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Day 71: JEE Mains Maths

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

  1. Question 1

    Probability. This type asked 3 times: 27 Jul 2022, 29 Jul 2022, 29 Jan 2024. This one: 29 Jan 2024 See all 3 of this type

    169
    An integer is chosen at random from the integers 1 , 2,3,…,502,3,\ldots,50. The probability that the chosen integer is a multiple of atleast one of 4,6 and 7 is

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  2. Question 2

    Sequences and Series. This type asked 3 times: 2021 Paper 16, 24 Jan 2023, 29 Jan 2024. This one: 29 Jan 2024 See all 3 of this type

    159
    If log⁡ea,log⁡eb,log⁡ec\log_{e}a,\log_{e}b,\log_{e}c are in an A.P. and log⁡ea−\log_{e}a - log⁡e2b,log⁡e2b−log⁡e3c,log⁡e3c−log⁡e\log_{e}2b,\log_{e}2b -\log_{e}3c,\log_{e}3c -\log_{e} a are also in an A.P, then a:b:ca:b:c is equal to

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  3. Question 3

    Conic Sections. This type asked 3 times: 2021 Paper 7, 27 Jun 2022, 27 Jan 2024. This one: 27 Jan 2024 See all 3 of this type

    178
    Consider a circle (x−α)2+(y−β)2=50(x-\alpha)^{2}+ (y-\beta)^{2}= 50, where α,β>0\alpha,\beta> 0. If the circle touches the line y+x=0y+x= 0 at the point PP, whose distance from the origin is 424\sqrt{2} , then (α+β)2(\alpha+\beta)^{2} is equal to........

  4. Question 4

    Differentiation. This type asked 3 times: 2021 Paper 17, 29 Jun 2022, 27 Jan 2024. This one: 27 Jan 2024 See all 3 of this type

    152
    Consider the function f:(0,2)→Rf:(0,2) \rightarrow R defined by f(x)=x2+2xf(x) =\frac{x}{2}+\frac{2}{x} and the function g(x)g(x) defined by g(x)={min⁡{f(t):0<t≤x},0<x≤132+x,1<x<2g(x) =\left\{ \begin{matrix} \min\{ f(t) : 0 < t \leq x\}, & 0 < x \leq 1 \\ \frac{3}{2}+ x, & 1 < x < 2 \end{matrix} \right.. Then

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  5. Question 5

    Three Dimensional Geometry. This type asked 3 times: 24 Jan 2023, 11 Apr 2023, 15 Apr 2023. This one: 15 Apr 2023 See all 3 of this type

    76
    Let the foot of perpendicular of the point P(3,−2,−9)P(3, - 2, - 9) on the plane passing through the points (−1,−2,−3),(9,3,4),(9,−2,1)( - 1, - 2, - 3),(9,3,4),(9, - 2,1) be Q(α,β,γ)Q(\alpha,\beta,\gamma). Then the distance of QQ from the origin is:

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