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Day 193: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 28 Jul 2022 (same type asked 3 times) See all 3 of this type

    71
    If the tangents drawn at the points PP and QQ on the parabola y2=2x−3y^{2}= 2x - 3 intersect at the point R(0,1)R(0,1), then the orthocentre of the triangle PQRPQR is:

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  2. Question 2

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

    165
    Let A,B,CA,B,C be three points whose position vectors respectively are:
    a→=i^+4j^+3k^\overrightarrow{a}=\widehat{i}+ 4\widehat{j}+ 3\widehat{k}
    b→=2i^+αj^+4k^,α∈R\overrightarrow{b}= 2\widehat{i}+ \alpha\widehat{j}+ 4\widehat{k},\alpha \in R
    c→=3i^−2j^+5k^\overrightarrow{c}= 3\widehat{i}- 2\widehat{j}+ 5\widehat{k}
    If α\alpha is the smallest positive integer for which a→,b→,c→\overrightarrow{a},\overrightarrow{b},\overrightarrow{c} are non-collinear, then the length of the median, in △ABC\bigtriangleup ABC, through AA is:

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  3. Question 3

    Application of Integrals. Asked once: 28 Jun 2022 (same type asked 3 times) See all 3 of this type

    159
    The area of the bounded region enclosed by the curve y=3−∣x−12∣−∣x+1∣y = 3 -\left| x -\frac{1}{2} \right|- |x + 1| and the xx-axis is

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  4. Question 4

    Differentiation. Asked once: 27 Jul 2022 (same type asked 3 times) See all 3 of this type

    176
    For the curve C:(x2+y2−3)+(x2−y2−1)5=0C:\left( x^{2}+y^{2}- 3 \right)+\left( x^{2}-y^{2}- 1 \right)^{5}= 0, the value of 3y′−y3y′′3y^{'}-y^{3}y^{''}, at the point (α,α),α>0(\alpha,\alpha),\alpha > 0, on CC, is equal to

  5. Question 5

    Binomial Theorem. Asked once: 2021 Paper 17 (same type asked 3 times) See all 3 of this type

    62
    A possible value of ' xx ', for which the ninth term in the expansion of {3log⁡325x−1+7+3(−18)log⁡3(5x−1+1)}10\left\{ 3^{\log_{3}\sqrt{25^{x- 1}+ 7}}+3^{\left( -\frac{1}{8} \right)\log_{3}\left( 5^{x- 1}+ 1 \right)} \right\}^{10} in the increasing powers of 3(−18)log⁡3(5x−1+1)3^{\left( -\frac{1}{8} \right)\log_{3}\left( 5^{x- 1}+ 1 \right)} is equal to 180 , is:

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