Medieval India was a period of great mathematical activity, with numerous mathematicians making important contributions to the field. From the 5th to the 15th century, Indian mathematicians made significant contributions to the development of mathematics and its applications in astronomy, engineering, and commerce.
These mathematicians, along with many others, helped to lay the foundations of modern mathematics in India and made important contributions to the development of the field. Their legacy continues to be celebrated and studied today.
One of the earliest and most prominent mathematicians of medieval India was Aryabhata, who lived in the 5th century. He made significant contributions to the fields of mathematics and astronomy, including the development of a numerical system for expressing very large numbers and the calculation of the value of π to four decimal places. His mathematical text, the “Aryabhatiya,” was a comprehensive work that covered a wide range of mathematical topics, including arithmetic, algebra, and trigonometry.
Another important mathematician of medieval India was Bhaskara II, who lived in the 12th century. He made significant contributions to the field of mathematics, including the development of several mathematical techniques and the creation of a comprehensive mathematical text called the “Bijaganita.” This text covered a wide range of mathematical topics, including arithmetic, algebra, trigonometry, and geometry, and it was widely used for centuries to come.
The 14th century saw the rise of the Kerala School of Astronomy and Mathematics, which was founded by Madhava of Sangamagrama. Madhava made important contributions to the field of mathematics, including the discovery of infinite series and the development of several mathematical techniques. He was also the first to use the Taylor series to represent functions, a technique that is widely used today.
Another notable mathematician of the Kerala School was Nilakantha Somayaji, who lived in the 15th century. He was a prolific mathematician and astronomer, and he made important contributions to the field of mathematics, including the development of several mathematical techniques and the creation of a comprehensive mathematical text called the “Tantrasangraha.” This text covered a wide range of mathematical topics, including algebra, trigonometry, and geometry, and it was widely used for centuries to come.
The medieval period also saw the development of several mathematical techniques and algorithms that were used for practical purposes, such as in commerce and engineering. For example, Indian mathematicians developed methods for solving linear and quadratic equations, as well as algorithms for performing various mathematical operations, such as multiplication and division. They also made important contributions to the field of astronomy, including the calculation of the positions of celestial bodies and the creation of astronomical tables.
In conclusion, medieval India was a period of significant mathematical activity, with numerous mathematicians making important contributions to the field. From the 5th to the 15th century, Indian mathematicians made significant contributions to the development of mathematics and its applications in astronomy, engineering, and commerce. Their legacy continues to be celebrated and studied today, and their contributions have had a lasting impact on the field of mathematics and its applications.
]]>One of the most important uses of mathematics in the gaming industry is in game design. Game designers use mathematical concepts such as probability, set theory, and algorithms to design game rules and mechanics. For example, a game designer might use probability to determine the odds of a certain event occurring in a game, such as a character landing a critical hit. Set theory is used to define the relationships between game elements, such as the relationship between characters and weapons in an RPG. Algorithms are used to create game mechanics such as character movements, random events, and score calculation.
Artificial intelligence (AI) is another area where mathematics is heavily used in the gaming industry. Math is used to program the behavior of nonplayer characters (NPCs) in a game, allowing them to make decisions and respond to player actions in a realistic way. This requires the use of mathematical concepts such as decision theory, game theory, and machine learning. For example, game designers might use decision theory to determine the best course of action for an NPC in a given situation, while game theory is used to analyze the relationships between NPCs and the player. Machine learning algorithms can be used to train NPCs to improve their behavior over time.
3D graphics are another important aspect of modern gaming, and mathematics plays a key role in their creation. Math is used to create and render 3D graphics, including character animations and environmental effects. This requires the use of mathematical concepts such as linear algebra, calculus, and computer graphics.
For example, linear algebra is used to manipulate the position and orientation of objects in 3D space, while calculus is used to create smooth animations and transitions. Computer graphics algorithms are used to render the final images that are displayed on the screen.
Some examples include:
Physics simulation is another important use of mathematics in the gaming industry. Math is used to simulate realistic physics in games, such as object collisions, realistic movements, and environmental effects. This requires the use of mathematical concepts such as classical mechanics, fluid dynamics, and particle systems. For example, classical mechanics is used to simulate the movements of rigid bodies, while fluid dynamics is used to simulate the behavior of liquids and gases. Particle systems are used to create special effects such as fire, smoke, and explosions.
In addition to the above, mathematics is also used in various other aspects of the gaming industry, such as in the development of algorithms for various aspects of gaming, such as pathfinding and resource management. Pathfinding algorithms are used to determine the best path for characters to follow in a game, while resource management algorithms are used to manage the distribution of resources, such as weapons and ammunition.
In conclusion, mathematics plays a crucial role in the gaming industry, as it is used in a variety of ways to develop and enhance the gaming experience. From designing game rules and mechanics, to programming artificial intelligence and simulating realistic physics, mathematics is integrated into every aspect of game development. With the continual advancement of technology, it is likely that the role of mathematics in the gaming industry will continue to grow and evolve, as game designers strive to create even more engaging and immersive gaming experiences for players.
]]>In this post we have explained how to secure your required marks in Mathematics. This post is targeted for the students who had a bad records in the class 12 terminal exams. This article will help you to score a good marks beyond your skills based on the previous years patterns. This article “How to Secure Your Target Marks in Class 12” is for all boards valid in India.
This post is applicable if you belong to any of the listed boards:
How to secure your Target Marks
Secure Passing Marks 
· Go through the questions given in this ebook.
· Try to attempt 60% of the questions. · What to skip? 1. Inverse Trigonometry 2. Approximation 3. Limit Sum Method 4. Second Exercise of LPP 5. Miscellaneous Exercises · Focus On 1. Probability: Baye’s Theorem & Probability Distribution. 2. 3 Dimensional Geometry Plane 3. Elementary Operation of Matrix to find inverse of the matrix. 4. Continuity · How to write the paper? – Do the questions that you are sure about.

Secure Above 60 Marks  · Go through the questions given in this ebook.
· What to skip? 1. Inverse Trigonometry 2. Approximation 3. Limit Sum Method 4. Second Exercise of LPP 5. Miscellaneous Exercises except 3D & Differentiability. · Focus On 1. Conceptual Questions of Vectors 2. Probability: Baye’s Theorem, Law of total probability & Probability Distribution. 3. 3 Dimensional Geometry of Lines and Planes 4. Elementary Operation of Matrix to find inverse of the matrix. · How to write the paper? – Do 1 Marks questions first. – Do the 6 marks questions that you are sure about.

Secure 90 Above  · Do everything from NCERT.
· Never skip any topic from PYQs · How to write the paper? – Do the paper serially and neatly.

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To pass board exams with better grades, students must use the right study materials. Studying the Class 12 Assam Board Recipe Book while practicing the Assam Board Class 12 Mathematics Questionnaire – 2022 can be the right choice of learning materials.
[Get All The Previous Year Papers – Here]
That’s why we have provided free Assamese Hs 2nd Year Math Problem Paper 2022 with solutions here.
Every year, AHSEC evaluates 2nd year HS students by passing their board exams. With his help, the committee decides which students will be considered to have passed or failed in the academic year. You can preview the solutions of the last year paper. Hope you like our post on “Class 12 Mathematics 2022 Paper Solutions (Assam Board – HS 2nd Year).”
class12assamboard2022solutionsFormulation of linear programming is the representation of a problem situation in a mathematical form. It involves welldefined decision variables, with an objective function and set of constraints.
Objective function:
The objective of the problem is identified and converted into a suitable objective function. The objective function represents the aim or goal of the system (i.e., decision variables) which has to be determined from the problem. Generally, the objective in most cases will be either to maximize resources or profits or, to minimize the cost or time.
Constraints:
When the availability of resources is in surplus, there will be no problem in making decisions. But in real life, organizations normally have scarce resources within which the job has to be performed in the most effective way. Therefore, problem situations are within confined limits in which the optimal solution to the problem must be found.
Nonnegativity constraint
Negative values of physical quantities are impossible, like producing a negative number of chairs, tables, etc., so it is necessary to include the element of nonnegativity as a constraint.
All the characteristics explored above give the following Linear Programming (LP).
A value of (x,y) is in the feasible region if it satisfies all the constraints and signs restrictions. This type of linear programming can be solved by two methods:
1) Graphical method
2) Simplex algorithm method
Step 1: Convert the inequality constraint as equations and find the coordinates of the line.
Step 2: Plot the lines on the graph. (Note: if the constraint is a type, then the solution zone lies away from the center. If the constraint is s type, then the solution zone is towards the center.)
Step 3: Obtain the feasible zone.
Step 4: Find the coordinates of the objectives function (profit line) and plot it on the graph representing it with a dotted line.
Step 5: Locate the solution point. (Note: If the given problem is maximization, Zmax then locates the solution point at the far most point of the feasible zone from the origin, and if minimization, Zmin then locates the solution at the shortest point of the solution zone from the origin).
Step 6: Solution type
i). If the solution point is a single point on the line, take the corresponding values of x and y.
ii). If the solution point lies at the intersection of two equations, then solve for x and y using the two equations.
iii). If the solution appears as a small line, then a multiple solution exists.
iv). If the solution has no confined boundary, the solution is said to be an unbound solution.
Question 1.
Two designers P and Q, earn ₹ 600 and ₹ 800 per day respectively. A can design 12 banners and 8 pairs of posters while B can design 20 banners and 8 pairs of posters per day. To find how many days should each of them work and if it is desired to produce at least 120 banners and 64 posters at a minimum labor cost, formulate this as an LPP.
Question 2.
A company produces two types of mobiles, A and B, that require silicon and plastic. Each unit of type A requires 3 g of silicon and 1 g of plastic while that of type B requires 1 g of silicon and 2 g of plastic. The company can use at the most 9 g of silicon and 8 g of plastic. If each unit of type A brings a profit of ₹ 40 and that of type B ₹ 50, find the number of units of each type that the company should produce to maximize profit. Formulate the above LPP and solve it graphically and also find the maximum profit.
Question 3.
A man wants to invest an amount of ₹5000. His broker recommends investing in two types of stocks A’ and ‘B’ yielding 30% and 27% return respectively on the invested amount. He decides to invest at least ₹ 2000 in stock A’ and at least ₹ 1000 in stock ‘B’. He also wants to invest at least as much in stock A’ as in stock ‘B’. Solve this linear programming problem graphically to maximise his returns.
Question 4.
Find graphically, the maximum value of Z = 2x + 5y,
subject to constraints given below
2x+ 4y ≤ 8;
3x + y ≤ 6;
x + y ≤ A;
x ≥ 0, y ≥ 0.
Question 5.
One kind of pizza requires 800 g of flour and 100 g of fat, and another kind of cake requires 400 g of flour and 200 g of fat. Find the maximum number of pizzas which can be made from 20 kg of flour and 4 kg of fat, assuming that there is no shortage of the other ingredients used in making the cakes. Make it an LPP and solve it graphically.
AHSEC Class 12 Mathematics Previous Question Paper 2016  Click Here 
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AHSEC Class 12 Mathematics Previous Question Paper 2019  Click Here 
AHSEC Class 12 Mathematics Previous Question Paper 2020  Click Here 
AHSEC Class 12 Mathematics Previous Question Paper 2021  Not Held 
AHSEC Class 12 Mathematics Previous Question Paper 2022  Click Here 
AHSEC Class 12 Mathematics Previous Question Paper 2023  Comming Soon 
Science is one subject that typically goes through a progressions occasionally. The progressions in the substance are made as per the development of the subject and for the most part to meet the arising needs of society. The ongoing AHSEC Board Class 12 Maths prospectus has been planned according to the Public Educational program Structure 2005 and as per the rules referenced in Spotlight Gathering on Educating of Arithmetic 2005. This has been essentially finished to meet the arising needs of all classes of understudies. The points that are picked are additionally considered to be exceptionally helpful, in actuality, circumstances and more prominent accentuation has been kept on the utilization of different ideas.
Title  Marks 
Relations and Functions (Chapters – 2)  10 
Algebra (Chapters – 2)  13 
Calculus (Chapters – 5)  44 
Vectors Algebra and ThreeDimensional Geometry  17 
Linear Programming  06 
Probability  10 
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They can additionally estimate their tentative marks and ranks. On the other hand, JEE 2022 aspirants can utilize these query papers to apprehend the paper sample, trouble level, and the form of questions requested inside the Joint Entrance Examination.
1. Let A=\{z \in \mathbf{C}: 1 \leqz(1+i) \leq 2\} and B=\{z \in A :z(1i)=1\}. Then, B :
(A) Is an empty set
(B) Contains exactly two elements
(C) Contains exactly three elements
(D) Is an infinite set
2.The remainder when 3^{2022} is divided by 5 is:
(A) 1
(B) 2
(C) 3
(D) 4
3. The surface area of a balloon of the spherical shape being inflated, increases at a constant rate. If initially, the radius of the balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :
(A) 9
(B) 10
(C) 11
(D) 12
5.Let x^{2}+y^{2}+A x+B y+C=0 be a circle passing through (0,6) and touching the parabola y=x^{2} at (2,4). Then A+C is equal to
(A) 16
(B) \frac{88}{5}
(C) 72
(D) 8
6. The number of values of \alpha for which the system of equations:
\begin{array}{l}
x+y+z=\alpha \\
\alpha x+2 \alpha y+3 z=1 \\
x+3 \alpha y+5 z=4
\end{array}
is inconsistent, is
(A) 0
(B) 1
(C) 2
(D) 3
9.Let S=\{\sqrt{n}: 1 \leq n \leq 50 and n is odd \}.
Let a \in S and A=\left[\begin{array}{ccc}1 & 0 & a \\ 1 & 1 & 0 \\ a & 0 & 1\end{array}\right]
If \sum_{a \in S} \operatorname{det}(\operatorname{adj} A)=100 \lambda, then \lambda is equal to :
(A) 218
(B) 221
(C) 663
(D) 1717
Overall, JEE Mains 2022 – Maths consists of some easy and timeconsuming questions that you can solve with less effort and some basic concepts.
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Calculus of Finite Difference :
Operators A and E. Construction of diagonal Difference tables. Estimation of missing values, Ideas of interpolation. Statements and applications of Newton’s Forward, Backward and Lagrange’s interpolation formulae. Idea of numerical integration, General quadrature formula. Statement and applications of trapezoidal rule, Simpsons 1/3rd rule and Simpsons 3/8th rule along with the conditions under which they are derived.
Basic concepts of Random experiment, Sample point, Sample space and Event, occurrence of an event, Union and intersection of events. Complement of an event. Certain and null events. Exhaustive, Mutually exclusive and equally likely events. Probability of an event: Classical, Emperical and axiomatic (without introducing idea of measure theory). Unconditional probability, conditional probability, Dependent and independent events. Addition rule of Probability, Generalized Addition rule of probability (upto three events). Statements and application of multiplication rule of Probabilities.
Random Variable and Distribution :
Random variable; discrete and continuous distribution of a random variable, p.m.f. and p.d.f, density function. Presentation of discrete probability distribution. Probability curve of a continuous distribution, Mathematical expectation of a random variable. Mathematical expectation of the function of a random variable. Theorems on expectation of the sum and product of random variablesonly application (without derivation)
Idea of Bernoulli Trials; Binomial distribution; Mathematical form, occurrence of the distribution. Derivation of the distribution, Calculation of Mean and variance. Poisson distribution; Mathematical form, Occurrence of the distribution, derivation as a limiting form of Binomial distribution, calculation of mean and variance. Normal distribution, Mathematical form (without proof). Important properties and their applications. Derivation of distribution of standard normal variate and its applications.
Sample and Sampling distribution. Unbiased estimate of a parameter. Standard error of sampling mean and sample proportion for random sampling (without Derivation)simple applications. Statistical hypothesisNull hypothesis, alternative hypothesis, Level of significance. Test (only two tailed test) for a hypothetical population mean on the basis of information supplied by a random sample drawn from a normal having known standard deviation (application only). Student ‘t’ test (only two tailed test) for an assumedmean (examples only), Large sample test (only two tailed test) for proportion (examples only). Examples on use of frequency x² for testing independence of attributes in 2 x 2 table
Sample Survey:
Sample survey and complete enumeration. Basic principles of sample survey, validity of optimization. Principal steps in a survey, Errors in a survey. Sampling and non sampling errors. Advantage of sample survey over complete enumeration.
Simple random sampling with and without replacementmethod of selection of SRS making use of Table of random number, Estimation population mean and total, use of formulamean and estimated population total. Limitations of SRS. Idea of stratified random sampling. Estimation of population mean (method of allocation not included). Preparation of Questionnaire and schedule. Idea of pilot survey.
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If there should arise an occurrence of grids one contrast is that they are commutative when added yet they are not generally commutative when they are duplicated. So for two genuine numbers, x, and y
AB= BA, consistently.
Yet, for two grids, A and B,
Generally AB ≠ BA
Another is that, while each non0 genuine number has a multiplicative opposite (corresponding), few out of every odd non0 framework has a reverse. Furthermore, numerically talking, division by x comprises augmentation by the reverse of x.
So to separate framework A from matrix B, we initially need to find the converse of B which could possibly exist. In any case, regardless of whether it exists in light of that noncommutativity thing in duplication about the frameworks, you have two methods for duplicating it onto A:
A * B^{1} or then again B^{1} * A , what’s more, those will usually be unique.
End Words:
So because of the different reasons referenced over partitioning the two matrices simply don’t function admirably when applied to networks. I hope now you got the answer to why matrices cannot divide.
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