Do JEE Main questions repeat?

The 549 most repeated JEE Main questions (free PDF)

Each one is a question pattern that JEE Main asked in two or more shifts from 2020 to 2026, near-identical or with new numbers, ranked by how many shifts asked it (see how we counted).

The PDFs print the latest version of each question, with every shift it was asked in, an answer key at the end and a link to its step-by-step solution online. Free, no login. Physics has 290 of them, Mathematics 173 and Chemistry 86. Chemistry questions come back as the same question or pattern less often (about 12% of its questions from 2021 on, against about 25% in Physics and about 18% in Mathematics), so it has fewer.

Times asked: how many different shifts from 2020 to 2026 asked the pattern, near-identical or with new numbers. Ties go to the pattern asked more recently, then in more years. The top twenty are shown here; the PDFs and the CSV have all of them. One pattern with no question we can print (held, or a figure we may not show) is left out.

Three kinds of repeat, counted apart

• Near-identical. The same question asked again: the same setup, the same given values and the same thing asked. Only the wording, letter names, the order of the options or the answer format (options or a typed number) changed.
• Same pattern, new numbers. The same setup and the same thing asked, solved step by step the same way, with different values (or a small change in the final ask).
• Same concept, different question. The setup or the thing asked is different, so it is not a renumbered copy, but both questions turn on the same core principle and the same key step: for example, two different rolling questions that both come down to taking torque about the point of contact. Sharing a chapter or a topic is not enough.

A question that matches an earlier one in more than one way is counted once, under its closest match. The counts combine pairs matched one by one with estimates from checked samples (see how we counted), so they are approximate.

Other published figures differ because the definitions differ: Competishun's analysis of 12,018 questions from 2019 to 2026 (published 27 Oct 2026) counts about 64% as repeats of a broader "pattern", grouping questions with the same concept and working by a method it does not publish, while we count a question only when an earlier year had it near-identical or with new numbers (about 18%), or about 39% with the concept level.

How many of each year's questions repeat an earlier year

near-identical same pattern, new numbers same concept (estimate)

Counts are rounded. Matched questions are counted one by one; the rest are estimated from checked samples, so every cell is approximate and the yearly concept figures are the roughest. Later years have more earlier papers in our bank to repeat from, so the shares are not a trend on their own.

Where repeats concentrate

By subject, about 25% of Physics, about 18% of Mathematics, about 12% of Chemistry questions from 2021 to 2026 were near-identical or new-numbers repeats of an earlier year. At the concept level, the estimate adds about 24% in Physics, about 19% in Chemistry, about 18% in Mathematics. The chapters with the highest share of near-identical and new-numbers repeats:

Chapters with forty or more questions from 2021 on and five or more such repeats, ranked by share. These count only the pairs we matched one by one, so the shares are a floor. Chapter names link to their free PYQ PDFs. The concept estimate is too rough to rank single chapters, so it is shown by subject only.

Within the same year: a later session against an earlier one

This compares each later session with the earlier session or sessions of the same year only (6,649 questions from later sessions), so the pool of earlier questions is much smaller than in the year-to-year count above. Of these, about 8% were near-identical or new-numbers repeats of that year's earlier session, and about 13% more repeated its concept.

Counts are rounded and partly estimated, as above. The same-concept estimate rests on a smaller sample here, so it is given only for all years together.

Example pairs, side by side

The earlier question is on the left (on top on phones). Stems are NTA's wording, without the options. For same-concept pairs, the line under the pair names the idea they share.

1. Near-identicalComplex Numbers

   Earlier: JEE Main 2 Sep 2020, Shift 1

   The value of
   $${\left( {{{1 + \sin {{2\pi } \over 9} + i\cos {{2\pi } \over 9}} \over {1 + \sin {{2\pi } \over 9} - i\cos {{2\pi } \over 9}}}} \right)^3}$$ is :

   Open this question →

   Later: JEE Main 24 Jan 2023, Shift 2

   The value of $${\left( {{{1 + \sin {{2\pi } \over 9} + i\cos {{2\pi } \over 9}} \over {1 + \sin {{2\pi } \over 9} - i\cos {{2\pi } \over 9}}}} \right)^3}$$ is

   Open this question →

2. Near-identicalBinomial Theorem

   Earlier: JEE Main 18 Mar 2021, Shift 2

   The term independent of x in the expansion of
   $${\left[ {{{x + 1} \over {{x^{2/3}} - {x^{1/3}} + 1}} - {{x - 1} \over {x - {x^{1/2}}}}} \right]^{10}}$$, x $\ne$ 1, is equal to ____________.

   Open this question →

   Later: JEE Main 2 Apr 2025, Shift 1

   The term independent of $x$ in the expansion of $\left(\frac{(x+1)}{\left(x^{2 / 3}+1-x^{1 / 3}\right)}-\frac{(x-1)}{\left(x-x^{1 / 2}\right)}\right)^{10}, x>1$, is :

   Open this question →

3. Near-identicalFluid Mechanics

   Earlier: JEE Main 6 Apr 2023, Shift 1

   A small ball of mass $\mathrm{M}$ and density $\rho$ is dropped in a viscous liquid of density $\rho_{0}$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

   Open this question →

   Later: JEE Main 6 Apr 2024, Shift 1

   A small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

   Open this question →

4. Near-identicalRelations & Functions (Basic)

   Earlier: JEE Main 12 Apr 2023, Shift 1

   The number of relations, on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is __________.

   Open this question →

   Later: JEE Main 22 Jan 2025, Shift 2

   Let $A=\{1,2,3\}$. The number of relations on $A$, containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is _________.

   Open this question →

5. Near-identicalAtomic Structure

   Earlier: JEE Main 29 Jan 2023, Shift 1

   The shortest wavelength of hydrogen atom in Lyman series is $\lambda$. The longest wavelength is Balmer series of He$^+$ is

   Open this question →

   Later: JEE Main 6 Apr 2026, Shift 1

   If shortest wavelength of hydrogen atom in Lyman series is $x$, then longest wavelength in Balmer series of ${\mathrm{He}}^{{+}}$is:

   Open this question →

6. Near-identicalRay Optics

   Earlier: JEE Main 24 Jan 2023, Shift 2

   A convex lens of refractive index 1.5 and focal length 18cm in air is immersed in water. The change in focal length of the lens will be ___________ cm.
   (Given refractive index of water $=\frac{4}{3}$)

   Open this question →

   Later: JEE Main 28 Jan 2026, Shift 1

   A convex lens of refractive index 1.5 and focal length $f=18{\ \mathrm{cm}}$ is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is $\alpha\times {\mathrm{f}}$. The value of $\alpha$ is $\_\_\_\_$ .
   (refractive index of water $=4/3$ )

   Open this question →

7. Same pattern, new numbersBinomial Theorem

   Earlier: JEE Main 13 Apr 2023, Shift 2

   The remainder, when $7^{103}$ is divided by 17, is __________

   Open this question →

   Later: JEE Main 29 Jan 2025, Shift 2

   The remainder, when $7^{103}$ is divided by 23, is equal to:

   Open this question →

8. Same pattern, new numbersThermodynamics

   Earlier: JEE Main 27 Jun 2022, Shift 2

   A diatomic gas ($\gamma$ = 1.4) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is __________ J.

   Open this question →

   Later: JEE Main 1 Feb 2024, Shift 2

   A diatomic gas $(\gamma=1.4)$ does $200 \mathrm{~J}$ of work when it is expanded isobarically. The heat given to the gas in the process is :

   Open this question →

9. Same pattern, new numbersThree Dimensional Geometry

   Earlier: JEE Main 27 Jan 2024, Shift 1

   The distance, of the point $(7,-2,11)$ from the line
   $\frac{x-6}{1}=\frac{y-4}{0}=\frac{z-8}{3}$ along the line $\frac{x-5}{2}=\frac{y-1}{-3}=\frac{z-5}{6}$, is :

   Open this question →

   Later: JEE Main 3 Apr 2025, Shift 2

   The distance of the point $(7,10,11)$ from the line $\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}$ along the line $\frac{x-9}{2}=\frac{y-13}{3}=\frac{z-17}{6}$ is

   Open this question →

10. Same pattern, new numbersIonic Equilibrium

    Earlier: JEE Main 29 Jul 2022, Shift 2

    $200 \mathrm{~mL}$ of $0.01 \,\mathrm{M} \,\mathrm{HCl}$ is mixed with $400 \mathrm{~mL}$ of $0.01 \,\mathrm{M} \,\mathrm{H}_{2} \mathrm{SO}_{4}$. The $\mathrm{pH}$ of the mixture is _________.
    Given: $\log {2}=0.30, \log 3=0.48, \log 5=0.70, \log 7=0.84, \log 11=1.04$

    Open this question →

    Later: JEE Main 30 Jan 2023, Shift 1

    $600 \mathrm{~mL}$ of $0.01~\mathrm{M} ~\mathrm{HCl}$ is mixed with $400 \mathrm{~mL}$ of $0.01~\mathrm{M} ~\mathrm{H}_{2} \mathrm{SO}_{4}$. The $\mathrm{pH}$ of the mixture is ___________ $\times 10^{-2}$. (Nearest integer)
    [Given $\log 2=0.30$
    $\log 3=0.48$
    $\log 5=0.69$
    $\log 7=0.84$
    $\log 11=1.04]$

    Open this question →

11. Same pattern, new numbersPermutations & Combinations

    Earlier: JEE Main 6 Apr 2024, Shift 2

    If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at $315^{\text {th }}$ position in this arrangement is :

    Open this question →

    Later: JEE Main 29 Jan 2025, Shift 2

    If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440^th position in this arrangement is :

    Open this question →

12. Same pattern, new numbersKinetic Theory of Gases

    Earlier: JEE Main 10 Apr 2023, Shift 2

    A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

    Open this question →

    Later: JEE Main 31 Jan 2024, Shift 2

    A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

    Open this question →

13. Same pattern, new numbersDeterminants

    Earlier: JEE Main 1 Feb 2024, Shift 1

    If the system of equations
    $$\begin{aligned} & 2 x+3 y-z=5 \\\\ & x+\alpha y+3 z=-4 \\\\ & 3 x-y+\beta z=7 \end{aligned}$$
    has infinitely many solutions, then $13 \alpha \beta$ is equal to :

    Open this question →

    Later: JEE Main 2 Apr 2025, Shift 1

    If the system of linear equations
    $$\begin{aligned} & 3 x+y+\beta z=3 \\ & 2 x+\alpha y-z=-3 \\ & x+2 y+z=4 \end{aligned}$$
    has infinitely many solutions, then the value of $22 \beta-9 \alpha$ is :

    Open this question →

14. Same concept, different questionDual Nature of Radiation & Matter

    Earlier: JEE Main 7 Jan 2020, Shift 2

    An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio
    of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c
    = speed of light in vaccuum)

    Open this question →

    Later: JEE Main 28 Jun 2022, Shift 1

    The de Broglie wavelengths for an electron and a photon are $\lambda$_e and $\lambda$_p respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two ?

    Open this question →

    Shared idea: At the same energy E, both compare the electron's de Broglie wavelength, h over the square root of 2mE, with the photon's wavelength, hc over E.

15. Same concept, different questionSimple Harmonic Motion

    Earlier: JEE Main 18 Mar 2021, Shift 1

    A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is ${1 \over a}$s. The value of 'a' to the nearest integer is _________.

    Open this question →

    Later: JEE Main 25 Jan 2023, Shift 2

    A particle executes simple harmonic motion between $x=-A$ and $x=+A$. If time taken by particle to go from $x=0$ to $\frac{A}{2}$ is 2 s; then time taken by particle in going from $x=\frac{A}{2}$ to A is

    Open this question →

    Shared idea: Both turn on the phase of simple harmonic motion: from the mean position, reaching half the amplitude takes one twelfth of a period.

16. Same concept, different questionRay Optics

    Earlier: JEE Main 22 Jul 2021, Shift 2

    A ray of light passing through a prism ($\mu$ = $\sqrt 3$) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is _____________ (in degrees).

    Open this question →

    Later: JEE Main 30 Jun 2022, Shift 1

    The refractive index of an equilateral prism is $\sqrt 2$. The angle of emergence under minimum deviation position of prism, in degree, is ___________.

    Open this question →

    Shared idea: At minimum deviation the ray passes through the prism symmetrically, so the angle of refraction is half the prism angle; then Snell's law at one face.

17. Same concept, different questionCoordination Compounds

    Earlier: JEE Main 29 Jun 2022, Shift 2

    For the reaction given below :
    CoCl₃ . xNH₃ + AgNO₃ (aq) $\to$
    If two equivalents of AgCl precipitate out, then the value of x will be _____________.

    Open this question →

    Later: JEE Main 25 Jan 2023, Shift 2

    Total number of moles of AgCl precipitated on addition of excess of AgNO$_3$ to one mole each of the following complexes $\mathrm{[Co(NH_3)_4Cl_2]Cl,[Ni(H_2O)_6]Cl_2,[Pt(NH_3)_2Cl_2]}$ and $\mathrm{[Pd(NH_3)_4]Cl_2}$ is ___________.

    Open this question →

    Shared idea: Only the chloride ions outside the coordination sphere precipitate as silver chloride.

18. Same concept, different questiond & f Block Elements

    Earlier: JEE Main 6 Sep 2020, Shift 1

    The species that has a spin-only magnetic
    moment of 5.9 BM, is :
    (T_d = tetrahedral)

    Open this question →

    Later: JEE Main 17 Mar 2021, Shift 1

    What is the spin-only magnetic moment value (BM) of a divalent metal ion with atomic number 25, in it's aqueous solution?

    Open this question →

    Shared idea: A spin-only moment near 5.9 BM means five unpaired electrons, as in high-spin manganese(II), a d5 ion.

19. Same concept, different questionProbability: Advanced

    Earlier: JEE Main 18 Mar 2021, Shift 2

    Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to :

    Open this question →

    Later: JEE Main 30 Jun 2022, Shift 1

    If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then ${{P(X = 2)} \over {P(X = 3)}}$ is equal to :

    Open this question →

    Shared idea: In a binomial distribution, the ratio of two neighbouring probabilities fixes p over q, and the rest follows.

20. Same concept, different questionDefinite Integration

    Earlier: JEE Main 5 Sep 2020, Shift 1

    The value of $$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{1 \over {1 + {e^{\sin x}}}}dx}$$ is:

    Open this question →

    Later: JEE Main 27 Aug 2021, Shift 1

    $$\int\limits_6^{16} {{{{{\log }_e}{x^2}} \over {{{\log }_e}{x^2} + {{\log }_e}({x^2} - 44x + 484)}}dx}$$ is equal to :

    Open this question →

    Shared idea: Add the integral to its mirror image under x to a + b - x: the two integrands add up to 1, so the answer is half the length of the interval.

Patterns asked in four or more years

These question patterns came back with new numbers (or unchanged) in at least four different years. Only near-identical and new-numbers pairs build a pattern.

1. System of three linear equations with infinitely many solutions: find the unknown constants

   Determinants · about 29 questions in seven years

   • 2020
   • 2021
   • 2022
   • 2023
   • 2024
   • 2025
   • 2026
   Latest: JEE Main 8 Apr 2026, Shift 2 · open

   If the system of linear equations :
   $\begin{array}{cc} & x+y+z=6 \\ & x+2y+5z=10 \\ & 2x+3y+\lambda z=\mu\end{array}$
   has infinitely many solutions, then the value of $\lambda+\mu$ equals:

2. Mean and variance given, find the two missing observations

   Statistics · about 11 questions in seven years

   • 2020
   • 2021
   • 2022
   • 2023
   • 2024
   • 2025
   • 2026
   Latest: JEE Main 23 Jan 2026, Shift 1 · open

   Let the mean and variance of 8 numbers $-10,-7,-1,x,y,9,2,16$ be $\frac{7}{2}$ and $\frac{293}{4}$, respectively.
   Then the mean of 4 numbers $x,y,x+y+1,|x-y|$ is :

3. Shortest distance between two skew lines given in symmetric form

   Three Dimensional Geometry · about 12 questions in six years

   • 2020
   • 2022
   • 2023
   • 2024
   • 2025
   • 2026
   Latest: JEE Main 6 Apr 2026, Shift 2 · open

   The shortest distance between the lines $\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3}$ and $\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5}$ is:

4. Carius method: percentage of bromine or chlorine from the mass of silver halide

   Purification & Characterisation of Organic Compounds · about 11 questions in six years

   • 2020
   • 2021
   • 2022
   • 2023
   • 2025
   • 2026
   Latest: JEE Main 23 Jan 2026, Shift 2 · open

   In Carius method 0.2425 g of an organic compound gave 0.5253 g silver chloride. The percentage of chlorine in the organic compound is

5. Mean and variance after correcting one wrongly recorded observation

   Statistics · about 10 questions in six years

   • 2020
   • 2021
   • 2022
   • 2023
   • 2024
   • 2025
   Latest: JEE Main 7 Apr 2025, Shift 1 · open

   The mean and standard deviation of 100 observations are 40 and 5.1 , respectively. By mistake one observation is taken as 50 instead of 40 . If the correct mean and the correct standard deviation are $\mu$ and $\sigma$ respectively, then $10(\mu+\sigma)$ is equal to

6. Plane electromagnetic wave: the electric field from the magnetic field at a point

   Electromagnetic Waves · about 9 questions in six years

   • 2020
   • 2021
   • 2023
   • 2024
   • 2025
   • 2026
   Latest: JEE Main 2 Apr 2026, Shift 2 · open

   An electromagnetic wave travels in free space along the x-direction. At a particular point in space and time, ${\vec{B}}=2\times {10}^{{-7}}{\hat{j}}$ T is associated with this wave. The value of corresponding electric field ${\vec{E}}$ at this point is _______ V/m.

7. Sum of a series with terms k over a quartic in k, which telescopes

   Sequences & Series · about 8 questions in five years

   • 2022
   • 2023
   • 2024
   • 2025
   • 2026
   Latest: JEE Main 5 Apr 2026, Shift 2 · open

   If the sum of the first 10 terms of the series $\frac{1}{1+1^{4}\times 4}+\frac{2}{1+2^{4}\times 4}+\frac{3}{1+3^{4}\times 4}+\frac{4}{1+4^{4}\times 4}+\ldots \ldots$. is $\frac{m}{n},\gcd (m,n)=1$, then $m+n$ is equal to :

8. A vector fixed by one cross product equation and one dot product

   Vectors · about 8 questions in five years

   • 2020
   • 2021
   • 2023
   • 2024
   • 2026
   Latest: JEE Main 5 Apr 2026, Shift 1 · open

   Let ${\vec{a}}=\sqrt{7}{\hat{i}}+{\hat{j}}-{\hat{k}}$ and ${\vec{b}}={\hat{j}}+2{\hat{k}}$. If ${\vec{r}}$ is a vector such that ${\vec{r}}\times {\vec{a}}+{\vec{a}}\times {\vec{b}}=\vec{0}$ and ${\vec{r}}\cdot {\vec{a}}=0$, then $|3{\vec{r}}|^{2}$ is equal to:

9. Photoelectric effect: threshold wavelength from stopping potentials at two wavelengths

   Dual Nature of Radiation & Matter · about 6 questions in five years

   • 2020
   • 2021
   • 2023
   • 2024
   • 2026
   Latest: JEE Main 2 Apr 2026, Shift 1 · open

   For a certain metal, when monochromatic light of wavelength $\lambda$ is incident, the stopping potential for photoelectrons is $3V_{0}$. When the same metal is illuminated by light of wavelength $2\lambda$, then the stopping potential becomes $V_{0}$. The threshold wavelength for photoelectric emission for the given metal is $\alpha\lambda$. The value of $\alpha$ is ______.

10. Vernier callipers with a zero error: the corrected reading

    Experimental Skills · about 6 questions in five years

    • 2020
    • 2021
    • 2022
    • 2023
    • 2026
    Latest: JEE Main 28 Jan 2026, Shift 1 · open

    When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, $4{}^{{\text{th}}}$ mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and $5^{{\text{th}}}$ division of vernier scale coincides with a main scale division. Measured length of cylinder is $\_\_\_\_$ mm.
    (Least count of Vernier calliper $=0.1{\ \mathrm{mm}}$ )

11. Young double slit: ratio of maximum to minimum intensity from the slit widths

    Wave Optics · about 6 questions in five years

    • 2021
    • 2022
    • 2023
    • 2024
    • 2025
    Latest: JEE Main 3 Apr 2025, Shift 2 · open

    Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is :

12. Mutual inductance of a small circular loop at the centre of a large square loop

    Electromagnetic Induction · about 5 questions in five years

    • 2021
    • 2022
    • 2023
    • 2024
    • 2026
    Latest: JEE Main 2 Apr 2026, Shift 2 · open

    A circular current loop of radius $R$ is placed inside square loop of side length $L$ ($L\gg R$) such that they are co-planar and their centers coincide. The permeability of free space is $\mu_{0}$. The mutual inductance between circular loop and square loop is ______.

13. Vernier callipers: least count from the vernier and main scale divisions

    Experimental Skills · about 9 questions in four years

    • 2021
    • 2022
    • 2024
    • 2026
    Latest: JEE Main 24 Jan 2026, Shift 2 · open

    In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division $=0.05{\ \mathrm{mm}}$, then the least count of the vernier callipers is $\_\_\_\_$ mm.

14. Sulphur estimation: percentage of sulphur from the mass of barium sulphate

    Purification & Characterisation of Organic Compounds · about 7 questions in four years

    • 2021
    • 2023
    • 2025
    • 2026
    Latest: JEE Main 4 Apr 2026, Shift 2 · open

    In sulphur estimation, $2.0\times {10}^{{-3}}{\ \mathrm{mol}}$ of an organic compound $({\mathrm{X}})$ (molar mass $76{\ \mathrm{g}}{\ \mathrm{mol}}^{{-1}}$ ) gave 0.4813 g of barium sulphate (molar mass $233{\ \mathrm{g}}{\ \mathrm{mol}}^{{-1}}$ ). The percentage of sulphur in the compound $({\mathrm{X}})$ is $\_\_\_\_$ $\times {10}^{{-1}}\%$ (Nearest integer)

15. Energy lost when a charged capacitor or sphere shares its charge with an uncharged one

    Electrostatics II: Potential & Capacitance · about 7 questions in four years

    • 2020
    • 2022
    • 2023
    • 2026
    Latest: JEE Main 6 Apr 2026, Shift 2 · open

    A sphere of capacitance 100 pF is charged to a potential of 100 V . Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha\times {10}^{{-7}}{\ \mathrm{J}}$. The value of $\alpha$ is $\_\_\_\_$ .
    (combined capacitance of spheres is 200 pF )

16. Capacitance with a dielectric slab filling part of the gap

    Electrostatics II: Potential & Capacitance · about 6 questions in four years

    • 2021
    • 2022
    • 2023
    • 2026
    Latest: JEE Main 21 Jan 2026, Shift 1 · open

    A parallel plate capacitor has capacitance $C$, when there is vacuum within the parallel plates. A sheet having thickness $\left(\frac{1}{3}\right)^{{{\mathrm{rd}}}}$ of the separation between the plates and relative permittivity $K$ is introduced between the plates. The new capacitance of the system is :

17. Maximum and minimum intensity when two coherent beams interfere

    Wave Optics · about 5 questions in four years

    • 2021
    • 2022
    • 2024
    • 2025
    Latest: JEE Main 3 Apr 2025, Shift 1 · open

    Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is $x \mathrm{I}$. The value of $x$ is___________ .

18. Viscous force on a ball falling at terminal velocity through a liquid

    Fluid Mechanics · about 5 questions in four years

    • 2022
    • 2023
    • 2024
    • 2025
    Latest: JEE Main 22 Jan 2025, Shift 2 · open

    A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

19. Kjeldahl's method: percentage of nitrogen from the acid neutralised

    Purification & Characterisation of Organic Compounds · about 5 questions in four years

    • 2021
    • 2022
    • 2024
    • 2026
    Latest: JEE Main 22 Jan 2026, Shift 2 · open

    When 1 g of compound $({\mathrm{X}})$ is subjected to Kjeldahl's method for estimation of nitrogen, 15 mL 1 M ${\mathrm{H}}_{2}{\mathrm{SO}}_{4}$ was neutralized by ammonia evolved. The percentage of nitrogen in compound $({\mathrm{X}})$ is :

20. Orbitals put in order of energy from their quantum numbers

    Atomic Structure · about 5 questions in four years

    • 2022
    • 2023
    • 2024
    • 2026
    Latest: JEE Main 5 Apr 2026, Shift 1 · open

    Arrange the following atomic orbitals of multi electron atoms in order of increasing energy.
    A. $n=3,l=2,m=+1$
    B. $n=4,l=0,m=0$
    C. $n=6,l=1,m=0$
    D. $n=5,l=1,m=+1$
    E. $n=2,l=1,m=+1$
    Choose the correct answer from the options given below:

21. Extension of a wire when its length, radius and load change

    Elasticity · about 5 questions in four years

    • 2021
    • 2022
    • 2023
    • 2024
    Latest: JEE Main 29 Jan 2024, Shift 2 · open

    A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$, its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

22. Van der Waals equation: dimensions of a combination of a and b

    Units, Dimensions & Errors · about 5 questions in four years

    • 2022
    • 2023
    • 2024
    • 2025
    Latest: JEE Main 2 Apr 2025, Shift 1 · open

    The equation for real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where $\mathrm{P}, \mathrm{V}, \mathrm{T}$ and R are the pressure, volume, temperature and gas constant, respectively. The dimension of $\mathrm{ab}^{-2}$ is equivalent to that of :

23. Distance of a point from a plane, measured parallel to a given line

    Three Dimensional Geometry · about 4 questions in four years

    • 2020
    • 2021
    • 2022
    • 2023
    Latest: JEE Main 24 Jan 2023, Shift 1 · open

    The distance of the point ($-1,9,-16$) from the plane
    $2x+3y-z=5$ measured parallel to the line
    ${{x + 4} \over 3} = {{2 - y} \over 4} = {{z - 3} \over {12}}$ is :

24. Charged drops coalescing into one big drop: the new potential

    Electrostatics II: Potential & Capacitance · about 4 questions in four years

    • 2021
    • 2022
    • 2023
    • 2026
    Latest: JEE Main 22 Jan 2026, Shift 2 · open

    Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

25. Molarity of a solution from its mass percentage and density

    Mole Concept & Stoichiometry · about 4 questions in four years

    • 2020
    • 2022
    • 2024
    • 2025
    Latest: JEE Main 28 Jan 2025, Shift 1 · open

    The molarity of a $70 \%$ (mass/mass) aqueous solution of a monobasic acid (X) is _________ $\times 10^{-1}$ M (Nearest integer)
    [Given: Density of aqueous solution of (X) is $1.25 \mathrm{~g} \mathrm{~mL}^{-1}$
    Molar mass of the acid is $70 \mathrm{~g} \mathrm{~mol}^{-1}$ ]

26. Potentiometer: internal resistance of a cell from two shunted balance lengths

    Current Electricity · about 4 questions in four years

    • 2022
    • 2023
    • 2024
    • 2026
    Latest: JEE Main 28 Jan 2026, Shift 1 · open

    In the potentiometer, when the cell in the secondary circuit is shunted with $4\Omega$ resistance, the balance is obtained at the length 120 cm of wire. Now when the same cell is shunted with $12\Omega$ resistance, the balance is shifted to a length of 180 cm . The internal resistance of cell is $\_\_\_\_$ $\Omega$

27. Time-dependent force on a body: the power delivered at time t

    Work, Energy & Power · about 4 questions in four years

    • 2023
    • 2024
    • 2025
    • 2026
    Latest: JEE Main 4 Apr 2026, Shift 1 · open

    A body of mass 2 kg begins to move under the influence of time dependent force $\overrightarrow{{\mathrm{F}}}=\left(2{\mathrm{t}}{\widehat{{\mathrm{i}}}}+6{\mathrm{t}}^{2}{\widehat{{\mathrm{j}}}}\right){\mathrm{N}}$, where ${\widehat{{\mathrm{i}}}}$ and ${\widehat{{\mathrm{j}}}}$ are unit vectors along $x$ and y -axis respectively. The power produced by the force at $t=2{\ \mathrm{s}}$ is $\_\_\_\_$ W.

28. Kp and Kc of a gas reaction, converted with RT to the power of the change in moles

    Chemical Equilibrium · about 4 questions in four years

    • 2020
    • 2021
    • 2023
    • 2024
    Latest: JEE Main 29 Jan 2024, Shift 1 · open

    For the reaction ${\mathrm{N}}_{2}{\mathrm{O}}_{{4({\ \mathrm{g}})}}\rightleftarrows 2{\mathrm{NO}}_{{2({\ \mathrm{g}})}},{\mathrm{K}}_{{{\mathrm{p}}}}=0.492{\ \mathrm{atm}}$ at $300{\ \mathrm{K}}.{\mathrm{K}}_{{{\mathrm{c}}}}$ for the reaction at same temperature is _________ $\times {10}^{{-2}}$.
    (Given : ${\mathrm{R}}=0.082{\ \mathrm{L}}{\ \mathrm{atm}}{\ \mathrm{mol}}^{{-1}}{\ \mathrm{K}}^{{-1}}$)

29. Coefficient of a power of x in (1 + x)^n + x(1 + x)^(n-1) + ... + x^n

    Binomial Theorem · about 4 questions in four years

    • 2020
    • 2022
    • 2023
    • 2026
    Latest: JEE Main 28 Jan 2026, Shift 2 · open

    The sum of the coefficients of $x^{{499}}$ and $x^{{500}}$ in $(1+x)^{{1000}}+x(1+x)^{{999}}+x^{2}(1+x)^{{998}}+\ldots +x^{{1000}}$ is :

30. Peak emf of a coil rotating in a uniform magnetic field

    Electromagnetic Induction · about 4 questions in four years

    • 2021
    • 2022
    • 2023
    • 2024
    Latest: JEE Main 1 Feb 2024, Shift 2 · open

    A coil of 200 turns and area $0.20 \mathrm{~m}^2$ is rotated at half a revolution per second and is placed in uniform magnetic field of $0.01 \mathrm{~T}$ perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2 \pi}{\beta}$ volt. The value of $\beta$ is _______.

31. de Broglie wavelength of the electron in a Bohr orbit of hydrogen

    Atomic Structure · about 4 questions in four years

    • 2020
    • 2023
    • 2024
    • 2025
    Latest: JEE Main 29 Jan 2025, Shift 1 · open

    If $a$₀ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (λ) of the electron present in the second orbit of hydrogen atom? [n : any integer]

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How we counted

• What we compared. Every JEE Main question in our bank with a recorded shift: 12,201 questions from 147 shifts, 2020 to 2026. 2020 is the first year we hold, so its questions can be matched by later ones but cannot repeat an earlier year. The year-to-year shares are out of the 2021 to 2026 questions.
• How the pairs were checked. Questions from different shifts were compared by their text and by their worked solutions. The candidate pairs were then checked in two independent reviews, plus a second check of the borderline ones. The reviews were AI-assisted. Where only a sample could be checked, it was scaled up to the whole and the counts come with a range. The two reviews agreed on about 87% of the pairs both checked.
• Data checks. No question was found entered twice inside one shift, so nothing was left out for that. Pairs from two shifts of the same session are in the CSV but not in any count above.

Limits

• Our bank covers 2020 to 2026 only. A question that repeats one from a paper before 2020 is not counted.
• A question decided by its figure, or a repeat filed under another chapter and worded differently, cannot be caught from the text, so the counts lean low.
• Where one concept ends and another begins is a judgment call, so read the same-concept numbers as approximate.
• A repeat here describes past papers only. It says nothing about which questions a future paper will ask.