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

Solve the following differential equation.

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

Solve the following differential equation.

`dy/dx + y` = 3

Solve the following differential equation.

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

Solve the following differential equation.

y dx + (x - y² ) dy = 0

Solve the following differential equation.

`dy/dx + 2xy = x`

Solve the following differential equation.

`(x + a) dy/dx = – y + a`

Solve the following differential equation.

dr + (2r)dθ= 8dθ

Choose the correct alternative.

The equation of tangent to the curve y = x² + 4x + 1 at (-1, -2) is 

Choose the correct alternative.

The equation of tangent to the curve x² + y² = 5 where the tangent is parallel to the line 2x – y + 1 = 0 are

Choose the correct alternative.

If elasticity of demand η = 1, then demand is

Choose the correct alternative.

If 0 < η < 1, then demand is

Choose the correct alternative.

If f(x) = 3x³ - 9x² - 27x + 15 then

Fill in the blank:

The slope of tangent at any point (a, b) is called as _______.

Fill in the blank:

If f(x) = x - 3x² + 3x - 100, x ∈ R then f''(x) is ______

Fill in the blank:

If f(x) = `7/"x" - 3`, x ∈ R x ≠ 0 then f ''(x) is ______

State whether the following statement is True or False:

The equation of tangent to the curve y = 4xe^x at `(-1, (- 4)/"e")` is ye + 4 = 0

State whether the following statement is True or False:

x + 10y + 21 = 0 is the equation of normal to the curve y = 3x² + 4x - 5 at (1, 2).

Find the equation of tangent and normal to the following curve.

xy = c² at `("ct", "c"/"t")` where t is parameter.

Find the equation of tangent and normal to the following curve.

y = x² + 4x at the point whose ordinate is -3.

Choose the correct alternative.

The differential equation of y = `k_1 + k_2/x` is