HSC Commerce (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Simplify the following and express in the form a + ib:

`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`

Simplify the following and express in the form a + ib:

`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`

Simplify the following and express in the form a + ib:

`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`

Find the value of : x³ + 2x² – 3x + 21, if x = 1 + 2i

Find the value of: x³ – 5x² + 4x + 8, if x = `10/(3 - "i")`.

Find the value of: x³ – 3x² + 19x – 20, if x = 1 – 4i

The demand D for a price P is given as D = `27/"P"`, find the rate of change of demand when price is Rs. 3/-.

Differentiate the following functions w.r.t.x. :`sqrtx`

Differentiate the followingfunctions.w.r.t.x. : 7^x

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)]`