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Day 616: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2021 Paper 4

    87
    If the curves x=y4x=y^{4} and xy=kxy=k cut at right angles, then (4k)6(4k)^{6} is equal to

  2. Question 2

    Complex Numbers. Asked once: 2021 Paper 5

    90
    Let zz and ww be two complex numbers such that w=zz‾−2z+2,∣z+iz−3i∣=1w = z\overline{z}- 2z + 2,\left| \frac{z + i}{z - 3i} \right|= 1 and Re(w)Re(w) has minimum value. Then, the minimum value of n∈Nn \in\mathbb{N} for which wnw^{n} is real, is equal to

  3. Question 3

    Conic Sections. Asked once: 6 Apr 2024

    82
    Let a conic C pass through the point (4,−2)(4, - 2) and P(x,y),x≥3P(x,y),x \geq 3, be any point on CC. Let the slope of the line touching the conic CC only at a single point PP be half the slope of the line joining the points PP and (3,−5)(3, - 5). If the focal distance of the point (7,1)(7,1) on CC is dd, then 12 d12\text{ }d equals

  4. Question 4

    Definite Integration. Asked once: 25 Jan 2023

    179
    If ∫133∣log⁡ex∣dx=mnlog⁡e(n2e)\int_{\frac{1}{3}}^{3} \left| \log_{e}x \right|dx =\frac{m}{n}\log_{e}\left( \frac{n^{2}}{e} \right), where mm and nn are coprime natural numbers, then m2+n2−5m^{2}+n^{2}- 5 is equal to

  5. Question 5

    Sequences and Series. Asked once: 28 Jul 2022

    79
    Consider the sequence a1,a2,a3a_{1},a_{2},a_{3}, such that a1=1,a2=2a_{1}= 1,a_{2}= 2 and an+2=2an+1+ana_{n + 2}=\frac{2}{a_{n + 1}}+a_{n} for n=1,2,3,…n = 1,2,3,\ldots If (a1+1a2a3)⋅(a2+1a3a4)⋅(a3+1a4a5)…..⋅(a30+1a31a32)=2α( 61C31)\left( \frac{a_{1}+\frac{1}{a_{2}}}{a_{3}} \right)\cdot\left( \frac{a_{2}+\frac{1}{a_{3}}}{a_{4}} \right)\cdot\left( \frac{a_{3}+\frac{1}{a_{4}}}{a_{5}} \right)\ldots.. \cdot\left( \frac{a_{30}+\frac{1}{a_{31}}}{a_{32}} \right)=2^{\alpha}\left( \ ^{61}C_{31} \right), then α\alpha is equal to:

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