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Pair of Straight Lines Test - 5

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Pair of Straight Lines Test - 5
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  • Question 1
    1 / -0

    Slope of a line is not defined if the line is


    Solution

    Vertical lines hve undefined slopes. Hence a line which is parallel to Y-axis has undefined slopes.

    Hence option 1 is correct

  • Question 2
    1 / -0

    The image of the point (α,β) with respect to the line x = y is

  • Question 3
    1 / -0
    Directions: The following question has four choices out of which ONLY ONE is correct.

    Consider a line pair ax2 + 3xy - 2y2 - 5x + 5y + c = 0 representing perpendicular lines intersecting each other at C and forming a triangle ABC with the x-axis.

    If the circle x2 + y2 - 4y + k = 0 is orthogonal with the circumcircle of the triangle ABC, find the value of k.
  • Question 4
    1 / -0

    The point which divides the joint of ( 1, 2 ) and ( 3,4 ) externally in the ratio 1 : 1 .

    Solution

    The point which divides the line in the ratio m:n externally is given by x =m(x2)−n(x1)/m−n


    Substituting the values we get,


    x = 1(3)−1(1)/1−1 which is undefined.


     
  • Question 5
    1 / -0
    Above x-axis, the equation of the common tangent to the circle (x - 3)2 + y2 = 9 and parabola y2 = 4x is
  • Question 6
    1 / -0

    The distance of the point ( x , y ) from Y axis is

    Solution

    The abscissa or the x co ordiate of a point  is the distance from the y- axis.

    Hence the distance is x

  • Question 7
    1 / -0
    Directions: The following question has four choices out of which ONLY ONE is correct.

    A line passing through P (4, 2) meets the x and the y-axis at A and B respectively. If O is the origin, the locus of the centre of the circumcircle of OAB is
  • Question 8
    1 / -0
    Consider a line pair ax2 + 3xy – 2y2 – 5x + 5y + c = 0 representing perpendicular lines intersecting each other at C and forming a triangle ABC with the x-axis.

    If x1 and x2 are intercepts on the x-axis and y1 and y2 are the intercepts on the y-axis, the sum (x1 + x2 + y1 + y2) is equal to
  • Question 9
    1 / -0
    Consider a line pair ax2 + 3xy – 2y2 – 5x + 5y + c = 0 representing perpendicular lines intersecting each other at C and forming a triangle ABC with the x-axis.

    The distance between the orthocentre and circumcentre of the triangle ABC is
  • Question 10
    1 / -0

    The distance between the lines 5x – 12y + 65 = 0 and 5x – 12y – 39 = 0

    1. 2

    2. none of these

    3. - 2

    4. 8

  • Question 11
    1 / -0
    The area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 is
  • Question 12
    1 / -0

    The image of the point (α,β) with respect to the line x = y is

  • Question 13
    1 / -0
    If the sum of the slopes of the lines given by x2 − 2cxy −7y2 = 0 is four times their product then c has the value
  • Question 14
    1 / -0
    Directions: The following question has four choices, out of which ONE or MORE is/are correct.

    Lines L1 : y – x = 0 and L2 : 2x + y = 0 intersect the line L3 : y + 2 = 0 at P and Q, respectively. The bisector of the acute angle between L1 and L2 intersects L3 at R and S, respectively. Then,
  • Question 15
    1 / -0
    Let PQR be a right angled isosceles triangle, right angled at P(2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is
  • Question 16
    1 / -0
    Let P (− 1, 0), Q (0, 0) and R (3, 3) be three points. Then, the equation of the bisector of angle PQR is
  • Question 17
    1 / -0
    A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at the points P and Q respectively. Then the point O divides the segment PQ in the ratio
  • Question 18
    1 / -0

    The lines 2x – 3y = 5 and 6x – 9y – 7 = 0 are

    Solution

    The given lines are paraallel lines

    Condition for the line to be parallel is a1/a2= b1b2 ≠C1/C2

    substituting the values,

    2/6 =−3/−9≠5/7

    Hence they are parallel lines.

    Option 1 is correct.

  • Question 19
    1 / -0

    The distance of the point (α,β) from X axis is

    1. none of these.

    2. α

    3. |β|

    4. |α|

    Solution

    The distance of a  point from X axis is its y coordinate.

    Hence the distance of the point (α,β) from X axis  is |β|

  • Question 20
    1 / -0

    The line through the points (a , b) and (- a , - b) passes through the point

    Solution

  • Question 21
    1 / -0
    Directions: The following question has four choices out of which ONE or MORE is/are correct.


    It is desired to construct a right angled triangle ABC (C = /2) in xy plane so that it`s sides are parallel to coordinates axis and the medians through A and B lie on the lines y = 3x + 1 and y = mx + 2 respectively. The values of `m`, for which such a triangle is possible, is /are 
  • Question 22
    1 / -0
    The equation of base of an equilateral triangle is x + y = 2 and the vertex opposite to this base is (2, − 1). Then the length of the side of triangle equals
  • Question 23
    1 / -0
    If one of the diagonals of a square is along the line x = 2y and one of its vertices is (3, 0), then its sides through this vertex are given by the equations
  • Question 24
    1 / -0
    A straight line through the point (2, 2) intersects the lines + y = 0 and x − y = 0 at points A and B. The equation of the line AB, so that triangle OAB is equilateral, is
  • Question 25
    1 / -0

    Projection (the foot of perpendicular) from ( x , y ) on the x – axis is

    Solution

    Let L be the foot of the perpendicular from the X axis. Therefore its y coocrdinate is zero

    Therefore the coordiantes of the point L is (x,0)

    Hence option 1 is the correct answer

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