Notopedia is a nonprofit organization with a mission to provide free learning support to all. Click here to donate or volunteer
Notopedia has a mission to provide free learning support. Click here to donate or volunteer.
OFFICIAL SYLLABUS
Maths (Theory)
UNIT I. RELATIONS AND FUNCTIONS
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.
2. Inverse Trigonometric Functions:
Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
UNIT-II: ALGEBRA
1. Matrices:
Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of nonzero 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).
2. Determinants:
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants,
minors, cofactors and applications of determinants in finding the area of a triangle.Adjoint 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.
UNIT-III: CALCULUS
1. Continuity and Differentiability:
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function.Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretations.
2. Applications of Derivatives:
Applications of derivatives: rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
3. Integrals:
Integration as inverse process of differentiation. Integration of a variaty of functions by substitution, by partial fractions and by parts, only simple integrals of the type
to be evaluated. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
4. Applications of the Integrals:
Applications in finding the area under simple curves, especially lines, areas of circles/ parabolas/ ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable).
5. Differential Equations:
Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type
UNIT-IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY
1. Vectors:
Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors.
2. Three - dimensional Geometry:
Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes. (iii) a line and a plane. Distance of a point from a plane.
UNIT-V: LINEAR PROGRAMMING
Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
UNIT-VI: PROBABILITY
Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution.
For more Information click this link : Click Here
Paper Format
Paper Type - Theory
Paper Marks - Theory (100 Marks)
Time duration - 3 hours
Unit & their Weightage
Unit | Marks | |
Unit I | Relations and Functions | 10 |
Unit II | Algebra | 13 |
Unit III | Calculus | 44 |
Unit IV | Vectors And Three - Dimensional Geometry | 17 |
Unit V | Linear Programming | 06 |
Unit VI | Probability | 10 |
Total | 100 |
For More Information:- Click Here
Conditions of eligibility for admission to class XII
1. Candidates who have been studying in a School recognised by or affiliated to this Board or any other recognised Board of Secondary Education in India.
2. Candidates can not take admission directly in class XII.
3. Candidates had completed a regular course of study for class XI and passed class XI examination from a school affilicated to this Board.
4. The candidates percentage for attendance should be 75% so that the Board to make him/her eligible for the Examinations.
5. Candidate can be admitted to a school only on the transfer of the parents(s) or shifting of their families from one place to another, after procuring from the student the marksheet and the Transfer Certificate duly countersigned by the Educational Authorities of the Board Concerned.
6. There is no age limit for candidates taking the Examination.
7. Candidate should have doucments in support of his having passed the qualifying or equivalent qualifying examination.
TIME TABLE 2023
Date & Day | Subject | Time Duration |
Saturday 25 March 2023 | Mathematics | 10:00 AM to 01:00 PM (3 Hrs.) |
Date & Day | Subject | Time Duration |
Thursday 16 March 2023 | Hindi, Agriculture Hindi (Only for Agriculture Part II) | 10:00 AM to 01:00 PM (3 Hrs.) |
Saturday 18 March 2023 | Geography, Geology | 10:00 AM to 01:00 PM (3 Hrs.) |
Monday 20 March 2023 | Urdu, Punjabi, Physics, Accountancy Agronomy Paper I (Only for Agriculture Part I) agronomy Paper VI (Only for Agriculture Part II) | 10:00 AM to 01:00 PM (3 Hrs.) |
Tuesday 21 March 2023 | Sociology | 10:00 AM to 01:00 PM (3 Hrs.) |
Thursday 23 March 2023 | Political Science Agricultural Botony Paper II (Only for Agriculture Part I) Agricultural Economics Paper VII (Only for Agriculture Part II) | 10:00 AM to 01:00 PM (3 Hrs.) |
Friday 24 March 2023 | Drawing & Painting | 10:00 AM to 01:00 PM (3 Hrs.) |
Saturday 25 March 2023 | Mathematics | 10:00 AM to 01:00 PM (3 Hrs.) |
Monday 27 March 2023 | Sanskrit, Agricultural Physics and Climatology Paper III (Only for Agricultural Part I) Agricultural Zoology Paper VIII (Only for Agriculture Part II) | 10:00 AM to 01:00 PM (3 Hrs.) |
Tuesday 28 March 2023 | Psychology, Education, Chemistry | 10:00 AM to 01:00 PM (3 Hrs.) |
Wednesday 29 March 2023 | Military Science, Computer Science | 10:00 AM to 01:00 PM (3 Hrs.) |
Friday 31 March 2023 | Economics | 10:00 AM to 01:00 PM (3 Hrs.) |
Saturday 01 April 2023 | Biology, Indian Music (Vocal), Indian Music (Mailodic Instrument), Indian Music (Purssion Instrument), Agricultural Engineering Paper IV (Only for Agriculture Part I) Agricultural Animal Husbandry and Veterinary Science Paper IX (Only for Agriculture Part II) | 10:00 AM to 01:00 PM (3 Hrs.) |
Monday 03 April 2023 | English | 10:00 AM to 01:00 PM (3 Hrs.) |
Wednesday 05 April 2023 | History Agricultural Mathematics and Preliminary Statistics Paper V (Only for Agriculture Part I) Agricultural Chemistry Paper X (Only for Agricultural Part II) | 10:00 AM to 01:00 PM (3 Hrs.) |
Thursday 06 April 2023 | Home Science, Business Study | 10:00 AM to 01:00 PM (3 Hrs.) |
For More Information:- Click Here
Paper Analysis
1. There are in all 28 questions in this question paper.
2. Question no.1 to 5 (1 marks each)
3. Question no. 6 to 13 (2 marks each)
4. Question no. 14 to 21 (4 marks each)
5. Question no. 22 to 28 (6 marks each)
And
There was no overall choice. However, an internal choice was given in two questions of 2 marks each, three questions of 4 marks each, and four questions of 6 marks each. Students needed to attempt only one of the alternatives in all such questions.
Comment
1. The difficulty level of the Maths paper 2020: Moderate.
2. The pattern of the Maths paper was similar to the latest Maths Sample Paper 2020.
3. All the questions in the paper were asked from the latest syllabus and based on NCERT textbooks.
4. The average range of expected marks was 60+ (out of 80).
1. There are total 28 questions in this question paper.
2. Question No. 1 is a multiple choice question, divided into 6 sections.
3. Each section is of 1 mark. 4 options are given for each section .
4. Question numbers 2 to 5 carry 1 mark each.
5. Question numbers 6 to 13 carry 2 marks each.
6. Question numbers 14 to 21 carry 4 marks each.
7. Question numbers 22 to 28 carry 6 marks each.
8. There was no overall choice in the question paper. However, two questions carrying 2 marks each, three questions of 4 marks each, and four questions of 6 marks each were given an internal choice .
9. The students were to attempt only one option out of all such questions.
UBSE announces Class 10 & 12 results 2025. Check pass percentages, toppers, and download your marksheet at ubse.uk.gov.in or uaresults.nic.in...
Posted On: 19 Apr, 2025 | |
Read More |
![]() |
![]() |
![]() |
© 2025 Notopedia All rights reserved.
This content has been book marked