Bihar Board Class 12 Maths Half-Yearly Exam 2026-27: Important Questions & Revision

Preparing for the Bihar Board Class 12 Maths Half-Yearly Exam 2026 can become difficult when students know the formulas but are unsure which concepts to revise first. For example, a student may understand the meaning of a reflexive relation but get confused when a question asks whether a given relation is reflexive, symmetric, or transitive. Similar confusion can occur while checking whether a function is injective or surjective.

The questions given below focus on these important concepts from Relations and Functions. They include descriptive questions, proof-based questions, and objective questions on empty and universal relations, equivalence relations, reflexive, symmetric, and transitive relations, and injective and surjective functions.

Practising these questions can help students understand how each property is applied in an actual question. It can also help them identify the difference between similar concepts and improve their approach to solving questions. For the Bihar Board Class 12 Maths Half-Yearly Exam 2026, these questions can therefore be used for focused revision and practice.

Bihar Board Class 12 Maths Half-Yearly Exam Important Questions

The following questions cover the main concepts and question types included in the study material. Revise the method used in each question and practise similar calculations while preparing for the Class 12 Maths Half-Yearly Syllabus. 

Question 1: Let A be the set of all students of a boys' school. Show that the relation R in A given by R={(a,b):a is sister of b} is the empty relation and R'={(a,b):the difference between heights of a and b is less than 3meters } is the universal relation. 

Question 2: Let T be the set of all triangles in a plane with R a relation in T given by R={(T1,T2):T1is congruent to T2}. Show that R is an equivalence relation.

Question 3: Determine whether each of the following relations are reflexive, symmetric and transitive: Relation R in the set A = {1, 2, 3,..., 13, 14} defined as R={(x,y):3x-y=0}  

Question 4 : A relation R in a set A is a subset of –

A) A

B) AA

C) AA

D) A-A

Question 5: If R=, then R is called –

A) Universal Relation

B) Equivalence Relation

C) Empty Relation

D) Symmetric Relation

Question 6: If A={1,2}, then the number of ordered pairs in the universal relation on A is –

A) 2

B) 3

C) 4

D) 5

Question 7: A relation R on A is reflexive if –

A) (a,b)R(b,a)R

B) (a,b),(b,c)R(a,c)R

C) (a,a)R, for every aA

D) R=

Question 8: If (2,5)R and R is symmetric, then –

A) (2,2)R

B) (5,5)R

C) (5,2)R

D) (2,5)R

Question 9: A relation is called an equivalence relation if it is –

A) Reflexive only

B) Symmetric only

C) Transitive only

D) Reflexive, Symmetric and Transitive

Question 10: Let A={1,2,3} and R={(1,1),(2,2),(3,3),(1,2),(2,1)}. Then R is –

A) Reflexive and Symmetric but not Transitive

B) Reflexive, Symmetric and Transitive

C) Symmetric only / केवल Symmetric

D) Transitive only / केवल Transitive

Question 11: Check whether the relation R defined in the set {1,2,3,4,5,6} as R={(a,b):b=a+1} is reflexive, symmetric or transitive.

Question 12: Show that the relation R in R defined as R={(a,b):ab}, is reflexive and transitive but not symmetric.

Question 13: Check the injectivity and surjectivity of the following functions:

1. f:NN given by f(x)=x2

2. f:ZZ given by f(x)=x2

3. f:RR given by f(x)=x2 

Bihar Board Class 12 Maths Half-Yearly Important Questions PDF

For detailed answers and more practice questions, students can download the Bihar Board Class 12 Maths Half-Yearly Important Questions PDF. It covers the important topics and questions included in the revision material.

How to Revise for Bihar Board Class 12 Maths Half-Yearly Exam 2026

A topic-wise revision plan can make the questions easier to manage. Start with definitions and formulas, then move to the numerical questions given in the material.

1. Relations and Functions

Revise empty, universal, reflexive, symmetric, transitive, and equivalence relations. Then practise checking these properties in the given relations. After this, revise one-one, onto, and bijective functions along with composition of functions.

2. Inverse Trigonometric Functions

First, revise the principal value branches. Then practise principal value questions. After that, revise the properties and identities of inverse trigonometric functions.

3. Matrices and Determinants

Revise matrix types, order, elements, and operations. Practise constructing matrices from given formulas. Then move to determinants, area of a triangle, adjoint, and inverse of a matrix.

4. Continuity and Differentiability

Start with limits and continuity. Practise piecewise functions and questions involving continuity at a particular point. Then revise differentiation rules, chain rule, and derivatives of standard functions.

5. Application of Derivatives

Practise implicit differentiation, inverse trigonometric derivatives, exponential and logarithmic functions, parametric differentiation, and second-order derivatives.

Bihar Board Class 12 Maths Half-Yearly Exam 2026 Revision Checklist

Before completing your revision, make sure you have covered the following areas:

• Empty, universal, reflexive, symmetric, transitive, and equivalence relations

• One-one, onto, and bijective functions

• Composition of functions

• Principal values of inverse trigonometric functions

• Properties of inverse trigonometric functions

• Types and order of matrices

• Matrix operations

• Determinants of different orders

• Area of a triangle using determinants

• Adjoint and inverse of a matrix

• Solving systems of equations using the matrix method

• Limits and continuity

• Differentiation and chain rule

• Implicit differentiation

• Derivatives of inverse trigonometric functions

• Exponential and logarithmic differentiation

• Parametric differentiation

• Second-order derivatives

Bihar Board Class 12 Preparation Resources

• PW's Class 12 Commerce Courses

• Bihar Board Class 12 Business Studies Half-Yearly Exams
• Bihar Board Class 12 Commerce Half Yearly Exam Date