JEE Main Question Paper 30 Jan 2024 Shift 1 (Available): PDF download Maths, Physics and Chemistry

JEE Main Question Paper 30 January 2024 Shift 1 (Image Credit: Pexels)

JEE Main Question Paper 30 January 2024 Shift 1 : JEE Main question paper 2024 for 30 January Shift 1 exam can be checked here for Physics, Chemistry and Mathematics. The Day 3 (January 30) Shift 1 exam is being conducted from 9 AM to 12 PM. The memory-based questions of JEE Main 30 Jan 2024 collected from the test takers of Shift 1 are provided here as there is no option to get a physical copy of the question paper immediately after the exam. The Day 1 and 2 exam of JEE Main 2024 Paper 1 B.Tech took place on January 27 and 29. The overall difficulty level of the JEE exam so far has been 'Moderate' with Mathematics turning out to be the toughest subject. As opposed to the earlier days, Physics paper saw an increase in difficulty and was moderate today while Mathematics saw a slight decrease in difficulty and was moderate to tough. Chemistry was moderate. The detailed analysis of today's paper can be checked here: JEE Main 2024 January 30 Shift 1 Exam Analysis . You can also check here JEE Main Shift 2 Analysis 30 January 2024 .

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JEE Main Question Paper 2024 30 January: Subject-wise

The subject-wise question paper of JEE Main 2024 January 30 can be downloaded here in PDF format. We will be adding the memory-based questions below from 12:30 PM onwards. Keep checking.

JEE Main Physics Questions 30 January 2024 Shift 1

Candidates can find here the memory-based questions for JEE Main 30 Jan 2024 Shift 1 Physics subject:

1. If two rings of equal radius R are arranged perpendicular to each other with a common centre at C and the rings carry an equal current I, then find the magnetic field at C.

2. Find the acceleration of a 2 kg block on a fixed inclined surface at 37° with the horizontal. The block is tied with a rope that passes over two pulleys (represented through a diagram) such that pulley 1 rests at the top of the inclined surface and pulley 2 carries a weight of 4 kg. Neglect friction.

3. A particle of mass m is projected from the ground with a speed u at an angle of 30° with the horizontal. Find its angular momentum about the point of projection when it reaches its maximum height.

4. Find the ratio of the kinetic energy and the potential energy in the 5th excited state of a hydrogen atom.

5. Find the potential difference V ₀ across the 700 Ω resistance.
   A diagram was given in which three resistances 3.5 kΩ, 200 Ω, and 700 Ω are connected in series across a 7 V battery.

6. A ball is released from a height of 1 m on a fixed smooth hemispherical surface. Find its velocity when it is at a height of 0.5 m from the ground. Take g = 10 m/s ² .

7. Find the current through the Zener diode if its breakdown voltage is 5 V. (Diagram was given.)

8. A ball released from a height of 10 m strikes the ground and rebounds to a height of 5 m. Find the impulse imparted by the ground during collision. It is given that the mass of the ball is 100 g and g = 10 m/s ² .

9. The electric potential due to the short electric dipole on the axial position at distance r from the dipole is proportional to ...? (Assume: r >> length of the dipole)

10. A block of mass 2 kg is placed on a disc that is rotating at a constant angular velocity of 4 rad/sec. Find the friction force in (N) between the block and disc if the block is not sliding.

11. If the distance between the virtual image, which is twice the size of the object placed in front of the mirror, and the object is 45 cm, what is the magnitude of the focal length of the mirror?

12. A particle is undergoing uniform acceleration. If its displacement from the t ^th to (t + 1) ^th second is 120 m and the change in velocity is 50 m/s. Find its displacement in metre in the (t + 2) ^th second.

13. A uniform disc of mass 5 kg and radius 2 m is rotating with an angular velocity of 10 rad/s. Now another identical disc is gently placed on the first disc. Because of the friction, both discs acquire a common angular velocity. What is the loss of kinetic energy in the process?

14. What is the maximum wavelength of the light source such that photoelectrons can be ejected from the material of work-function 3 eV?

15. A long wire carrying current √2A is placed in the uniform magnetic field of 3 x10 ^-5 T. If the magnetic field is perpendicular to the wire, find the magnetic force on a unit length of wire.

16. The electric field in an electromagnetic wave is moving in a free space given as E = E ₀ sin(ωt – kz)i. What will be the corresponding magnetic field?

17. If the area of a cross-section is halved and the length of a wire having Young's modulus Y is doubled, then what will be its new Young's modulus?

18. In an electric transformer, 220 V is applied on the primary coil having 100 turns. A secondary coil with 10 turns is placed next to it having resistances 2Ω and 3 Ω. Find out the output current through the 3 Ω resistance.

19. Find the temperature of H ₂ gas at which its RMS speed is equal to that of O ₂ at 47°C.

20. In an AC circuit with source voltage E = 20 sin (1000 t) is connected to a series L - R circuit whose power factor is 1/√2. If E = 25 sin (2000 t), find the new power factor.

21. At P, a point away from a planet of radius 6400 km, the gravitational potential and field are -6.4 × 10 ⁷ SI units and 6.4 SI units, respectively. Find the height of that point above the surface of the planet.

22. A wire has a resistance of 60 Ω at a temperature of 27°C. When it is connected to a 220 V DC supply, a current 2.75 A flows through it at a certain temperature. Find the value of the temperature, if the coefficient of thermal resistance is 2 × 10 ^-4 /°C.

23. Match the following:
    Column I: i. Surface Tension, ii. Viscosity, iii. Angular Momentum, iv. Rotational Kinetic Energy
    Column II: a. [ML ² T ^-2 ], b. [ML ² T ^-1 ], c. [ML ^-1 T ^-1 ], d. [ML ⁰ T ^-2 ]

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JEE Main Chemistry Questions 30 January 2024 Shift 1

Candidates can find here the memory-based questions for JEE Main 30 Jan 2024 Shift 1 Chemistry subject:

1. Find out the sum of the coefficients of all the species involved in the balanced equation:
   2MnO4 + I ^- → (in the presence of a slightly alkaline medium) → Product

2. Find out the maximum number of hybrid orbitals formed when 2s and 2p orbitals are mixed.

3. Find out the work done in Joules for the cyclic process ABCA such that P _A = 30 kPa, V _A = 10 dm ³ , P _B = 10 kPa, V _B = 30 dm ³ , P _C = 10 kPa, V _C = 10 dm ³ (as per the given graph).

4. Identify the given reaction.
   C ₆ H ₆ –C=O–Cl → (in the presence of H ₂ , Pd/BaSO ₄ ) → Product
   i. Etard Reaction
   ii. Stephen's Reaction
   iii. Wolff Kishner Reduction
   iv. Rosenmund Reaction

5. Which of the given compounds will not give the Fehling test?
   i. Lactose
   ii. Maltose
   iii. Sucrose
   iv. Glucose

6. Which of the following sets contain both diamagnetic ions?
   i. Ni ²⁺ , Cu ²⁺
   ii. Eu ³⁺ , Gd ³⁺
   iii. Cu ⁺ , Zn ²⁺
   iv. Ce ⁴⁺ , Pm ³⁺

7. Identify the halogen which has allylic halogen. (A diagrammatic representation of compounds was given).

8. Find the final product when C ₆ H ₆ –Br reacts with i. Mg, Dry Ether, ii. CO ₂ , H ⁺ , iii. NH ₃ , heat, and iv. Br ₂ , KOH

9. Identify the correct structure for the compound named "3-Methylpent-2-enal" as per IUPAC nomenclature.

10. Identify the most stable compound/ion among the given options.

11. Statement I: For hydrogen atoms, 3p and 3d are degenerate.
    Statement II: Degenerate orbitals have the same energy.
    i. Both statements I and II are correct.
    ii. Both statements I and II are incorrect.
    iii. Statement I is correct and statement II is incorrect.
    iv. Statement I is incorrect and statement Il is correct.

12. What is the geometry of Aluminium chloride in an aqueous solution?
    i. Square planar
    ii. Octahedral
    iii. Tetrahedral
    iv. Square pyramidal

13. The number of atoms in a silver plate having an area of 0.05 cm ² and a thickness of 0.05 cm is m x 10 ¹⁹ . If the density of silver is 7.9 g/cm ³ ,  find the value of m .

14. What is the group number of unununnium?

15. Match the following:
    Column I: i. BrF5, ii. H2O, iii. ClF3, iv. SF4
    Column II: a. Sea-Saw, b. T-Shape, c. Bent, d. Square Pyramidal

16. If a 250 mL solution of CH ₃ COONa of molarity 0.35 M is to be prepared, what is the mass of CH ₃ COONa required in grams? Round off the answer to the nearest integer.

17. The K _sp of Mg(OH) ₂ is 1 x 10 ^-12 . Find the limiting pH at 25 °C at which 0.01 M Mg ²⁺ ions will precipitate.

18. Assertion (A): From N to P covalent radius increases significantly, but from As to Bi, only a small increase is observed.
    Reason (R): For a particular oxidation state, covalent radii and ionic radii increase down the group.
    i. Both (A) and (R) are correct and (R) is the correct explanation of (A).
    ii. Both (A) and (R) are correct but (R) is not the correct explanation of (A).
    iii. (A) is correct but (R) is incorrect.
    iv. (A) is incorrect but (R) is correct.

19. Find A and B if:
    CH ₃ – C ≡ CH → (reacts with Na) → Product A → (reacts with B) → CH ₃ – C ≡ C – CH ₂ – CH ₂ – CH ₃

20. Find A and B if:
    C ₆ H ₆ –NH ₂ → (reacts with A) → C ₆ H ₆ –N ₂ ⁺ → (reacts with B) → Orange-Red Precipitate

21. Match the following:
    Column I: i. Mn ²⁺ , ii. V ⁺ , iii. Cr ⁺ , iv. Fe ²⁺
    Column II: a. 3d ³ 4s ¹ , b. 3d ⁵ 4s ⁰ , c. 3d ⁶ 4s ⁰ , d. 3d ⁴ s ¹

22. What happens to the freezing point of benzene, when a small amount of naphthalene is added to benzene?

23. A mixture is heated with dilute H ₂ SO ₄ and the lead acetate paper turns black by the evolved gas. The mixture contains:
    i. Sulphite
    ii. Sulphide
    iii. Sulphate
    iv. Thiosulphate

24. A → P
    In a first-order reaction, the concentration of reactant A is 0.04 M at 10 mins and 0.03 M at 20 mins. Calculate the half-life of the first-order reaction in mins. [log2 = 0.3, log3 = 0.48]

JEE Main Mathematics Questions 30 January 2024 Shift 1

Candidates can find here the memory-based questions for JEE Main 30 Jan 2024 Shift 1 Maths subject:

1. If the foot of the perpendicular from (1, 2, 3) to the line (x + 1)/2 = (y - 2)/5 = (z - 4)/1 is (α, β, γ), then find α + β + γ.

2. In an arithmetic progression, if the sum of 20 terms is 790 and the sum of 10 terms is 145, then S ₁₅ - S ₅ = ?

3. Find the value of the maximum area possible (in sq.units) of △ ABC with vertices A(0, 0), B(x, y) and C(-x, y) such that y = - 2x ² + 54x.

4. What is the range of r for which circles (x + 1) ² + (y + 2) ² = r ² and x ² + y ² - 4x - 4y + 4 = 0 coincide at two distinct points.

5. Find the eccentricity of an ellipse whose length of the minor axis is equal to half of the length between foci.

6. The domain of y = cos ^-1 | ( ( 2 - | x | ) / 4 ) | + log ( 3 - x ) ^-1 is [ α, β) - {γ}, then find α + β + γ.

7. A line passes through (9,0), making angle 30° with positive direction of x-axis. It is rotated byangle of 15° with respect to (9,0). Find the equation of the new line.

8. For a non-zero complex number z satisfying z ² + iz̄ = 0, then value of |z| ² is?

9. If |a| = 1, |b| = 4, a · b = 2 and c = 2(a x b) - 3b, then what is the angle between b and c?

10. Set S= {0, 1, 2, 3 ,...,10}
    If a random ordered pair (x, y) of elements of S is chosen, then find probability that | x - y | > 5.

11. Find the number of integral terms in the binomial expansion:
    ( 7 ^1/2 + 11 ^1/6 ) ⁸²⁴

12. In a class, there are 40 students.
    16 students passed in Chemistry.
    20 students passed in Physics.
    25 students passed in Maths.
    15 students passed in both Math and Physics.
    15 students passed in both Math and Chemistry
    10 students passed in both Physics and Chemistry.
    Find the maximum number of students that passed in all the subjects.

13. Set A = {1, 2, 3, 4, 5, 6,7}
    If the number of functions from Set A to Power Set A can be expressed as m ⁿ (where m is the least integer), the find m + n.

14. Find the value of 20M, if M is the median of the following data:

    x i	f i	C.F.
    0 - 4	2	2
    4 - 8	4	6
    8 - 12	7	13
    12 - 16	8	21
    16 - 20	6	27

JEE Main Question Paper 30 January 2024 Shift 1 PDF

Download the JEE Main 2024 question paper by CollegeDekho for the 30 January morning shift in PDF format here:

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JEE Main Question Paper PDF 30 January 2024 Shift 1 by Coaching Institutes

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