JEE Main Question Paper 2024 January 31 Shift 1 (Available): PDF download Physics, Chemistry and Mathematics

JEE Main Question Paper 2024 January 31 Shift 1

JEE Main Question Paper 2024 January 31 Shift 1 : The Day 4 and Shift 1 exam of JEE Main 2024 Session 1 is being conducted on January 31 from 9 AM to 12 PM. As it was until Day 3 of the exam, the overall difficulty level has remained 'Moderate' today as well. However, Chemistry was reported to be the easiest section today while Physics was the easiest until Day 3. On the other hand, Mathematics has remained the same, the toughest of all sections with an above-moderate difficulty level. You may check the detailed analysis for the morning shift today here: JEE Main 2024 January 31 Shift 1 Exam Analysis .

JEE Main question paper 2024 for the January 31 Shift 1 exam can be downloaded here in PDF format for Physics, Chemistry and Mathematics. The memory-based questions collected from the test takers of the Shift 1 exam of January 31 will be available here as the physical copy of the official question paper will not be available till the release of the response sheet.

JEE Main Question Paper 2024 January 31 Shift 1

JEE Main Physics Question Paper 2024 January 31 Shift 1

The memory-based questions for JEE Main 31 Jan 2024 Shift 1 Physics subject are as follows:

1. If the stopping potential is 8 V for incident light with wavelength λ and it is 2 V for a wavelength of 3λ, then find the threshold wavelength.

2. If two charges Q and 3Q are kept in a line separated by a distance R, the electric field is zero at a distance x from origin O. Find the value of x.

3. The mass defect in a nuclear reaction is 0.4 u. If the Q value of the reaction is x/10 MeV, then find x. (Take 1 u = 930.5 MeV/c ² )

4. What is the logic gate equivalent to the given logic circuit?
   

5. A pulley is placed on top of a triangular surface such that it forms 53° and 37° with the horizontal. The pulley carries two blocks of masses M and m on the 53° incline and 37° incline respectively. If M = 10 kg has an acceleration of  2 m/s ² in the direction of the 53° incline plane, then find the mass m.

6. If the percentage error in measuring the length and diameter of a wire is 0.1% each, then find the percentage error of the resistance of the wire.

7. Four identical particles of mass m each are placed at 4 corners of a square. The gravitational force exerted on one of the masses by other masses is [(2√2+1)/32] Gm ² /l ² . Find the length of the side of the square.

8. A ball dropped from height H rebounds up to height h after colliding with a horizontal surface. If the coefficient of restitution for collision is e = 1/2, then find H/h.

9. For a 1-D motion, relation between position x and time t is t = αx ² + βx. Find the relation between velocity v and acceleration a.

10. Two resistances having the coefficient of variation of resistivity α ₁ and α ₂ have equal resistance. Find the equivalent temperature coefficient of resistivity in series and parallel combinations.

11. The fundamental frequency of a closed organ pipe is equal to the frequency of the first overtone of an open organ pipe of length 60 cm. What is the length of the closed organ pipe?

12. Force F depends on distance x and time t as F = ax ² + bt ^1/2 . What final b ² /a dimension?

13. Two charges q and 3q are placed at a distance r from each other. Find the distance from q where the electric field is zero.

14. The refractive index of a thin prism of an apex angle A is cot (A/2). Find the minimum angle of deviation.

15. In a single electron atom/ion, the first member of the Lyman series is 1, then find the wavelength of the second member of their series.

16. In YDSE, the intensity at two sources is in the ratio of 1:9. If the source is incoherent then the intensity at the central point is I ₁ , and if the sources are coherent (and phase differs by 60°) then the intensity at the central point is I ₂ then I ₁ /I ₂ is?

17. Calculate the average energy density of an electromagnetic wave whose electric field is oscillating with amplitude 50 V/m and frequency 5 x 10 ¹⁰ Hz.

18. A uniform disk of mass 50 kg is rolling without slipping with a speed of 0.4 m/s. Find the minimum energy required to bring the disk to rest (in J).

19. At any instant, the magnetic field inside a coil is 3000 T and it changes to 2000 T in the next 2 seconds. If the average induced emf through the coil is 22 V, then find the number of turns in the coil. (Area of turn is 2 × 10 ^-3 m ² )

20. A parallel plate capacitor with plates separated by 5 mm then it draws a current of I ₀ from the AC source. Now a dielectric of thickness 2 mm is inserted between plates then current draws increase by 25%. Find dielectric constant.

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JEE Main Chemistry Question Paper 2024 January 31 Shift 1

The memory-based questions for JEE Main 31 Jan 2024 Shift 1 Chemistry subject are as follows:

1. Find out the final product C for the reaction:
   CH ₃ –CH ₂ –CH ₂ –Br → (in presence of alcoholic KOH, heat) → Product A
   Product A → (in presence of HBr) → Product B
   Product B → (in presence of aqueous KOH) → Product C

2. Which of the following options contain amphoteric oxide(s) only?
   i. SnO ₂ and SiO
   ii. SiO ₂
   iii. SnO ₂ and PbO ₂
   iv. CO and SiO

3. How many of the following compounds have sp ³ hybridized central atom?
   H ₂ O, NH ₃ , SiO ₂ , SO ₂ , CO and BF ₃

4. Which of the following compounds is white in colour?
   i. ZnSO4
   ii. CuSO4
   iii. FeSO4
   iv. FeCl3

5. On which of the following factors does the electrical conductivity of an electrolytic cell does not depend?
   i. Concentration of electrolyte
   ii. Amount of electrolyte added
   iii. Temperature
   iv. Nature of electrode

6. Arrange the following elements (magnitude only) in the decreasing order of electron gain enthalpy.
   Sulphur - A, Bromine - B, Fluorine - C, Argon - D

7. Moles of CH ₄ required for formation of 22 g of CO ₂ is m x 10 ^-2 . Find the value of m.

8. Find the total number of different alkanes formed when the following mixture is subjected to electrolysis (do not consider disproportionation reaction):
   CH ₃ COONa (aq) and C ₂ H ₅ COONa (aq)

9. How many of the following compounds have sp ³ hybridized central atom?
   BF ₃ , BeCl ₂ , NH ₃ , CH ₄ , H ₂ O, SO ₂ , CO ₂

10. If one faraday of electricity is used in the discharging of Cu ²⁺ , then find the mass (in grams) of Cu deposited. (Round off the answer to the nearest integer.)

11. The spin-only magnetic moment of complex ion [Ni(NH ₃ ) ₆ ] ²⁺ is A x 10 ^-1 BM. Find the value of A.

12. Which of the following solutions shows a positive deviation from Raoult's law?
    i. CHCl ₃ + C ₆ H ₆
    ii. CH ₃ COCH ₃ + CS ₂
    iii. CH ₃ COCH ₃ + CHCI ₃
    iv. CH ₃ COCH ₃ + C ₆ H ₅ NH ₂

13. Species having carbon with a sextet of valence electrons and acting as an electrophile is?
    i. Carbanion
    ii. Carbocation
    iii. Free Radical
    iv. Nitrene

14. Assertion(A): Noble gases have very high boiling points.
    Reason(R): Noble gases have strong dispersion forces. Hence, they liquefy at low temperatures and hence they have a high boiling point.
    i. Both A and R are true and R is the correct explanation of A.
    ii. Both A and R are true and R is not the correct explanation of A.
    iii. Both A and R are false.
    iv. A is true but R is false.

15. How many of the following statements are true?
    (i) Chromate ion is square planar.
    (ii) Green manganate ion is diamagnetic.
    (iii) Dichromate can be prepared using chromate.
    (iv) Dark green KMnO4 disproportionates in acidic medium and neutral medium.
    (v) For d-block elements, ionic character decreases for increasing oxidation number of metal in oxides.

16. Assertion: The pK value of phenol is 10.0 while that of ethanol is 15.9.
    Reason: Ethanol is a stronger acid than phenol.
    i. Both A and R are true and R is the correct explanation of A.
    ii. Both A and R are true and R is not the correct explanation of A.
    iii. Both A and R are false.
    iv. A is true but R is false.

17. The adsorption principle is used in
    i. Distillation
    ii. Differential Extraction
    iii. Chromatography
    iv. Vacuum Distillation

18. How many of the following can be used as electrodes in batteries?
    (i) Zinc
    (ii) Zinc - Mercury amalgam
    (iii) Lead
    (iv) Graphite

19. If the energy of radiation having a wavelength of 242 nm is X x 10 ^-19 , then find the nearest integer value of X. Given: Planck's constant = 6.6 x 10 ^-34 Js and c = 3 x 10 ⁸ m/s.

Also Read | JEE Main Chemistry Marks vs Percentile 2024

JEE Main Mathematics Question Paper 2024 January 31 Shift 1

The memory-based questions for JEE Main 31 Jan 2024 Shift 1 Maths subject are as follows:

1. [ 1 / ( 1 - 3 (1) ² + 1 ⁴ ) ] + [ 2 / ( 2 - 3 (2) ² + 2 ⁴ ) ] + [ 3 / ( 3 - 3 (3) ² + 3 ⁴ ) ] + ... (up to n = 10) = ?

2. If one of the diameters of the circle x ² + y ² - 10x + 4y + 13 = 0 is a chord of another circle and whose centre is the point of intersection of the lines 2x + 3y = 12 and 3x - 2y = 5. then the radius of the circle is?

3. An urn contains 15 red, 10 white, 60 orange, and 15 green balls. If 2 balls are taken with replacement, find the probability 1 ball is red and the other ball is white.

4. lim (x→0) [ (e ^|2sinx| - 2|sinx|-1) / x ² ] = ?

5. If three vectors are:
   a = 3i + j - 2k
   b = 4i + j + 7k
   c = i - 3j + 4k
   If p is a vector such that p x b = c x b and p·a = 0, then find p·(i - j - k).

6. Find the solution of the differential equation y dy/dx = x (log _e x - log _e y + 1), x > 0, y > 0 and passes through (e, 1).

7. f(x) = (4x + 3)/(6x - 4) and g(x) = f(f(x)), then find g(g(g(g(x)))).

8. A = { 1, 2, 3, 4 }, R = { (1, 2), (2, 3), (2, 4) }, R ⊆ S and S is an equivalence relation, then the minimum number of elements to be added to R is n. Find the value of n.

9. ABCD is a parallelogram where A(α, β), B(1,0), C(γ, δ), and D(3,2) and AB = √10. Find the value of 2(α + β + γ + δ).

10. The distance of the point Q(0,2,-2) from the line passing through the point P(5,-4,3) and perpendicular to the line r = (-3i + 2k) + λ(2i + 3j + 5k), λ ∈ R and r = (i - 2j + k) + μ (- i + 3j + 2k), μ ∈ R is?

11. Let S be the set of positive integral value of a for which
    [( ax ² + 2 (a + 1) x + 9a + 4 ) / ( x ² + 8x + 32 )] < 0 ∀x ∈ R.
    Find the number of elements in S.

12. For α, β, γ ≠ 0, if sin ^-1 α + sin ^-1 β + sin ^-1 γ = π and (α + β + γ)*(α - γ + β) = 3αβ, then find the value of γ.

13. If |a| = 1, |b| = 4 and a·b = 2. Also, c = (3a x b) - b and α is the angle between b and c, then what is the value of 192 sin ² α?

14. If the system of linear equation x - 2y + z = - 4, 2x + αy + 32 =5 & 3x - y + βz = 3 has infinitely many solutions then find the value of 12α + 13β.

Also Read | JEE Main Mathematics Marks vs Percentile 2024

JEE Main Question Paper 2024 January 30 Shift 1 PDF Links

Find here the links to download JEE Main 2024 question paper by CollegeDekho for the 31 January morning shift in a PDF format:

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JEE Main Question Paper PDF 31 January 2024 Shift 1 by Coaching Institutes

For Day 4 Shift 1, the subject-wise memory-based questions released by the top JEE Main coaching institutes will be updated as and when available:

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JEE Main January 2024 Day-Wise Question Paper Links |

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