Algebra, arithmetic, reasoning.
Choose an option to check your answer.
Three distinct objects can be arranged in 3! ways.
Thus, 3! = 3 × 2 × 1 = 6.
Choose an option to check your answer.
Equal sides in an isosceles triangle face equal angles.
This is the base-angle theorem.
Choose an option to check your answer.
Corresponding angles between parallel lines are equal.
Therefore, the other angle is also 110°.
Choose an option to check your answer.
Sector area is angle/360 × πr².
Thus, 60/360 × 36π = 6π cm².
Choose an option to check your answer.
The union contains every distinct element from either set.
Thus, A ∪ B = {1, 2, 3}.
Choose an option to check your answer.
The number of arrangements of 5 distinct objects is 5!.
Thus, 5! = 120.
Choose an option to check your answer.
By Pythagoras, c² = 6² + 8² = 100.
Thus, c = 10 cm.
Choose an option to check your answer.
Alternate interior angles formed by parallel lines are equal.
Thus, the matching angle is 65°.
Choose an option to check your answer.
Cube volume is side cubed.
Thus, 4³ = 64 cm³.
Choose an option to check your answer.
The complement contains universal-set elements not in A.
Removing 2 and 4 leaves 1, 3, and 5.
Choose an option to check your answer.
Selection without order uses combinations.
5C2 = 5 × 4 ÷ 2 = 10.
Choose an option to check your answer.
For a right triangle, the square of the longest side equals the sum of the other squares.
Here, 5² + 12² = 13².
