Sets Chapter 1 Quiz

Chapter 1 - Sets

• A set is a well-defined collection of distinct objects.
• Elements of a set are enclosed within curly braces {}.
• Sets are usually denoted by capital letters (e.g., A, B, S).
• Elements are denoted by small letters (e.g., a, b, x).
• Empty set (null set) is a set containing no elements, denoted by {} or Ø.
• Finite sets have a definite number of elements.
• Infinite sets have an unlimited number of elements.
• Subset: If every element of set A is also an element of set B, then A is a subset of B (A ⊆ B).
• Proper subset: A is a proper subset of B if A is a subset of B, but A is not equal to B (A ⊂ B).
• Equal sets: Two sets A and B are equal if they have the same elements.
• Universal set: The largest set that contains all the elements under consideration.
• Complement of a set: The elements present in the universal set but not in the set.
• Venn diagrams: Used to represent relationships between sets visually.
• Union of sets: Contains all the elements of both sets (A ∪ B).
• Intersection of sets: Contains only the common elements of both sets (A ∩ B).
• Difference of sets: Contains elements that are in one set but not in the other (A - B or B - A).
• Disjoint sets: Two sets have no common elements (A ∩ B = Ø).

Chapter 2 - Relations and Functions

• Relation from set A to set B: A relation from set A to a set B is a subset of the Cartesian product A × B.
• Function: A special type of relation where each element of the domain is associated with exactly one element of the codomain.
• Domain: The set of all possible input values (x- values).
• Codomain: The set of all possible output values (y-values).
• Range: The set of actual output values (y-values) that are obtained when the function is applied to all elements in its domain.
• Types of functions: one-one (injective), onto (surjective), one-one onto (bijective).

Chapter 3 - Trigonometric Functions

• Trigonometric ratios: Defined for acute angles in a right-angled triangle.
• Sine, cosine, tangent, cosecant, secant, cotangent ratios.
• Relationship between trigonometric ratios for complementary angles.
• Trigonometric identities.

Chapter 4 - Quadratic Equations

• Quadratic equation: An equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
• Finding roots of a quadratic equation using the quadratic formula.
• Nature of roots based on discriminant (b² - 4ac).
• Relationship between roots and coefficients.

Chapter 5 - Arithmetic Progressions

• Arithmetic progression (AP): A sequence where the difference between consecutive terms is constant.
• nth term of an AP.
• Sum of n terms of an AP.

Chapter 6 - Linear Inequations

• Linear inequalities: Inequalities involving linear expressions.
• Solving linear inequalities.
• Representing solutions on the number line.

Chapter 7 - Permutations and Combinations

• Permutation: An arrangement of objects in a specific order.
• Combination: A selection of objects without regard to order.
• Fundamental principle of counting.
• Permutation formulas.
• Combination formulas.

Chapter 8 - Introduction to Trigonometry

• Trigonometric ratios for any angle.
• Trigonometric identities.
• Trigonometric ratios for specific angles.
• Trigonometric graphs.

Chapter 9 - Circles

• Definition and properties of circles.
• Tangents to a circle and their properties (e.g., length of tangents from an external point).

Chapter 10 - Constructions

• Geometric constructions using straight edge and compass.
• Construction of tangents to a circle, etc.

Chapter 11 - Heights and Distances

• Application of trigonometry to solve problems involving heights and distances.

Chapter 12 - Areas Related to Circles

• Area of a circle, sector, segment.
• Other areas related to circles.

Chapter 13 - Surface Areas and Volumes

• Surface area and volume of various 3D shapes (cubes, cuboids, cylinders, cones, spheres).

Chapter 14 - Statistics

• Collection, organization, presentation, interpretation of data.
• Measures of central tendency (mean, median, mode).
• Measures of dispersion (range, variance, standard deviation).

Chapter 15 - Probability

• Basic concepts of probability.
• Calculating probability of events.
• Probability of complementary events.
• Conditional probability.