HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Use De Moivres theorem and simplify the following:

`(cos5theta + "i"sin5theta)/((cos3theta - "i"sin3theta)^2`

Use De Moivres theorem and simplify the following:

`(cos  (7pi)/13 + "i"sin  (7pi)/13)^4/(cos  (4pi)/13 - "i"sin  (4pi)/13)^6`

Express the following in the form a + ib, a, b ∈ R, using De Moivre's theorem:

(1 − i)⁵ 

Express the following in the form a + ib, a, b ∈ R, using De Moivre's theorem:

(1 + i)⁶

Express the following in the form a + ib, a, b ∈ R, using De Moivre's theorem:

`(1 - sqrt(3)"i")^4`

Express the following in the form a + ib, a, b ∈ R, using De Moivre's theorem:

`(-2sqrt(3) - 2"i")^5`

Select the correct answer from the given alternatives:

If z = r(cos θ + i sin θ), then the value of `"z"/bar("z") + bar("z")/"z"`

How many 4 letter words can be formed using letters in the word MADHURI if letters cannot be repeated

Find the number of permutations of letters in the following word:

DIVYA

Find the number of permutations of letters in the following word:

SHANTARAM

Find the number of permutations of letters in the following word:

REPRESENT

Find the number of permutations of letters in the following word:

COMBINE

Find the number of permutations of letters in the following word:

BALBHARATI

You have 2 identical books on English, 3 identical books on Hindi, and 4 identical books on Mathematics. Find the number of distinct ways of arranging them on a shelf

A coin is tossed 8 times. In how many ways can we obtain 4 heads and 4 tails?

A coin is tossed 8 times. In how many ways can we obtain at least 6 heads?

A bag has 5 red, 4 blue, and 4 green marbles. If all are drawn one by one and their colours are recorded, how many different arrangements can be found?

Find the number of ways of arranging letters of the word MATHEMATICAL How many of these arrangements have all vowels together?

Find the number of different arrangements of letters in the word MAHARASHTRA. How many of these arrangements have letters R and H never together?

Find the number of different arrangements of letters in the word MAHARASHTRA. How many of these arrangements have all vowels together?