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Day 471: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 24 Jan 2025

    138
    Suppose A and B are the coefficients of 30th30^{\text{th}} and 12th12^{\text{th}} terms respectively in the binomial expansion of (1+x)2n−1(1 +x)^{2n- 1}. If 2A=5B2A= 5B, then nn is equal to:

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  2. Question 2

    Complex Numbers. Asked once: 7 Apr 2025

    136
    If the locus of z∈Cz\in C, such that
    Re(z−12z+i)+Re(zˉ−12zˉ−i)=2,Re\left( \frac{z- 1}{2z+ i} \right)+ Re\left( \frac{\bar{z}- 1}{2\bar{z}- i} \right)= 2,
    is a circle of radius r and center (a,b)(a,b) then 15abr2\frac{15ab}{r^{2}} is equal to:

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  3. Question 3

    Conic Sections. Asked once: 6 Apr 2026 S1

    62
    Let chord PQ of length 3133\sqrt{13} of the parabola y2=12xy^{2}= 12x be such that the ordinates of points PP and Q are in the ratio 1:21:2. If the chord PQ subtends an angle α\alpha at the focus of the parabola, then sin⁡α\sin\alpha is equal to :

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  4. Question 4

    Definite Integration. Asked once: 4 Apr 2026 S1

    69
    Let ∫−22(∣sin⁡x∣+[xsin⁡x])dx=2(3−cos⁡2)+β\int_{- 2}^{2} (|\sin x| + \lbrack x\sin x\rbrack)dx= 2(3 - \cos2) +\beta, where [⋅]\lbrack \cdot \rbrack is the greatest integer function . Then βsin⁡(β2)\beta\sin\left( \frac{\beta}{2} \right) equals.

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  5. Question 5

    Determinants. Asked once: 29 Jan 2024

    75
    Let A=[1000αβ0βα]A =\begin{bmatrix} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{bmatrix} and ∣2 A∣3=221|2\text{ }A|^{3}=2^{21} where α,β∈Z\alpha,\beta \in Z, Then a value of α\alpha is

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