HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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`

Find the equation of tangent and normal to the curve at the given points on it.

y = 3x² - x + 1 at (1, 3)

Find the equation of tangent and normal to the curve at the given points on it.

2x² + 3y² = 5 at (1, 1)

Find the equation of tangent and normal to the curve at the given points on it.

x² + y² + xy = 3 at (1, 1)

Find the equations of tangent and normal to the curve y = x² + 5 where the tangent is parallel to the line 4x − y + 1 = 0.

Find the equations of tangent and normal to the curve y = 3x² - 3x - 5 where the tangent is parallel to the line 3x − y + 1 = 0.

Solve the following differential equation.

`x^2 dy/dx = x^2 +xy - y^2`