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Day 495: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 1 Feb 2024

    156
    Let mm and nn be the coefficients of seventh and thirteenth terms respectively in the expansion of (13x13+12x23)18\left( \frac{1}{3}x^{\frac{1}{3}}+\frac{1}{2x^{\frac{2}{3}}} \right)^{18}. Then (nm)13\left( \frac{n}{m} \right)^{\frac{1}{3}} is:

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  2. Question 2

    Complex Numbers. Asked once: 23 Jan 2025

    147
    Let α,β\alpha,\beta be the roots of the equation x2−ax−b=0x^{2}- ax - b = 0 with Im(α)<Im(β)Im(\alpha) < Im(\beta). Let Pn=αn−βnP_{n}=\alpha^{n}-\beta^{n}. If P3=−57i, P4=−37i, P5=117iP_{3}= - 5\sqrt{7}i,\ P_{4}= - 3\sqrt{7}i,\ P_{5}= 11\sqrt{7}i and P6=457iP_{6}= 45\sqrt{7}i, then ∣α4+β4∣\left| \alpha^{4}+\beta^{4} \right| is equal to  ___\ \_\_\_ .

  3. Question 3

    Conic Sections. Asked once: 2 Apr 2026 S2

    73
    Let A be the point (3,0)(3,0) and circles with variable diameter AB touch the circle x2+y2=36x^{2} + y^{2} = 36 internally. Let the curve C be the locus of the point B. If the eccentricity of C is e , then 72e272e^{2} is equal to ____\_\_\_\_ .

  4. Question 4

    Definite Integration. Asked once: 23 Jan 2026 S2

    73
    The number of elements in the set S={x:x∈[0,100]S = \left\{ x:x \in \lbrack 0,100\rbrack \right. and  ∫0xt2sin⁡(x−t)dt=x2}\left. \ \int_{0}^{x} t^{2}\sin(x - t)dt = x^{2} \right\} is.....

  5. Question 5

    Determinants. Asked once: 24 Jan 2023

    63
    Let α\alpha be a root of the equation (a−c)x2+(b−a)x+(c−b)=0(a-c)x^{2}+ (b-a)x+ (c-b) = 0 where a,b,ca,b,c are distinct real numbers such that the matrix [α2α1111abc]\begin{bmatrix} \alpha^{2} & \alpha & 1 \\ 1 & 1 & 1 \\ a & b & c \end{bmatrix} is singular. Then, the value of (a−c)2(b−a)(c−b)+(b−a)2(a−c)(c−b)+(c−b)2(a−c)(b−a)\frac{(a-c)^{2}}{(b-a)(c-b)}+\frac{(b-a)^{2}}{(a-c)(c-b)}+\frac{(c-b)^{2}}{(a-c)(b-a)} is

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