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Day 549: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 11 Apr 2023

    168
    For a∈Ca \in C, let A={z∈C:Re(a+z‾)>Im(a‾+z)}\mathbf{A = \{ z \in C:Re(a +}\overline{z}) > Im(\overline{a}+ z)\} and B={z∈C:Re(a+zˉ)<Im(aˉ+z)}\mathbf{B = \{ z \in C:Re(a +}\bar{z}) < Im(\bar{a}+ z)\}. Then among the two statements: (S1): If Re(A),Im(A)>0Re(A),Im(A) > 0, then the set A contains all the real numbers (S2): If Re(A),Im(A)<0Re(A),Im(A) < 0, then the set BB contains all the real numbers,

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  2. Question 2

    Conic Sections. Asked once: 4 Apr 2025

    131
    Let the values of pp, for which the shortest distance between the lines x+13=y4=z5\frac{x+ 1}{3}=\frac{y}{4}=\frac{z}{5} and r→=(pi^^+2j^+k^)+λ(2i^+3j^+4k^)\overrightarrow{r}= (\widehat{p\widehat{i}}+ 2\widehat{j}+\widehat{k}) +\lambda(2\widehat{i}+ 3\widehat{j}+ 4\widehat{k}) is 16\frac{1}{\sqrt{6}}, be a,ba,b, (a<b)(a < b). Then the length of the latus rectum of the ellipse x2a2+y2b2=1\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1 is :-

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  3. Question 3

    Definite Integration. Asked once: 6 Apr 2024

    63
    ∫0π/4cos⁡2xsin⁡2x(cos⁡3x+sin⁡3x)2dx\int_{0}^{\pi/4} \frac{\cos^{2}x\sin^{2}x}{\left( \cos^{3}x+\sin^{3}x \right)^{2}}dx is equal to

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  4. Question 4

    Indefinite Integration. Asked once: 2021 Paper 9

    67
    The integral ∫(2x−1)cos⁡(2x−1)2+54x2−4x+6dx\int\frac{(2x- 1)\cos\sqrt{(2x- 1)^{2}+ 5}}{\sqrt{4x^{2}- 4x+ 6}}dx is equal to (where cc is a constant of integration)

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  5. Question 5

    Limits and Continuity. Asked once: 29 Jun 2022

    155
    The value of lim⁡x→1(x2−1)sin⁡2(πx)x4−2x3+2x−1\lim_{x \rightarrow 1} \frac{\left( x^{2}- 1 \right)\sin^{2}(\pi x)}{x^{4}- 2x^{3}+ 2x - 1} is equal to:

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