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22 Jan Shift 2 JEE Main 2026 Paper Solution 😱 | Full Questions & Answers

22 January Shift 2 – JEE Main 2026 😱
Full Paper Solution & Review

🔵 PHYSICS

Q1. The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelength of Paschen and Balmer series is nearly.

(1) 1217 nm

(2) 656 nm

(3) 1875 nm

(4) 820 nm

Correct Answer: (1)
Q2. A cylindrical conductor of length 2 m and area of cross section 0.2 mm² carries an electric current of 1.6 A when its ends are connected to 2 V battery. Mobility of electrons in the conductor is α × 10⁻³ m²/V·s. The value of α is
[Electron concentration = 5 × 10²⁸ /m³ and Electron charge = 1.6 × 10⁻¹⁹ C]

(1) 1

(2) 2

(3) 3

(4) 4

Correct Answer: (1)
Q3. An insulated cylinder of volume 60 cm³ is filled with a gas at 27°C and 2 atmospheric pressure. Then the gas is compressed making the final volume as 20 cm³ while allowing the temperature to rise to 77°C. The final pressure is ___ atm.
Answer: 7 atm
Q4. A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T that is perpendicular to the axis of rotation. When the loop is rotated by 30° from the horizontal position the induced EMF is 15.4 mV. The radius of the loop is ___ mm.
Answer: 14 mm
Q5. Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius r = 0.1 m. The pulley is mounted in a vertical plane and is free to rotate about its axis. Final speed of 2m when it descends by a distance of 3.6 metre.
[Assume string does not slip and g = 10 m/s²]
Answer: 2 m/s
Q6. The wavelength of light when it is passing through water is 540 nm. The refractive index of water is 4/3. The wavelength of the same light when it is passing through a transparent medium having refractive index of 3/2 is.

(1) 840 nm

(2) 480 nm

(3) 400 nm

(4) 356 nm

Correct Answer: (2)
Q7. When a part of straight capillary tube is placed vertically in liquid, the liquid rises up to certain height h. If the inner radius of capillary tube, density of the liquid and the surface tension of the liquid decreases by 1% each, then the height of liquid in the tube will change by ___ %.

(1) −3

(2) +3

(3) −1

(4) +1

Correct Answer: (4)
Q8. S-I: For a mechanical system of many particles, total kinetic energy is the sum of kinetic energies of all the particles.
S-II: The total kinetic energy can be the sum of kinetic energy of the centre of mass with respect to origin and the kinetic energy of all the particles with respect to the centre of mass as reference.

(1) S-I is true but S-II is false

(2) Both S-I and S-II are true

(3) S-I is false but S-II is true

(4) Both S-I and S-II are false

Correct Answer: (2)
Q9. In an open organ pipe f₃ and f₆ are 3rd and 6th harmonic frequencies respectively and if f₆ − f₃ = 2200 Hz. Then the length of pipe is (in mm).

(1) 225

(2) 200

(3) 250

(4) 275

Correct Answer: (1)
Q10. 3 small identical bubbles of water having same charge on each coalesce to form bigger bubbles. The ratio of the potentials on one initial bubble & that on the resultant bigger bubble is:

(1) 1 : 32/3

(2) 32/3 : 1

(3) 1 : 22/3

(4) 1 : 31/3

Correct Answer: (1)
Q11. Which of the following are right about single slit diffraction
A. Width of central maxima increases with increasing wavelength keeping slit width constant
B. Width of central maxima increases with decrease in wavelength keeping slit width constant
C. Width of central maxima increases with decrease in slit width at constant wavelength
D. Width of central maxima increases with increase in slit width at constant wavelength
E. Brightness of central maxima increases for decrease in wavelength at constant slit width

(1) A, C

(2) B, C only

(3) A, D only

(4) B, D

Correct Answer: (1)
Q12. Figure shows a circuit that contains 3 resistances (9Ω each) & two inductors (4 mH). The reading of ammeter when switch K is turned ON, is ___ A.

(1) 3

(2) 0

(3) 2

(4) 1

Correct Answer: (4)
Q13. For the given logic gate find output function.

(1) A̅·B̅ + C + D

(2) A̅ + B̅ + C̅·D̅

(3) AB + CD

(4) AB + C̅·D̅

Correct Answer: (4)
Q14. A laser beam has intensity of 4.0 × 10¹⁴ W/m². The amplitude of magnetic field associated with the beam is ___ T.

(1) 1.83

(2) 5.5

(3) 18.3

(4) 2.0

Correct Answer: (1)

🧪 CHEMISTRY

Q1. Which of the following mixture gives a buffer solution with pH = 9.5 ? Given pKb (NH₄OH) = 4.75

(1) 0.2 M NH₄OH (0.4 L) + 0.1 M HCl (1 L)

(2) 0.4 M NH₄OH (1 L) + 0.1 M HCl (1 L)

(3) 0.5 M NH₄OH (0.2 L) + 0.2 M HCl (0.5 L)

(4) 0.2 M NH₄OH (0.5 L) + 0.1 M HCl (0.5 L)

Correct Answer: (4)
Q2. The energy of first (lowest) Balmer line of H atom is x J. The energy (in J) of second Balmer line of H atom is.

(1) x / 1.35

(2) x²

(3) 2x

(4) 1.35x

Correct Answer: (4)
Q3. Given below are two statements.
Statement-I: C < O < N < F is the correct order in terms of first ionization enthalpy values.
Statement-II: S > Se > Te > Po > O is the correct order in terms of the magnitude of electron gain enthalpy values.
In the light of the above statements, which is the correct option.

(1) Both statement-I and statement-II are correct

(2) Both statement-I and statement-II are incorrect

(3) Statement-I is correct and statement-II is incorrect

(4) Statement-I is incorrect and statement-II is correct

Correct Answer: (1)
Q4. When 1 g of compound (X) is subjected to Kjeldahl's method for estimation of Nitrogen, 15 mL 1M H₂SO₄ was neutralized by Ammonia evolved. The percentage of nitrogen in compound (X) is

(1) 21

(2) 0.21

(3) 42

(4) 0.42

Correct Answer: (3)
Q5. Name of IUPAC of the following.

(1) 2-Bromo-5-methyl propanoate

(2) n-propyl-1-bromo-4-methyl hexanoate

(3) 2-Bromo-5-methyl hexyl propanoate

(4) n-propyl-2-bromo-5-methyl heptanoate

Correct Answer: (4)
Q6. 100 g of 98% H₂SO₄ aqueous solution mixed with 100 g of 49% H₂SO₄ aqueous solution. The mole fraction of H₂SO₄ is

(1) 0.667

(2) 0.336

(3) 0.1

(4) 0.9

Correct Answer: (1)
Q7. The dibromo compound [P] of molecular formula (C₆H₄Br₂) when heated with excess sodamide followed by treatment with dilute HCl gives [Q]. On warming [Q] with Mercuric sulphate and dilute sulphuric acid yield (R). Which gives positive iodoform test but negative Tollens' test. The compound [P] is
Answer: (Structure as given in paper)
Q8. Which of the following is a mixed oxide?

(1) Fe₂O₃

(2) PbO₂

(3) Pb₃O₄

(4) BaO₂

Correct Answer: (3)
Q9. Correct order of ionization enthalpy is

(1) F > Cl > Cl⁻ > F⁻

(2) F > Cl⁻ > F > Cl

(3) Cl > F > Cl⁻ > F⁻

(4) F > Cl > F⁻ > Cl⁻

Correct Answer: (1)
Q10. Consider the following reaction,
CH₃NH₂ (benzene ring) → PhCOCl / Pyridine → (X) → LiAlH₄ → (Y)
The correct structure of Y is

(1) PhCH₂NHCOPh

(2) Ph – CH₂NHCH₂Ph

(3) PhNH₂CH₂Ph

(4) PhCH₃

Correct Answer: (2)
Q11. Which of the following is basic buffer?

(1) NaOH + CH₃COONa

(2) NaOH + Na₂SO₄

(3) K₂SO₄ + H₂SO₄

(4) NH₄OH + NH₄Cl

Correct Answer: (4)
Q12. Match the following List-I with List-II and choose the correct option.

(1) a(i), b(ii), c(iii), d(iv)

(2) a(iv), b(i), c(ii), d(iii)

(3) a(iv), b(ii), c(iii), d(i)

(4) a(i), b(ii), c(iv), d(iii)

Correct Answer: (2)
Q13. Which of the following mixture gives methanal as one of the products on reductive ozonolysis? Its structure is

(1) —

(2) —

(3) —

(4) —

Correct Answer: (2)
Q14. An alkene on reductive ozonolysis gives methanal as one of the products. Its structure is

(1) —

(2) —

(3) —

(4) —

Correct Answer: (2)
Q15. Consider the following data and find lattice energy of NaCl(s).

(1) −786 kJ mol⁻¹

(2) −628 kJ mol⁻¹

(3) −428 kJ mol⁻¹

(4) −393 kJ mol⁻¹

Correct Answer: (1)
Q16. 5.8 g Aniline is converted into benzamide with some reaction sequences. Calculate mass of benzamide formed, if percentage yield of reaction is 82%.
Answer: 10.1 g

📘 MATHEMATICS

Q1. If the mean deviation about the median of the numbers k, 2k, 3k, …, 1000k is 500, then k² is equal to
Answer: 4
Q2. Let S = { z ∈ ℂ : 4z² + z̄ = 0 }. Find ∑z∈S |z|²
Answer: 3/16
Q3. The number of elements in the relation R = { (x, y) : 4x² + y² < 52, x, y ∈ ℤ }
Answer: 77
Q4. The area of the region A = { (x, y) : 4x² + y² ≤ 8 and y² ≤ 4x }

(1)

(2)

(3)

(4)

Correct Answer: (3)
Q5. Let P(10, 2√15) be a point on the hyperbola x²/a² − y²/b² = 1

(1) 900

(2) 4200

(3) 1462

(4) 2700

Correct Answer: (4)
Q6. Let ⟨Cr⟩ denote the coefficient of xʳ in the binomial expansion. If Pn = C₀ − C₁ + (2²/3)C₂ − (2³/4)C₃ + … + [(-2)ⁿ/(n+1)]Cₙ then find ∑n=125 1 / P2n

(1) 650

(2) 675

(3) 580

(4) 525

Correct Answer: (2)
Q7. Let f(x) = [x]² − [x + 3] − 3

(1)

(2) f(x) = 0 for finitely many values of x

(3) f(x) > 0 only for x ∈ [4, ∞)

(4) f(x) < 0 only for x ∈ [−1, 3)

Correct Answer: (4)
Q8. Suppose a, b, c are in A.P. and √a, √b, √c are in G.P. If a < b < c and a + b + c = 1, then find 9(a² + b² + c²)
Answer: (As per paper)
Q9. Let L₁ : (x+1)/2 = (y+1)/3 = (z+3)/6 L₂ : (x+1)/2 = (y+1)/3 = (z−9)/0 If S is the set of points of intersection, then find ∑(a + b + c)

(1) 34

(2) 6

(3) 28

(4) 40

Correct Answer: (1)
Q10. Among the statements: S₁: If A(5, −1) and B(−2, 3) are two vertices of a triangle whose orthocenter is (0, 0), then its third vertex is (−4, −7). S₂: If positive numbers 2a, b, c are three consecutive terms of an A.P., then the lines ax + by + c = 0 are concurrent at (2, −2).

(1) Both are correct

(2) Only S₁ is correct

(3) Both are incorrect

(4) Only S₂ is correct

Correct Answer: (4)
Q11. Let a⃗ = 2î − ĵ + k̂, b⃗ = λ ĵ + 2k̂, λ ∈ ℤ, c⃗ = a⃗ × b⃗. If d⃗ is a unit vector, then the maximum possible value of (c⃗ · d⃗)²

(1) 208

(2) 52

(3) 104

(4) 26

Correct Answer: (1)

Updated for JEE Main 2026: This PYQ is important for JEE Mains, JEE Advanced and other competitive exams. Practice more questions from this chapter.

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