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Day 84: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked 2 times: 29 Jan 2024*, 9 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    160
    lim⁡x→π2(∫x3(π/2)3(sin⁡(2t1/3)+cos⁡(t1/3))dt(x−π2)2)\lim_{x \rightarrow\frac{\pi}{2}} \left( \frac{\int_{x^{3}}^{(\pi/2)^{3}} \left( \sin\left( 2t^{1/3} \right)+ \cos\left( t^{1/3} \right) \right)dt}{\left( x -\frac{\pi}{2} \right)^{2}} \right) is equal to:

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  2. Question 2

    Straight Lines. Asked 2 times: 29 Jun 2022*, 8 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    162
    If the line segment joining the points (5,2)(5,2) and (2, a) subtends an angle π4\frac{\pi}{4} at the origin, then the absolute value of the product of all possible values of aa is:

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  3. Question 3

    Vector Algebra. Asked 2 times: 28 Jul 2022*, 8 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    78
    The set of all α\alpha, for which the vector a→=αti^+6j^−3k^\overrightarrow{a}= \alpha t\widehat{i}+ 6\widehat{j}- 3\widehat{k} and  b→=ti^−2j^−2αtk^\ \overrightarrow{b}= t\widehat{i}- 2\widehat{j}- 2\alpha t\widehat{k} are inclined at an obtuse angle for all t∈Rt \in R is :

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  4. Question 4

    Conic Sections. Asked 2 times: 2021 Paper 2*, 6 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    155
    If the locus of the point, whose distances from the point (2,1)(2,1) and (1,3)(1,3) are in the ratio 5:45:4, is ax2+by2+cxy+dx+ey+170=0ax^{2}+by^{2}+ cxy + dx + ey + 170 = 0, then the value of a2+2b+3c+4d+ea^{2}+ 2b + 3c + 4d + e is equal to:

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  5. Question 5

    Differential Equations. Asked 2 times: 29 Jan 2023*, 6 Apr 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    78
    Let y=y(x)y = y(x) be the solution of the differential equation (2xlog⁡ex)dydx+2y=3xlog⁡ex,x>0\left( 2x\log_{e}x \right)\frac{dy}{dx}+ 2y =\frac{3}{x}\log_{e}x,x > 0 and y(e−1)=0y\left( e^{- 1} \right)= 0. Then, y(e)y(e) is equal to

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