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Day 2: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Determinants. This type asked 19 times: 2021 Paper 4, 2021 Paper 19, 26 Jun 2022, 28 Jun 2022, 27 Jul 2022, 24 Jan 2023, 25 Jan 2023, 8 Apr 2023, 10 Apr 2023, 13 Apr 2023, 15 Apr 2023, 31 Jan 2024, 5 Apr 2024, 6 Apr 2024, 9 Apr 2024, 22 Jan 2025, 2 Apr 2025, 3 Apr 2025, 7 Apr 2025. This one: 7 Apr 2025 See all 19 of this type

    65
    Let AA be a 3×33 \times 3 matrix such that ∣adj(adj(adjA))∣=81|adj(adj(adjA))| = 81. If
    S={n∈Z:(∣adj(adjA)∣)(n−1)22=∣A∣(3n2−5n−4)}S =\left\{ n \in\mathbb{Z}:(|adj(adjA)|)^{\frac{(n- 1)^{2}}{2}}= |A|^{\left( 3n^{2}- 5n- 4 \right)} \right\}
    then ∑n∈S∣A(n2+n)∣\sum_{n\in S}^{} \left| A^{\left( n^{2}+n \right)} \right| is equal to.

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  2. Question 2

    Vector Algebra. This type asked 18 times: 2021 Paper 3, 2021 Paper 6, 2021 Paper 7, 24 Jan 2023, 29 Jan 2023, 31 Jan 2023, 1 Feb 2023, 8 Apr 2023, 13 Apr 2023, 31 Jan 2024, 1 Feb 2024, 5 Apr 2024, 8 Apr 2024, 29 Jan 2025, 3 Apr 2025, 24 Jan 2026 S2, 5 Apr 2026 S1, 8 Apr 2026 S2. This one: 8 Apr 2026 S2 See all 18 of this type

    64
    Let a→=4i^−j^+3k^,b→=10i^+2j^−k^\overrightarrow{a}= 4\widehat{i}-\widehat{j}+ 3\widehat{k},\overrightarrow{b}= 10\widehat{i}+ 2\widehat{j}-\widehat{k} and a vector c→\overrightarrow{c} be such that 2(a→×b→)+3(b→×c→)=0→2(\overrightarrow{a}\times\overrightarrow{b}) + 3(\overrightarrow{b}\times\overrightarrow{c}) =\overrightarrow{0}. If a→⋅c→=15\overrightarrow{a}\cdot\overrightarrow{c}= 15, then c→⋅(i^+j^−3k^)\overrightarrow{c}\cdot (\widehat{i}+\widehat{j}- 3\widehat{k}) is equal to :

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  3. Question 3

    Limits and Continuity. This type asked 16 times: 2021 Paper 10, 2021 Paper 14, 2021 Paper 18, 2021 Paper 22, 2021 Paper 26, 26 Jul 2022, 29 Jul 2022, 27 Jan 2024, 31 Jan 2024, 4 Apr 2024, 23 Jan 2025, 3 Apr 2025, 23 Jan 2026 S1, 23 Jan 2026 S2, 24 Jan 2026 S2, 8 Apr 2026 S2. This one: 8 Apr 2026 S2 See all 16 of this type

    69
    Let f(x)={13,x≤π/2b(1−sin⁡x)(π−2x)2,x>π/2f(x) =\left\{ \begin{matrix} \frac{1}{3} & , & x\leq\pi/2 \\ \frac{b(1 - \sin x)}{(\pi- 2x)^{2}} & , & x>\pi/2 \end{matrix} \right., If ff is continuous at x=π/2x =\pi/2, then the value of ∫03 b−6∣x2+2x−3∣dx\int_{0}^{3\text{ }b - 6} \left| x^{2}+ 2x - 3 \right|dx is :

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  4. Question 4

    Three Dimensional Geometry. This type asked 15 times: 2021 Paper 2, 2021 Paper 7, 2021 Paper 18, 2021 Paper 19, 2021 Paper 20, 2021 Paper 21, 2021 Paper 22, 28 Jun 2022, 26 Jul 2022, 24 Jan 2023, 25 Jan 2023, 1 Feb 2023, 6 Apr 2023, 8 Apr 2023, 13 Apr 2023. This one: 13 Apr 2023 See all 15 of this type

    80
    Let the equation of plane passing through the line of intersection of the planes x+2y+az=2x + 2y + az = 2 and x−y+z=3x - y + z = 3 be 5x−11y+bz=6a−15x - 11y + bz = 6a - 1. For c∈Zc \in Z, if the distance of this plane from the point (a,−c,c)(a, - c,c) is 2a\frac{2}{\sqrt{a}}, then a+bc\frac{a + b}{c} is equal to

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  5. Question 5

    Determinants. This type asked 14 times: 2021 Paper 1, 2021 Paper 21, 2021 Paper 22, 2021 Paper 24, 14 Jun 2022, 25 Jun 2022, 26 Jun 2022, 27 Jun 2022, 28 Jun 2022, 25 Jul 2022, 10 Apr 2023, 23 Jan 2025, 21 Jan 2026 S2, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 14 of this type

    53
    Let α,β∈R\alpha,\beta\in R be such that the system of linear equations
    x+2y+z=5x+ 2y+z= 5
    2x+y+αz=52x+y+\alpha z= 5
    8x+4y+βz=188x+ 4y+\beta z= 18
    has no solution. Then βα\frac{\beta}{\alpha} is equal to :

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