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Day 10: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. This type asked 8 times: 2021 Paper 3, 28 Jul 2022, 22 Jan 2025, 23 Jan 2025, 29 Jan 2025, 3 Apr 2025, 4 Apr 2025, 21 Jan 2026 S1. This one: 21 Jan 2026 S1 See all 8 of this type

    60
    Let f:R→(0,∞)f:R \rightarrow (0,\infty) be a twice differentiable function such that f(3)=18,f′(3)=0f(3) = 18,f^{'}(3) = 0 and f′′(3)=4f^{''}(3) = 4. Then lim⁡x→1(log⁡e(f(2+x)f(3))18(x−1)2)\lim_{x \rightarrow 1} \left( \log_{e}\left( \frac{f(2 + x)}{f(3)} \right)^{\frac{18}{(x - 1)^{2}}} \right) is equal to :

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  2. Question 2

    Binomial Theorem. This type asked 8 times: 2021 Paper 10, 2021 Paper 18, 2021 Paper 25, 24 Jan 2023, 8 Apr 2024, 3 Apr 2025, 4 Apr 2025, 7 Apr 2025. This one: 7 Apr 2025 See all 8 of this type

    150
    The sum of the series
    2×1× 20C4−3×2× 20C5+4×3× 20C6−5×4× 20C7+…+18×17× 20C20, is equal to .\begin{matrix} & 2 \times 1 \times \ ^{20}C_{4} - 3 \times 2 \times \ ^{20}C_{5} + 4 \times 3 \times \ ^{20}C_{6} - 5 \times 4 \times \\ & \ ^{20}C_{7} + \ldots + 18 \times 17 \times \ ^{20}C_{20},\text{~is equal to~}\text{.} \end{matrix}

  3. Question 3

    Quadratic Equations. This type asked 8 times: 2021 Paper 4, 2021 Paper 26, 29 Jul 2022, 27 Jan 2024, 6 Apr 2024, 9 Apr 2024, 2 Apr 2025, 3 Apr 2025. This one: 3 Apr 2025 See all 8 of this type

    53
    Let α\alpha and β\beta be the roots of x2+3x−16=0x^{2}+\sqrt{3}x- 16 = 0, and γ\gamma and δ\delta be the roots of x2+3x−1=0x^{2}+ 3x - 1 = 0. If Pn=αn+βnP_{n}=\alpha^{n}+\beta^{n} and Qn=γn+δnQ_{n}=\gamma^{n}+\delta^{n}, then P25+3P242P23+Q25−Q23Q24\frac{P_{25}+\sqrt{3}P_{24}}{2P_{23}}+\frac{Q_{25}-Q_{23}}{Q_{24}} is equal to

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  4. Question 4

    Sequences and Series. This type asked 8 times: 2021 Paper 9, 2021 Paper 24, 25 Jul 2022, 29 Jul 2022, 30 Jan 2023, 9 Apr 2024, 24 Jan 2025, 28 Jan 2025. This one: 28 Jan 2025 See all 8 of this type

    138
    For positive integers nn, if 4an=(n2+5n+6)4a_{n}=\left( n^{2}+ 5n + 6 \right) and Sn=∑k=1n(1ak)S_{n}=\sum_{k = 1}^{n} \left( \frac{1}{a_{k}} \right), then the value of 507 S2025507{\text{ }S}_{2025} is :

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  5. Question 5

    Application of Integrals. This type asked 8 times: 2021 Paper 1, 27 Jul 2022, 29 Jan 2023, 10 Apr 2023, 11 Apr 2023, 8 Apr 2024, 9 Apr 2024, 22 Jan 2025. This one: 22 Jan 2025 See all 8 of this type

    68
    The area of the region, inside the circle (x−23)2+y2=12(x - 2\sqrt{3})^{2}+y^{2}= 12 and outside the parabola y2=23xy^{2}= 2\sqrt{3}x is

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