Mathematics is considered the mother of all sciences because it provides tools to solve problems in other sciences like biology, chemistry, and physics. Other subjects are based on mathematical concepts like structure, quantity, and change. Calculus is fundamental to modern science, and fields like game theory and operations research use mathematics and have significant applications. A math graduate would be a good fit for the Bangladesh Bank because banking relies heavily on mathematics and data analysis. Those with a background in math are also strong problem solvers able to work with complex models.

1. ভাইভায় গিণত
1. গিণতেক েকন "মাদার অব সাইন" বলা হয়?
Answer: Mathematics is considered as the mother of all sciences because it is a tool which solves problems of
every other science. Other subjects like biology, Chemistry or Physics is based on simple chemical solutions.
If we start with the question, What is Mathematics? Mathematics is the study of structure, quantity and changes.
All the subjects of science like Physics, Chemistry, Astronomy, Biology deals with either structure or quantity or
changes. So it is nearly impossible to understand these subjects without basic knowledge of mathematics. Again
a study in 2003 in Taiwan reveals that, Research on cognitive neuroscience identifies a biologically determined
part in human brain for the domain of quantity . For this reason mathematics becomes an school subject all over
the world.
Calculus is called the foundation of modern science as it is being used in most of the scientific research and
without Calculus scientific research is nearly impossible.
Game theory, a part of Linear programming has immense effect in economics and finance in making decisions.
Operation research is used in many sector for finding best result of problems.
2. Why we should hire you, give five reasons.
Answer: There are many reasons BB should hire as I can add value to the duties in BB. Some of the
valid reasons are as follows:
1. Banking has an extensive use of mathematics and mathematical formulas for which as a maths
graduate I will be the right choice.
2. As a central bank of Bangladesh, Bangladesh Bank has to work with huge data about different
sectors and to have these data sorted out perfectly by looking at numbers all the day and make
the right decision for policy making though research, a math graduate like me will be more
appropriate then others.
3. Mathematics is used throughout the world as an essential tool in many fields, including science,
engineering, medicine, finance, economics etc for solving different types of problems.
4. Those who studies mathematics are keen problem solvers, eager to make sense of even the most
advanced equations.
5. Mathematical theories and formulas like linear programming, Operation research, financial
mathematics, mathematical modeling etc are widely used in making decisions for banks and
large multinational companies for which these subjects are studied in Finance, economics etc. A
basic understanding of Algebra, Calculus, Linear Programming, Operations Research will help
to find the optimal solution to problems that a math graduate has and I will do better in using
these tools of mathematics then anyone else from other subjects.
6. Mathematical Modeling is used to make predictions and math graduates are best at making best
use of the mathematical modeling. For this reason American Banks hire more than 20% of total
math graduates as they very much rely on these predictions which are ought to be accurate.
7. Again “Quantitative Analysis” is an important tool for Central Bank for predicting future events
that may take place in macroeconomic field such as
1. growth rate analysis,
2. nominal changes for changes in volumes and prices,
3. calculating expected export-import and exchange rate therein,
4. Change in domestic market with relevance to International market,
5. Calculating Elasticity that is the measure of the percent change in a variable when a second
variable to which it is related grows or decreases by 1% , elasticity can help in forecasting
when we have a forecast of one variable (e.g. GDP) and a model relating some other
variable to it.
8. Problem solving ability and adaptability is a special quality that a math graduate has and for
different situations in Central Bank, an employee has to formulate and solve different tricky,

2. tenacious and complex mathematical models that requires extensive math skills, intense
precision and accuracy which a well grounded mathematician is capable of providing.
9. As BB controls all the banks and NBFI's in BD, a practical experience of four years of working
in private bank (Pubali Bank Ltd) and govt. owned specialized bank(BKB) will help me to take
necessary decisions in policy making in accordance with my experience.
3. িরেয়ল নামার ও ন্াচারাল নামার িক?
Answer:Real Number: In Mathematics a real number is a value that represents a quantity along a
continuous line called the number line or real line.
Imaginary Number: An Imaginary Number is a number that can not be identified in real line.
Imaginary Numbers are expressed as a sum of two quantity as a+ib where i=Sqrt(-1) and a,b is real no.
Natural Number: the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.
4. েরশনাল নামার ও ইেরশনাল নামার িক?
Answer: Rational Number: The numbers which can be expressed as a ratio of two integers.
Irrational Numbers : The numbers which can't be expressed as a ratio of two integers. Square root of
any prime number is an irrational number.
5. এমন একিট সংখ্া বেলন েযিটেক বগর করেল মাইনাস আেস।
Answer: i
6. আই এর উপর বগর হেল কত হয়? Ans: -1
7. What is cardinal and ordinal number?
Answer:
Cardinal Numbers: Cardinal Number is a number that says quantity or how many of something there
are, such as one, two, three etc.
Ordinal Number: An ordinal number is a number that says the position of something in a list such as
1st
, second, third fourth etc.
Nominal Number: A Nominal Number is a number used only as a name, or to identify something (not
as an actual value or position) Nominal = Name
Example: The number on the back of a player: "8"
a zip code: "91210"
a model number: "380"
8. What is the fundamental theorem of calculus?
9. What is arithmetic series and geometric series?
Answer: Arithmetic Series: Arithmetic Series is the sum of a sequence of numbers in which each term
differs from the preceding one by a constant quantity (e.g. 1, 2, 3, 4, etc.; 9, 7, 5, 3, etc.). The difference
may be positive or negative.
Geometric Series: Arithmetic Series is the sum of a sequence of terms in which ratio of two
consecutive terms is a constant. The ratio may be positive or negative. Ex: 2,4,8,16 etc
10. What is a continuous function.
Answer: Continuous Function: A continuous is a function for which sufficiently small changes in the
input results in sufficiently small changes in the output.
A function continuous at a value of x.
We say that a function f(x) that is defined at x = c is continuous at x = c
if the limit of f(x) as x approaches c is equal to the value of f(x) at x = c.
In symbols, if

3. then f(x) is continuous at x = c.
11. What is a graph?
Answer: A graph is a mathematical diagram which shows the relationship between two or more sets of
numbers or measurements.
A graph is a diagram representing a system of connections or interrelations among two or more things
by a number of distinctive dots, lines, bars etc.
12. Superscript & Subscript েকানটা িকভােব িলখেত হয়?
13. "১৫ এর কম েপেল েফইল আর সমান বা েবিশ েপেল পাশ" এটার জন্ এেকল এ িকভােব
িলখেত হয়? ফরমুলা িলখুন।
14. িবন্াস ও সমােবশ িক? এেদর মেধ্ পাথরক্ িক?
Answer: the various ways in which objects from a set may be selected, generally without replacement,
to form subsets. This selection of subsets is called a permutation when the order of selection is a
factor, a combination when order is not a factor.
For combination, we just choose or select the subjects but for permutation we have to arrange the
subjects in a defined way with some conditions.
Permutation: Permutation refers to the rearranging a set of objects or values in an ordered manner.
More precisely, permutation refers to arrangement of a set of values into a certain order.
Combination is a collection of things in which order doesn't matter.
If the Order does not matters its a combination.
If the order matters, its a permutation.
Permutation is a ordered combination.
Permutation => Position Matters
কতগেলা বস েথেক কেয়কিট বা সবকয়িট িনেয় পিতবার যতগিল দল গঠন করা যায় তােদর পেত্কিটেক এক একিট
সমােবশ বেল। দল িবধায় সমােবেশ অনভুরক বসগেলার কম উেপকা করা হয়।
উদাঃ যিদ বলা হয় ১৫ জন িকেকটার েথেক জাতীয় দেলর জন্ ১১ জন েবেচ েনওয়া হয় তাহেল এই েবেচ েনওয়াটা হেব
সমােবশ/combination। িকন যিদ তােদরেক ব্ািটং কম আকাের সাজােনা হয় তেব তা হেব একিট িবন্াস/permutation.
Ex: মেন কির a,b,c িতনিট িভন অকর েদয়া আেছ। এেদর দই দইিটেক এেকবাের িনেয় সাজােল আমরা পাই
ab, ba, ac, ca, bc, cb
এেদর পেত্কিট িতনিট িভন অকেরর পিতবাের দইিট কের িনেয় পাপ এক একিট িবন্াস। অতএব িতনিট িভন বসর
পিতবাের দইিট কের িনেয় িবন্াস সংখ্া ৬ িকন ২িট কের িনেয় অকরগেলার সাজােনার কম উেপকা করেল দল পাওয়া
যায় ৩িট। অতএব িতনিট িবিভন িজিনেসর পিতবার দইিট কের িনেয় পাপ সমােবেশর সংখ্া হয় ৩।
npr = n!/(n-r)!, nCr= n!/{r!*(n-r)!}
সবগেলা িভন নেয় এরপ বসর িবন্াসঃ x=n!/(p!*q!*r!)
** n সংখ্ক িবিভন বস েথেক পিতবাের েযেকান সংখ্ক বস িনেয় গিঠত েমাট সমােবশ সংখ্া = (2^n)-1
যিদ বনু ২ জন থােক তাহেল দাওয়াত সংখ্া হেব (2^2)-1=4-1=3
পথেম ২ জনেকই েদয়। এরপর একজন কের দাওয়াত িদেল েমাট দাওয়াত সংখ্া ২+১=৩ হেব
15. ৫জন েলাক পরসেরর সােথ হাত েমলােল কতগেলা হ্ানেশক হেব?

4. Answer: ৫!/২! = ৬০
16. িবিভন িবষেয়র জনক
িবষয় জনক জাতীয়তা
সংখ্াতত িপথােগারাস গীক
জ্ািমিত ইউিকড় গীক
ক্ালকু লাস িনউটন English Mathematician, astronomer
Gottfried Wilhelm Leibniz German Mathematician and philosopher
ম্ািটক আথরার েকইেল ইংিলশ গিণতিবদ
Trigonometry Hippar Chus Greek Astronomer
Logarithm John Napier Scottish Mathematician
Financial
Mathematics
Louis Bachelier French Mathematician
Dynamics/Kinetics Galilio
Statics Archimidies
17. What is Zero?
Answer: Zero is a number in real line that represents the absence of any quantity i.e empty or nothing.
This is the only integer ( and in-fact the only real number which is neither negative nor positive). The
concept of ZERO and its operation was originally developed in India and Indian Mathematician
Brahmaguta (Indian Astronomer and mathematician) first defined it in 628 in his Book “Brahmasputha
Siddhanta (The Opening of the Universe)” whereas the Indian Mathematician and astronomer
Aryabhatta (আযরভট) had been credited for invention of ZERO as a place holder in his number system.
18. What is a fraction?
Answer: Fraction: Any Fraction represents a part of a whole thing or generally any number of equal
things. A fraction describes how many parts of a certain size there are for example one-fifth, 2-3rd
etc.
A fraction is in the form (a/b) where a & b are integer numbers. The upper integer a is called the
numerator and lower integer b is called denominator.
Fractions are of two types: Proper Fraction & Improper Fraction.
Proper Fraction: A fraction is called proper fraction when the absolute value of the fraction is less
than 1 I.e when the denominator is greater than the numerator. Ex: 5/13, 3/19 etc
Improper Fraction: A fraction is called improper fraction when the absolute value of the fraction is
greater than 1 I.e when the denominator is less than the numerator. Ex: 13/5, 19/3 etc
19. What is Co-prime?
Answer: In number theory, two integers a and b are said to be relatively prime, mutually prime or co-
prime (also written co-prime) if the only positive integer (factor) that divides both of them is 1 I,e their
greatest common divisor is 1. Ex: 14 & 15 are co-prime as their only divisor is 1.
20. What is a prime number?
Answer: The numbers greater than 1 which has no divisor except 1 and the number itself is called a

5. prime number. There are 25 prime numbers in 1-100 as follows: 4 4 2 2 3 2 2 3 2 1
Range List of prime Numbers No. of prime Numbers
1-10 2,3,5,7 4
15
11-20 11,13,17,19 4
21-30 23,29 2
31-40 31,37 2
41-50 41,43,47 3
51-60 53,59 2
10
61-70 61,67 2
71-80 71,73,79 3
81-90 83,89 2
91-100 97 1
Total 25
21. What is a composite number (কৃ িতম সংখ্া)?
Answer: The numbers which has factors other than 1 and the number itself is called a composite
number. 4,6,2344 etc
22. What is Able Prize?
Answer: Abel Prize is the Norwegian Prize awarded annually by the king of Norway to one or more
outstanding Mathematicians. It was name after Norwegian Mathematician Niels Henrick Abel and
directly modeled after the Nobel Prize. It comes with a monetary award of 6 million Norwegian
Kroner. In August 2001, the Norwegian government announced that the prize would be awarded
beginning in 2002, the two-hundredth anniversary of Abel's birth by the Norwegian Academy of
Science and Letters with funding directly from Norwegian Government. Atle Selberg received an
honorary Abel Prize in 2002, but the first actual Abel Prize was awarded in 2003. The first Abel Prize
winner in 2003 is Jean Pierre Serre of France and Robert Langlands of USA is the last winner of Abel
Prize-2018 for his visionary program connecting “representation theory to number theory”.
23. What is a set?
Answer: A set is a well-defined collection of distinct objects. The objects that make up a set (also
known as the set's elements or members) can be anything: numbers, people, letters of the alphabet,
other sets, and so on. All the elements of a set must have a property or character in common. German
Mathematician George Cantor is the founder of Set. Sets are conventionally denoted by Capital Letters.
Elements or member of the set: The objects that make up a set are called elements of the set.
Sets are expressed in two forms: 1. Tabular Form.
2. Set Building Method.
Tabular Form: Listing all the elements of a set, separated by commas and enclosed within braces or
curly brackets{}.
Ex: A={2,4,5}, B={Red, green, Blue}

6. Set Building Method: Writing in symbolic form the common characteristics shared by all the elements
of the set.
A={x:2x+1=3}
B={x:x>2} are the example of set builder method.
∅–empty set (also {} are common)
N – natural numbers
Z – integers (from Zahl, German for number).
Set of Integers Z = {…, -3, -2, -1, 0, +1, +2, +3, …} = {0, ±1, ±2, ±3, …}
{“Z” stands for the first letter of the German word for integer: Zahlen.}
Q – rational numbers (from quotient)
R – real numbers
C – complex numbers
SUBSET: If A & B are two sets, A is called a subset of B, written A ⊆ B, if, and only if, any element
of A is also an element of B.
Symbolically: A ⊆ B ⇔ if x A then x B
When A ⊆ B, then B is called a superset of A.
When A is not subset of B, then there exist at least one x A such that x ∉ B.
Every set is a subset of itself.
EQUAL SETS: Two sets A and B are equal if, and only if, every element of A is in B and every
element of B is in A and is denoted A = B.
Symbolically: A = B iff A ⊆ B and B ⊆ A
EXAMPLE: Let A={1, 2, 3, 6},B=the set of positive divisors of 6,C={3, 1, 6, 2},D={1, 2, 2, 3, 6, 6, 6}
Then A, B, C, and D are all equal sets.
NULL SET: A set which contains no element is called a null set, or an empty set or a void set. It is
denoted by the Greek letter ∅ (phi) or { }.
EXAMPLE: A = {x | x is a person taller than 10 feet} = ∅ ( Because there does not exist any human
being which is taller then 10 feet )
B = {x | x2 = 4, x is odd} = ∅ (Because we know that there does not exist any odd whose square is 4)
∅ is regarded as a subset of every set.
UNIVERSAL SET: The set of all elements under consideration is called the Universal Set. The
Universal Set is usually denoted by U.
Complement Set: In set theory, the complement of a set A refers to elements not in A. When
all sets under consideration are considered to be subsets of a given set U, the absolute complement of
A is the set of elements in U but not in A.
VENN DIAGRAM: A Venn diagram is a graphical representation of relation between finite collection
sets by regions in the plane. The Universal Set is represented by the interior of a rectangle, and the
other sets are represented by disks lying within the rectangle.

7. Power sets:The power set of a set S is the set of all subsets of S. The power set contains S itself and the
empty set because these are both subsets of S.
For example, the power set of the set {1, 2, 3} is {{1, 2, 3}, {1, 2}, {1, 3}, {2, 3}, {1}, {2}, {3}, ∅}.
The power set of a set S is usually written as P(S).
The power set of a finite set with n elements has 2^n elements. For example, the set {1, 2, 3} contains
three elements, and the power set shown above contains 2^3 = 8 elements.
Set theory: It is a branch of mathematics that deals with the properties of well-defined collections of
objects, which may or may not be of a mathematical nature, such as numbers or functions.
Cartesian Product: If A and B are two non-empty sets, then their Cartesian product A × B is the set
of all ordered pair of elements from A and B.
A × B = {(x, y) : x a A, y a B}
Suppose, if A and B are two non-empty sets, then the Cartesian product of two sets, A and set B is the
set of all ordered pairs (a, b) such that a a A and ba B which is denoted as A × B.
For Example: If A = {7, 8} and B = {2, 4, 6}, then
A × B = {(7, 2); (7, 4); (7, 6); (8, 2); (8, 4); (8, 6)}
24. Describe the Morgan's Law.
Answer: For sets, De Morgan's Laws are simply observations about the relation between sets and their
complements. De Morgan has two laws for sets.
Law -1: The complement of the intersection of sets A and b is equal to the union of A complement and
B complement i.e
Law – 2: The complement of the union of sets Aand B is equal to the intersection of complement of A
and Complement of B i.e
25. What is CO-ordinate system?
Answer: In geometry, a co-ordinate system is a system which use two or more numbers to uniquely
determine the position of a point or other geometric element on a manifold such as Euclidean Space.
26. What is the distance between the points P(x1,y1) & Q(x2,y2)?
Answer:1. Distance between P & Q that is PQ is:
2. Distance between the point P(x,y) is:
3. Equation of the x-axis is y = 0
4. Equation of the y-axis is x = 0 5.
5. Equation of a straight line parallel to x-axis and passing through the point P(a, b) is y = b.
6. Equation of a straight line parallel to y-axis and passing through the point P(a, b) is x = a.
7. Slope of a straight line= m = tan θ = y2 − y1 x2 − x1 where (θ) is the inclination of the straight
line and (x1, y1) and (x2, y2) are any two points on the line.
8. Equation of a line in the slope-intercept form is y = mx + b.
9. Equation of a straight line in point-slope form is (y − y1) = m(x − x1).
10. Equation of a straight line in two-points form is

8. 11. Equation of a straight line in double-intercept form is:
12. For a straight line whose equation is ax + by + c = 0
13. The straight lines with slopes (m) and (m' ) are mutually perpendicular if m*m' = −1.
14. The straight line with slopes (m) and (m0 ) are parallel to each other if m = m' .
27. Can you tell me the Subjects you read in your Course?
Answer:
Year Major Course Course Code
First Year
01. Fundamental of Mathematics 101
02. Calculus I 102
03. Analytic and Vector Geometry 103
04. Linear Algebra I 104
05. FORTRAN Programming 105
06. Mathematica I 150
Second Year 01. Real Analysis I 201
02. Calculus II 202
03. Ordinary Differential Equations I 203
04. Linear Algebra II 204
05. Numerical Analysis I 205
06. Mathematica II 250
Third Year
01. Real Analysis II 301
02. Complex Analysis 302
03. Ordinary Differential Equations II 303
04. Abstract Algebra 304
05. Numerical Analysis II 305
06. Mathematical Methods 306
07. Mechanics 307
08. Linear Programming 308
09. Fundamentals of Topology 309
10. Mathematica III 350
Fourth Year 01. Introduction to Functional Analysis 401

9. 02. Tensor Analysis 402
03. Partial Differential Equations 403
05. Differential Geometry 404
06. Theory of Numbers 405
07. Hydrodynamics 407
08. Astronomy 410
09. Mathematical Modeling in Biology 413
10. Mathematical Modeling in Finance and
Business Management
414
28. What is a function?
Answer: Relation: If A & B are two sets, then any non-empty subset of the curtesian product set of set
A and set B is called a relation.
Function: A function is a process or a relation that associates each element x of a set X, the domain
of the function, to a single element y of another set Y (possibly the same set), the codomain of the
function. If the function is called f, this relation is denoted y = f (x) the element x is the argument or
input of the function, and y is the value of the function, the output, or the image of x by f.
Domain: The domain of a function is the complete set of possible values of the independent variable.
Codomain or Range: The range of a function is the complete set of all possible resulting values of the
dependent variable (y, usually), after we have substituted the domain.
One One Function: A function for which every element of the range of the function corresponds to
exactly one element of the domain. Ex: f(x)= x^3, x, 1/x etc.
Identity Function: A function is called Identity function if it returns the same value as the value of the
independent variable or If the function relates a elements of a set with the same element of another set
then the function is called Identity Function. Ex: f(x)=x, is an Identity Variable.
Onto Function: In Mathematics a function from the set X to set Y is Onto
Function if for every element y in the set Y there exists at least one element x
in the domain X such that y=f(x).
Linear functions: These are functions of the form: y=mx+ c,
where m and c are constants. A typical use for linear functions is converting
from one quantity or set of units to another. Graphs of these functions are
straight lines. m is the slope and c is the y intercept. If m is positive then the
line rises to the right and if m is negative then the line falls to the right.

10. Quadratic functions: These are functions of the form: y= ax^2+ bx +c,
where a, b and c are constants. Their graphs are called parabolas. This is the
next simplest type of function after the linear function. Falling objects move
along parabolic paths. If a is a positive number then the parabola opens
upward and if a is a negative number then the parabola opens downward.
Power functions: These are functions of the form:
y=axb, where a and b are constants. They get their name from the fact that the
variable x is raised to some power. Many physical laws (e.g. the gravitational
force as a function of distance between two objects, or the bending of a beam
as a function of the load on it) are in the form of power functions. We will
assume that a = 1 and look at several cases for b:
The power b is a positive integer, (Fig-1)
When x = 0 these functions are all zero. When x is big and positive they are
all big and positive. When x is big and negative then the ones with even
powers are big and positive while the ones with odd powers are big and
negative.
The power b is a negative integer. (Fig-2)
When x = 0 these functions suffer a division by zero and therefore are all
infinite. When x is big and positive they are small and positive. When x is big
and negative then the ones with even powers are small and positive while the
ones with odd powers are small and negative.
The power b is a fraction between 0 and 1.
When x = 0 these functions are all zero. The curves are vertical at the origin
and as x increases they increase but curve toward the x axis.
Polynomial functions. These are functions of the form:
y = an ·xn + an −1 · x n−1+ … +a2·x2+a1·x+a0,
where a^n, a^(n−1), …,a2,a1,a0are constants. Only whole number powers of x are allowed. The highest
power of x that occurs is called the degree of the polynomial.
Exponential functions. These are functions of the form: y = a bx,
where x is in an exponent and a and b are constants.If the base b is greater than 1 then the result is
exponential growth. If the base b is less than 1 then the result is exponential decay.
Logarithmic functions. There are many equivalent ways to define logarithmic functions. We will define
them to be of the form: y = a ln (x) + b,
where x is in the natural logarithm and a and b are constants. They are only defined for positive x. For
small x they are negative and for large x they are positive but stay small. Logarithmic functions
accurately describe the response of the human ear to sounds of varying loudness and the response of the
human eye to light of varying brightness.

11. Inverse Function: Suppose A and B are nonempty sets and f : A → B is a function. A function g : B →
A is called an inverse function for f if it satisfies the following condition: For every a a A and b a B, f(a)
= b if and only if g(b) = a.
29. What is Imaginary Number?
Answer: complex number: A complex number is a number that
can be expressed in the form a+bi, where a and b are real
numbers, and I is a solution of the equation x^2 = −1. Because no
real number satisfies this equation, I is called an imaginary
number. For the complex number a+bi, a is called the real part,
and b is called the imaginary part.
A complex number can be visually represented as a pair of
numbers (a, b) forming a vector on a diagram called an Argand
diagram, representing the complex plane. "Re" is the real axis,
"Im" is the imaginary axis, and i satisfies i^2= −1.
30. What is Geometry?
Answer: Geometry: the branch of mathematics concerned with the properties and relations of points,
lines, surfaces, solids, and higher dimensional analogues.
Geometry can be divided into two parts:
(1) Plane Geometry: Plane Geometry is about shapes like lines, circles and triangles I.e shapes
that can be drawn on a paper.
(2) Solid Geometry: Solid Geometry is about 3-dimensional objects like cubes, prisms, cylinders
and spheres.
31. What is the perimeter & Area of a Triangle?
Answer: Perimeter: The perimeter is the distance around the edge of a triangle/rectangle/square.
Perimeter is the boundary of a closed plane figure.
Area: Area is the measurement of surface. The extent part of a surface enclose within a boundary.
32. What is Pi and value of Pi?
Answer: Pi is the ratio of the circumference to the diameter of a circle.
Value of Pi is 3.1415926535
33. What is Circumference and Diameter of a circle?
Answer:
Circumference: The distance around a circle on the
other hand is called the circumference (c).
The circumference of a circle is found using this
formula:
C=π⋅d =2π⋅r
Diameter: A line that is drawn straight through the
midpoint of a circle and that has its end points on the
circle border is called the diameter
Half of the diameter, or the distance from the midpoint
to the circle border, is called the radius of the circle (r).

12. 34. What is a line?
Answer: A line a straight path that is endless in both direction with negligible breadth. In modern
geometry a line in the plane is often defined as the set of points whose coordinates satisfy a given linear
equation. General Equation of Line is y=mx+c where m & c are constants and x is the variable.
35. What is an angle?
Answer: In plane geometry, an angle is the figure formed by two rays, called the sides of the angle,
sharing a common endpoint, called the vertex of the angle.
36. What is
Answer: In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a
fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that “the
square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the
other two sides”. The theorem can be written as an equation relating the lengths of the sides a, b and c,
often called the "Pythagorean equation":
where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.
37. When we use Matrix.
Answer: Matrix: Matrix is a collection of numbers or objects which are arranged in a specific way in
vertical columns and horizontal rows and the dimension of the matrix is xXy where x is the number of
rows and y is the number of columns.
Square Matrix: A square matrix is a matrix who has the same number of rows and columns.
Identity Matrix: An identity matrix is a matrix whose nXn element I.e a11, a22, a33 etc are 1 and other
elements are 0 so that multiplication with this matrix with other matrices is the same as original matrix.
Inverse Matrix: If there is a matrix A and another matrix B such that multiplication of A & B is equals
to identity matrix I.e AB=I=BA then B is called the inverse matrix of A and written as A^-1.
Diagonal Matrix: A square matrix is called diagonal matrix if at least one element of principle diagonal
is non zero and all other elements are zero.
Scalar Matrix: A diagonal matrix is called scalar matrix if all its diagonal elements are same.
Triangular Matrix: A square matrix is said to be triangular if all of its elements above the principal
diagonal are zero (lower triangular matrix) or all of its elements below the principal diagonal are
zero (upper triangular matrix). Ec: Upper Diagonal.
Null or Zero Matrix:
A matrix is said to be a null or zero matrix if all of its elements are equal to zero. It is denoted by O.
Transpose of a Matrix:
Suppose A is a given matrix, then the matrix obtained by interchanging its rows into columns is called
the transpose of A. It is denoted by At.
If then Transpose of A is

13. 38. What is reciprocal number?
Answer: Two numbers is reciprocal to each other if their product is Identity I.e 1
39. What is inequality?
Answer:inequality:Inequality tells us about the relative size of two values.
The things that are not equal we term these as Inequalities.
Properties of Inequality:
1. Transitive Property: If a<b , b<c then a<c
2. Reversal Property: If a<b then b>a
3. Law of Trichotomy: The law of Trichotomy says that only one of the following is true:
a>b, or a=b or a<b
40. What is Game theory?
Answer:
Game Theory: The branch of mathematics concerned with the analysis of strategies for dealing with
competitive situations where the outcome of a participant's choice of action depends critically on the
actions of other participants. Game theory has been applied to contexts in war, business, and biology.
Game theory, branch of applied mathematics (Operation Research) that provides tools for analyzing
situations in which parties, called players, make decisions that are interdependent. This
interdependence causes each player to consider the other player’s possible decisions, or strategies, in
formulating his own strategy. A solution to a game describes the optimal decisions of the players, who
may have similar, opposed, or mixed interests, and the outcomes that may result from these decisions.
41. What is exponential function and logarithmic function.
Answer: Exponential Function: For mathematics, exponential is a function of the form f(x)=a^x
where “x” is a variable and “a” is called the base of the function.
Logarithmic Function:
42. What is arithmetic mean, Geometric Mean and Standard deviation.
43. What is a venn diagram?
Answer: Venn Diagram is a diagram that represents all possible mathematical or logical relations
between a finite collection of different sets pictorially as circles or closed curves within an enclosing
rectangle (the universal set), common elements of the sets being represented by intersections of the
circles. These diagrams depict elements as points in the plane, and sets as regions inside closed curves.
A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set.
44. What are the three basic principle of Dynamics by Newton?
Answer:
45. International Measurement:
1 Lac 10^5 1,00,000
1 Million 10^6 10,00,000
I crore 10^7 10 Million=10,000,000
USA System 1 Billion 10^9=100*10^7 100 Crore=1000 Million=a thousand million
1 Trillion 10^12=1000*10^9 1000 Billion=a Million Million
Now British are using American Method for avoiding controversy.

14. 46. 1 Meter =?
Answer: িবষুব েরখা েথেক উতর েমর পযরন েমাট দূরেতর ১ েকািট ভােগ্র ১ ভাগ হল িমটার।
47. Write the name of Some Great Mathematician of Bangladesh?
Answer: Name of some great mathematicians of Bangladesh are as follows:
Name Details
Jamal Nazrul Islam
AFM Mujibu Rahman
48. Write the name of Some Great Mathematician of Asia?
Answer:
Name Details
Radhanath Sikder Sikder was an Indian Mathematician best known for calculating
Height of Mount Everest.
Srinivasa Ramanujan Was an Indian Mathematician who lived during the British Rule
in India. He made substantial contributions to the mathematical
analysis, number theory, infinite series and continued fractions.
Brahmagupta
49. Write the name of Some Great Mathematician of World?
Name Work
Isaac Newton
Archimedes
Carl F Gauss (Friedrich) "Prince of Mathematics," Gauss may be the greatest theorem
prover ever. Several important theorems and lemmas bear his
name; his proof of Euclid's Fundamental Theorem of Arithmetic
(Unique Prime Factorization) is considered the first rigorous
proof; he extended this Theorem to the Gaussian (complex)
integers; and he was first to produce a rigorous proof of the
Fundamental Theorem of Algebra (that an n-th degree
polynomial has n complex roots); his Theorema Egregium
("Remarkable Theorem") that a surface's essential curvature
derived from its 2-D geometry laid the foundation of differential
geometry.Gauss built the theory of complex numbers into its
modern form
Leonhard Euler
Bernhard Riemann
Joseph-Louis Lagrange
Gottfried W. Leibniz

15. John von Neumann
Niels Abel
Leonardo `Fibonacci' Fibonacci Number
Pythagoras of Samos
Muhammed al-Khowârizmi
Jacob Bernoulli
Panini of Shalatula
50. What is Fibonacci Number?
Answer: Fibonacci Series is a series of numbers in which each number ( Fibonacci number ) is the sum
of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, 13, 21, 34 etc.
51. What is Conic? General Equation of Ellipse, Parabola & Hyperbola?
Answer: In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the
surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the
ellipse.
General Equation of Ellipse is :
General Equation of Parabola is :
General Equation of Hyperbola is :
Tangent: In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the
straight line that "just touches" the curve at that point.
52. What is a Circle?
Answer: A circle is a simple closed shape. It is the set of all points in a plane that are at a fixed
distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so
that its distance from a given point is constant. The distance between any of the points and the centre is
called the radius.
53. িদঘাত সমীকরণ িক?
উতরঃ েয সমীকরেণর চলেকর সেবরাচ ঘাত ২ তােক িদঘাত সমীকরণ বা Quadratic Equation বেল।

16. 54. Geometric Series
55. Summation
Answer:
Sum of n terms where a=1st
term, d=General
Difference, n=no. of terms
56. সংজা িদন

17. 57. What is secant line, Tangent Line?
Answer:
A secant line, also simply called a secant, is a line passing
through two points of a curve.As the two points are
brought together (or, more precisely, as one is brought
towards the other), the secant line tends to a tangent line.
In Geometry, the tangent line to a plane curve at a given
point is the straight line that “Just Touches” the curve at
that point.

18. 58. What is slope?
Answer: Slope is the measure of a quantity which gives the inclination of a curve or line with respect to
another curve or line. It describes both the direction and the steepness of the line.Slope is often denoted
by the letter m; there is no clear answer to the question why the letter m is used for slope, but it might
be from the "m for multiple" in the equation of a straight line "y = mx + b" or "y = mx + c". The
steepness, incline, or grade of a line is measured by the absolute value of the slope. The direction of a
line is either increasing, decreasing, horizontal or vertical.
59. What is Limit, derivative and differentiation?
Answer: Limit: Limit is the study of how a function behaves near a specific point.
Derivative: The derivative of a function of real variable measures the sensitivity of the function to the
change of a quantity ( a function or dependent variable) which is determined by another quantity ( the
independent variable).
Slope of the tangent line to a function at a point is equal to derivative of the function at that point.
Differentiation of a function in Mathematics is the process of finding the derivative or rate of change
of the function.

19. 60. What are the application of Differentiation?
Answer: Some of the applications of Differentiations is as follows:
(1) Finding Tangent and normals
(2) For solving tricky equation that can not be solved by algebra and need to solve using newtons
formula
(3) In finding related rate where two variables are changing over time and there is a relationship
between them.
(4) In solving maximum and minimum problems.
61. Define Rolle's Theorem and Mean Value Theorem?
Answer: Rolle's Theorem:
Let f be a continuous function on a closed interval [a,b] and differentiable on the open interval (a,b).
If f(a) = f(b) , then there exists at least one point c in (a,b) such that
f'(c)=0
Mean Value Theorem: If f' exists on a<x<b, then there must be at least one point c where
f'(c)={f(b)-f(a)}/(b-a)
62. What is Integration?
Answer: There are two answers:
1) Integrating a function can give the area between the graph of that function and the x axis. This
type of integration is called definite integration.
2) Integration can be thought of as the inverse of differentiation. In the same way that subtraction
can be thought of as undoing addition, integration undoes differentiation. This type of
integration is called indefinite integration.

20. 63. What are the application of Integration?
Answer:
(1) To find the area under a curve.
(2) To find the are between 2 curves.
(3) To find the volume of a solid of revolution.
(4) To find the average value of function.
(5) To find distance from velocity and velocity from acceleration.
(6) In finding the centroid of an area, moment if inertia, electric charges,
average value of a curve etc.
64. What is Linear Programming?
Answer: A Linear programming problem may be defined as the problem of maximizing or minimizing
a linear function of a number of variables subject to linear constraints.
There are various methods used to solve LPP such as:
(a) Graphical Solution.
(b) Simplex Method.
(c) Artificial Variable Method.
(d) Big-M Method
(e) Dual Simplex Method
Simplex method is the widely used method for solving Linear Programming Problems.
Feasible Solution: Feasible solution is an n-tuple (x1, x2, x3, ….,xn) of real numbers which satisfies
the constraints of Linear Programming Problem.
Optimal Solution: Any Feasible solution which optimizes the objective function of a LPP.

21. Application of Linear Programming: Linear Programming has a wide range of application in normal
and business life. Some of these applications are as follows:
(a)Business Allocation: Most business resource allocation problems require the design maker to take
into account various types of Constraints such as
1. Capital,
2. Labour, &
3. Behavioral restrictions.
Linear Programming Techniques can be used to provide relatively simple and realistic solutions to such
problems.
(b) A wide variety of Production, Finance, Marketing and distribution problems are being formulated
and solved using LP.
(c)Portfolio Optimization: Risk can be minimized by using Linear Programming in allocation of
assets and taking investment decisions. Many investment companies are now using optimization and
linear programming extensively to decide how to allocate assets. The increase in the speed of
computers has enabled the solution of far larger problems, taking some of the guesswork out of the
allocation of assets.
( d ) Food and Agriculture: Farmers apply linear programming techniques to their work. By
determining what crops they should grow, the quantity of it and how to use it efficiently, farmers can
increase their revenue.
In nutrition, linear programming provides a powerful tool to aid in planning for dietary needs. In order
to provide healthy, low-cost food baskets for needy families, nutritionists can use linear programming.
Constraints may include dietary guidelines, nutrient guidance, cultural acceptability or some
combination thereof. Mathematical modeling provides assistance to calculate the foods needed to
provide nutrition at low cost, in order to prevent noncommunicable disease. Unprocessed food data and
prices are needed for such calculations, all while respecting the cultural aspects of the food types. The
objective function is the total cost of the food basket. Linear programming also allows time variations
for the frequency of making such food baskets.
(d) Applications in Engineering: Engineers also use linear programming to help solve design and
manufacturing problems. For example, in airfoil meshes, engineers seek aerodynamic shape
optimization. This allows for the reduction of the drag coefficient of the airfoil. Constraints may
include lift coefficient, relative maximum thickness, nose radius and trailing edge angle. Shape
optimization seeks to make a shock-free airfoil with a feasible shape. Linear programming therefore
provides engineers with an essential tool in shape optimization.
(e) Transportation Optimization: Transportation systems rely upon linear programming for cost and
time efficiency. Bus and train routes must factor in scheduling, travel time and passengers. Airlines use
linear programming to optimize their profits according to different seat prices and customer demand.
Airlines also use linear programming for pilot scheduling and routes. Optimization via linear
programming increases airlines' efficiency and decreases expenses.
(f) Efficient Manufacturing: Manufacturing requires transforming raw materials into products that
maximize company revenue. Each step of the manufacturing process must work efficiently to reach
that goal. For example, raw materials must past through various machines for set amounts of time in an
assembly line. To maximize profit, a company can use a linear expression of how much raw material to

22. use. Constraints include the time spent on each machine. Any machines creating bottlenecks must be
addressed. The amount of products made may be affected, in order to maximize profit based on the raw
materials and the time needed.
(g) Energy Industry: Modern energy grid systems incorporate not only traditional electrical systems,
but also renewables such as wind and solar photovoltaics. In order to optimize the electric load
requirements, generators, transmission and distribution lines, and storage must be taken into account.
At the same time, costs must remain sustainable for profits. Linear programming provides a method to
optimize the electric power system design. It allows for matching the electric load in the shortest total
distance between generation of the electricity and its demand over time. Linear programming can be
used to optimize load-matching or to optimize cost, providing a valuable tool to the energy industry.
(h)Telecommunications:
(1) Call routing: Many telephone calls from New York to Los Angeles, from Houston to Atlanta,
etc. How should these calls be routed through the telephone network?
(2) Network design: If we need to build extra capacity, which links should we concentrate on?
Should we build new switching stations?
(3) Internet traffic: For example, there was a great deal of construction of new networks for
carrying internet traffic a few years ago.
65. What is Operations Research? What are the scope and techniques of OR?
Answer: Operations Research: Operations Research is the scientific approach to execute decision
making, which consists of
1. The art of mathematical modeling of complex situations
2. The science of the development of solution techniques used to solve these models.
3. The ability to effectively communicate the results to the decision maker.
Operations research is the organized application of modern science, mathematics and computer
techniques to complex military, government, business or industrial problems arising in the direction
and management of large systems of men, materials, money and machines.
66. What is the equation of ellipse? Answer: x2/ a2+ y2/ b2= 1
67. Draw the graph of Sinx
68. সরলেরখার সমীকরণ িলেখন? Answer: X/a+Y/b=1 এেক েদখান।
69. একিট িলিনয়ার ইকু েয়শন িলেখন?
70. েভকর িক?
71. Answer:
72. এই রেম আেছ এমন একটা নাল েসেটর উদাহরণ িদন।
73. গিণেত ম্ািপং িক?
74. ৫ এর ৭৫%
75. Mean, Median & Mode িক? মেন করন একজন ব্িক নদী পাড় হেব। িকন নদীর পািন িবেশষণ
কের েদখা েগেছ এর েডউ েকাথাও েবিশ আবার েকাথাও কম। এই অবসায় িমন, িমিডয়ান ও
মুড এর মেধ্ েকানিটর পেয়াগ বুিদমােনর কাজ হেব।
76. ৫৫ এর ৫% কত হেব?
77. একজন েদাকানদার েকােনা একটা পেণ্র দাম ১০% বািড়েয় িলেখ রাখল। এরপর আবার ১০%
ছাড় িদল। তাহেল েস পকৃ তপেক কত পােসরন বাড়াল বা কমােলা।