The image of the pair of lines represented by ax2 + 2hxy + by2 = 0 by the line mirror y = 0 is
1) ax2 – 2hxy – by2 = 0 2) bx2 – 2hxy – ay2 = 0 3) bx2 + 2hxy... View Article
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If the pair of lines ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 intersect on the y-axis, then
1) 2fgh = bg2 + ch2 2) bg2 ≠ ch2 3) abc = 2fgh 4) None of these Solution: Given... View Article
The lines p(p2 + 1) x – y + q = 0 and (p2 + 1)2 x + (p2 + 1)y + 2q = 0 are perpendicular to a common line for
1) No value of p 2) Exactly one value of p 3) Exactly two values of p 4) More than... View Article
The area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals
1) |(m + n)|/(m – n)2 2) 2/|(m + n)| 3) 1/|(m + n)| 4) 1/|(m – n)| Solution: Let... View Article
The diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + n’ = 0, mx + ly + n = 0, mx + ly + n’ = 0 include an angle
1) π/2 2) π/4 3) π/3 4) none of these Solution: Given sides of parallelogram are lx + my +... View Article
Equation of one of the sides of an isosceles right-angled triangle whose hypotenuse is 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2), will be
1) x – 7y + 12 = 0 2) 7x + y – 12 = 0 3) x – 7y... View Article
Coordinates of the vertices of a quadrilateral are (2, -1), (0, 2), (2, 3) and (4, 0). The angle between its diagonals will be
1) 900 2) 00 3) tan-1(2) 4) tan-1(1/2) Solution: Let A(2, -1), B(0, 2), C(2, 3) and D(4, 0) be... View Article
For the straight lines given by the equation (2 + k)x + (1 + k)y = 5 + 7k, for different values of k which of the following statements is true
1) Lines are parallel 2) Lines pass through the point (–2, 9) 3) Lines pass through the point (2, –9)... View Article
The straight line passing through the point of intersection of the straight lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and having infinite Slope and at a distance of 2 units from the origin, has the equation
1) x = 2 2) 3x + y – 1= 0 3) y = 1 4) None of these Solution:... View Article
In the equation y – y1 = m(x – x1 ) if m and x1 are fixed and different lines are drawn from the different value of y1, then
1) The lines will pass through a single point 2) There will be a set of parallel lines 3) There... View Article
The line joining two points A(2, 0), B(3, 1) is rotated about A in anti-clockwise direction through an angle of 150. The equation of the line in the new position, is
1) √3x – y – 2√3 = 0 2) x – 3√y – 2 = 0 3) √3x + y... View Article
The three lines px + qy + r = 0, qx + ry + p = 0, rx + py + q = 0 are concurrent if
1) p + q + r = 0 2) p2 + q2 + r2 = pq + qr + pr... View Article
If f(?) = x cos ? + y sin ? – p(?), then the lines f(?) = 0 and f(?) = 0 are perpendicular to each other, if
If f(α) = x cos α + y sin α – p(α), then the lines f(α) = 0 and f(β)... View Article
The area of the triangle formed by the lines x = 0, y = 0 and x/a + y/b = 1 is
1) ab 2) ab/2 3) 2ab 4) ab/3 Solution: The lines x = 0 and y = 0 are y... View Article
The line 3x + 2y = 24 meets y-axis at A and x-axis at B. The perpendicular bisector of AB meets the line through (0, -1) parallel to x-axis at C. The area of the triangle ABC is
1) 182 sq.units 2) 91 sq.units 3) 48 sq.units 4) None of these Solution: Given equation of line is 3x... View Article
Given the four lines with equations x + 2y = 3, 3x + 4y = 7, 2x + 3y = 4 and 4x + 5y = 6, then these lines are
1) Concurrent 2) Perpendicular 3) The sides of a rectangle 4) None of these Solution: Given x + 2y =... View Article
The vertices of a triangle are (2, 1), (5, 2), and (4, 4). The lengths of the perpendicular from these vertices on the opposite sides are
1) 7/√5, 7/√13, 7/√6 2) 7/√6, 7/√8, 7/√10 3) 7/√5, 7/√8, 7/√15 4) 7/√5, 7/√13, 7/√10 Solution: Let A(2, 1),... View Article
Given vertices A(1, 1), B(4, -2) and C(5, 5) of a triangle, then the equation of the perpendicular dropped from C to the interior bisector of the angle A is
1) y – 5 = 0 2) x – 5 = 0 3) y + 5 = 0 4) x... View Article
A line 4x + y = 1 passes through the point A(2, -7) meets the lines BC whose equation is 3x – 4y + 1 = 0 at the point B. The equation of the line AC so that AB = AC, is
1) 52x + 89y + 519 = 0 2) 52x + 89y – 519 = 0 3) 89x + 52y... View Article
If x1, x2, x3 and y1, y2, y3 are both in G.P. with the same common ratio, then the points (x1, y1) , (x2, y2) and (x3, y3)
1) Lie on a straight line 2) Lie on an ellipse 3) Lie on a circle 4) Are vertices of... View Article
