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Day 369: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 2021 Paper 7 (same type asked 7 times) See all 7 of this type

    77
    Choose the incorrect statement about the two circles whose equations are x2+y2−10x−10y+41=0x^{2}+y^{2}-10x-10y+41=0 and x2+y2−16x−10y+80=0x^{2}+y^{2}-16x-10y+80=0:

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  2. Question 2

    Definite Integration. Asked once: 31 Jan 2024 (same type asked 7 times) See all 7 of this type

    171
    ∣120π3∫0πx2sin⁡xcosxsin⁡4x+cos⁡4xdx∣\left| \frac{120}{\pi^{3}}\int_{0}^{\pi} \frac{x^{2}\sin xcosx}{\sin^{4}x + \cos^{4}x}dx \right| is equal to.

  3. Question 3

    Probability. Asked once: 28 Jul 2022 (same type asked 7 times) See all 7 of this type

    179
    A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let XX be the number of white balls, among the drawn balls. If σ2\sigma^{2} is the variance of XX, then 100σ2100\sigma^{2} is equal to

  4. Question 4

    Binomial Theorem. Asked once: 2021 Paper 2 (same type asked 7 times) See all 7 of this type

    88
    For integers nn and rr, let (nr)={ nCr, if n≥r≥00, otherwise \begin{pmatrix} n \\ r \end{pmatrix}=\left\{ \begin{matrix} \ ^{n}C_{r}, & \text{~if~}n\geq r\geq 0 \\ 0, & \text{~otherwise~} \end{matrix} \right. The maximum value of kk for which the sum ∑i=0k(10i)(15k−i)+∑i=0k+1(12i)(13k+1−i)\sum_{i= 0}^{k} \begin{pmatrix} 10 \\ i \end{pmatrix}\begin{pmatrix} 15 \\ k-i \end{pmatrix}+\sum_{i= 0}^{k+ 1} \begin{pmatrix} 12 \\ i \end{pmatrix}\begin{pmatrix} 13 \\ k+ 1 -i \end{pmatrix} exists, is equal to

  5. Question 5

    Application of Derivatives. Asked once: 2021 Paper 22 (same type asked 7 times) See all 7 of this type

    62
    The number of real roots of the equation e4x+2e3x−ex−6=0e^{4x}+ 2e^{3x}-e^{x}- 6 = 0 is :

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