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Day 602: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 2021 Paper 13

    49
    A=[010100001]A=\begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}, number of matrices ' BB ' which can be formed such that AB=BAAB = BA; B can have elements {1,2,3,4,5}\left\{ 1,2,3,4,5 \right\}

  2. Question 2

    Relations and Functions. Asked once: 2021 Paper 10

    64
    Let f:R−{3}→R−{1}f\mathbf{:R - \{ 3\} \rightarrow R - \{ 1\}} be defined by f(x)=x−2x−3f(x) =\frac{x- 2}{x- 3}. Let g:R→Rg:R\rightarrow R be given as g(x)=2x−3g(x) = 2x- 3. Then, the sum of all the values of xx for which f−1(x)+g−1(x)=132f^{- 1}(x) +g^{- 1}(x) =\frac{13}{2} is equal to

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  3. Question 3

    Sequences and Series. Asked once: 8 Apr 2023

    173
    Let 0<z<y<x0 < z < y < x be three real numbers such that 1x,1y,1z\frac{1}{x},\frac{1}{y},\frac{1}{z} are in an arithmetic progression and xx, 2y,z\sqrt{2}y,z are in a geometric progression. If xy+yzxy + yz +zx=32xyz+ zx =\frac{3}{\sqrt{2}}xyz, then 3(x+y+z)23(x + y + z)^{2} is equal to

  4. Question 4

    Straight Lines. Asked once: 2021 Paper 25

    72
    The triangle formed by the lines x−y=0x - y = 0, x+2y=3x + 2y = 3 and 2x+y=62x + y = 6 is a:

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  5. Question 5

    Application of Derivatives. Asked once: 2021 Paper 26

    80
    The triangle of maximum area that can be inscribed in a given circle of radius ' rr ' is:

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