PYQ Vault
EbooksTutor

Day 514: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 28 Jan 2026 S1

    53
    Let y=xy=x be the equation of a chord of the circle C1C_{1} (in the closed half-plane x≥0x\geq 0 ) of diameter 10 passing through the origin. Let C2C_{2} be another circle described on the given chord as its diameter. If the equation of the chord of the circle C2C_{2}, which passes through the point (2,3)(2,3) and is farthest from the center of C2C_{2}, is x+ay+b=0x + ay + b = 0, then a−ba - b is equal to :

    Tap an option to check your answer.

  2. Question 2

    Definite Integration. Asked once: 21 Jan 2026 S1

    62
    The value of ∫−π/6π/6(π+4x111−sin⁡(∣x∣+π/6))dx\int_{- \pi/6}^{\pi/6} \left( \frac{\pi + 4x^{11}}{1 - \sin(|x| + \pi/6)} \right)dx is equal to

    Tap an option to check your answer.

  3. Question 3

    Determinants. Asked once: 2021 Paper 22

    79
    If ar=cos⁡2rπ9+isin⁡2rπ9,r=1,2,3,…,i=−1a_{r}= \cos\frac{2r\pi}{9}+i\sin\frac{2r\pi}{9},r = 1,2,3,\ldots,i=\sqrt{- 1}, then the determinant ∣a1a2a3a4a5a6a7a8a9∣\left| \begin{matrix} a_{1} & a_{2} & a_{3} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9} \end{matrix} \right| is equal to :

    Tap an option to check your answer.

  4. Question 4

    Differentiation. Asked once: 26 Jul 2022

    158
    The value of log⁡e2ddx(log⁡cos⁡xcsc⁡x)\log_{e}2\frac{d}{dx}\left( \log_{\cos x}\csc x \right) at x=π4x =\frac{\pi}{4} is

    Tap an option to check your answer.

  5. Question 5

    Indefinite Integration. Asked once: 10 Apr 2023

    78
    If I(x)=∫esin⁡2x(cos⁡xsin⁡2x−sin⁡x)dxI(x) = \int e^{\sin^{2}x}(\cos x\sin2x - \sin x)dx and I(0)=1I(0) = 1, then I(π3)I\left( \frac{\pi}{3} \right) is equal to

    Tap an option to check your answer.