Archives

The perpendicular bisector of the line segment joining P(1, 4) and Q (k, 3) has y-intercept – 4. Then, the possible value of k is

1) - 4 2) 1 3) 2 4) - 2 Solution: Given points are P(1, 4) and Q (k, 3). Slope of PQ, m1 = (y2 - y1)/(x2 - x1) = (3 - 4)/(k - 1) = -1/(k -1)... View Article

If the lines kx – 2y – 1 = 0 and 6x – 4y – m = 0 are identical (coincident) lines, then the values of k and m are

1) k = 3, m = 2 2) k = - 3, m = 2 3) k = - 3, m = - 2 4) k = 3, m = - 2 Solution: Given lines are kx - 2y - 1 = 0 …(i) 6x - 4y - m = 0 …(ii)... View Article

A line passing through origin and is perpendicular to two given lines 2x + y + 6 = 0 and 4x + 2y – 9 = 0. The ratio in which the origin divides the line, is

1) 1 : 2 2) 2 : 1 3) 4 : 2 4) 4 : 3 Solution: Given 2x + y + 6 = 0 ..(i) The equation of line perpendicular to 2x + y + 6 = 0 and pass... View Article

The pairs of straight lines x² – 3xy + 2y²= 0 and x²– 3xy + 2y²+ x – 2 = 0 form a

1) square but not rhombus 2) rhombus 3) parallelogram 4) rectangle but no a square Solution: Given x2 - 3xy + 2y2 = 0 …(i) x2 - 3xy + 2y2 +... View Article

The angle between the line joining the points (1, -2), (3, 2) and the line x + 2y – 7 = 0 is

1) π 2) π/2 3) π/3 4) π/6 Solution: Let the given points be A(1, -2), B(3, 2). Slope of AB, m1 = (y2 - y1)/(x2 - x1) = (2 - (-2))/(3 - 1) =... View Article

The angle between lines joining origin and intersection points of line 2x + y = 1 and curve 3x² + 4yx – 4x + 1 = 0

1) π/2 2) π/3 3) π/4 4) π/6 Solution: Given 3x2 + 4yx - 4x + 1 = 0 3x2 + 4yx - 4x(1) + (1)2 = 0…(i) Given 2x + y = 1…(ii) Substitute (ii) in... View Article

The lines represents by ax² + 2hxy + by² = 0 are perpendicular to each other, if

1) h2 = a + b 2) a + b = 0 3) h2 = ab 4) h = 0 Solution: Given ax2 + 2hxy + by2 = 0 Let θ be the angle between the lines tan θ = 2√(h2 -... View Article

The area (in square unit) of the triangle formed by x + y + 1 = 0 and the pair of straight lines x² – 3xy + 2y²= 0 is

1) 7/12 2) 5/12 3) 1/12 4) 1/6 Solution: Given pair of straight lines x2 - 3xy + 2y2 = 0 => x2 - 2xy -xy + 2y2 = 0 => x(x - 2y) - y(x... View Article

The line parallel to the X-axis and passing through the point of intersection of the line ax + 2by + 3b = 0 and bx – 2ay – 3a = 0, where (a, b) ≠ (0, 0), is

1) above the X-axis at a distance of 3/2 2) above the X-axis at a distance of 2/3 3) below the X-axis at a distance of 2/3 4) below the X-axis... View Article

If line (tan² θ + cos² θ) x² – 2 tan θ xy + sin² θ y² = 0 makes angles α and β with X – axis, then tan α – tan β is equal to

1) 2 2) 4 3) tan θ 4) 2 tan θ Solution: Given (tan2 θ + cos2 θ) x2 - 2 tan θ xy + sin2 θ y2 = 0 Let m1 and m2 be the slopes of the given... View Article

Let α be the distance between the lines – x + y = 2 and x – y = 2 and β be the distance between the lines 4x – 3y = 5 and 6y – 8x = 1, then

1) 20√2β = 11α 2) 20√2α = 11β 3) 11√2β = 20α 4) None of the above Solution: Equation of given lines - x + y = 2 => y = x + 2 And x - y =... View Article

The distance between the pair of parallel lines given by x² – 1005x + 2006 = 0 is

1) 1001 2) 1000 3) 1005 4) 2006 Solution: Given x2 - 1005x + 2006 = 0 (x - 2) (x - 1003) = 0 => x = 2 , x = 1003 Distance between... View Article

The Orthocentre of a triangle with vertices (0, 0), (3, 4), and (4, 0) is

(1) (3, 12) (2) (3, ¾) (3) (3, 9) (4) none of these Solution: Let O(0, 0), A (4, 0) and B(3, 4) be the vertices of the triangle. Let H be... View Article

L is a variable line such that the algebraic sum of the distances of the points (1, 1), (2, 0), and (0, 2) from the line is equal to zero. The line L will always pass-through

1) (1, 1) 2) (2, 1) 3) (1, 2) 4) (2, 2) Solution: Let the equation of line L be y = mx + c => y - mx - c = 0 The distance of a line from... View Article

The number of integral points (integral point means both the coordinates should be an integer) exactly in the interior of the triangle with vertices (0,0), (0,21), and (21,0), is

1) 133 2) 190 3) 233 4) 105 Solution: Let the vertices of the triangle be O(0,0), P(0,21), and Q(21,0). The integral points must be on the... View Article

M	T	W	T	F	S	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30
31