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Day 83: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked 2 times: 27 Jun 2022*, 22 Jan 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    133
    Let f(x)=∫0x2t2−8t+15etdt,x∈Rf(x) =\int_{0}^{x^{2}} \frac{t^{2}- 8t + 15}{e^{t}}dt,x \in R. Then the numbers of local maximum and local minimum points of ff, respectively, are :

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  2. Question 2

    Relations and Functions. Asked 2 times: 12 Apr 2023, 22 Jan 2025 See all 2 times it was asked

    150
    Let A={1,2,3}\mathbf{A = \{ 1,2,3\}}. The number of relations on A , containing (1,2)(1,2) and (2,3)(2,3), which are reflexive and transitive but not symmetric, is  ____\ \_\_\_\_

  3. Question 3

    Trigonometric Equations. Asked 2 times: 26 Jul 2022, 22 Jan 2025 See all 2 times it was asked

    143
    The sum of all values of θ∈[0,2π]\theta \in \lbrack 0,2\pi\rbrack satisfying 2sin⁡2θ=cos⁡2θ2\sin^{2}\theta = \cos2\theta and 2cos⁡2θ=3sin⁡θ2\cos^{2}\theta = 3\sin\theta is

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  4. Question 4

    Vector Algebra. Asked 2 times: 29 Jan 2024*, 9 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    70
    Let OA→=2a→,OB→=6a→+5b→\overrightarrow{OA}= 2\overrightarrow{a},\overrightarrow{OB}= 6\overrightarrow{a}+ 5\overrightarrow{b} and OC→=3b→\overrightarrow{OC}= 3\overrightarrow{b}, where OO is the origin. If the area of the parallelogram with adjacent sides OA→\overrightarrow{OA} and OC→\overrightarrow{OC} is 15 sq. units, then the area (in sq. units) of the quadrilateral OABCOABC is equal to:

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  5. Question 5

    Differential Equations. Asked 2 times: 2021 Paper 22*, 9 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    153
    Let ∫0x1−(y′(t))2dt=∫0xy(t)dt,0≤x≤3,y≥0\int_{0}^{x} \sqrt{1 -\left( y^{'}(t) \right)^{2}}dt =\int_{0}^{x} y(t)dt,0 \leq x \leq 3,y \geq 0, y(0)=0y(0) = 0. Then at x=2,y"+y+1x = 2,y" + y + 1 is equal to:

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