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Day 634: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 1 Feb 2023

    176
    The line x=8x = 8 is the directrix of the ellipse ellipse E:x2a2+y2b2=1E:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1 with the corresponding focus (2,0)(2,0). If the tangent to EE at the point PP in the first quadrant passes through the point (0,43)(0,4\sqrt{3}) and intersects that xx-axis at QQ then (3PQ)  2\ ^{2} equl to

  2. Question 2

    Definite Integration. Asked once: 2021 Paper 23

    79
    If [x]\lbrack x\rbrack is the greatest integer ≤x\leq x, then π2∫02(sin⁡πx2)(x−[x])[x]dx\pi^{2}\int_{0}^{2} \left( \sin\frac{\pi x}{2} \right)(x- \lbrack x\rbrack)^{\lbrack x\rbrack}dx is equal to :

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  3. Question 3

    Sequences and Series. Asked once: 2021 Paper 2

    67
    Let a,b,ca,b,c be in arithmetic progression. Let the centroid of the triangle with vertices (a,c),(2,b)(a,c),(2,b) and (a,b)(a,b) be (103,73)\left( \frac{10}{3},\frac{7}{3} \right). If α,β\alpha,\beta are the roots of the equation ax2+bx+1=0ax^{2}+bx+ 1 = 0, then the value of α2+β2−αβ\alpha^{2}+\beta^{2}-\alpha\beta is:

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  4. Question 4

    Conic Sections. Asked once: 1 Feb 2023

    163
    Let P(x0,y0)P\left( x_{0},y_{0} \right) be the point on the hyperbola 3x2−4y2=363x^{2}- 4y^{2}= 36, which is nearest to the line 3x+2y=13x + 2y = 1. Then 2(y0−x0)\sqrt{2}\left( y_{0}-x_{0} \right) is equal to:

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  5. Question 5

    Definite Integration. Asked once: 2021 Paper 22

    81
    Let [t]\lbrack t\rbrack denote the greatest integer ≤t\leq t. Then the value of 8⋅∫−121([2x]+∣x∣)dx8 \cdot\int_{-\frac{1}{2}}^{1} (\lbrack 2x\rbrack + |x|)dx is