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Day 587: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 27 Jun 2022

    67
    The lengths of the sides of a triangle are 10+x210 +x^{2}, 10+x210 +x^{2} and 20−2x220 - 2x^{2}. If for x=kx = k, the area of the triangle is maximum, then 3k23k^{2} is equal to:

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  2. Question 2

    Application of Integrals. Asked once: 29 Jun 2022

    158
    If ∫02(2x−2x−x2)dx=\int_{0}^{2} \left( \sqrt{2x}-\sqrt{2x -x^{2}} \right)dx =
    ∫01(1−1−y2−y22)dy+∫12(2−y22)dy+I\int_{0}^{1} \left( 1 -\sqrt{1 -y^{2}}-\frac{y^{2}}{2} \right)dy +\int_{1}^{2} \left( 2 -\frac{y^{2}}{2} \right)dy + I
    then II is equal to

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  3. Question 3

    Complex Numbers. Asked once: 25 Jul 2022

    151
    For z∈Cz \in C if the minimum value of (∣z−32∣+∣z−p2i∣)(|z - 3\sqrt{2}| + |z - p\sqrt{2}i|) is 525\sqrt{2}, then a value of pp is

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  4. Question 4

    Conic Sections. Asked once: 28 Jan 2025

    144
    If AA and BB are the points of intersection of the circle x2+y2−8x=0x^{2}+y^{2}- 8x = 0 and the hyperbola x29−y24=1\frac{x^{2}}{9}-\frac{y^{2}}{4}= 1 and a point PP moves on the line 2x−3y+4=02x - 3y + 4 = 0, then the centroid of △PAB\bigtriangleup PAB lies on the line :

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  5. Question 5

    Definite Integration. Asked once: 15 Apr 2023

    78
    If ∫011(5+2x−2x2)(1+e(2−4x))dx=1αlog⁡e(α+1β)\int_{0}^{1} \frac{1}{\left( 5 + 2x - 2x^{2} \right)\left( 1 +e^{(2 - 4x)} \right)}dx =\frac{1}{\alpha}\log_{e}\left( \frac{\alpha + 1}{\beta} \right), α,β>0\alpha,\beta > 0, then α4−β4\alpha^{4}-\beta^{4} is equal to:

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