These 10 sample questions reflect the style and difficulty of JEE Advanced across Physics, Chemistry, and Mathematics. Each question is followed by a step-by-step solution that explains the reasoning — not just the final answer. Use them to gauge your preparation level and identify areas to strengthen.
Physics
Question 1 (Mechanics)
A block of mass 2 kg slides down a frictionless incline of height 5 m and then moves on a rough horizontal surface with coefficient of kinetic friction 0.4. How far does it travel on the horizontal surface before stopping?
Solution:
- Potential energy at top = mgh = 2 × 10 × 5 = 100 J.
- This converts entirely to kinetic energy at the bottom: KE = 100 J.
- On the rough surface, friction force = μmg = 0.4 × 2 × 10 = 8 N.
- Work done by friction = force × distance = 8 × d.
- This equals the kinetic energy: 8d = 100 → d = 12.5 m.
Question 2 (Electromagnetism)
A circular loop of radius 0.1 m carries a current of 5 A. Find the magnetic field at its center.
Solution:
- Magnetic field at center of a circular loop = μ₀I / (2R).
- μ₀ = 4π × 10⁻⁷ T·m/A.
- B = (4π × 10⁻⁷ × 5) / (2 × 0.1) = (20π × 10⁻⁷) / 0.2 = 100π × 10⁻⁷ = 3.14 × 10⁻⁵ T.
Question 3 (Thermodynamics)
An ideal gas undergoes an isothermal expansion at 300 K from 2 L to 5 L. If the initial pressure is 3 atm, find the work done by the gas (in Joules). (1 atm·L = 101.3 J)
Solution:
- For isothermal process: W = nRT ln(V₂/V₁).
- First find n: PV = nRT → n = PV/RT = (3 × 2) / (0.0821 × 300) ≈ 0.243 mol.
- W = 0.243 × 8.314 × 300 × ln(5/2) ≈ 0.243 × 2494.2 × 0.9163 ≈ 555 J.
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Chemistry
Question 4 (Physical Chemistry)
The rate constant for a first-order reaction is 0.0231 min⁻¹. What is the half-life?
Solution:
- For first-order: t₁/₂ = ln2 / k = 0.693 / 0.0231 ≈ 30.0 min.
Question 5 (Organic Chemistry)
Identify the product when benzene is treated with CH₃Cl in the presence of anhydrous AlCl₃.
Solution:
- This is Friedel-Crafts alkylation.
- The electrophile is CH₃⁺ generated from CH₃Cl and AlCl₃.
- Product: toluene (methylbenzene).
Question 6 (Inorganic Chemistry)
What is the geometry and magnetic moment of [Ni(CN)₄]²⁻? (Atomic number of Ni = 28)
Solution:
- Ni²⁺: [Ar] 3d⁸. CN⁻ is a strong field ligand → causes pairing.
- Hybridization: dsp² → square planar.
- All electrons paired → diamagnetic, magnetic moment = 0 BM.
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Mathematics
Question 7 (Calculus)
Find the derivative of f(x) = x³ sin(x).
Solution:
- Use product rule: f'(x) = 3x² sin(x) + x³ cos(x).
Question 8 (Algebra)
If the sum of the roots of the quadratic equation 2x² - 4x + k = 0 is 2, find k.
Solution:
- Sum of roots = -(-4)/2 = 2 → always true for this equation.
- Product of roots = k/2.
- No additional condition given, so k can be any real number. But typically JEE expects you to note that the sum is independent of k.
Question 9 (Coordinate Geometry)
Find the distance between the lines 3x + 4y - 5 = 0 and 3x + 4y + 10 = 0.
Solution:
- Lines are parallel. Distance = |c₂ - c₁| / √(a² + b²) = |10 - (-5)| / √(9+16) = 15/5 = 3 units.
Question 10 (Probability)
A bag contains 3 red and 5 blue balls. Two balls are drawn without replacement. What is the probability that both are red?
Solution:
- P(first red) = 3/8.
- P(second red | first red) = 2/7.
- P(both red) = (3/8) × (2/7) = 6/56 = 3/28.