Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

31.

The equation of the pair of lines joining the origin to the points of intersection of x2 + y2 = 9 and x + y = 3, is

  • x2 + 3 - y2 = 9

  • 3 + y2 + y2 = 9

  • x2 - y2 = 9

  • xy = 0


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32.

Let L be the line joining the origin to the point of intersection of the lines represented by 2x - 3xy - 2y + 10x + 5y = 0. If L is perpendicular to the line kx + y + 3 = 0, then k is equal to

  • 12

  • - 12

  •  - 1

  • 13


B.

- 12

We have,2x2 - 3xy - 3y2 + 10x + 5y = 0 2x + yx - 2y + 5 = 0Now, equation of line passing through origin is 2x + y = 0Slope of this line is - 2Since, this line is perpendicular to the line kx + y + 3 = 0  - 2 - k = - 1  k = - 12


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33.

A circle S = 0 with radius 2 touches the line x + y - z = 0 at(1, 1). Then, the length of the tangent drawn from the point(1, 2) to S = 0 is

  • 1

  • 2

  • 3

  • 2


34.

The normal drawn at P(- 1, 2) on the circle x2 + y2 - 2x - 2y - 3 = 0 meets the circle at another point Q. Then the coordinates of Q are

  • (3, 0)

  • ( - 3, 0)

  • (2, 0)

  • ( - 2, 0)


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35.

If the lines kx + 2y - 4 = 0 and 5x - 2y - 4 = 0 are conjugate with respect to the circle x2 + y2 - 2x - 2y - 1 = 0, then k is equal to

  • 0

  • 1

  • 2

  • 3


36.

The angle between the, tangents drawn from the origin to the circle x2 + y2 + 4x - 6y + 4 = 0 is

  • tan-1513

  • tan-1512

  • tan-1- 125

  • tan-1135


37.

If the angle between the circles x2 + y2 - 2x - 4y + c = 0 and x2 + y2 - 4x - 2y + 4 = 0 is 60°, then c is equal to

  • 3 ± 52

  • 6 ± 52

  • 9 ± 52

  • 7 ± 52


38.

A circle S cuts three circles

x2 + y2 - 4x - 2y +4 = 0x2 + y2 - 2x - 4y + 1 = 0and x2 +y2 +4x +2y +1 = 0

Orthogonally. Then the radius of S is

  • 298

  • 2811

  • 297

  • 295


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39.

The distance between the vertex and the focus of the parabola x2 - 2x + 3y - 2 = 0 is

  • 45

  • 34

  • 12

  • 56


40.

If (x1, y1) and (x2, y2) are the end points of a focal chord of the parabola y2 = 5x, then 4x1x2 + y1y2, is equal to

  • 25

  • 5

  • 0

  • 54


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