HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve the following differential equation:

`dy/dx + y/x = x^3 - 3`

Solve the following differential equation:

`cos^2 "x" * "dy"/"dx" + "y" = tan "x"`

Solve the following differential equation:

`("x" + 2"y"^3) "dy"/"dx" = "y"`

Solve the following differential equation:

`"dy"/"dx" + "y" * sec "x" = tan "x"`

Solve the following differential equation:

`"x" "dy"/"dx" + "2y" = "x"^2 * log "x"`

Solve the following differential equation:

`("x + y") "dy"/"dx" = 1`

Solve the following differential equation:

`("x + a")"dy"/"dx" - 3"y" = ("x + a")^5`

Solve the following differential equation:

dr + (2r cotθ + sin2θ)dθ = 0

Solve the following differential equation:

y dx + (x - y²) dy = 0

Solve the following differential equation:

`(1 - "x"^2) "dy"/"dx" + "2xy" = "x"(1 - "x"^2)^(1/2)`

Solve the following differential equation:

`(1 + "x"^2) "dy"/"dx" + "y" = "e"^(tan^-1 "x")`

Find the equation of the curve which passes through the origin and has the slope x + 3y - 1 at any point (x, y) on it.

Find the equation of the curve passing through the point `(3/sqrt2, sqrt2)` having a slope of the tangent to the curve at any point (x, y) is -`"4x"/"9y"`.

The curve passes through the point (0, 2). The sum of the coordinates of any point on the curve exceeds the slope of the tangent to the curve at any point by 5. Find the equation of the curve.

If the slope of the tangent to the curve at each of its point is equal to the sum of abscissa and the product of the abscissa and ordinate of the point. Also, the curve passes through the point (0, 1). Find the equation of the curve.

Form the differential equation of all circles which pass through the origin and whose centers lie on X-axis.

Represent the truth of the following statement by the Venn diagram.

Some hardworking students are obedient.

Represent the truth of the following statement by the Venn diagram.

No circles are polygons.

Represent the truth of the following statement by the Venn diagram.

All teachers are scholars and scholars are teachers.

Represent the truth of the following statement by the Venn diagram.

If a quadrilateral is a rhombus, then it is a parallelogram.