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Day 92: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked 2 times: 2021 Paper 6*, 25 Jan 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    174
    For the two positive numbers a, b, if a, b and 118\frac{1}{18} are in a geometric progression, while 1a,10\frac{1}{a},10 and 1 b\frac{1}{\text{ }b} are in an arithmetic progression, then 16a+b16a + b is equal to

  2. Question 2

    Complex Numbers. Asked 2 times: 2021 Paper 19*, 24 Jan 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    65
    Let p,q∈Rp,q \in R and (1−3i)200=2199(p+iq),i=−1(1 -\sqrt{3}i)^{200}=2^{199}(p + iq),i =\sqrt{- 1} Then p+q+q2p + q +q^{2} and p−q+q2p - q +q^{2} are roots of the equation

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  3. Question 3

    Three Dimensional Geometry. Asked 2 times: 2021 Paper 20*, 24 Jan 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    76
    The distance of the point (−1,9,−16)( - 1,9, - 16) from the plane 2x+3y−z=52x + 3y - z = 5 measured parallel to the line x+43=2−y4=z−312\frac{x + 4}{3}=\frac{2 - y}{4}=\frac{z - 3}{12} is

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  4. Question 4

    Definite Integration. Asked 2 times: 2021 Paper 26*, 29 Jul 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    75
    If f(α)=∫1αlog⁡10t1+tdt,α>0f(\alpha) =\int_{1}^{\alpha} \frac{\log_{10}t}{1 + t}dt,\alpha > 0, then f(e3)+f(e−3)f\left( e^{3} \right)+ f\left( e^{- 3} \right) is equal to :

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  5. Question 5

    Application of Derivatives. Asked 2 times: 2021 Paper 21*, 28 Jul 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    157
    The sum of the absolute maximum and absolute minimum values of the function f(x)=tan⁡−1(sin⁡x−cos⁡x)f(x) =\tan^{- 1}(\sin x - \cos x) in the interval [0,π]\lbrack 0,\pi\rbrack is

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