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

Solve the following:

A machine produces parts that are either good (90%), slightly defective (2%), or obviously defective (8%). Produced parts get passed through an automatic inspection machine, which is able to detect any part that is obviously defective and discard it. What is the quality of the parts that make it throught the inspection machine and get shipped?

Use De Moivres theorem and simplify the following:

`(cos2theta + "i"sin2theta)^7/(cos4theta + "i"sin4theta)^3`

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?