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Day 48: JEE Mains Maths

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

  1. Question 1

    Inverse Trigonometric Functions. This type asked 4 times: 2021 Paper 24, 27 Jun 2022, 31 Jan 2023, 31 Jan 2024. This one: 31 Jan 2024 See all 4 of this type

    166
    If a=sin⁡−1(sin⁡(5))a =\sin^{- 1}(\sin(5)) and b=cos⁡−1(cos⁡(5))b =\cos^{- 1}(\cos(5)), then a2+b2a^{2}+b^{2} is equal to

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  2. Question 2

    Application of Derivatives. This type asked 4 times: 2021 Paper 23, 29 Jun 2022, 28 Jul 2022, 30 Jan 2024. This one: 30 Jan 2024 See all 4 of this type

    67
    Let g:R→Rg:R \rightarrow R be a non constant twice differentiable such that g′(12)=g′(32)g^{'}\left( \frac{1}{2} \right)=g^{'}\left( \frac{3}{2} \right). If a real valued function ff is defined as f(x)=12[ g(x)+g(2−x)]f(x) =\frac{1}{2}\lbrack\text{ }g(x) + g(2 - x)\rbrack, then

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  3. Question 3

    Differential Equations. This type asked 4 times: 2021 Paper 26, 14 Jun 2022, 6 Apr 2023, 30 Jan 2024. This one: 30 Jan 2024 See all 4 of this type

    171
    Let Y=Y(X)Y = Y(X) be a curve lying in the first quadrant such that the area enclosed by the line Y−y=Y′(x)(X−x)Y - y =Y^{'}(x)(X - x) and the co-ordinate axes, where ( x,yx,y ) is any point on the curve, is always −y22Y′(x)+1,Y′(x)≠0\frac{-y^{2}}{2Y^{'}(x)}+ 1,Y^{'}(x) \neq 0. If Y(1)=1Y(1) = 1, then 12Y(2)12Y(2) equals

  4. Question 4

    Relations and Functions. This type asked 4 times: 2021 Paper 3, 28 Jun 2022, 27 Jul 2022, 27 Jan 2024. This one: 27 Jan 2024 See all 4 of this type

    80
    The function f:N−{1}→N\mathbf{f:N - \{ 1\} \rightarrow N}; defined by f(n)=f(n) = the highest prime factor of nn, is :

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  5. Question 5

    Sequences and Series. This type asked 4 times: 2021 Paper 23, 27 Jun 2022, 29 Jun 2022, 11 Apr 2023. This one: 11 Apr 2023 See all 4 of this type

    175
    For k∈Nk \in N, if the sum of the series 1+4k+8k2+13k3+19k4+…1 +\frac{4}{k}+\frac{8}{k^{2}}+\frac{13}{k^{3}}+\frac{19}{k^{4}}+ \ldots is 10, then the value of kk is