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Day 72: JEE Mains Maths

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

  1. Question 1

    Conic Sections. This type asked 3 times: 28 Jun 2022, 30 Jan 2023, 13 Apr 2023. This one: 13 Apr 2023 See all 3 of this type

    160
    Let the centre of a circle CC be (α,β)(\alpha,\beta) and its radius r<8r < 8. Let 3x+4y=243x + 4y = 24 and 3x−4y=323x - 4y = 32 be two tangents and 4x4x +3y=1+ 3y = 1 be a normal to CC. Then (α−β+r)(\alpha - \beta + r) is equal to

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  2. Question 2

    Definite Integration. This type asked 3 times: 2021 Paper 4, 24 Jan 2023, 12 Apr 2023. This one: 12 Apr 2023 See all 3 of this type

    89
    If ∫−0.150.15∣100x2−1∣dx=k3000\int_{- 0.15}^{0.15} \left| 100x^{2}- 1 \right|dx =\frac{k}{3000}, then kk is equal to

  3. Question 3

    Quadratic Equations. This type asked 3 times: 2021 Paper 11, 2021 Paper 16, 12 Apr 2023. This one: 12 Apr 2023 See all 3 of this type

    62
    Let α,β\alpha,\beta be the roots of the quadratic equation x2+6x+3=0x^{2}+\sqrt{6}x + 3 = 0. Then α23+β23+α14+β14α15+β15+α10+β10\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}} is equal to

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  4. Question 4

    Differentiation. This type asked 3 times: 2021 Paper 5, 26 Jun 2022, 11 Apr 2023. This one: 11 Apr 2023 See all 3 of this type

    170
    Let ff and gg be two functions defined by f(x)={x+1,x<0∣x−1∣,x≥0f(x) =\left\{ \begin{matrix} x + 1, & x < 0 \\ |x - 1|, & x \geq 0 \end{matrix} \right. and g(x)={x+1,x<01,x≥0g(x) =\left\{ \begin{matrix} x + 1, & x < 0 \\ 1, & x \geq 0 \end{matrix} \right.. Then (gof) (x) is

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  5. Question 5

    Three Dimensional Geometry. This type asked 3 times: 29 Jul 2022, 6 Apr 2023, 10 Apr 2023. This one: 10 Apr 2023 See all 3 of this type

    173
    Let the foot of perpendicular from the point A(4,3A(4,3, 1) on the plane P:x−y+2z+3=0P:x - y + 2z + 3 = 0 be NN. If B(5B(5, α,β),α,β∈Z\alpha,\beta),\alpha,\beta \in Z is a point on plane PP such that the area of the triangle ABNABN in 323\sqrt{2}, then α2+β2+αβ\alpha^{2}+\beta^{2}+ \alpha\beta is equal to