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Day 283: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 27 Jul 2022 (same type asked 3 times) See all 3 of this type

    153
    If α,β\alpha,\beta are the roots of the equation x2−(5+3log⁡35−5log⁡53)x+3(3(log⁡35)13−5(log⁡53)23−1)=0x^{2}-\left( 5 +3^{\sqrt{\log_{3}5}}-5^{\sqrt{\log_{5}3}} \right)x+ 3\left( 3^{\left( \log_{3}5 \right)^{\frac{1}{3}}}-5^{\left( \log_{5}3 \right)^{\frac{2}{3}}}- 1 \right)= 0 then the equation, whose roots are α+1β\alpha +\frac{1}{\beta} and β+1α\beta +\frac{1}{\alpha}, is

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  2. Question 2

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

    61
    Let f(x)=x−1x+1,x∈R−{0,−1,1)f(x) =\frac{x - 1}{x + 1}\mathbf{,x \in R - \{ 0, - 1,1)}. If fn+1(x)=f(fn(x))f^{n + 1}(x) = f\left( f^{n}(x) \right) for all n∈Nn\in N, then f6(6)+f7(7)f^{6}(6) +f^{7}(7) is equal to:

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  3. Question 3

    Trigonometric Equations. Asked once: 29 Jul 2022 (same type asked 3 times) See all 3 of this type

    162
    The number of elements in the set S={x∈R:2cos⁡(x2+x6)=4x+4−x}S =\left\{ x\in R:2\cos\left( \frac{x^{2}+ x}{6} \right)=4^{x}+4^{- x} \right\} is:

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  4. Question 4

    Permutations and Combinations. Asked once: 31 Jan 2023 (same type asked 3 times) See all 3 of this type

    178
    If  2n+1Pn−1: 2n−1Pn=11:21\ ^{2n + 1}P_{n - 1}:\ ^{2n - 1}P_{n}= 11:21, then n2+n+15n^{2}+ n + 15 is equal to:

  5. Question 5

    Relations and Functions. Asked once: 2021 Paper 12 (same type asked 3 times) See all 3 of this type

    46
    Let f:R−{α6}→Rf:\mathbb{R}-\left\{ \frac{\alpha}{6} \right\}\rightarrow R be defined by f(x)=5x+36x−αf(x) =\frac{5x + 3}{6x -\alpha}. Then the value of α\alpha for which (fof) (x)=x(x) =x, for all x∈R−{α6}x \in R -\left\{ \frac{\alpha}{6} \right\}, is:

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