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Day 224: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 2021 Paper 20 (same type asked 2 times) See all 2 of this type

    61
    If 0<x<10 <x< 1, then 32x2+53x3+74x4+….\frac{3}{2}x^{2}+\frac{5}{3}x^{3}+\frac{7}{4}x^{4}+ \ldots.. , is equal to :

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  2. Question 2

    Conic Sections. Asked once: 2021 Paper 5 (same type asked 2 times) See all 2 of this type

    78
    The locus of the midpoints of the chord of the circle, x2+y2=25x^{2}+y^{2}= 25 which is tangent to the hyperbola, x29−y216=1\frac{x^{2}}{9}-\frac{y^{2}}{16}= 1 is:

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  3. Question 3

    Limits and Continuity. Asked once: 2021 Paper 16 (same type asked 2 times) See all 2 of this type

    55
    f(x)=f(x) = minimum {x−[x], 1+[x]−x}\{ x - \lbrack x\rbrack,\ 1 + \lbrack x\rbrack - x\}, [0,3]→R\lbrack 0,3\rbrack \rightarrow R, pp is the number of points where it is discontinuous, qq is the number of points where it is not differentiable. Find p+qp+q.

  4. Question 4

    Trigonometric Identities. Asked once: 2021 Paper 5 (same type asked 2 times) See all 2 of this type

    65
    If for x∈(0,π2),log⁡10sin⁡x+log⁡10cos⁡x=−1x\in\left( 0,\frac{\pi}{2} \right),\log_{10}\sin x+\log_{10}\cos x= - 1 and log⁡10(sin⁡x+cos⁡x)=12(log⁡10n−1),n>0\log_{10}(\sin x + \cos x) =\frac{1}{2}\left( \log_{10}n - 1 \right),n > 0, then the value of nn is equal to:

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  5. Question 5

    Sequences and Series. Asked once: 2021 Paper 6 (same type asked 2 times) See all 2 of this type

    90
    Let Sn(x)=log⁡a1/2x+log⁡a1/3x+log⁡a1/6xS_{n}(x) =\log_{a^{1/2}}x+\log_{a^{1/3}}x+\log_{a^{1/6}}x
    +log⁡a1/11x+log⁡a1/18x+log⁡a1/27x+…+\log_{a^{1/11}}x+\log_{a^{1/18}}x+\log_{a^{1/27}}x+ \ldots
    up to n-terms, where a>1a> 1. If S24(x)=1093S_{24}(x) = 1093 and S12(2x)=265S_{12}(2x) = 265, then value of aa is equal to