HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions

A box contains 10 red balls and 15 green balls. Two balls are drawn in succession without replacement. What is the probability that, one is red and the other is green?

An urn contains 4 black, 5 white and 6 red balls. Two balls are drawn one after the other without replacement. What is the probability that at least one of them is black?

Solve the following:

There are 6 positive and 8 negative numbers. Four numbers are chosen at random, without replacement, and multiplied. Find the probability that the product is a positive number.

Simplify : `sqrt(-16) + 3sqrt(-25) + sqrt(-36) - sqrt(-625)`

Simplify : `4sqrt(-4) + 5sqrt(-9) - 3sqrt(-16)`

Find a and b if a + 2b + 2ai = 4 + 6i

Find a and b if (a – b) + (a + b)i = a + 5i

Find a and b if (a+b) (2 + i) = b + 1 + (10 + 2a)i

Find a and b if abi = 3a − b + 12i

Find a and b if `1/("a" + "ib")` = 3 – 2i

Find a and b if (a + ib) (1 + i) = 2 + i

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(−1)`. State the values of a and b:

(1 + 2i)(– 2 + i)

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(−1)`. State the values of a and b:

(1 + i)(1 − i)⁻¹ 

Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(−1)`. State the values of a and b:

`("i"(4 + 3"i"))/((1 - "i"))`

Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:

`((2 + "i"))/((3 - "i")(1 + 2"i"))`

Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:

`((1 + "i")/(1 - "i"))^2`

Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:

`(3 + 2"i")/(2 - 5"i") + (3 -2"i")/(2 + 5"i")`

Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:

(1 + i)⁻³ 

Express the following in the form of a + ib, a, b ∈ R i = `sqrt(−1)`. State the values of a and b:

`(2 + sqrt(-3))/(4 + sqrt(-3))`

Express the following in the form of a + ib, a, b ∈ R i = `sqrt(−1)`. State the values of a and b:

`(- sqrt(5) + 2sqrt(-4)) + (1 -sqrt(-9)) + (2 + 3"i")(2 - 3"i")`