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Day 624: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 27 Jul 2022

    68
     I=∫π/4π/3(8sin⁡x−sin⁡2xx)dx\ I =\int_{\pi/4}^{\pi/3} \left( \frac{8\sin x - \sin2x}{x} \right)dx. Then

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  2. Question 2

    Sequences and Series. Asked once: 26 Jun 2022

    87
    Let A={n∈NA\mathbf{= \{ n \in N} : H.C.F. (n,45)=1}(n,45) = 1\} and Let B={2k:k∈{1,2,…,100}}\mathbf{B = \{ 2k:k \in \{ 1,2,\ldots,100\}\}}. Then the sum of all the elements of A∩BA \cap B is

  3. Question 3

    Conic Sections. Asked once: 29 Jan 2024

    69
    Let (5,a4)\left( 5,\frac{a}{4} \right), be the circumcenter of a triangle with vertices A(a,−2),B(a,6)A(a, - 2),B(a,6) and C(a4,−2)C\left( \frac{a}{4}, - 2 \right). Let α\alpha denote the circumradius, β\beta denote the area and γ\gamma denote the perimeter of the triangle. Then α+β+γ\alpha + \beta + \gamma is

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  4. Question 4

    Definite Integration. Asked once: 27 Jul 2022

    159
    ∫02(∣2x2−3x∣+[x−12])dx\int_{0}^{2} \left( \left| 2x^{2}- 3x \right|+\left\lbrack x -\frac{1}{2} \right\rbrack \right)dx, where [t]\lbrack t\rbrack is the greatest integer function, is equal to:

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  5. Question 5

    Sequences and Series. Asked once: 26 Jun 2022

    89
    Let A=∑i=110∑j=110min{i,j}A =\sum_{i = 1}^{10} \sum_{j = 1}^{10}\mathbf{ min\{ i,j\}} and B=∑i=110∑j=110max{i,j}B=\sum_{i= 1}^{10} \sum_{j= 1}^{10}\mathbf{ max\{}i,j\}. Then A+BA+B is equal to