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Day 88: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked 2 times: 29 Jul 2022, 27 Jan 2024 See all 2 times it was asked

    176
    If the solution curve, of the differential equation dydx=x+y−2x−y\frac{dy}{dx}=\frac{x + y - 2}{x - y} passing through the point (2,1)(2,1) is tan⁡−1(y−1x−1)−1βlog⁡e(α+(y−1x−1)2)=log⁡e∣x−1∣\tan^{- 1}\left( \frac{y - 1}{x - 1} \right)-\frac{1}{\beta}\log_{e}\left( \alpha +\left( \frac{y - 1}{x - 1} \right)^{2} \right)=\log_{e}|x - 1|, then 5β+α5\beta + \alpha is equal to

  2. Question 2

    Straight Lines. Asked 2 times: 1 Feb 2023*, 15 Apr 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    75
    If (α,β)(\alpha,\beta) is the orthocentre of the triangle ABCABC with vertices A(3,−7),B(−1,2)A(3, - 7),B( - 1,2) and C(4,5)C(4,5), then 9α−6β+609\alpha - 6\beta + 60 is equal to:

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  3. Question 3

    Conic Sections. Asked 2 times: 28 Jun 2022*, 13 Apr 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    178
    The foci of a hyperbola are (±2,0)( \pm 2,0) and its eccentricity is 32\frac{3}{2}. A tangent, perpendicular to the line 2x+3y=62x + 3y = 6, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the xx - and yy-axes are aa and bb respectively, then ∣6a∣+∣5b∣|6a| + |5b| is equal to

  4. Question 4

    Three Dimensional Geometry. Asked 2 times: 26 Jun 2022*, 12 Apr 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    75
    Let the plane P:4x−y+z=10P:4x-y+z=10 be rotated by an angle π2\frac{\pi}{2} about its line of intersection with the plane x+y−z=4x+y-z=4. If α\alpha is the distance of the point (2,3,−4)(2,3,-4) from the new position of the plane PP, then 35α35\alpha is

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  5. Question 5

    Conic Sections. Asked 2 times: 24 Jan 2023*, 11 Apr 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    164
    If the radius of the largest circle with centre (2,0)(2,0) inscribed in the ellipse x2+4y2=36x^{2}+ 4y^{2}= 36 is rr, then 12r212r^{2} is equal to

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