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Day 642: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 27 Jul 2022

    89
    If the length of the latus rectum of the ellipse x2+x^{2}+ 4y2+2x+8y−λ=04y^{2}+ 2x + 8y - \lambda = 0 is 4, and ll is the length of its major axis, then λ+l\lambda + l is equal to

  2. Question 2

    Conic Sections. Asked once: 26 Jul 2022

    161
    The acute angle between the pair of tangents drawn to the ellipse 2x2+3y2=52x^{2}+ 3y^{2}= 5 from the point (1,3)(1,3) is

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  3. Question 3

    Conic Sections. Asked once: 26 Jul 2022

    164
    If the line x−1=0x - 1 = 0, is a directrix of the hyperbola kx2−y2=6kx^{2}-y^{2}= 6, then the hyperbola passes through the point

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  4. Question 4

    Conic Sections. Asked once: 26 Jul 2022

    89
    Let the function f(x)=2x2−log⁡ex,x>0f(x) = 2x^{2}-\log_{e}x,x > 0, be decreasing in (0,a)(0,a) and increasing in (a,4)(a,4). A tangent to the parabola y2=4axy^{2}= 4ax at a point PP on it passes through the point (8a,8a−1)(8a,8a - 1) but does not pass through the point (−1a,0)\left( -\frac{1}{a},0 \right). If the equation of the normal at PP is xα+yβ=1\frac{x}{\alpha}+\frac{y}{\beta}= 1, then α+β\alpha + \beta is equal to-

  5. Question 5

    Conic Sections. Asked once: 25 Jul 2022

    162
    If the ellipse x2a2+y2b2=1\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1 meets the line x7+y26=1\frac{x}{7}+\frac{y}{2\sqrt{6}}= 1 on the xx-axis and the line x7−y26=1\frac{x}{7}-\frac{y}{2\sqrt{6}}= 1 on the yy-axis, then the eccentricity of the ellipse is

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