**School Name:**
**Himalaya Public School****, ****Sector 13****, Rohini, Delhi 110085 India**
**Class:**
**12th Standard (CBSE)**
**Subject:**
**Mathematics**
**Time Duration:**
**03 Hours**
**Maximum Marks:**
**80**
**Date:**
**28 / 06 / ****2022**

### General Instructions: 12th Pre-Mid Term Maths Exam

**SECTION A**: Q (1 to S) short answer type Questions of 1 marks each.
**SECTION B**: Q (6 to 12) of 2 marks each.
**SECTION C**: Q (13 to 24) long answer type Questions of 3 marks each.
**SECTION D**: Q (25 to 29) long answer type Questions of 5 marks each.

## Syllabus For 12th Pre-Mid Term Maths

### Unit I: Relations and Functions

**Chapter 1: Relations and Functions**

- Types of relations:
- Reflexive
- Symmetric
- transitive and equivalence relations
- One to one and onto functions
- composite functions
- inverse of a function
- Binary operations

**Chapter 2: Inverse Trigonometric Functions**

- Definition, range, domain, principal value branch
- Graphs of inverse trigonometric functions
- Elementary properties of inverse trigonometric functions

### Unit II: Algebra

**Chapter 1: Matrices**

- Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices.
- Operation on matrices: Addition and multiplication and multiplication with a scalar
- Simple properties of addition, multiplication and scalar multiplication
- Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2)
- Concept of elementary row and column operations
- Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

**Chapter 2: Determinants**

- Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle
- Ad joint and inverse of a square matrix
- Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix

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