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

Find the combined equation of the following pair of line:

x + 2y - 1 = 0 and x - 3y + 2 = 0

Find the combined equation of the following pair of lines passing through point (2, 3) and parallel to the coordinate axes.

Find the combined equation of the following pair of lines:

Passing through (2, 3) and perpendicular to the lines 3x + 2y – 1 = 0 and x – 3y + 2 = 0.

Find the combined equation of the following pair of line passing through (−1, 2), one is parallel to x + 3y − 1 = 0 and other is perpendicular to 2x − 3y − 1 = 0

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

3y² + 7xy = 0 

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

x² - 4xy = 0 

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

`3"x"^2 - 2sqrt3"xy" - 3"y"^2 = 0`

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

x² + 2(cosec α)xy + y² = 0

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

x² + 2xy tan α - y² = 0

Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by following equation:

5x² - 8xy + 3y² = 0 

Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:

5x² + 2xy - 3y² = 0 

Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:

xy + y² = 0 

Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:

3x² − 4xy = 0 

Choose correct alternatives:

Auxiliary equation of 2x² + 3xy - 9y² = 0 is

Choose correct alternatives:

If two lines ax² + 2hxy + by² = 0 make angles α and β with X-axis, then tan (α + β) = _____.

If the slope of one of the two lines given by `"x"^2/"a" + "2xy"/"h" + "y"^2/"b" = 0` is twice that of the other, then ab : h² = ______.

The joint equation of the lines through the origin and perpendicular to the pair of lines 3x² + 4xy – 5y² = 0 is _______.

Choose correct alternatives:

If the equation 3x² – 8xy + qy² + 2x + 14y + p = 1 represents a pair of perpendicular lines, then the values of p and q are respectively ______.

The area of triangle formed by the lines x² + 4xy + y² = 0 and x - y - 4 = 0 is ______.

Choose correct alternatives:

The combined equation of the coordinate axes is