JEE Advanced Maths Questions with Solutions: 11 Most Difficult Questions in Past 10 Years, Download PDF Here

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:

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. 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:

Year	JEE Advanced Maths questions with solutions
2024	Paper 1 - Download here Paper 2 - Download here
2023	Paper 1 - Download PDF Paper 2 - Download PDF
2022	Paper 1 - Download PDF Paper 2 - Download PDF
2021	Paper 1 - Download PDF Paper 2 - Download PDF
2020	Paper 1 - Download PDF Paper 2 - Download PDF
2019	Paper 1 - Download PDF Paper 2 - Download PDF

Also Check:

JEE Advanced Physics Questions

JEE Advanced Chemistry Questions

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:

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:

Section	Number of questions and total marks	Marking Scheme
1	4 questions of 12 marks	+3 If ONLY the correct option is chosen 0 If none of the options is chosen (i.e. the question is unanswered) -1 in all other cases
2	3 questions of 12 marks	+4 ONLY if (all) the correct option(s) is(are) chosen +3 If all four options are correct but ONLY three options are chosen +2 If three or more options are correct but ONLY two options are chosen, both of which are correct +1 If two or more options are correct but ONLY one option is chosen and it is a correct option 0 If none of the options is chosen (i.e. the question is unanswered) -2 In all other cases
3	6 questions of 24 marks	+4 for the correct answer 0 for no attempts
4	4 questions of 12 marks	+3 If ONLY the correct option is chosen 0 If none of the options is chosen (i.e. the question is unanswered) -1 for the wrong attempts

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