HSC Science (General) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If ω(≠1) is a cube root of unity and (1 + ω)⁷ = A + Bω, then A and B are respectively the numbers ______.

If α and β are complex cube roots of unity, prove that (1 − α)(1 − β) (1 − α²)(1 − β²) = 9.

Answer the following:

If ω is a complex cube root of unity, prove that (1 − ω + ω²)⁶ +(1 + ω − ω²)⁶ = 128

If ω is the cube root of unity then find the value of `((-1 + "i"sqrt(3))/2)^18 + ((-1 - "i"sqrt(3))/2)^18`

In how many different ways can 8 friends sit around a table?

A party has 20 participants. Find the number of distinct ways for the host to sit with them around a circular table. How many of these ways have two specified persons on either side of the host?

Delegates from 24 countries participate in a round table discussion. Find the number of seating arrangments where two specified delegates are always together

Delegates from 24 countries participate in a round table discussion. Find the number of seating arrangments where two specified delegates are never together

Find the number of ways for 15 people to sit around the table so that no two arrangements have the same neighbours

A committee of 10 members sits around a table. Find the number of arrangements that have the president and the vice-president together.

Five men, two women, and a child sit around a table. Find the number of arrangements where the child is seated between the two women

Five men, two women, and a child sit around a table. Find the number of arrangements where the child is seated between two men

Eight men and six women sit around a table. How many of sitting arrangements will have no two women together?

Find the number of seating arrangements for 3 men and 3 women to sit around a table so that exactly two women are together.

Four objects in a set of ten objects are alike. Find the number of ways of arranging them in a circular order

Fifteen persons sit around a table. Find the number of arrangements that have two specified persons not sitting side by side.

Answer the following:

There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many lines are there in total.

Answer the following:

There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many lines pass through D.

Answer the following:

There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many triangles are determined by lines.

Answer the following:

There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many triangles have on vertex C.