HSC Science (General) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

Solve the following differential equation y²dx + (xy + x²) dy = 0

Solve the following differential equation

`x^2  ("d"y)/("d"x)` = x² + xy − y² 

Solve the differential equation

`y (dy)/(dx) + x` = 0

If A = `[(3, -1),(4, 2)]`, B = `[(2),(-1)]`, find X such that AX = B.

Solve the differential equation

`x + y dy/dx` = x² + y²

If A = `[(cosθ, -sinθ, 0),(sinθ, cosθ, 0),(0, 0, 1)]`, find A^–1

Find the matrix X such that AX = B, where A = `[(2, 1),(-1, 3)]`, B = `[(12, -1),(1, 4)]`.

Solve the differential equation `dy/dx + xy = xy^2` and find the particular solution when y = 4, x = 1.

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:

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