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Day 476: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 4 Apr 2025

    130
    Let the product of ω1=(8+i)sin⁡θ+(7+4i)cos⁡θ\omega_{1}=\left( 8 +i \right)\sin\theta+\left( 7 + 4i \right)\cos\theta and ω2=(1+8i)sin⁡θ+(4+7i)cos⁡θ\omega_{2}=\left( 1 + 8i \right)\sin\theta+ (4 + 7i)\cos\theta be α+iβ\alpha+ i\beta, i=−1i =\sqrt{- 1}. Let p and q be the maximum and the minimum values of α+β\alpha+\beta respectively. Then p+qp+q is equal to

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  2. Question 2

    Conic Sections. Asked once: 5 Apr 2026 S2

    62
    Let the directrix of the parabola P:y2=8xP:y^{2}= 8x, cut x -axis at the point A . Let B(α,β),α>1B(\alpha,\beta),\alpha> 1, be a point on P such that the slope of AB is 3/53/5. If BC is a focal chord of P , then six times the area of △ABC\bigtriangleup ABC is:

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  3. Question 3

    Definite Integration. Asked once: 2 Apr 2026 S1

    69
    Let [.] denote the greatest integer function. Then the value of ∫03(ex+e−x[x]!)dx\int_{0}^{3} \left( \frac{e^{x}+e^{- x}}{\lbrack x\rbrack!} \right)dx is:

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  4. Question 4

    Determinants. Asked once: 27 Jan 2024

    162
    The values of α\alpha, for which ∣132α+32113α+132α+33α+10∣=0\left| \begin{matrix} 1 & \frac{3}{2} & \alpha +\frac{3}{2} \\ 1 & \frac{1}{3} & \alpha +\frac{1}{3} \\ 2\alpha + 3 & 3\alpha + 1 & 0 \end{matrix} \right|= 0, lie in the interval

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  5. Question 5

    Differential Equations. Asked once: 26 Jul 2022

    87
    Let a curve y=y(x)y = y(x) pass through the point (3,3)(3,3) and the area of the region under this curve, above the xx-axis and between the abscissae 3 and x(>3)x( > 3) be (yx)3\left( \frac{y}{x} \right)^{3}. If this curve also passes through the point (α,610)(\alpha,6\sqrt{10}) in the first quadrant, then α\alpha is equal to