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Day 452: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 2 Apr 2026 S1

    52
    Let xx and yy be real number such that 50(2x1+3i−y1−2i)=31+17i,i=−150\left( \frac{2x}{1 + 3i}-\frac{y}{1 - 2i} \right)= 31 + 17i,i=\sqrt{- 1}. Then the value of 10(x−3y)10(x- 3y) is :

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  2. Question 2

    Conic Sections. Asked once: 6 Apr 2026 S2

    61
    The eccentricity of an ellipse E with center at the origin OO is 32\frac{\sqrt{3}}{2} and its directrices are x=±463x= \pm\frac{4\sqrt{6}}{3}. Let H:x2a2−y2b2=1H:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1 be a hyperbola whose eccentricity is equal to the length of semi-major axis of E , and whose length of latus rectum is equal to the length of minor axis of E . Then the distance between the foci of H is :

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  3. Question 3

    Definite Integration. Asked once: 5 Apr 2026 S2

    68
    Let (21−a+21+a),f(a),(3a+3−a)\left( 2^{1 - a}+2^{1 + a} \right),f(a),\left( 3^{a}+3^{- a} \right) be a A. P. and α\alpha be the minimum value of f(a)f(a). Then the value of the integral ∫log⁡e(α−1)log⁡e(α)dx(e2x−e−2x)\int_{\log_{e}(\alpha- 1)}^{\log_{e}(\alpha)} \frac{dx}{\left( e^{2x}-e^{- 2x} \right)} is :

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  4. Question 4

    Determinants. Asked once: 24 Jan 2025

    140
    For some a,ba,b, let
    f(x)=∣a+sin⁡xx1ba1+sin⁡xxba1b+sin⁡xx∣, x≠0f(x) =\left| \begin{matrix} a +\frac{\sin x}{x} & 1 & b \\ a & 1 +\frac{\sin x}{x} & b \\ a & 1 & b +\frac{\sin x}{x} \end{matrix} \right|,\ x \neq 0
    lim⁡x→0f(x)=λ+μa+vb\lim_{x \rightarrow 0} f(x) = \lambda + \mu a + vb. Then (λ+μ+v)2(\lambda + \mu + v)^{2} is equal to:

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  5. Question 5

    Differential Equations. Asked once: 6 Apr 2024

    154
    Suppose the solution of the differential equation dydx=(2+α)x−βy+2βx−2αy−(βγ−4α)\frac{dy}{dx}=\frac{(2 + \alpha)x - \beta y + 2}{\beta x - 2\alpha y - (\beta\gamma - 4\alpha)} represents a circle passing through origin. Then the radius of this circle is:

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