HSC Science (Computer Science) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Solve the following:

For three events A, B and C, we know that A and C are independent, B and C are independent, A and B are disjoint, P(A ∪ C) = `2/3`, P(B ∪ C) = `3/4`, P(A ∪ B ∪ C) = `11/12`. Find P(A), P(B) and P(C)

Solve the following:

A and B throw a die alternatively till one of them gets a 3 and wins the game. Find the respective probabilities of winning. (Assuming A begins the game)

Solve the following:

Consider independent trails consisting of rolling a pair of fair dice, over and over What is the probability that a sum of 5 appears before sum of 7?

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?