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Day 458: JEE Mains Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 7 Apr 2025

    147
    If ∫(1x+1x3)(3x−24+x−2623)dx=−α3(α+1)(3xβ+xγ)α+1α+C, x>0\int\left( \frac{1}{x} + \frac{1}{x^{3}} \right)\left( \sqrt[23]{3x^{- 24} + x^{- 26}} \right)dx = - \frac{\alpha}{3(\alpha + 1)}\left( 3x^{\beta} + x^{\gamma} \right)^{\frac{\alpha + 1}{\alpha}} + C,\ x > 0 (α,β,γ∈Z)(\alpha,\beta,\gamma \in Z), where CC is the constant of integration, then α+β+γ\alpha + \beta + \gamma is equal to .

  2. Question 2

    Inverse Trigonometric Functions. Asked once: 31 Jan 2024

    75
    For α,β,γ≠0\alpha,\beta,\gamma\neq 0. If sin⁡−1α+sin⁡−1β+sin⁡−1γ=π\sin^{- 1}\alpha+\sin^{- 1}\beta+\sin^{- 1}\gamma=\pi and (α+β+γ)(α−γ+β)=3αβ(\alpha+\beta+\gamma)(\alpha-\gamma+\beta) = 3\alpha\beta, then γ\gamma equal to

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  3. Question 3

    Limits and Continuity. Asked once: 7 Apr 2025

    51
    lim⁡x→0+tan⁡(5(x)13)log⁡e(1+3x2)(tan⁡−13x)2(e5(x)43−1)\underset{x\rightarrow0^{+}}{\lim} \frac{\tan\left( 5(x)^{\frac{1}{3}} \right)\log_{e}\left( 1 + 3x^{2} \right)}{\left( \tan^{- 1}3\sqrt{x} \right)^{2}\left( e^{5(x)^{\frac{4}{3}}}- 1 \right)} is equal to.

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  4. Question 4

    Matrices. Asked once: 28 Jan 2026 S1

    66
    Let A,BA,B and C be three 2×22 \times 2 matrices with real entries such that B=(I+A)−1B = (I + A)^{- 1} and A+C=IA + C = I If BC=[1−5−12]BC =\begin{bmatrix} 1 & - 5 \\ - 1 & 2 \end{bmatrix} and CB[x1x2]=[12−6],CB\begin{bmatrix} x_{1} \\ x_{2} \end{bmatrix}=\begin{bmatrix} 12 \\ - 6 \end{bmatrix}, then x1+x2x_{1}+x_{2} is

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  5. Question 5

    Permutations and Combinations. Asked once: 7 Apr 2025

    75
    For n≥2n \geq 2, let SnS_{n} denote the set of all subsets of {1,2,…,n}\{1,2,\ldots,n\} with no two consecutive numbers. For example {1,3,5}∈S6\{1,3,5\}\in S_{6}, but {1,2,4}∉S6\{1,2,4\}\notin S_{6}. Then n(S5)n(S_{5}) is equal to