HSC Science (Computer Science) इयत्ता १२ वी - Maharashtra State Board Important Questions

Find the area of the ellipse `x^2/36 + y^2/64` = 1, using integration

The area bounded by the curve y = x³, the X-axis and the Lines x = –2 and x = 1 is ______.

Find the area of the region bounded by the curve y² = 4x, the X-axis and the lines x = 1, x = 4 for y ≥ 0.

Find the area of the region bounded by the curve y = x² and the line y = 4.

Find the area of the region bounded by the curve y = x², and the lines x = 1, x = 2, and y = 0.

Solve the differential equation (x² + y²)dx- 2xydy = 0

Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`

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`

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = A cos (log x) + B sin (log x)

Solve the following differential equation:

cos x . cos y dy − sin x . sin y dx = 0

Solve the following differential equation:

`(cos^2y)/x dy + (cos^2x)/y dx` = 0

Solve the following differential equation:

(x² + y²)dx - 2xy dy = 0

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

Solve the following differential equation:

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

Solve the following differential equation:

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

Solve the following differential equation:

dr + (2r cotθ + sin2θ)dθ = 0

In a certain culture of bacteria, the rate of increase is proportional to the number present. If it is found that the number doubles in 4 hours, find the number of times the bacteria are increased in 12 hours.