Mastering Unit 1 (Mathematics Class XII)

Unit 1 consists of two chapters. These are: ‘Relations and Functions’ and ‘Inverse Trigonometric Functions’. Together these chapters contribute to a maximum of 10 marks.

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Important topics:

• Determine whether a given relation is reflexive/symmetric/transitive/equivalence (or not) and related deductions like finding the set of all elements related to a particular element (Equivalence class)
• Identifying a given function as injective, surjective or bijective/invertible (or not)
• Composition of two given functions
• Formation of binary operation table for a given binary operation, and also showing the binary operation as commutative, associative (or not)
• Finding the identity element for a binary operation (if exists) and also finding inverse of an element.

Questions asked in previous years

1. State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive. [1 mark, 2011]
2. Consider the binary operation * on the set {1, 2, 3, 4, 5} defined by a * b = min. {a, b}. Write the operation table of the operation *.
   [4 marks, 2011]
3. [1 Marks, 2010]
4. Show that the relation S in the set A = {x ∈ Z: 0 ≤ x ≤ 12} given by S = {(a, b): a, b ∈ Z, |a − b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. [4 marks, 2010]
5. [1 Marks, 2009]
6. [4 Marks, 2009]
7. [4 Marks, 2008]

INVERSE TRIGNOMETRIC FUNCTIONS

Important topics:

• Evaluation of principal value of a given trigonometric function
• Proving a given relation using properties of inverse trigonometric functions

Questions asked in previous years:

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Wish you all the very best for your Mathematics Exam.

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