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Day 613: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 25 Jan 2023

    90
    Let A1,A2,A3A_{1},A_{2},A_{3} be the three A.P. with the same common difference dd and having their first terms as A,A+1, A+2A,A + 1,\text{ }A + 2, respectively. Let a,b,ca,b,c be the 7th ,9th ,17th 7^{\text{th~}},9^{\text{th~}},17^{\text{th~}} terms of A1, A2, A3A_{1},{\text{ }A}_{2},{\text{ }A}_{3}, respectively such that ∣a712b171c171∣+70=0\left| \begin{matrix} a & 7 & 1 \\ 2b & 17 & 1 \\ c & 17 & 1 \end{matrix} \right|+ 70 = 0. If a=29a = 29, then the sum of first 20 terms of an AP whose first term is c−a−bc - a - b and common difference is d12\frac{d}{12}, is equal to

  2. Question 2

    Straight Lines. Asked once: 2021 Paper 7

    63
    In a triangle PQRPQR, the co-ordinates of the points PP and QQ are (−2,4)( - 2,4) and (4,−2)(4, - 2) respectively. If the equation of the perpendicular bisector of PR is 2x−y+2=02x - y + 2 = 0, then the centre of the circumcircle of the △PQR\bigtriangleup PQR is:

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  3. Question 3

    Application of Derivatives. Asked once: 2021 Paper 8

    82
    Let f:[−1,1]→Rf:[-1,1]\rightarrow \mathbb{R} be defined as f(x)=ax2+bx+cf(x)=ax^{2}+bx+c for all x∈[−1,1]x\in[-1,1], where a,b,c∈Ra,b,c\in\mathbb{R} such that f(−1)=2, f′(−1)=1f(-1)=2,\ f'(-1)=1 and for x∈(−1,1)x\in(-1,1) the maximum value of f′′(x)f''(x) is 12\frac{1}{2}. If f(x)≤αf(x)\le\alpha for x∈[−1,1]x\in[-1,1], then the least value of α\alpha is equal to

  4. Question 4

    Complex Numbers. Asked once: 2021 Paper 8

    69
    Let S1,S2S_{1},S_{2} and S3S_{3} be three sets defined as
    S1={z∈C:∣z−1∣≤2}S_{1}\mathbf{= \{}z\in\mathbb{C}:|z- 1| \leq\sqrt{2}\}
    S2={z∈C:Re((1−i)z)≥1}S_{2}\mathbf{= \{ z \in}\mathbb{C}:Re((1 - i)z) \geq 1\}
    S3={z∈C:Im(z)≤1}S_{3}\mathbf{= \{ z \in}\mathbb{C}:Im(z) \leq 1\}
    Then the set S1∩S2∩S3S_{1}\cap S_{2}\cap S_{3}

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  5. Question 5

    Conic Sections. Asked once: 6 Apr 2024

    67
    Let CC be the circle of minimum area touching the parabola y=6−x2y= 6 -x^{2} and the lines y=3∣x∣y=\sqrt{3}|x|. Then, which one of the following points lies on the circle C?

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