HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions

Area of the region bounded by y = x⁴, x = 1, x = 5 and the X-axis is _______.

Using definite integration, area of the circle x² + y² = 49 is _______.

Find the area of the region bounded by y = x², the X-axis and x = 1, x = 4.

Find the area of the region bounded by the parabola y² = 25x and the line x = 5.

Choose the correct alternative:

Area of the region bounded by the parabola y² = 25x and the lines x = 5 is ______

The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x)  "d"x`

Find the area of the region bounded by the curve y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3

Find the area of the region bounded by the curve y = (x² + 2)², the X-axis and the lines x = 1 and x = 3

Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5

The slope of a tangent to the curve y = 3x² – x + 1 at (1, 3) is ______.

The area of the region bounded by the curve y = x², x = 0, x = 3, and the X-axis is ______.

Find the area between the two curves (parabolas)

y² = 7x and x² = 7y.

Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.

Determine the order and degree of the following differential equation:

`(dy)/(dx) = (2sin x + 3)/(dy/dx)`

Determine the order and degree of the following differential equation:

`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`

Solve the following differential equation:

`x * dy/dx - y + x * sin(y/x) = 0`

Solve the following differential equation:

`x^2.  dy/dx = x^2 + xy + y^2`

Solve the following differential equation:

(x² – y²)dx + 2xy dy = 0

Find the differential equation whose general solution is

x³ + y³ = 35ax.

Solve the following differential equation.

`dy/dx + y` = 3