JEE Mains 2024 Question Paper PDF Without Solutions

Candidates who are going to appear in the April session of JEE Must go through the JEE Mains 2024 Question Paper as it will help to understand the difficulty level & types of questions in this session. To make things easier, the JEE Main 2024 question paper without solution PDF Download links are given in this post.

JEE Main 2024 Question Paper without Solution

jee main 2024 question paper without solution is a great reference for students who appear in the January Session examination, want to cross-check their answers after taking the exam, and also assess their predicted scores. Not only appeared candidates’ theses. Candidates who plan to take the JEE in April would benefit from this question paper. As jee mains 2024 january session question papers will provide Crucial insights into the examination pattern, difficulty level, and most essential chapters in JEE Mains for candidates taking the exam in Session 2.

All JEE Mains 2024 Question Paper PDF without Solutions

The memory-based jee mains 2024 January session question paper PDF with solutions is shared based on the students ‘ reviews. As this is an online exam, only memory-based questions will be gathered. The NTA will conduct JEE Main 2024 in two shifts. A first shift runs from 9 a.m. to 12 p.m., followed by a second shift from 3 p.m Candidates can check the jee mains 2024 all shift question paper pdf in the table below.

JEE mains 2024 January session question paper PDF
Exam Date	JEE Mains 2024 Shift 1 Paper PDF Download	JEE Mains 2024 Paper Shift 2 PDF Download
JEE Main 2024 January 24	Click here
JEE Mains 2024 27 January Paper	JEE Mains 2024 Question Paper 27 Jan Shift 1 PDF	JEE Mains 2024 Question Paper 27 Jan Shift 2 PDF
JEE Mains 2024 Question Paper of January 29	JEE Mains 2024 Question Paper 29 Jan Shift 1 PDF	JEE Mains 2024 Question Paper 29 Jan Shift 2 PDF
JEE Mains 2024 Question Paper of January 30	JEE Mains 2024 Question Paper 30 Jan Shift 1 PDF	JEE Mains 2024 Question Paper 30 Jan Shift 2 PDF
JEE Mains 2024 Paper for January 31st	JEE Mains 2024 Question Paper 31 Jan Shift 1 PDF	JEE Mains 2024 Question Paper 31 Jan Shift 2 PDF
JEE Mains 2024 Paper February 1st	JEE Mains 2024 Question Paper 1 Feb Shift 1 PDF	JEE Mains 2024 Question Paper 1 Feb Shift 2 PDF

JEE Mains 2024 Session 1 Question Paper Pattern

The National Testing Agency (NTA) administers the JEE Main Paper 1 exam for admission to the BE/BTech programme. The JEE Main 2024 question paper contains 90 questions divided into three categories: Mathematics, Physics, and Chemistry. These JEE Main 2024 Session 1 Question papers will help students understand the Question paper’s nature, difficulty level, and types of questions that will be asked in the upcoming April session. Candidates can find the JEE Mains 2024 Question paper PDF of each shift of session 1 is available to download on this page.

. Here we discussed the paper pattern for the Jee main 2024 question paper.

• The Jee Mains 2024 question paper consists of 90 multiple-choice questions worth 300 points.
• The Jee Mains 2024 question paper will consist of 30 questions in Physics, Chemistry, and Mathematics each.
• Each Section of JEE Main 2024 paper 1 contains 20 multiple-choice questions (MCQs) and 10 numerical value questions, with only 5 of them necessary.
• The exam will be held in 13 languages, including Assamese, Bengali, Kannada, Malayalam, Marathi, Odia, Punjabi, Tamil, Telugu, and Urdu, in addition to Hindi, English, and Gujarati.

JEE Main 2024 January Session Question Paper with Solutions

JEE Main 2024 Question Paper enables students to understand the difficulty level of the January session exam, which helps them to prepare accordingly for upcoming shifts. Before addressing the Jee Mains 2024 january question paper pdf with solutions, aspirants should check the JEE Main 2024 Exam Analysis to learn about the experts’ thoughts on the paper.

JEE Mains 2024 Question Paper- 1 Feb

The National Testing Agency (NTA) has begun shift 1 for the final day of the Joint Entrance Examination (JEE) Main 2024 exam on February 1. The first shift of the JEE Main 2024 February 1 will take place from 9 a.m. to 12 p.m., followed by the second session from 3 p.m The Memory-based JEE Mains 2024 1 February Paper 2024 for Shift 1 and 2 is available here after the exam.

JEE Main Question Paper 2024 (1 February) Shift 1

Physics

Q. A vernier caliper has 10 main scale divisions coinciding with 11 vernier scale divisions equals 5 mm. What is the least count of the device?

Q. Determine Min. Energy released when an electron jumps to ground state in Balmer series from infinity.
Q. On increasing temperature, the elasticity of a material will:
i. Increase
ii. Decrease
iii. Remain constant
iv. May increase or decrease

Q.Two particles, each of mass 2 kg are placed in the x – y plane such that mx is 4 m on the negative x-axis and my is 4 m on the positive y-axis. If the distance of the center of mass from the origin is [ (4√2)/x ], find x.

Q. What are the dimensions of an angular impulse?

Q. With rise in temperature the young’s modulus of elasticity
A. Increases
B. Decreases
C. Remaining constant
D. None of these

Q. If a bullet of mass 10-2 kg and velocity 200 m/s gets embedded inside the bob of mass 1 kg of a simple pendulum, then what will be the maximum height that the system rises by in cm?

Q..A vernier caliper has 10 main scale divisions coinciding with 11
vernier scale division equals 5 mm. the least count of the device is :
A. ½
B. 5/12
C. 5/11
D. 0.3

Q.The length of a seconds pendulum, if it is placed at height 2R (where R = the radius of the earth) from the
surface of the earth, is [ 10/xπ2] m. Find x.

Q. In case of isoelectronic species the size of F, No and Nat is attected by:
(a) Principle Quantum number (n)
(b) Electron – electron interaction
(c) Nuclear change (z)
(d) None of the factors because their size is the same

Q. Determine the lowest energy of a photon emitted in the Balmer Series of a hydrogen atom.

Q. Find percentage change in capacitance if potential difference across it has been changed from V to 2V.

Chemistry

Q.If mass defect in a nuclear reaction is 0.4gm then find the Q-value of the reaction.

Q. The total number of deactivating groups among the following is:
-CN, -NH-CO-CH3, -CO-CH3 , -NH-CH3

Q.What is the pH of CH3COONH4 +? (At 25°C)
Given: Ka of CH3COOH = 1.8 x 10-5 , Kb of NH4OH = 1.8 x 10-5

Q. We are given with following cell reaction:
2H+ + 2 e- → H2
PH2= 2 atm
[H+]= 1M
(2.303RT / F = 0.06)
If Ecell of the reaction is given by -x * 10-3 V. Find out x.

Q. Statement I: PH3 will have a lower boiling point than NH3.
Statement II: There are strong van der Waals forces in NH3 and strong hydrogen bonding in PH3.
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.

Q. Find out the total possible optical isomers of 2-chlorobutane.

Q. In the case of isoelectronic species the size of F-, Na and Na+ is affected by:
A. Principle of Quantum number(n)
B. Electron – electron interaction
C. Nuclear change (z)
D. None of the factors because their size is the same

Q.Which of the following is the correct for adiabatic free expansion against vacuum?
i. q = 0, ΔU = 0, w = 0
ii. q ≠ 0, w = 0, ΔU = 0
iii. q = 0, ΔU ≠ 0, w = 0
iv. q = 0, ΔU ≠ 0, w ≠ 0

Q. In Kjeldahl’s method for estimation of nitrogen, CuSO4 acts as
A. Oxidizing agent
B. Reducing agent
C. Catalytic agent
D. Hydrolysis agent

Q. Complementary stand of DNA ATGCTTCA is:
i. TACGAAGA
ii. TACGAAGT
iii. TAGCAACA
iv. TAGCTACT

Mathematics

Q. 3, a, b, c are in Ap 3, a-1, b+1,c+9 → GP Then AM of a, b, c is
Q. 3 , 7 , 1 ,……., 404 and 4 , 7, 10 ,……, 403 sum of common terms
Q. The value of the integral
Q. Number of ways of arranging 5 officers in 4 rooms.

Q.intersect L1 and L2 at P and Q respectively. If (α, β, γ) is the mid point of the line segment PQ, then 2(α, β, γ) is equal to

JEE Mains 2024 Question Paper (1 February) Shift 2

Q. Two trains run on North-South parallel tracks. Train A moves with velocity 20 m/s towards North and train B moves with velocity 30 m/s towards South. Then find the velocity of train B with respect to train A.

Q. A body of mass of 4kg experiences two forces then acceleration acting on the body R

Q. A source produced electromagnetic wave of frequency 60MHz. Find the wavelength of this wave in air.

Q. A Big drop is formed by coalescing 1000 small droplets of water. The surface water. The surface energy will become.

Chemistry

Q. What is the order of reducing character for AsH3, NH3, PH3 (group 15 hydrides)?

1. NH3 > PH3 > AsH3
2. PH3> NH3 > AsH3
3. AsH3> PH3 > NH3
4. NH3 > AsH3 > PH3

Q. Number of radial nodes present in 3p are

1. 0
2. 1
3. 2
4. 4

Q. Which of the following has the highest 3rd ionization energy? A. Mn

1. V
2. Cr
3. Fe

Q. Which of the following compounds have colour due to d-d transition?

1. KMnO4
2. K2Cr2O7
3. K2CrO4
4. CuSO4.5H2O

Q. A 10 mL hydrocarbon (C₂H₄) on combustion give 40 mL CO₂ and 50 mL H20. Calculate the value of x+y

Q. Solubility of Ca3(PO4)2in 100 mL of pure water is W gm. Find out Ksp of Ca3(PO4)2is:

(M: Molecular mass of Ca3(PO4)2)

1. 108 * (W/M)5
2. 108 * 105 * [W/M]5
3. 108 * 104 * [W/M]5
4. 108 * 106 * [W/M]5

Q. Which of the following compounds in 3d series does not show +3 oxidation state?

1. V
2. Cr
3. Mn
4. Cu

Q. Which of the following sets of elements can be detected by Lassaigne’s Test ?

1. N and S only
2. N, P and S only
3. P and halogens only
4. N, P, S and halogens

Q. Which of the following compounds has intramolecular hydrogen bonding in it?

1. NH3
2. H20

Mathematics

Q. Let α and ẞ the roots of equation px² + qx – r = 0, where P≠ 0. If p,q,r be the consecutive term of non constant G.P and 1/α + 1/β = 3/4 then the value of (α – β)² is:

Q. If the mirror image of the point P(3,4,9) in the Line is (α,β,γ) then find 14(a+ẞ+y) is:

Q. Let the system of equations x+2y+3z = 5, 2x+3y+z = 9, 4x+3y+λz = μ have an infinite number of solutions. Then λ + 2μ is equal to

JEE Mains 2024 Question Paper- 31st Jan

The Memory-based JEE Mains 2024 31 January Paper 2024 for Shift 1 and 2 are shared here.

JEE Main Question paper 2024- 31 Jan Shift 1

According to the initial views of students who took the JEE Main January 31 Shift 1 exam, the general difficulty of the paper was moderate. Students noted that the Mathematics session was challenging and lengthy. The physics component was said to be easy but challenging. Students rated the chemistry portion as easy. Students also claimed that the Chemistry section contained more NCERT-based questions than the Physics section, which contained mostly formula-based questions.

Candidates can find memory-based questions for each subject on the JEE Mains 2024 31 Jan paper Shift 1 below.

Physics

Q. 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.

Q. 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/s2
in the direction of the 53° incline plane, then find the mass m.
Q. 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.
Q. If the mass defect in a nuclear reaction is 0.4 gm, then find the Q-value of the reaction.

Q. 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.

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

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

Q. 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.

Chemistry

Q. Which of the following options contain amphoteric oxide(s) only?
i. SnO2 and SiO
ii. SiO2
iii. SnO2 and PbO2
iv. CO and SiO

Q. Find out the final product C for the reaction:
CH3–CH2–CH2–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

Q. How many of the following compounds have sp3 hybridized central atom?
H2O, NH3 , SiO2, SO2 , CO and BF3

Q. 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.

Q. 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.
Q. The adsorption principle is used in
i. Distillation
ii. Differential Extraction
iii. Chromatography
iv. Vacuum Distillation
Q. How many of the following can be used as electrodes in batteries?
(i) Zinc
(ii) Zinc – Mercury amalgam
(iii) Lead
(iv) Graphite

Mathematics

Q. 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.
Q. 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).
Q. 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.
Q. Let S be the set of positive integral value of a for which
[( ax2 + 2 (a + 1) x + 9a + 4 ) / ( x2 + 8x + 32 )] < 0 ∀x ∈ R.
Find the number of elements in S.
Q. 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?
Q. If one of the diameters of the circle x2 + y2 – 10x + 4y + 13 = 0 is a chord of another circle and whose center
is the point of intersection of the lines 2x + 3y = 12 and 3x – 2y = 5. then the radius of the circle is?
Q. 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.Q4. lim (x→0) [ (e|2sinx| – 2|sinx|-1) / x2 ] = ?
Q. 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).
Q. Find the solution of the differential equation y dy/dx = x (logex – logey + 1), x > 0, y > 0 and passes through (e, 1).
Q. f(x) = (4x + 3)/(6x – 4) and g(x) = f(f(x)), then find g(g(g(g(x)))).
Q. For α, β, γ ≠ 0, if sin-1α + sin-1β + sin-1γ = π and (α + β + γ)*(α – γ + β) = 3αβ, then find the value of γ.
Q. 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 sin2α?

 

JEE Mains 2024 Question Paper- 31 January Shift 2

Physics

Q. Find the value of x when 3 moles of oxygen gas and 2 moles of argon gas are mixed together. If the total energy of the mixture is xRT.
Q. Find the mass number of nucleus Y when A nucleus X has mass number 192 and a second nucleus Y has radius half of X,
Q. A point object is placed at 100 cm from a convex spherical refractive surface having a radius of curvature of 200 cm and a refractive index of the refractive surface is 1.5. Find image distance.
Q. If the mass of the moon is 1/144 times of a planet, and the diameter of the moon is 1/16 times of the diameter of a given planet, then find the escape velocity on the moon if the escape velocity on the planet is v.
Q. A particle is projected at an angle of 45° with horizontal speed u. Find the angular momentum of the particle about the point of projection at the time when it reaches maximum height.
Q. Magnetic flux passing through a loop of resistance 8 Ohms is given by Phi = 5t2- 36t +5. Find the current in the loop at t = 2 sec.

Q. The speed of sound in oxygen in STP will be approximately?
Given that R=8.3 and y=1.4
Q. Find the speed of sound at STO if the Gama of air is 1.4 (given R = 80134J/mol-K)

Chemistry

Q. Find the work done by gas At a temperature of 300 kelvin, 5 moles of gas are expanded from 10 liters to 100 liters.
Q. The half-life of a first-order reaction is 36 hr. Find out the time (in hours) required for the concentration of reactant to get reduced by 90%.
Q. If 5 mole of an idan gas expands from 10 L to a volume of 100 L at 300 K under isothermal and reversible conditions then work W s xJ. Given R = 80134 Jmol-1 /K.

Q. What is the Number of isomeric products formed by monochlorination Of 2-methyl butane in the presence of sunlight?

Q. If 5 moles of an ideal gas expands from 10 L to a volume of 100 L at 300k under isothermal and reversible conditions then work, W, is – x J. The value of x is (even n = 8.314 J K-¹ mol-¹)

Q. A compound (x) with a molar mass of 108 g mol-1 undergoes acetylation to give a product with a molar mass of 192 g mol-1

Q. Half-life of a first-order reaction is 36hr. Find out the time (in hours) required for the concentration of reactant to get reduced by 90%.

Mathematics

Q. The number of ways to distribute the 21 identical apples to three children so that each child gets at least 2 apples is?

Q. A coin is biased so that a head is twice as likely as a tail. If the coin is tossed 3 times, then find the probability of getting two tails and one head.

Q. The number of solutions of equation e sinx – 2e -sinx = 2 is
A. more than 2
B. 2
C. 1
D. 0

Q. If A = {1, 2, 3, … 100}, R = {(x, y) | 2x = 3y, x, y ∈ A} is a symmetric relation on A and the number of elements in R is n, the smallest integer value of n is

Q. If (alpha, beta, gamma) is a mirror image of the point (2, 3, 4) with respect to the line 123 234 xy z −−− = = .Then 2 alpha + 3 beta + 4 gama i
Q. Let mean and variance of 6 observations a, b, 68, 44, 40, 60 be 55 and 194. If a > b then find a + 3b.

JEE Mains 2024 Paper- 30 January

JEE Main 2024 for paper 1 was completed on  January 30, by (NTA) in two shifts. The JEE Mains 2024 30 January Question Paper Papers for Shifts 1 and 2 are available here after the exam. The Memory Based  JEE Mains 2024 30 January Paper Shift 1 & 2 is Updated here.

JEE Mains 2024 Question Paper (30 January) Shift 1

According to students’ initial reactions, JEE Main 2024 January 30 Shift 1 was moderately demanding. The mathematics component was moderate to challenging, and the physics section was intermediate. The JEE Main 2024 January 30 Shift 1 Chemistry section was straightforward to moderate and entirely NCERT-based. The majority of the questions in Chemistry were from Organic. Candidates can discover below the memory-based questions for JEE Main 30 Jan 2024 Shift 1 of each subject.

Physics

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

Q. 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.

Q. Young’s modulus of a material of length L. and cross sectional area A Is Y. If the length is doubled and cross-sectional area is halved then young’s modulus will be
A)Y/4
b) 4Y
C) Y
d) 2Y
Q. Find the ratio of the kinetic energy and the potential energy in the 5th excited state of a hydrogen atom.
Q. 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.

Q, Two current-carrying rings of radius R are mutually perpendicular and their center coincides. Find the magnetic field at center ‘O’.

Q. The work function of a metal is 3 eV. Find its threshold wavelength.

Q. A particle of mass m is projected from ground with 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.
A. mv³/16g
B. √mv/16g
C. mv³/3g
D. √3mv³/16g

Q. The ratio of KE : PE IN 5th excited state of hydrogen atom is
A. -2
B. 2
C. -½
D. 1/2

Q. Find the potential difference V0 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.

A. 2V
B. 0.5V
C. 1.1V
D. Zero

Q. In a convex lens, the distance between the object and the image is 45 cm, and the magnification produced by the lens is two. Find the focal length of the lens.
Q. A particle of mass m is projected at an angle of 30° with initial velocity u. Find its angular momentum about the point of projection at maximum height.

Q. At which temperature the r.m.s velocity of the hydrogen molecule is equal to that of oxygen molecule at 47°C

Chemistry

Q. Identify the given reaction.
C6H6–C=O–Cl → (in the presence of H2 , Pd/BaSO4) → Product
i. Etard Reaction
ii. Stephen’s Reaction
iii. Wolff Kishner Reduction
iv. Rosenmund Reaction

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

Q. 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

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

Q. If a 250 mL solution of CH3COONa of molarity 0.35 M is to be prepared, what is the mass of CH3COONa required in grams? Round off the answer to the nearest integer.

Q. Match the following:

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

Q. Which of the following sets contain both diamagnetic ions?
i. Ni2+, Cu2+
ii. Eu3+, Gd3+
iii. Cu+, Zn2+
iv. Ce4+, Pm3+

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

Q . 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.

Q. Identify the correct structure for the compound named “3-Methylpent-2-enal” as per IUPAC nomenclature.

Q . Find the final product when C6H6–Br reacts with i. Mg, Dry Ether, ii. CO2, H+, iii. NH3, heat, and iv. Br2, KOH

Q. The number of atoms in a silver plate having an area of 0.05 cm2 and a thickness of 0.05 cm is m x 1019. If the density of silver is 7.9 g/cm3, find the value of m.
Q. What is the group number of unununnium?

Q. Identify the correct structure for the compound named “3-Methylpent-2-enal” as per IUPAC nomenclature.

Mathematics

Q, If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is.

Q. Let A(2,3,5) and C(- 3, 4, – 2) be ‘opposite vertices of a Parallelogram ABCD. If the diagonal vec BD = hat i +2 hat j +3 hat k then the area of the Parallelogram is equal to.

Q. Let (α, β, y) be the foot of perpendicular form the point (1,2,3) on the line (x + 3)/5 = (y – 1)/2 = (z + 4)/3 then 19 (α+ β+ y)Q. If z = x + iy, xy ≠ 0 satisfies the equation z² + iz = 0, then |z²|; equal to

Q. Let A(2,3,5) and C(- 3, 4, – 2) be ‘opposite vertices of a Parallelogram ABCD. If the diagonal vec BD = hat i +2 hat j +3 hat k then the area of the Parallelogram is equal to.

Q. 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 = – 2×2 + 54x.
Q. What is the range of r for which circles (x + 1)² + (y + 2)² = r² and x² + y²
– 4x – 4y + 4 = 0 coincide at two distinct points

Q5. Find the value of

Q . 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.
Q. In an arithmetic progression, if the sum of 20 terms is 790 and the sum of 10 terms is 145, then S15 – S5 = ?

Get the Solutions of JEE Mains 2024 30 January Question Paper Shift 1

JEE Mains 2024 Question Paper (30 January) Shift 2

The examination authorities have successfully conducted the JEE Main Shift 2 exam for January 30, 2024. According to the students’ views, the JEE Mains 30 Jan shift 2 exam was moderately difficult. Candidates found the Chemistry section to be the simplest, while the Physics and Math sections were more difficult. Physics contains formula-based integer-type questions. One inquiry is about present electricity. Chemistry includes questions about the d-block, the periodic table, and chemical bonding. The question paper is NCERT-based.

Check subjectwise JEE Mains 2024 Shift 2 Question Paper 2024 is shared below.

Physics

1. Find the work done by the friction force when 1kg of block is placed on the inclined surface. 10 N force is applied to the block in the upward direction and the displacement is 10 meters (mu = 0.1).
2. Find the ratio of their respective initial velocities when two balls are thrown from a height 400 m, at an angle 60° and 45° with horizontal, respectively. Their range and time of flight are same

Chemistry

1. Find the mole fraction of C when C is added to a solution of A and B?

2. What is the reason behind the KMnO4 displaying colour?

JEE Mains 2024 Question Paper- 29 January

The National Testing Agency (NTA) is holding the Joint Entrance Examination (JEE Main 2024) for Engineering applicants (BE/BTech paper 1)on January 29. The exam is being conducted in two shifts. The JEE Mains 2024 Question Paper for 29 January Papers for Shifts 1 and 2 are available here after the exam.

JEE Mains 2024 Paper- 29 January Shift 2

Shift 2 of JEE Mains 2024 Day 2 is ended. According to the early reactions of students who took the JEE Main session 1 January 29 shift 2 exam 2024, the exam’s overall difficulty level ranged from easy to moderate. Students thought the Mathematics paper to be more lengthy than shift 1. Questions in the Physics paper were formula-based, whereas the Chemistry paper was simple. Mostly straightforward and not too difficult.

JEE Mains 2024 Physics Questions 29 January Shift 2

1. A rod of length 2m moving with velocity 2mn/sec along the positive z-axis and B = 2T along the negative side x-axis. Find the emf induce in the rod
2. In a simple pendulum of length 10 m, the string is initially kept horizontal and the bob is released. 10% of energy is lost till the bob reaches the lowermost position. Then find the speed of bob at the lowermost position.
   a 6 m/s
   b 6√5 m/s
   C 7√5 m/s
   d 4√2 m/s
3. A planet at a distance r from the sun takes 200 days to complete one revolution around the sun. what will be the period for a planet at a distance r/4 from the sun?
4. Find the speed of the bob at the lowermost position, If a simple pendulum of length 10 m, the string is initially kept horizontal and the bob is released. 10% of energy is lost till the bob reaches the lowermost position.
5. The intensity at each slit is equal for a YDSE and it is maximum Imax at central maxima. If Iis intensity for phase difference 7pi/2 between two waves at the screen. Then I/Imax is？

JEE Mains 2024 Shift 2 Chemistry Questions 29 January

1.  What will be the reason behind the oxygen showing anomalous behaviour?
2. What will be the IPUC Name of the compound where there is a cyclohexane ring the aleken is in the second position and in the first position there is alcohol (OH)
3. Among the given options which has the highest ionization enthalpy (Si, Al, C, N)? 1. Among the given ions which is the best-reducing agent (Lu3+, Nd3+, Ce4+, Gd2+)?
4. What will be the oxidation state of Iron in the complex formed in the brown ring test?
5. Neslers Reagent given brown colour with?
6. Along the given list which of the following compounds has zero dipole moment (NH3, H2O, HF, CO2, SO, BF3, CH4)?

JEE Mains 2024 Mathematics Questions 29 Jan Shift 2

1. Find the probability that the number is a multiple of 4 or 6 or 7 If in the given set = (1, 2, 3, …., 50} one number is selected randomly from a set.
2. What will be the remainder when
   ${{64}^{32}}^{32}$

    is divided by 9?

3. What will be the value of 12 A if the area bounded by 0< (equal to) y< (equal to), min {x+2, 2x + 2}, x is an element of [3,0]?
4. A=(1, 2, 3, 4} minimum number of elements added to make it equivalence relation on set A containing (1, 3) & (1, 2) in it

JEE Mains 2024 Paper- 29 Jan Shift 1

Shift 1 of JEE Mains 2024 29 January is over. According to the student’s initial reaction, the JEE Main 2024 January 29 Shift 1 exam was moderate in nature. Students considered the Mathematics paper to be lengthy, tricky, and a little difficult and hard.
The Physics paper was straightforward because the majority of the questions were formula-based. The Chemistry paper in shift 1 was easy, according to the pupils. Most of the questions were in organic chemistry and metallurgy.

JEE Mains 2024 Physics Questions Shift 1

1.  A body of mass 100 kg travelled 10 m before coming to rest. If μ = 0.4, then find the work done against friction.
2. Assume the motion is happening on a horizontal surface and g = 10 m/s².
   If an object has the same weight at the same distance above and below the surface of the earth. Find its distance from the surface of the earth.
3. A solid sphere of radius 4a units is placed with its centre at the origin. Two charges -2q at (-5a, 0) and 5q at (3a, 0) are placed. If the flux through the sphere is xq/ε0 , then find x.
4. The voltage applied across the resistance R is 200+5 and the current in resistance is 20+0.2 then find % error in resistance.
   A. 3.5 %
   B. 5 %
   C. 7 %
   D. 3 %
5. If a particle starting from rest having constant acceleration covers distance S1
   in the first (P – 1) seconds & S2 in the first P seconds, then determine the time for which displacement is S1 + S2.
6. If the ratio of the centripetal acceleration of two particles moving on the same circular path is 3: 4, then find the ratio of their speed.
7. If the De-Broglie wavelength of a proton and an electron is the same, then find the ratio of the kinetic energy of the electron to that of the proton.

JEE Mains 2024 Chemistry Questions 29 Jan Shift 1

1. Calculate the Molarity of a Solution having density = 1.25 g/ml. %(w/w) of Solute is 36% and the Molecular weight of Solute is 36 g/mol
2. Which of the following pairs will be formed by the decomposition of KMnO4 ?
   i. MnO4, MnO2
   ii. K2MnO4 , MnO2
   iii. KMnO4, MnO2
   iv. MnO2, H2O
3. Appearance of Red color on treatment with Na fusion extract of an organic compound with FeSo4 in the presence of Conc. H2SO4indicate element
   A. N
   B. Br
   C. S
   D. N & S
4. Determine products A and B when toluene reacts with Cl2 in the presence of sunlight (Product A) and in the presence of CCl4 (Product B).
5. Determine the major product for a given reaction.
6. What is the energy difference between the actual structure and its most stable resonating structure having the least energy is called as?
7. Energy difference between actual structure and its most stable resonating structure having least energy is called
   A. Electromeric effect
   B. Resonance Energy
   C. Inductive effect
   D. Hyperconjugation
8. Interaction b/w π bond & Lone pair of e-s on adjacent atoms
   A. Resonance
   B. Hyperconjugation
   C. Inducting Effect
   D. Electronic & effect
9. If alkaline KMnO4 is oxidised iodide to give a particular product (A), then determine the oxidation state of iodine in the compound (A).
10. Which of the following statements is incorrect?
    i. ΔG = 0 for reversible reaction
    ii. ΔG < 0 for spontaneous process
    iii. ΔG > 0 for spontaneous process
    iv. ΔG < 0 for non-spontaneous process
11. Energy difference between actual structure and its most stable resonating structure having least energy is called as?
12. What is the effect that occurs between a lone pair and a pi bond?
    i. Inductive effect
    ii. Electromeric effect
    iii. Resonance effect
    iv. Hyperconjugation

JEE Mains 2024 Maths Question Paper 29 Jan Shift 1

1.  If a die is rolled until 2 is obtained, then what is the probability that 2 is obtained on an even-numbered toss?
2. Let a die roll till 2 is obtained. The probability that 2 obtained on even numbered toss is equal to:
   A. 5/11
   B. ⅚
   C. 1/11
   D. 6/11
3.  A GP has 64 terms such that (Sn) total = 7(Sn)odd. Find the common ratio r.
4.  What is the rank of the word GTWENTY in the dictionary?
5. 
6. 

JEE Mains Paper 2024- 27 January

Check out the Memory-based JEE Mains 2024 27 January Question Paper of Shift 1 and shift 2 given below.

JEE Mains 2024 27 January Paper Shift 1

JEE Main 2024 Jan 27 Shift 1 Exam for B.Tech /B.E is now over. According to the first reaction of students who took the exam, the JEE Main 27 January shift 1 paper was quite difficult. The paper was the same as last year, with no changes in pattern. Maths was as lengthy as usual, whereas Physics was really dry. In Physics, the majority of the questions were from current physics. The Chemistry section was easy to moderate. Check out some memory-based questions which are asked in the JEE MAins Question Paper 2024 27 January Shift 1.

Question 1 (Maths)

X²/25 + y²/16=1

Chord length with mid point (1,2/5). Determine the length of the chord.

Question 2 (Physics)
A wire of length L and resistance R is cut into 5 equal parts and those part are connected in parallel the Req across it will be
1) 25R
2) 5/R
3) 5R
4) R/25
Answer: 4) R/25

Question 3 (Physics)
A wire of length L and resistance R is cut into 5 equal parts and those part are connected in parallel the Req across it will be
1) 25R
2) 5/R
3) 5R
4) R/25
Answer: 4) R/25

Question 4 (Maths)

$8= 3+\frac{3+p}{4}+\frac{3+2p}{4^2}........\infty$

a) 9,    b)3/4,

c) 3,     d) 1

Question 5 (Physics)
A Body of of mass 1000 kg has velocity 6m/s if extra 200 kg is embedded in it new velocity of the combined mass?

1) 5 m/s
2) 3 m/s
3) 10 m/s
4) 2 m/s

Question 6(Physics)
If the electron revolving in the 3rd Bohr’s orbit of Hydrogen species has radius is R. Then what will be its radius in 4th orbit in terms of R?

1) (25/9)R
2) (16/9)R
3) (36/9)R
4) (9/16)R

Question 7 (Physics)
A wire of length L and resistance R is cut into 5 equal parts and those part are connected in parallel the Req across it will be
1) 25R
2) 5/R
3) 5R
4) R/25
Answer: 4) R/25

Question 8 (Physics)

A body of mass 1000 kg has velocity 6m/s if extra 200kg mass is embedded in it new velocity of the combined mass?

(1) 5 m/s
(2) 3 m/s
(3) 10 m/s
(4) 2 m/s

Question 9 (Physics)

A nucleoid (A = 236) ‘ Binding energy is 7.6 MeV/nucleon in a fission reaction.

${A}^{236}–>B^{118}$

. The binding energy of B is 8.6 MeV/nucleon. Find the energy released in the process in …….(MeV)?

Question 10 (Physics)

A particle performing SHM has an amplitude 4 cm and maximum 10 cm/s. What is the displacement Spoed form mean position when the particle has speed 5 cm/s
(1) 3 cm
(3) 2√2cm
(2) 2 cm
(4) 2√3cm

Question 11 (Physics)

Two parallel infinite long infinite current-carrying wires have current 10 A in opposite direction have a separation is 10 cm if the magnetic field at the midpoint is B × 10−5 Tesla finds the value B.

Question 12 (Physics)

When a convex lens of focal length 40cm is placed in front of a photo- electric cell, then then the current produced is I, The lens forming the image is then replaced by another of the same diameter but of focal length 20 cm. The photoelectric current in this case is
(1) I
(3) 4I
(2) 2I
(4) I/2

JEE Mains 27 Jan Shift 2 Question Paper PDF-Based Questions

Physics Question Paper

1. 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
2. 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.
3. If two bodies with masses 4 kg and 5 kg have the same kinetic energy, then find the ratio of their linear momentum.
4. If the work function of a metal is 6.63 eV, then find the threshold frequency for the photoelectric effect.
5. 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
6. Find the total kinetic energy of 1 mole of oxygen gas at 27°C. Take R = 25/3 J/(mol-K).
7. 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.
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. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. In an adiabatic process, the pressure of a gas is proportional to the cube of absolute temperature, then the ratio of C_p/C_v is?
15. 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?
16. A particle moves 80 m in the last 2 seconds of free fall of height h, then find the height h.
17. 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?
18. 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.

Memory-based Math questions for JEE Main 27 Jan 2024 Shift 2

1. 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?
2. ∫₀^π dx / ( 1 – 2a cosx + a² ) = ?
3. If the line x + y = 0 is tangent to the circle (x – λ)² + (y – β)² = 50, then (λ + β)² = ?
4. 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) = ?
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 2tan²θ – 5 secθ = 1 has exactly 7 solutions in [θ, nπ/2] for the least value of n ∈ N, then Σⁿ_k=1 (k/2ⁿ) is equal to?
10. If dy/dx = ( x + y – 2 ) / ( x – y ), and y(0) = 2, then find y(2).
11. Find the 20th term from the end of the progression:
    20, 19(1/4), 18(1/2), 17(3/4), …, -129(1/4)
12. The area bounded by 0 ≤ y ≤ min{2x, 6x – x²} and x-axis is A. then 12A is:

Memory-based Chemistry questions for JEE Main 27 Jan 2024 Shift 2

1. Find the magnetic moment of complex [Pd(NH₃)₂Cl₂].
2. When 9.3 g of aniline is reacted with acetic anhydride, mass of acetanilide obtained is m grams. Find out the value of 2m.
3. Which structure of protein is intact after coagulation of egg white on boiling?
4. What is the molecular formula of the second homologue in the homologous series of monocarboxylic acid?
5. 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
6. 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.
7. Which of the following quantity changes with the temperature?
   i. Mole Fraction
   ii. Mass Percentage
   iii. Molarity
   iv. Molality
8. Which of the following can not act as an oxidising agent?
   i. MnO₄^–
   ii. SO₄^2-
   iii. N^3-
   iv. BrO₃^–
9. What is the technique used for the purification of steam volatile water-immiscible substance?
10. 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
11. 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
12. The reduction potential at pH = 3 for a hydrogen electrode of a standard half cell is?
13. Compare the stability of resonating structures. (A diagrammatic representation of three compounds was given.)
14. How many compound(s) given below have chiral carbon? (A diagrammatic representation of four compounds was given.)
15. 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-
16. For a first-order reaction, t_99.9% = xt_50% Find out the value of x.
17. If the longest wavelength for the Paschen Series in H-atom is α, Find α/7R.
18. 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

How to Download NTA JEE Question Paper 2024 Response Sheet?

The National Testing Agency will release the official Jee Mains 2024 Question Paper all shifts along with the answer key. Aspirants can obtain the jee mains 2024 exam question paper along with their responses sheet at jeemain.nta.ac.in by entering their application number and date of birth. Candidates can get the jee mains 2024 exam question paper using the steps outlined below.

• Visit the official website of JEE Main at jeemain.nta.ac.in.
• On the home page, Click on the JEE Mains Question Paper 2024 link.
• Access the candidate login using the application number and password.
• Download the JEE Main Question Paper 2024 answer key and analyze it.

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