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Day 640: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 29 Jul 2022

    77
    Let the focal chord of the parabola P:y2=4xP:y^{2}= 4x along the line L:y=mx+c,m>0L:y = mx + c,m > 0 meet the parabola at the points MM and NN. Let the line LL be a tangent to the hyperbola H:x2−y2=4H:x^{2}-y^{2}= 4. If OO is the vertex of PP and FF is the focus of HH on the positive xx-axis, then the area of the quadrilateral OMFN is:

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  2. Question 2

    Definite Integration. Asked once: 2021 Paper 3

    79
    The value of ∫−11x2e[x3]dx\int_{- 1}^{1} x^{2}e^{\left\lbrack x^{3} \right\rbrack}dx, where [t]\lbrack t\rbrack denotes the greatest integer ≤t\leq t, is :

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  3. Question 3

    Conic Sections. Asked once: 28 Jul 2022

    164
    Let the hyperbola H:x2a2−y2b2=1H:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1 pass through the point (22,−22)(2\sqrt{2}, - 2\sqrt{2}). A parabola is drawn whose focus is same as the focus of HH with positive abscissa and the directrix of the parabola passes through the other focus of HH. If the length of the latus rectum of the parabola is e times the length of the latus rectum of HH, where ee is the eccentricity of HH, then which of the following points lies on the parabola?

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  4. Question 4

    Definite Integration. Asked once: 2021 Paper 2

    80
    Let f(x)f(x) be a differentiable function defined on [0,2]\lbrack 0,2\rbrack such that f′(x)=f′(2−x)f^{'}(x) =f^{'}(2 -x) for all x∈(0,2),f(0)=1x\in (0,2),f(0) = 1 and f(2)=e2f(2) =e^{2}. Then the value of ∫02f(x)dx\int_{0}^{2} f(x)dx is:

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  5. Question 5

    Conic Sections. Asked once: 28 Jul 2022

    173
    Let the tangents at the points PP and QQ on the ellipse x22+y24=1\frac{x^{2}}{2}+\frac{y^{2}}{4}= 1 meet at the point R(2,22−2)R(\sqrt{2},2\sqrt{2}- 2). If SS is the focus of the ellipse on its negative major axis, then SP2+SQ2SP^{2}+SQ^{2} is equal to