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Day 347: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 2021 Paper 21 (same type asked 6 times) See all 6 of this type

    68
    If the solution curve of the differential equation (2x−10y3)dy+ydx=0\left( 2x- 10y^{3} \right)dy+ydx= 0, passes through the points (0,1)(0,1) and (2,β)(2,\beta), then β\beta is a root of the equation:

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  2. Question 2

    Definite Integration. Asked once: 14 Jun 2022 (same type asked 6 times) See all 6 of this type

    157
    lim⁡n→∞(n2(n2+1)(n+1)+n2(n2+4)(n+2)+n2(n2+9)(n+3)+…+n2(n2+n2)(n+n))\lim_{n \rightarrow \infty} \left( \frac{n^{2}}{\left( n^{2}+ 1 \right)(n + 1)}+\frac{n^{2}}{\left( n^{2}+ 4 \right)(n + 2)}+\frac{n^{2}}{\left( n^{2}+ 9 \right)(n + 3)}+ \ldots +\frac{n^{2}}{\left( n^{2}+n^{2} \right)(n + n)} \right) is equal to

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  3. Question 3

    Differential Equations. Asked once: 2021 Paper 18 (same type asked 6 times) See all 6 of this type

    64
    Let y=y(x)y=y(x) be a solution curve of the differential equation (y+1)tan⁡2xdx+tan⁡xdy+ydx=0(y+ 1)\tan^{2}xdx+ \tan xdy+ydx= 0, x∈(0,π2)x\in\left( 0,\frac{\pi}{2} \right). If lim⁡x→0+xy(x)=1\lim_{x\rightarrow 0 +} xy(x) = 1, then the value of y(π4)y\left( \frac{\pi}{4} \right) is:

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  4. Question 4

    Vector Algebra. Asked once: 8 Apr 2023 (same type asked 6 times) See all 6 of this type

    161
    The area of the quadrilateral ABCDABCD with vertices A(2,1,1),B(1,2,5),C(−2,−3,5)A(2,1,1),B(1,2,5),C( - 2, - 3,5) and D(1,−6,−D(1, - 6, - 7) is equal to

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  5. Question 5

    Limits and Continuity. Asked once: 2021 Paper 24 (same type asked 6 times) See all 6 of this type

    61
    Let f:R→Rf:R \rightarrow R be a continuous function. Then lim⁡x→π4π4∫2sec⁡2xf(x)dxx2−π216\lim_{x\rightarrow\frac{\pi}{4}} \frac{\frac{\pi}{4}\int_{2}^{\sec^{2}x} f(x)dx}{x^{2}-\frac{\pi^{2}}{16}} is equal to:

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