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Day 553: JEE Mains Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 2021 Paper 9

    88
    If f(x)=∫5x8+7x6(x2+1+2x7)2 dxf(x)=\int\dfrac{5x^{8}+7x^{6}}{\left(x^{2}+1+2x^{7}\right)^{2}}\,dx, (x≥0)(x\geq 0), f(0)=0f(0)=0 and f(1)=1Kf(1)=\dfrac{1}{K}, then the value of KK is

  2. Question 2

    Limits and Continuity. Asked once: 28 Jun 2022

    174
    If lim⁡x→1sin⁡(3x2−4x+1)−x2+12x3−7x2+ax+b=−2\lim_{x\rightarrow 1} \frac{\sin\left( 3x^{2}- 4x+ 1 \right)-x^{2}+ 1}{2x^{3}- 7x^{2}+ax+b}= - 2, then the value of (a−b)(a-b) is equal to

  3. Question 3

    Matrices. Asked once: 29 Jan 2023

    177
    Let AA be a symmetric matrix such that ∣A∣=2|A| = 2 and [21332]A−[12αβ]\begin{bmatrix} 2 & 1 \\ 3 & \frac{3}{2} \end{bmatrix}A -\begin{bmatrix} 1 & 2 \\ \alpha & \beta \end{bmatrix}. If the sum of the diagonal elements of AA is ss, then βsα2\frac{\beta s}{\alpha^{2}} is equal to

  4. Question 4

    Permutations and Combinations. Asked once: 25 Jul 2022

    153
    The number of bijective functions f:{1,3,5,7,…,99}→{2,4,6,8,…,100}f:\{ 1,3,5,7,\ldots,99\} \rightarrow \{ 2,4,6,8,\ldots,100\}, such that f(3)≥f(9)≥f(15)≥f(21)≥…≥f(99),f(3) \geq f(9) \geq f(15) \geq f(21) \geq \ldots \geq f(99), is

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  5. Question 5

    Probability. Asked once: 29 Jun 2022

    166
    The probability that a relation RR from {x,y}\mathbf{\{ x,y\}} to {x,y}\mathbf{\{ x,y\}} is both symmetric and transitive, is equal to:

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