If the pair of straight lines xy - x - y + 1 = 0 and the line ax

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 Multiple Choice QuestionsMultiple Choice Questions

211.

The distance of the point (1,  2, 3) from the plane x  y + z = 5 measured parallel to the line x2 = y3 = z - 6 is :

  • 17

  • 7

  • 1

  • 75


212.

If the perpendicular bisector of the line segment joining the points P(1, 4) and Q(k, 3) has y-intercept equal to – 4, then a value of k is ;

  • 15

  •  4

  •  - 2

  • 14


213.

If (a, b, c) is the image of the point (1, 2, – 3) in the line,

x + 12 = y - 3 - 2 = z - 1, then a + b + c is equal to :

  • 3

  • - 1

  • 2

  • 1


 Multiple Choice QuestionsShort Answer Type

214.

If the line, 2x – y + 3 = 0 is at a distance 15 and 25 from the lines 4x - 2y + α = 0 and 6x - 3y + β = 0,

hen the sum of all possible values of α and β is_


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 Multiple Choice QuestionsMultiple Choice Questions

215.

If for some α  R, the linesL1 : x + 12 = y - 2 - 1 = z - 11 andL2 :x + 2α = y + 15 - α = z + 11 are coplanar, then the line L2 passes through point :

  • (2, - 10, - 2)

  • (10, 2, 2)

  • ( - 2, 10, 2)

  • (10, - 2, - 2)


216.

Which of the following points lies on the tangent to the curvex4ey + 2y + 1 = 3 at the point (1, 0)

  • (- 2, 4)

  • (2, 2)

  • ( - 2, 6)

  • (2, 6)


217.

A ray of light coming from the point (2, 23) is incident at an angle 30° on the line x = 1 at the point A. The ray gets reflected on the line x = 1 and meets x-axis at the point B. Then, the line AB passes through the point ;

  • 4, - 32

  • 3, - 3

  • (4, - 3)

  • 3, - 13


218.

Let L denote the line in the xy-plane with x and y intercepts as 3 respectively. Then the image of the point (– 1, – 4) in the line is :

  • 85, 295

  • 115, 285

  • 295, 85

  • 295, 115


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219.

If the pair of straight lines xy - x - y + 1 = 0 and the line ax + 2y - 3a = 0 are concurrent, then a is equal to

  • 0

  • 1

  • - 1

  • 3


B.

1

We have,xy - x - y + 1 = 0     ...i   ax + 2y - 3a = 0     ...iiOn compairing Eqs. i with,ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, we geta = 0, b = 0, h = 12, g = - 12,  f = - 12,  c=1The point of concurrent is hf - bgab - h2, gh - afab - h2    = 12 - 12 - 00 - 122,  - 1212 - 00 - 122 = 1, 1The point lies on equation ii, thena + 2 - 3a = 0  2a = 2                 a = 1


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220.

The mid-point of the line segment joining the centroid and the orthocentre of the triangle whose vertices are (a, b),(a, c) and (d, c), is

  • 5a +d6, b + 5c6

  • `a + 5d6, 5b + c6

  • (a, 0)

  • (0, 0)


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