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Day 23: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. This type asked 5 times: 31 Jan 2023, 6 Apr 2024, 23 Jan 2025, 24 Jan 2025, 6 Apr 2026 S2. This one: 6 Apr 2026 S2 See all 5 of this type

    74
    Let the image of the point P(0,−5,0)P(0, - 5,0) in the line x−12=y1=z+1−2\frac{x - 1}{2} = \frac{y}{1} = \frac{z + 1}{- 2} be the point RR and the image of the point Q(0,−12,0)Q\left( 0,\frac{- 1}{2},0 \right) in the line x−1−1=y+94=z+11\frac{x - 1}{- 1} = \frac{y + 9}{4} = \frac{z + 1}{1} be the point S. Then the square of the area of the parallelogram PQRS is ____\_\_\_\_ .

  2. Question 2

    Application of Integrals. This type asked 5 times: 14 Jun 2022, 24 Jan 2023, 30 Jan 2024, 4 Apr 2024, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 5 of this type

    69
    The area of the region {(x,y):0≤y≤6−x, y2≥4x−3, x≥0}\{(x,y):0 \leq y \leq 6 - x,\ y^{2}\geq 4x - 3,\ x \geq 0\} is :

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  3. Question 3

    Relations and Functions. This type asked 5 times: 2021 Paper 9, 2021 Paper 11, 11 Apr 2023, 4 Apr 2026 S1, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 5 of this type

    51
    Let [.] denote the greatest integer function. If the domain of the function f(x)=sin⁡−1(x+[x]3)f(x) =\sin^{- 1}\left( \frac{x+ \lbrack x\rbrack}{3} \right) is [α,β)\lbrack\alpha,\beta), then α2+β2\alpha^{2}+\beta^{2} is equal to:

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  4. Question 4

    Sequences and Series. This type asked 5 times: 31 Jan 2023, 6 Apr 2023, 13 Apr 2023, 4 Apr 2025, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 5 of this type

    55
    The value of 13−23+33−….+1531^{3}-2^{3}+3^{3}- \ldots. +15^{3} is:

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  5. Question 5

    Three Dimensional Geometry. This type asked 5 times: 28 Jun 2022, 26 Jul 2022, 1 Feb 2024, 4 Apr 2025, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 5 of this type

    64
    Let a triangle PQR be such that P and Q lie on the line x+38=y−42=z+12\frac{x+ 3}{8}=\frac{y- 4}{2}=\frac{z+ 1}{2} and are at a distance of 6 units from R(1,2,3)R(1,2,3). If (α,β,γ)(\alpha,\beta,\gamma) is the centroid of ΔPQR\Delta PQR, then α+β+γ\alpha+\beta+\gamma is equal to:

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