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Day 637: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 2021 Paper 17

    80
    Let f:(a,b)→Rf:(a,b) \rightarrow R be twice differentiable function such that f(x)=∫axg(t)dtf(x) =\int_{a}^{x} g(t)dt for a differentiable function g(x)g(x). If f(x)=0f(x) = 0 has exactly five distinct roots in (a,b)(a,b), then g(x)g′(x)=0g(x)g^{'}(x) = 0 has at least:

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  2. Question 2

    Conic Sections. Asked once: 29 Jan 2023

    167
    If the tangent at a point PP on the parabola y2=3xy^{2}= 3x is parallel to the line x+2y=1x + 2y = 1 and the tangents at the points QQ and RR on the ellipse x24+y21=1\frac{x^{2}}{4}+\frac{y^{2}}{1}= 1 are perpendicular to the line x−y=2x - y = 2, then the area of the triangle PQRPQR is :

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  3. Question 3

    Definite Integration. Asked once: 2021 Paper 15

    47
    ∫−11log⁡(x+x2+1)dx\int_{- 1}^{1} \log\left( x+\sqrt{x^{2}+ 1} \right)dx

  4. Question 4

    Conic Sections. Asked once: 29 Jan 2023

    173
    A triangle is formed by the tangents at the point (2,2)(2,2) on the curves y2=2xy^{2}= 2x and x2+y2=4xx^{2}+y^{2}= 4x, and the line x+y+2=0x + y + 2 = 0. If rr is the radius of its circumcircle, then r2r^{2} is equal to

  5. Question 5

    Definite Integration. Asked once: 2021 Paper 11

    45
    The value of the integral ∫−11log⁡e(1−x+1+x)dx\int_{- 1}^{1} \log_{e}(\sqrt{1 -x}+\sqrt{1 +x})dx is equal to :

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