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Day 601: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 14 Jun 2022

    83
    Let A(3a,a),a>0A\left( \frac{3}{\sqrt{a}},\sqrt{a} \right),a> 0, be a fixed point in the xy-plane. The image of A in y-axis be B and the image of BB in xx-axis be CC. If D(3cos⁡θ,asin⁡θ)D(3\cos\theta,a\sin\theta) is a point in the fourth quadrant such that the maximum area of △ACD\bigtriangleup ACD is 12 square units, then a is equal to

  2. Question 2

    Application of Derivatives. Asked once: 14 Jun 2022

    70
    f(x)=4log⁡e(x−1)−2x2+4x+5,x>1f(x) = 4\log_{e}(x - 1) - 2x^{2}+ 4x + 5,x > 1, which one of the following is NOT correct?

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  3. Question 3

    Complex Numbers. Asked once: 2021 Paper 21

    84
    Let z1z_{1} and z2z_{2} be two complex numbers such that arg(z1−z2)=π4arg\left( z_{1}-z_{2} \right)=\frac{\pi}{4} and z1,z2z_{1},z_{2} satisfy the equation ∣z−3∣=Re(z)|z- 3| = Re(z). Then the imaginary part of z1+z2z_{1}+z_{2} is equal to

  4. Question 4

    Conic Sections. Asked once: 22 Jan 2025

    141
    Let E:x2a2+y2 b2=1,a>bE:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{{\text{ }b}^{2}}= 1,a > b and H:x2 A2−y2 B2=1H:\frac{x^{2}}{{\text{ }A}^{2}}-\frac{y^{2}}{{\text{ }B}^{2}}= 1. Let the distance between the foci of EE and the foci of HH be 232\sqrt{3}. If a−A=2a - A = 2, and the ratio of the eccentricities of EE and HH is 13\frac{1}{3}, then the sum of the lengths of their latus rectums is equal to :

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  5. Question 5

    Definite Integration. Asked once: 6 Apr 2023

    164
    Let f(x)f(x) be a function satisfying f(x)+f(π−x)=f(x) + f(\pi - x) = π2,∀x∈R\pi^{2},\forall x \in R. Then ∫0πf(x)sin⁡xdx\int_{0}^{\pi} f(x)\sin xdx is equal to

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