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Day 597: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 2021 Paper 20

    65
    If the matrix A=[02K−1]A=\begin{bmatrix} 0 & 2 \\ K & - 1 \end{bmatrix} satisfies A(A3+3I)=2IA\left( A^{3}+ 3I \right)= 2I, then the value of KK is:

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  2. Question 2

    Quadratic Equations. Asked once: 2021 Paper 5

    61
    The number of elements in the set {x∈R:(∣x∣−3) ∣x+4∣=6}\{x \in \mathbb{R} : (|x|-3)\,|x+4| = 6\} is equal to:

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  3. Question 3

    Relations and Functions. Asked once: 2021 Paper 13

    46
    If the domain f(x)=cos⁡−1x2−x+1sin⁡−1(2x−12)f(x) =\frac{\cos^{- 1}\sqrt{x^{2}-x+ 1}}{\sqrt{\sin^{- 1}\left( \frac{2x- 1}{2} \right)}} is the integral (α,β)(\alpha,\beta) then α+β\alpha+\beta is

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  4. Question 4

    Sequences and Series. Asked once: 11 Apr 2023

    80
    Let x1,x2….,x100x_{1},x_{2}\ldots.,x_{100} be in an arithmetic progression, with x1=2x_{1}= 2 and their mean equal to 200. If yi=i(xi−i),1≤i≤100y_{i}= i\left( x_{i}- i \right),1 \leq i \leq 100, then the mean of y1,y2y_{1},y_{2}, y100y_{100} is.

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  5. Question 5

    Straight Lines. Asked once: 28 Jun 2022

    162
    Let a triangle be bounded by the lines L1:2x+5y=10L_{1}:2x + 5y = 10; L2:−4x+3y=12L_{2}: - 4x + 3y = 12 and the line L3L_{3}, which passes through the point P(2,3)P(2,3), intersect L2L_{2} at AA and L1L_{1} at BB. If the point PP divides the line-segment ABAB, internally in the ratio 1:31:3, then the area of the triangle is equal to

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