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Day 600: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 23 Jan 2025

    54
    If the line 3x−2y+12=03x - 2y + 12 = 0 intersects the parabola 4y=3x24y = 3x^{2} at the points AA and BB, then at the vertex of the parabola, the line segment ABAB subtends an angle equal to

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  2. Question 2

    Definite Integration. Asked once: 11 Apr 2023

    154
    Let the function f:[0,2]→Rf:\lbrack 0,2\rbrack \rightarrow R be defined as
    f(x)={emin⁡{x2,x−[x]},x∈[0,1)e[x−log⁡ex],x∈[1,2]f(x) =\left\{ \begin{matrix} e^{\min\left\{ x^{2},x - \lbrack x\rbrack \right\}}, & x \in \lbrack 0,1) \\ e^{\left\lbrack x -\log_{e}x \right\rbrack}, & x \in \lbrack 1,2\rbrack \end{matrix} \right.
    where [t] denotes the greatest integer less than or equal to tt. Then the value of the integral ∫02xf(x)dx\int_{0}^{2} xf(x)dx is

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  3. Question 3

    Matrices. Asked once: 2021 Paper 17

    79
    Let AA and BB be two 3×33 \times 3 real matrices such that (A2−B2)\left( A^{2}-B^{2} \right) is invertible matrix. If A5=B5A^{5}=B^{5} and A3B2=A2B3A^{3}B^{2}=A^{2}B^{3}, then the value of the determinant of the matrix A3+B3A^{3}+B^{3} is equal to:

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  4. Question 4

    Relations and Functions. Asked once: 2021 Paper 10

    76
    Define a relation RR over a class of n×nn \times n real matrices A and B as "ARB iff there exists a non-singular matrix PP such that PAP−1=BPAP^{- 1}= B ". Then which of the following is true?

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  5. Question 5

    Sequences and Series. Asked once: 10 Apr 2023

    79
    Let the first term aa and the common ratio rr of a geometric progression be positive integers. If the sum of its squares of first three terms is 33033, then the sum of these three terms is equal to

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