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

A, B, and C are mutually exclusive and exhaustive events associated with the random experiment. Find P(A), given that P(B) = `3/2` P(A) and P(C) = `1/2` P(B).

Two-third of the students in a class are boys and rest are girls. It is known that the probability of girl getting first class is 0.25 and that of boy getting is 0.28. Find the probability that a student chosen at random will get first class.

Show that 1 + i¹⁰ + i²⁰ + i³⁰ is a real number.

Find the value of i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰ 

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")`.