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Day 633: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 14 Jun 2022

    87
    Let Max0≤x≤2{9−x25−x}=αMax_{0 \leq x\leq 2}\left\{ \frac{9 -x^{2}}{5 -x} \right\}=\alpha and Min0≤x≤2{9−x25−x}=βMin_{0 \leq x\leq 2}\left\{ \frac{9 -x^{2}}{5 -x} \right\}=\beta If ∫β−832α−1Max{9−x25−x,x}dx=α1+α2log⁡e(815)\int_{\beta-\frac{8}{3}}^{2\alpha- 1} Max\left\{ \frac{9 -x^{2}}{5 -x},x \right\}dx=\alpha_{1}+\alpha_{2}\log_{e}\left( \frac{8}{15} \right) then α1+α2\alpha_{1}+\alpha_{2} is equal to

  2. Question 2

    Sequences and Series. Asked once: 2021 Paper 5

    81
    Consider an arithmetic series and a geometric series having four initial terms from the set {4,8,11,16,21,26,32}\{4,8,11,16,21,26,32\}. If the last terms of these series are the maximum possible four-digit numbers, then the number of common terms in these two series is equal to ______.

  3. Question 3

    Conic Sections. Asked once: 6 Apr 2023

    170
    In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is α\alpha and the number of persons who speak only Hindi is β\beta, then the eccentricity of the ellipse 25(β2x2+α2y2)=α2β225\left( \beta^{2}x^{2}+\alpha^{2}y^{2} \right)=\alpha^{2}\beta^{2} is

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  4. Question 4

    Definite Integration. Asked once: 2021 Paper 24

    70
    Let Jn,m=∫012xnxm−1dx, ∀ n>mJ_{n,m}=\int_{0}^{\frac{1}{2}}\frac{x^{n}}{x^{m}-1}dx,\ \forall\, n>m and n,m∈Nn,m\in N. Consider a matrix A=[aij]3×3A=[a_{ij}]_{3\times3} where aij={J6+i,3−Ji+3,3,i≤j0,i>ja_{ij}=\begin{cases} J_{6+i,3}-J_{i+3,3}, & i\leq j \\ 0, & i>j \end{cases}. Then ∣adj⁡A−1∣\left|\operatorname{adj}A^{-1}\right| is:

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  5. Question 5

    Sequences and Series. Asked once: 2021 Paper 3

    81
    Let A1,A2,A3,….A_{1},A_{2},A_{3},\ldots.. be squares such that for each n≥1n \geq 1, the length of the side of AnA_{n} equals the length of diagonal of An+1A_{n + 1}. If the length of A1A_{1} is 12 cm12\text{ }cm, then the smallest value of nn for which area of AnA_{n} is less than one, is