JEE (Advanced) 2024 Paper 1
1/10
SECTION 1 (Maximum Marks: 12)
• This section contains FOUR (04) 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 : If ONLY the correct option is chosen;
Zero Marks : If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : In all other cases.
Q.1
Let
()fx
be a continuously differentiable function on the interval
(0, )
such that
(1) 2f =
and
10 10
99
() ()
lim 1
tx
tfx xft
tx
→
−
=
−
for each
0.x
Then, for all
0,x
()fx
is equal to
(A)
10
31 9
11 11
x
x
−
(B)
10
913
11 11
x
x
+
(C)
10
931
11 11
x
x
−
+
(D)
10
13 9
11 11
x
x
+
Q.2
A student appears for a quiz consisting of only true-false type questions and answers all the questions.
The student knows the answers of some questions and guesses the answers for the remaining
questions. Whenever the student knows the answer of a question, he gives the correct answer.
Assume that the probability of the student giving the correct answer for a question, given that he has
guessed it, is
1
.
2
Also assume that the probability of the answer for a question being guessed, given
that the student’s answer is correct, is
1
.
6
Then the probability that the student knows the answer of
a randomly chosen question is
(A)
1
12
(B)
1
7
(C)
5
7
(D)
5
12
Mathematics
Answer: (B)
Answer: (C)
JEE (Advanced) 2024 Paper 1
2/10
Q.3
Let
2
x
be such that
5
cot .
11
x
−
=
Then
( ) ( )
11 11
sin sin 6 cos 6 cos sin 6 cos6
22
xx
xx xx
−+ +
is equal to
(A)
11 1
23
−
(B)
11 1
23
+
(C)
11 1
32
+
(D)
11 1
32
−
Q.4
Consider the ellipse
22
1.
94
xy
+=
Let
(,)Spq
be a point in the first quadrant such that
22
1.
94
pq
+
Two tangents are drawn from
S
to the ellipse, of which one meets the ellipse at one
end point of the minor axis and the other meets the ellipse at a point
T
in the fourth quadrant. Let
R
be the vertex of the ellipse with positive
x
-coordinate and
O
be the center of the ellipse. If the
area of the triangle
ORT
is
3
,
2
then which of the following options is correct?
(A)
2, 3 3qp==
(B)
2, 4 3qp==
(C)
1, 5 3qp==
(D)
1, 6 3qp==
Answer: (B)
Answer: (A)
JEE (Advanced) 2024 Paper 1
3/10
SECTION 2 (Maximum Marks: 12)
• This section contains THREE (03) questions.
• Each question has FOUR options (A), (B), (C) and (D). 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 to each question will be evaluated according to the following marking scheme:
Full Marks : ONLY if (all) the correct option(s) is(are) chosen;
Partial Marks : If all the four options are correct but ONLY three options are chosen;
Partial Marks : If three or more options are correct but ONLY two options are chosen, both of
which are correct;
Partial Marks : If two or more options are correct but ONLY one option is chosen and it is a
correct option;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : In all other cases.
• For example, in a question, if (A), (B) and (D) are the ONLY three options corresponding to correct
answers, then
choosing ONLY (A), (B) and (D) will get marks;
choosing ONLY (A) and (B) will get marks;
choosing ONLY (A) and (D) will get marks;
choosing ONLY (B) and (D) will get marks;
choosing ONLY (A) will get +1 mark;
choosing ONLY (B) will get +1 mark;
choosing ONLY (D) will get +1 mark;
choosing no option (i.e. the question is unanswered) will get 0 marks; and
choosing any other combination of options will get marks.
Q.5
Let
2 : , ,Sab ab=+
( )
1
12 :
n
Tn=−+
, and
( )
2
12 : .
n
Tn=+
Then which of the following statements is (are) TRUE?
(A)
12
TT S
(B)
1
1
0,
2024
T
=
, where
denotes the empty set.
(C)
( )
2
2024,T
(D) For any given
, ,ab
( )
( )
( )
( )
cos 2 sin 2ab i ab
++ +
if and only if
0,b =
where
1i =−
.
Answer: (A), (C), (D)
JEE (Advanced) 2024 Paper 1
4/10
Q.6
Let
2
denote
.
Let
22 2
( , , ) : , , and 2 0 for all ( , ) (0,0) .Sabcabc axbxycy xy=++−
Then which of the following statements is (are) TRUE?
(A)
7
2, , 6
2
S
(B) If
1
3, , ,
12
bS
then
|2 |b
1.
(C) For any given
( )
,, ,abc S
the system of linear equations
1
1
ax by
bx cy
+=
+=−
has a unique solution.
(D) For any given
( )
,, ,abc S
the system of linear equations
( 1) 0
(1) 0
a x by
bx c y
++=
++ =
has a unique solution.
Q.7
Let
3
denote the three-dimensional space. Take two points
(1, 2, 3)P =
and
(4,2,7).Q =
Let
(,)dist X Y
denote the distance between two points
X
and
Y
in
3
.
Let
( ) ( )
22
3
: ( , ) ( , ) 50SX distXP distXQ= − =
and
( ) ( )
22
3
: ( , ) ( , ) 50 .TY distYQ distYP= − =
Then which of the following statements is (are) TRUE?
(A) There is a triangle whose area is 1 and all of whose vertices are from
.S
(B) There are two distinct points
L
and
M
in
T
such that each point on the line segment
LM
is also in
.T
(C) There are infinitely many rectangles of perimeter 48, two of whose vertices are from
S
and
the other two vertices are from
.T
(D) There is a square of perimeter 48, two of whose vertices are from
S
and the other two vertices are
from
.T
Answer: (B), (C), (D)
Answer: (A), (B), (C), (D)
JEE (Advanced) 2024 Paper 1
5/10
Q.8
Let
32a =
and
1/6
1
56
b =
. If
,xy
are such that
( )
5
4
32 log18
a
xy+=
and
( )
2log1080,
b
xy−=
then
45xy+
is equal to ________.
Q.9
Let
432
()fx x ax bx c=+ + +
be a polynomial with real coefficients such that
(1) 9.f =−
Suppose
that
3i
is a root of the equation
32
43 2 0,xaxbx++=
where
1i =−
. If
123 4
,,, and
are
all the roots of the equation
() 0,fx=
then
2222
1234
+++
is equal to ______.
Q.10
Let
, where
denotes the
determinant of . Then the number of elements in is _______.
Q.11
A group of
9
students,
12 9
,, ,,ss s
is to be divided to form three teams
, , and XY Z
of sizes
2,3, and 4,
respectively. Suppose that
1
s
cannot be selected for the team
,X
and
2
s
cannot be
selected for the team
.Y
Then the number of ways to form such teams, is _______.
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 on-
screen 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 : If ONLY the correct integer is entered;
Zero Marks : In all other cases.
Answer: 8
Answer: 20
Answer: 16
Answer: 665
JEE (Advanced) 2024 Paper 1
6/10
Q.12
Let
11
ˆˆ
ˆˆ ˆ ˆ
, OP i j k OQ i j k
−−
=++ =++
and
1
ˆ
ˆˆ
2
OR i j k=++
be three vectors, where
,0
−
and
O
denotes the origin. If
( )
0OP OQ OR=
and the point
(, ,2)
lies on
the plane
33 0,xyzl+−+=
then the value of
l
is ________.
Q.13
Let
X
be a random variable, and let
()PX x=
denote the probability that
X
takes the value
.x
Suppose that the points
( )
,( )xPX x=
,
0,1, 2, 3, 4,x =
lie on a fixed straight line in the
xy
-plane,
and
()0PX x==
for all
0,1,2,3, 4 .x−
If the mean of
X
is
5
2
, and the variance of
X
is
,
then the value of
24
is ______.
Answer : 5
Answer: 42
JEE (Advanced) 2024 Paper 1
7/10
Q.14
Let
and
be the distinct roots of the equation
2
1 0.xx+−=
Consider the set
1, , .T
=
For a
33
matrix
( )
33
,
ij
Ma
=
define
123ii i i
Ra a a=++
and
123jjjj
Caa a=++
for
1, 2, 3i =
and
1, 2,3.j =
Match each entry in List-I to the correct entry in List-II.
List-I
List-II
(P) The number of matrices
( )
33
ij
Ma
=
with
all entries in
T
such that
0
ij
RC==
for all , ,ij
is
(1) 1
(Q) The number of symmetric matrices
( )
33
ij
Ma
=
with all entries in
T
such that
0 for all ,
j
Cj=
is
(2) 12
(R) Let
( )
33
ij
Ma
=
be a skew symmetric
matrix such that
ij
aT
for
ij
. Then
the number of elements in the set
12
23
: , , , 0
xxa
yxyz My
zza
=
−
is
(3) infinite
(S) Let
( )
33
ij
Ma
=
be a matrix with all
entries in
T
such that
0 for
i
R =
all
.i
Then the absolute value of the determinant
of
M
is
(4) 6
(5) 0
The correct option is
(A)
(P) (4) (Q) (2) (R) (5) (S) (1)→→→→
(B)
(P) (2) (Q) (4) (R) (1) (S) (5)→→→→
(C)
(P) (2) (Q) (4) (R) (3) (S) (5)→→→→
(D)
(P) (1) (Q) (5) (R) (3) (S) (4)→→→→
SECTION 4 (Maximum Marks: 12)
• 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.
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : ONLY if the option corresponding to the correct combination is chosen;
Zero Marks : If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : In all other cases.
Answer: (C)
JEE (Advanced) 2024 Paper 1
8/10
Q.15
Let the straight line
2yx=
touch a circle with center
(0, ), > 0,
and radius
r
at a point
1
.A
Let
1
B
be the point on the circle such that the line segment
11
AB
is a diameter of the circle. Let
5 5.r
+=+
Match each entry in List-I to the correct entry in List-II.
List-I
List-II
(P)
equals
(1)
(2,4)−
(Q)
r
equals
(2)
5
(R)
1
A
equals
(3)
(2,6)−
(S)
1
B
equals
(4)
5
(5)
(2, 4)
The correct option is
(A)
(P) (4) (Q) (2) (R) (1) (S) (3)→→→→
(B)
(P) (2) (Q) (4) (R) (1) (S) (3)→→→→
(C)
(P) (4) (Q) (2) (R) (5) (S) (3)→→→→
(D)
(P) (2) (Q) (4) (R) (3) (S) (5)→→→→
Answer: (C)
JEE (Advanced) 2024 Paper 1
9/10
Q.16
Let
be such that the lines
1
11 21 29
:
123
xyz
L
+++
==
and
2
16 11 4
:
32
xyz
L
+++
==
intersect. Let
1
R
be the point of intersection of
1
L
and
2
.L
Let
(0,0,0),O =
and
ˆ
n
denote a unit
normal vector to the plane containing both the lines
1
L
and
2
.L
Match each entry in List-I to the correct entry in List-II.
List-I
List-II
(P)
equals
(1)
ˆ
ˆˆ
ijk−− +
(Q) A possible choice for
ˆ
n
is
(2)
3
2
(R)
1
OR
equals
(3)
1
(S) A possible value of
1
ˆ
OR n
is
(4)
12 1
ˆ
ˆˆ
66 6
ijk−+
(5)
2
3
The correct option is
(A)
(P) (3) (Q) (4) (R) (1) (S) (2)→→→→
(B)
(P) (5) (Q) (4) (R) (1) (S) (2)→→→→
(C)
(P) (3) (Q) (4) (R) (1) (S) (5)→→→→
(D)
(P) (3) (Q) (1) (R) (4) (S) (5)→→→→
Answer: (C)
JEE (Advanced) 2024 Paper 1
10/10
Q.17
Let
:f →
and
:g →
be functions defined by
1
| | sin , 0,
()
0, 0,
xx x
fx
x
x
=
=
and
1
12, 0 ,
()
2
0, otherwise .
xx
gx
−
=
Let
,,, .abcd
Define the function
:h →
by
( )
1
() () () () (), .
2
hx af x b gx g x c x gx dgx x
=+ +−+−+
Match each entry in List-I to the correct entry in List-II.
List-I
List-II
(P) If
0, 1, 0, and 0,abc d=== =
then
(1)
h
is one-one.
(Q) If
1, 0, 0, and 0,ab c d=== =
then
(2)
h
is onto.
(R) If
0, 0, 1, and 0,abc d=== =
then
(3)
h
is differentiable on
.
(S) If
0, 0, 0, and 1,abc d=== =
then
(4) the range of
h
is
0,1 .
(5) the range of
h
is
0,1 .
The correct option is
(A)
(P) (4) (Q) (3) (R) (1) (S) (2)→→→→
(B)
(P) (5) (Q) (2) (R) (4) (S) (3)→→→→
(C)
(P) (5) (Q) (3) (R) (2) (S) (4)→→→→
(D)
(P) (4) (Q) (2) (R) (1) (S) (3)→→→→
END OF THE QUESTION PAPER
Answer: (C)
JEE (Advanced) 2024 Paper 1
1/8
SECTION 1 (Maximum Marks: 12)
• This section contains FOUR (04) 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 : If ONLY the correct option is chosen;
Zero Marks : If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : In all other cases.
Q.1
A dimensionless quantity is constructed in terms of electronic charge , permittivity of free space
, Planck’s constant , and speed of light . If the dimensionless quantity is written as
and is a non-zero integer, then is given by
(A)
(B)
(C)
(D)
Q.2
An infinitely long wire, located on the -axis, carries a current along the +-direction and
produces the magnetic field
. The magnitude of the line integral
along a straight line from
the point
to is given by
[
is the magnetic permeability of free space.]
(A)
(B)
(C)
(D)
Q.3
Two beads, each with charge and mass , are on a horizontal, frictionless, non-conducting,
circular hoop of radius . One of the beads is glued to the hoop at some point, while the other one
performs small oscillations about its equilibrium position along the hoop. The square of the angular
frequency of the small oscillations is given by
[
is the permittivity of free space.]
(A)
(B)
(C)
(D)
Q.4
A block of mass 5 kg moves along the x-direction subject to the force
, with
the value of in metre. At time , it is at rest at position . The position and
momentum of the block at are
(A) m, kg m/s
(B) m, kg m/s
(C) m, kg m/s
(D) m, 5 kg m/s
Physics
Answer: (A)
Answer: (A)
Answer: (B)
Answer: (C)
JEE (Advanced) 2024 Paper 1
2/8
SECTION 2 (Maximum Marks: 12)
• This section contains THREE (03) questions.
• Each question has FOUR options (A), (B), (C) and (D). 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 to each question will be evaluated according to the following marking scheme:
Full Marks : ONLY if (all) the correct option(s) is(are) chosen;
Partial Marks : If all the four options are correct but ONLY three options are chosen;
Partial Marks : If three or more options are correct but ONLY two options are chosen, both of
which are correct;
Partial Marks : If two or more options are correct but ONLY one option is chosen and it is a
correct option;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : In all other cases.
• For example, in a question, if (A), (B) and (D) are the ONLY three options corresponding to correct
answers, then
choosing ONLY (A), (B) and (D) will get marks;
choosing ONLY (A) and (B) will get marks;
choosing ONLY (A) and (D) will get marks;
choosing ONLY (B) and (D) will get marks;
choosing ONLY (A) will get +1 mark;
choosing ONLY (B) will get +1 mark;
choosing ONLY (D) will get +1 mark;
choosing no option (i.e. the question is unanswered) will get 0 marks; and
choosing any other combination of options will get marks.
Q.5
A particle of mass is moving in a circular orbit under the influence of the central force
, corresponding to the potential energy
, where is a positive force
constant and is the radial distance from the origin. According to the Bohr’s quantization rule, the
angular momentum of the particle is given by , where , is the Planck’s
constant, and a positive integer. If and are the speed and total energy of the particle,
respectively, then which of the following expression(s) is(are) correct?
(A)
(B)
(C)
(D)
Answer: (A), (B), (C)
JEE (Advanced) 2024 Paper 1
3/8
Q.6
Two uniform strings of mass per unit length and 4, and length and , respectively, are joined
at point O, and tied at two fixed ends P and Q, as shown in the figure. The strings are under a
uniform tension . If we define the frequency
, which of the following statement(s)
is(are) correct?
(A) With a node at O, the minimum frequency of vibration of the composite string is
.
(B) With an antinode at O, the minimum frequency of vibration of the composite string is
.
(C) When the composite string vibrates at the minimum frequency with a node at O, it has 6 nodes,
including the end nodes.
(D) No vibrational mode with an antinode at O is possible for the composite string.
Q.7
A glass beaker has a solid, plano-convex base of refractive index , as shown in the figure. The
radius of curvature of the convex surface (SPU) is , while the planar surface (STU) acts as a
mirror. This beaker is filled with a liquid of refractive index up to the level QPR. If the image of
a point object O at a height of (OT in the figure) is formed onto itself, then, which of the
following option(s) is(are) correct?
(A) For , .
(B) For , .
(C) For , .
(D) For cm.
Answer: (A), (C), (D)
Answer: (A), (B)
JEE (Advanced) 2024 Paper 1
4/8
Q.8
The specific heat capacity of a substance is temperature dependent and is given by the formula
, where is a constant of suitable dimensions in SI units, and is the absolute
temperature. If the heat required to raise the temperature of kg of the substance from
C to
C is , the value of is _____.
[Given:
.]
Q.9
A disc of mass and radius is free to rotate about its vertical axis as shown in the figure. A
battery operated motor of negligible mass is fixed to this disc at a point on its circumference.
Another disc of the same mass and radius is fixed to the motor’s thin shaft. Initially, both
the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular
speed . If the angular speed at which the large disc rotates is , then the value of is _____.
Q.10
A point source S emits unpolarized light uniformly in all directions. At two points A and B, the
ratio
of the intensities of light is 2. If a set of two polaroids having angle between
their pass-axes is placed just before point B, then the new value of will be _____.
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 on-
screen 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 : If ONLY the correct integer is entered;
Zero Marks : In all other cases.
Answer: 25000
Answer: 12
Answer: 8
JEE (Advanced) 2024 Paper 1
5/8
Q.11
A source (S) of sound has frequency Hz. When the observer (O) and the source move towards
each other at a speed with respect to the ground (as shown in Case 1 in the figure), the observer
measures the frequency of the sound to be Hz. However, when the observer and the source
move away from each other at the same speed with respect to the ground (as shown in Case 2 in
the figure), the observer measures the frequency of sound to be Hz. The value of is _____.
Q.12
Two large, identical water tanks, 1 and 2, kept on the top of a building of height , are filled with
water up to height in each tank. Both the tanks contain an identical hole of small radius on their
sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to
tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through
the holes, the times taken to empty the tanks are
and
, respectively. If
, then the
ratio
is _____.
Q.13
A thin uniform rod of length and certain mass is kept on a frictionless horizontal table with a
massless string of length fixed to one end (top view is shown in the figure). The other end of the
string is pivoted to a point O. If a horizontal impulse is imparted to the rod at a distance
from the mid-point of the rod (see figure), then the rod and string revolve together around the point
O, with the rod remaining aligned with the string. In such a case, the value of is _____.
Answer: 200
Answer: 3
Answer: 18
JEE (Advanced) 2024 Paper 1
6/8
Q.14
One mole of a monatomic ideal gas undergoes the cyclic process J→ K→ L→ M→ J, as shown in
the P-T diagram.
Match the quantities mentioned in List-I with their values in List-II and choose the correct option.
[is the gas constant.]
List-I
List-II
(P) Work done in the complete cyclic process
(1)
(Q) Change in the internal energy of the gas in the
process JK
(2) 0
(R) Heat given to the gas in the process KL
(3)
(S) Change in the internal energy of the gas in the
process MJ
(4)
(5)
(A) P → 1; Q → 3; R → 5; S → 4
(B) P → 4; Q → 3; R → 5; S → 2
(C) P → 4; Q → 1; R → 2; S → 2
(D) P → 2; Q → 5; R → 3; S → 4
SECTION 4 (Maximum Marks: 12)
• 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.
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : ONLY if the option corresponding to the correct combination is chosen;
Zero Marks : If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : In all other cases.
Answer: (B)
JEE (Advanced) 2024 Paper 1
7/8
Q.15
Four identical thin, square metal sheets,
,
,
and
, each of side are kept parallel to each
other with equal distance ( ) between them, as shown in the figure. Let
, where
is the permittivity of free space.
Match the quantities mentioned in List-I with their values in List-II and choose the correct option.
List-I
List-II
(P) The capacitance between
and
, with
and
not connected, is
(1)
(Q) The capacitance between
and
, with
shorted to
, is
(2)
(R) The capacitance between
and
, with
shorted to
, is
(3)
(S) The capacitance between
and
, with
shorted to
, and
shorted to
, is
(4)
(5)
(A) P → 3; Q → 2; R → 4; S → 5
(B) P → 2; Q → 3; R → 2; S → 1
(C) P → 3; Q → 2; R → 4; S → 1
(D) P → 3; Q → 2; R → 2; S → 5
Q.16
A light ray is incident on the surface of a sphere of refractive index at an angle of incidence
.
The ray partially refracts into the sphere with angle of refraction
and then partly reflects from
the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The
total angle of deviation of the emergent ray with respect to the incident ray is . Match the
quantities mentioned in List-I with their values in List-II and choose the correct option.
List-I
List-II
(P) If and , then all the
possible values of
will be
(1) and
(Q) If
and , then all the
possible values of
will be
(2) and
(R) If
and , then all the
possible values of
will be
(3) and
(S) If
and
, then all the
possible values of will be
(4)
(5)
(A) P → 5; Q → 2; R→ 1; S→ 4
(B) P → 5; Q → 1; R→ 2; S→ 4
(CP → 3; Q → 2; R→ 1; S→ 4
(D) P → 3; Q → 1; R→ 2; S→ 5
Answer: (C)
Answer: (A)
JEE (Advanced) 2024 Paper 1
8/8
Q.17
The circuit shown in the figure contains an inductor , a capacitor
, a resistor
and an
ideal battery. The circuit also contains two keys K
1
and K
2
. Initially, both the keys are
open and there is no charge on the capacitor. At an instant, key K
1
is closed and
immediately after this the current in
is found to be
After a long time, the current
attains a steady state value
. Thereafter, K
2
is closed and simultaneously K
1
is opened and
the voltage across
oscillates with amplitude
and angular frequency
.
Match the quantities mentioned in List-I with their values in List-II and choose the correct option.
List-I
List-II
(P) The value of
in Ampere is
(1) 0
(Q) The value of
in Ampere is
(2) 2
(R) The value of
in kilo-radians/s is
(3) 4
(S) The value of
in Volt is
(4) 20
(5) 200
(A) P → 1; Q → 3; R → 2; S → 5
(B) P → 1; Q → 2; R → 3; S → 5
(C) P → 1; Q → 3; R → 2; S → 4
(D) P → 2; Q → 5; R → 3; S → 4
END OF THE QUESTION PAPER
Answer: (A)
JEE (Advanced) 2024 Paper 1
1/12
SECTION 1 (Maximum Marks: 12)
• This section contains FOUR (04) 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 : If ONLY the correct option is chosen;
Zero Marks : If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : In all other cases.
Q.1
A closed vessel contains 10 g of an ideal gas X at 300 K, which exerts 2 atm pressure. At the same
temperature, 80 g of another ideal gas Y is added to it and the pressure becomes 6 atm. The ratio of
root mean square velocities of X and Y at 300 K is
(A)
(B)
(C)
(D)
Q.2
At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid
(HNO
2
) gives the species
(A) H
3
O
+
, NO
3
−
and NO
(B) H
3
O
+
, NO
3
−
and NO
2
(C) H
3
O
+
, NO
−
and NO
2
(D) H
3
O
+
, NO
3
−
and N
2
O
Chemistry
Answer: (D)
Answer: (A)
JEE (Advanced) 2024 Paper 1
2/12
Q.3
Aspartame, an artificial sweetener, is a dipeptide aspartyl phenylalanine methyl ester. The structure
of aspartame is
Structures of phenylalanine and aspartic acid are given below.
(A)
(B)
(C)
(D)
Q.4
Among the following options, select the option in which each complex in Set-I shows geometrical
isomerism and the two complexes in Set-II are ionization isomers of each other.
[en = H
2
NCH
2
CH
2
NH
2
]
(A) Set-I: [Ni(CO)
4
] and [PdCl
2
(PPh
3
)
2
]
Set-II: [Co(NH
3
)
5
Cl]SO
4
and [Co(NH
3
)
5
(SO
4
)]Cl
(B) Set-I: [Co(en)(NH
3
)
2
Cl
2
] and [PdCl
2
(PPh
3
)
2
]
Set-II: [Co(NH
3
)
6
][Cr(CN)
6
] and [Cr(NH
3
)
6
][Co(CN)
6
]
(C) Set-I: [Co(NH
3
)
3
(NO
2
)
3
] and [Co(en)
2
Cl
2
]
Set-II: [Co(NH
3
)
5
Cl]SO
4
and [Co(NH
3
)
5
(SO
4
)]Cl
(D) Set-I: [Cr(NH
3
)
5
Cl]Cl
2
and [Co(en)(NH
3
)
2
Cl
2
]
Set-II: [Cr(H
2
O)
6
]Cl
3
and [Cr(H
2
O)
5
Cl]Cl
2
∙H
2
O
Answer: (B)
Answer: (C)
JEE (Advanced) 2024 Paper 1
3/12
SECTION 2 (Maximum Marks: 12)
• This section contains THREE (03) questions.
• Each question has FOUR options (A), (B), (C) and (D). 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 to each question will be evaluated according to the following marking scheme:
Full Marks : ONLY if (all) the correct option(s) is(are) chosen;
Partial Marks : If all the four options are correct but ONLY three options are chosen;
Partial Marks : If three or more options are correct but ONLY two options are chosen, both of
which are correct;
Partial Marks : If two or more options are correct but ONLY one option is chosen and it is a
correct option;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : In all other cases.
• For example, in a question, if (A), (B) and (D) are the ONLY three options corresponding to correct
answers, then
choosing ONLY (A), (B) and (D) will get marks;
choosing ONLY (A) and (B) will get marks;
choosing ONLY (A) and (D) will get marks;
choosing ONLY (B) and (D) will get marks;
choosing ONLY (A) will get +1 mark;
choosing ONLY (B) will get +1 mark;
choosing ONLY (D) will get +1 mark;
choosing no option (i.e. the question is unanswered) will get 0 marks; and
choosing any other combination of options will get marks.
Q.5
Among the following, the correct statement(s) for electrons in an atom is(are)
(A) Uncertainty principle rules out the existence of definite paths for electrons.
(B) The energy of an electron in 2s orbital of an atom is lower than the energy of an electron that
is infinitely far away from the nucleus.
(C) According to Bohr’s model, the most negative energy value for an electron is given by n = 1,
which corresponds to the most stable orbit.
(D) According to Bohr’s model, the magnitude of velocity of electrons increases with increase in
values of n.
Answer: (A), (B), (C)
JEE (Advanced) 2024 Paper 1
4/12
Q.6
Reaction of iso-propylbenzene with O
2
followed by the treatment with H
3
O
+
forms phenol and a
by-product P. Reaction of P with 3 equivalents of Cl
2
gives compound Q. Treatment of Q with
Ca(OH)
2
produces compound R and calcium salt S.
The correct statement(s) regarding P, Q, R and S is(are)
(A) Reaction of P with R in the presence of KOH followed by acidification gives
(B) Reaction of R with O
2
in the presence of light gives phosgene gas
(C) Q reacts with aqueous NaOH to produce Cl
3
CCH
2
OH and Cl
3
CCOONa
(D) S on heating gives P
Q.7
The option(s) in which at least three molecules follow Octet Rule is(are)
(A) CO
2
, C
2
H
4
, NO and HCl
(B) NO
2
, O
3
, HCl and H
2
SO
4
(C) BCl
3
, NO, NO
2
and H
2
SO
4
(D) CO
2
, BCl
3
, O
3
and C
2
H
4
Answer: (A), (B), (D)
Answer: (A), (D)
JEE (Advanced) 2024 Paper 1
5/12
Q.8
Consider the following volume−temperature (V−T) diagram for the expansion of 5 moles of an
ideal monoatomic gas.
Considering only P-V work is involved, the total change in enthalpy (in Joule) for the
transformation of state in the sequence X→Y→Z is ______.
[Use the given data: Molar heat capacity of the gas for the given temperature range, C
V, m
= 12 J K
−1
mol
−1
and gas constant, R = 8.3 J K
−1
mol
−1
]
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 on-
screen 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 : If ONLY the correct integer is entered;
Zero Marks : In all other cases.
Answer: 8120
JEE (Advanced) 2024 Paper 1
6/12
Q.9
Consider the following reaction,
( ) ( ) ( ) ( )
222
2H g + 2NO g N g + 2H g O→
which follows the mechanism given below:
( ) ( ) ( )
1
1
22
2NO g N O g fast equlibrium
k
k
−
( ) ( ) ( ) ( ) ( )
2
22 2 2 2
NO g + H g NOg + HOg slow reaction
k
→
( ) ( ) ( ) ( ) ( )
3
22 22
NOg + H g N g + HOg fast reaction
k
→
The order of the reaction is ______.
Q.10
Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. NaOH
solution, gives P and Q. Compound P does not give Tollens’ test, whereas Q on acidification gives
positive Tollens’ test. Treatment of P with excess cyclohexanone in the presence of catalytic
amount of p-toluenesulfonic acid (PTSA) gives product R.
Sum of the number of methylene groups (-CH
2
-) and oxygen atoms in R is ______.
Q.11
Among
,
,
,
,
,
,
, and
,
the total number of species isoelectronic with
is ______.
[Given, atomic number: V = 23, Cr = 24, Mn = 25, Fe = 26, Co = 27, Ni = 28, Cu = 29, Ir = 77]
Answer: 3
Answer: 18
Answer: 3
JEE (Advanced) 2024 Paper 1
7/12
Q.12
In the following reaction sequence, the major product P is formed.
Glycerol reacts completely with excess P in the presence of an acid catalyst to form Q. Reaction of
Q with excess NaOH followed by the treatment with CaCl
2
yields Ca-soap R, quantitatively.
Starting with one mole of Q, the amount of R produced in gram is ______.
[Given, atomic weight: H = 1, C = 12, N = 14, O = 16, Na = 23, Cl = 35, Ca = 40]
Q.13
Among the following complexes, the total number of diamagnetic species is ______.
[Mn(NH
3
)
6
]
3+
, [MnCl
6
]
3−
, [FeF
6
]
3−
, [CoF
6
]
3−
, [Fe(NH
3
)
6
]
3+
, and [Co(en)
3
]
3+
[Given, atomic number: Mn = 25, Fe = 26, Co = 27;
en = H
2
NCH
2
CH
2
NH
2
]
Answer: 909
Answer: 1
JEE (Advanced) 2024 Paper 1
8/12
SECTION 4 (Maximum Marks: 12)
• 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.
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : ONLY if the option corresponding to the correct combination is chosen;
Zero Marks : If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : In all other cases.
JEE (Advanced) 2024 Paper 1
9/12
Q.14
In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a
larger volume of titrate of much lower concentration, and the conductance is measured after each
addition.
The limiting ionic conductivity (
values (in mS m
2
mol
−1
) for different ions in aqueous solutions
are given below:
Ions
2
6.2
7.4
5.0
35.0
7.2
7.6
16.0
19.9
4.1
For different combinations of titrates and titrants given in List-I, the graphs of ‘conductance’
versus ‘volume of titrant’ are given in List-II.
Match each entry in List-I with the appropriate entry in List-II and choose the correct option.
List-I
List-II
(P) Titrate: KCl
Titrant: AgNO
3
(1)
(Q) Titrate:
AgNO
3
Titrant: KCl
(2)
(R) Titrate: NaOH
Titrant: HCl
(3)
(S) Titrate: NaOH
Titrant: CH
3
COOH
(4)
(5)
(A) P-4, Q-3, R-2, S-5
(B) P-2, Q-4, R-3, S-1
(C) P-3, Q-4, R-2, S-5
(D) P-4, Q-3, R-2, S-1
Answer: (C)
JEE (Advanced) 2024 Paper 1
10/12
Q.15
Based on VSEPR model, match the xenon compounds given in List-I with the corresponding
geometries and the number of lone pairs on xenon given in List-II and choose the correct option.
List-I
List-II
(P) XeF
2
(1) Trigonal bipyramidal and two lone pair of electrons
(Q) XeF
4
(2) Tetrahedral and one lone pair of electrons
(R) XeO
3
(3) Octahedral and two lone pair of electrons
(S) XeO
3
F
2
(4) Trigonal bipyramidal and no lone pair of electrons
(5) Trigonal bipyramidal and three lone pair of electrons
(A) P-5, Q-2, R-3, S-1
(B) P-5, Q-3, R-2, S-4
(C) P-4, Q-3, R-2, S-1
(D) P-4, Q-2, R-5, S-3
Answer: (B)
JEE (Advanced) 2024 Paper 1
11/12
Q.16
List-I contains various reaction sequences and List-II contains the possible products. Match each
entry in List-I with the appropriate entry in List-II and choose the correct option.
List-I
List-II
(P)
(1)
(Q)
(2)
(R)
(3)
(S)
(4)
(5)
(A) P-3, Q-5, R-4, S-1
(B) P-3, Q-2, R-4, S-1
(C) P-3, Q-5, R-1, S-4
(D) P-5, Q-2, R-4, S-1
Answer: (A)
JEE (Advanced) 2024 Paper 1
12/12
Q.17
List-I contains various reaction sequences and List-II contains different phenolic compounds.
Match each entry in List-I with the appropriate entry in List-II and choose the correct option.
List-I
List-II
(P)
(1)
(Q)
(2)
(R)
(3)
(S)
(4)
(5)
(A) P-2, Q-3, R-4, S-5
(B) P-2, Q-3, R-5, S-1
(C) P-3, Q-5, R-4, S-1
(D) P-3, Q-2, R-5, S-4
END OF THE QUESTION PAPER
Answer: (C)
