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Day 473: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 22 Jan 2026 S1

    63
    If A=[2335]A =\begin{bmatrix} 2 & 3 \\ 3 & 5 \end{bmatrix}, then the determinant of the matrix ( A2025−3 A2024+A2023A^{2025}- 3{\text{ }A}^{2024}+A^{2023} ) is

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  2. Question 2

    Permutations and Combinations. Asked once: 2 Apr 2025

    141
    The number of ways, in which the letters A,B,CA,B,C, D , E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is :

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  3. Question 3

    Probability. Asked once: 29 Jan 2025

    140
    Let A=[aij]A =\left\lbrack a_{ij} \right\rbrack be a 2×22 \times 2 matrix such that aij∈{0,1}a_{ij}\mathbf{\in \{ 0,1\}} for all i and j . Let the random variable X denote the possible values of the determinant of the matrix AA. Then, the variance of X is:

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  4. Question 4

    Quadratic Equations. Asked once: 23 Jan 2026 S1

    58
    If α\alpha and β(α<β)\beta(\alpha < \beta) are the roots of the equation (−2+3)(∣x−3∣)+(x−6x)+(9−23)=0( - 2 +\sqrt{3})(|\sqrt{x}- 3|) + (x - 6\sqrt{x}) + (9 - 2\sqrt{3}) = 0, x≥0x \geq 0, then βα+αβ\sqrt{\frac{\beta}{\alpha}}+\sqrt{\alpha\beta} is equal to :

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  5. Question 5

    Relations and Functions. Asked once: 28 Jan 2025

    139
    Let f:[0,3]→f:\lbrack 0,3\rbrack \rightarrow A be defined by f(x)=2x3−15x2+36x+7f(x) = 2x^{3}- 15x^{2}+ 36x + 7 and g:[0,∞)→Bg:\lbrack 0,\infty) \rightarrow B be defined by g(x)=x2025x2025+1g(x) =\frac{x^{2025}}{x^{2025}+ 1}. If both the functions are onto and S={x∈Z:x∈A\mathbf{S = \{ x \in Z:x \in A} or x∈B}x \in B\}, then n(S)n(S) is equal to :

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