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Day 651: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 2021 Paper 6

    72
    If the points of intersection of the ellipse x216+y2b2=1\frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}= 1 and the circle x2+y2=4b,b>4x^{2}+y^{2}= 4b,b> 4 lie on the curve y2=3x2y^{2}= 3x^{2}, then bb is equal to:

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  2. Question 2

    Conic Sections. Asked once: 2021 Paper 6

    69
    Let the lengths of intercepts on xx-axis and yy-axis made by the circle x2+y2+ax+2ay+c=0x^{2}+y^{2}+ax+ 2ay+c= 0, (a<0)(a< 0) be 222\sqrt{2} and 252\sqrt{5}, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x+2y=0x + 2y = 0, is euqal to:

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  3. Question 3

    Conic Sections. Asked once: 2021 Paper 5

    83
    Let ABCDABCD be a square of side of unit length. Let a circle C1C_{1} centered at AA with unit radius is drawn. Another circle C2C_{2} which touches C1C_{1} and the lines ADAD and ABAB are tangent to it, is also drawn. Let a tangent line from the point CC to the circle C2C_{2} meet the side ABAB at EE. If the length of EBEB is α+3β\alpha +\sqrt{3}\beta, where α,β\alpha,\beta are integers, then α+β\alpha + \beta is equal to

  4. Question 4

    Conic Sections. Asked once: 2021 Paper 5

    67
    If the three normals drawn to the parabola, y2=2xy^{2}= 2x pass through the point (a,0)a≠0(a,0)a\neq 0, then 'a' must be greater than:

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  5. Question 5

    Conic Sections. Asked once: 2021 Paper 3

    83
    The point of intersection of the lines 3 kx+ky−43=0\sqrt{3}\,kx + ky - 4\sqrt{3} = 0 and 3 x−y−43 k=0\sqrt{3}\,x - y - 4\sqrt{3}\,k = 0, as kk varies, traces a conic whose eccentricity is