9 Most Difficult Questions in JEE Main with Answers

Most Difficult Questions in JEE Main covers organic and inorganic chemistry, electrostatics, mechanics, differential equations, thermodynamics, optics, etc. Candidates must practise these topics and other physics, chemistry and mathematics chapters to gain good scores in the JEE main exam. 

Further, they must understand the JEE main syllabus thoroughly along with the JEE main exam pattern for a better understanding of the question paper for each subject.

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Top 9 Most Difficult Questions in JEE Main

In the JEE Main syllabus there are numerous chapters and each chapter has concepts that are important for the examinees. Yet, there are some sets of questions that are the most difficult questions in the JEE main exam paper. 

Students can go through the most difficult questions in JEE Main given below.

Q1. 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

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Q2. For x∈R, f(x) = |log2 – sinx| and 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)

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Q3. If a curve y = f(x) passes through the point (1, –1) and fulfill the given differential equation, y(1 + xy) dx = x dy, then f(-1/2) is equal to:

1. 4/5
2. -2/5
3. -4/5
4. 2/5

Ans. ⅘

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Q4. 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+

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Q5. A wire of length two units is cut into two parts, 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. 2r

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Q6. 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

Also Check: JEE Main Model Questions with Solutions - Download PDF

Q7. The region between two concentric spheres of radii ‘a’ and ‘b’ has volume charge density ρ=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

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Q8. The 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 mol min-1

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Q9. 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

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