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Day 32: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. This type asked 5 times: 2021 Paper 17, 28 Jun 2022, 24 Jan 2023, 31 Jan 2023, 11 Apr 2023. This one: 11 Apr 2023 See all 5 of this type

    171
    The number of points, where the curve f(x)=e8x−e6x−3e4x−e2x+1,x∈Rf(x) =e^{8x}-e^{6x}- 3e^{4x}-e^{2x}+ 1,x \in R cuts xx-axis, is equal to

  2. Question 2

    Three Dimensional Geometry. This type asked 5 times: 2021 Paper 1, 28 Jun 2022, 25 Jul 2022, 30 Jan 2023, 11 Apr 2023. This one: 11 Apr 2023 See all 5 of this type

    62
    If equation of the plane that contains the point (−2,3,5)( - 2,3,5) and is perpendicular to each of the planes 2x+4y+5z=82x + 4y + 5z = 8 and 3x−2y+3z=53x - 2y + 3z = 5 is αx+βy+γz+97=0\alpha x + \beta y + \gamma z + 97 = 0 then α+β+γ=\alpha + \beta + \gamma =

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  3. Question 3

    Three Dimensional Geometry. This type asked 5 times: 25 Jul 2022, 27 Jul 2022, 31 Jan 2023, 8 Apr 2023, 11 Apr 2023. This one: 11 Apr 2023 See all 5 of this type

    178
    Let the line l:x=1−y−2=z−3λ,λ∈R\mathcal{l:}x = \frac{1 - y}{- 2} = \frac{z - 3}{\lambda},\lambda \in R meet the plane P:x+2y+3z=4P:x + 2y + 3z = 4 at the point (α,β,γ)(\alpha,\beta,\gamma). If the angle between the line l\mathcal{l} and the plane PP is cos⁡−1(514)\cos^{- 1}\left( \sqrt{\frac{5}{14}} \right), then α+2β+6γ\alpha + 2\beta + 6\gamma is equal to

  4. Question 4

    Conic Sections. This type asked 5 times: 2021 Paper 1, 2021 Paper 23, 2021 Paper 26, 26 Jun 2022, 10 Apr 2023. This one: 10 Apr 2023 See all 5 of this type

    157
    Let AA be the point (1,2)(1,2) and BB be any point on the curve x2+y2=16x^{2}+y^{2}= 16. If the centre of the locus of the point PP, which divides the line segment ABAB in the ratio 3:23:2 is the point C(α,β)C(\alpha,\beta), then the length of the line segment ACAC is

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  5. Question 5

    Conic Sections. This type asked 5 times: 2021 Paper 8, 2021 Paper 23, 29 Jun 2022, 28 Jul 2022, 6 Apr 2023. This one: 6 Apr 2023 See all 5 of this type

    167
    If the tangents at the points PP and QQ on the circle x2+y2−2x+y=5x^{2}+y^{2}- 2x + y = 5 meet at the point R(94,2)R\left( \frac{9}{4},2 \right), then the area of the triangle PQRPQR is

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