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Day 28: JEE Mains Maths

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

  1. Question 1

    Matrices. This type asked 5 times: 2021 Paper 10, 29 Jan 2023, 6 Apr 2023, 2 Apr 2025, 4 Apr 2025. This one: 4 Apr 2025 See all 5 of this type

    136
    Let the matrix A=[100101010]A=\begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix} satisfy An=An−2+A2−A^{n}=A^{n- 2}+A^{2}- I for n≥3n \geq 3. Then the sum of all the elements of A50A^{50} is :-

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  2. Question 2

    Sequences and Series. This type asked 5 times: 6 Apr 2023, 8 Apr 2023, 10 Apr 2023, 30 Jan 2024, 3 Apr 2025. This one: 3 Apr 2025 See all 5 of this type

    57
    The sum 1+3+11+25+45+71+…1 + 3 + 11 + 25 + 45 + 71 + \ldots upto 20 terms, is equal to

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  3. Question 3

    Application of Integrals. This type asked 5 times: 26 Jun 2022, 26 Jul 2022, 10 Apr 2023, 13 Apr 2023, 2 Apr 2025. This one: 2 Apr 2025 See all 5 of this type

    73
    If the area of the region {(x,y):∣4−x2∣≤y≤x2,y≤4,x≥0}\left\{ (x,y):\left| 4 - x^{2} \right| \leq y \leq x^{2},y \leq 4,x \geq 0 \right\} is (802α−β),α,β∈N\left( \frac{80\sqrt{2}}{\alpha} - \beta \right),\alpha,\beta \in N, then α+β\alpha + \beta is equal to.

  4. Question 4

    Binomial Theorem. This type asked 5 times: 2021 Paper 5, 2021 Paper 15, 11 Apr 2023, 30 Jan 2024, 29 Jan 2025. This one: 29 Jan 2025 See all 5 of this type

    58
    The least value of n for which the number of integral terms in the Binomial expansion of (73+1112)n(\sqrt[3]{7}+\sqrt[12]{11})^{n} is 183, is :

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  5. Question 5

    Determinants. This type asked 5 times: 2021 Paper 3, 2021 Paper 12, 30 Jan 2023, 23 Jan 2025, 29 Jan 2025. This one: 29 Jan 2025 See all 5 of this type

    136
    Let α,β(α≠β)\alpha,\beta(\alpha \neq \beta) be the values of m , for which the equations x+y+z=1;x+2y+4z=mx + y + z = 1;x + 2y + 4z = m and x+4y+10z=m2x + 4y + 10z =m^{2} have infinitely many solutions. Then the value of ∑n=110(nα+nβ)\sum_{n = 1}^{10} \left( n^{\alpha}+n^{\beta} \right) is equal to :

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