# JEE Main Previous Year Papers, JEE Mains 2024 Question Paper

JEE Main examination is conducted in online mode by NTA in two shifts on multiple days. The difficulty level of JEE Main question paper is the same for all days and shifts. Here you can download JEE Mains previous year papers with answer key and solution in PDF format.

JEE Main previous year question papers are one of the important and very useful study resources for JEE aspirants. Solve previous year papers of JEE Main for better preparation of the exam. Practice JEE Mains past year papers and online mock tests in a time bound manner, like you are solving the real paper in a 3 hour duration.

Recommended for JEE 2024 : Best Online Crash Course for IIT JEE 2024

## JEE Mains 2024 Question Paper

JEE Mains 2024 question paper 27 January is available now. Candidates can download the JEE Mains question paper 2024 with answer key from the direct links provided on this page. NTA is conducting the JEE Main 2024 session-1 on January 24, 27, 29, 30, 31 & February 1.

Given below are the memory based questions from JEE Mains 2024 exam on 27th January:

### JEE Mains 2024 Question Paper Math

1. If 2tan2θ - 5 secθ = 1 has exactly 7 solutions in [θ, nπ/2] for the least value of n ∈ N, then Σnk=1 (k/2n) is equal to?
2. If dy/dx = ( x + y - 2 ) / ( x - y ), and y(0) = 2, then find y(2).
3. Find the 20th term from the end of the progression:
20, 19(1/4), 18(1/2), 17(3/4), ..., -129(1/4)
4. 0π dx / ( 1 - 2a cosx + a2 ) = ?
5. An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability that the first draw gives all white balls and the second draw gives all black balls is:
6. Considering the principal values of inverse trigonometric functions, find the positive real values of x satisfying tan-1(x) + tan-1(2x) = π/4.
7. Let R be the interior region between the lines 3x - y + 1 = 0 and x + 2y - 5 = 0 containing the origin. The set of all values of a for which points (a2 a + 1) lie is?
8. The position vectors of vertices A, B, C of a triangle are i +2 j +3 k , i + j +3 k ,2 i + j +3 k respectively. Let x  is the length of the angle bisector of angle BAC, then the value of x2 is?
9. If A is a 2 x 2 matrix and I is an Identity matrix of order 2 & | A - λ*I | = 0 gives values of λ as -1 & 3. Then, the trace of A2 is equal to?
10. The area bounded by 0 ≤ y ≤ min{2x, 6x - x2} and x-axis is A. then 12A is:
11. If the line x + y = 0 is tangent to the circle (x - λ)2 + (y - β)2 = 50, then (λ + β)2 = ?
12. If the mean of 15 observations is 12 and the standard deviation is 3. If 12 is replaced by 10 in data, then the new mean is μ and variance is σ2 then what is the value of 15(μ + μ2 + σ2) = ?

### JEE Mains 2024 Question Paper Physics

1. If the work function of a metal is 6.63 eV, then find the threshold frequency for the photoelectric effect.
2. If (p - a/V2)(V - b) = nRT where P, V, R, & T are pressure, volume, universal gas constant, and temperature, then a/b2 has the same dimensional formula as that of:
i. R
ii. PV
iii. RT
iv. P
3. Statement 1: Positive zero error is added to the measured value.
Statement 2: Defects may occur during the manufacturing of measuring instruments
i. Statement 1 is true while statement 2 is false
ii. Statement 1 is false while Statement 2 is true
iii. Both statements are true
iv. Both statements are false
4. Find the total kinetic energy of 1 mole of oxygen gas at 27°C. Take R = 25/3 J/(mol-K).
5. A particle loses 1/3rd of its velocity when it strikes a block and covers a distance of 4 cm inside the fixed block. Then find D, if D is the distance covered by the particle inside the block and comes at rest.
6. A ring and solid sphere of the same mass and radius slide down an inclined plane of the same angle θ. Find the ratio of their kinetic energies.
7. If two bodies with masses 4 kg and 5 kg have the same kinetic energy, then find the ratio of their linear momentum.
8. A train moving at a speed of 12 m/s takes a circular turn of radius 500 m. The rails are 1.5m apart, then by what height the outer rail should be raised with respect to the inner rail?
9. In an adiabatic process, the pressure of a gas is proportional to the cube of absolute temperature, then the ratio of Cp/Cv is?
10. A ball suspended by a thread swings in a vertical plane so that its acceleration in the extreme position and lowest position are equal. The angle 0 of thread deflection in the extreme position will be?
11. A particle moves 80 m in the last 2 seconds of free fall of height h, then find the height h.
12. If a current of 200 µA deflects the coil of a moving galvanometer through 60°, then what is the current required to cause deflection through π/10 radians?
13. A uniform ring and uniform solid sphere roll down the same inclined plane at the same distance. If the ratio of their translational kinetic energies is 7/x then find x. It is given that the mass and radius of the ring and sphere are equal and the situation is pure rolling.
14. There exists a uniform electric field of 20 î N/C. A dipole of dipole moment |P| = 15c - m is placed at an angle of 30° with the electric field, then find the torque on the dipole.
15. If a man is carrying the weight of a rod with mass m leaning against his head such that the rod forms an angle of 60° with the horizontal, then find the weight of the rod experienced by him.
16. A bullet is fired into a fixed target. It loses 1/3rd of its velocity after 3 travelling for 4 cm. It penetrates further p × 10-3 m before coming to rest. Find p.
17. If the primary side of a transformer is connected with 230 V, 50 Hz AC supply and the ratio of the number of turns of primary to the secondary winding is 10:1. The load resistance at the secondary coil is 46 Ω then find the power of the secondary winding output.
18. Three voltmeters (V1, V2, V3) are connected in a circuit such that V1 and V2 are in series with each other and both are in parallel with V3. Find the correct relation among their readings.

### JEE Mains 2024 Question Paper Chemistry

1. Which of the following quantity changes with the temperature?
i. Mole Fraction
ii. Mass Percentage
iii. Molarity
iv. Molality
2. Which of the following can not act as an oxidising agent?
i. MnO4-
ii. SO42-
iii. N3-
iv. BrO3-
3. The phenolic group can be identified by a positive result by which of the following tests?
i. Lucas test
ii. Carbylamine test
iii. Phthalein test
iv. Tollen's test
4. The reduction potential at pH = 3 for a hydrogen electrode of a standard half cell is?
5. Identify the following species in which d²sp³ hybridization is shown by central atom.
i. BrF5
ii. SF6
iii. [Co(NH3)6]3+
iv. [PtCl4]2-
6. Which structure of protein is intact after coagulation of egg white on boiling?
7. What is the molecular formula of the second homologue in the homologous series of monocarboxylic acid?
8. In which of the options do all the elements have a d10 configuration in their ground state?
i. Cu, Zn, Cd, Ag
ii. Cd, Au, Hg, Ni
iii. Sc, Ti, Fe, Zn
iv. Fe, Cr, Co, Ni
9. For a first-order reaction, t99.9% = xt50% Find out the value of x.
10. If the longest wavelength for the Paschen Series in H-atom is α, Find α/7R.
11. Which of the following will not give SN1?
i. CH2=CH-CH2-CI
ii. Ph-CH2-CI
iii. CH3-CH=CH-CI
iv. (H3C)C-CI
12. Compare the stability of resonating structures. (A diagrammatic representation of three compounds was given.)
13. How many compound(s) given below have chiral carbon? (A diagrammatic representation of four compounds was given.)
14. Find the magnetic moment of complex [Pd(NH3)2Cl2].
15. When 9.3 g of aniline is reacted with acetic anhydride, mass of acetanilide obtained is m grams. Find out the value of 2m.
16. If X is the major product obtained when Ph - CH = CH2 reacts in the presence of (1) B2H6/THF/H2O2/O-, (2) HBr, (3) Mg, Dry Ether, and (4) HCHO, then find F.
17. What is the technique used for the purification of steam volatile water-immiscible substance?
18. Which of the following statements is correct:
i. Ce+4 is an oxidising agent
ii. Ce+4 is a reducing agent
iii. Ce+3 has a noble gas configuration
iv. Ce has a stable configuration

Candidates can download JEE Mains previous year question papers with answer key and solutions for various years from the below tables. Students can download these JEE Main papers PDF without registration. Avoid those websites which ask you to submit your personal details in order to view and download JEE previous year papers.

### JEE Mains 2023 Question Paper With Solution (January, Session-1)

JEE Main 2023 Paper (Exam Date) Shift-1 (Morning) Shift-2 (Evening)

### JEE Mains 2023 Question Paper With Solution (April, Session-2)

JEE Main 2023 Paper (Exam Date) Shift-1 (Morning) Shift-2 (Evening)

### JEE Mains 2022 Question Paper Session-1

JEE Main 2022 Session-1 Question Papers (June) :

JEE Main 2022 Session-1 Question Paper (Exam Date) Shift-1 (Morning) Shift-2 (Evening)

### JEE Mains 2022 Question Paper Session-2

JEE Main 2022 Session-2 Question Papers (July) :

JEE Main 2022 Exam Date Physics Chemistry Math

### JEE Mains 2021 Question Paper

JEE Main 2021 Question Paper of all shifts (February) :

JEE Main 2021 February Question Paper (Exam Date) Shift-1 (Morning) Shift-2 (Evening)

JEE Main 2021 Question Paper of all shifts (March) :

JEE Main 2021 March Question Paper (Day and Shift) Physics Chemistry Math
16th March - Day 1, Shift 1 Physics Chemistry Math
16th March - Day 1, Shift 2 Physics Chemistry Math
17th March - Day 2, Shift 1 Physics Chemistry Math
17th March - Day 2, Shift 2 Physics Chemistry Math
18th March - Day 3, Shift 1 Physics Chemistry Math
18th March - Day 3, Shift 2 Physics Chemistry Math

### JEE Mains 2020 Question Paper

JEE Main 2020 Question Paper of all shifts (January) :

### JEE Mains 2019 Question Paper

JEE Main 2019 Online Question Papers of all shifts (January and April) :

JEE Main 2019 January Question Papers JEE Main 2019 April Question Papers
9th January 2019 Shift 1 8th April 2019 Shift 1
9th January 2019 Shift 2 8th April 2019 Shift 2
10th January 2019 Shift 1 9th April 2019 Shift 1
10th January 2019 Shift 2 9th April 2019 Shift 2
11th January 2019 Shift 1 10th April 2019 Shift 1
11th January 2019 Shift 2 10th April 2019 Shift 2
12th January 2019 Shift 1 12th April 2019 Shift 1
12th January 2019 Shift 2 12th April 2019 Shift 2

### JEE Main 2018 Paper (Offline)

Download : Set A | Set B | Set C | Set D

### JEE Main 2017 Paper (Offline)

Download : Set A | Set B | Set C | Set D

### JEE Main 2017 Paper (Online)

Download : Day 1 Physics Chemistry Mathematics | Day 2 Physics Chemistry

### JEE Main 2016 Paper (Offline)

Download : Set E | Set F | Set G | Set H

### JEE Main 2015 Paper (Offline)

Download : Set A | Set B | Set C | Set D