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Day 99: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. This type asked 2 times: 28 Jun 2022, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 2 of this type

    56
    Let A1, A2, A3,……..,A39A_{1},{\text{ }A}_{2},{\text{ }A}_{3},\ldots\ldots..,A_{39} be 39 arithmetic means between the numbers 59 and 159. Then the mean of A25, A28, A31A_{25},{\text{ }A}_{28},{\text{ }A}_{31} and A36A_{36} is equal to:

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  2. Question 2

    Permutations and Combinations. This type asked 2 times: 5 Apr 2024, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 2 of this type

    71
    Let A={1,2,3,4,5,6}A = \{ 1,2,3,4,5,6\}. The number of one-one functions f:A→Af:A \rightarrow A such that f(1)≥3,f(3)≤4f(1) \geq 3,f(3) \leq 4 and f(2)+f(3)=5f(2) + f(3) = 5, is ____\_\_\_\_ .

  3. Question 3

    Statistics. This type asked 2 times: 30 Jan 2024, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 2 of this type

    58
    The mean deviation about the mean for the data
    xix_{i}579101215
    fif_{i}862226
    is equal to :

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  4. Question 4

    Application of Derivatives. This type asked 2 times: 13 Apr 2023, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 2 of this type

    62
    max⁡0≤x≤π(16sin⁡(x2)cos⁡3(x2))\max_{0 \leq x \leq\pi} \left( 16\sin\left( \frac{x}{2} \right)\cos^{3}\left( \frac{x}{2} \right) \right) is equal to :

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  5. Question 5

    Conic Sections. This type asked 2 times: 23 Jan 2026 S2, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 2 of this type

    61
    Let H:x2a2−y2 b2=1H:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{{\text{ }b}^{2}}= 1 be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is 83\frac{8}{3}. If the line x=αx =\alpha intersects the hyperbola H at the points A and B such that the area of the triangle AOB is 4154\sqrt{15}, where O is the origin, then α2\alpha^{2} equals

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