HSC Commerce: Marketing and Salesmanship इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

The marginal cost of producing x items is given by C = x² + 4x + 4. Find the average cost and the marginal cost. What is the marginal cost when x = 7.

Show that the following equations are consistent: 2x + 3y + 4 = 0, x + 2y + 3 = 0, 3x + 4y + 5 = 0

Find k, if the following equations are consistent: x + 3y + 2 = 0, 2x + 4y – k = 0, x – 2y – 3k = 0

Find k, if the following equations are consistent:

(k – 1)x + (k – 1)y = 17, (k – 1)x + (k – 2)y = 18, x + y = 5

Find the value (s) of k, if the following equations are consistent: 3x + y – 2 = 0, kx + 2y – 3 = 0 and 2x – y = 3

Find the value (s) of k, if the following equations are consistent: kx + 3y + 4 = 0, x + ky + 3 = 0, 3x + 4y + 5 = 0

Evaluate the following limits: `lim_(z -> 2) [(z^2 - 5z + 6)/(z^2 - 4)]`

Evaluate the following limits: `lim_(x -> - 3)[(x + 3)/(x^2 + 4x + 3)]` 

Evaluate the following limits: `lim_(y -> 0)[(5y^3 + 8y^2)/(3y^4 - 16y^2)]`

Evaluate the following limits: `lim_(x -> -2)[(-2x - 4)/(x^3 + 2x^2)]`

Evaluate the following limits: `lim_(u -> 1)[(u^4 - 1)/(u^3 - 1)]`

Evaluate the following limits: `lim_(x -> 3) [1/(x - 3) - (9x)/(x^3 - 27)]`

Evaluate the following limits: `lim_(x -> 2)[(x^3 - 4x^2 + 4x)/(x^2 - 1)]`

Evaluate the following limit:

`lim_(x -> - 2)[(x^7 + x^5 + 160)/(x^3 + 8)]`

Evaluate the following limits: `lim_(y -> 1/2)[(1 - 8y^3)/(y - 4y^3)]`

Evaluate the following limits: `lim_("v" -> sqrt(2))[("v"^2 + "v"sqrt(2) - 4)/("v"^2 - 3"v"sqrt(2) + 4)]`

Evaluate the following limits: `lim_(x -> 3)[(x^2 + 2x - 15)/(x^2 - 5x + 6)]`

Evaluate the following Limits: `lim_(x -> 2)[((x - 2))/(2x^2 - 7x + 6)]`

Evaluate the following limit:

`lim_(x -> 1)[(x^3 - 1)/(x^2 + 5x - 6)]`

Evaluate the following Limits: `lim_(x -> 3)[(x - 3)/(sqrt(x - 2) - sqrt(4 - x))]`