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Day 522: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 31 Jan 2023

    81
    Let α>0\alpha > 0, be the smallest number such that the expansion of (x23+2x3)30\left( x^{\frac{2}{3}}+\frac{2}{x^{3}} \right)^{30} has a term βx−α,β∈N\beta x^{- \alpha},\beta \in N. Then α\alpha is equal to

  2. Question 2

    Complex Numbers. Asked once: 31 Jan 2024

    153
    Let z1z_{1} and z2z_{2} be two complex number such that z1z_{1} +z2=5+z_{2}= 5 and z13+z23=20+15iz_{1}^{3}+z_{2}^{3}= 20 + 15i. Then ∣z14+z24∣\left| z_{1}^{4}+z_{2}^{4} \right| equals-

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  3. Question 3

    Conic Sections. Asked once: 24 Jan 2026 S1

    52
    Let a circle of radius 4 pass through the origin O , the points A(−3a,0)A( -\sqrt{3}a,0) and B(0,−2 b)B(0, -\sqrt{2}\text{ }b), where a and b are real parameters and ab≠0ab \neq 0. Then the locus of the centroid of △OAB\bigtriangleup OAB is a circle of radius

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  4. Question 4

    Definite Integration. Asked once: 2 Apr 2025

    71
    Let [•] denote the greatest integer function. If ∫0e3[1ex−1]dx=α−log⁡e2\int_{0}^{e^{3}} \left\lbrack \frac{1}{e^{x - 1}} \right\rbrack dx = \alpha - \log_{e}2, then α3\alpha^{3} is equal to

  5. Question 5

    Determinants. Asked once: 2021 Paper 15

    50
    If −π4≤x≤π4-\frac{\pi}{4}\leq x\leq\frac{\pi}{4} and ∣sin⁡xcos⁡xcos⁡xcos⁡xsin⁡xcos⁡xcos⁡xcos⁡xsin⁡x∣=0\left| \begin{matrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \end{matrix} \right|= 0, then the number of solutions is