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Day 40: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. This type asked 4 times: 2021 Paper 3, 2021 Paper 21, 27 Jun 2022, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 4 of this type

    70
    Let the direction cosines of two lines satisfy the equations: 4l+m−n=04\mathcal{l +}m - n = 0 and 2mn+10nl+3lm=02mn + 10n\mathcal{l +}3\mathcal{l}m = 0. Then the cosine of the acute angle between these lines is :

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  2. Question 2

    Three Dimensional Geometry. This type asked 4 times: 29 Jan 2023, 24 Jan 2025, 2 Apr 2025, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 4 of this type

    65
    The vertices B and C of a triangle ABC lie on the line x1=1−y−2=z−23\frac{x}{1}=\frac{1 - y}{- 2}=\frac{z - 2}{3}. The coordinates of A and B are ( 1,6,31,6,3 ) and ( 4,9,α4,9,\alpha ) respectively and C is at a distance of 10 units from B . The area (in sq. units) of △ABC\bigtriangleup ABC is:

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  3. Question 3

    Conic Sections. This type asked 4 times: 24 Jan 2025, 2 Apr 2025, 4 Apr 2025, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 4 of this type

    66
    Let SS and S′S^{'} be the foci of the ellipse x225+y29=1\frac{x^{2}}{25}+\frac{y^{2}}{9}= 1 and P(α,β)P(\alpha,\beta) be a point on the ellipse in the first quadrant. If (SP)2+(S′P)2−SP∙S′P=37(SP)^{2}+\left( S^{'}P \right)^{2}- SP \bullet S^{'}P = 37, then α2+β2\alpha^{2}+\beta^{2} is equal to :

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  4. Question 4

    Relations and Functions. This type asked 4 times: 27 Jul 2022, 3 Apr 2025, 4 Apr 2025, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 4 of this type

    64
    Let the domain of the function f(x)=log⁡3log⁡5(7−log⁡2(x2−10x+85))+sin⁡−1(∣3x−717−x∣)f(x) =\log_{3}\log_{5}\left( 7 -\log_{2}\left( x^{2}- 10x + 85 \right) \right)+\sin^{- 1}\left( \left| \frac{3x - 7}{17 - x} \right| \right) be (α,β](\alpha,\beta\rbrack. Then α+β\alpha + \beta is equal to :

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  5. Question 5

    Vector Algebra. This type asked 4 times: 28 Jul 2022, 27 Jan 2024, 8 Apr 2024, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 4 of this type

    71
    Let a vector a→=2i^−j^+λk^,λ>0\overrightarrow{a} = \sqrt{2}\widehat{i} - \widehat{j} + \lambda\widehat{k},\lambda > 0, make an obtuse angle with the vector b→=−λ2i^+42j^+42k^\overrightarrow{b} = - \lambda^{2}\widehat{i} + 4\sqrt{2}\widehat{j} + 4\sqrt{2}\widehat{k} and an angle θ,π6<θ<π2\theta,\frac{\pi}{6} < \theta < \frac{\pi}{2}, with the positive zz-axis. If the set of all possible values of λ\lambda is (α,β)−{γ}(\alpha,\beta) - \{\gamma\}, then α+β+γ\alpha + \beta + \gamma is equal to ____\_\_\_\_ .