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Day 615: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 2021 Paper 6

    70
    The least value of ∣z∣|z| where zz is complex number which satisfies the inequality
    exp⁡((∣z∣+3)(∣z∣−1)∣∣z∣+1∣log⁡e2)≥log⁡2∣57+9i∣\exp\left( \frac{(|z| + 3)(|z| - 1)}{||z| + 1|}\log_{e}2 \right)\geq\log_{\sqrt{2}}|5\sqrt{7}+ 9i|
    i=−1i =\sqrt{- 1}, is equal to:

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  2. Question 2

    Conic Sections. Asked once: 6 Apr 2024

    85
    Let L1, L2L_{1},{\text{ }L}_{2} be the lines passing through the point P(0,1)P(0,1) and touching the parabola 9x2+12x+18y−14=09x^{2}+ 12x+ 18y- 14 = 0. Let QQ and RR be the points on the lines L1L_{1} and L2L_{2} such that the △PQR\bigtriangleup PQR is an isosceles triangle with base QRQR. If the slopes of the lines QRQR are m1m_{1} and m2m_{2}. then 16(m12+m22)16\left( m_{1}^{2}+m_{2}^{2} \right) is equal to

  3. Question 3

    Definite Integration. Asked once: 25 Jan 2023

    160
    The integral 16∫12dxx3(x2+2)216\int_{1}^{2} \frac{dx}{x^{3}\left(x^{2}+2\right)^{2}} is equal to

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  4. Question 4

    Sequences and Series. Asked once: 24 Jan 2023

    174
    If 13+23+33+⋯ up to n terms 1⋅3+2⋅5+3⋅7+⋯ up to n terms =95\frac{1^{3}+2^{3}+3^{3}+ \cdots\text{~up to~}n\text{~terms~}}{1 \cdot 3 + 2 \cdot 5 + 3 \cdot 7 + \cdots\text{~up to~}n\text{~terms~}}=\frac{9}{5}, then the value of nn is

  5. Question 5

    Straight Lines. Asked once: 2021 Paper 1

    64
    A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 14\frac{1}{4}. Three stones A, B and C are placed at the points (1,1)(1,1), (2,2)(2,2) and (4,4)(4,4) respectively. Then which of these stones is/are on the path of the man?

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