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Day 581: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 14 Jun 2022

    166
    Let a^\widehat{a} and b^\widehat{b} be two -unit vectors such that ∣(a^+b^)+2(a^×b^)∣=2|(\widehat{a}+\widehat{b}) + 2(\widehat{a}\times\widehat{b})| = 2. If θ∈(0,π)\theta \in (0,\pi) is the angle between a^\widehat{a} and b^\widehat{b}, then among the statements: (S1) : 2∣a^×b^∣=∣a^−b^∣2|\widehat{a}\times\widehat{b}| = |\widehat{a}-\widehat{b}| (S2) : The projection of a^\widehat{a} on (a^+b^)(\widehat{a}+\widehat{b}) is 12\frac{1}{2}

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  2. Question 2

    Application of Derivatives. Asked once: 25 Jul 2022

    66
    If the absolute maximum value of the function f(x)f(x) =(x2−2x+7)e(4x3−12x2−180x+31)=\left( x^{2}- 2x + 7 \right)e^{\left( 4x^{3}- 12x^{2}- 180x + 31 \right)} in the interval [−3\lbrack - 3, 0]0\rbrack is f(α)f(\alpha), then:

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  3. Question 3

    Application of Integrals. Asked once: 28 Jul 2022

    160
    The area enclosed by the curves y=log⁡e(x+e2)y =\log_{e}\left( x +e^{2} \right), x=log⁡e(2y)x =\log_{e}\left( \frac{2}{y} \right) and x=log⁡e2x =\log_{e}2, above the line y=1y = 1 is

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  4. Question 4

    Complex Numbers. Asked once: 28 Jul 2022

    75
    Let S1={z1∈C:∣z1−3∣=12}S_{1}=\left\{ z_{1}\in C:\left| z_{1}- 3 \right|=\frac{1}{2} \right\} S2={z2∈C:∣z2−∣z2+1∣∣=∣z2+∣z2−1∣∣}.S_{2}=\left\{ z_{2}\in C:\left| z_{2}- \right|z_{2}+ 1|| =\left| z_{2}+ \right|z_{2}- 1|| \right\}. Then, for z1∈S1z_{1}\in S_{1} and z2∈S2z_{2}\in S_{2}, the least value of ∣z2−z1∣\left| z_{2}-z_{1} \right| is:

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  5. Question 5

    Conic Sections. Asked once: 29 Jan 2025

    53
    Two parabolas have the same focus (4,3)(4,3) and their directrices are the xx-axis and the yy-axis, respectively. If these parabolas intersects at the points AA and BB, then (AB)2(AB)^{2} is equal to

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