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Day 486: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 28 Jan 2026 S1

    62
    Let ff be a polynomial function such that f(x2+1)=x4+5x2+2f\left( x^{2}+ 1 \right)=x^{4}+ 5x^{2}+ 2, for all x∈Rx\in\mathbb{R}. Then ∫03f(x)dx\int_{0}^{3} f(x)dx is equal to

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  2. Question 2

    Determinants. Asked once: 11 Apr 2023

    151
    If ∣x+1xxxx+λxxxx+λ2∣=98(103x+81)\left| \begin{matrix} x + 1 & x & x \\ x & x + \lambda & x \\ x & x & x +\lambda^{2} \end{matrix} \right|=\frac{9}{8}(103x + 81), then λ\lambda, λ3\frac{\lambda}{3} are the roots of the equation

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  3. Question 3

    Differential Equations. Asked once: 25 Jul 2022

    161
    Let a smooth curve y=f(x)y = f(x) be such that the slope of the tangent at any point (x,y)(x,y) on it is directly proportional to (−yx)\left( \frac{- y}{x} \right). If the curve passes through the point (1,2)(1,2) and (8,1)(8,1), then ∣y(18)∣\left| y\left( \frac{1}{8} \right) \right| is equal to

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  4. Question 4

    Differentiation. Asked once: 13 Apr 2023

    68
    For the differentiable function f:R−{0}→Rf:R - \{ 0\} \rightarrow R, let 3f(x)+2f(1x)=1x−103f(x) + 2f\left( \frac{1}{x} \right)=\frac{1}{x}- 10, then ∣f(3)+f′(14)∣\left| f(3) +f^{'}\left( \frac{1}{4} \right) \right| is equal to

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  5. Question 5

    Indefinite Integration. Asked once: 6 Apr 2024

    169
    If ∫1a2sin⁡2x+b2cos⁡2xdx=112tan⁡−1(3tan⁡x)+\int\frac{1}{a^{2}\sin^{2}x +b^{2}\cos^{2}x}dx =\frac{1}{12}\tan^{- 1}(3\tan x) + constant, then the maximum value of asin⁡x+bcos⁡xa\sin x + b\cos x, is :

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