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If 3 and 4 are intercepts of a line L = 0, then the distance of L = 0 from the origin is

1) 5 units 2) 12 units 3) 5/12 unit 4) 12/5 units Solution: Given x intercept = 3 y intercept = 4 Equation of line in intercept form is x/a... View Article

The distance between the parallel lines y = x + a, y = x + b is

(1) |(b - a)|/√2 (2) |(a - b)| (3) |(a + b)| (4) |(b + a)|/√2 Solution: Given lines are y = x + a y = x + b Here a1 = 1, b1 = -1, c1 = a, c2... View Article

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

1) 4 2) 16 3) 2 4) 8 Solution: Given lies are 5x - 12y + 65 = 0 5x - 12y - 39 = 0 The slope of these two lines are equal. So these are... View Article

The distance of the point (1, 2) from the line x + y + 5 = 0 measured along the line parallel to 3x – y = 7 is equal to

1) 4√10 2) 40 3) √40 4) 10√2 Solution: Given equation of line is 3x - y = 7 => y = 3x - 7 Here slope m = 3 The parallel line will have... View Article

A straight line through the point (1, 1) meets the X-axis at A and Y-axis at B. The locus of the midpoint of AB is

1) 2xy + x + y = 0 2) x + y - 2xy = 0 3) x + y + 2 = 0 4) x + y - 2 = 0 Solution: Let A = (a, 0) and B = (0, b) The equation in intercept... View Article

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

1) 2 2) 0 3) 4 4) 1 Solution: Given 3x + 4y = 9 ..(i) y = mx + 1 ..(ii) Solving (i) and (ii) We get x = 5/(3 + 4m) For x to be an integer,... View Article

If the lines ax + ky + 10 = 0, bx + (k + 1)y + 10 = 0 and cx + (k + 2)y + 10 = 0 are concurrent, then

1) a,b, c are in GP 2) a ,b, c are in HP 3) a ,b ,c are in AP 4) (a + 1)2 = c Solution: Given ax + ky + 10 = 0 bx + (k + 1)y + 10 = 0 cx +... View Article

Let PS be the median of the triangle with vertices P(2, 2), Q(6, –1) and R(7, 3). The equation of the line passing through (1,–1) and parallel to PS is

1) 2x – 9y – 7 = 0 2) 2x – 9y – 11 = 0 3) 2x + 9y – 11 = 0 4) 2x + 9y + 7 = 0 Solution: Given vertices are P(2, 2), Q(6, –1) and R(7, 3)... View Article

If point P (a, b) lies on the straight line 3x + 2y = 13 and the point Q (b, a) lies on the straight line 4x – y = 5, then equation of the line PQ is

1) x - y = 5 2) x + y = 5 3) x + y = -5 4) x - y = -5 Solution: Given P (a, b) lies on 3x + 2y = 13 => 3a + 2b = 13 ..(i) Q (b, a) lies... View Article

If the slope of one of the lines represented by ax²+ 2hxy + by² = 0 is the square of the other, then (a + b)/h + (8h²/ab) is

1) 3 2) 4 3) 5 4) 6 Solution: Given ax2 + 2hxy + by2 = 0 .(i) Let m be the slope. Then the other line has slope m2. The equation of line (y... View Article

Joint equation of pair of lines through (3, – 2) and parallel to x² – 4xy + 3y² = 0 is

1) x2 +3y2 - 4xy - 14x + 24y + 45 = 0 2) x2 +3y2 + 4xy -14x + 24y + 45 = 0 3) x2 +3y2 + 4xy - 14x + 24y - 45 = 0 4) x2 +3y2 + 4xy - 14x - 24y... View Article

The equations of the lines through (1, 1) and making angles of 45⁰ with the line x + y = 0 are

1) x - 1= 0, x - y = 0 2) x - y = 0, y - l = 0 3) x + y - 2 = 0, y - 1 = 0 4) x - 1 = 0, y - 1 = 0 Solution: Given line x + y = 0 => y =... View Article

The equation of a straight line, which passes through the point (a cos³ θ, a sin³θ) and perpendicular to the line x sec θ + y cosec θ = a, is

1) x cos θ - y sin θ = a cos 2 θ 2) x cos θ + y sin θ = a cos 2 θ 3) x cos θ + y sin θ - a cos 2 θ = 1 4) x cos θ -y sin θ + a cos 2 θ = -1... View Article

The equations y = ±√3x, y = 1 are the sides of

1) an equilateral triangle 2) a right-angled triangle 3) an isosceles triangle 4) a scalene triangle Solution: Given y = √3x ..(i) y = -√3x... View Article

The straight line 3x + y = 9 divides the line segment joining the points (1, 3) and (2, 7) in the ratio

1) 3 : 4 externally 2) 3 : 4 internally 3) 4 : 5 internally 4) 5 : 6 externally Solution: By section formula if a point (x,y) divides the... View Article

The equations to a pair of opposite sides of parallelogram are x² – 5x + 6 = 0 and y² – 6y + 5 = 0, the equations to its diagonals are

1) x + 4y = 13, y = 4x – 7 2) 4x + y = 13, 4y = x – 7 3) 4x + y = 13, y = 4x – 7 4) y – 4x = 13, y + 4x = 7 Solution: x2 - 5x + 6 = 0 …(i)... View Article

The point of intersection of lines represented by the equation 3x² + 8xy – 3y² + 29x – 3y + 18 = 0 is

(1) (-3/2, -5/2) (2) (2/3, 5/2) (3) (3, -5) (4) none of these Solution: Given 3x2 + 8xy - 3y2 + 29x - 3y + 18 = 0 Comparing above equation... View Article

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

1) square 2) circle 3) straight line 4) two intersecting lines Solution: Consider that the perpendicular lines are chosen along the x-axis... View Article

Let A (2, – 3) and B (- 2, 1) be vertices of a ∆ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line

1) 3x - 2y = 3 2) 2x + 3y = 9 3) 2x - 3y = 7 4) 3x + 2y = 5 Solution: The equation of centroid of a triangle = [(x1+x2+x3)/3, (y1+y2+y3)/3]... View Article

Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q, then

(1) a2 + b2 = p2 + q2 (2) a2 + p2 = b2 + q2 (3) 1/a2 + 1/b2 = 1/p2 + 1/q2 (4) none of these Solution: Consider the axes are rotated in the... View Article

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