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Day 484: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 3 Apr 2025

    130
    Consider the lines x(3λ+1)+y(7λ+2)=17λ+5x(3\lambda+ 1) +y(7\lambda+ 2) = 17\lambda+ 5, λ\lambda being a parameter, all passing through a point P . One of these lines (say L) is farthest from the origin. If the distance of LL from the point (3,6)(3,6) is d , then the value of d2d^{2} is.

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  2. Question 2

    Three Dimensional Geometry. Asked once: 12 Apr 2023

    84
    Let the plane x+3y−2z+6=0x + 3y - 2z + 6 = 0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABCABC is (α,β,67)\left( \alpha,\beta,\frac{6}{7} \right), then 98(α+β)298(\alpha + \beta)^{2} is equal to

  3. Question 3

    Trigonometric Equations. Asked once: 27 Jul 2022

    169
    Let S={θ∈(0,π2):∑m=19sec(θ+(m−1)π6)sec(θ+mπ6)=−83}S =\left\{ \theta \in\left( 0,\frac{\pi}{2} \right):\sum_{m = 1}^{9} sec\left( \theta + (m - 1)\frac{\pi}{6} \right)sec\left( \theta +\frac{m\pi}{6} \right)= -\frac{8}{\sqrt{3}} \right\}. Then

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  4. Question 4

    Trigonometric Identities. Asked once: 23 Jan 2025

    65
    The value of (sin⁡70∘)(cot⁡10∘cot⁡70∘−1)\left( \sin70^{\circ} \right)\left( \cot10^{\circ}\cot70^{\circ}- 1 \right) is

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  5. Question 5

    Vector Algebra. Asked once: 23 Jan 2025

    132
    Let the point A divide the line segment joining the points P(−1,−1,2)P( - 1, - 1,2) and Q(5,5,10)Q(5,5,10) internally in the ratio r:1(r>0)r:1(r > 0). If OO is the origin and (OQ→⋅OA→)−15∣OP→×OA→∣2=10(\overrightarrow{OQ}\cdot\overrightarrow{OA}) -\frac{1}{5}|\overrightarrow{OP}\times\overrightarrow{OA}|^{2}= 10, then the value of r is :

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