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12th Standard Maths Two Dimensional Analytical Geometry-II English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

    (a)

    \(0,-\frac { 40 }{ 9 } \)

    (b)

    0

    (c)

    \(\frac { 40 }{ 9 } \)

    (d)

    \(\frac { -40 }{ 9 } \)

  2. The radius of the circle3x2+by2+4bx−6by+b2 =0 is

    (a)

    1

    (b)

    3

    (c)

    \( \sqrt {10}\)

    (d)

    \( \sqrt {11}\)

  3. The equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
    2x+4y=3 is

    (a)

    x+2y=3

    (b)

    x+2y+3= 0

    (c)

    2x+4y+3=0

    (d)

    x−2y+3= 0

  4. If the normals of the parabola y2 = 4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2+(y+2)2=r2 , then the value of r2 is

    (a)

    2

    (b)

    3

    (c)

    1

    (d)

    4

  5. The equation of the circle passing through the foci of the ellipse  \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1\) 1having centre at
    (0,3) is

    (a)

    x2+y2−6y−7=0

    (b)

    x2+y2−6y+7=0

    (c)

    x2+y2−6y−5=0

    (d)

    x2+y2−6y+5=0

  6. If the two tangents drawn from a point P to the parabolay2 = 4x are at right angles then the locus of P is

    (a)

    2x+1=0

    (b)

    x = −1

    (c)

    2x−1=0

    (d)

    x =1

  7. If (0, 4) and (0, 2) are the vertex and focus of a parabola then its equation is

    (a)

    x2 + 8y = 32

    (b)

    y2 + 8x = 32

    (c)

    x2 - 8y= 32

    (d)

    y2 - 8x = 32

  8. Equation of tangent at (-4, -4) on x2 = -4y is

    (a)

    2x - y + 4 = 0

    (b)

    2x + y - 4 = 0

    (c)

    2x - y - 12 = 0

    (d)

    2x + y + 4 = 0

  9. In an ellipse, the distance between its foci is 6 and its minor axis is 8, then e is

    (a)

    \(\frac { 4 }{ 5 } \)

    (b)

    \(\frac { 1 }{ \sqrt { 52 } } \)

    (c)

    \(\frac { 3 }{ 5 } \)

    (d)

    \(\frac { 1 }{ 2 } \)

  10. The locus of the foot of perpendicular from the focus on any tangent to y2 = 4ax is

    (a)

    x2 + y2 = a2 - b2

    (b)

    x2 + y2 = a2

    (c)

    x2 + y2 = a2 - b2

    (d)

    x = 0

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