Number System Complete Revision: Classification, Divisibility, BODMAS for Competitive Exams

Hello, dear children, I extend a special warm welcome to all of you. I hope you're all well and your studies

are going well. Children, in today's class, we're going to completely finish the number system. The class may be a

little long, so you'll need to be patient. But rest assured, if you finish today's class, you'll have a

couple of questions in your stomach, as arithmetic carries five marks. You'll definitely get two questions from

today's class. Theory has been covered, as well as previous years. What types of questions might be expected in our

exam? All of those questions have been asked. This class has been designed with a focus on the stomach. However,

the standard of questions is comparable to those of anyone preparing for other papers, whether they're preparing for

NTPC, Railways, or SSC. That too will be beneficial. Because one's basic, theoretical portion never changes. So,

my son, I have come with full enthusiasm and awareness. You know, just as you love me in the 9:00 am

class, you have to give me the same love in this class, children. Today's class is a little different because

there we are practicing the number of questions and our focus is on the chapter-wise series. Is it clear, dear

children? So, you will not interrupt and say, "Sir, I am hungry. I need to drink water. I have to do this." You

must stay connected until the end because only then will the entire class run smoothly. Now, let me take comments

from my dear children, as I can see in the comments. These were the first to arrive. Nandini Pandey, good evening.

Ah, Sanjana Maurya, Aditya Patel, Nikta Nishad, Tanya Yadav, Ajay Kumar, Deepak Kumar, okay, okay, okay, okay. Monu

Mishra has arrived. I don't know if he is just chatting with someone. Okay, okay, okay. Miss Sharma has arrived.

Happy Navratri, Guruji. Yes, look, I forgot. I was thinking earlier. Happy Navratri to all of you, my children.

And today I pray to Mother Goddess that you have jobs by the time next Navratri comes. Okay? So tell me, are you all

ready? In a way, send a thumbs up or a heart. Then I'll start the class, son, and we'll study slowly and patiently.

If you have patience, you'll get selected quickly. You'll get flustered, right? Some of the students interrupt

me and say, "Sir, hurry up, do this or that. Just keep going as I'm going. I'll get you into a new position." Okay

. Now tell me quickly, dear children. Then I'll start the class. Tell me quickly, let me check the comments. Oh,

ho, ho, Sushma has arrived. Very, very good. Let's send it quickly, friend. Ajit Kumar, your name has been

mentioned, brother. Be happy. Okay, keep working hard, stay connected with us, kid. Now, just watch one more thing

. I've taken everyone's comments and seen which kids are connected. Gradually, more will join. Now, don't

expect this from me, kid. Think of our class as if it were a movie; you just keep watching. I'll talk to you

occasionally, and when I do, you'll have to reply. Otherwise, you'll have to ask questions like, "How are you in

love?""Where are you from?" You shouldn't do that at all. Because, if you don't get selected, you know no one

will support you. So, kid, without wasting any time, I'm starting the class. Is that okay? Yes. Let's start

with the number system. The kids I've assigned to today's class mainly cover a few other chapters: whole numbers,

fractions, and decimals; general arithmetic questions; exponents and quotients; and powers. Equations with

one variable, a lot of things mixed into the number system, you'll see in today's class. Various arithmetic

questions, which I think are miscellaneous, are also included in today's class. So, without wasting time

, children, I'm starting with the basics. First, let me explain a little about the number system. One question

will be directly related to the basics in your paper. Look, this slide is white. The rest are black. Don't worry

at all. The question is asking this. What is the question, dear children? The question is this. The question is

about the classification of numbers. The classification of numbers. Basically, we're teaching you by

dividing them into two categories. In this, we have the same thing in front of us, son. There's a slash here. It's

not different. Okay? So, we divide it into two categories. One is real numbers, and the other is imaginary

numbers, children. The Hindi word for real number is real numbers, and imaginary number is also non-real

number or unreal number. Both of these have the same meaning. Imaginary number or non-real number, both are the same.

So, what are real numbers, children? Real number means all the numbers from minus infinity to plus infinity, which

category do they all fall into? They fall into real numbers. For example, -1 , -2, -3, -4, and then start with plus,

1, 2, 3, 4, 5, 6, up to infinity. All these numbers are real. So, imaginary means, children, like under root, if

there is a minus, -1, -2, -3, etc., this type of number is called imaginary number. So, in a way, it goes into

minus, son. In minus, there is an i. For which i is also replaced with 0. It is also called ai ot. Dear children,

this. However, you don't need to do it according to your stomach. My children, you just need to keep this one thing in

mind. How do you recognize imaginary numbers? It should be inside the minus under the root. Actually, we can see

this number in our imagination. This number doesn't exist in reality. And when it comes to real numbers, all

numbers from minus infinity to plus infinity are called real numbers. I hope this slide is clear to you. I'll

move on to the next slide. There are a few things, my children. I've written them down directly to save us some time

. Otherwise, even if I were to teach these things in writing, it would take more time. That's why I've written them

down in today's class. For example, if I talk to you, my children, about natural numbers, I'm talking to you,

dear children, about natural numbers. Natural numbers mean numbers that are given to us by nature. So, they are

given by nature, like one, two, three, four, five; All numbers of this type are real, natural numbers. It's also

written that the set of numbers used in counting is called natural numbers. It is represented by n. It's a simple

thing. Natural numbers start with one. I hope this is clear to you. Now, let's move on, children. I've noted it here.

Even this often leads to the child making the mistake of saying, "Sir, zero isn't a natural number." That's

absolutely correct, child. If a number starts with zero, like 0, 1, 2, 3, 4, then they are natural numbers, and if a

number starts with zero, then they are, in a way, whole numbers. The next slide will explain: "Zero is not a natural

number." Zero is not a natural number. No negative number is a natural number. All natural numbers are positive. You

have to memorize these three points. I'll upload this PDF to Telegram after class is over. So, whenever you take

the exam or after class ends, my child, you have to read this entire theoretical portion once. The question

says zero is not a natural number. The second one says no negative number is a natural number. All natural numbers are

positive. All three points should be clear. Now I'll move on, son. What does he say next? The smallest number of n

numbers. Well, this is often a big confusion for children. Comment once, the new student, sir, please,

Radhe-Radhe. Okay. New student, Kiran Kumari, Radhe-Radhe to all of you. Look , Ranveer has also come. No, son, you

don't have to talk. You know when your teacher is teaching so seriously. Right now, I feel like I'll finish the theory

as soon as I get it done. When you come to the question, I'll give you the question, wait for your answer, and

you'll answer, then I'll explain. But I won't teach you the theory. I haven't even studied it myself. So, children,

you just have to listen; I'll upload the PDF later. You don't have to read it by looking for screenshots or

anything else. Okay? You'll get the full PDF. I asked you what the smallest n-digit number is. This can be very

confusing. For example, if I say, "Tell me the smallest five-digit number," or "Tell me the largest five-digit number,

" you have to think a little. So, keeping this in mind, what did I do, child? I created a result for the

smallest n-digit number, which is always written as n-1. For example, if I ask you, "What is the smallest

three-digit number?" What is the value of n here, son? What is the value of n? What is the smallest n-digit number? It

will be n. Now, you can convert it to n -1. If you multiply n-1, what happens there, son? If you multiply n-1, add

two zeros. How many zeros will you add after that, son? Two zeros. Because here, the smallest n-digit number is

mentioned. So, basically, if someone were to ask you, "Two," forget the smallest two-digit number, everyone

knows that. Now, tell me, what is the smallest three-digit number? What would be the smallest three-digit number, son

? So, you would subtract one from n, the smallest three-digit number. If you go to 1000, son, it would be four

digits. So, you would subtract 1 from it, as there are three zeros. If there are three zeros, then you would

subtract one from three, only then you would get triple 9. Yes or no? And here , if we talk about the largest n-digit

number, n is the answer. And it is written in this format. For example, if I were to ask you, "What would be the

largest three-digit number?" So, triple , the largest four-digit number, it will appear four times. What is the

largest five-digit number? Five times nine will appear. It's simple. Zero comes in this. Just remember this and

subtract one. Is it clear, dear children? It's a very simple matter. You must have understood it. Let's move

on to the next question, dear children. In the next question, I worked hard and wrote down three formulas in one place

for you. I know, son, but it's the last time, so revision is necessary. It's the last time. So, in today's class,

I'll have you revise. Completely. What are you saying? The formula for the sum of the first n natural numbers is "n (n

+ 1)/2." After that, the formula for the sum of the squares of the first n natural numbers is "n (n + 1)(2n + 1)/6

." After that, the formula for the sum of the cubes of the first n natural numbers is "n (n + 1)/2," and we'll

round it off by bracketing the total and making it a whole square. Although I taught this in the average class, I

still felt it was important to share it with the children. So, children, all these formulas should be ingrained in

your minds. Now, there's no time left to think about revising them after a month. No, son, there's no time now.

I'm teaching today, so we have to finish it today. I don't need any pending work at all. After that, I've

written a few small things about what integers are? The group of numbers that includes cubes, negative integers,

integers, and zero is called integer numbers. For example, zero. Now, let's assume that we represent the integer

number here as a number, son. For example, let's say zero, then moving from 0 to -1, -2, -3, -4, and moving

from 0 to +1, +2, +3, +4, and up to infinity. So, these are negative integers and these are positive

integers. But the question arises: what is zero, sir? Is zero negative or positive? So, child, you will say that

zero is neither negative nor positive. It is neither positive nor negative. It is neutral, in the middle. It must be

written somewhere. If it is not written , then you can write it down. Zero is neither a positive integer nor a

negative integer. It is neutral, son. What is it? It is indifferent. It is neutral. This brother is not with

anyone. It is just that since you have come, he is supporting you, saying, " Brother, I am with you." The other one

has come. Brother, I am with you too. I don't want to harm anyone. So, what is zero like, son? It's neutral,

indifferent. It's neither negative nor positive. You have to keep this in mind . Let me continue, dear children. It

says "Integer Number,""Perfect Number." Well, sometimes questions are asked about this. I've written the theory.

I'll explain it through two or three examples. Don't worry, my son. The question says, "Son, if the sum of all

the divisors of a number n, excluding n , equals a given number n. Except n, such numbers are called integer numbers

. Meaning, they're called perfect numbers." Now, I know I've said it very clearly. You might not have understood.

Now, let me take an example. I'll explain it through it. For example, let's say I took the example number

first, son. I said, "Example Number First," like the one in front of you. Suppose I said 3n, then which numbers

divide three? So you'll say one is divided by three, and one is divided by one. Now he's saying excluding n,

meaning excluding three. If I exclude three, how much does it equal? One. So, does one equal three? Then you'll say,

"No, sir." That means, brother, this isn't a perfect number. What kind of number is this not, son? This isn't a

perfect number. Another example, brother, what other example? Suppose I took six. Now, dear children, break six

down. So, six is divided by one, divided by two, divided by three, and divided by six. The definition says to

leave n out, brother. So, here, n is left out, left out. Now add it up. What is 1 + 2 + 3, son? This is six. And

what was this? Six. When added, the factors equaled this. Exactly. Did the factors equal this or not? Exactly. So,

they equaled this. This means it's a perfect number. This is the story, children. Let's take one more example.

I said eight. So what divides eight? One, two, four, and eight. Leave eight aside. Add the rest. So, what is 1 + 2

+ 4? What equals this? No. This means eight is not a perfect number. I'm not talking about a perfect square. I'm

talking about a perfect number. I'm talking about integers, my children. So , through these examples I've shared,

my sons, please tell me once whether your concept has become clear or not. Tell me quickly, my children. Tell me

quickly, my son, is this thing clear? Now, comment once: Sir, everything is going well, because I'll be asking you

questions every two or four minutes. Tell me, so far, whatever I've explained, you've become 100%clear on

the theoretical portion. Tell me quickly, my children. I need students studying in today's class. I need to

get them selected. So, in a way, we need an audience that's willing to read . These love stories are useless.

There's no point in getting such praise , son. Well, how will you recognize Sir ? Son, we'll have to break it down and

see it, only then will we be able to recognize it. You won't know it by looking directly at it. Speak quickly.

All clear. Okay. Okay. Now I'll move on . I'll talk to you again later. Let me finish this for now. After that, I'll

stop and talk to you again. After that, this is a very small matter. I won't waste even two seconds on this. The

question is asking, what are even numbers? So, you all know that the set of natural numbers divisible by two is

called the set of even numbers. Any even number is in the form 2n. Why would it be in the form 2n? When

divided by two, it will definitely fall into the table of two. So, understand this way: all numbers divisible by two

are even numbers. They are even numbers . That's how my children come here in the case of odd. So what are odd

numbers? The set of natural numbers that are not exactly divisible by two is called the group of odd numbers. Or,

numbers that are not even are called odd numbers. Simply put, numbers that are not divisible by two are odd

numbers. Now, you know this, but I know that I've included some things just for your revision, because these are known.

But there are some things that I've included for revision. I'm not taking up too much time on this. I won't spend

time on things that you already know. Now, I've marked some stars and written some points here. You should memorize

them. What is the smallest prime number , son? It is two. What is the smallest and only even prime number, son? It is

two. Two is a number that, despite being even, is still a prime number. Despite being even, it is also a prime

number. There's no number in the rest of the world that's both even and prime . Except for whom, son? Except for two.

Two is both even and prime. Meaning, even and prime. So, you have to keep this in mind. Yes. If you ask for the

smallest odd prime number, sir. If you're asked, "Sir," the smallest odd prime number, you should say three.

After that, I said that every prime number has two factors. Yes, I'm absolutely right, son. Prime numbers

are prime numbers. Prime numbers have two factors, don't they? How many factors do they have? Two. So,

understand it this way, my children: any number that is divisible by itself and one, and not divisible by anything

else, is called a prime number. Numbers that are divisible by themselves and one are called prime numbers. What did

I say after that? A prime number greater than five or five is of the form 2 plus -1. If a number is greater

than five, son, you can check it by adding 2 and subtracting 1. You'll get a prime number. For example, if it's

seven, you'll substitute 7 for it: 7*6 = 42. Add one to 42 to get 43 and subtract one to get 41. Both are prime.

If you know this, you can check it that way, no problem. Let's move on, dear children. Look, I've talked about

primes. Now let's talk about divisible numbers, meaning composite numbers. Look, son, a prime number means one

that has two factors, and more than two . This means a number is divisible by any number other than one and itself.

All of them are composite numbers. So, what are numbers in Hindi? They are composite numbers. Son, if a number is

divisible by itself and any number other than one, then that number is a composite number. For example, if I

tell you that four is divisible by one, by two, and by four. So look, one, two, three have become factors. This means

what number has it become? It's a divisible number. Just like six is divided by one, two, three, and six. So

, where does this fall? The divisible number. You have to keep this in mind. Okay, sir. What do you have to note

down? Look how hard I've put into this PDF, children. I've mentioned every single thing that's wrong in today's

class. If someone ever asks you what kind of number one is? One is neither a composite number nor a prime number.

One is neither prime nor composite. Son , one is neither divisible nor prime. You have to keep this in mind. One is

neither divisible nor prime. Is it clear, dear children? So, you have to note this down. Let's move on. What did

he say next? A prime number. There's a lot of confusion, children. A prime number, a co-prime number. A pair of

two numbers that have no common divisor other than one are called coprime numbers. If you didn't understand,

understand it this way: two numbers whose HCF is the same, whose HCF is the same, whose HCF is the same, with

nothing in common other than one. What are such numbers called, son? They are called prime numbers. For example, if I

tell you, this is nine. This is 25. Now look, nine is not a prime number, and 25 is also not a prime number. But both

are prime numbers. What kind of numbers are they, son? They are prime numbers. Because 25 and nine have nothing in

common. You can take other examples from around the world. Take three, take five, write seven, write nine, write

anything, or any number written with a gap of two. Will all of them go into what? Will they all come in coprime?

Yes or no? Not with a gap of two, meaning write any number consecutively. For example, if you write two, write

three. These are coprime numbers. Write 10, write 11. If you write two consecutive conjunct numbers, two

consecutive conjunct numbers, they will be coprime. Is it clear, dear children? Okay? Let's move on. Yes. Now, son,

understand this a little. There's a lot of confusion between rational and irrational numbers. They're called

rational numbers, son. Rational numbers mean numbers that we can write in p/q form. Meaning, we can write them in an

up form. For example, if this is 3/5, we write any number in 3/5. Meaning, it's written. So, what is this, son?

It's a rational number. It's a rational number. Or we can write it by removing the point. And what does it say? A

number that can be represented in the form p/q where p and q are integers and q is not zero. If q becomes zero, it

becomes infinity. If the value below, for example, you write five above and then zero, it will become infinity. So

this is not possible. Just make sure that the value of q is not zero. Okay? Let's move on. Next, he said, "Son,

what are irrational numbers?" Numbers that aren't rational are irrational. Meaning, what are those numbers that

can't be written in the p/q form, son? They are irrational. They are irrational numbers. But you also have

to write a note. What did I write in the note? Now, look, we often know that the value of pi is 22/7. Pi also has a

value of 3.14. Children, there's a difference between the two. If it's written normally, that pi is an

irrational number. Talking about pi, pi is irrational. Whereas if he writes 22/7 for you. If he writes 22/7 for you

, it's a rational number. Because this form is p/q. But the value of pi, which you write as 3.144, goes on and on.

It's never ending. Not ending means it can't be in p/q form. So, what does this mean? We can't call it a rational

number. So, keep this in mind: those whose pi by q form is written are rational, and those whose pi by q form

isn't written are irrational. If someone asks you what pi is, say it's irrational. If someone asks you what

22/7 is, say it's a rational number. Because children get very confused because they'll say the value of pi is

22/7, so the result should be the same. No, no. If it's written as pi, it's because the value of pi varies so much.

Many people have done research on this. Books have been written asking what the exact value of pi is. To this day, it's

still unclear. It goes on and on in integers. That thing just doesn't end. So if pi comes, it's irrational, and if

22/7 comes, it's rational. Tell me quickly, son, is it clear? Now, leave a comment and tell me, Sir, that we have

no doubts about this. After that, I'll move on, because I'll definitely talk to you in between and I'll have a drink

of water. My throat is dry. Yes, sir! Where are you guys coming from? Rajput ji, you're coming so late, how will

things work? Class for you guys...And I told you before, son, that I'll start class today at 4:00, but you guys don't

come on time. Look, this is wrong, son! The teacher is working so hard, and you're not coming on time. This is

wrong. Right now, Kumar is saying, " Blue flower, yellow flower, Sir, you're beautiful." Hey, brother, I'm not

beautiful at all; I'm Kalu. "Sir, I'm on the job, sorry, sir. Okay." Okay, okay, no one, no one. Chief Minister

2027, Jai! Oh man, what a name you've come up with, Chief Minister 2027! Aditya Patel, sir, recite a poem. Hey,

friend, I'll recite it later. I can't. Just read it now, let me finish some theory. I'll recite it for you after

that. Don't worry. Finish the theory. When we get to the questions, I'll give you the questions. Then I'll have some

time left. Right now, I'm just teaching a little bit. Okay? No one. No, no, son Rajput, it's not an issue. Let's get

started now. Let's move on, dear children. Okay. Oh, ho, ho, wow, the questions are here. Look, it's not like

that yet; the theory is complete. Now, the basic things, the little things, are often missed. So my effort was to

ensure that these were not missed, and I hope you've noticed that I only studied the small things, but sometimes

, if a direct question arises on these, it gets missed, son. Now, I'm teaching you what questions can be made related

to these. And all the chapters are mixed. It's not like that. There are all these questions on rational,

irrational, unit, digit, surds, ends, decimals, largest value, smallest value in the entire class. Today's class is

going to be a long one. Now do this question quickly. Do it, son. Hum, hum, I've moved aside, son. Look, now I'll

coordinate a little bit. Since the theory is complete, I'll give you some time too. Now tell me the answer to

this quickly. Tell me the answer to this quickly. Let's see whose answer comes first. Hum, hum, three is coming.

Three is coming. But think a little about whose answer came first. Sorry for the delay. Sanjay Kumar, no one.

Kiran Kumari, "Sir, please, I understood. Sir, please, Sir, please, I didn't understand. Sir, please." Kiran

Kumari, tell me what you didn't understand. I haven't taught any questions yet, and tell me what you

didn't understand. Whatever I taught was written on the board; I just explained it. There's no question of

understanding or not understanding. I've shown you at least 15 or 16 slides so far. Tell me which point you have

doubts about. I'll explain it to you in a better way. Don't worry, just in case there's a particular point. Okay? The

question is asking about prime numbers greater than four and smaller than 16. So, one greater than four is five, one

is seven, one is 11, and one is 13. Add them all up. What's the point, son? So how much does this amount to? If you

add 12, 12, and 13, then the sum of 25, 35, 36 becomes 36. Now it says 1/4 of the sum. So subtract 1/4 of the sum,

then divide it by four and you get nine . What number is this square of? So, son, what is nine the square of? Three.

He's not asking directly. Look how he's twisted it. Add the numbers greater than four and less than 16 and take 1/4

of it. How much? If you take 1/4, what will the resulting number be the square of? It will be the square of three.

There's no time to waste time. Tell me the answer to the next question. How is a prime number greater than five

represented? I've already explained it. It's 6k + -1. 6k + 1 is -1. 6k + 1 is -1. Is it clear, children? I've taught

you this in theory. Is it clear? Let's move on, dear children. The next question for you is: tell me the

product of the first five whole numbers . What is it? What will be the product of the first five whole numbers? How

much? You asked a fake question. Whole numbers start with zero. After zero, there's one, two, and so on. Forget

about five, up to infinity. Write 500,000. Once zero is reached, any number multiplied by zero will make

everything equal to zero. It will make everything equal to zero. Yes or no? It will make everything equal to zero, son

. Tell me further. How many digits will be needed to write numbers from one to 50? Tell me, my son. How many digits

will be needed to write numbers from one to 50? Brother, there's no point in getting into political discussions here

. Study quietly, and figure out who will succeed and who won't. But if you don't get a job, trust me, your life

will be hell. Those who don't succeed have such wealth. These are the kings and emperors you're talking about. No

matter what happens, his seven generations can live off it. If he doesn't make a single penny, you

understand, right? I teach here, so my family can survive, and you'll get a job. So, put these things aside. Son,

let's not talk politics. I'm a teacher here, right? And you're my student. Whenever these things are discussed, we

don't do it like this. Sometimes, sitting down and talking is a different matter, but right now, your focus

should be on studying. Son, Mahi Chaudhary ji, you're coming so late, my friend! 91 is up, very good. Look, son,

it's a simple matter. Sometimes we make mistakes. So, from one to nine, it's a simple matter: nine is up. Now, son, if

you subtract nine from 50, you're left with 41, and 41 is left with those two-digit numbers. Hey, tell me one

thing: from one to nine, it's a single digit, so nine is up. Now if we subtract nine from 50 then 41 is left,

so the remaining 41 numbers are all two digits. So if you multiply it by two then it becomes 82, so add 82 and raise

it to nine, sorry, add 82 and raise it to nine, how much will you add, son? 82 will become ours. 91 is the correct

answer of this question. 91 is the correct answer of this question. 91 is the correct answer of this question. Is

it clear dear children? Yes. Let's move on to the next question. The next question is about the different concept

which was absolutely basic of our number system, that has been completed. The next concept has come. A new

concept has come which is related to board mass. You must be understanding board mass. All these are orders. You

know the order of writing BODMAS while solving. Whenever we solve a simplification question, we will write

BORD MAAS like this. BORD MAAS and the full form of all the words is written. However, technically, there is another

bar after this. The viculum that appears, we solve the bar first. If it comes, otherwise, board maas has to be

kept in mind. B means bracket. OFF means of. It means multiplication indirectly. But look at multiply, here

too there is multiply and if both multiply and OFF come, then we will first solve the multiplication with OFF

, then the real multiplication. D means division, M means multiplication, A means addition and sab means

subtraction. You have to remember this, Boss! Well, our children get confused with some brackets. Son, this bar that

is placed above any number, we basically call it bar in our language; By the way, it's written as a ventricle

, or it's also called a line or bar bracket. Sometimes, this bracket is called a small bracket in our language.

This one is called a curly bracket. It's called a major bracket in Hindi. And it's also called a square bracket

or a large bracket in our language. So, remember them by their shape. The paper won't ask what their name is. What's

their name? First, understand that if all these brackets are in a question, this one is solved first. Then comes

this one, and then this one. Memorize them by their shape. If all the brackets are in a question, the small

one is solved first. Then comes this one, and then this one. Is it clear, son? You have to keep this in mind. Now

, what's the next question? We've raised questions related to this. Let's discuss that. Children, you'll solve

this question first. I'll step aside a bit. Now I'll give you time. Quickly, my children, tell me the correct answer

. This question is written. 5 minus the large bracket is opened. 96/4 of 3- small bracket. 16-55/5-small bracket

and large bracket are closed. Quickly, tell me what the correct answer is. Do it, children. Tell me the correct

answer. Mahi Chaudhary, I'll come to check if everyone is studying. Okay, today's class is private. All children,

please pay attention to this. This class is not very live, as many children are not coming right now. You

might be thinking we'll see later, but this class will definitely be private; because the chapter-wise class on the

number system is very technical. If children join now, it will be beneficial for them. Two of our

children are coming, C...we...let's solve it, dear children. Look, first of all, let's break the small bracket. Son

, if I divide this by 5, I get 11. And look, son, let's not just write it down , let's use some common sense. Divide

55 by 11 and subtract 11 from it. Are you getting it right? Subtract 11 and 11 from it, and you'll get five. What's

the value of this? Five. Okay? Inside this bracket. Now let's check something here. First, the OFF will be solved.

Son, will it be solved? Like, if we write BORD MASS (), BORD MASS; so first the bracket, then the OFF. So, if we

solve OFF, it means multiply. If we do this, we get 12, so 12 will subtract 96. So, 5-the big bracket is 8. And how

much is going on here, son? If you subtract 5 and 5 from this, you'll be left with three, and there's already a

minus here. And 3 taken from 5, you'll be left with two, dear children. So, the correct answer to your question

will be two questions. Let's move on to the next question. My children, the next question is something like this.

Please read this question carefully and answer it. The question says if 48/72*3 close the bracket-15/8*small bracket

40-32 close the bracket-10 close the large bracket. And later it is written + 2p = 6/2, then find the value of p.

You have to tell me, dear children, how much will it be. You have to tell me how much p will be. Hurry up, my

children. Kiran, is it a mistake? Is it my mistake? Sir, what happened? Please tell me, what is your doubt? Tell me

once, write a long comment, I will read your comment, son, don't worry. Just tell me what the problem is. Do this

question once, dear children, break it down to four. Very good, very good, the public is going with four. Tell me

quickly, friend, what will happen? The value of p will be three. Ranveer is saying three. Okay. Yes, sir. Let's go

with three, our child. Let me check the rest. Look, son, there's not a lot of writing involved. A little bit of

thinking is required. But you have to keep this in mind: if the board's remainder is even slightly off, the

answer will be wrong. Then, first, the smaller number in the bracket is 8. How much will it be, son? Eight. Now tell

me, divide, and which one will be solved first? First, subtract 8, then divide, then multiply. So, first,

divide, so I'll divide 15 by 8 and add 8, then this will cancel out. So, basically, solving this, we'll have 15

here and 10 there, so I'll solve it all from here to here, son. So, five. How much will I get? Five. Now, let's come

here, son, and look at it in the brackets. So, this is 48 divided by 72, and add 8 will be 3. Okay, this is how

we'll cut it...are you doing it right? Or subtract 24 from this and subtract 24 from this twice, and you get 2. Okay

, so I'll write it here, son. This gives you 2, and this gives you minus 5 , minus 5 = 2p, and equal to 2. Divide

this by 3, and we get 3. Now, subtract this from this, and -3 = 2p, and + 3, -3, goes here and becomes plus 3. So,

the value of p should be 3, son. Look, is it 3? The D option should be, according to me. Sometimes silly

mistakes happen, so please check it once. It must be 3, son. D is the correct answer to this question, clear?

Let's move on to the next question, dear children. Okay, son, everyone has answered. Very good, Rajput ji, it was

yours that was wrong. No problem. Move on to the next question. The next question seems simple. Tell me quickly,

my dear. What's the answer? Oh, yes, yes, son! Tell me the correct answer quickly. Do this one too, friend,

quickly. Why are you taking so long, son? I told you to solve the smaller one in the brackets first, paying

attention to the board mass. The board must be kept in mind. If you don't pay attention, you'll get the wrong answer.

So, bracket, then after that, solve off . Bracket, and after that, what will you solve off? Off. So, children, if I

solve this bracket once, you add them together, their sum becomes 11, and 11 is subtracted from this, it becomes

seven. Now, seven divided by 14, it remains seven. Then divided by 16, it leaves nine. Then nine divided by 25,

it leaves 16. It should come out to 16, son. You'll see, you're getting 16 too. Tell me clearly once, quickly. It

should come out to 16, dear children. The correct answer should be 16. Clear? 16 is the correct answer to this

question. Let's move on to the next question. The next question, kids, is very simple. I've asked you many such

questions in practice sets. So I hope you can answer it correctly. You'll treat these numbers as real numbers.

Nothing will happen to you. Just consider this as a and this as b. And break the question down. How? What it's

trying to say is that a + b squared is a² + b² + 2ab. If you open it there, it becomes a² + b²-2ab. And it's

written twice below, it becomes a*a². This a² and this b², the minus and plus, will cancel out, and the top

becomes 2 a² + 2 b², and the bottom becomes a² + b². If we take the two common ones from the top, it means a²

+ b²/a² + b². This cancels out. The answer is two. If you use real values, you'll go crazy. You won't be able to

solve the question. So, basically, consider this number a. Consider this b . Once the question is solved, this

thing is useless. It becomes two. Is it clear? I hope it's clear. Let's move on to the next question. The question says

, "Look, this is a different type of question, kid. This will be new for you . So, try to understand this a little.

It's saying that this form is expressed in the equivalent form p/q. How can we write it in p/q form?" If you ever get

a question like this, understand what you'll do, son? What do you do if you get a question like this? Listen! Look

at this bar, this bar. How many digits are there below this bar? So, one, two. How many digits are there? One and two.

So, we write nine below the number of digits below the bar. What do we write? This is a bar, how many digits are

there below it? One and two. So there are two digits, so write two nines below and subtract them from nine 9*7

63 and 9*1 = 9, 9*1 = 9 7 11 is there anywhere? Exactly, B option is the correct answer of this question. B

option is the correct answer of this question. Tell me quickly my children, is it clear or not? Tell me quickly.

Let's move on to the next question. Four-five questions will be cleared like this. Tell me, break this question

and tell me. 0.3183181818 Now see from where is the repetition starting son? The repetition is happening that 18818

so to avoid repetition what will be placed above 188 sir? A bar will be placed above it. It will not be placed

above three because three is a single number. The repetition starts after that. 18818, so a bar appears above

188. Now, understand the concept here: how will it be written? How do you break it down? So, first, write down

the entire number. Will you write 318 like this? Absolutely. Now, tell me, which number doesn't have a bar? Three.

So, the number without a bar becomes a minus. So, brother, three is divided by three. Okay, how many digits are there

below the bar? One and two. So two become nine. How many digits are there without a bar? One. So, that becomes

zero. Clear? Didn't you understand? See what I'm saying, son? First, the repetition will come above the number

18818. So, it won't come above the three; it's above 188. How do you break it down after that? Like, 318, write

down the entire 318. Then, the number without a bar becomes a minus. How many digits are there below the bar? One,

two, so as many digits as there are nines. So nine appears twice, and how many times there is no bar? One, so as

many zeros as there are no bars. So this is one zero. Now if you subtract this and write it down, 315 divided by

990 should probably be subtracted by nine. Let's check this once. Subtract 9 from 9. 9*3 = 27. And what is the

difference, son? 9*5 = 45 9*1 = 9 9*1 = 9. You will subtract 5 seven times. You will subtract 5 two 22 times. 9 by 7/2

should be 7/22. 7/2 means option A is the correct answer to this question. Option A is the correct answer to this

question. My son, A is the correct answer. Tell me, is A the correct answer? Is it clear? Tell me, is it

clear, son? A is the correct answer. Tell me quickly. Hey, tell me. We'll move on to the next question, son. The

next question is something like this. Solve it quickly, son. Solve it quickly , friend. This won't work. Look, now

you have to see that there was a zero on the other side of the point. There's a one here. So, leave the one as it is.

Don't disturb it. Put a plus sign and write it as 13. How many numbers don't have a bar? Subtract one from the other

. How many numbers are below the bar? If there's a nine without a bar, this is 0. So, 1 + 12 and upon 90, if you

subtract six from six twice, you subtract 15 times. So, this gives 1 + 2/15. 15*1 = 15. And if you add two,

17/15 is the correct answer to this question. Where is 17/15, son? It's given in option D. So, option D will be

the correct answer to your question. Option D will be the correct answer to your question. Tell me quickly, it's

clear. Write question number six once, which one is it telling me, son Ranveer , write the answer of which number six

once, I will tell you. Come on, the next question is in front of you, son. Do it quickly. Let's hurry up, dear

children, let's do it, son, quickly, let's do this question. Let's do this question. Then we will take your doubts

. Son, we will see what it is. There is no need to worry. Write this down: 5 78. Now tell me, you will subtract five

from 5 78. Okay? And how many numbers are there below the bar? 99 and this without the bar. Now subtract this from

this, son. So it will come to 582. Okay ? And after this, 990. Now cut it apart , son. Tell me, by what should we

subtract it? Let's subtract this. It will be subtracted by nine. 10 and 15 will not be subtracted. By what should

we subtract this? If we sum them, 15 will be subtracted by three. Or by any bigger number because if you subtract

this from 87 then 82 will be left. Come on, subtract it. You subtract it by three. So 3*1 = 3, okay sir. 3*1 = 3,

two are left, 7, 21, 3, 8, 24, 3, 9, 27 and 3*4 = 12, 194 and this 3 0, now by what should you subtract, son? Now

subtract by two, so subtract by two; 2* 2 = 18, 9 and 2*7, 14, 97 and you will subtract by two, 2*1 = 2, 2*6 = 12 and

57 by 2 97/1 165 97/1, 165 is the correct answer of this question. 97/1 165 is the correct answer of this

question. Is it clear, dear children? Is it clear? And I don't know what Ranveer is saying in one question, "Sir

, I have a doubt. Let's explain it. Which one is the 16? Let's look at it, son. There's no problem. Okay, this is

the one I'm doubting, son. Let's try it again. There might be some silly mistake. Let's follow Boss. The thing

is, if you don't pay even a little attention, the answer will be wrong. In this, son, first we'll solve the small

bracket. This one, if we look at minus and plus, what comes first? First, the big addition, and then the subtraction.

So, if I add this to this, it becomes 11. And if we take -11 from 18, son, it becomes seven. There's no problem with

that. This inside value is seven. Okay? Now, after that, I'll bracket this one. This one is 7 and -7. So, when you

subtract this from this, son, seven will remain. How much will be left? Seven, and this bracket is going to be

16. If you subtract this from this, you get seven. And after this, there's just an empty number. No problem. Then

you'll solve this bracket. So, my child , when you subtract this from 16, you get nine, and if you subtract nine from

this, you get 16! 16 is fine, son. Are you having any doubt about this? Ranveer, how will it be 10? Okay, 16

will be the answer. Why are you having doubt about this, tell me. Sir, it's negative eight! Where is negative eight

, brother? This seven is left here. Okay, this is negative eight. So first, you'll solve the plus. In this, go to

the board exam, son. Brackets of divide , multiply, addition, subtraction. So first, you'll do the addition, then the

subtraction. So, first, you'll add this , then you'll come to this. If you subtract this from this, you're doing

10 and 10 and 10, 10 and plus 3, so you get 13, and 13 is getting one, and then you're subtracting one from 15. I

understand what you're doing. When you subtract this from this, the minus sign will become 10, and then you subtract

one from 13, and if you subtract this from this, son, how much will you get, 15, and if you subtract 15 from 25, how

much will you get, 10. But if you go to the definition, board mass ()— addition, subtraction, first you add,

then subtract. So first you add to this , son, first you add this to this, you add this to this, then you subtract

this from this. You won't subtract this from this first; first, if this is next to this, you'll add it, the addition,

then subtract this from this. Okay? You're getting confused, that's how it is. Is it clear or not? Tell me quickly

. Okay, this question is homework, son, because it's the same type. I've given you four or five questions, so you can

do whatever answer you get. Or you can tell me in the comments, or you can't, but you should definitely do it,

there's no problem. Now, let's introduce the concept of divisibility from here. Come on, son, let's move on

to divisibility. Come on, come on, okay , son. One thing to keep in mind, Aditya Patel, whoever you are, you're

this Google? Do you know that everything written on Google is 100% correct? Google throws up all sorts of

wrong things, so never trust Google so much. When we've told you that this is the case and even provided proof that

this will be solved first, and then this, Google is in for a rude shock! When we've written here, yes, sometimes

a silly mistake happens, it's accepted and a session is declared. But what is Google saying? Chat GPT makes all sorts

of mistakes. If I send you four questions and have him do it, and he'll send you the wrong ones, then that

means you don't trust the teacher, you trust him. Okay, no problem. The divisibility rule of 2, 4, and 8. Why

are all three of them written together, my child? Why are all three of them written together? The divisibility rule

of two, four, and eight. Look, son, two is pretty straightforward. The last digit should be divisible by two. If

the last digit is divisible by two, that number will be subtracted from two . It's very simple. Everyone knows it.

And the divisibility rule for four says the last two. Look, two is the last digit, and four is the last two digits.

Four is the last two digits, and if we're talking about eight, the last three are on the next slide. But the

last three digits, my child, if the last three digits are subtracting from eight, then that number will be

subtracting from eight. If the last two digits are subtracting from four, then that number will be subtracting from

four. And if the last digit is subtracting from two, then that number will be subtracting from two. So, all

three are the same. Please pay attention to this. Is it clear, dear children? Let's move on to the next

question, dear children. Do this next question. Do it quickly. Tell me the answer to this question, my children.

Tell me quickly, what is the correct answer? Side set. Well, I've already told you that. Look, eight has three

digits. After that, I'll move on. Look, we'll come, listen, my son. The question asks for the divisibility rule

of 3 and n. What does the divisibility rule of 3 and n say, son? If the sum of all digits—by the way, I've taught

you all this in the practice set, son —that if a number is divisible by three, the sum of its digits, the sum

of all digits, should be divisible by three. And the same rule applies for nine: the sum of all digits should be

divisible by n. If the sum of the digits is divisible by three, the number will also be divisible by three.

If the sum of the digits is divisible by nine, the number will also be divisible by nine. Is this clear? Let's

move on to the next question, son. Look , it's a simple matter: there's no need to memorize the divisibility rule of

six. Because if a number is divisible by two and three, what will it be divisible by? It will be divisible by

six. And we've already studied the rule for two and three. So, that's what we've covered here. After that,

divisibility by 11 is important. Read this once, dear children. Read the divisibility of 11 once. After that, I

will move on. Let me step aside. Look, all of you, children, read this once. Listen to me carefully, children. The

divisibility rule of 11 is very important, and what do you have to read in it? If the difference between the

sum of the digits at odd places and the sum of the digits at even places is zero or a multiple of 11. Now, you may

not have understood this through language. Do one thing, dear children. Do one thing, pick up your mobile and I

will see your comments. Don't use your mobile to Google two or three examples of multiples of 11. I am telling you

this in advance. Then you will say wrong. You will say that Google is making you do this. Open the calculator

in your mobile. Tell me the multiples of 11 on the calculator. If you want any big number. Now, don't just say

1331. Everyone knows that. Like five, six, seven, eight, nine. Any big number like that. Give me two examples. I'll

prove it by looking in the comments and writing it here, explaining the rule. While I'm drinking water. Tell me

quickly. Tell me quickly, dear children . Tell me quickly. Answer what I'm saying.

>> Otherwise, I'll use my calculator to tell you something. You tell me. Aditya Patel sent one. He didn't send it from

Google, son. 156, 7, 85 is fine. Send me one more example, son, and then I'll solve both. Mahi's number is 176, 25,

61. It'll be clear with just two. Now, how many will you ask me to write? It hasn't even come yet, but if anyone

else did, I would have told you. Look, look, Alia has also come. I've written down the 85 number. Okay. Okay. Okay.

Okay. Let's understand from both. Then listen, child. Now understand the language of what was written. It said

to sum the alternate digits. Like one after leaving one. Like this is five. You add seven to five. If you add five

to 12 and 12, it becomes 17. So from this side, it becomes 17. Now add from the other side. 1 and 6, 7 and 7 and 18

= 8, so 8 + 2 = 16, this is 15, this is 15. Check the difference once. This becomes 5 and this 12 = 12, and you add

this, oh yes, 12 and 5 = 17, and you add this seven seven from here, and add this, how much does it become? 15, the

difference will be two. You must have asked this from Google itself, Aditya Patel, take it, it is not deducting

from 11, now don't say that it is deducting from Google too. Now look here. Mahi sent this, let's check it.

One and five, six and six, 12 and one, 13. 13 is already here. Now let's go from the opposite side. 7 and two, 7

and two, 9 and 9, and son, how much do you make it? 6, 15, brother, what are you doing? This number won't even be

subtracted from 11. huh? Where are you sending this from? You're sending anything, anything. Divide it and see,

use a calculator. Come on, how much is this? 1 5 6 7 8 and after that 5/11, where is it subtracting? This is going

into points, after that, see it. 1 17 6 25 and after that 61 by 11, this is also going into points. Where are you

sending from? You must have Googled this. I think. These two numbers won't be subtracted. This one won't be

subtracted. This one won't be subtracted. I told you to send a multiple of 11. Ranveer, come on,

Ranveer sent it. Come on, see, this boy is fine. 1, 2, 3, 4, 5. Let's check it. Look, add five and three, it's eight.

Eight and one makes nine, nine from here. And if you add this and that, how much will you get? This makes five, the

difference is four, and that won't add up either. Hey, are you crazy? Okay, no problem, son. You must have understood

the definition. You can't send examples , so what can I do about it? I have examples waiting ahead, I'll get them

done. There's no issue. You're sending random examples. It's not making any sense. He sent another one. Let's check

it further. 6 7 8 1 5 Look, add five to this. 8 13 and 13 and this, add six. What's the result? 19 and from here,

let's subtract eight from this, 11. This number will be deducted 100% because 19 divided by 8 is 11, a

multiple of 11. Either zero or a multiple of 11, you're sending anything , friend. Okay, let's go. The questions

will come, we'll answer them. Two examples weren't sent to you properly. Are you preparing to become an

inspector? Huh? This is too much! I said that using my mobile phone, it's not like you couldn't tell using a

calculator. So what's the point of fooling me, son? I'm just proving it. If it's not zero or 11, it won't be

deducted from 11. So my question is, the examples they sent won't be deducted, and if it had been zero or 11

, it would have been deducted. What's the problem with that? Anyway, tell me the answer to this question. If the

number in front of you is exactly divisible by 2564, tell me which one is the correct answer? Read the entire

question and say the answer quickly. Hurry up. Okay, C! That's fine for you guys, okay, sir. C means two will be

substituted for this. Very good, very good, my child, very good! How smart are you? Brother, didn't you read the

question? It says which of these digits can't replace this dollar. This means three can, and the divisibility rule

for four says that if I substitute six, it becomes 64; if I substitute five, it becomes 54; if I substitute two, it

becomes 24; and if I substitute eight, it becomes 84. So this also gets subtracted, this also gets subtracted,

this also gets subtracted. So, son, what is 54 not divisible by? It is not divisible by four. That means five.

Option B is the correct answer. I have not asked you. I have not asked you. Read the first question. Which one

cannot come? Three options can come. Fourth cannot come. So five will be the correct answer. Tell me the answer to

the next question dear. Whose name do you want to take brother? Come on son, tell me the answer to this. He is

saying that this number is written as A , what is the smallest value that can be given to A to divide it by eight?

What is the smallest value that will come in place of A? Four options are given. Tell me and do you know the

divisibility rule of eight, son. How many digits? Last three digits are divisible by 8. Apply this rule quickly

and tell me the correct answer. Ranu Yadav has forgotten you. How are you commenting like this? You have not

forgotten, you are an old student, child. Do it my son. Tell me the correct answer to this. You're going

with three, last for three. So this is 6 a 32. If you divide it by eight, it will be subtracted. 8*7 56. How many

are left from 56? Four and 72. So this will be subtracted. It will be subtracted by three, son. Okay? Three

will be the correct answer. B is the right answer. Come on, tell me the correct answer, son. This is a simple

question. Now it says it's divisible by three, so what will be the maximum value of p? Brother, it's divisible by

three, so first eliminate the pairs of threes. This is divisible by three. This is divisible by three. And add

these two, and this is it, friend. This is also divisible by three. Their sum gives the value of p. So the value of p

will be a multiple of three. What did it say? What will be the maximum value of p? So this is also possible. This is

also possible. This is also possible. So what is the maximum value of p? And p is a single digit. Pi is a digit,

right? So this is not possible. Now, if we look at these, this is also possible . This is not possible at all. So, if

the largest possible value is no a, then a is the correct answer to this question. We, we are fine, son. Look,

it's simple. Don't get confused about why it's not 12, because pi is a digit, and a digit is a single digit. 12 is a

two-digit number, so we shouldn't look at it anyway, because p is a single digit. Where do the digits go up to

nine? Like 1, 2, 3, 4, 5, 6, 7, 8, 9, 12 can't be, it could be nine, it could be six, but it said the largest value,

so nine is the only possible value. Let's move on to the next question. Find the value of a that is divisible

by nine. So first, remove the 9's from the table. Look, six and three, 9. Remove that. Then, add eight and six,

and this is eight. 8 + 1. Now, tell me, what should I put in place of a, son? What should it subtract from? Aa should

subtract from nine. So, if I put six, it won't subtract 14. And if I put seven, 7 2 won't subtract 14 15. If I

put eight, it won't subtract 16. Son, this is coming up. Find the value of the divisible a. This is going wrong.

Did I make a mistake somewhere? This cancels it out. That's absolutely correct. Well, there's also four in it.

Oh, ho, ho, this is a complete game. This cancels it out. And if I look at it, one comes out of 10 10, and two 3 +

a needs to be satisfied. So, six is also possible. Seven won't happen. I'll put eight, I'll put 11 10, 13. It will

be six, son. It will be six. Six is six . It is six. Six is the correct answer to this question. It is six, son. Okay?

Well, first, remove the numbers that appear in the 9's table. Like this six and this three. Remove this. Remove six

and three, 9. Now, look, I divided 10 and four, 10 and four, sorry, six and four, 10 by nine and took one out. And

then added one and two, so 3 + a. Now, as soon as I replace a with six, it will appear in the 9's table. The next

question is before you: Which of the following numbers is divisible by 11? Here's an example; you won't need it.

You were telling the wrong one, right? Now tell me which one is correct. There was a boy, where did he go? Did he

block me by calling him Vishal Yadav? I have to cook food. What do I have to do ? Tell me again, the public is going

with A. Now, it will become clear here. Look, add the alternates. What is it saying? It is divisible. For example, 1

and 3, 4 and 1, 5 and 5, 10, so from one side it's 10. Now, from the other side, 2 and 4, 6 and 6 and 4, 10, so

from the other side it's 10 too, and 10 is subtracted from 10. A zero appears. This means this number is subtracted

from 11. This is the divisibility rule of 11. Okay, son? Please pay attention to this. Tell me clearly quickly. Pammi

Sharma ji is saying," Sir, you haven't seen a single message from me. "Please tell me, sir. Tell me, brother, you

sent a message. I'll look at all your messages. Only after that will I teach, because your selection will be based on

these messages. What I'm teaching here. This won't help you in your paper. Your messages will come. What are you

sending, son? Tell me quickly. Tell me, brother! Tell me quickly, my friend. Pammi, whatever it is, someone's ID is

from Ayansh Verma's...Sir, my elder brother, he looks at it like Bhaiya. Absolutely, no one, he's your brother.

Hey, will you comment now? What's up, brother? Pammi Sharma, don't look at the comments. And I stop and check your

comments, but you're not commenting. Then, when I'm teaching from behind, I'm not even looking at the comments,

but they just slip away, brother. There are a lot of students studying behind here, them...look at his comment. Tell

me quickly, if it's divisible by 11, tell me the value of k. Break it down quickly, quickly, an important class is

going on. Excellent, sir, class was at 7:00. Who said Muskan ji? It was at 7:00, will you tell me once? Tell me,

who said class was at 7:00? I had a class at 7:00. The thumbnail on the poster has a link to a class from two

days ago. Is sir angry? Hey brother, why would I be angry? Hey friend, why would I be angry with you guys? You

talk like this, son, and I'll get angry too. Tell me, can I do anything for you from this closed room in the studio?

Even if you abuse me, I can't do anything. I can only block you. I can't do anything beyond that. Tell me,

children have their own values. We're teaching here, son. We're giving you education. We're giving you education,

and that too for free, without charging any money. Now, if you say anything, we can't do anything about it from here,

son. Tell me, what can you do? Because neither you're a graduate with me, nor am I, so this doesn't make any sense.

Don't get angry, son. Anyway, look at the value of k. Use the same concept. I've written the alternate one in great

detail. Start adding from here. Come on . Add four to this, 12 12, and 5 to that, and 17 to eight, and you get 25.

So, from one side, you've got 25. Add the minus sign. From the other side, let's look at 7 and 4, 11 11, and K.

Now, add five to 11. So, if I add five to 11, it becomes 16 + k. 16 + k, this becomes 16 + k, son. Tell me this

quickly. Now tell me, what should I put in place of k? If it's 16, then you can make it 11. The maximum value we can

put in this is anything, like nine, I can put nine, son. If I put nine in place of 16, it will become 25. If I

put nine in place of k, it will become 25, so it will become 0; I don't think any value below that will satisfy me.

Even if I put six, no, no, no, it will be nine, son. As soon as I put nine in place of k, this 25 and this 25-25 + 25

will also be subtracted. It will become 0. Brother, I don't know what all these things are you saying today. Aditya is

saying," Sir, I won't answer now. "Son, I told you something. You tell me this. You think I'm angry with you? Yeah,

don't say that. I teach you guys with so much love. I don't know what your name is. Angry Girl Kumu, your name

must be something else. Okay. Let's move on to the next question, kids. Here's a new type. Tell me quickly,

dear children, what's the correct answer? Tell me quickly. Tell me quickly, what's the correct answer?

Keep breaking this down, son. Tell me quickly. Let's see what the correct answer is. Hey, where are you going,

Ranveer Singh? I don't want to go, son. Wait, wait, wait, study. Aditya Patel, I'll see. If you're so insistent, I'll

see, son. There's no problem. Study now , okay? Study now, my child. Tell me the answer to this? Tell me once, solve

it, friend. If I solve this number from the bottom, it means 3/2, right? And if we flip it and write it, this is the

second step, 1 + 2 ≡ 3, and if we solve it, it becomes 5/3. So this will happen with this, if we solve 1 + 1 +

5/3, it becomes 1/8/...sorry, sorry, sorry, sorry, sorry, this 8...1 second, where did you mess up? This is 3/2,

okay. And if we link 3/2 with it, it becomes 1 + 3/2, so it becomes 5 ≡ 2, and then we flip it and write it, 1 +

≡...hum...hum...oh, let's do it again . No problem, son. Look, if I solve this function, it means, sir, what is

3/2, son? 3/2, and we will flip it, because if we go up, it becomes 2 ≡ 3 , and if we write 2/3, it becomes 5/3.

Now, if we write 5/3 in reverse order, it becomes 1 + 3/5, and then we write it as 8/5. 8/5 becomes 1/8/5, so the 5

gets flipped to the top. So, sorry, it should be 5/8. Son, the answer to this question is 5/8. 'Is the correct answer

to this question?' 5/8 'Is the correct answer to this question?' Okay? 5/8 Let's do it quickly, son. We won't

waste time. There's still a little bit left. Wait just a little bit. I'll get it done quickly. Don't worry. Whenever

you get a question like this, look at this. For example, this is four. Write four. Below it is five. Write five. How

many times does this one appear? 1 2 3 Look, 1 2 3. Now add the next number to it. Add four to five, you get nine. You

add five to nine to get 14, and son, add this to 14 to get 23. How much do you get? 23. So, son, 23 will come up,

and what's just below that? First, 14, so 23/14, that is, option C is the correct answer to this question. Hurry

up, let's do it quickly. Tell me quickly, what's the correct answer? Hey , wait, read for a while. Your data

gets exhausted very quickly. Now do this question like this. Look, 1 2 3 4 5, so 1 2 3 4 5, and this is written as

two, and for that, it's written as three. Keep adding and writing. You add two to three to get five. You add two

to five to get eight. Add this to eight to get 13. Add this to 13 to get 21. Add 34 to 21 to get 34. How much is

just above that? 21 Tell me, isn't there a great trick? Did you enjoy it? So, this is how we break down such

questions, son. This is how we break down such questions. Is it clear? Tell me quickly. Next question. Do the next

question. Come on, son. This is the last type. It will be covered. Hurry up . Look, son, sometimes they'll ask you

to tell the largest fraction, or the smallest fraction. So, whenever such a question comes up, there are many ways.

But, son, what do you want them to do? Do them in semi-finals. Do them in semi-finals. How? This is 3/5, and this

is 2/3, and this is 1/2. What do you want them to do, son? Look, cross multiply. If I multiply this here, it

becomes 15. If I do it here, it becomes 8*3 = 24. So, 24 is greater than 15, so this is subtracted because you were

asked for a larger number. Now do this with this. If you do this with this, this will become 9, and this will

become 10. Hey, if you do this with this, nine will come and this will become 10. So this has been cut from

here. Now do these. This four has come and if it goes here then three will come. So this has fallen short. Remove

this. So where is 2/3? 2/3 2/3 C option is the correct answer of this question. 2/3 is the correct answer of this

question. 2/3 is the correct answer of this question. Dear children, let's move on to the next question. Solve the

next question in the same way quickly. What has been asked? The largest has been asked. The largest has been asked.

So see, you will put seven here. 7*4 for 28 9*5 = 45 Hey, if I do this here then this will become 45. This will

become 28. So cut this off beforehand. What is the need to write it? 13*5 = 65 and 77 so 65 has fallen short of this.

Now the son of 13 is 169 and 17*1 = seven of 17 and 17*1 = 17 and one 18 so this becomes 187 so if this falls short

then 11/13 will be bigger. 11/13 means D option is the correct answer of this question. D option is the correct

answer of this question. Tell me quickly. D option will be the correct answer to the question. So son, you

have to handle such questions like this . Tell me quickly. Which of the following friction is the largest? Now

sometimes he will give you options and ask which one is the largest among these? Tell me which one is the largest

among these? Tell me quickly son. Tell me quickly which one is the largest? Now see I am moving fast. Let me get

you through the maximum number of questions quickly son. You also have less time because data is also consumed

friend. It is not just like that. Quickly tell me which one. Okay, tell me quickly. I'm waiting for your

comment. Hey, tell me, 7/8 is coming for Ranveer. Let's see, brother. Okay, let's get a question like this. What

happened in the previous question was that we had given four values. I crossed it out. Now how about this, sir

? So, here, son, you can either go logical or do one thing: get the semi-finals. Semi-finals means get them

done like this. Write down the starting two. Get the semi-finals in the starting two and get the semi-finals in

the last two. Get the semi-finals, get the last two. Pick any two. It depends on you. It's not a problem. Now pick

from these. 13*4 = 52, this will become 520. 16*1 = 16 16*3 = 48 49 49. So, brother, this is smaller. So, from the

top one, I got the bigger one. Okay? Now let's look here. 8*7 = 56, this will become eight. 8*3 = 24 plus 4 and

8*6 = 48 49 50 This becomes 504 and this 560. This is eliminated from this. This is eliminated from this. So now we

have these two numbers. Now finalize them. So 13 by 6 and son, this 7/8. Now do 13 here, get 13 here, read the table

of 13. 13*8 = 104 and here 16*7 = 112. So, 104 is the smaller number, so which one is the bigger one? 700, sorry, 7/8.

7/8 is the correct answer. So, look, both of them have different approaches to asking the question. If I had four

numbers, I would cross-multiply and check. But here, there are not four numbers. There are four options. So,

you pick two each. First, I picked the starting two, got the bigger one, and then picked the last two, got the

bigger one. So, they'll have them do the semifinals first, and then the finals. Is it clear? Let's move on to

the next question. Son, you can do this question, son. I'll give it to you as homework. Tell me, what's in it? Son,

can't you do it? I've made you do three or four" What is the largest number? " questions. You can do it quickly; it's

no problem. Is it clear? Tell me! Do it , son, it's simple. Let's move on. What is the smallest number to multiply 2940

by so that the product becomes a perfect square? You'll see questions like this in the paper. Quickly tell me

the correct answer. Tell me the answer, my children. Alia Sir is going to the temple. Wait 15 minutes, go to the

temple, and I'll finish it after that. Go on. Look, son, what's the point of this question? Do it using the

factorization method. Factor it out. For example, brother, this is written as 2940. Now subtract it. By what, son?

First, if I look at the sum, will 14 be subtracted from seven? Should we try with two first? Let's do it with two. 2

*1 = 2. Then subtract two four times. One is left over from two. Okay? This is four. Then subtract two. So 2 7 14 2

*1 2 and seven times, no, this is subtracted seven times. 2*3 = 6 and 2*5 = 10, we get 35. Now by what, son? Five

. Subtract it from seven. 7*1 = 7 0 7*5 = 35. Subtract it from seven. 7*1 = 7 7 *5 = 35, okay? Divide 15 by three, it

will be five. Then five will be five. Now look at the pair. Look, son, this is a complete pair and seven also has a

complete pair. But here, a pair is needed with three, and a pair is needed with five. So, one needs three and one

needs five. So, 3*5 means, how much more do you need, son? 15. That means, option D is the correct answer to this

question. D option is my child's question. Yes, Rajput ji, you have come . Very good. Okay? So, son, the correct

answer to this would be 15. Try one more question like this and tell me. By which smallest number should 2100 be

divided? Look, it's obvious. If we look at 2100 as 21*100, then 100 is a perfect square. If we want to make 21

also a perfect square, then we need another 21. So, what will we need? 21. Only then will it become a perfect

square. Hey, don't factor it. You can write 2100 as 100*21. So 100 itself is the square of 10. But this isn't. So if

I need another 21, I simply multiply it by 21*21 to get 441. So 21 is the correct answer to this question.

Quickly, son, tell me this question. Look, where did this question come from ? I told you there's a trick. A person

has some chickens and some cows. Each of them has legs. Represent them with the letter L. Dear children, the number

of legs is 140, and the number of heads (head means head) is 48. So, you've been asked to tell the number of

chickens. Meaning, you've been asked to find the number of two-legged ones. You've been asked to find the number of

two-legged ones...So, I told you how to find the number of four-legged ones. I told you, divide the number of legs by

half, 70, and subtract 48 from it. Subtract 48 from this. So, how much is left? 22. Now, 22, so which ones are

included in this, son? 22 are those with four legs, meaning crows. Now, how many were there in total? 48. So,

subtract 22 from 48, and you get six, these two. So, 26 will be the correct answer to this question. What will it

be, children? 26. There are many ways to solve this question, dear children, but I have told you the best approach.

You have to fulfill this condition. Okay? Yes. Look, you might not know this thing. You might be having doubts.

Look, what did I tell you? How many legs are there? 140. How many heads? Head means you need heads. How many?

48. So, son, if you're ever asked about four-legged animals, divide the number of legs by half and subtract the number

of heads, you get four. So, legs equals 140, which is halved. How many do you get? 70, and if you subtract the number

of heads from 70, how many do you get? 22. Now, 22 are the cows, cows, etc., meaning they have four legs. But he

asked about a hen, which has two legs. So, how many were there in total for 22 ? 48. If you subtract 48 from 48, then

26 is the correct answer to this question. Let's move on to the next question, son. Look, this new type has

come. In this too, you have to tell which of the largest among the numbers is the biggest. Which is the biggest

number among these? This is a very good question. Tell me quickly. Hum Hum Hum, Miss Sharma is saying, I will copy. If

you want to copy, then you have to ask a question only. There are many things in the world. Copy Katrina Kaif. Copy

Deepika Padukone. Copy Alia. Move ahead in life. You have to do the questions. Only then will you get a job. How will

you get one by copying? Son, you tell me. Oh, ho, ho. Let me get you to do one such question. After that, Ranveer

is asking for the next one. Now, everyone, pay attention. See how you will do this question. Look, dear

children, if the under root is five, then it means basically 5 to the power 1/2. Now, if q is 7, then it means 7 to

the power 1/3. And if it is 13, then we will write it as 13 to the power 1/4. Write this much. After that, pay

attention to the denominator of the power. This is two. This is three, and this is four. So, tell the LCM of 2 3 2

3 4. Tell the LCM of 2 3 4. So the LCM of 2 3 4 will be 12. So, we will make these 12. We will make these 12 and

these 12. So this will be divided by this, sir, six times. Yes. Okay? How many times will this be divided by this

? Four times. And this will be divided by this, three times. Now understand the logic, son. 5 to the power is six.

Okay? And what is this to the power of seven? It is four. And son, how much does this become? It is 13. What is the

power of 13? It is three. What is the power of 13, son? It is three. Now I have got this much. Now you try solving

it. Let's be a little logical. You tell me, 6 to the power of 25 is. I don't know what it is. But 3 to the power of

25 is 125, right? So 125*125 must be this number. Yes or no? Now how much is this? 4 to the power of 7, so I don't

know 4 to the power of 7. So what is the square of 7? 49*49 must be this number. Is it clear, dear children? Now

this is the cube of 13. No matter how much it becomes, if you multiply 13*13* 13, you'll go crazy. Don't do it. You

need to use a little bit of intelligence. Look, if you see these three numbers, then I see that if we

multiply 125*125, this will be the largest number. This will go on the second number, this on the third.

Because tell me one thing, what will be the cube of 13? What is the cube of 12? 17, 17 28; what will be 2197 for 13?

2197 is only 2197 as far as it goes. So this number is smaller than this, and if you multiply it, it becomes 24 001,

and this will go much higher. So this is the largest number. This corresponds to this, so it means you've been asked

for the largest number here. So the largest option is the correct answer to this question. Option A is the correct

answer to this question. Apply logic to this question. If you think you'll do it by extracting the exact data, you'll

go crazy. I didn't even multiply. Just look at this, the approach has reached this point. What does 5 to the power of

6 mean? 5 to the power of 3*5 to the power of 3 means 125*125. 7 to the power of 4 means 49*49. Now, will 125*

125 be greater than 49*49? Don't multiply. And the cube of 13 will be smaller than both of these. It's

clearly visible. So, this is the bigger number. If you had asked for the smaller number, this number would have

been the cube of 13, and 13 was corresponding to this and this was corresponding to this. So, this number

would be the smallest, sir, and this number would be the largest. Tell me quickly, is your concept clear or not?

Now you'll think, multiply this. Hey, I'm not making you do any calculations. You're being asked which is bigger and

which is smaller? Tell me quickly, is it clear or not? There's just a little more time left, son. Let's do it

quickly. We have five or seven minutes left because we'll miss the question. It won't be fun. Hmm, hmm, let's do

this question quickly. Is this a repeat ? No, no, no. Tell me quickly. For example, write 1/3 of 6 as 1/5 of 5 as

1/6 of 12 as 1/6 of 12 as 1/6 of 12. Do it quickly. Do it quickly. Now, son, take the LCM of all of them. Tell me

the LCM quickly. What will you get? It will be 30. Tell me quickly, which one is bigger? You don't have to multiply.

You have to use logic. Ranu Yadav, you didn't understand. You'll get this question right away. If we do this

question, it will become more complicated. Don't worry. Don't worry. Tell me what the correct answer is.

Don't multiply. We won't calculate the exact data. Calculating the exact data will waste a lot of time. Option 1:

Okay, now tell me, like this is in the denominator, isn't it? This is three, and what is this? Five. And what is

this? Six. Look carefully at the children who had doubts. So, their LCM is calculated. What did you get, son?

30 is the answer. Anything less than 30 won't work. So, write*30 and*30 is the answer. This calculation is getting

very lengthy. 30 is subtracting this from this, and it gives 10. 5 is subtracting this from this, and 12 is

subtracting this from this, and what is the power of 12? It gives five. Okay? This question has become quite lengthy,

son. It doesn't even cover this much. All are equal. All are not equal. Who is the biggest? Okay? Now, look, in

this, we have to write 6*6 10 times, and 5 15 times. Tell me, this is a very lengthy calculation. How was this data

obtained? Because even if we were to solve it on paper, I would explain it right now, but according to the paper,

it would be very lengthy. Tell me. What else can we do? This square q doesn't become anyone's. This is 5 to the power

of 6. What did you get, son? This is a very lengthy calculation. 6 3, but you couldn't have calculated it exactly,

son. Who calculated it exactly? Not with a mobile calculator, but without a calculator, because we don't get a

calculator on paper, son. Okay, this is correct, correct, correct, correct, correct. This, this, this was written

wrong, no one. This won't be 15. Well, if you subtract this from this, it will be 6, so six is obtained. So this is 10

of 6, and this is, so this is eliminated here, this is eliminated, which means it won't be 5. The 5 one

won't mean this. It's gone. Remove it. Now, we have to sort this out from the two. We need to apply a little logic

here. So, this is 12 to the power of 12 , and this is 6 to the power of 10. If I use logic, I can write this, son. I

can write this, 36 to the power of 5. Oh, yes or no? Okay, of course I can write this, the square of 6 to its

power. And if I use logic, this becomes 5 to the power of 12. Done! Look at the logic! It took me so long to understand

! Come on, look at this, son! I'll explain it to you all. I wrote this one by mistake, no problem. Now, first look

at this one: 5 to the power of 6, and this one to the power of 10, so this one has already been removed. Now, I

was getting confused between 6 to the power of 10 and 12 to the power of 5. What is 5? So tell me, can I also write

10 to the power of 6 as 5 to the power of 36? Oh, this 6 is the square of 6, because the power of 6 is 10, so I can

also write it this way: 10 to the square of 6 and 5 to the power of 5. When we do this, it becomes 10. So, 5

to the power of 36 and 5 to the power of 12, brother, when the power is the same, the number with the larger base

becomes the larger number. So, the one with six will become the largest number , son. This means this number is the

largest, and if asked for the smallest, you can find it. This one came in the first place as the smallest. Yes, you

saw here, we're not working out the exact number, but we're taking a little approach. Tell me, is it clear, son? Is

it clear? Say it quickly. Yes, let's do such questions, dear children. I'll get you to do one more such question. This

is the last one. After that, do two or four more questions if you don't have any left. Well, that's it. This is the

last question, and after that, I'll bring a couple of questions into the practice set and I'll get you cleared

there. Don't worry, son. Look at this question and see how it's broken down. Look at this question and see how it's

broken down, son. Let's see how we break it down, I'll explain. This is a power, son. If you look at the HCF of

this power, you'll see the highest common factor as 50. How much is it? 50 , nothing is visible above 50, sir. So,

if I divide this by 50, I divide this by 50, it'll be divided five times, and write its power as 50. Okay? If I

divide this by 50, write it three times and its power as 50. If I divide this by 50, it'll be divided twice, and its

power as 50. And then I'll divide it by 50, so how many times? Son, if I divide by 50, it will be four times and its

power will be 50. Now look at the base. 2 to the power of 5 means 32. So, brother, 32 to the power of 5 is 50;

cube of 3 is 27, 27 to the power of 50 is 50; square of 5 is 25, 25 to the power of 50 is 16*16 i.e. 256 and its

power is 50. My son, all powers are the same. The one with the bigger base is bigger. The one with the smaller base

is smaller. Now you were asked which is the smallest number? So which is the smallest base? 25 and 25 are

corresponding to this. And what is this corresponding to? Five means this 100. This number is coming, son, the third

one. This will be the smallest. This will be the smallest. And the largest one is this last one. Where did this

last one go? This is this 4 to the power of this and in this this one will become the largest. Tell me quickly, is

it clear or not? Son, I didn't do anything. The HCF of all these powers is 50. Divide it by 50 five times. So,

2 to the power of 5 means write 32 to the power of 50. Divide it by 50, write 3 to the power of 27 to the power of

50. Divide it by 50, write 25 to the power of 50. And divide it by 50 four times, and 16 to the power of 4 means

256 to the power of 50. This is the base...because all the powers are the same, so the number with the larger

base will be larger; the number with the smaller base will be smaller. Meaning, if its base is small, it will

be small; if its base is large, it will be largest. Tell me quickly, is this trick clear to you or not? Tell me

quickly, dear children, is the concept clear or not? Oh, tell me quickly, okay . Yes. Very good, son. So, in such

questions, we don't extract the exact data. We'll try to find some ideas. The rest of today's class will be limited

to this, son. See you tomorrow. I won't have class today. I've already taken Sunday evening, and tomorrow is Monday.

Tomorrow is our time from 9:00 to 10:00 , and you'll get the practice sets with them. Miss Sharma, did you really

understand? Okay, that's good, clear. Okay, son, then enjoy yourself. We'll meet in the next class. Be sure to

watch today's class once later; it's a very important class. Okay, say it quickly. If anyone has something to say

, you'll say it again. Ranveer, enjoy it, son. See you in the next class. See you tomorrow. Okay, son. Rajput ji,

very good, son. Okay, okay. Yadav, Ranu , Alia, Miss Sharma, thank you. Okay, sir, very nice class. Okay, okay, okay,

thank you so much. Angry girl, Komu, clear sir, very good. Come on, son, we'll see you again tomorrow at 9:00

with practice sets. Okay, we'll end today's class here. Thank you so much, dear children, thank you so much for

staying tuned for so long, and see you tomorrow. Thank you so much.