A line passing through the point of intersection of x + y = 4 and

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 Multiple Choice QuestionsMultiple Choice Questions

41.

The straight lines x + y = 0, 5x + y = 4 and x + 5y = 4 form

  • an isosceles triangle

  • an equilateral triangle

  • a scalene triangle

  • a right angled triangle


42.

If z = x + iy, where x and y are real numbers and i = - 1, then the points (x, y) for which z - 1z - i is real, lie on

  • an ellipse

  • a circle

  •  a parabola

  • a straight line


43.

The equation 2x2 + 5xy - 12y2 = 0 represents a

  • circle

  • pair of non-perpendicular intersecting straight lines

  • pair of perpendicular straight lines

  • hyperbola


44.

The number oflines which pass through the point (2, - 3) and are at a distance 8 from the point (- 1, 2) is

  • infinite

  • 4

  • 2

  • 0


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45.

A line passing through the point of intersection of x + y = 4 and x - y = 2 makes an angle tan-134 with the x-axis. It intersects the parabola y2 = 4(x - 3) at points (x1, y1) and (x2, y2) respectively. Then, x1 - x2 is equal to

  • 169

  • 329

  • 409

  • 809


B.

329

Given lines are x + y = 4 and x - y = 2

On solving these lines, we get

x = 3 and y = 1

Now, the equation of line which passes through the intersection point (3, 1) having slope,

θ = tan-134 is y - 1 = 34x - 3                        4y - 4 = 3x - 9                       3x - 4y = 5

Now tor the intersection point of the line (i) with parabola y2 = 4(x - 3). Put y = 3x - 54, then we get

                  3x - 5216 = 4x - 3   9x2 + 25 - 30x = 64x - 192 9x2 - 94x + 217 = 0    x = 94 ± 8836 - 781218           = 94 ± 3218 = 12818 or 6218  x1 = 213 = 7and x2 = 319 x1 - x2 = 7 - 319 = 329 = 329


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46.

The line joinining Abcosα, bsinα and Bacosβ, asinβ, where a b, is produced to the point M(x, y) so that AM : MB = b : a. Then, xcosα + β2 + ysinα + β2 is equal to

  • 0

  • 1

  • - 1

  • a2 + b2


47.

The number of integer values of m, for which the x - coordinate of the point of intersection of the lines 3x + 4y= 9 and y =mx + 1 is also an integer, is

  • 0

  • 2

  • 4

  • 1


48.

If a straight line passes through the point (α, β) and the portion of the line intercepted between the axes is divided equally at that point, then xα + yβ is

  • 0

  • 1

  • 2

  • 4


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49.

A straight line through the point of intersection of the lines x + 2y = 4 and 2x + y = 4 meets the coordinate axes at A and B. The locus of the mid-point of AB is

  • 3(x + y) = 2xy

  • 2(x + y) = 3xy

  • 2(x + y) = xy

  • x + y = 3xy


 Multiple Choice QuestionsShort Answer Type

50.

Find the image of the point (- 8, 12) with respect to the line 4x + 7y + 13 = 0.


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