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

Fill in the Blank.

If 3x²y + 3xy² = 0, then `(dy)/(dx)` = ______.

If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`

For each of the following differential equations find the particular solution.

`y (1 + logx)dx/dy - x log x = 0`,

when x=e, y = e².

For  the following differential equation find the particular solution.

`dy/ dx = (4x + y + 1),

when  y = 1, x = 0

Solve the following differential equation.

xdx + 2y dx = 0

The derivative of f(x) = a^x, where a is constant is x.a^x-1.

State whether the following is True or False:

The derivative of polynomial is polynomial.

`d/dx(10^x) = x*10^(x - 1)`

Solve the following:

If y = (6x³ - 3x² - 9x)¹⁰, find `"dy"/"dx"` 

If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`.

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25 + 30x  – x².

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(5x + 7)/(2x - 13)`

Find `"dy"/"dx"`, if y = x^x.

Solve the following differential equation.

y² dx + (xy + x² ) dy = 0

Find `"dy"/"dx"`, if y = `2^("x"^"x")`.

Solve the following differential equation.

x²y dx − (x³ + y³) dy = 0

Solve the following differential equation.

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

Solve the following differential equation.

(x² − y² ) dx + 2xy dy = 0

Differentiate `"e"^("4x" + 5)` with respect to 10^4x.

Solve the following differential equation.

`xy  dy/dx = x^2 + 2y^2`