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Day 606: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2021 Paper 25

    73
    The maximum slope of the curve y=12x4−5x3+18x2−19xy=\frac{1}{2}x^{4}- 5x^{3}+ 18x^{2}- 19x occurs at the point:

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  2. Question 2

    Complex Numbers. Asked once: 2021 Paper 13

    56
    Let ω\omega be a non-real cube root of unity. Three dice are thrown and r1,r2,r3r_{1},r_{2},r_{3} are the numbers obtained. Then the probability that ωr1+ωr2+ωr3=0\omega^{r_{1}}+\omega^{r_{2}}+\omega^{r_{3}}= 0 is

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  3. Question 3

    Conic Sections. Asked once: 9 Apr 2024

    176
    Let A,BA,B and CC be three points on the parabola y2=6xy^{2}= 6x and let the line segment ABAB meet the line LL through CC parallel to the xx-axis at the point DD. Let MM and NN respectively be the feet of the perpendiculars from AA and BB on LL. Then (AM⋅BNCD)2\left( \frac{AM \cdot BN}{CD} \right)^{2} is equal to

  4. Question 4

    Definite Integration. Asked once: 1 Feb 2023

    167
    The value of the integral ∫−π4π4x+π42−cos⁡2xdx\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{x +\frac{\pi}{4}}{2 - \cos2x}dx is :

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  5. Question 5

    Matrices. Asked once: 2021 Paper 8

    87
    Let A=[abcd]A =\begin{bmatrix} a & b \\ c & d \end{bmatrix} and B=[αβ]≠[00]B =\begin{bmatrix} \alpha \\ \beta \end{bmatrix}\neq\begin{bmatrix} 0 \\ 0 \end{bmatrix} such that AB=BAB=B and a+d=2021a+d= 2021, then the value of ad−bcad - bc is equal to