HSC Commerce (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions

A question paper has 6 questions. How many ways does a student have if he wants to solve at least one question?

Three groups of children contain respectively 3 girls and 1 boy, 2 girls and 2 boys and 1 girl and 3 boys. One child is selected at random from each group. What is the chance that three selected consists of 1 girl and 2 boys?

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")`