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Day 12: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. This type asked 7 times: 29 Jun 2022, 30 Jan 2023, 1 Feb 2023, 27 Jan 2024, 1 Feb 2024, 4 Apr 2025, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 7 of this type

    55
    Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 6. Then the number of elements in A∩BA\cap B, which are divisible by 3 , is :

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  2. Question 2

    Trigonometric Identities. This type asked 7 times: 2021 Paper 19, 26 Jun 2022, 25 Jul 2022, 8 Apr 2023, 10 Apr 2023, 24 Jan 2026 S1, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 7 of this type

    61
    If sin⁡(π18)sin⁡(5π18)sin⁡(7π18)=K\sin\left( \frac{\pi}{18} \right)\sin\left( \frac{5\pi}{18} \right)\sin\left( \frac{7\pi}{18} \right)= K, then the value of sin⁡(10Kπ3)\sin\left( \frac{10K\pi}{3} \right) is :

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  3. Question 3

    Differential Equations. This type asked 7 times: 2021 Paper 19, 2021 Paper 25, 6 Apr 2023, 31 Jan 2024, 8 Apr 2024, 4 Apr 2025, 28 Jan 2026 S1. This one: 28 Jan 2026 S1 See all 7 of this type

    70
    Let y=y(x)y=y(x) be the solution of the differential equation xdydx−sin⁡2y=x3(2−x3)cos⁡2y,x≠0.x\frac{dy}{dx}- \sin{2y}=x^{3}\left( 2 -x^{3} \right)\cos^{2}y,x\neq 0. If y(2)=0y(2) =0, then tan⁡(y(1))\tan(y(1)) is equal to

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  4. Question 4

    Permutations and Combinations. This type asked 7 times: 2021 Paper 1, 2021 Paper 5, 25 Jun 2022, 27 Jun 2022, 29 Jul 2022, 31 Jan 2023, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 7 of this type

    75
    The number of 3×23 \times 2 matrices A , which can be formed using the elements of the set {−2,−1,0,1,2}\{ - 2, - 1,0,1,2\} such that the sum of all the diagonal elements of ATAA^{T}A is 5, is ____\_\_\_\_

  5. Question 5

    Trigonometric Equations. This type asked 7 times: 2021 Paper 25, 14 Jun 2022, 25 Jun 2022, 29 Jun 2022, 2 Apr 2025, 3 Apr 2025, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 7 of this type

    66
    Number of solutions of 3cos⁡2θ+8cos⁡θ+33=0,θ∈[−3π,2π]\sqrt{3}\cos2\theta + 8\cos\theta + 3\sqrt{3}= 0,\theta \in \lbrack - 3\pi,2\pi\rbrack is:

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