🔥Basic To Pro।।class 9 higher math chapter 1 2026।।সেট ও ফাংশন Class 9। Raj Sir। ১ ক্লাসেই বস!!!

Introduction to Higher Mathematics: Sets and Functions

Overview of the Class

• The instructor greets the audience and expresses hope that everyone is doing well. They introduce the topic of higher mathematics, specifically focusing on sets and functions, promising a comprehensive understanding of the basics.

• Emphasis is placed on developing a strong foundation in basic concepts, indicating that this class will be foundational for future learning. Students are encouraged to pay close attention during the session.

Class Structure and Expectations

• The instructor notes that mastering sets and functions requires multiple classes, suggesting at least two or three sessions to cover all necessary material thoroughly. Students are advised to follow instructions closely for effective learning progression from basic to advanced levels.

• For those who have previously studied general mathematics, this class will be relatively easier; however, they should expect some challenges as the content may be more complex than what they have encountered before.

Detailed Explanation of Concepts

Teaching Methodology

• The instructor plans to explain each example in detail, ensuring students understand every line presented in their materials. This approach aims to clarify all mathematical concepts covered in the chapter on Cartesian products.

• Future classes will build upon today's lesson by addressing board questions and important school questions related to sets and functions comprehensively, aiming for complete mastery of the subject matter.

Importance of Online Course Enrollment

• Students are encouraged to enroll in an online paid academic course currently offered at a discounted price (3000 Taka) for a full year’s access, which includes live classes, recorded sessions, practice sheets by chapter, monthly exams, and additional features being added regularly. This investment is framed as essential for thorough preparation in mathematics subjects including ICT and science disciplines.

Understanding Sets

Definition of Sets

• A set is defined as a well-defined collection of objects from either the real world or conceptual thought processes; it can include tangible items or abstract ideas like numbers or symbols. The importance of distinguishing between these two realms (real vs conceptual) is highlighted here.

Examples Illustrating Sets

• An example involving a chicken farm illustrates how specific collections (like types of chickens) form a set; capital letters are used when denoting sets formally (e.g., "R" for Raj's farm). This visual representation helps solidify understanding among students about what constitutes a set based on defined criteria within their context.

Elements Within Sets

Characteristics of Set Elements

• Each element within a set must be clearly defined; elements can include various types such as white chickens or black chickens mentioned earlier—these examples serve as practical illustrations reinforcing theoretical definitions discussed previously.

Notation Used in Set Theory

• It’s emphasized that elements within sets are enclosed within curly brackets while using small letters for individual elements signifies their membership within larger groups represented by capital letters—this notation system aids clarity when discussing mathematical relationships involving sets.

This structured approach ensures students grasp both fundamental principles surrounding sets/functions while also preparing them adequately through detailed explanations paired with relevant examples throughout their learning journey.

Understanding Set Theory and Its Applications

Introduction to Sets

• The speaker introduces the concept of sets, emphasizing that they can be represented in two ways: list method and set-builder method.

• In the list method, elements are enclosed within curly braces and separated by commas. This is a straightforward way to represent multiple elements.

Set-Builder Method

• The set-builder method allows for defining sets based on specific conditions or properties. For example, "x belongs to N" indicates that x is an element of natural numbers.

• The speaker explains how to express conditions for elements in a set, such as specifying ranges (e.g., x > 10 and x < 15).

Characteristics of Elements

• Elements can be defined using various symbols; for instance, "x ∈ N" means x is a member of the natural numbers.

• The distinction between listing elements explicitly versus defining them through conditions is highlighted as crucial in understanding set theory.

Practical Example with Numbers

• A practical example involves explaining a given set S with specific values. The speaker discusses how to interpret these values mathematically.

• The discussion transitions into perfect squares, where it’s explained that perfect squares are numbers obtained by squaring integers (e.g., 1² = 1, 2² = 4).

Perfect Squares Defined

• Perfect squares are defined as products of integers multiplied by themselves. Examples include:

• 2 times 2 = 4

• 3 times 3 = 9

• 4 times 4 = 16

Analyzing Set S

• The speaker lists several perfect square numbers up to a certain limit (100), reinforcing their definition and significance in mathematics.

• It’s emphasized that all listed numbers belong to the category of perfect squares.

Formulating Set S

• A clear formulation of set S is presented: it consists of all perfect square numbers less than or equal to 100.

• Conditions for membership in this set are discussed—specifically focusing on being less than or equal to a specified number.

Conclusion on Set Definition

• The final definition clarifies that set S includes all perfect square numbers not exceeding 100, establishing its boundaries clearly.

• Ultimately, the speaker concludes that this collection can indeed be classified as a valid mathematical set due to its well-defined criteria.

This structured overview captures key concepts from the transcript while providing timestamps for easy reference back to specific parts of the discussion.

Set Formation and Universal Sets

Understanding Set Formation

• The discussion begins with the formation of a set, denoted as S, where x is defined such that x is not greater than 100 and represents perfect square numbers.

• The speaker emphasizes that x must be a perfect square number less than or equal to 100, indicating the constraints on the values of x.

Defining Universal Sets

• A universal set is described as a superset containing all relevant sets in discussion. It serves as a reference point for other sets.

• An example is provided: if the universal set U contains values 1, 2, 3, 4, 5, 6, then subsets A = 2, 4 and B = 1, 3 can be derived from it.

Relationship Between Subsets and Universal Sets

• The relationship between subsets (like A and B) and the universal set (U) is clarified; A and B are considered subsets because their elements exist within U.

• If another subset C includes an element not found in U (e.g., zero), then C cannot be classified as a subset of U.

Real Numbers: Definitions and Classifications

Characteristics of Real Numbers

• Real numbers are introduced as encompassing all rational (whole numbers and fractions) and irrational numbers.

• The speaker explains that real numbers include every conceivable number type—fractions, decimals, positive integers, negative integers—essentially everything except imaginary numbers.

Rational vs. Irrational Numbers

• Rational numbers are defined as those expressible in the form p/q where both p and q are integers. Examples include simple fractions like 1/2.

• In contrast, irrational numbers cannot be expressed in this fraction form. Examples given include non-repeating decimals like √2 or π.

Distinguishing Between Number Types

• The distinction between rationality is further illustrated by discussing decimal representations; some decimals can convert into fractions while others cannot.

• For instance, √2 approximates to an infinite decimal value (approximately 1.42), confirming its classification as an irrational number.

Positive and Negative Real Numbers

Positive Real Numbers

• Positive real numbers are defined as any real number greater than zero. This includes whole numbers like one or two but also extends to fractional values above zero.

Negative Real Numbers

• Conversely, negative real numbers encompass all values less than zero. Examples include -1 or -√2 which clearly fall below zero on the number line.

Summary of Whole Number Sets

• Finally, whole number sets are discussed; they consist of all positive integers including zero along with their negative counterparts forming complete integer sets.

Understanding the Concept of Whole Numbers and Subsets

Definition of Whole Numbers

• The term "whole numbers" refers to all positive integers including zero, which are indivisible (not fractional).

• Whole numbers include zero, positive integers like 1, 2, 3, etc., but do not include fractions or decimals such as 0.5 or 0.6.

• Positive whole numbers are defined as natural numbers excluding zero; they consist solely of positive integers.

Characteristics of Natural Numbers

• Natural numbers are a subset of whole numbers that exclude zero and consist only of positive integers.

• A key property is that the value 'p' in a set cannot equal zero when discussing rational numbers; this is often tested in exams.

Rational vs. Irrational Numbers

• Rational numbers can be expressed as fractions or decimals, while irrational numbers cannot be represented in such forms.

• An example includes square roots that cannot be simplified into fractions; these values remain irrational.

Understanding Subsets

• A subset consists of elements derived from a larger set; every combination formed from the original set's elements qualifies as a subset.

• For instance, if we have three elements (A, B, C), subsets can be formed by selecting any combination of these elements.

Identifying Subset Relationships

• The number of subsets can be calculated using the formula 2^n, where n is the number of elements in the original set.

• The empty set is considered a subset of every set; it holds significance in mathematical definitions and proofs.

Understanding Positive Integers and Subsets

Definition of Positive Integers

• The discussion begins with the definition of positive integers, which are all whole numbers greater than zero. Examples include 1, 2, 3, and so on, indicating an infinite set without a defined endpoint.

Relationship Between Sets A and B

• The speaker introduces two sets: A and B. Set A contains elements that are part of the positive integers while discussing whether elements from B also belong to set X (the universal set).

Subset Relationships

• It is established that both sets A and B can be subsets of set X. However, it is noted that beta (another element or subset) does not belong to set A.

Describing Subsets of Set X

• The task involves describing three subsets derived from the universal set X, which consists of positive integers. The speaker emphasizes understanding what constitutes a subset in relation to the universal set.

Identifying Values in Subsets

• Three specific subsets are proposed:

• A: Positive integers,

• B: Negative integers,

• C: Even numbers.

• Each subset's values are checked against the definitions provided for clarity.

Exploring Negative Numbers and Even Numbers

Understanding Negative Integers

• Negative integers are defined as all whole numbers less than zero excluding zero itself. Examples include -1, -2, etc., highlighting their distinction from positive integers.

Characteristics of Even Numbers

• Even numbers are discussed as those divisible by two within the context of both negative and positive ranges extending infinitely.

Validating Membership in Set X

• The speaker checks if values from sets A (positive), B (negative), and C (even numbers) exist within the universal set X. This validation confirms their membership based on previously established definitions.

Subset Analysis Between Sets

Establishing Non-overlapping Subsets

• Two distinct subsets are identified:

• A: Contains even numbers,

• B: Contains odd numbers.

• It is emphasized that neither subset overlaps with each other but both remain subsets of the larger universal set X.

Listing Elements in Each Subset

• An example is given where even numbers extend infinitely while odd numbers do similarly; this illustrates how these subsets can be represented through listing methods up to infinity.

Confirming Element Inclusion Across Sets

• There’s a focus on confirming whether elements from one subset appear in another. While some elements may overlap with the universal set X, they do not overlap between sets A and B directly.

Conclusion on Subset Relationships

Final Thoughts on Set Relationships

• The discussion concludes by reiterating that while sets A and B contain unique elements relative to each other, they still qualify as subsets under the broader umbrella of set X.

Understanding Subsets and Empty Sets

Definition of Subsets

• A subset B is not a subset of A, meaning that the elements of AB are not contained in BO. This leads to the conclusion that A is a subset of X and B is also a subset of X.

Concept of Empty Set

• An empty set, or null set, contains no elements. It can be represented as or using parentheses (∅). The concept is illustrated with examples involving real numbers.

Real Numbers and Their Properties

• Real numbers include all rational and irrational numbers. Understanding this helps in determining conditions for subsets based on squaring values.

Conditions for Squaring Values

• When testing if the square of a number (e.g., 2) is less than zero, it fails since 4 is not less than zero. Negative numbers like -1 also do not satisfy this condition when squared.

Exploring Decimal Values

• Testing decimal values such as 0.5 shows that their squares (0.25) still do not meet the condition of being less than zero, reinforcing that no real number satisfies this criterion leading to an empty set.

Examples Leading to Empty Sets

World Cup Winners Example

• The example discusses countries from Africa winning the World Cup up until 2014, concluding it results in an empty set since no African country has won.

Equality of Sets

• Two sets are equal if they contain exactly the same elements. For instance, if Set A = 1, 2, 3 and Set B = 2, 3, they are not equal because they differ by one element.

Proper Subsets Explained

Definition and Examples

• Proper subsets contain fewer elements than the original set. For example, if Set A = 1, 2, 3, then 1 or 2 would be proper subsets but 1, 2 would not be considered proper since it does not have fewer elements than A.

Identifying Proper Subsets

• To determine proper subsets from a given set involves ensuring at least one element differs from the original set's count; otherwise it's just a subset.

Calculating Number of Proper Subsets

Formula for Finding Proper Subsets

• The formula for calculating proper subsets involves using 2^n - 1, where n represents the total number of elements in the original set minus one to exclude itself from counting as a proper subset.

Clarification on Definitions

• Distinguishing between subsets and proper subsets emphasizes that every element must be accounted for correctly when defining relationships between sets.

Understanding Set Operations

Basic Concepts of Set Differences

• The speaker emphasizes the importance of understanding what constitutes a "true subset" and how it relates to set operations. A true subset must meet specific criteria.

• Clarification is provided on distinguishing between subsets and proper subsets, highlighting that not all subsets are necessarily proper.

• An example is given where the difference between two sets (A and B) is illustrated, showing how elements from the first set remain after removing those in the second set.

Performing Set Subtraction

• The process of determining the difference between two sets is explained, using an example where elements are systematically removed from one set based on another.

• The speaker warns against common mistakes when performing these operations, particularly regarding which elements remain after subtraction.

Understanding Universal Sets and Complements

• Introduction to universal sets as a foundational concept for understanding complements; a universal set contains all possible elements under consideration.

• The complement of a set A is defined as the universal set minus A. This relationship is crucial for solving problems involving complements.

Practical Application of Complements

• To find the complement, one must subtract the values in set A from those in the universal set. This operation illustrates how to derive meaningful results from basic principles.

• The significance of understanding complements in various contexts, especially for multiple-choice questions (MCQs), is emphasized.

Course Offerings and Educational Opportunities

• Information about an educational offer for science students highlights a discounted course price aimed at providing comprehensive coverage across subjects including math and ICT.

• Details about additional subjects included in the course package are shared, emphasizing its value for students looking to enhance their learning experience.

Course Overview and Features

Course Pricing and Structure

• The course is available for a one-time payment of 8000 Taka, which has been reduced to 2200 Taka for arts students. This fee covers the entire year.

• Subjects included in the course are Bengali, English, Mathematics, ICT, BGS (Bangladesh and Global Studies), General Science, and more. Monthly payments are not required; it's a single upfront payment.

Course Features

• The course offers various features such as type-based MCQ questions, recorded classes, chapter-wise practice sheets, and monthly exams for students of the month. Additional features will also be introduced soon.

Mathematical Concepts Explained

Universal Set Definition

• A universal set (U) is defined as the set of all whole numbers including negative integers (e.g., -3, -2, -1). It encompasses all integers without any restrictions on limits or conditions.

Complement of a Set

• The complement of a set refers to elements that belong to the universal set but not to the specified subset. For example, if U includes all integers from negative infinity to positive infinity minus certain values like -1 or -2 would yield their complements in relation to U.

Power Set Explanation

• A power set consists of all subsets formed from a given set's elements. To find it for a set with three elements (e.g., A,B,C), one must list every possible combination including empty sets and full sets. This process illustrates how subsets combine into larger sets through brackets indicating grouping.

Practical Application in Set Theory

Listing Sets Using Conditions

• When tasked with listing subsets based on specific conditions from a universal set (e.g., 1, 2, 3,...7), one must adhere strictly to provided criteria while ensuring clarity in representation through list format or condition-based expressions like "x belongs to U."

Conditional Elements in Sets

• An example condition might state that x must be greater than five within the context of the universal set; thus only values satisfying this condition should be included when forming subsets or answering related queries about element inclusion based on defined parameters.

Mathematical Problem Solving and Logical Reasoning

Exploring Equations and Inequalities

• The speaker discusses the process of solving equations, emphasizing that certain values lead to false statements. For example, when x = 10 , it is deemed incorrect.

• The discussion continues with testing various values for x . When x = 15 or x = 30 , these also yield false results, indicating a systematic approach to finding valid solutions.

• The speaker highlights the importance of understanding conditions in mathematical problems. They mention that students can suggest values up to 11 based on given conditions.

• Transitioning to the next problem, the speaker outlines a condition involving an equation where adding five to x must be less than twelve. This sets up a framework for further calculations.

• A methodical approach is taken as they substitute different values into the equation, checking if they satisfy the inequality conditions laid out earlier.

Validating Solutions through Testing

• The speaker emphasizes continuous testing of values until reaching a contradiction. For instance, substituting x = 6 leads to evaluating whether certain sums exceed specified limits.

• Further exploration reveals that some proposed solutions do not meet established criteria (e.g., being greater than six but less than seventeen).

• The conversation shifts towards identifying valid sets of numbers derived from previous calculations, confirming their correctness through logical reasoning.

• An error is noted regarding inequalities; specifically, how certain expressions fail to meet required conditions when evaluated against set parameters.

Finalizing Results and Conclusions

• As conclusions are drawn about potential solutions for x , clarity emerges around which numbers fit within defined boundaries (greater than six and less than seventeen).

• The speaker reiterates that while some numbers may seem valid at first glance, they ultimately do not satisfy all necessary conditions upon deeper inspection.

• A final review confirms acceptable ranges for possible answers while dismissing those that contradict established rules or lead to inconsistencies in logic.

• Ultimately, the session concludes with a summary of correct answers identified throughout the problem-solving process—highlighting both successful strategies and common pitfalls encountered along the way.

Understanding Mathematical Concepts and Set Theory

Exploring the Universal Set and Its Elements

• The discussion begins with determining values for x in relation to numbers 25, 36, and 37, establishing that x must be less than or equal to 36.

• The speaker emphasizes the importance of listing elements systematically as part of mathematical problem-solving, specifically focusing on universal sets.

• Positive integers are defined as starting from one and going up to a maximum of twenty, which is crucial for understanding the constraints on x .

• The speaker clarifies that positive integers exclude zero and should be listed from one up to twenty based on given conditions.

• Multiples of two are discussed, indicating that all multiples must remain within the universal set's boundaries.

Working with Multiples

• The conversation shifts to finding multiples of five; examples include 5, 10, 15, and so forth until reaching a limit.

• Next steps involve calculating multiples of ten similarly by listing them out while adhering to previously established limits.

• A task is introduced where students need to identify subsets based on provided information about set C in relation to set B.

Analyzing Subsets

• The speaker prompts an examination of whether certain values belong to specific subsets (C being a subset of B).

• It’s confirmed that some values (10 and 20) exist in both sets C and B, validating C as a subset of B.

• However, it is noted that not all elements from B can be found in C (e.g., missing value '15'), leading to conclusions about subset relationships.

Power Sets Calculation

• A new topic arises regarding power sets; the number of elements determines how many subsets can be formed (2^n rule).

• With five elements identified (A, B, C, D), calculations show there will be 2^5 = 32 possible subsets.

Constructing Subsets Methodically

• The process for writing down combinations systematically is explained; starting with individual elements before moving onto pairs and larger groups.

• Emphasis is placed on practicing these combinations repeatedly for mastery over identifying different types of subsets effectively.

Understanding Set Operations and Subsets

Introduction to Set Operations

• The discussion begins with the process of selecting elements from sets A, B, C, D, and E. The speaker emphasizes the importance of systematically choosing elements for clarity.

• The speaker reiterates the selection process, indicating that they will take elements from set A multiple times to form combinations with other sets.

• There is a focus on completing tasks related to sets B and D. The speaker mentions taking elements from these sets in a structured manner.

Working with Multiple Sets

• The conversation shifts towards combining different sets (B and D), highlighting how to approach this task methodically.

• The speaker confirms that they have successfully counted 32 elements across various selections made from the sets discussed earlier.

Power Sets and Unions

• An example is introduced where the power set of set A needs to be determined. This involves calculating all possible subsets of A.

• After determining the power set for both A and B, the next step is to find their union. This union must include all unique elements from both power sets.

Understanding Subsets

• The concept of subsets is clarified; if all elements of one set are contained within another, it qualifies as a subset.

• The speaker explains how to derive values for each set's power set while ensuring that empty sets are included in calculations.

Final Steps in Set Analysis

• As they finalize their calculations, emphasis is placed on ensuring that every element has been accounted for correctly during unions and intersections.

• They discuss verifying whether certain conditions hold true regarding subsets derived from previous operations involving unions.

Conclusion on Set Relationships

• Ultimately, it’s concluded that certain relationships between power sets can be established based on their contents being present or absent in respective unions.

• The session wraps up by addressing potential misconceptions about subset relationships among different powersets discussed throughout the analysis.

Understanding Set Operations

Intersection of Sets

• The discussion begins with the identification of sets A and B, focusing on calculating the probability of their intersection. The speaker emphasizes the need to clarify definitions before proceeding.

• The speaker outlines how to derive the power set for both A and B, indicating that it includes elements 1, 2, and an empty set. This step is crucial for understanding intersections.

• An explanation follows about what constitutes an intersection: common elements between two sets. The speaker illustrates this by identifying which elements are present in both sets.

• Further clarification is provided regarding the values derived from the intersection operation, reinforcing that only shared elements will be included in the result.

• The speaker concludes this section by stating that P(A cap B) = P(A cap B') , highlighting a key relationship between probabilities of intersections.

Solving Problems with Set Operations

• Transitioning into problem-solving, the speaker indicates that determining P(A) involves similar steps as previously discussed—calculating based on given values (1, 2).

• Next, they introduce union operations between sets A and B. They explain how to calculate this using all unique elements from both sets.

• The process continues with a detailed breakdown of combining all unique elements from both sets while ensuring no duplicates are counted in unions.

• As they finalize calculations for P(A cup B) , they emphasize checking if any element appears more than once across combined results.

Complement of a Set

• Moving forward, the concept of complements is introduced. The speaker explains how to visualize complements using universal sets and subsets effectively through diagrams.

• They illustrate how to find areas not covered by a specific set within a universal context—highlighting practical applications in set theory.

• Emphasis is placed on understanding that finding a complement involves subtracting known areas (elements in set S from universal U).

Union Sets Explained

• Finally, union operations are defined clearly: combining all distinct elements from two or more sets into one comprehensive set without repetition.

• An example is provided to solidify understanding; it demonstrates how union encompasses every element across specified sets while maintaining clarity on overlaps.

Understanding Set Operations

Union of Sets

• The example illustrates the union of two sets A and B, where values from both sets are combined. Each element is taken once, regardless of how many times it appears.

• The union operation allows for the representation of set A ∪ B, indicating that all elements from both sets are included in the result.

• It is emphasized that the values in set B must also be present in the union with set A, reinforcing the concept of combining elements.

Intersection of Sets

• The intersection operation identifies common elements between two sets. For instance, if set A contains 1, 2, 3 and set B contains 3, then their intersection will yield 3.

• To find the intersection (A ∩ B), one must look for shared elements; here, '3' is a common value between both sets.

• The notation "A ∩ B" signifies that only those elements found in both sets will be included in the resulting set.

Complement of Sets

• The complement refers to all elements not contained within a specific set but present in a universal set. This can be expressed as U - A or U - B.

• When calculating complements, it's crucial to identify which universal set is being referenced and subtract accordingly to find remaining values.

Example Problem Analysis

• An example problem involving prime numbers and odd numbers illustrates how to determine unions and intersections effectively using defined parameters.

• In discussing positive integers versus negative integers, it’s noted that if no common elements exist after an intersection operation, it results in an empty or null set.

Conclusion on Set Theory Concepts

• Understanding these operations—union, intersection, and complement—is fundamental for working with sets in mathematics. They provide essential tools for analyzing relationships between different groups of numbers or objects.

Understanding Real Numbers and Set Operations

Introduction to Real Numbers

• The discussion begins with the definition of real numbers, which include both rational and irrational numbers. It emphasizes that real numbers are greater than zero and less than two.

Natural Numbers and Their Properties

• Natural numbers are defined as positive integers excluding zero (1, 2, 3, etc.). The value of x must be greater than or equal to zero but less than two.

Conditions for Selecting Values

• The conditions for selecting values of x are reiterated: it must be a real number greater than zero and less than two. Various types of real numbers such as decimal fractions are mentioned.

Examples of Valid Values

• Specific examples like 0.5 and 1 are provided as valid selections for x since they meet the criteria set forth earlier.

Union and Intersection of Sets

• The concept of union (A ∪ B) is introduced, where all elements from both sets A and B are included. It is stated that if certain values satisfy the conditions, they can be part of the union.

Analyzing Set Membership

• A check is performed to see if set B's values fall within set A's parameters. This leads to confirming that certain values indeed belong to both sets.

Solving Set Operations

• The solution process for finding A ∪ B involves listing all possible values from both sets while ensuring they adhere to the defined conditions.

Further Exploration of Intersections

• When exploring intersections (A ∩ B), common elements between sets A and B are identified. This includes checking specific numerical values against each other.

Example Problem Analysis

• An example problem involving unions is presented, demonstrating how to combine elements from different sets based on given conditions.

Final Thoughts on Set Relationships

• Concluding remarks emphasize understanding whether intersections yield empty sets or contain common elements based on previously established criteria in set theory discussions.

Course Offer and Structure

Overview of Course Content

• The instructor discusses the completion of a task related to mathematical concepts, emphasizing the importance of understanding Cartesian products.

• Students are encouraged to join a private batch for focused learning on type-based mathematics problems, which will help them solve board and school questions effectively.

• The instructor highlights that while free content is available, joining the private batch is essential for achieving high marks (90-100%) in exams.

Enrollment and Discounts

• A discount is currently being offered; details on how to enroll and contact information will be provided in the video comments.

• The instructor encourages students to engage with their peers in group discussions about specific subjects they need help with, fostering a supportive learning environment.

Comprehensive Course Details

Pricing and Subjects Offered

• A full-year science course priced at 8000 Taka is currently available for only 3000 Taka as part of a limited-time offer.

• In addition to science subjects, students will also receive instruction in Bengali, English, Mathematics, ICT, and BGS within this package.

Features of the Course

• The course includes live classes for doubt-solving, practice sheets by chapter, monthly exams, and recognition for top-performing students (Student of the Month).

• Commerce students have similar offerings at reduced prices; all subjects including general science are covered under one payment plan without monthly fees.

Arts Course Information

Arts Program Details

• An arts course has been launched at a promotional price of 2200 Taka for an entire year with one-time payment options.

• This program covers various subjects such as Bengali, English, Mathematics, ICT, BGS along with features like type-based MCQs and recorded classes.

Call to Action

• Students interested in enrolling should quickly reach out using provided contact numbers to secure their spots before offers expire.