HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Choose correct alternatives:

If slope of one of the lines ax² + 2hxy + by² = 0 is 5 times the slope of the other, then 5h² = ______

Choose correct alternatives:

If distance between lines (x - 2y)² + k(x - 2y) = 0 is 3 units, then k = ______.

Find the joint equation of the line:

x - y = 0 and x + y = 0

Find the joint equation of the line:

x + y − 3 = 0 and 2x + y − 1 = 0

Find the joint equation of the line passing through the origin having slopes 2 and 3.

Find the joint equation of the line passing through the origin and having inclinations 60° and 120°.

Find the joint equation of the line passing through (1, 2) and parallel to the coordinate axes

Find the joint equation of the line passing through (3, 2) and parallel to the lines x = 2 and y  = 3.

Find the joint equation of the line which are at a distance of 9 units from the Y-axis.

Find the joint equation of the line passing through the point (3, 2), one of which is parallel to the line x - 2y = 2, and other is perpendicular to the line y = 3.

Find the joint equation of the line passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18

Find the joint equation of the line passing through (-1, 2) and perpendicular to the lines  x + 2y + 3 = 0 and 3x - 4y - 5 = 0

Show that the following equations represents a pair of line:

x² + 2xy - y² = 0

Show that the following equations represents a pair of line:

4x² + 4xy + y² = 0

Show that the following equations represent a pair of line:

x² - y² = 0

Show that the following equations represent a pair of line:

x² + 7xy - 2y² = 0

Show that the following equations represent a pair of line:

`"x"^2 - 2sqrt3"xy" - "y"^2 = 0`

Find the separate equation of the line represented by the following equation:

6x² - 5xy - 6y² = 0

Find the separate equation of the line represented by the following equation:

x² - 4y² = 0

Find the separate equation of the line represented by the following equation:

3x² - y² = 0