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Day 490: JEE Mains Maths

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

  1. Question 1

    Application of Integrals. Asked once: 29 Jan 2025

    128
    Let the area enclosed between the curves ∣y∣=1−|y| = 1 - x2x^{2} and x2+y2=1x^{2}+y^{2}= 1 be α\alpha. If 9α=βπ+γ;β,γ9\alpha = \beta\pi + \gamma;\beta,\gamma are integers, then the value of ∣β−γ∣|\beta - \gamma| equals

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  2. Question 2

    Binomial Theorem. Asked once: 4 Apr 2024

    86
    Let a=1+ 2C23!+ 3C24!+ 4C25!+…a = 1 +\frac{\ ^{2}C_{2}}{3!}+\frac{\ ^{3}C_{2}}{4!}+\frac{\ ^{4}C_{2}}{5!}+ \ldots,
    b=1+ 1C0+ 1C11!+ 2C0+ 2C1+ 2C22!+ 3C0+ 3C1+ 3C2+ 3C33!+…b = 1 +\frac{\ ^{1}C_{0}+\ ^{1}C_{1}}{1!}+\frac{\ ^{2}C_{0}+\ ^{2}C_{1}+\ ^{2}C_{2}}{2!}+\frac{\ ^{3}C_{0}+\ ^{3}C_{1}+\ ^{3}C_{2}+\ ^{3}C_{3}}{3!}+ \ldots
    Then 2 ba2\frac{2\text{ }b}{a^{2}} is equal to

  3. Question 3

    Complex Numbers. Asked once: 23 Jan 2025

    142
    The number of complex numbers zz, satisfying ∣z∣=1|z| = 1 and ∣zzˉ+zˉz∣=1\left| \frac{z}{\bar{z}}+\frac{\bar{z}}{z} \right|= 1, is :

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  4. Question 4

    Conic Sections. Asked once: 4 Apr 2026 S1

    72
    Consider the parabola P:y2=4kxP:y^{2} = 4kx and the ellipse E:x2a2+y2 b2=1E:\frac{x^{2}}{a^{2}} + \frac{y^{2}}{{\text{ }b}^{2}} = 1. Let the line segment joining the points of intersection of P and E be their latus rectums. If the eccentricity of E is e , then e2+22e^{2} + 2\sqrt{2} is equal to ____\_\_\_\_ .

  5. Question 5

    Definite Integration. Asked once: 28 Jan 2026 S1

    74
    The value of ∑r=120(∣π(∫0rx∣sin⁡πx∣dx)∣)\sum_{r = 1}^{20} \left( \left| \sqrt{\pi\left( \int_{0}^{r} x|\sin\pi x|dx \right)} \right| \right) is ....... .