# Worksheet: Properties of Permutations

In this worksheet, we will learn how to use the properties of permutations to simplify expressions and solve equations.

Q1:

Find the value of given that .

Q2:

If , find .

Q3:

If , find the value of .

Q4:

Find the solution set of the equation .

• A
• B
• C
• D

Q5:

Find the smallest value of satisfying the inequality .

Q6:

If the middle factor in the expansion of is 69, find the value of .

Q7:

Find the value of satisfying the equation .

Q8:

Evaluate .

Q9:

Find the value of such that .

Q10:

Evaluate given that .

Q11:

If and , find .

Q12:

If and , find the value of .

Q13:

If and , find .

Q14:

Given that , determine the value of .

Q15:

If , find .

Q16:

Find such that .

Q17:

If , find the value of .

Q18:

If and , find and .

• A,
• B,
• C,
• D,

Q19:

Find the value of such that .

Q20:

If , find .

Q21:

Find the smallest value of which satisfies the inequality .

Q22:

Evaluate .

Q23:

Evaluate .

Q24:

Find the value of given that .

Q25:

Find the value of given that .