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JEE Advanced 2026: Paper 1

  • Paper code: Paper 1
  • Language: English
  • 34 pages
JEE Advanced 2026 question paper, JEE (Advanced) 2026, Paper 1, page 1 of 34
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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 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, ∞)




  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




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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




  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




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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 )




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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)
                                                                                                     √




  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




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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




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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 _____________.



     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 (− 2 , 2 ) at which f is NOT differentiable.

            Then the value of α + β is ___________.




     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 _____________.



     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 _____________.




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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)

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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)




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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)




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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)



                                  END OF THE QUESTION PAPER




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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




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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 d 2 ≫ 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




  Q.3                                                                                                gR
            A solid cylinder of radius R rolls without slipping with a center of mass speed v0 = √           on a
                                                                                                     3
            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




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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)




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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        nvn     v
                      Magnitude of change in kinetic energy of electron can be expressed as          |         − 1 |.
                                                                                                4π       rn      r1

            (B)       Magnitude of change in de Broglie wavelength of the electron can be expressed as
                      e2       1       1
                           |       −        |.
                      4ε0 Kn           K1

            (C)                                                                 e2    1    1
                      Frequency of the radiation emitted can be expressed as         ( − ).
                                                                               8πε0 ℎ r1   rn

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




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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 =       ms −1 .
                                               2
            (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 ( ), then v = 125√g ms −1 .
                                     5




  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 =                   . The correct statement(s) is/are:
                                                              Qin
            [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.




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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 − (3ĵ + 4k̂ ) direction.
                                                  5
            (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
                         sin(3y + 4z + ωt)(4ĵ − 3k̂ ).
                      c




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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:




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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 =        =     . The value of η is:
                                                                          Q0       243




  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
                                                                                              ΔT0
            S1 and S2 is ΔT0 . The time it takes for the temperature difference to become           is nxR/KA, where
                                                                                               2
            R is the universal gas constant. The value of n is:
            [ Given: ln 2 ≈ 0.7 ]




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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
                                                         nμ0 QR2 ω
            point (0,0, z) , where z ≫ R and z ≫ ℎ, is               . The value of n is:
                                                         4π   z3




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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




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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




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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

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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)       ml 2
                                                                          4




             (Q)                                                          1
                                                                    (2)       ml 2
                                                                          6




             (R)                                                          1
                                                                    (3)        ml 2
                                                                          12




             (S)                                                          2
                                                                    (4)       ml 2
                                                                          3




                                                                          1
                                                                    (5)        ml 2
                                                                          3




            (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

                                     END OF THE QUESTION PAPER



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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



  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)




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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



  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.




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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)




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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.


  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.




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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.




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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    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 ____.



     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– )



     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 ____.




     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 ____.




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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




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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




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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



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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




                                 END OF THE QUESTION PAPER


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Source: Organising IIT for the year. Question paper published by Organising IIT for the year.