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Day 18: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. This type asked 6 times: 28 Jun 2022, 1 Feb 2023, 11 Apr 2023, 31 Jan 2024, 5 Apr 2024, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 6 of this type

    65
    The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

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  2. Question 2

    Definite Integration. This type asked 6 times: 2021 Paper 7, 2021 Paper 14, 2021 Paper 20, 24 Jan 2023, 23 Jan 2025, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 6 of this type

    60
    The value of the integral ∫π245π24dx1+tan⁡2x3\int_{\frac{\pi}{24}}^{\frac{5\pi}{24}} \frac{dx}{1 +\sqrt[3]{\tan2x}} is :

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  3. Question 3

    Relations and Functions. This type asked 6 times: 8 Apr 2023, 15 Apr 2023, 30 Jan 2024, 4 Apr 2024, 3 Apr 2025, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 6 of this type

    64
    If the domain of the function f(x)=sin⁡−1(5−x3+2x)+1log⁡e(10−x)f(x) =\sin^{- 1}\left( \frac{5 - x}{3 + 2x} \right)+\frac{1}{\log_{e}(10 - x)} is (−∞,α]∪[β,γ)−{δ}\mathbf{( - \infty,\alpha\rbrack \cup \lbrack\beta,\gamma) - \{\delta\}}, then 6(α+β+γ+δ)6(\alpha + \beta + \gamma + \delta) is equal to

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  4. Question 4

    Straight Lines. This type asked 6 times: 2021 Paper 3, 8 Apr 2024, 22 Jan 2025, 24 Jan 2025, 29 Jan 2025, 21 Jan 2026 S2. This one: 21 Jan 2026 S2 See all 6 of this type

    75
    If P is a point on the circle x2+y2=4,Qx^{2} + y^{2} = 4,Q is a point on the straight line 5x+y+2=05x + y + 2 = 0 and x−y+1=0x - y + 1 = 0 is the perpendicular bisector of PQ , then 13 times the sum of abscissa of all such point P is ____\_\_\_\_ .

  5. Question 5

    Determinants. This type asked 6 times: 2021 Paper 6, 2021 Paper 9, 2021 Paper 16, 2021 Paper 18, 1 Feb 2023, 29 Jan 2025. This one: 29 Jan 2025 See all 6 of this type

    52
    Let M and m respectively be the maximum and the minimum values of
    f(x)=∣1+sin⁡2xcos⁡2x4sin⁡4xsin⁡2x1+cos⁡2x4sin⁡4xsin⁡2xcos⁡2x1+4sin⁡4x∣,x∈Rf(x) =\left| \begin{matrix} 1 +\sin^{2}x & \cos^{2}x & 4\sin4x \\ \sin^{2}x & 1 +\cos^{2}x & 4\sin4x \\ \sin^{2}x & \cos^{2}x & 1 + 4\sin4x \end{matrix} \right|,x \in R
    Then M4−m4M^{4}-m^{4} is equal to :

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