HSC Commerce: Marketing and Salesmanship 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the value of i + i² + i³ + i⁴ 

Find the value of: x³ –  x² + x + 46, if x = 2 + 3i

Find the value of: 2x³ – 11x² + 44x + 27, if x = `25/(3 - 4"i")`

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

`3 + sqrt(-64)`

Find the derivative of the following function by the first principle: `(x - 1)/(2x + 7)`

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

(2i³)² 

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

(2 + 3i)(1 – 4i)

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

`5/2"i"(- 4 - 3 "i")`

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

(1 + 3i)² (3 + i)

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

`(4 + 3"i")/(1 - "i")`

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

`(1 + 2/i)(3 + 4/i)(5 + i)^-1`

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:

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