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Day 175: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 26 Jun 2022 (same type asked 4 times) See all 4 of this type

    62
    Let A={z∈C:∣z+1z−1<1∣}A =\left\{ z \in C:\left| \frac{z + 1}{z - 1}< 1 \right| \right\} and B={z∈C:arg(z−1z+1)=2π3}B =\left\{ z \in C:arg\left( \frac{z - 1}{z + 1} \right)=\frac{2\pi}{3} \right\}. Then A∩BA \cap B is:

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  2. Question 2

    Conic Sections. Asked once: 25 Jun 2022 (same type asked 4 times) See all 4 of this type

    179
    Let the eccentricity of the hyperbola x2a2−y2b2=1\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1 be 54\frac{5}{4}. If the equation of the normal at the point (85,125)\left( \frac{8}{\sqrt{5}},\frac{12}{5} \right) on the hyperbola is 85x+βy=λ8\sqrt{5}x+\beta y=\lambda, then λ−β\lambda-\beta is equal to

  3. Question 3

    Probability. Asked once: 2021 Paper 26 (same type asked 4 times) See all 4 of this type

    71
    A seven- digit number is formed using digit 3,3,4,4,4,5,53,3,4,4,4,5,5. The probability, that number so formed is divisible by 2, is:

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  4. Question 4

    Quadratic Equations. Asked once: 2021 Paper 25 (same type asked 3 times) See all 3 of this type

    85
    The number of solutions of the equation log⁡4(x−1)=log⁡2(x−3)\log_{4}(x- 1) =\log_{2}(x- 3) is

  5. Question 5

    Application of Derivatives. Asked once: 22 Jan 2026 S1 (same type asked 3 times) See all 3 of this type

    55
    Let f(x)=x2025−x2000,x∈[0,1]f(x) =x^{2025}-x^{2000},x \in \lbrack 0,1\rbrack and the minimum value of the function f(x)f(x) in the interval [0,1]\lbrack 0,1\rbrack be (80)80(n)−81(80)^{80}(n)^{- 81}. Then n is equal to

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