| Updated On - Nov 9, 2024
JEE Main 30 Jan Shift 2 2024 question paper with solutions and answers pdf is available here. NTA conducted JEE Main 2024 Jan 30 Shift 2 exam from 3 PM to 6 PM. The question paper for JEE Main 2024 Jan 30 Shift 2 includes 90 questions equally divided into Physics, Chemistry and Maths. Candidates must attempt 75 questions in a 3-hour time duration. The memory-based JEE Main 2024 question paper pdf for the Jan 30 Shift 2 exam will be available for download using the link below.
To check JEE Main 2024 Session 2 Question Paper and Solutions, Click Here
JEE Main 30 Jan Shift 2 2024 Question Paper PDF Download
| JEE Main 2024 Question Paper PDF | JEE Main 2024 Answer Key PDF | JEE Main 2024 Solutions ODF |
|---|---|---|
| Download PDF | Download PDF | Download PDF |
JEE Main 30 Jan Shift 2 2024 Questions with Solution
| Question Number | Question | Answer | Solution |
|---|---|---|---|
| 1 | Consider the system of linear equations x + y + z = 5, x + 2y + 2z = 9, x + 3y + λz = µ, where λ, µ ∈ R. Then, which of the following statements is NOT correct? | (4) System has unique solution if λ = 1 and µ ≠ 13 | Convert the system to matrix form and perform row reduction: (steps omitted for brevity) |
| 2 | For α, β ∈ (0, π/2), let 3 sin(α + β) = 2 sin(α − β), and a real number k be such that tanα = k tan β. Then the value of k is equal to: | (2) k = −5 | Using trigonometric identities, expand sin(α + β) and sin(α− β): sin(α + β) = sinα cos β + cosα sin β, sin(α− β) = sinα cos β − cosα sin β (steps omitted for brevity) |
| 3 | Let A(10, 0) and B(0, β) be the points on the line 5x + 7y = 50. Let the point P divide the line segment AB internally in the ratio 7 : 3. Let 3x−25 = 0 be a directrix of the ellipse x²/a² + y²/b² = 1 and the corresponding focus be S. | (4) 32/5 | Substitute x = 0 and y = β in the line equation 5x+ 7y = 50 to find β: 7β = 50 ⇒ β = 50/7. Using the section formula, P = (3, 5) (steps omitted for brevity) |
| 4 | The variance σ² of the data xi 0 1 5 6 10 12 17 with frequencies fi 3 2 3 2 6 3 3. | (4) 29.09 | Calculate sums ∑fi, ∑fixi, and ∑fix²i to find variance σ²: σ² = 29.09. |
| 5 | A potential difference V is applied across a wire of resistance R, resulting in dissipation W. If the wire is halved and connected in parallel across the same supply, find the new dissipation. | (4) 4W | Dissipation is inversely proportional to resistance. After halving and paralleling, Req = R/4, leading to P' = 4W. |
| 6 | Let A(10,0) and B(0,β) be points on the line 5x+7y=50, with P dividing AB in ratio 7:3. Find the length of latus rectum of ellipse passing through S. | (4) 32/5 | Find β by substitution; use section formula for P coordinates; derive latus rectum length. |
| 7 | Let a⃗ and b⃗ be vectors with |b⃗| = 1 and |b⃗× a⃗| = 2. Find |(b⃗× a⃗)− b⃗|². | (2) 5 | Apply vector magnitudes and cross products; simplifying, |(b⃗× a⃗)− b⃗|² = 5. |
| 8 | For four consecutive terms in the expansion of (1 + x)^n, suppose coefficients 2-p, p, 2-α, α exist. Find p² − α² + 6α + 2p. | (2) 10 | Set up equations with binomial coefficients; solve for p and α. Calculate expression value as 10. |
| 9 | Evaluate the integral ∫ 4√3 to 8√3 of x³g(x) dx given g(x) = f(f(f(x))) for f(x) = x / (1 + x⁴)^(1/4). | (4) 39 | Use substitution and nested function properties; integrate resulting form to find 39. |
| 10 | For domain f(x) = log((2x+3)/(4x²+x−3)) + cos⁻¹((2x−1)/(x+2)), with (α, β] as domain limits, find 5β − 4α. | (2) 12 | Determine domains of log and cos⁻¹ parts; intersect for overall domain. Calculate expression as 12. |
| 11 | Bag A contains 3 white, 7 red balls, and bag B contains 3 white, 2 red balls. One bag is selected at random, and a ball is drawn from it. The probability of drawing the ball from bag A, if the ball drawn is white, is: | (3) 1/3 | Using Bayes' theorem: P(E1|E) = P(E|E1) * P(E1) / (P(E|E1) * P(E1) + P(E|E2) * P(E2)). Substituting, P(E1|E) = 1/3. |
| 12 | Let f : R → R be defined by f(x) = ae²ˣ + beˣ + c. If f(0) = -1, f′(logₑ 2) = 21, and ∫ logₑ 4 0 (f(x) − cx) dx = 39/2, then determine f(x). | (4) Complex result; derived using calculus and function properties | Given values allow construction of system of equations solved to yield correct f(x) form. |
| 13 | For α, β ∈ (0, π/2), let 3 sin(α + β) = 2 sin(α − β), and a real number k such that tanα = k tan β. Then the value of k is: | (2) -5 | Using trigonometric identities, expand sin(α + β) and sin(α − β); solve for k as -5. |
| 14 | The coordination geometry around the manganese in decacarbonylmanganese(0) is: | (1) Octahedral | Coordination number and arrangement of ligands suggest octahedral geometry. |
| 15 | If z is a complex number, then the number of common roots of the equations z¹⁹⁸⁵ + z¹⁰⁰ + 1 = 0 and z² + z + 1 = 0 is: | (3) 0 | Roots analysis using complex roots of unity reveals no common roots. |
| 16 | Suppose 2−p, p, 2−α, α are the coefficients of four consecutive terms in the expansion of (1 + x)ⁿ. Then p² − α² + 6α + 2p equals: | (2) 10 | Use binomial expansion and sequence formulas to solve. |
| 17 | Let P be a point on the hyperbola H: x²/9 − y²/4 = 1, in the first quadrant such that the area of the triangle formed by P and the two foci of H is √13. Then the square of the distance of P from the origin is: | (3) 22 | Use hyperbolic geometry properties and area calculation. |
| 18 | If the domain of the function f(x) = logₑ ((2x+3)/(4x²+x−3)) + cos⁻¹((2x−1)/(x+2)) is (α, β], then 5β − 4α equals: | (2) 12 | Intersection of domain conditions gives correct range for function. |
| 19 | Let f : R → R be defined by f(x) = x / (1 + x⁴)^(1/4) and g(x) = f(f(f(x))). Then ∫ 4√3 8√3 x³g(x) dx equals: | (4) 39 | Nested function integral solved with substitution and simplification. |
| 20 | For R = (x 0 0 / 0 y 0 / 0 0 z), let V = x + y + z and determine if diagonal entries are nonzero. | (Answer determined by specific matrix characteristics) | Calculation with specified matrix properties yields correct value. |
| 21 | Let Y = Y(X) be a curve lying in the first quadrant such that the area enclosed by the line Y − y = Y′(x)(X − x) and the coordinate axes is A = - y² / (2Y′(x)) + 1. If Y(1) = 1, then 12Y(2) equals: | 20 | Differentiate and use initial condition to solve for Y(2). Result is 20. |
| 22 | A line passing through point (−1, 2, 3) intersects lines L1 and L2 at M and N. Then the value of (α + β + γ)² / (a + b + c) equals: | 196 | Use parametric forms and simultaneous equations for intersection points, giving 196. |
| 23 | For circles C1: x²+y² = 25 and C2: (x−α)² + y² = 16, with α ∈ (5,9), find angle between two radii drawn to each circle. | sin⁻¹(√63 / 8) | Calculate intersection and apply angle formula for radius vectors. |
| 24 | If f(x) is defined on [-5, 5], tangents at (1, f(1)) and (3, f(3)) make angles π/6 and π/4. Evaluate 2 ∫ ((f'(t))² + 1) f''(t) dt: | 26 | Integrate using given conditions and derivatives to find α + β = 26. |
| 25 | Calculate variance σ² for data xi and fi. | 29.09 | Compute ∑fix²i and mean, followed by variance formula application for σ² = 29.09. |
| 26 | If 50 Vernier divisions equal 49 main scale divisions of a microscope, and smallest main scale reading is 0.5 mm, the Vernier constant is: | 0.01 mm | Calculate using VC = 1 MSD − 1 VSD, obtaining 0.01 mm. |
| 27 | A 1 kg block pushed up an inclined surface by 10 N force over 10 m distance. Work done against friction: | 5 J | Using Work = µk × N × d, obtain work done as 5 J. |
| 28 | For the photoelectric effect, what does the slope of Ek vs. frequency graph represent? | Planck's constant | The slope, representing h, relates to photon energy per frequency. |
| 29 | For f(x) = (x+3)(x−2)²(x+1), x ∈ [-4,4], calculate M − m. | 608 | Critical points evaluated at M=392, m=-216, yielding M - m = 608. |
| 30 | Stability order of hydrides in group 15 is: | NH3 > PH3 > AsH3 > SbH3 > BiH3 | Order is based on increasing atomic size and bond dissociation energy down the group. |
| 31 | If 50 Vernier divisions equal 49 main scale divisions of a microscope with smallest main scale reading 0.5 mm, calculate the Vernier constant. | (4) 0.01 mm | Vernier constant (VC) = MSD - VSD = 0.5 mm - 0.49 mm = 0.01 mm. |
| 32 | A 1 kg block is pushed up an incline by 10 N over 10 m. Calculate the work against friction. | (2) 5 J | Work = µk × N × d, yielding 5 J. |
| 33 | Photoelectric effect: Slope of Ek vs. frequency graph represents: | (4) Planck's constant | The slope of Ek vs. frequency graph equals Planck's constant (h). |
| 34 | Heating ice at -10°C to steam at 100°C involves: | (4) Correct graph represents phase changes | Stages: ice warms, melts, water warms, boils, steam warms; flat sections for phase changes. |
| 35 | In nuclear fission, speed of daughter nuclei in terms of mass defect ∆M: | (3) c√(2∆M/M) | Using E = mc², derive v = c√(2∆M/M). |
| 36 | Processes A & B: correct statements for PV relations. | (1 & 3) PVⁿ = k (B), PV = k (A) | Isothermal (A): PV = k; Adiabatic (B): PVⁿ = k. |
| 37 | An electron in nth Bohr orbit has magnetic moment µ. Find x if µn = µ. | (2) x = 1 | µₙ/µ₁ = n²; for n = 1, x = 1. |
| 38 | An AC voltage 220 sin 100t V applied to a 50Ω load. Time for current to rise from half to peak. | (2) 3.3 ms | Calculate with trigonometric functions; Δt ≈ 3.3 ms. |
| 39 | A 1 kg block on a surface y = x² with µ = 0.5. Max height without slipping. | (1) 1/4 m | Balance forces; max height h = 1/4 m. |
| 40 | Total energy of 6.48×10⁵ J to a surface; find momentum. | (2) 2.16×10⁻³ kg·m/s | p = E/c; substituting values, p = 2.16×10⁻³ kg·m/s. |
| 41 | A beam of unpolarised light of intensity I₀ passes through Polaroid A and then Polaroid B at a 45° angle. The intensity of emergent light is: | (1) I₀/4 | After the first polaroid, intensity is I₀/2; second polaroid reduces it to I₀/4 due to cos²(45°). |
| 42 | Consider the function f(x) = logₑ ((2x+3)/(4x²+x−3)) + cos⁻¹((2x−1)/(x+2)). Find 5β - 4α for its domain limits (α, β]. | (2) 12 | Analyze each function part's domain and intersect them, yielding (3/4, 3] and result 5β - 4α = 12. |
| 43 | If three moles of a monoatomic gas (γ = 5/3) are mixed with two moles of a diatomic gas (γ = 7/5), calculate γ for the mixture. | (3) 1.52 | Using γ_mix formula, weighted γ yields γ ≈ 1.52 for the mixture. |
| 44 | Find tensions T₁ and T₂ if a 10 kg mass is pulled by 80 N on a smooth surface in a three-block system. | (1) T₁ = 40 N, T₂ = 64 N | Apply F=ma to each block in sequence to calculate T₁ and T₂. |
| 45 | Voltage across a load RL in a circuit with resistances and input voltage 15V. | (1) 8.75 V | Use voltage division rule with equivalent resistance calculation, yielding 8.75 V across RL. |
| 46 | In a large water droplet formed by 1000 small drops, find ratio E₁:E₂ if E₂ is the surface energy of the big drop. | 10:1 | Calculate each energy using surface area, and find E₁:E₂ as 10:1. |
| 47 | For an AC voltage applied to a 50Ω resistor, find time for current rise from half to peak. | (2) 3.3 ms | Calculate time using sinusoidal waveform properties, resulting in 3.3 ms. |
| 48 | If resistance R is cut in half and halves are parallel, find new dissipation rate. | (4) 4W | Equivalent resistance becomes R/4, quadrupling power dissipation to 4W. |
| 49 | Match Gauss's law and Faraday's law with their expressions. | Gauss: ∮E·da = Q/ε₀, Faraday: ∮E·dl = -dΦ/dt | Recognize key electromagnetic laws and match to expressions. |
| 50 | In a circuit with transformers, calculate output current given 90% efficiency and specified values. | 45 A | Use power conservation and efficiency to find I_out = 45 A. |
JEE Main 2024 Jan 30 Shift 2 Question Paper by Coaching Institute
| Coaching Institutes | Question Paper with Solutions PDF |
|---|---|
| Aakash BYJUs | Download PDF |
| Reliable Institute | Physics Chemistry |
| Resonance | Physics Chemistry Maths |
| Vedantu | Download PDF |
| Sri Chaitanya | To be updated |
| FIIT JEE | To be updated |
JEE Main 30 Jan Shift 2 2024 Paper Analysis
JEE Main 2024 Jan 30 Shift 2 paper analysis for B.E./ B.Tech is updated here with details on the difficulty level of the exam, topics with the highest weightage in the exam, section-wise difficulty level, etc. after the conclusion of the exam.
JEE Main 2024 Question Paper Pattern
| Feature | Question Paper Pattern |
|---|---|
| Examination Mode | Computer-based Test |
| Exam Language | 13 languages (English, Hindi, Assamese, Bengali, Gujarati, Kannada, Malayalam, Marathi, Odia, Punjabi, Tamil, Telugu, and Urdu) |
| Number of Sections | Three- Physics, Chemistry, Mathematics |
| Exam Duration | 3 hours |
| Sectional Time Limit | None |
| Total Marks | 300 marks |
| Total Number of Questions Asked | 90 Questions |
| Total Number of Questions to be Answered | 75 questions |
| Type of Questions | MCQs and Numerical Answer Type Questions |
| Section-wise Number of Questions | Physics- 20 MCQs and 10 numerical type, Chemistry- 20 MCQs and 10 numerical type, Mathematics- 20 MCQs and 10 numerical type |
| Marking Scheme | +4 for each correct answer |
| Negative Marking | -1 for each incorrect answer |
Read More:
- JEE Main 2024 question paper pattern and marking scheme
- Most important chapters in JEE Mains 2024, Check chapter wise weightage here
JEE Main 2024 Question Paper Session 1 (January)
Those appearing for JEE Main 2024 can use the links below to practice and keep track of their exam preparation level by attempting the shift-wise JEE Main 2024 question paper provided below.
| Exam Date and Shift | Question Paper PDF |
|---|---|
| JEE Main 24 Jan Shift 2 2024 Question Paper | Check Here |
| JEE Main 27 Jan Shift 1 2024 Question Paper | Check Here |
| JEE Main 27 Jan Shift 2 2024 Question Paper | Check Here |
| JEE Main 29 Jan Shift 1 2024 Question Paper | Check Here |
| JEE Main 29 Jan Shift 2 2024 Question Paper | Check Here |
| JEE Main 30 Jan Shift 1 2024 Question Paper | Check Here |
| JEE Main 31 Jan Shift 1 2024 Question Paper | Check Here |
| JEE Main 31 Jan Shift 2 2024 Question Paper | Check Here |
| JEE Main 1 Feb Shift 1 2024 Question Paper | Check Here |
| JEE Main 1 Feb Shift 2 2024 Question Paper | Check Here |
JEE Main Previous Year Question Paper
JEE Main Questions
1. To determine the resistance \( R \) of a wire, a circuit is designed below. The V-I characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in the figure. The value of \( R \) is \( \dots \dots \dots \Omega \).
To determine the resistance \( R \) of a wire, a circuit is designed below. The V-I characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in the figure. The value of \( R \) is \( \dots \dots \dots \Omega \).
2. Monochromatic light of wavelength \( 500 \, \text{nm} \) is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index \( = 1.5 \)), the central maximum is shifted to a position previously occupied by the 4\textsuperscript{th} bright fringe. The thickness of the glass plate is ___________ \( \mu \text{m} \).
Monochromatic light of wavelength \( 500 \, \text{nm} \) is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index \( = 1.5 \)), the central maximum is shifted to a position previously occupied by the 4\textsuperscript{th} bright fringe. The thickness of the glass plate is ___________ \( \mu \text{m} \).
3. A force \( (3x^2 + 2x - 5) \, \text{N} \) displaces a body from \( x = 2 \, \text{m} \) to \( x = 4 \, \text{m} \). The work done by this force is _________ J.
A force \( (3x^2 + 2x - 5) \, \text{N} \) displaces a body from \( x = 2 \, \text{m} \) to \( x = 4 \, \text{m} \). The work done by this force is _________ J.
4. UV light of 4.13 eV is incident on a photosensitive metal surface having work function 3.13 eV. The maximum kinetic energy of ejected photoelectrons will be
UV light of 4.13 eV is incident on a photosensitive metal surface having work function 3.13 eV. The maximum kinetic energy of ejected photoelectrons will be
- 4.13 eV
- 1 eV
- 3.13 eV
- 7.26 eV
5. A spherical ball of radius \( 1 \times 10^{-4} \, \text{m} \) and density \( 10^5 \, \text{kg/m}^3 \) falls freely under gravity through a distance \( h \) before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of \( h \) is approximately: \[ \text{(The coefficient of viscosity of water is } 9.8 \times 10^{-6} \, \text{N s/m}^2 \text{)} \]
A spherical ball of radius \( 1 \times 10^{-4} \, \text{m} \) and density \( 10^5 \, \text{kg/m}^3 \) falls freely under gravity through a distance \( h \) before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of \( h \) is approximately: \[ \text{(The coefficient of viscosity of water is } 9.8 \times 10^{-6} \, \text{N s/m}^2 \text{)} \]
- 2296 m
- 2249 m
- 2518 m
- 2396 m
6. At room temperature (\( 27^\circ\text{C} \)), the resistance of a heating element is \( 50 \, \Omega \). The temperature coefficient of the material is \( 2.4 \times 10^{-4} \, ^\circ\text{C}^{-1} \). The temperature of the element, when its resistance is \( 62 \, \Omega \), is _________\(\degree C\).
At room temperature (\( 27^\circ\text{C} \)), the resistance of a heating element is \( 50 \, \Omega \). The temperature coefficient of the material is \( 2.4 \times 10^{-4} \, ^\circ\text{C}^{-1} \). The temperature of the element, when its resistance is \( 62 \, \Omega \), is _________\(\degree C\).
Comments