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

Solve the following:

Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). Find `"P"("B'"/"A")`

Solve the following:

Find the probability that a year selected will have 53 Wednesdays

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"`

Evaluate the following :

`lim_(x -> ∞) [("a"x^3 + "b"x^2 + "c"x + "d")/("e"x^3 + "f"x^2 + "g"x + "h")]`

Evaluate the following :

`lim_(x -> ∞) [(x^3 + 3x + 2)/((x + 4)(x - 6)(x - 3))]`

Evaluate the following :

`lim_(x -> ∞) [(7x^2 + 5x - 3)/(8x^2 - 2x + 7)]`

Evaluate the following :

`lim_(x -> ∞) [(7x^2 + 2x - 3)/(sqrt(x^4 + x + 2))]`

Evaluate the following :

`lim_(x -> ∞) [sqrt(x^2 + 4x + 16) - sqrt(x^2 + 16)]`

Evaluate the following :

`lim_(x -> ∞) [sqrt(x^4 + 4x^2) - x^2]`