JEE Advanced Maths Questions PYQ with Solutions PDF: 11 Most Difficult Questions in Past 10 Years

1. a = 0, k = 8
2. 4a-k+8=0
3. det(Padj(Q)) = 2⁹
4. det(Qadj(P)) = 2¹³

Ans: B and C

Q3: Let a and ẞ be the roots of x² - x - 1 = 0 a > β. For all positive integers n, define a_n = (αⁿ- βⁿ)/a- β >= 1, b₁ = 1 and b_n = a_n-1+a_n+1, n >= 2. Then which of the following options is/are correct? (JEE Advanced 2019, Paper 1)

1. ^∞∑_n=1 b_n/10ⁿ = 8/89
2. b_n = αⁿ + βⁿ for all n>=1
3. a₁+a₂+a₃+....+a_n = a_n+2 - 1
4. ^∞∑_n=1 a_n/10ⁿ = 10/89

Ans: B, C and D

Q4: Let S_n = ⁴ⁿ∑_k=1(-1)^k(k+1)/2K^2. Then Sn can take value(s). (JEE Advanced 2013, Paper 1)

1. 1056
2. 1088
3. 1120
4. 1332

Ans: A and D

Q5:

(JEE Advanced 2020, Paper 2)

1. g (m, n) = g (n, m) for all positive integers m, n
2. g (m, n+1) = g (m+1, n) for all positive integers m, n
3. g (2m, 2n) = 2g (m, n) for all positive integers m, n
4. g (m,n) = (g (n,m))² for all positive integers m, n

Ans: A, B and D

Q6: Let |X| denote the number of elements in a set X. Let S = {1, 2, 3, 4, 5, 6} be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered pairs (A, B) such that 1≤ |B|<|A|, equals (JEE Advanced 2019, Paper 2)

Ans: 422

Q7: Considering only the principal values of the inverse trigonometric functions, the value of is___________ (JEE Advanced 2022, Paper 1)

Ans: 3π/4

Q8: (JEE Advanced 2016, Paper 2)

1. f(1/2) >= f(1)
2. f(1/3) <= f(2/3)
3. f'(2) <= 0
4. f'(3)/f(3) >= f'(2)/f(2)

Ans: B

Q9: Let ABC be the triangle with AB = 1, AC = 3 and ∠BAC = π/2. If a circle of radius r > 0 touches the sides AB, AC and also touches internally the circumcircle of the triangle ABC, then the value of r is (JEE Advanced 2022, Paper 1)

Ans: 0.83 or 0.84

Q10: Consider the hyperbola x²/100 - y²/64 = 1 with foci at S and S₁, where S lies on the positive x-axis. Let P be a point on the hyperbola, in the first quadrant. Let ∠SPS = α, with a < π/2. The straight line passing through the point s and having the same slope as that of the tangent at P to the hyperbola, intersects the straight line S₁P at P₁. Let δ be the distance of P from the straight line SP₁ and β = S₁P. Then the greatest integer less than or equal to βδ/9.sinα/2 is ____________ (JEE Advanced 2022, Paper 2)

Ans: 7.11

Q11:  Let R³ denote the 3-D space. Take two points P(1, 2, 3) and Q(4, 2, 7). Let dist(X, Y) denote the distance between two points X and Y in R³.

Let S = {X ∈ R³ : (dist(X, P))² - (dist(X, Q))² = 50} and

T = {Y ∈ R³: (dist(Y, Q))² - (dist(Y, P))² = 50}

Then which of the following statements is (are) TRUE? (JEE Advanced 2024, Paper 1)

1. There is a triangle whose area is 1 and all of whose vertices are from S.
2. There are two distinct points Land M in T such that each point on the line segment LM is also in T.
3. There are infinitely many rectangles of perimeter 48, two of whose vertices are from S and the other two vertices are from T.
4. There is a square of perimeter 48, two of whose vertices are from S and the other two vertices are from T.

Ans: All four options are correct

Also Read:

• JEE Advanced Syllabus for Chemistry
• JEE Advanced Syllabus for Physics
• JEE Advanced Syllabus for Mathematics

All JEE Advanced Maths Questions From Previous Years

Above we curated and provided you the most difficult questions in JEE Advanced Maths over the past 10 years as well as JEE Advanced PYQ chapterwise PDF. However, candidates who wish to have all the previous year JEE Advanced maths questions for practice, can download the PDF files below:

JEE Advanced Maths Questions with Solutions 2024 to 2019:

Check below the JEE Advanced Maths questions with solutions PDF:

Also Check:

JEE Advanced Maths Section Overview

Check below the details regarding the JEE Advanced maths section in JEE Advanced question paper followed in the past 2 years. It will help in JEE Advanced Maths preparation for the upcoming exam.

Total Marks in JEE Advanced Maths section: 120

• 60 marks in JEE Advanced paper 1
• 60 marks in JEE Advanced paper 2

In each paper of JEE Advanced, the Maths section has the following sections:

• Sec-I (Max. marks-12)
• Sec-II (Max. Marks-12)
• Sec-III (Max. marks-24)
• Sec-IV (Max. marks-12)

Number of questions and marks distribution in each of the sections is as follows:

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• JEE Advanced Chapter Wise Weightage for Maths, Physics, Chemistry