t is applied across
points A and B where the are AMB subtends an angle 240° at the center as
shown below. What is the peak value of magnetic induction at the center
3
due to the current in the loop? Take c = . Ignore self induction.
R

30V0 30V0 0V0

(A) Zero (B) (C) (D)
4aR 8aR 4 2 aR

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3. Figure shows a metal sphere of radius a with a charge q1 inside a

concentric metallic shell of radius of radius b(a < b) with charge q2 . Both
are connected by a switch S. Initially the switch was open and potential at
the center O is V1. The potential at the center becomes V2 after the switch
is closed. Find V1 – V2 .

q1  1 1  (q1 + q2 )  1 1 
(A) – (B) –
40  a b  80  a b 

q2 1 1  q1 – q2 1 1
(C)
40  b – a  (D)
80  a – b 

4. A thin rod AB with a length 0.75R is positioned along the principal axis of a concave mirror with a radius
of curvature R. The rod’s image is of same size and overlaps with the original rod.

The center of curvature C of the mirror must divide the rod AB in a ratio:

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

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SECTION-2
This section consists of 3 Multiple Correct Answers Type Questions. Each question has 4 choices (A), (B), (C) and
(D), out of which ONE OR MORE THAN ONE CHOICE is correct.
5. A circular loop of radius a is made out of a uniform wire of diameter d (such that d  a) and resistivity  .
The loop is fixed in the X-Y plane, in the presence of a magnetic field B = B0 sin ( t ) kˆ, where B0 and 
are constants. Let the maximum magnitude of the induced current in the loop be I M and let the average
rate of heat dissipation in the loop be H AV . Which of these options is/are correct?

 B0  a d 2  B0  a 2d
(A) IM = (B) IM =
8 8

2 B02 2 a d 3 2 B02 2 a 3 d 2
(C) H AV = (D) H AV =
16  16 

6. An insulating hemispherical shell of radius R is fixed and charged uniformly over its curved surface with
charge per unit area . Let O be the centre of the circular base. Which of these options is/are correct?

(A) The circular base is an equipotential surface

(B) The electric field at O is zero

(C) The work done in moving a point charge +q from infinity to

Rq
O is
2 0

(D) The electric potential at a point in the same plane as the circular base, and at a distance 2R from O,
R
is
4 0

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7. Two circular metal plates, each with a radius R, are placed coaxially along the x-axis. Their centers are at
 −d  d 
C1  , 0, 0  and C2  , 0, 0  with a distance d (d  R) apart.
 2  2 
The plates are connected by a thin long wire along x-axis, carrying a constant current I. Plates were initially
uncharged.

(A) The displacement current in between the plates is I

(B) The magnetic induction at P(0, 2 R, 2 R) and at Q(2d , 2R, 2R) are equal

 R R  R R
(C) The magnetic induction at M  0, ,  and N  2d , ,  are equal
 2 2  2 2

(D) If the current I in the wire continues to flow, the charge will eventually start leaking from the
plates.

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SECTION-3
This section consists of 6 NON-NEGATIVE INTEGER Type Questions. For each question, enter the correct integer
corresponding to the answer.
1. A parallel plate capacitor of capacitance 10 F is charged to 60V. It is then disconnected from the battery.
A dielectric slab, with dielectric constant 2, having same lateral dimensions as that of the plates and the
width equal to separation between the plates, is gradually inserted in between the plates. When it fills half
of the volume between the plates, the work done against electric field in inserting the slab is − x mJ .
Find x.

2. The figure below shows a long straight wire placed along x-axis
carrying current I1 . Another wire AB extends from A(0, a ,–a) to
B(0, a , a) and carries current I 2 . The torque experienced by wire
1 1
AB due to the current in the long wire is 0 I1I 2 a −  . Find x.
 x

3. An equilateral prism of refractive index 2 is placed on top of a large horizontal plane mirror. A light ray
passes through the prims symmetrically and after emergence, it is incident on the mirror. Find the total
deviation suffered by the light ray in degrees.

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4. Two coils of self-inductance L1 = 1 mH and L2 = 2 mH and negligible internal resistance are connected in
parallel across a battery. The mutual inductance of the coils is negligible. Initially, the switch is open and
current through both coils is zero. A long time after the switch is closed, the ratio of the current in the
I
coils, 1 is equal to _____________.
I2

5. An inductor (inductance L = 90 mH), a capacitor (capacitance C = 25F ), a

battery (emf V0 = 15V ) and a switch S are present in a circuit shown below.
Initially the switch was open and capacitor was uncharged. Find maximum
current through the circuit after the switch is closed in mA. You may use the
fact the energy supplied by the battery will be stored in inductor and capacitor
combined without any heat loss.

6. Two identical bulbs B1 and B2 are connected to an AC voltage source as shown below.

If both the bulbs glow equally bright, the frequency of the AC source is n10 Hz. Find n.
3

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SECTION-4
This section consists TWO (02) paragraphs. Based on each paragraph, there are TWO (02) questions. The answer to
each question is a NUMERICAL VALUE. If the numerical value has more than two decimal places, truncate/round-off
the value to TWO decimal places.

PARAGRAPH FOR Q-7 & 8

When a charged body is placed in a uniform electric field, it may experience a torque. To calculate this torque, we
use a method similar to calculating torque on a body due to a uniform gravitational field, where its entire mass is
considered to be concentrated at the center of mass. Similarly, for a charged body in a uniform electric field, the
entire charge can be considered to be concentrated at a point called the center of charge in order to calculate torque
due to the electric field. If the charge distribution on the body is similar to its mass distribution the center of charge
coincides with the center of mass.

Consider a ring of mass m = 500 g and radius r = 10 cm kept on a rough surface (coefficient of friction is  = 0.6 ).

Its upper half carries a uniform linear charge density  = 50Cm −1 and its lower half carries a uniform linear

charge density − = −50Cm −1 . There is uniform horizontal electric field E = 0.1 V/m. Take the center of mass of
2r
a semi-circular ring to be at a distance of from the center.


7. Find the net dipole moment of the ring in C-m.

8. If the ring is released from the configuration shown in the figure above, then maximum value of friction on
ring during its subsequent motion will be x N. Assume rolling without slipping. Find x.

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PARAGRAPH FOR Q-9 & 10

A thin lens can be viewed as a combination of multiple truncated thin prisms made from the same material but with
different prism angles. For paraxial rays, we can use the deviation formula for a thin lens :  = ( − 1) A, which is
independent of small angle of incidence.

Consider a thin convex lens made of glass of refractive index 1.5.

A ray OP is incident on the lens at P making an angle 1º with the
principal axis of the lens. It emerges from point Q and the
emergent ray QI makes angle 2º with the principal axis. You may
use tan    for small angle  .

9. Let the tangents drawn to convex faces of the glass at P and Q meet at R. The PRQ is__________
degrees.
10. If point O on the principal axis is at a distance of 60 cm from the lens, then focal length of the lens
is _________ cm.

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SUBJECT II: CHEMISTRY 60 MARKS

SECTION-1
This section consists of 4 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which
ONLY ONE CHOICE is correct.
1. Predict the major products for the following reactions.

(A) No Reaction

(B)

(C)

(D)

2. Predict the major products of the following reaction.

(A) (B)

(C) (D)

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3. Predict the major product, and select the correct mechanism step.

(A)

(B)

(C)

(D)

4. Which of the following order is correct for reactivity of labelled benzene rings in electrophilic aromatic
substitution reaction?

(A) 1>2>3 (B) 3>2>1 (C) 2>1>3 (D) 3>1>2

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SECTION-2
This section consists of 3 Multiple Correct Answers Type Questions. Each question has 4 choices (A), (B), (C) and
(D), out of which ONE OR MORE THAN ONE CHOICE is correct.
5. Which of the following is correct for product (P) obtained industrially by the auto oxidation of
2-ethylanthraquinol (Q)? As shown in following reaction?

(A) Product (P) is concentrated by distillation under reduced pressure

(B) Product of electrolytic oxidation of acidified sulphate solution at high current density on
hydrolysis yields product (P)
(C) Product (P) is used for synthesis of hydroquinone from phenol
(D) Maleic acid on reaction with (P) undergo epoxidation to form epoxide, epoxide on hydrolysis form
racemic tartaric acid.

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6. Consider reaction scheme I and II and choose correct option(s).

(A) (P) and (Q) are diastereomers

(B) (R) and (S) are separated by fractional distillation
(C) Reaction scheme-I is stereoselective and reaction scheme-II is regioselective
(D) Reaction in reaction scheme-I is regiospecific and reaction in reaction scheme-II is stereospecific
7. Three organic compounds (P), (Q) and (R) are prepared by following reactions.

Which of the following is correct for (P), (Q) and (R)?

(A) (P) and (Q) can be distinguished by cerric ammonium nitrate test
(B) (P) and (R) can be distinguished by phthalein dye test
(C) A mixture of (P), (Q) and (R) is separated on silica gel thin layer chromatography plate using
hexane eluant, highest retardation factor value is observed for (R)
(D) A mixture of (P), (Q) and (R) on fractional distillation, pure liquid (R) is collected first in a
receiver.

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SECTION-3
This section consists of 6 NON-NEGATIVE INTEGER Type Questions. For each question, enter the correct integer
corresponding to the answer.

1. The esterification of a monobasic acid by alcohol proceeds according to the following reaction.
HCl
H(CH2 )10 COOH + C2H5OH ⎯⎯⎯
→ H(CH2 )10 COOC2H5 + H2O
The rate of ester formation is given by the equation:
d[ester group]
= k[COOH][H+ ]
dt
The reactivity of one carboxyl group in the dibasic acid is unaffected by esterification of the other.
Consequently, the same rate equation holds for the esterification of both monobasic and dibasic acids.
For carboxyl group and HCl concentrations of 103 and 10−2 geq/L, respectively, the rate of esterification
was found to be 7.6 10−3 g-eq/ L /s. For the esterification of the dibasic acid (CH2 )1000 (COOH)2 , how
much ester (in kg) is formed in a 8-h day shift using a 100- L reactor if the carboxyl group concentration is
102 g-eq/ L and the acid (HCl) concentration is 10−3 g-eq/ L?
2. When 1.76 g of some organic compound X (containing C, H and O) was burned, a mixture of gases with a
volume of 3.584 L (at STP) was formed. When this mixture was passed through lime water, a precipitate
weighing 8.0 g was formed. It is known that compound X contains 4 carbon atoms, does not react with 2,4-
dinitrophenyl hydrazine (indicating absence of carbonyl functional group) and alkali solution, and the
solution of this compound has a neutral pH. When interacting with sodium or sodium hydride in an inert
solvent, gas release is observed. There are N possible isomers of X that match the properties described
above and have a carbocycle (cyclopropane or cyclobutane) in their structure, taking into account
stereochemistry. Find value of N.
3. How many benzenoid contributors are possible for organic compound (P) formed by dehydrochlorination?

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4. Find sum of number of asymmetric carbon atoms in (P) and number of hetero atoms in (Q).

5. For a zero-order reaction P → Q, the concentration of P becomes half of its initial concentration in 30
minutes after starting the reaction.
The concentration of P becomes zero at _________ minutes.
(rounded off to the nearest integer)
6. The data provided in the table were obtained for the following reaction, carried out at 273 K.
A+B→C
Initial concentration Initial concentration Initial rate of formation
-1 -1
of [A] mol L of [B] mol L of [C] mol L-1S-1
0.2 0.2 0.3
0.4 0.2 0.6
0.4 0.4 2.4
The overall order of the reaction is ___________ .

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SECTION-4
This section consists TWO (02) paragraphs. Based on each paragraph, there are TWO (02) questions. The answer to
each question is a NUMERICAL VALUE. If the numerical value has more than two decimal places, truncate/round-off
the value to TWO decimal places.

PARAGRAPH FOR Q-7 & 8

Compound P1 and P2 contains a carbon-carbon single bond (C2–C3), rotation around this C–C axis results into
infinite number of spatial arrangements of groups attached to one carbon atom (C2) with respect to the groups
attached to the other carbon atom (C3). These spatial arrangements are called as conformational isomers. Thus,
there are infinite number of conformations of a compound. However, there are conformations having minimum
repulsive forces, minimum energy and maximum stability of the molecule. Dihedral angle between two H atoms,
two Me groups and two OH groups is X°,Y° and Z° respectively. [Me is methyl group]
1.H /Lindlar cat
Me−  −Me ⎯⎯⎯⎯⎯⎯⎯
2
2.Cold,alk.KMnO
→ P1
4
1.Na/NH3 ( )
Me−  −Me ⎯⎯⎯⎯⎯⎯⎯
2.Cold,alk.KMnO4
→ P2

7. Find sum of x, y and z in most stable conformer of P1 wrt C2–C3 bond.

8. Find sum of x, y and z in most stable conformer of P2 wrt C2–C3 bond.

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PARAGRAPH FOR Q-9 & 10

Arenes are characterized by electrophilic substitution reactions. Arenes reacts with halogens in the presence of a
Lewis acid catalyst to yield haloarenes. When monosubstituted benzene is subjected to further substitution, three
possible disubstituted products are not formed in equal amounts. Two types of behaviour are observed. Either ortho
and para products or meta product is predominantly formed. It has also been observed that this behaviour depends
on the nature of the substituent already present in the benzene ring and not on the nature of the entering group. In
the following reaction schemes (Q) and (R) are predominantly formed products. Dipole moment of (Q) is lower
compared to dipole moment of (R). M and N are number of all possible organic products formed.
Br
Ph − H ⎯⎯2⎯
Fe
→(P)
Cl
(P) ⎯⎯⎯⎯⎯ 2
anhyd.AlCl
→(Q) + (R) + (S)
3 (traces)
Br
(Q) ⎯⎯⎯ 2 →M
FeBr 3
Br2
(R) ⎯⎯⎯
FeBr3
→N
9. Find sum of (M) and (N).
10. How many products are similar in (M) and (N).

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SUBJECT III: MATHEMATICS 60 MARKS

SECTION-1
This section consists of 4 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which
ONLY ONE CHOICE is correct.
1. Let cos −1 ( x) + cos −1 (2 x) + cos −1 (3 x) = . If x satisfies the cubic ax3 + bx 2 − 1 = 0, then (a + b) has the
value equal to: (a, b are integers)
(A) 24 (B) 25 (C) 26 (D) 27

2. The value of the limit, lim 5

( sin x − x )2 + 1 − cos x3 is equal to:
x→0 x sin x + (1 − cos x) 2 (2 x 2 − sin x 2 )

19 4 19
(A) (B) (C) (D) 0
45 9 25
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1
n
tan −1 (nx)
3. Let Cn =  −1
sin (nx)
dx then lim n2  Cn equals:
n→
1
n+1
1
(A) 1 (B) 0 (C) −1 (D)
2
4. If the differential equation of the family of curve given by y = Ax + Be2x where A and B are arbitrary
d  dy   dy 
constants is of the form (1 − 2 x)  + ly  + k  + ly  = 0 then the ordered pair (k , l ) is:
dx  dx   dx 
(A) (2, − 2) (B) (−2, 2) (C) (2, 2) (D) (−2, − 2)

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SECTION-2
This section consists of 3 Multiple Correct Answers Type Questions. Each question has 4 choices (A), (B), (C) and
(D), out of which ONE OR MORE THAN ONE CHOICE is correct.
x
5. Indicate all correct alternatives if, f ( x) = − 1, then on the interval [0, ] :
2
1
(A) tan( f ( x)) and are both continuous
f ( x)
1
(B) tan( f ( x)) and are both discontinuous
f ( x)
(C) tan( f ( x)) and f −1 ( x) are both continuous
1
(D) tan( f ( x)) is continuous but is discontinuous
f ( x)
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6. Let f ( x) = sin −1 sin x + cos −1 (cos x). Which of the following statement(s) is/are true?
(A) f ( f (3)) = 
(B) f ( x) is periodic with fundamental period 2
(C) f ( x) is neither even nor odd
(D) Range of f ( x) is [0, 2]

 
 cos x 0 x
 2
7. Consider f ( x) =  2 such that f is periodic with period , then:
  − x  
x
 2 
 2
 2 
(A) The range of f is 0, 
 4 
(B) f is continuous for all real x, but not differentiable for some real x
(C) f is non differentiable at only one point in [0, ]
 3 
(D) The area bounded by y = f ( x) and the x-axis from x = −n to x = n is 2n 1 +  for a given
 24 

n N
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SECTION-3
This section consists of 6 NON-NEGATIVE INTEGER Type Questions. For each question, enter the correct integer
corresponding to the answer.

 2  a
1. If the sum  tan −1  n2 + n + 4  is equal to tan −1   , where a, b  N , then find the least value of
b
n=1
(a + b).

( )
2
 j3 −1  n 1 + k −1
n
 4 n
2. Let L =  1 − 2 ; M =   3  and N =  , then find the value of
 −1
i= 3  i  j =2  j +1  k =1 1 + 2k

(
lim L−1 + M −1 + N −1
n→
)
   
3. If f ( x) = ln(1 + x ) + tan
2 −1
x, x  0 and g ( x) = f −1
( x), then find the value of 27 g "  ln  2e 4  
  
  
where g "( x) denotes second derivative of g ( x) .

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 sin x + sin 3x + sin 5x + sin 7 x + sin 9 x + sin11x + sin13x + sin15 x 

4. If   cos x + cos3x + cos5x + cos 7 x + cos9 x + cos11x + cos13x + cos15x  dx equals
ln(sec mx)
+ c where m, n  N , find (m + n). (c is constant of integration)
n

 (1 − x )
1
50 99 100
x dx
m
5. Let 0
=
 (1 − x )
1 n
50 100 100
x dx
0
m − n −1
Where m and n are coprime natural numbers, then is_______.
20
dy
6. Given y (0) = 2000 and = 32000 − 20 y 2 , then find the value of lim y( x).
dx x→

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SECTION-4
This section consists TWO (02) paragraphs. Based on each paragraph, there are TWO (02) questions. The answer to
each question is a NUMERICAL VALUE. If the numerical value has more than two decimal places, truncate/round-off
the value to TWO decimal places.

PARAGRAPH FOR Q-7 & 8

dy −y
For the curve x2 y3 = (2 x + 3 y)5 , = where g ( x) is a real valued function.
dx g ( x)
Define h( x) = 2 g ( x) + 3( g ( x)) 2/3.
( g ( x))2 + g ( x) + 1
7. Minimum value of P( x) = is equal to k, then 6k is _________.
x2 + x + 1
8. The ordinate of the point on the curve y = h( x) where tangent is parallel to line y = 2 x + 4, is_________.

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PARAGRAPH FOR Q-9 & 10

Let the function f satisfy
f ( x)  f '(− x) = f (− x)  f '( x) for all x and f (0) = 3.
51
dx
9.  3 + f ( x )
has the value equal to_________.
−51
10. Number of roots of f ( x) = 0 in [−2, 2] is_________.

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• • • End of JEE Advanced – 2 (Paper - 2) | JEE 2025 • • •

VMC | JEE-2025 26 JEE Advanced - 2 | Paper - 2