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Day 525: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 4 Apr 2024

    63
    The vertices of a triangle are A(−1,3),B(−2,2)A( - 1,3),B( - 2,2) and C(3,−1)C(3, - 1). A new triangle is formed by shifting the sides of the triangle by one-unit inwards. Then the equation of the side of the new triangle nearest to origin is:

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  2. Question 2

    Three Dimensional Geometry. Asked once: 29 Jan 2023

    86
    Let the equation of the plane PP containing the line x+10=8−y2=zx + 10 =\frac{8 - y}{2}= z be ax+by+3z=2(a+b)ax + by + 3z = 2(a + b) and the distance of the plane PP from the point (1,27,7)(1,27,7) be cc. Then a2+b2+c2a^{2}+b^{2}+c^{2} is equal to

  3. Question 3

    Trigonometric Identities. Asked once: 2021 Paper 17

    67
    If tan⁡(π9),x,tan⁡(7π18)\tan\left( \frac{\pi}{9} \right),x,\tan\left( \frac{7\pi}{18} \right) are in arithmetic progression and tan⁡(π9),y,tan⁡(5π18)\tan\left( \frac{\pi}{9} \right),y,\tan\left( \frac{5\pi}{18} \right) are also in arithmetic progression, then ∣x−2y∣|x- 2y| is equal to:

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  4. Question 4

    Vector Algebra. Asked once: 11 Apr 2023

    156
    If four distinct points with position vectors a→,b→,c→\overrightarrow{a},\overrightarrow{b},\overrightarrow{c} and d→\overrightarrow{d} are coplanar; then [a→b→c→]\lbrack\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\rbrack is equal to

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  5. Question 5

    Application of Derivatives. Asked once: 15 Apr 2023

    89
    Consider the triangles with vertices A(2,1)B(0,0)A(2,1)B(0,0) and C(t,4),t∈[0,4]C(t,4),t \in \lbrack 0,4\rbrack. If the maximum and the minimum perimeters of such triangles are obtained at t=αt = \alpha and t=βt = \beta respectively, then 6α+21β6\alpha + 21\beta is equal to