JEE Toughest Questions Ever

The JEE (Joint Entrance Examination) is a national-level entrance exam for admission to IITs and other leading engineering institutes in India. It is considered one of the toughest exams due to its vast syllabus and high competition, with students appearing every year, including NRI Students in USA and aspirants from the Middle East (UAE).

Even students with a strong academic base may find JEE challenging, which is why structured preparation and proper guidance are important for JEE 2026 and onward, especially for NRI Students in USA and students studying in the Middle East (UAE).

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If you are standing in the ending days of your JEE exam (JEE Main 2026 and onward), let’s go through some tough questions that would be interrupted you on your exam day. Let’s understand this thoroughly so that you would crack it smartly. This is especially helpful for NRI Students in USA and students preparing from the Middle East (UAE) who want final-day mixed practice.

1. For x∈Rx \in Rx∈R, f(x)=∣log2–sinx∣f(x) = |log2 – sinx|f(x)=∣log2–sinx∣ and g(x)=f(f(x))g(x) = f(f(x))g(x)=f(f(x)), then:
   (1) g is differentiable at x = 0 and g'(0) = –sin(log2)
   (2) g is not differentiable at x = 0
   (3) g'(0) = cos(log2)
   (4) g'(0) = –cos(log2)
   Ans. g'(0) = cos(log2)
   
2. If a curve y=f(x)y = f(x)y=f(x) passes through the point (1, –1) and fulfill the given differential equation, y(1+xy)dx=xdyy(1 + xy)dx = xdyy(1+xy)dx=xdy, then f(−1/2)f(-1/2)f(−1/2) is equal to:
   (1) 4/5
   (2) -2/5
   (3) -4/5
   (4) 2/5
   Ans. 4/5
   
3. If the sum of the first ten terms of the series is (13/5) + (13/5) + (13/5) + 4 + (13/5) +…, is (16/5)m, then m is equal to:
   (1) 99
   (2) 102
   (3) 101
   (4) 100
   Ans. 101
   
4. A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then:
   (1) (4-π)x = πr
   (2) x = 2r
   (3) 2x = r
   (4) 2x = (π + 4)r
   Ans. x = 2r
   
5. The pair having the same magnetic moment is: [At. No.: Cr = 24, Mn = 25, Fe = 26, Co = 27]
   (1) [Cr(H2O)6]2+ and [Fe(H2O)6]2+
   (2) [Mn(H2O)6]2+ and [Cr(H2O)6]2+
   (3) [CoCl4]2– and [Fe(H2O)6]2+
   (4) [Cr(H2O)6]2+ and [CoCl4]2–
   Ans. [Cr(H2O)6]2+ and [Fe(H2O)6]2+
   
6. The region between two concentric spheres of radii ‘a’ and ‘b’, respectively, has volume charge density ρ=A/r\rho=A/rρ=A/r, where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:
   (1) Q/[2π(b2-a2)]
   (2) 2Q/[π(b2-a2)]
   (3) 2Q/πa2
   (4) Q/2πa2
   Ans. Q/2πa2
   
7. Which one of the following complexes shows optical isomerism?
   (1) cis[Co(en)2Cl2]Cl
   (2) trans[Co(en)2Cl2]Cl
   (3) [Co(NH3)4Cl2]Cl
   (4) [Co(NH3)3Cl3] (en = ethylenediamine)
   Ans. cis[Co(en)2Cl2]Cl
   
8. A uniform string of length 20m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is: (take g = 10 ms–2)
   (1) 2 s
   (2) 2√2 s
   (3) √2s
   (4) 2π√2 s
   Ans. 2√2 s
   
9. Decomposition of H2O2 follows a first order reaction. In fifty minutes the concentration of H2O2 decreases from 0.5 to 0.125 M in one such decomposition. When the concentration of H2O2 reaches 0.05 M, the rate of formation of O2 will be:
   (1) 6.93×10-4 mol min-1
   (2) 2.66 L min–1 at STP
   (3) 1.34×10-2 mol min-1
   (4) 6.93×10-2 mol min-1
   Ans. 6.93×10-4 (unit depends on volume; strictly this comes out as mol L⁻¹ min⁻¹ unless a reaction volume is specified)

It’s time to prepare the JEE with a great enthusiasm. Never lose hope. May be you will be the part of the top list.

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FAQs

1. What are considered the toughest questions in JEE?

The toughest JEE questions are those that test deep conceptual understanding, multi-step problem-solving, and application across Physics, Chemistry, and Mathematics. Such questions often combine multiple topics and are designed to differentiate top-performing students in highly competitive exam conditions.

2. Are these toughest questions relevant for JEE Main 2026?

Yes, these toughest questions remain relevant for JEE Main 2026 and onward as they reflect the conceptual depth and difficulty level expected in the exam. They are useful for final revision and strengthening problem-solving skills under exam pressure.

3. How should students use toughest JEE questions for preparation?

Students should use toughest JEE questions to identify weak areas, improve analytical thinking, and practise handling complex problems. These questions are best attempted after completing syllabus coverage and are especially effective during last-week or final-phase revision.

4. Are toughest JEE questions equally important for all students?

Toughest JEE questions are most beneficial for students targeting high ranks. However, even average aspirants can benefit by learning advanced approaches and common traps, as these questions improve conceptual clarity and confidence, especially for competitive exam environments.

5. How useful are toughest questions for NRI Students in USA?

For NRI Students in USA, toughest JEE questions provide exposure to Indian exam-style problem-solving, which may differ from international curricula. They help bridge gaps in application-based learning and prepare students effectively for JEE Main 2026 and beyond.

6. Can students from the Middle East (UAE) rely on these questions?

Students from the Middle East (UAE) can use toughest JEE questions as a strong practice resource. These questions help manage time, build exam temperament, and prepare for higher-difficulty problems commonly seen in JEE Main and Advanced-level exams.

7. Do toughest questions repeat in JEE exams?

Exact toughest questions usually do not repeat, but similar concepts, patterns, and difficulty levels often reappear. Practising such questions helps students recognise familiar problem structures and apply learned strategies quickly during the actual JEE exam.

8. Should toughest questions be solved before or after mock tests?

Toughest questions are best solved after attempting mock tests. This allows students to analyse mistakes, improve advanced techniques, and fine-tune their preparation. They work well as a supplement to mock exams rather than a replacement.

9. Are toughest questions more important than basic questions?

Both are important. Basic questions build accuracy and speed, while toughest questions develop depth and rank-improving skills. A balanced approach ensures students are not only confident with fundamentals but also capable of handling challenging problems in JEE Main.

10. How many toughest questions should be practised before JEE?

There is no fixed number, but practising a limited set of high-quality toughest questions from each subject is sufficient. The focus should be on understanding solutions and concepts rather than solving a large volume without proper analysis.