HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`

Order and degree of the differential equation `[1+(dy/dx)^3]^(7/3)=7(d^2y)/(dx^2)` are respectively 

(A) 2, 3

(B) 3, 2

(C) 7, 2

(D) 3, 7

Find the combined equation of the following pair of lines:

2x + y = 0 and 3x − y = 0

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:

5x² – 9y² = 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 = ______.