60 Most Important Questions for JEE Advanced 2026: Physics, Chemistry & Math

JEE Advanced is known for its complex, multi-concept problems. To help you prepare, we have curated 60 Must-Solve Questions (20 per subject) that cover the highest-weightage topics for 2026.

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Section 1: Physics (Top 20 Questions)

Focus: Mechanics, Electrodynamics & Modern Physics

1. Question (Rotational Motion): A solid sphere of mass $M$ and radius $R$ rolls without slipping down an inclined plane of height $H$. Find its linear velocity at the bottom.

   • Solution: By conservation of energy: $MgH = \frac{1}{2}Mv^2 + \frac{1}{2}I\omega^2$. Since $I = \frac{2}{5}MR^2$ and $\omega = v/R$, we get $MgH = \frac{1}{2}Mv^2 + \frac{1}{5}Mv^2 = \frac{7}{10}Mv^2$. Thus, $v = \sqrt{\frac{10gH}{7}}$.

2. Question (Electrostatics): Two point charges $+q$ and $-q$ are placed at distance $d$. Find the work done in bringing a charge $+Q$ from infinity to the midpoint.

   • Solution: Potential at midpoint due to $+q$ and $-q$ is $V = \frac{kq}{d/2} + \frac{k(-q)}{d/2} = 0$. Work done $W = Q \times \Delta V = Q(0 - 0) = 0$.

3. Question (Modern Physics): The half-life of a radioactive substance is 10 days. How long will it take for 75% of the substance to decay?

   • Solution: 75% decay means 25% (or 1/4) remains. $N/N_0 = (1/2)^n$, so $1/4 = (1/2)^n \Rightarrow n = 2$. Total time $t = n \times T_{1/2} = 2 \times 10 = 20$ days.

[...Remaining 17 questions follow similar high-impact patterns involving EMI, Optics, and Fluid Mechanics...]

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Section 2: Chemistry (Top 20 Questions)

Focus: Organic Mechanisms, Coordination & Kinetics

1. Question (Chemical Kinetics): For a first-order reaction $A \rightarrow B$, the rate constant $k$ is $0.693 , \text{min}^{-1}$. Find the time required for 90% completion.

   • Solution: $t = \frac{2.303}{k} \log \frac{a}{a-x}$. $t = \frac{2.303}{0.693} \log \frac{100}{10} = \frac{2.303}{0.693} \times 1 \approx 3.32$ min. (Note: $k = \ln 2 \approx 0.693$).

2. Question (Coordination Compounds): Predict the hybridization and geometry of $[Ni(CN)_4]^{2-}$.

   • Solution: $Ni^{2+}$ is $d^8$. $CN^-$ is a strong field ligand, causing pairing. This leaves one $d$, one $s$, and two $p$ orbitals for hybridization ($dsp^2$). Geometry: Square Planar.

3. Question (Organic Chemistry): What is the major product when Propene reacts with $HBr$ in the presence of Peroxide?

   • Solution: This follows Anti-Markovnikov’s rule via free radical mechanism. The major product is 1-Bromopropane.

[...Remaining 17 questions cover GOC, Thermodynamics, p-block trends, and Biomolecules...]

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Section 3: Mathematics (Top 20 Questions)

Focus: Calculus, Probability & Matrices

1. Question (Calculus - Integration): Evaluate $\int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} dx$.

   • Solution: Let $I = \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} dx$. Using property $\int_{0}^{a} f(x) = \int_{0}^{a} f(a-x)$, we get $I = \int_{0}^{\pi/2} \frac{\cos x}{\cos x + \sin x} dx$. Adding both: $2I = \int_{0}^{\pi/2} 1 dx = \pi/2 \Rightarrow I = \pi/4$.

2. Question (Probability): If $P(A) = 0.6$, $P(B) = 0.4$, and $P(A \cap B) = 0.2$, are A and B independent?

   • Solution: For independence, $P(A) \times P(B) = P(A \cap B)$. Here $0.6 \times 0.4 = 0.24 \neq 0.2$. Hence, they are Not Independent.

3. Question (Matrices): If $A$ is an idempotent matrix, find $(I+A)^n$.

   • Solution: $A^2 = A$. $(I+A)^2 = I + 2A + A^2 = I + 3A$. By induction, $(I+A)^n = I + (2^n - 1)A$.

[...Remaining 17 questions cover Limits, Vectors 3D, Conics, and Quadratic Equations...]

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Download the Full PDF Guide

Since JEE Advanced involves deep derivations, we recommend practicing these 60 questions on paper first.

👉 Download Full 60 Questions + Detailed Steps PDF

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Final Pro-Tip for JEE Advanced

Don't just look at the solution. Try to solve each question for at least 15 minutes before checking the answer. JEE Advanced is about the journey of solving, not just reaching the final number.

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