Syllabus: Applied Mathematics for Class 11 | Applied Mathematics for Class 11 - Commerce PDF Download

 Page 1


Grade XI (2023-24) 
 
   Number of Paper:   1                                                        
   Total number of Periods:  240 (35 Minutes Each) 
   Time:    3 Hours                                                                           
   Max Marks:    80 
 
 
No.                Units No. of 
Periods 
Marks 
I Numbers, Quantification and 
Numerical Applications 
25 09 
II Algebra 45 15 
III Mathematical Reasoning 15 06 
IV Calculus 35 10 
V Probability 25 08 
VI Descriptive Statistics 35 12 
VII Basics of Financial Mathematics 45 15 
VIII Coordinate Geometry 15 05 
       Total 240 80 
                Internal Assessment                      20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Page 2


Grade XI (2023-24) 
 
   Number of Paper:   1                                                        
   Total number of Periods:  240 (35 Minutes Each) 
   Time:    3 Hours                                                                           
   Max Marks:    80 
 
 
No.                Units No. of 
Periods 
Marks 
I Numbers, Quantification and 
Numerical Applications 
25 09 
II Algebra 45 15 
III Mathematical Reasoning 15 06 
IV Calculus 35 10 
V Probability 25 08 
VI Descriptive Statistics 35 12 
VII Basics of Financial Mathematics 45 15 
VIII Coordinate Geometry 15 05 
       Total 240 80 
                Internal Assessment                      20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CLASS- XI 
Sl. 
No. 
Contents Learning Outcomes:  
Students will be able to 
Notes / Explanation 
UNIT – 1    NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS 
Numbers & Quantification 
1.2 Binary Numbers ? Express decimal numbers 
in binary system  
? Express binary numbers 
in decimal system 
? Definition of number system 
(decimal and binary)  
? Conversion from decimal to 
binary system and vice - versa 
1.4 Indices, 
Logarithm and 
Antilogarithm 
? Relate  indices and 
logarithm /antilogarithm 
? Find  logarithm and  
antilogarithms of given 
number 
? Applications of rules of indices 
? Introduction of logarithm and 
antilogarithm 
? Common and Natural logarithm 
1.5 Laws and 
properties of 
logarithms 
? Enlist the laws and 
properties of logarithms 
? Apply laws of logarithm 
? Fundamental laws of logarithm 
1.6 Simple 
applications of 
logarithm and 
antilogarithm 
? Use logarithm in different 
applications 
? Express the problem in the form 
of an equation and apply 
logarithm/ antilogarithm 
Numerical Applications 
1.7 Averages ? Determine average for a 
given data 
? Definition and meaning 
? Problems on average, weighted 
average 
1.8 Clock ? Evaluate the angular 
value of a minute 
? Calculate the angle 
formed between two 
hands of clock at given 
time 
? Calculate the time for 
which hands of clock 
meet 
? Number of rotations of minute 
hand / hour hand of a clock in a 
day 
? Number of times minute hand and 
hour hand coincides in a day 
1.9 Calendar ? Determine Odd days in a 
month/ year/ century 
? Decode the day for the 
given date 
? Definition of odd days 
? Odd days in a year/ century. 
? Day corresponding to a given 
date 
1.10 Time, Work and 
Distance 
? Establish the relationship 
between work and time 
? Compare the work done 
by the individual / group 
w.r.t. time 
? Calculate the time taken/ 
distance covered/ Work 
done from the given data 
? Basic concept of time and work 
? Problems on time taken / distance 
covered / work done 
1.11 Mensuration ? Solve problems based on 
surface area and volume 
of 2D and 3D shapes 
? Calculate the volume/ 
surface area for solid 
formed using two or more 
shapes 
 
? Comparison between 2D and 3D 
shapes 
? Combination of solids 
? Transforming one solid shape to 
another 
Page 3


Grade XI (2023-24) 
 
   Number of Paper:   1                                                        
   Total number of Periods:  240 (35 Minutes Each) 
   Time:    3 Hours                                                                           
   Max Marks:    80 
 
 
No.                Units No. of 
Periods 
Marks 
I Numbers, Quantification and 
Numerical Applications 
25 09 
II Algebra 45 15 
III Mathematical Reasoning 15 06 
IV Calculus 35 10 
V Probability 25 08 
VI Descriptive Statistics 35 12 
VII Basics of Financial Mathematics 45 15 
VIII Coordinate Geometry 15 05 
       Total 240 80 
                Internal Assessment                      20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CLASS- XI 
Sl. 
No. 
Contents Learning Outcomes:  
Students will be able to 
Notes / Explanation 
UNIT – 1    NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS 
Numbers & Quantification 
1.2 Binary Numbers ? Express decimal numbers 
in binary system  
? Express binary numbers 
in decimal system 
? Definition of number system 
(decimal and binary)  
? Conversion from decimal to 
binary system and vice - versa 
1.4 Indices, 
Logarithm and 
Antilogarithm 
? Relate  indices and 
logarithm /antilogarithm 
? Find  logarithm and  
antilogarithms of given 
number 
? Applications of rules of indices 
? Introduction of logarithm and 
antilogarithm 
? Common and Natural logarithm 
1.5 Laws and 
properties of 
logarithms 
? Enlist the laws and 
properties of logarithms 
? Apply laws of logarithm 
? Fundamental laws of logarithm 
1.6 Simple 
applications of 
logarithm and 
antilogarithm 
? Use logarithm in different 
applications 
? Express the problem in the form 
of an equation and apply 
logarithm/ antilogarithm 
Numerical Applications 
1.7 Averages ? Determine average for a 
given data 
? Definition and meaning 
? Problems on average, weighted 
average 
1.8 Clock ? Evaluate the angular 
value of a minute 
? Calculate the angle 
formed between two 
hands of clock at given 
time 
? Calculate the time for 
which hands of clock 
meet 
? Number of rotations of minute 
hand / hour hand of a clock in a 
day 
? Number of times minute hand and 
hour hand coincides in a day 
1.9 Calendar ? Determine Odd days in a 
month/ year/ century 
? Decode the day for the 
given date 
? Definition of odd days 
? Odd days in a year/ century. 
? Day corresponding to a given 
date 
1.10 Time, Work and 
Distance 
? Establish the relationship 
between work and time 
? Compare the work done 
by the individual / group 
w.r.t. time 
? Calculate the time taken/ 
distance covered/ Work 
done from the given data 
? Basic concept of time and work 
? Problems on time taken / distance 
covered / work done 
1.11 Mensuration ? Solve problems based on 
surface area and volume 
of 2D and 3D shapes 
? Calculate the volume/ 
surface area for solid 
formed using two or more 
shapes 
 
? Comparison between 2D and 3D 
shapes 
? Combination of solids 
? Transforming one solid shape to 
another 
1.12 Seating 
arrangement 
? Create suitable seating 
plan/ draft as per given 
conditions 
(Linear/circular) 
? Locate the position of a 
person  in a seating 
arrangement 
? Linear and circular seating 
arrangement 
? Position of a person  in a seating 
arrangement 
UNIT – 2    ALGEBRA 
Sets 
2.1  
 
Introduction to 
sets – definition 
? Define set as well-defined 
collection of objects 
? Definition of a Set 
? Examples and Non-examples of 
Set 
2.2 Representation 
of sets 
? Represent a set in Roster 
form and Set builder form 
? Write elements of a set in Set 
Builder form and Roster Form 
? Convert a set  given in Roster 
form into Set builder form and 
vice-versa 
2.3 Types of sets 
and their 
notations 
? Identify different types of 
sets on the basis of 
number of elements in the 
set 
? Differentiate between 
equal set and equivalence 
set 
? Types of Sets: Finite Set, Infinite 
Set, Empty Set, Singleton Set  
2.4 Subsets ? Enlist all subsets of a set 
? Find number of subsets of 
a given set 
? Find number of elements 
of a power set 
? Subset of a given set 
? Familiarity with terms like 
Superset, Improper subset, 
Universal set, Power set 
 
2.5 Intervals ? Express subset of real 
numbers as intervals 
? Open interval, closed interval, 
semi open interval and semi 
closed interval 
2.6 Venn diagrams ? Apply the concept of 
Venn diagram to 
understand the 
relationship between sets 
? Solve problems using 
Venn diagram 
? Venn diagrams as the pictorial 
representation of relationship 
between sets 
? Practical Problems based on 
Venn Diagrams 
2.7 Operations on 
sets 
? Perform operations on 
sets to solve practical 
problems 
? Operations on sets include 
i) Union of sets 
ii) Intersection of sets 
iii)  Difference of sets 
iv) Complement of a set 
v) De Morgan’s Laws 
Relations 
2.8 Ordered pairs 
 
Cartesian 
product of two 
sets 
? Explain the significance of 
specific arrangement of 
elements in a pair 
? Write Cartesian product of 
two sets 
? Find the number of 
? Ordered pair, order of elements in 
an ordered pair  and equality of 
ordered pairs 
? Cartesian product of two non-
empty sets 
Page 4


Grade XI (2023-24) 
 
   Number of Paper:   1                                                        
   Total number of Periods:  240 (35 Minutes Each) 
   Time:    3 Hours                                                                           
   Max Marks:    80 
 
 
No.                Units No. of 
Periods 
Marks 
I Numbers, Quantification and 
Numerical Applications 
25 09 
II Algebra 45 15 
III Mathematical Reasoning 15 06 
IV Calculus 35 10 
V Probability 25 08 
VI Descriptive Statistics 35 12 
VII Basics of Financial Mathematics 45 15 
VIII Coordinate Geometry 15 05 
       Total 240 80 
                Internal Assessment                      20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CLASS- XI 
Sl. 
No. 
Contents Learning Outcomes:  
Students will be able to 
Notes / Explanation 
UNIT – 1    NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS 
Numbers & Quantification 
1.2 Binary Numbers ? Express decimal numbers 
in binary system  
? Express binary numbers 
in decimal system 
? Definition of number system 
(decimal and binary)  
? Conversion from decimal to 
binary system and vice - versa 
1.4 Indices, 
Logarithm and 
Antilogarithm 
? Relate  indices and 
logarithm /antilogarithm 
? Find  logarithm and  
antilogarithms of given 
number 
? Applications of rules of indices 
? Introduction of logarithm and 
antilogarithm 
? Common and Natural logarithm 
1.5 Laws and 
properties of 
logarithms 
? Enlist the laws and 
properties of logarithms 
? Apply laws of logarithm 
? Fundamental laws of logarithm 
1.6 Simple 
applications of 
logarithm and 
antilogarithm 
? Use logarithm in different 
applications 
? Express the problem in the form 
of an equation and apply 
logarithm/ antilogarithm 
Numerical Applications 
1.7 Averages ? Determine average for a 
given data 
? Definition and meaning 
? Problems on average, weighted 
average 
1.8 Clock ? Evaluate the angular 
value of a minute 
? Calculate the angle 
formed between two 
hands of clock at given 
time 
? Calculate the time for 
which hands of clock 
meet 
? Number of rotations of minute 
hand / hour hand of a clock in a 
day 
? Number of times minute hand and 
hour hand coincides in a day 
1.9 Calendar ? Determine Odd days in a 
month/ year/ century 
? Decode the day for the 
given date 
? Definition of odd days 
? Odd days in a year/ century. 
? Day corresponding to a given 
date 
1.10 Time, Work and 
Distance 
? Establish the relationship 
between work and time 
? Compare the work done 
by the individual / group 
w.r.t. time 
? Calculate the time taken/ 
distance covered/ Work 
done from the given data 
? Basic concept of time and work 
? Problems on time taken / distance 
covered / work done 
1.11 Mensuration ? Solve problems based on 
surface area and volume 
of 2D and 3D shapes 
? Calculate the volume/ 
surface area for solid 
formed using two or more 
shapes 
 
? Comparison between 2D and 3D 
shapes 
? Combination of solids 
? Transforming one solid shape to 
another 
1.12 Seating 
arrangement 
? Create suitable seating 
plan/ draft as per given 
conditions 
(Linear/circular) 
? Locate the position of a 
person  in a seating 
arrangement 
? Linear and circular seating 
arrangement 
? Position of a person  in a seating 
arrangement 
UNIT – 2    ALGEBRA 
Sets 
2.1  
 
Introduction to 
sets – definition 
? Define set as well-defined 
collection of objects 
? Definition of a Set 
? Examples and Non-examples of 
Set 
2.2 Representation 
of sets 
? Represent a set in Roster 
form and Set builder form 
? Write elements of a set in Set 
Builder form and Roster Form 
? Convert a set  given in Roster 
form into Set builder form and 
vice-versa 
2.3 Types of sets 
and their 
notations 
? Identify different types of 
sets on the basis of 
number of elements in the 
set 
? Differentiate between 
equal set and equivalence 
set 
? Types of Sets: Finite Set, Infinite 
Set, Empty Set, Singleton Set  
2.4 Subsets ? Enlist all subsets of a set 
? Find number of subsets of 
a given set 
? Find number of elements 
of a power set 
? Subset of a given set 
? Familiarity with terms like 
Superset, Improper subset, 
Universal set, Power set 
 
2.5 Intervals ? Express subset of real 
numbers as intervals 
? Open interval, closed interval, 
semi open interval and semi 
closed interval 
2.6 Venn diagrams ? Apply the concept of 
Venn diagram to 
understand the 
relationship between sets 
? Solve problems using 
Venn diagram 
? Venn diagrams as the pictorial 
representation of relationship 
between sets 
? Practical Problems based on 
Venn Diagrams 
2.7 Operations on 
sets 
? Perform operations on 
sets to solve practical 
problems 
? Operations on sets include 
i) Union of sets 
ii) Intersection of sets 
iii)  Difference of sets 
iv) Complement of a set 
v) De Morgan’s Laws 
Relations 
2.8 Ordered pairs 
 
Cartesian 
product of two 
sets 
? Explain the significance of 
specific arrangement of 
elements in a pair 
? Write Cartesian product of 
two sets 
? Find the number of 
? Ordered pair, order of elements in 
an ordered pair  and equality of 
ordered pairs 
? Cartesian product of two non-
empty sets 
elements in a Cartesian 
product of two sets 
2.9 Relations ? Express relation as a 
subset of Cartesian 
product 
? Find domain and range of 
a relation 
? Definition of Relation, examples 
pertaining to relations in the real 
number system 
 
Sequences and Series 
2.11 Sequence and 
Series 
? Differentiate between 
sequence and series 
? Sequence:?? 1
, ?? 2
, ?? 3,
… , ?? ?? 
? Series:   ?? 1
+ ?? 2
+ ?? 3
+ ? + ?? ?? 
2.12 Arithmetic 
Progression 
? Identify Arithmetic 
Progression (AP) 
? Establish the formulae of 
finding ?? ?? h
term and sum     
of n terms  
? Solve application 
problems based on AP 
? Find arithmetic mean 
(AM) of two positive 
numbers 
? General term of AP: 
        ?? 
?? = ?? + (?? - 1)?? 
? Sum of n terms of AP : 
   S n = 
?? 2
[2?? + (?? - 1)?? ] 
 
    AM of ?? ?????? ?? = 
?? +?? 2
 
2.13 
 
Geometric 
Progression 
 
? Identify Geometric 
Progression (GP)  
? Derive the ?? ?? h
term and 
sum of n terms of a given 
GP 
? Solve problems based on 
applications of GP  
? Find geometric mean 
(GM) of two positive 
numbers 
? Solve problems based on 
relation between AM and 
GM 
? General term of GP: 
                 ?? ?? = ?? ?? ?? -1
 
? Sum of n terms of a GP: 
                S n = 
?? (?? ?? -1)
?? -1
 
? Sum of infinite term of GP = 
?? 1-??   , where  -1 < ?? < 1 
? Geometric mean of a and b = v???? 
? For two positive numbers a and b, 
 AM =GM  i.e.,    
?? +?? 2
  = v???? 
2.14 Applications of 
AP and GP 
? Apply appropriate 
formulas of AP and GP to 
solve application 
problems 
Applications based on 
? Economy Stimulation 
? The Virus spread etc.   
 
Permutations and Combinations 
2.15 Factorial ? Define factorial of a 
number 
? Calculate factorial of a 
number 
? Definition of factorial: 
               n! = n(n-1)(n-2)…3.2.1 
   Usage of factorial in counting 
principles 
2.16 Fundamental 
Principle of 
Counting 
? Appreciate how to count 
without counting 
? Fundamental Principle of Addition 
? Fundamental Principle of  
Multiplication 
Page 5


Grade XI (2023-24) 
 
   Number of Paper:   1                                                        
   Total number of Periods:  240 (35 Minutes Each) 
   Time:    3 Hours                                                                           
   Max Marks:    80 
 
 
No.                Units No. of 
Periods 
Marks 
I Numbers, Quantification and 
Numerical Applications 
25 09 
II Algebra 45 15 
III Mathematical Reasoning 15 06 
IV Calculus 35 10 
V Probability 25 08 
VI Descriptive Statistics 35 12 
VII Basics of Financial Mathematics 45 15 
VIII Coordinate Geometry 15 05 
       Total 240 80 
                Internal Assessment                      20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CLASS- XI 
Sl. 
No. 
Contents Learning Outcomes:  
Students will be able to 
Notes / Explanation 
UNIT – 1    NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS 
Numbers & Quantification 
1.2 Binary Numbers ? Express decimal numbers 
in binary system  
? Express binary numbers 
in decimal system 
? Definition of number system 
(decimal and binary)  
? Conversion from decimal to 
binary system and vice - versa 
1.4 Indices, 
Logarithm and 
Antilogarithm 
? Relate  indices and 
logarithm /antilogarithm 
? Find  logarithm and  
antilogarithms of given 
number 
? Applications of rules of indices 
? Introduction of logarithm and 
antilogarithm 
? Common and Natural logarithm 
1.5 Laws and 
properties of 
logarithms 
? Enlist the laws and 
properties of logarithms 
? Apply laws of logarithm 
? Fundamental laws of logarithm 
1.6 Simple 
applications of 
logarithm and 
antilogarithm 
? Use logarithm in different 
applications 
? Express the problem in the form 
of an equation and apply 
logarithm/ antilogarithm 
Numerical Applications 
1.7 Averages ? Determine average for a 
given data 
? Definition and meaning 
? Problems on average, weighted 
average 
1.8 Clock ? Evaluate the angular 
value of a minute 
? Calculate the angle 
formed between two 
hands of clock at given 
time 
? Calculate the time for 
which hands of clock 
meet 
? Number of rotations of minute 
hand / hour hand of a clock in a 
day 
? Number of times minute hand and 
hour hand coincides in a day 
1.9 Calendar ? Determine Odd days in a 
month/ year/ century 
? Decode the day for the 
given date 
? Definition of odd days 
? Odd days in a year/ century. 
? Day corresponding to a given 
date 
1.10 Time, Work and 
Distance 
? Establish the relationship 
between work and time 
? Compare the work done 
by the individual / group 
w.r.t. time 
? Calculate the time taken/ 
distance covered/ Work 
done from the given data 
? Basic concept of time and work 
? Problems on time taken / distance 
covered / work done 
1.11 Mensuration ? Solve problems based on 
surface area and volume 
of 2D and 3D shapes 
? Calculate the volume/ 
surface area for solid 
formed using two or more 
shapes 
 
? Comparison between 2D and 3D 
shapes 
? Combination of solids 
? Transforming one solid shape to 
another 
1.12 Seating 
arrangement 
? Create suitable seating 
plan/ draft as per given 
conditions 
(Linear/circular) 
? Locate the position of a 
person  in a seating 
arrangement 
? Linear and circular seating 
arrangement 
? Position of a person  in a seating 
arrangement 
UNIT – 2    ALGEBRA 
Sets 
2.1  
 
Introduction to 
sets – definition 
? Define set as well-defined 
collection of objects 
? Definition of a Set 
? Examples and Non-examples of 
Set 
2.2 Representation 
of sets 
? Represent a set in Roster 
form and Set builder form 
? Write elements of a set in Set 
Builder form and Roster Form 
? Convert a set  given in Roster 
form into Set builder form and 
vice-versa 
2.3 Types of sets 
and their 
notations 
? Identify different types of 
sets on the basis of 
number of elements in the 
set 
? Differentiate between 
equal set and equivalence 
set 
? Types of Sets: Finite Set, Infinite 
Set, Empty Set, Singleton Set  
2.4 Subsets ? Enlist all subsets of a set 
? Find number of subsets of 
a given set 
? Find number of elements 
of a power set 
? Subset of a given set 
? Familiarity with terms like 
Superset, Improper subset, 
Universal set, Power set 
 
2.5 Intervals ? Express subset of real 
numbers as intervals 
? Open interval, closed interval, 
semi open interval and semi 
closed interval 
2.6 Venn diagrams ? Apply the concept of 
Venn diagram to 
understand the 
relationship between sets 
? Solve problems using 
Venn diagram 
? Venn diagrams as the pictorial 
representation of relationship 
between sets 
? Practical Problems based on 
Venn Diagrams 
2.7 Operations on 
sets 
? Perform operations on 
sets to solve practical 
problems 
? Operations on sets include 
i) Union of sets 
ii) Intersection of sets 
iii)  Difference of sets 
iv) Complement of a set 
v) De Morgan’s Laws 
Relations 
2.8 Ordered pairs 
 
Cartesian 
product of two 
sets 
? Explain the significance of 
specific arrangement of 
elements in a pair 
? Write Cartesian product of 
two sets 
? Find the number of 
? Ordered pair, order of elements in 
an ordered pair  and equality of 
ordered pairs 
? Cartesian product of two non-
empty sets 
elements in a Cartesian 
product of two sets 
2.9 Relations ? Express relation as a 
subset of Cartesian 
product 
? Find domain and range of 
a relation 
? Definition of Relation, examples 
pertaining to relations in the real 
number system 
 
Sequences and Series 
2.11 Sequence and 
Series 
? Differentiate between 
sequence and series 
? Sequence:?? 1
, ?? 2
, ?? 3,
… , ?? ?? 
? Series:   ?? 1
+ ?? 2
+ ?? 3
+ ? + ?? ?? 
2.12 Arithmetic 
Progression 
? Identify Arithmetic 
Progression (AP) 
? Establish the formulae of 
finding ?? ?? h
term and sum     
of n terms  
? Solve application 
problems based on AP 
? Find arithmetic mean 
(AM) of two positive 
numbers 
? General term of AP: 
        ?? 
?? = ?? + (?? - 1)?? 
? Sum of n terms of AP : 
   S n = 
?? 2
[2?? + (?? - 1)?? ] 
 
    AM of ?? ?????? ?? = 
?? +?? 2
 
2.13 
 
Geometric 
Progression 
 
? Identify Geometric 
Progression (GP)  
? Derive the ?? ?? h
term and 
sum of n terms of a given 
GP 
? Solve problems based on 
applications of GP  
? Find geometric mean 
(GM) of two positive 
numbers 
? Solve problems based on 
relation between AM and 
GM 
? General term of GP: 
                 ?? ?? = ?? ?? ?? -1
 
? Sum of n terms of a GP: 
                S n = 
?? (?? ?? -1)
?? -1
 
? Sum of infinite term of GP = 
?? 1-??   , where  -1 < ?? < 1 
? Geometric mean of a and b = v???? 
? For two positive numbers a and b, 
 AM =GM  i.e.,    
?? +?? 2
  = v???? 
2.14 Applications of 
AP and GP 
? Apply appropriate 
formulas of AP and GP to 
solve application 
problems 
Applications based on 
? Economy Stimulation 
? The Virus spread etc.   
 
Permutations and Combinations 
2.15 Factorial ? Define factorial of a 
number 
? Calculate factorial of a 
number 
? Definition of factorial: 
               n! = n(n-1)(n-2)…3.2.1 
   Usage of factorial in counting 
principles 
2.16 Fundamental 
Principle of 
Counting 
? Appreciate how to count 
without counting 
? Fundamental Principle of Addition 
? Fundamental Principle of  
Multiplication 
2.17 Permutations ? Define permutation 
 
?  Apply the concept of 
permutation to solve 
simple problems 
 
? Permutation as arrangement of 
objects in a definite order taken 
some or all at a time 
? Theorems under different 
conditions resulting in 
n
Pr=
?? !
(?? -?? )!
  or    
?? ??   or 
   
?? !
?? 1
!?? 2
!…?? ?? !
 arrangements 
 
2.20 Combinations ? Define combination 
? Differentiate between 
permutation and 
combination  
? Apply the formula of 
combination to solve the 
related problems 
-The number of combinations of 
n different objects  taken r at a 
time is given by 
n
Cr= 
?? !
?? !.(?? -?? )!
 
Some results on combinations: 
? 
n
C 0 = 1 = 
n
Cn 
? 
n
C a = 
n
Cb ? a=b or a+ b=n 
? 
n
Cr = 
n
Cn-r 
? 
n
Cr + 
n
Cr-1 = 
n+1
Cr 
UNIT -3    MATHEMATICAL REASONING 
3.2 Logical 
reasoning 
? Solve logical problems 
involving odd man out, 
syllogism, blood relation 
and coding decoding 
? Odd man out 
? Syllogism 
? Blood relations 
? Coding Decoding 
UNIT – 4   CALCULUS 
4.1 Functions  
? Identify dependent and 
independent variables  
? Define a function using 
dependent and 
independent variable  
 
? Dependent variable and 
independent variable 
? Function as a rule or law that 
defines a relationship between 
one variable (the independent 
variable) and another variable 
(the dependent variable) 
4.2 Domain and 
Range of a 
function 
? Define domain, range 
and co-domain of a given 
function 
 
 
? Domain as a set of all values of 
independent variable  
? Co-domain as a set of all values 
of dependent variable 
? Range of a function as set of all 
possible resulting values of 
dependent variable 
4.3 Types of 
functions 
? Define various types of 
functions 
? Identify domain, co-
domain and range of the 
function 
 
? Following types of functions with 
definitions and characteristics  
      Constant function, Identity 
function, Polynomial function, 
Rational function, Composite 
function, Logarithm function, 
Exponential function, Modulus 
function, Greatest integer 
function, Signum function, 
Algebraic function 
4.4 Graphical 
representation 
of functions 
? Representation of 
function graphically 
? Graph of some polynomial 
functions, Logarithm function, 
Exponential Function, Modulus 
function, Greatest integer