Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Find the particular solution of the differential equation:

2y e^x/y dx + (y - 2x e^x/y) dy = 0 given that x = 0 when y = 1.

If `A = [(1, 2, -3),(5, 0, 2),(1, -1, 1)], B = [(3, -1, 2),(4, 2, 5),(2, 0, 3)] and C = [(4, 1, 2),(0, 3, 2),(1, -2, 3)]` then compute (A + B) and (B – C). Also verify that A + (B – C) = (A + B) – C.

If ` A = [(2/3, 1, 5/3),(1/3, 2/3, 4/3),(7/3, 2, 2/3)]` and `B = [(2/5, 3/5, 1),(1/5, 2/5, 4/5),(7/5, 6/5, 2/5)]`, then compute 3A – 5B.

Simplify `cos theta[(cos theta, sintheta),(-sin theta, cos theta)] + sin theta[(sin theta, -cos theta), (cos theta, sin theta)]`

Show that `[(5, -1),(6, 7)][(2, 1),(3, 4)] ≠ [(2, 1),(3, 4)][(5, -1),(6, 7)]`

Show that `[(1, 2, 3),(0, 1, 0),(1, 1, 0)][(-1, 1, 0),(0, -1, 1),(2, 3, 4)] ≠ [(-1, 1, 0),(0, -1, 1),(2, 3, 4)][(1, 2, 3),(0, 1, 0),(1, 1, 0)]`

Find A² – 5A + 6I, if A = `[(2, 0, 1),(2, 1, 3),(1, -1, 0)]`

Show that the given differential equation is homogeneous and solve them.

(x² + xy) dy = (x² + y²) dx

Show that the given differential equation is homogeneous and solve them.

`y' = (x + y)/x`

Show that the given differential equation is homogeneous and solve them.

(x – y) dy – (x + y) dx = 0

Show that the given differential equation is homogeneous and solve them.

(x² – y²) dx + 2xy dy = 0

Show that the given differential equation is homogeneous and solve them.

`x^2 dy/dx = x^2 - 2y^2 + xy`

Show that the given differential equation is homogeneous and solve them.

`x  dy - y  dx =  sqrt(x^2 + y^2)   dx`

Show that the given differential equation is homogeneous and solve them.

`{xcos(y/x) + ysin(y/x)}ydx = {ysin (y/x) -  xcos(y/x)}xdy`

Show that the given differential equation is homogeneous and solve them.

`x dy/dx - y +  x sin (y/x) = 0`

Show that the given differential equation is homogeneous and solve them.

`y  dx + x log(y/x)dy - 2x  dy = 0`

Show that the given differential equation is homogeneous and solve them.

`(1+e^(x/y))dx + e^(x/y) (1 - x/y)dy = 0`

For the differential equation find a particular solution satisfying the given condition:

(x + y) dy + (x – y) dx = 0; y = 1 when x = 1

For the differential equation find a particular solution satisfying the given condition:

x² dy + (xy + y²) dx = 0; y = 1 when x = 1

For the differential equation find a particular solution satisfying the given condition:

`[xsin^2(y/x - y)] dx + x  dy = 0; y = pi/4 "when"  x = 1`