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

Solve the following differential equation:

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

Find the area of the region bounded by the following curves, X-axis and the given lines : y² = x, x = 0, x = 4

Find the area of the region bounded by the following curves, X-axis and the given lines: y² = 16x, x = 0, x = 4

Solve the following differential equation:

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

Find the area of the region bounded by the parabola y² = 16x and its latus rectum.

Solve the following differential equation:

x dy = (x + y + 1) dx

Find the area of the region bounded by the parabola: y = 4 – x² and the X-axis.

Solve the following differential equation:

`"dy"/"dx" + "y cot x" = "x"^2 "cot x" + "2x"`

Solve the following differential equation:

y log y = (log y² - x) `"dy"/"dx"`

Find the area of the region included between y² = 2x and y = 2x.

Solve the following differential equation:

`"dx"/"dy" + "8x" = 5"e"^(- 3"y")`

Find the area of the region included between: y² = 4x, and y = x

Find the particular solution of the following differential equation:

`("x + 2y"^2) "dy"/"dx" = "y",` when x = 2, y = 1

Find the area of the region included between: y = x² and the line y = 4x

Find the particular solution of the following differential equation:

`"dy"/"dx" - 3"y" cot "x" = sin "2x"`, when `"y"(pi/2) = 2`

Find the area of the region included between: y² = 4ax and the line y = x

Find the particular solution of the following differential equation:

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

Find the area of the region included between y = x² + 3 and the line y = x + 3.

Choose the correct option from the given alternatives :

The area bounded by the regional 1 ≤ x ≤ 5 and 2 ≤ y ≤ 5 is given by ______.

Find the particular solution of the following differential equation:

y(1 + log x) = (log x^x) `"dy"/"dx"`, when y(e) = e²