JEE Advanced 2026 Paper 1 Answer Key

JEE (Advanced) 2026 Paper 1

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 : +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.

Q.1 Consider the function 𝑓: (0, ∞) → (−∞, ∞) given by

𝑓(𝑥) = √𝑥 log e (𝑥) − 𝑥 + 1 .

Then which one of the following statements is TRUE ?

(A) The derivative of the function 𝑓 is decreasing in the interval (0, 1)
(B) The function 𝑓 has a local maximum at some point 𝑎 ∈ (0, ∞)
(C) The function 𝑓 has a local minimum at some point 𝑏 ∈ (0, ∞)
(D) The function 𝑓 has NEITHER a point of local maximum NOR a point of local minimum in
the interval (0, ∞)

Answer Q1: D

Q.2 Let 𝑃 be the point on the parabola 𝑦 = 𝑥 2 such that the slope of the tangent to the parabola at the
point 𝑃 is 4 . Let 𝑄 be the point in the first quadrant lying on the circle 𝑥 2 + 𝑦 2 = 2 such that the
slope of the tangent to the circle at the point 𝑄 is −1 . Let 𝑅 be the point in the first quadrant lying
1
on the ellipse 𝑥 2 + 4𝑦 2 = 8 such that the slope of the tangent to the ellipse at the point 𝑅 is − 2 .
Then the radius of the circle passing through the points 𝑃, 𝑄 and 𝑅 is

(A) √10 (B) √5 (C) (D) 2√5
5
√
2

Answer Q2: C

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JEE (Advanced) 2026 Paper 1

Q.3 Which one of the following matrices can be obtained by performing elementary row transformations
on the 3 × 3 identity matrix ?

(A) 1 1 1 (B) 1 1 1
[1 1 1] [2 3 4]
1 1 1 1 2 1
(C) 1 1 1 (D) 1 1 1
[2 3 4] [ −1 1 2]
2 5 8 0 2 3

Answer Q3: B

Q.4 Considering only the principal values of the inverse trigonometric functions, the value of

1
cot −1 (cot(−11)) + 10 sin (2 cos−1 ( )) + 10 sin(2 tan−1 (2))
√2
is

(A) 3𝜋 + 7 (B) 7 (C) 4𝜋 + 7 (D) 3𝜋 − 5

Answer Q4: C

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JEE (Advanced) 2026 Paper 1

SECTION 2 (Maximum Marks: 16)

• This section contains FOUR (04) 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 : +4 ONLY if (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;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : −1 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 +4 marks;
choosing ONLY (A) and (B) will get +2 marks;
choosing ONLY (A) and (D) will get +2 marks;
choosing ONLY (B) and (D) will get +2 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 −1 marks.

Q.5 Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green
balls. All the balls of Box I and Box II are mixed together and a ball is chosen at random from them.
Let 𝐸1 be the event that the ball chosen belonged to Box I and let 𝐸2 be the event that the ball chosen
belonged to Box II. Let 𝐹1 be the event that the ball chosen is red and let 𝐹2 be the event that the ball
chosen is green.

Then which of the following statements is (are) TRUE ?

(A) The events 𝐸1 and 𝐹1 are independent
(B) The events 𝐸2 and 𝐹2 are dependent
(C) The conditional probability 𝑃(𝐹1 | 𝐸1 ) is equal to the conditional probability 𝑃(𝐹1 | 𝐸2 )
(D) The conditional probability 𝑃(𝐹1 | 𝐸1 ) is greater than the conditional probability 𝑃(𝐹2 | 𝐸2 )

Answer Q5: AC

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JEE (Advanced) 2026 Paper 1

Q.6 𝑥−1 𝑦−3 𝑧+2
Let 𝑃 be the plane such that it contains the straight line 2
= 3 = 1 and is perpendicular to
the plane 𝑥 + 2𝑦 + 3𝑧 = 4 . Let 𝑃1 be the plane which passes through the point (4, 2, 2) and is
parallel to 𝑃 .

Then which of the following statements is (are) TRUE ?

(A) The equation of the plane 𝑃 is 7𝑥 − 5𝑦 + 𝑧 = −10
(B) The distance between the planes 𝑃 and 𝑃1 is 30
(C) The distance of the plane 𝑃 from the origin is 2√3
(D) 1
The acute angle between the plane 𝑃 and the plane 2𝑥 + 2𝑦 + 𝑧 = 3 is cos−1 (3 3)
√

Answer Q6: AD

Q.7 Let ℝ denote the set of all real numbers. Let 𝑓 ∶ ℝ → ℝ be an arbitrary function and let
𝑔 ∶ ℝ → ℝ be the function defined by

𝑔(𝑥) = 𝑥𝑓(𝑥) , for all 𝑥 ∈ ℝ .

Then which of the following statements is (are) TRUE ?

(A) The function 𝑔 is always continuous at 𝑥 = 0
(B) If 𝑓 is continuous at 𝑥 = 0 , then 𝑔 is differentiable at 𝑥 = 0
(C) If 𝑔 is differentiable at 𝑥 = 0 , then 𝑓 is continuous at 𝑥 = 0
(D) If 𝑔 is differentiable at 𝑥 = 0 , then lim 𝑓(𝑥) exists
𝑥→0

Answer Q7: BD

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JEE (Advanced) 2026 Paper 1

Q.8 Consider the matrix
2 −1
𝑀=[ ].
1 0

Let 𝑝 , 𝑞 , 𝑟 , 𝑠 , 𝑎 , 𝑏 , 𝑐 and 𝑑 be integers such that

26
26 𝑝 𝑞 𝑎 𝑏
𝑀 =[ ] and ∑ 𝑀𝑘 = [ ].
𝑟 𝑠 𝑐 𝑑
𝑘=1

Then which of the following statements is (are) TRUE ?

(A) There exists a 2 × 2 invertible matrix 𝑁 with real entries such that
1 1
𝑀𝑁 = 𝑁 [ ]
0 1

(B) The value of 𝑎 is 378

(C) For any two given integers 𝑚 and 𝑛, there exist unique integers 𝑥 and 𝑦 such that

𝑝𝑥 + 𝑞𝑦 = 𝑚 and 𝑟𝑥 + 𝑠𝑦 = 𝑛

(D) For each positive real number 𝑡, the system of linear equations

(𝑎 + 𝑡)𝑥 + 𝑏𝑦 = 1
𝑐𝑥 + (𝑑 + 𝑡)𝑦 = −1
has a unique solution

Answer Q8: ACD

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JEE (Advanced) 2026 Paper 1

SECTION 3 (Maximum Marks: 16)

• This section contains FOUR (04) questions.
• The answer to each question is a NUMERICAL VALUE.
• For each question, enter the correct numerical value corresponding to the answer in the designated
place using the mouse and the on-screen virtual numeric keypad.
• 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 : +4 If ONLY the correct numerical value is entered in the designated place;
Zero Marks : 0 In all other cases.

Q.9 Let 𝑆 = {1, 2, 3, … , 10} . Consider the set

𝑋 = {𝑅 ∶ 𝑅 is an equivalence relation on the set 𝑆 such that 𝑅 has exactly 42 elements} .

Then the number of elements in 𝑋 is _____________.

Answer Q9: [2520]

Q.10 Consider the function 𝑓 ∶ (− 𝜋 , 𝜋) → (−∞, ∞) defined by
2 2

𝑓(𝑥) = (|𝑥| + |𝑥 − 1|) sin 𝑥 + [𝑥 sin 𝑥] ,

where [𝑥 sin 𝑥] is the greatest integer less than or equal to 𝑥 sin 𝑥 .

𝜋 𝜋
Let α be the total number of points in the interval (− 2 , 2 ) at which 𝑓 is NOT continuous, and
𝜋 𝜋
let 𝛽 be the total number of points in the interval (− , ) at which 𝑓 is NOT differentiable.
2 2

Then the value of 𝛼 + 𝛽 is ___________.

Answer Q10: [5]

Q.11 The number of ways to distribute 10 identical red pens and 14 identical blue pens among four
persons such that each person gets 6 pens, is _____________.

Answer Q11: [206]

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JEE (Advanced) 2026 Paper 1

Q.12 Let
𝜋 3𝜋 9𝜋 27𝜋 81𝜋
𝛼 = (1 − 2 cos ( )) (1 − 2 cos ( )) (1 − 2 cos ( )) (1 − 2 cos ( )) (1 − 2 cos ( )) .
11 11 11 11 11

Then the value of 5 − 𝛼 2 is _____________.

Answer Q12: [3.9 TO 4.1]

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JEE (Advanced) 2026 Paper 1

SECTION 4 (Maximum Marks: 16)

• 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 : +4 ONLY if the option corresponding to the correct combination 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.

Q.13
Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I List-II

(P) If 𝛼 and 𝛽 are the distinct roots of the (1) 𝑥 2 + 𝑥 + 1 = 0
equation 𝑥 2 + 𝑥 + 1 = 0, then the
quadratic equation with roots
1 1
(𝛼+1)2026
and (𝛽+1)2026 is

(Q) If 𝛼 and 𝛽 are the distinct roots of the (2) 𝑥 2 − 𝑥 + 1 = 0
equation 𝑥 2 + 𝑥 + 1 = 0, then the
quadratic equation with roots
1 1
(𝛼+1)2027
and (𝛽+1)2027 is

(R) If 𝛾 and 𝛿 are the distinct roots of the (3) 𝑥 2 + 𝑥 − 1 = 0
equation 𝑥 2 − 𝑥 + 1 = 0, then the value
1 1
of (𝛾−1)2026 + (𝛿−1)2026 is

(S) If 𝑝 and 𝑟 are the distinct roots of the (4) −1
equation 𝑥 2 + 𝑥 − 1 = 0, then the value
1 1
of (𝑝+1)3 + (𝑟+1)3 is

(5) −4

(A) (P) → (1), (Q) → (2), (R) → (5), (S) → (4)
(B) (P) → (3), (Q) → (1), (R) → (4), (S) → (5)
(C) (P) → (1), (Q) → (2), (R) → (4), (S) → (5)
(D) (P) → (2), (Q) → (3), (R) → (5), (S) → (4)
Answer Q13: C

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JEE (Advanced) 2026 Paper 1

Q.14

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I List-II

(P) The number of elements in the set (1) is 1

{𝑥 ∈ [−𝜋, 𝜋] ∶ sin6 𝑥 + cos4 𝑥 = 1}

(Q) The number of elements in the set (2) is 2
𝜋 𝜋
{𝑥 ∈ [− , ] ∶ sin2 𝑥 + cos6 𝑥 = 1}
2 2

(R) The number of elements in the set (3) is 3

𝑥 1
{𝑥 ∈ [−𝜋, 𝜋] ∶ cos 2 ( ) − sin2 𝑥 = }
2 2

(S) The number of elements in the set (4) is 4
𝑥
{𝑥 ∈ [−2𝜋, 2𝜋] ∶ 6 sin2 ( ) − cos 3𝑥 = 3}
2

(5) is 5

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

Answer Q14: B

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JEE (Advanced) 2026 Paper 1

Q.15
For real numbers 𝛼, 𝛽, 𝛾, 𝛿 and 𝜇 , consider the matrix
1 1
𝛼 − 2
√2 √
𝑀= 1 1 .
𝛽
√3 √3
[𝛾 𝛿 𝜇 ]

Suppose that 𝑀𝑀𝑇 = 𝐼 , where 𝑀𝑇 is the transpose of the matrix 𝑀, and 𝐼 is the 3 × 3 identity
matrix. Let

1 1 1 1
𝑢
⃗ = 𝛼 𝑖̂ + 𝑗̂ + 𝛾 𝑘̂ , 𝑣= 𝑖̂ + 𝛽𝑗̂ + 𝛿𝑘̂ and 𝑤
⃗⃗ = − 𝑖̂ + 𝑗̂ + 𝜇𝑘̂ .
√3 √2 √2 √3

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I List-II

(P) The value of 𝛾 2 + 𝛿 2 is (1) 0

(Q) If 𝑥𝑢
⃗ + 𝑦𝑣 + 𝑧𝑤
⃗⃗ = 𝑗̂ for some real (2) 1
numbers 𝑥, 𝑦 and 𝑧, then the value
of 𝑥 is

(R) The value of |𝑢
⃗ ⋅ (𝑣 × 𝑤
⃗⃗ )| is 1
(3)
√2

(S) The value of |𝑢
⃗ × (𝑣 × 𝑤
⃗⃗ )| is 1
(4)
√3

5
(5)
6

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

Answer Q15: A

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JEE (Advanced) 2026 Paper 1

Q.16
Match each entry in List-I to the correct entry in List-II and choose the correct option.

List-I List-II

(P) The circle with centre (1, 2) and touching (1) the point (1, 1)
the straight line 3𝑥 + 4𝑦 = 1, passes
through

(Q) The common tangent to the circle (2) the point (7, 9)
𝑥 2 + 𝑦 2 = 2 and the parabola 𝑦 2 = 8𝑥
with positive slope, passes through

(R) Let 𝑀 be the end point of the latus rectum (3) the point (3, 2)
of the ellipse 3𝑥 2 + 4𝑦 2 = 48 such that
𝑀 lies in the first quadrant. Then the normal
to the ellipse drawn at 𝑀 passes through

(S) Let 𝐻 be the hyperbola whose centre is at (4) the point (2, 5)
the origin, one of the foci is at (5, 0), and
one directrix is 5𝑥 + 16 = 0 .
Then 𝐻 passes through

(5) the point (8, 3√3 )

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

Answer Q16: B

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JEE (Advanced) 2026 Paper 1

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 : +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.

Q.1 Consider a large disk of radius 𝑅 and two smaller disks, each of radius 𝑟 = 𝑅/50, lying on its
circumference, as shown in the figure. The smaller disks are initially in contact with each other,
with an angular separation Δ𝜃 between their centers. They are made to roll without slipping in
opposite directions, with constant angular velocities 𝜔 and 2𝜔 while the large disk is held
stationary. The time 𝜏 at which the smaller disks are again in contact is:
[Use sin(Δ𝜃) = Δ𝜃 and ignore gravity.]

(A) 4 (B) 2
𝜏 = 51 × (2𝜋 − ) /𝜔 𝜏 = 51 × (2𝜋 − ) /3𝜔
51 51
(C) 4 (D) 2
𝜏 = 51 × (2𝜋 − ) /3𝜔 𝜏 = 51 × (2𝜋 − ) /𝜔
51 51

Answer Q1: C

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JEE (Advanced) 2026 Paper 1

Q.2 Consider a circuit consisting of a capacitor of capacitance 𝐶 and a coil with 𝑁 turns per unit length,
cross sectional area 𝑆 and length 𝑑, where 𝑑2 ≫ 𝑆. There is another coil of length 𝑑/2, cross
sectional area 𝑆/2 and 2𝑁 turns per unit length completely inside the larger coil, as shown in the
figure. The ends of this smaller coil are connected with each other by an insulated conducting wire.
The self-inductance of the larger coil is 𝐿. Neglecting edge effects and all the Ohmic resistances,
the resonant frequency of the circuit is:

(A) 4 (B) 6 (C) 2 (D)
2
√15 𝐿𝐶 √5 𝐿𝐶 √3 𝐿𝐶 √
3 𝐿𝐶

Answer Q2: C

Q.3 𝑔𝑅
A solid cylinder of radius 𝑅 rolls without slipping with a center of mass speed 𝑣0 = √ 3 on a
horizontal surface with a vertical edge, as shown in the figure. Here, 𝑔 is the acceleration due to the
gravity. At the moment when the cylinder loses contact with the surface due to rotation around the
corner, the speed of its center of mass is:

(A) 0 (B) (C) (D)
5𝑔𝑅 𝑔𝑅 3𝑔𝑅
√ √ √
7 15 7

Answer Q3: B

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JEE (Advanced) 2026 Paper 1

Q.4 A double convex lens made of glass of refractive index 1.5 and radii of curvature of the curved
surfaces 20 cm each is immersed in a liquid of refractive index 𝑛𝐿 . The correct plot showing the
variation of the power, in the units of diopter (𝐷), as a function of 𝑛𝐿 is:

(A) (B)

(C) (D)

Answer Q4: A or B

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JEE (Advanced) 2026 Paper 1

SECTION 2 (Maximum Marks:16)

 This section contains FOUR (04) 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 : +4 ONLY if (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;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : −1 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 +4 marks;
choosing ONLY (A) and (B) will get +2 marks;
choosing ONLY (A) and (D) will get +2 marks;
choosing ONLY (B) and (D) will get +2 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 −1 marks.

Q.5 Consider a hydrogen atom with 𝑣𝑘 , 𝑟𝑘 , and 𝐾𝑘 denoting the velocity, orbital radius and kinetic
energy of the electron in the 𝑘 th orbit, respectively. The electron undergoes a transition from the
𝑛th orbit, emitting radiation corresponding to the Lyman series. Considering ℎ to be the Planck’s
constant and 𝜖0 the permittivity of the free space, the correct statement(s) is/are:

(A) ℎ 𝑛𝑣 𝑣
Magnitude of change in kinetic energy of electron can be expressed as 4𝜋 | 𝑟 𝑛 − 𝑟1 |.
𝑛 1

(B) Magnitude of change in de Broglie wavelength of the electron can be expressed as
𝑒2 1 1
| − 𝐾 |.
4𝜖0 𝐾𝑛 1

(C) 𝑒2 1 1
Frequency of the radiation emitted can be expressed as 8𝜋𝜖 ℎ (𝑟 − 𝑟 ).
0 1 𝑛

(D) ℎ 𝑣 𝑛𝑣
Magnitude of change in total energy of the electron can be expressed as 2𝜋 | 𝑟1 − 𝑟 𝑛 |.
1 𝑛

Answer Q5: AC

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JEE (Advanced) 2026 Paper 1

Q.6 A particle is thrown with a speed 𝑣 from a point 𝑂 at an angle 𝜃 with the horizontal plane such that
it passes through the point 𝑃 at a height of 1 m and horizontal distance of 5 m from 𝑂, as shown in
the figure. If acceleration due to gravity is 𝑔 ms−2, then the correct statement(s) is/are:

(A) 5 𝑔
If 𝜃 = 45o , then 𝑣 = √2 ms−1.
(B) If 𝜃 = 45o , the particle reaches its maximum height before it reaches 𝑃.
(C) If 𝜃 = 30o , the particle reaches its maximum height after reaching 𝑃.
(D) 1
If 𝜃 = tan−1 (5), then 𝑣 = 125√𝑔 ms−1.

Answer Q6: AB

Q.7 A quasi-static cycle of a monoatomic ideal gas contains an isothermal process (𝒂𝒃), followed by an
isochoric process (𝒃𝒄) and an adiabatic process (𝒄𝒂) as shown in the figure. The volumes of the gas
are 𝑉1 and 𝑉2 at 𝒂 and 𝒃, respectively. If the cycle has heat input 𝑄in and output 𝑄out , then the
𝑄in −𝑄out
efficiency of the cycle is defined as 𝜂 = 𝑄in
. The correct statement(s) is/are:
[Given: ln 2 ≈ 0.7]

(A) If 𝑉2 /𝑉1 = 8, the heat released in the process 𝒃𝒄 is smaller than the heat absorbed in the
process 𝒂𝒃.
(B) For a given value of 𝑉2 /𝑉1, 𝜂 does not depend on the temperature of the isothermal process.
(C) If 𝑉2 /𝑉1 = 8, then the temperature of the gas at 𝒂 is 4 times the temperature of the gas at 𝒄.
(D) If 𝑉2 /𝑉1 = 8, then the pressure of the gas at 𝒂 is 4 times the pressure of the gas at 𝒃.

Answer Q7: ABC

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JEE (Advanced) 2026 Paper 1

Q.8 The electric field associated with an electromagnetic wave travelling in vacuum is given by
𝐸0 sin(3𝑦 + 4𝑧 + 𝜔𝑡)𝑖̂, where 𝜔 is the angular frequency. All quantities are in SI units. The correct
statement(s) about this wave is/are:
[Given: speed of light in vacuum 𝑐 = 3 × 108 ms−1.]

1
(A) The wave is travelling in − 5 (3𝑗̂ + 4𝑘̂ ) direction.
(B) The magnitude of the wave vector is 0.5 m−1 .
(C) The value of 𝜔 is 1.5 × 109 rad s −1.
(D) The magnetic field associated with this wave is given by
𝐸0
𝑐
sin(3𝑦 + 4𝑧 + 𝜔𝑡)(4𝑗̂ − 3𝑘̂ ).

Answer Q8: AC

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JEE (Advanced) 2026 Paper 1

SECTION 3 (Maximum Marks:16)

 This section contains Four (04) questions.
 The answer to each question is a NUMERICAL VALUE.
 For each question, enter the correct numerical value corresponding to the answer in the designated
place using the mouse and the on-screen virtual numeric keypad.
 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 : +4 If ONLY the correct numerical value is entered in the designated place;
Zero Marks : 0 In all other cases.

Q.9 A tank contains two immiscible liquids of densities 6𝜌 and 2𝜌. The higher density liquid is filled
up to a height 𝐿/2 from the bottom. A thin rod of density 𝜌 and length 𝐿 is fully immersed and
hinged at the bottom so that it can oscillate freely, as shown in the figure. If the rod is slightly
2𝜋 𝐿
disturbed from its equilibrium, the time period of small oscillations is
𝑛
√𝑔, where 𝑔 is the
acceleration due to gravity. The value of 𝑛 is:

Answer Q9: [1.70 to 1.75]

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JEE (Advanced) 2026 Paper 1

Q.10 As shown in the figure, five Carnot engines, each with efficiency 𝜂 and same number of cycles per
unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one
engine is completely absorbed by the next engine. Consider 𝑄0 to be the amount of heat absorbed
per cycle by the first engine and 𝑊 as the amount of total work done by all the engines per cycle,
𝑊 211
then the net efficiency of the system is found to be 𝜂net = 𝑄 = 243. The value of 𝜂 is:
0

Answer Q10: [0.32 to 0.34]

Q.11 As shown in the figure, an insulated container is fitted with a thermally conducting but immovable
partition (𝑃1 ) and a freely movable but thermally insulated piston (𝑃2 ). The partition 𝑃1 with
thermal conductivity 𝐾, cross sectional area 𝐴 and width 𝑥 divides the container into two sections,
𝑆1 and 𝑆2 , each containing one mole of a monoatomic gas. The piston 𝑃2 moves freely such that the
gas in 𝑆2 is always at the atmospheric pressure. Initially, the difference between the temperatures of
Δ𝑇
𝑆1 and 𝑆2 is Δ𝑇0 . The time it takes for the temperature difference to become 20 is 𝑛𝑥𝑅/𝐾𝐴, where
𝑅 is the universal gas constant. The value of 𝑛 is:
[ Given: ln 2 ≈ 0.7 ]

Answer Q11: [0.63 to 0.70]

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JEE (Advanced) 2026 Paper 1

Q.12 A hollow, right circular cone of base radius 𝑅 and height ℎ, with its tip at the origin is rotating
about the Z-axis with an angular velocity 𝜔, as shown in the figure. The cone carries a total
charge 𝑄 uniformly distributed on its curved surface. The magnitude of magnetic field at a
𝑛𝜇 𝑄𝑅2 𝜔
point (0,0, 𝑧) , where 𝑧 ≫ 𝑅 and 𝑧 ≫ ℎ, is 4𝜋0𝑧3
. The value of 𝑛 is:

Answer Q12: [0.50]

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JEE (Advanced) 2026 Paper 1

SECTION 4 (Maximum Marks:16)

 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 : +4 ONLY if the option corresponding to the correct combination 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.

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JEE (Advanced) 2026 Paper 1

Q.13 List-I shows four configurations made of straight and semi-circular narrow tubes containing air. A sound
wave of wavelength 𝜆 = 0.29 m enters these structures at the point 𝑆 and a sound detector is placed at 𝐷.
Between the points 𝑆 and 𝐷, the sound travels only through the tubes. List-II contains the possible smallest
values of 𝑙 (refer to the figures) for which the detector 𝐷 records maximum amplitude. Ignore effects of
sharp corners. [Given cos(15°) = 0.97]
Choose the option that best describes the match between the entries in List-I to those in List-II.

List-I List-II

(P) (1) 1.32 m

(Q) (2) 1.19 m

(R) (3) 0.51 m

(S) (4) 0.29 m

(5) 0.13 m

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

Answer Q13: D

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JEE (Advanced) 2026 Paper 1

Q.14 In the List-I, four optical effects are mentioned. The physical phenomena of light which are
essential to describe these optical effects are given in List-II. Choose the option which describes
the correct match between the entries in List-I to those in List-II.

List-I List-II

(P) Colorful sky in north polar region (Aurora (1) Dispersion and reflection
Borealis)
(Q) Partially polarized sun light (2) Total internal reflection
(R) Rainbow (3) Diffraction
(S) Dark and bright fringes (4) Scattering of light by molecules in the
atmosphere
(5) Emission of radiation from oxygen
and nitrogen atoms excited by charged
particles

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

Answer Q14: A

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JEE (Advanced) 2026 Paper 1

Q.15 List-I contains four conducting loops lying in the 𝑋𝑌 plane, as shown in the figures. The loops
are rotating about 𝑍 axis passing through the point 𝑂 with time period 𝑇 in clockwise direction.
The region 𝑥 > 0 contains a uniform magnetic field 𝐵 in the +𝑧 direction. List-II contains the
qualitative variation of the induced current 𝑖(𝑡) for each of these loops. Choose the option which
describes the correct match between the entries in List-I to those in List-II.

List-I List-II

(P) (1)

(Q) (2)

(R) (3)

(S) (4)

(5)

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

Answer Q15: C

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JEE (Advanced) 2026 Paper 1

Q.16 List-I shows four planar structures made of uniform solid rods each of mass 𝑚 and length 𝑙. In the List-II
the possible moment of inertia of these structures about an axis 𝑂𝐶𝑂′ , which lies in the plane of the
structures, are given.
Choose the option that describes the correct match between the entries in List-I to those in List-II.

List-I List-II

(P) 5
(1) 4 𝑚𝑙 2

(Q) 1
(2) 6 𝑚𝑙 2

(R) 1
(3) 12 𝑚𝑙 2

(S) 2
(4) 𝑚𝑙 2
3

1
(5) 3 𝑚𝑙 2

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

Answer Q16: A

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JEE (Advanced) 2026 Paper 1

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 : +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.

Q.1 An ideal gas (0.5 mol), initially at 2 bar pressure, is compressed at a constant temperature of 600 K
in two steps: first, against a constant external pressure of P bar (2 < P < 8), and then against constant
external pressure of 8 bar. At each step, the compression is stopped only when the pressure of the gas
becomes equal to the external pressure. The total work done on the gas in these steps is W.
Considering all possible values of P (2 < P < 8) and taking the gas constant as R (in J K−1 mol−1), the
minimum value of |W| (in J) is

(A) 207R (B) 600R (C) 630R (D) 900R

Answer Q1: B

Q.2 For a reversible reaction R ⇌ P, at constant temperature, both the forward and the backward reactions
are first order elementary reactions with rate constants kf and kb, respectively. At time zero, the
concentration of R is [R]0 and the concentration of P is zero. At any given time, [R] and [P] are the
concentrations of R and P, respectively. If kb = 4kf, the correct graphical representation of the reaction
is

(A) (B)

(C) (D)

Answer Q2: C
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JEE (Advanced) 2026 Paper 1

Q.3 The correct order of dipole moments for the given species is

(A) BF3 = NH4+ < NF3 < NH3
(B) BF3 < NH4+ < NF3 < NH3
(C) NH4+ < BF3 < NH3 < NF3
(D) BF3 < NH4+ < NH3 < NF3

Answer Q3: A

Q.4 Considering LiBH4 reduces an ester group to the corresponding alcohol and does not reduce a
carboxylic acid group, the correct statement about the major products P, Q, R and S is

(A) P & Q are identical, and R & S are diastereomers.
(B) P & Q are diastereomers, and R & S are identical.
(C) P & Q are diastereomers, and R & S are diastereomers.
(D) P & Q are identical, and R & S are identical.

Answer Q4: C

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JEE (Advanced) 2026 Paper 1

SECTION 2 (Maximum Marks: 16)

• This section contains FOUR (04) 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 : +4 ONLY if (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;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : −1 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 +4 marks;
choosing ONLY (A) and (B) will get +2 marks;
choosing ONLY (A) and (D) will get +2 marks;
choosing ONLY (B) and (D) will get +2 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 −1 marks.

Q.5 The 2s and the 2p orbital energies of hydrogen atom are E2s(H) and E2p(H), respectively. The 2s and
the 2p orbital energies of lithium atom are E2s(Li) and E2p(Li), respectively. The correct option(s)
about the orbital energies is(are)

(A) E2s(Li) < E2p(Li)
(B) E2s(H) = E2p(H)
(C) E2p(H) < E2s(Li)
(D) E2s(H) > E2s(Li)

Answer Q5: ABD

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JEE (Advanced) 2026 Paper 1

Q.6 Correct statement(s) about the compounds X, Y and Z is(are)

(A) X is used for sterilizing drinking water.
(B) Y has a planar structure.
(C) Z is used in the enrichment of 235U.
(D) Y is a stronger Lewis base than ammonia.

Answer Q6: AC

Q.7 Reaction of PtF6 with oxygen (O2) gas results in the formation of an ionic compound, X+Y–.
Correct statement(s) is(are)

(A) The bond order of X+ is 1.5.
(B) Valence d-orbitals of the metal ion in X+Y– has 5 electrons.
(C) PtF6 acts as an oxidant in this reaction.
(D) PtF6 acts as a fluorinating agent in this reaction.

Answer Q7: BC

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JEE (Advanced) 2026 Paper 1

Q.8 In the following reaction sequence, Q, R, S and T are the major products.

The correct statement(s) about Q, R, S and T is(are)

(A) S on warming with ammoniacal AgNO3 results in the formation of silver mirror.
(B) Q on treatment with Cl2(excess)/UV gives gammaxane.
(C) T is a heterocyclic compound.
(D) R on acid catalyzed intramolecular cyclization followed by treatment with Zn-Hg/HCl gives
9,10-dihydroxyanthracene.

Answer Q8: ABC

5/10

JEE (Advanced) 2026 Paper 1

SECTION 3 (Maximum Marks: 16)

• This section contains FOUR (04) questions.
• The answer to each question is a NUMERICAL VALUE.
• For each question, enter the correct numerical value corresponding to the answer in the
designated place using the mouse and the on-screen virtual numeric keypad.
• 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 : +4 If ONLY the correct numerical value is entered in the designated place;
Zero Marks : 0 In all other cases.

Q.9 Two cylinders, both fitted with frictionless pistons, are filled with mixtures of He and Ar gases. In
the first cylinder, the masses of He and Ar are 𝑚1 and 𝑚2 , respectively. In the second cylinder, the
masses of He and Ar are 𝑚2 and 𝑚1 , respectively. The molar mass of Ar is 10 times the molar mass
of He. The external pressure applied by the piston on the first cylinder needs to be 5 times that on the
second cylinder so that the volume of the gas mixtures in both the cylinders are equal at the same
temperature. Assuming He and Ar behave like ideal gases, the value of (𝑚1 /𝑚2 ) is ____.

Answer Q9: [9.80]

Q.10 The total number of all possible isomers for the square planar complex with formula
K[M(NCS)(NO2)(gly)] is ____.

(M = metal ion and gly = NH2CH2COO– )

Answer Q10: [8]

Q.11 The sum of total number of carbonyl groups ( >C=O ) present in the major products X and Y in the
following reactions is ____.

Answer Q11: [4]

Q.12 Treatment of buta-1,3-diyne with NaNH2 (2 equivalents), followed by reaction with excess of
trans-CH3-CH=CH-CH2-Br gives X as the major product. The maximum number of carbon atoms
that are collinear (in a straight line) in X is ____.

Answer Q12: [6]

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JEE (Advanced) 2026 Paper 1

SECTION 4 (Maximum Marks: 16)

• 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 : +4 ONLY if the option corresponding to the correct combination 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.

Q.13 List-I contains various physical/chemical processes, and List-II contains combinations of changes
in enthalpy (ΔH) and entropy (ΔS). Match each entry in List-I to the appropriate entry in List-II,
and choose the correct option.

List-I List-II

(P) Physisorption (1) ΔH > 0 and ΔS > 0

(Q) Diamond ⟶ Graphite (2) ΔH < 0 and ΔS < 0

(R) Denaturation of protein (3) ΔH < 0 and ΔS = 0

(S) Propene ⟶ Cyclopropane (4) ΔH > 0 and ΔS < 0

(5) ΔH < 0 and ΔS > 0

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

Answer Q13: C

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JEE (Advanced) 2026 Paper 1

Q.14 Consider the following species:

SOCl2, XeOF4, ClF3, ClF5, XeF5+, SO32–, XeF3+, SF4

List-I contains different molecular shapes and List-II contains total number of species with the
same molecular shapes from the given species. Match each entry in List-I with the appropriate
entry in List-II and choose the correct option.

List-I List-II

(P) See-saw (1) one

(Q) T-Shaped (2) two

(R) Trigonal Planar (3) three

(S) Square Pyramidal (4) four

(5) zero

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

Answer Q14: A

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JEE (Advanced) 2026 Paper 1

Q.15 The List-II contains products obtained from the reaction of compounds in List-I with O3/Zn-H2O
followed by cyclization (via more stable enolate) in the presence of aqueous NaOH. Match each
entry in List-I with 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 ⟶ 4; R ⟶ 1; S ⟶ 3
(B) P ⟶ 3; Q ⟶ 4; R ⟶ 5; S ⟶ 2
(C) P ⟶ 2; Q ⟶ 1; R ⟶ 5; S ⟶ 3
(D) P ⟶ 3; Q ⟶ 5; R ⟶ 4; S ⟶ 2

Answer Q15: C

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JEE (Advanced) 2026 Paper 1

Q.16 Match the major products obtained in the reactions given in List-I with the corresponding
structures 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 ⟶ 1; R → 5; S ⟶ 4
(B) P → 1; Q ⟶ 2; R → 4; S ⟶ 5
(C) P → 1; Q ⟶ 2; R → 3; S ⟶ 4
(D) P → 2; Q ⟶ 1; R → 3; S ⟶ 5

Answer Q16: B

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