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Day 188: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 6 Apr 2024 (same type asked 3 times) See all 3 of this type

    160
    If the function f(x)=(1x)2x;x>0f(x) =\left( \frac{1}{x} \right)^{2x};x > 0 attains the maximum value at x=1ex =\frac{1}{e} then :

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  2. Question 2

    Relations and Functions. Asked once: 25 Jan 2023 (same type asked 3 times) See all 3 of this type

    169
    Let f:R→Rf:R \rightarrow R be a function defined by f(x)=log⁡m{2(sin⁡x−cos⁡x)+m−2}f(x) =\log_{\sqrt{m}}\mathbf{\{}\sqrt{2}(\sin x - \cos x) + m - 2\}, for some mm, such that the range of ff is [0,2]\lbrack 0,2\rbrack. Then the value of mm is

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  3. Question 3

    Differentiation. Asked once: 4 Apr 2024 (same type asked 3 times) See all 3 of this type

    79
    Let f(x)=x5+2ex/4f(x) =x^{5}+ 2e^{x/4} for all x∈Rx \in R. Consider a function g(x)g(x) such that (gof)(x)=x(gof)(x) = x for all x∈Rx \in R. Then the value of 8g′(2)8g^{'}(2) is:

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  4. Question 4

    Limits and Continuity. Asked once: 8 Apr 2023 (same type asked 3 times) See all 3 of this type

    167
    If α>β>0\alpha > \beta > 0 are the roots of the equation ax2+bx+1=0ax^{2}+ bx + 1 = 0, and lim⁡x→1α(1−cos⁡(x2+bx+a)2(1−αx)2)12=1k(1β−1α)\lim_{x \rightarrow\frac{1}{\alpha}} \left( \frac{1 - \cos\left( x^{2}+ bx + a \right)}{2(1 - \alpha x)^{2}} \right)^{\frac{1}{2}}=\frac{1}{k}\left( \frac{1}{\beta}-\frac{1}{\alpha} \right), then kk is equal to

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  5. Question 5

    Relations and Functions. Asked once: 26 Jun 2022 (same type asked 3 times) See all 3 of this type

    151
    Let f:R→Rf:R \rightarrow R be defined as f(x)=x−1f(x) = x - 1 and g:R−{1,−1}→R\mathbf{g:R - \{ 1, - 1\} \rightarrow R} be defined as g(x)=x2x2−1g(x) =\frac{x^{2}}{x^{2}- 1}. Then the function fog is:

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