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Day 629: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 2021 Paper 22

    63
    The sum of 10 terms of the series 312×22+522×32+732×42+…\frac{3}{1^{2}\times2^{2}}+\frac{5}{2^{2}\times3^{2}}+\frac{7}{3^{2}\times4^{2}}+ \ldots. is:

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  2. Question 2

    Conic Sections. Asked once: 11 Apr 2023

    71
    Consider ellipses Ek:kx2+k2y2=1,k=1,2,…E_{k}:kx^{2}+k^{2}y^{2}= 1,k = 1,2,\ldots 20. Let CkC_{k} be the circle which touches the four chords joining the end points (one on minor axis and another on major axis) of the ellipse EkE_{k}, If rkr_{k} is the radius of the circle CkC_{k}, then the value of ∑k=1201rk2\sum_{k = 1}^{20} \frac{1}{r_{k}^{2}} is

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  3. Question 3

    Definite Integration. Asked once: 27 Jun 2022

    159
    The integral ∫0117[1x]dx\int_{0}^{1} \frac{1}{7^{\left\lbrack \frac{1}{x} \right\rbrack}}dx, where [.] denotes the greatest integer function is equal to

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  4. Question 4

    Sequences and Series. Asked once: 2021 Paper 20

    62
    If for x,y∈R,x>0x,y\in R,x> 0, y=log⁡10x+log⁡10x1/3+log⁡10x1/9+….y=\log_{10}x +\log_{10}x^{1/3}+\log_{10}x^{1/9}+ \ldots.. upto ∞\infty terms and 2+4+6+…+2y3+6+9+….+3y=4log⁡10x\frac{2 + 4 + 6 + \ldots + 2y}{3 + 6 + 9 + \ldots. + 3y}=\frac{4}{\log_{10}x}, then the ordered pair (x,y)(x,y) is equal to:

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  5. Question 5

    Conic Sections. Asked once: 10 Apr 2023

    62
    Let the ellipse E:x2+9y2=9E:x^{2}+ 9y^{2}= 9 intersect the positive xx - and yy-axes at the points AA and BB respectively Let the major axis of EE be a diameter of the circle C. Let the line passing through A and B meet the circle CC at the point PP. If the area of the triangle which vertices A,PA,P and the origin OO is mn\frac{m}{n}, where mm and nn are coprime, then m−nm - n is equal to

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