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

Form the differential equation of all the lines which are normal to the line 3x + 2y + 7 = 0.

Find the area of the region bounded by the following curves, X-axis and the given lines: x = 2y, y = 0, y = 4

Find the area of the region bounded by the following curves, X-axis and the given lines : y = sin x, x = 0, x = `pi/(2)`

Find the area of the region bounded by the following curves, X-axis and the given lines : x = 0, x = 5, y = 0, y = 4

Form the differential equation of the hyperbola whose length of transverse and conjugate axes are half of that of the given hyperbola `"x"^2/16 - "y"^2/36 = "k"`.

Find the area of the region bounded by the following curves, X-axis and the given lines: xy = 2, x = 1, x = 4

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