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Day 191: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 29 Jul 2022 (same type asked 3 times) See all 3 of this type

    79
    Let S={1,2,3,…,2022}\mathbf{S = \{ 1,2,3,\ldots,2022\}}. Then the probability, that a randomly chosen number nn from the set SS such that HCF(n,2022)=1HCF(n,2022) = 1, is:

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  2. Question 2

    Sequences and Series. Asked once: 24 Jan 2023 (same type asked 3 times) See all 3 of this type

    67
    For three positive integers p, q , r, xpq2=yqr=zp2rx^{pq^{2}}=y^{qr}=z^{p^{2}r} and r=pq+1r = pq + 1 such that 3,3log⁡yx,3log⁡zy3,3\log_{y}x,3\log_{z}y, 7log⁡xz7\log_{x}z are in A.P. with common difference 12\frac{1}{2}. Then r−p−qr - p - q is equal to

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  3. Question 3

    Conic Sections. Asked once: 27 Jun 2022 (same type asked 3 times) See all 3 of this type

    179
    Let a circle CC of radius 5 lie below the xx-axis. The line L1=4x+3y+2L_{1}= 4x + 3y + 2 passes through the centre PP of the circle CC and intersects the line L2:3x−4y−11=0L_{2}:3x - 4y - 11 = 0 at QQ. The line L2L_{2} touches CC at the point QQ. Then the distance of PP from the line 5x−12y+51=05x - 12y + 51 = 0 is

  4. Question 4

    Differentiation. Asked once: 29 Jun 2022 (same type asked 3 times) See all 3 of this type

    64
    Let f:R→Rf:R \rightarrow R be a function defined by:
    f(x)={max⁡{t3−3t:t≤x},x≤2x2+2x−6,2<x<3[x−3]+9,3≤x≤52x+1,x>5f(x) =\begin{cases} \max\left\{ t^{3}- 3t : t \leq x \right\}, & x \leq 2 \\ x^{2}+ 2x - 6, & 2 < x < 3 \\ \lbrack x - 3\rbrack + 9, & 3 \leq x \leq 5 \\ 2x + 1, & x > 5 \end{cases}
    Where [t]\lbrack t\rbrack is the greatest integer less than or equal to tt. Let mm be the number of points where ff is not differentiable and I=∫−22f(x)dxI =\int_{- 2}^{2} f(x)dx. Then the ordered pair (m, I) is equal to:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 11 Apr 2023 (same type asked 3 times) See all 3 of this type

    160
    Let PP be the plane passing through the points (5,3(5,3, 0),(13,3,−2)0),(13,3, - 2) and (1,6,2)(1,6,2). For α∈N\alpha \in N, if the distances of the points A(3,4,α)A(3,4,\alpha) and B(2,α,a)B(2,\alpha,a) from the plane PP are 2 and 3 respectively, then the positive value of aa is

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