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Day 527: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 2021 Paper 8

    72
    If x,y,zx,y,z are in arithmetic progression with common difference d,x≠3 dd,x \neq 3\text{ }d, and the determinant of the matrix [342x452y5kz]\begin{bmatrix} 3 & 4\sqrt{2} & x \\ 4 & 5\sqrt{2} & y \\ 5 & k & z \end{bmatrix} is zero, then the value of k2k^{2} is

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  2. Question 2

    Differentiation. Asked once: 2021 Paper 8

    75
    Consider the function f:R→Rf:\mathbb{R}\to\mathbb{R} defined by f(x)={(2−sin⁡1x)∣x∣,x≠00,x=0f(x)=\begin{cases}\left(2-\sin\frac{1}{x}\right)|x|, & x\neq 0 \\ 0, & x=0\end{cases}. Then ff is:

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  3. Question 3

    Indefinite Integration. Asked once: 30 Jan 2023

    177
    If ∫sec⁡2x−1dx=αlog⁡e∣cos⁡2x+β+cos⁡2x(1+cos⁡1βx)∣+\int\sqrt{\sec2x - 1}dx = \alpha\log_{e}\left| \cos2x + \beta +\sqrt{\cos2x\left( 1 + \cos\frac{1}{\beta}x \right)} \right|+ constant, then β−α\beta - \alpha is equal to

  4. Question 4

    Inverse Trigonometric Functions. Asked once: 2021 Paper 2

    63
    A possible value of tan⁡(14sin⁡−1638)\tan\left( \frac{1}{4}\sin^{- 1}\frac{\sqrt{63}}{8} \right) is:

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  5. Question 5

    Limits and Continuity. Asked once: 29 Jan 2023

    62
    Let x=2x = 2 be a root of the equation x2+px+q=0x^{2}+ px + q = 0 and
    f(x)={1−cos⁡(x2−4px+q2+8q+16)(x−2p)4,x≠2p0,,x=2pf(x) =\left\{ \begin{matrix} \frac{1 - \cos\left( x^{2}- 4px +q^{2}+ 8q + 16 \right)}{(x - 2p)^{4}} & ,x \neq 2p \\ 0, & ,x = 2p \end{matrix} \right.
    lim⁡x→2p+[f(x)]\lim_{x \rightarrow 2p^{+}} \lbrack f(x)\rbrack
    where [⋅]\lbrack \cdot \rbrack denotes greatest integer function, is

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