CUET Exam Syllabus for Mathematics - Commerce PDF Download

 Page 1


 
Mathematics/Applied Mathematics (319) 
 
2 
 
 
 
 
 
 
 
 
 
 
 
SECTION A  
1. Algebra 
(i) Matrices and types of Matrices 
(ii) Equality of Matrices, transpose of a Matrix, 
Symmetric and Skew Symmetric Matrix 
(iii) Algebra of Matrices 
(iv) Determinants 
(v) Inverse of a Matrix 
(vi) Solving of simultaneous equations using Matrix 
Method 
2. Calculus 
(i) Higher order derivatives 
(ii) Tangents and Normals 
 (iii) Increasing and Decreasing Functions 
(iv). Maxima and Minima 
3. Integration and its Applications 
(i) Indefinite integrals of simple functions 
(ii) Evaluation of indefinite integrals 
(iii) Definite Integrals 
(iv). Application of Integration as area under the 
curve 
4. Differential Equations 
(i) Order and degree of differential equations 
(ii) Formulating and solving of differential equations 
with variable separable 
5. Probability Distributions 
(i) Random variables and its probability distribution 
(ii) Expected value of a random variable 
(iii) Variance and Standard Deviation of a random 
variable 
(iv). Binomial Distribution 
6. Linear Programming 
(i) Mathematical formulation of Linear 
Programming Problem 
(ii) Graphical method of solution for problems in two 
variables 
(iii) Feasible and infeasible regions 
(iv). Optimal feasible solution 
 
 
 
 
Note:  
There will be one Question Paper which will contain Two Sections i.e. Section A and Section B [B1 and 
B2].  
Section A will have 15 questions covering both i.e. Mathematics/Applied Mathematics which will be 
compulsory for all candidates 
 
Section B1 will have 35 questions from Mathematics out of which 25 questions need to be attempted. 
Section B2 will have 35 questions purely from Applied Mathematics out of which 25 question will be 
attempted. 
Page 2


 
Mathematics/Applied Mathematics (319) 
 
2 
 
 
 
 
 
 
 
 
 
 
 
SECTION A  
1. Algebra 
(i) Matrices and types of Matrices 
(ii) Equality of Matrices, transpose of a Matrix, 
Symmetric and Skew Symmetric Matrix 
(iii) Algebra of Matrices 
(iv) Determinants 
(v) Inverse of a Matrix 
(vi) Solving of simultaneous equations using Matrix 
Method 
2. Calculus 
(i) Higher order derivatives 
(ii) Tangents and Normals 
 (iii) Increasing and Decreasing Functions 
(iv). Maxima and Minima 
3. Integration and its Applications 
(i) Indefinite integrals of simple functions 
(ii) Evaluation of indefinite integrals 
(iii) Definite Integrals 
(iv). Application of Integration as area under the 
curve 
4. Differential Equations 
(i) Order and degree of differential equations 
(ii) Formulating and solving of differential equations 
with variable separable 
5. Probability Distributions 
(i) Random variables and its probability distribution 
(ii) Expected value of a random variable 
(iii) Variance and Standard Deviation of a random 
variable 
(iv). Binomial Distribution 
6. Linear Programming 
(i) Mathematical formulation of Linear 
Programming Problem 
(ii) Graphical method of solution for problems in two 
variables 
(iii) Feasible and infeasible regions 
(iv). Optimal feasible solution 
 
 
 
 
Note:  
There will be one Question Paper which will contain Two Sections i.e. Section A and Section B [B1 and 
B2].  
Section A will have 15 questions covering both i.e. Mathematics/Applied Mathematics which will be 
compulsory for all candidates 
 
Section B1 will have 35 questions from Mathematics out of which 25 questions need to be attempted. 
Section B2 will have 35 questions purely from Applied Mathematics out of which 25 question will be 
attempted. 
 
Mathematics/Applied Mathematics (319) 
 
3 
 
 
Section B1: Mathematics 
 
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 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). 
 
2. Determinants  
Determinant of a square matrix (up to 3 × 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. Concepts of exponential, logarithmic functions. 
Derivatives of log x
 
and e
x
. Logarithmic differentiation. Derivative of functions expressed in parametric 
forms. Second-order derivatives. R o l l e ’ s and L a g r a n g e ’ s Mean Value Theorems (without proof) 
and their geometric interpretations. 
 
2. Applications of Derivatives  
Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and 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). Tangent and Normal.  
 
 
Page 3


 
Mathematics/Applied Mathematics (319) 
 
2 
 
 
 
 
 
 
 
 
 
 
 
SECTION A  
1. Algebra 
(i) Matrices and types of Matrices 
(ii) Equality of Matrices, transpose of a Matrix, 
Symmetric and Skew Symmetric Matrix 
(iii) Algebra of Matrices 
(iv) Determinants 
(v) Inverse of a Matrix 
(vi) Solving of simultaneous equations using Matrix 
Method 
2. Calculus 
(i) Higher order derivatives 
(ii) Tangents and Normals 
 (iii) Increasing and Decreasing Functions 
(iv). Maxima and Minima 
3. Integration and its Applications 
(i) Indefinite integrals of simple functions 
(ii) Evaluation of indefinite integrals 
(iii) Definite Integrals 
(iv). Application of Integration as area under the 
curve 
4. Differential Equations 
(i) Order and degree of differential equations 
(ii) Formulating and solving of differential equations 
with variable separable 
5. Probability Distributions 
(i) Random variables and its probability distribution 
(ii) Expected value of a random variable 
(iii) Variance and Standard Deviation of a random 
variable 
(iv). Binomial Distribution 
6. Linear Programming 
(i) Mathematical formulation of Linear 
Programming Problem 
(ii) Graphical method of solution for problems in two 
variables 
(iii) Feasible and infeasible regions 
(iv). Optimal feasible solution 
 
 
 
 
Note:  
There will be one Question Paper which will contain Two Sections i.e. Section A and Section B [B1 and 
B2].  
Section A will have 15 questions covering both i.e. Mathematics/Applied Mathematics which will be 
compulsory for all candidates 
 
Section B1 will have 35 questions from Mathematics out of which 25 questions need to be attempted. 
Section B2 will have 35 questions purely from Applied Mathematics out of which 25 question will be 
attempted. 
 
Mathematics/Applied Mathematics (319) 
 
3 
 
 
Section B1: Mathematics 
 
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 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). 
 
2. Determinants  
Determinant of a square matrix (up to 3 × 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. Concepts of exponential, logarithmic functions. 
Derivatives of log x
 
and e
x
. Logarithmic differentiation. Derivative of functions expressed in parametric 
forms. Second-order derivatives. R o l l e ’ s and L a g r a n g e ’ s Mean Value Theorems (without proof) 
and their geometric interpretations. 
 
2. Applications of Derivatives  
Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and 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). Tangent and Normal.  
 
 
 
Mathematics/Applied Mathematics (319) 
 
4 
 
3. Integrals  
Integration as inverse process of differentiation. Integration of a variety 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, arcs of circles/parabolas/el- 
lipses (in standard form only), area between the two above said curves (the region should be cleraly 
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 – 
 
dy 
? Py ? Q , 
where P and Q are functions of x or constant 
dx 
 
 
dx 
? Px 
dy 
? Q , 
where P and Q are functions of y or constant 
Page 4


 
Mathematics/Applied Mathematics (319) 
 
2 
 
 
 
 
 
 
 
 
 
 
 
SECTION A  
1. Algebra 
(i) Matrices and types of Matrices 
(ii) Equality of Matrices, transpose of a Matrix, 
Symmetric and Skew Symmetric Matrix 
(iii) Algebra of Matrices 
(iv) Determinants 
(v) Inverse of a Matrix 
(vi) Solving of simultaneous equations using Matrix 
Method 
2. Calculus 
(i) Higher order derivatives 
(ii) Tangents and Normals 
 (iii) Increasing and Decreasing Functions 
(iv). Maxima and Minima 
3. Integration and its Applications 
(i) Indefinite integrals of simple functions 
(ii) Evaluation of indefinite integrals 
(iii) Definite Integrals 
(iv). Application of Integration as area under the 
curve 
4. Differential Equations 
(i) Order and degree of differential equations 
(ii) Formulating and solving of differential equations 
with variable separable 
5. Probability Distributions 
(i) Random variables and its probability distribution 
(ii) Expected value of a random variable 
(iii) Variance and Standard Deviation of a random 
variable 
(iv). Binomial Distribution 
6. Linear Programming 
(i) Mathematical formulation of Linear 
Programming Problem 
(ii) Graphical method of solution for problems in two 
variables 
(iii) Feasible and infeasible regions 
(iv). Optimal feasible solution 
 
 
 
 
Note:  
There will be one Question Paper which will contain Two Sections i.e. Section A and Section B [B1 and 
B2].  
Section A will have 15 questions covering both i.e. Mathematics/Applied Mathematics which will be 
compulsory for all candidates 
 
Section B1 will have 35 questions from Mathematics out of which 25 questions need to be attempted. 
Section B2 will have 35 questions purely from Applied Mathematics out of which 25 question will be 
attempted. 
 
Mathematics/Applied Mathematics (319) 
 
3 
 
 
Section B1: Mathematics 
 
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 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). 
 
2. Determinants  
Determinant of a square matrix (up to 3 × 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. Concepts of exponential, logarithmic functions. 
Derivatives of log x
 
and e
x
. Logarithmic differentiation. Derivative of functions expressed in parametric 
forms. Second-order derivatives. R o l l e ’ s and L a g r a n g e ’ s Mean Value Theorems (without proof) 
and their geometric interpretations. 
 
2. Applications of Derivatives  
Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and 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). Tangent and Normal.  
 
 
 
Mathematics/Applied Mathematics (319) 
 
4 
 
3. Integrals  
Integration as inverse process of differentiation. Integration of a variety 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, arcs of circles/parabolas/el- 
lipses (in standard form only), area between the two above said curves (the region should be cleraly 
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 – 
 
dy 
? Py ? Q , 
where P and Q are functions of x or constant 
dx 
 
 
dx 
? Px 
dy 
? Q , 
where P and Q are functions of y or constant 
 
Mathematics/Applied Mathematics (319) 
 
4 
 
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, scalar triple product. 
 
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, 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 constrains). 
 
Unit VI: Probability  
Multiplications theorem on probability. Conditional probability, independent events, total probability, 
B a y e ’ s theorem. Random variable and its probability distribution, mean and variance of haphazard 
variable. Repeated independent (Bernoulli) trials and Binomial distribution. 
 
Section B2: Applied Mathematics 
Unit I: Numbers, Quantification and Numerical Applications 
A. Modulo Arithmetic 
? Define modulus of an integer 
? Apply arithmetic operations using modular arithmetic rules  
B. Congruence     Modulo 
? Define congruence modulo 
? Apply the definition in various problems 
 
C. Allegation and Mixture 
? Understand the rule of allegation  to produce a mixture at a given price 
? Determine the mean price of a mixture 
? Apply rule of allegation 
 
D. Numerical  Problems 
? Solve real life problems mathematically 
 
 
 
Page 5


 
Mathematics/Applied Mathematics (319) 
 
2 
 
 
 
 
 
 
 
 
 
 
 
SECTION A  
1. Algebra 
(i) Matrices and types of Matrices 
(ii) Equality of Matrices, transpose of a Matrix, 
Symmetric and Skew Symmetric Matrix 
(iii) Algebra of Matrices 
(iv) Determinants 
(v) Inverse of a Matrix 
(vi) Solving of simultaneous equations using Matrix 
Method 
2. Calculus 
(i) Higher order derivatives 
(ii) Tangents and Normals 
 (iii) Increasing and Decreasing Functions 
(iv). Maxima and Minima 
3. Integration and its Applications 
(i) Indefinite integrals of simple functions 
(ii) Evaluation of indefinite integrals 
(iii) Definite Integrals 
(iv). Application of Integration as area under the 
curve 
4. Differential Equations 
(i) Order and degree of differential equations 
(ii) Formulating and solving of differential equations 
with variable separable 
5. Probability Distributions 
(i) Random variables and its probability distribution 
(ii) Expected value of a random variable 
(iii) Variance and Standard Deviation of a random 
variable 
(iv). Binomial Distribution 
6. Linear Programming 
(i) Mathematical formulation of Linear 
Programming Problem 
(ii) Graphical method of solution for problems in two 
variables 
(iii) Feasible and infeasible regions 
(iv). Optimal feasible solution 
 
 
 
 
Note:  
There will be one Question Paper which will contain Two Sections i.e. Section A and Section B [B1 and 
B2].  
Section A will have 15 questions covering both i.e. Mathematics/Applied Mathematics which will be 
compulsory for all candidates 
 
Section B1 will have 35 questions from Mathematics out of which 25 questions need to be attempted. 
Section B2 will have 35 questions purely from Applied Mathematics out of which 25 question will be 
attempted. 
 
Mathematics/Applied Mathematics (319) 
 
3 
 
 
Section B1: Mathematics 
 
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 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). 
 
2. Determinants  
Determinant of a square matrix (up to 3 × 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. Concepts of exponential, logarithmic functions. 
Derivatives of log x
 
and e
x
. Logarithmic differentiation. Derivative of functions expressed in parametric 
forms. Second-order derivatives. R o l l e ’ s and L a g r a n g e ’ s Mean Value Theorems (without proof) 
and their geometric interpretations. 
 
2. Applications of Derivatives  
Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and 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). Tangent and Normal.  
 
 
 
Mathematics/Applied Mathematics (319) 
 
4 
 
3. Integrals  
Integration as inverse process of differentiation. Integration of a variety 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, arcs of circles/parabolas/el- 
lipses (in standard form only), area between the two above said curves (the region should be cleraly 
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 – 
 
dy 
? Py ? Q , 
where P and Q are functions of x or constant 
dx 
 
 
dx 
? Px 
dy 
? Q , 
where P and Q are functions of y or constant 
 
Mathematics/Applied Mathematics (319) 
 
4 
 
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, scalar triple product. 
 
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, 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 constrains). 
 
Unit VI: Probability  
Multiplications theorem on probability. Conditional probability, independent events, total probability, 
B a y e ’ s theorem. Random variable and its probability distribution, mean and variance of haphazard 
variable. Repeated independent (Bernoulli) trials and Binomial distribution. 
 
Section B2: Applied Mathematics 
Unit I: Numbers, Quantification and Numerical Applications 
A. Modulo Arithmetic 
? Define modulus of an integer 
? Apply arithmetic operations using modular arithmetic rules  
B. Congruence     Modulo 
? Define congruence modulo 
? Apply the definition in various problems 
 
C. Allegation and Mixture 
? Understand the rule of allegation  to produce a mixture at a given price 
? Determine the mean price of a mixture 
? Apply rule of allegation 
 
D. Numerical  Problems 
? Solve real life problems mathematically 
 
 
 
 
Mathematics/Applied Mathematics (319) 
 
4 
E. Boats and Streams 
? Distinguish between upstream and downstream 
? Express the problem in the form of an equation 
F. Pipes and Cisterns 
? Determine the time taken by two or more pipes to fill or 
G. Races and Games  
? Compare the performance of two players w.r.t. time, 
? distance taken/ distance covered/ Work done from the given     data 
H. Partnership 
? Differentiate between active partner and sleeping partner 
? Determine the gain or loss to be divided among the partners in the ratio of their investment 
with due 
? consideration of the time volume/ surface area for solid formed using two or more shapes 
I. Numerical Inequalities  
? Describe the basic concepts of numerical inequalities 
? Understand and write numerical inequalities 
 
 
 UNIT II: ALGEBRA 
A. Matrices and types of matrices  
? Define matrix 
? Identify different kinds of matrices 
 
B. Equality of matrices, Transpose of a matrix, Symmetric and Skew symmetric matrix 
? Determine equality of two matrices 
? Write transpose of given matrix 
? Define symmetric and skew symmetric matrix  
 
 
UNIT III: CALCULUS 
 
A. Higher Order Derivatives  
? Determine second and higher order derivatives 
? Understand differentiation of parametric functions and implicit functions Identify dependent 
and independent variables 
 
B. Marginal Cost and Marginal Revenue using derivatives 
? Define marginal cost and marginal revenue 
? Find marginal cost and marginal revenue 
 
C. Maxima and Minima 
? Determine critical points of the function 
? Find the point(s) of local maxima and local minima and corresponding local maximum and 
local minimum values 
? Find the absolute maximum and absolute minimum value of a function 
 
UNIT IV: PROBABILITY DISTRIBUTIONS 
 
A. Probability Distribution 
? Understand the concept of Random Variables and its Probability Distributions 
? Find probability distribution of discrete random variable