CMA Foundation Maths | Permutation and Combination | L5 | Dec 2026 & June 27 |CMA Pushkaraj

[00:01:08]Hello hello hello hello hello hello good afternoon everyone how are you everyone is eating chips yes very good afternoon to all of you yes join let's start all set all good yes come on Princess is speaking would you like to say something about the protest? Don't say anything. Don't talk about maths, let's talk about maths. Isn't it? Let's talk about maths. So if we talk about work in life then there is no time left to talk about other things. So let's talk about work.

[00:02:40]Why?

[00:02:45]What? Yes, five minutes remain until the last [laughs].

[00:02:47]Correct. Correct. Correct. Ok friends let's begin.

[00:02:53]So till now in permutation combination we have done factorial questions. Did the permutation questions. Did the combination questions.

[00:03:02]Now two concepts are left. We will complete two concepts today and end the chapter. Come on, yes.

[00:03:13]So write it down in your notebook.

[00:03:19]Then you also go to the protest.

[00:03:24][laughs] Circular Permitation Toh Phir TV Pe Dikkha Tu. I went to Jantar Mantar [laughs] Did you play Kabaddi then, you used to be seen on DD Sports, okay, different Kabaddi [laughs] You will be seen playing Kabaddi with the police Circular permutation [laughs] Okay friends, write down the number of ways in the circle of permutation. The number of ways in case of circular arrangements is equal to n-1. Real huge congratulations to you, you passed that n-1. Okay, listen, what does circular permutation mean? The permutation questions that we have done till now are called linear permutation. Linear means arrange in a line.

[00:05:13]When we were forming equal words, we were arranging the letters in a line but when we talk about circular permutation, the letters are arranged in a circle.

[00:05:26]Maybe some people may have a circular dining table at home or if you go to a restaurant, there may be a circular dining table there. So if the arrangement has to be done in that type, then conceptually it becomes a little different and the formula becomes n - 1 ordinal. Let's see how it is made. Ah, don't write, just look at it.

[00:05:47]If I write an arrangement A, B and C it is an arrangement. But if I write it like this then friends this is not a different arrangement.

[00:06:02]This is the same thing. Just like the previous arrangement, this arrangement is the same. Now why is this the same arrangement? Because if you look from A's point of view, A is looking towards the table.

[00:06:17]So where is B? It is on his right side.

[00:06:19]Equally, and here also you can see B is on its right side. So there is no difference in the arrangement. Both of them are the same.

[00:06:28]Then if I want to create a different arrangement, how should I do it? See this. What needs to be done in this? A person's position has to be fixed.

[00:06:40]I fixed the position of A with the lats.

[00:06:42]Ok? And if I write like this now, will these become two different arrangements? Isn't it? This A B C arrangement and this AC CB arrangement look different. Right? So what did we do in such a case? The position of one person was fixed. Fixed A. And we arranged for the remaining two people. So if I ask you how many ways can you arrange two people? So we can simply write 2p2 equal to two people to arrange, so two people are available to two people.

[00:07:19]Both have to be arranged. So what condition will you write? How to solve 2p2 and 2p2? 2 * 1 means what will be your answer? Two. Now I have told you the logic behind it that after fixing one person, the remaining two people have to be arranged.

[00:07:36]But instead of sitting and applying logic in all these exams, it is better to use the formula directly.

[00:07:42]So in the formula, n - 1orial means 3 - 1 log 3, right? So how much will 3 - 1orial cost? 2 means how much? 2 * 1 vs 2 so we have seen it logically. The answer will come and by using the formula we found it out directly. If it is equal then you can definitely use this formula in the exam in case of circular permutation.

[00:08:14]equal to n - 1orial, rest of the conditions that come, always together, never together, we have to proceed in the same way as we did in linear permutation, you remember vowels always together etc., we had talked about such things, the same will apply here also, I will teach you how to do it by taking some questions.

[00:08:37]Ok? Let's write the first question.

[00:08:40]First Questions Let's start with the basic questions.

[00:08:44]In how many bases In how many ways five persons can be arranged at a round table at a round table okay. Underline the round table.

[00:09:13]This will make you understand that this is a case of circular permutation. Will the table be round or in a circle or to form a ring? Have to form a ring. What does this mean? Circle of permutation has to be done. Ok?

[00:09:27]How many people are available? Five.

[00:09:30]Arrange them in a circle of patterns. What condition will you write? n-1orial means how?

[00:09:36]5 - 1 so this will come 4 means 24 that's it, answer yes 24 correct equals so first question is done now we will do second question in this I am going to make you do three different questions, okay note down three boys and three girls are available.

[00:10:14]Three boys and three girls are available.

[00:10:23]In How Many Ways?

[00:10:31]In How Many Ways? First question they can be arranged at a round table in how many ways they can be arranged at a round table second sub question in how many ways in how many ways girls are always together in how many ways girls are always together and third sub question in how many ways girls are never together in how many ways girls are never together okay. Well, the first basic question is this. The first question is basic. What can be done in this? How many people are there in total? There are six. Three boys and three girls. Number of ways they can arrange at a round table.

[00:11:47]The formula is n - 1orial. Meaning there are six people.

[00:11:52]6 - 1 that is equal to 5 vs. that is equal to 120 so the first answer is straight forward simple done equal till here. Okay, let's see what the second question says.

[00:12:14]Girls Are Always Together. Okay listen, there are three boys.

[00:12:19]And there are three girls. Ok? Do you remember the condition of Always Together? What did I keep you doing? Let's create a group in Always Together.

[00:12:32]What do you do with those who have to be kept together? Let's form a group. So write it down like this in your notebook.

[00:12:38]These will be considered as one. These will be considered as one.

[00:12:42]And the remaining three are boys. And we will total them.

[00:12:47]3 + 1 that is equal to 4, did you understand till here? Ok. Now four persons at a round table can be arranged in how many ways? Four Persons at a Round Table. For how much?

[00:13:03]4 - 1orial 24 No re. Round table. Have you forgotten? 4 - 1oriel. This is the first thing that came. Ok? 4 - 1 Do you understand how this four happened? How did it happen?

[00:13:21]A group was formed of those who needed to be kept together. I accepted him as one. The remaining three are boys. 3 + 1 together makes four. 4 - Why did 1oriel -1? This is the formula for circular permutation. 4 - 1orial. But this is not the only answer.

[00:13:40]I told you one more thing in the case of Always Together.

[00:13:43]Internal arrangement.

[00:13:46]How many people are in the group for internal arrangements? There are three. Equal. Now those three people have to arrange all three of them. There are three available and all three have to be arranged internally. Its condition will be written as 3p3. What will you write? 3p3. Now a question may arise in your mind.

[00:14:08]Sir why didn't you do 3-1orial here? Here I have done 3p3. At first you were doing 4 - 1orial. Listen to the reason for this. The reason for this is why did I ask you to do -1?

[00:14:25]One had to be fixed. Now that one has been fixed here, what is the need to fix the other one? So this n-1orial has to be done only once.

[00:14:35]And then normal 3 p3 equals. Now solve this and tell me what is your answer? They are saying 36 is coming.

[00:14:44]So this 3ial will come as 3 * 2 * 1 6 and this 3p3 means it will come as 3 * 2 * 1 so this will also come as 6 * 6 means 36 correct.

[00:15:00]So what did we do in this?

[00:15:03]A group was formed of those who want to always stay together. Then the remaining three and one group together made four. Four people have to be arranged in a circular way. So did 4 - 1orial.

[00:15:15]And then not only their arrangements but internal arrangements also have to be made. There are three people in that internal group. All three have to be arranged. So the condition is written as 3p3 done. This is the answer to the second question 36.

[00:15:31]What is the third question?

[00:15:34]Never together. remember what? For Never Together.

[00:15:37]What do you do? Have you done the total minus Always Together total, what is the result? 120 and Always Together total is 36, so subtract Never Together, yes 84, 120 - 36 = 84, so basically you are understanding that the concepts of Always Together and Never Together remain the same. Only this is a circular permutation so n-1 is coming to the real. It is equally correct.

[00:16:10]So far so good. Okay, you will ask yourself the next question.

[00:16:14]You will ask yourself the next question.

[00:16:20]In How Many Ways?

[00:16:23]In How Many Ways?

[00:16:26]Four boys and four girls.

[00:16:32]Four boys and four girls can be arranged.

[00:16:37]Can be arranged at a round table At a round table True that True that girls are always together True that girls are always together I have just asked the question of always together so think like you did it and solve it perfectly.

[00:17:12]Solving it properly. Yes yes correct yes how did you do it? 576 Can you tell? What does Girls Always Together have to do? Have to form a group.

[00:17:41]How many people were there in total? 4 + 1 Who will do this?

[00:17:47]Who will +1? Yes. So there are five people.

[00:17:51]Five Persons at Around Table 5 - 1orial. It is correct. Do you want to stay here after this?

[00:17:59]No. Then what to do? The internal arrangement is four, right? So what condition will we write for it?

[00:18:06]4P [screaming voice] 4p3 is saying that all four of them have to be arranged, right? 4p [screaming voice] 4, so this will come 4, meaning 24, this will also come 4 * 3 * 2 * 1, meaning this will also come 24, the final answer is 576, have you understood, yes, let's do one more question, I will make it a little shorter and add a twist to it. Should I tell you? Ok. Write.

[00:18:42]A B C D E & F A B C D E & F Are to be arranged Are to be arranged at a round table in how many ways?

[00:19:11]In how many ways?

[00:19:15]F is always F is always on the immediate right of e.

[00:19:29]Yes.

[00:19:31]F is on immediate right of E.

[00:19:42]So think and solve it and tell me the answer, I am getting 24 for it. Your 48 is coming up.

[00:20:23]Your 48 is coming. Online students are speaking 24. Some people are saying 48.

[00:20:33]Well F is on immediate right of e. So tell me what did you do?

[00:20:40]They formed a group.

[00:20:42]Ok. So how many people are there in total?

[00:20:45]Four these A B C D plus one group.

[00:20:50]How many are there in total? Five. Equals five persons at a round table. Tell me the condition.

[00:20:57]5 - 1 then its 24 will come, internal arrangement is saying 2p2, he is saying 2p2, you are also saying 2p2, are there two people, will they do it here and there, it cannot happen, why can't it happen, it is fixed, why is it like this, it is given, what is given, it is immediate right, immediate right, if someone sitting on my right, let's say I move him here and there, then he will come to my left, right. Are you understanding the matter? So there will be no internal arrangement.

[00:21:35]So the only condition is 5 - 1orial. Did you understand? So what will be the answer? 24 Do n't get trapped like this, just like that.

[00:21:56]How are you? What kind of Kabaddi player are you? If the person in front of you gets you out and goes away, you will remain sitting. Only we are seeing you, we are seeing you in place of Manjeet Chillar.

[00:22:12]You are busy here in the small party. What about that, let's take one last question of this type.

[00:22:40]Universe Boss but now a baby boss has arrived.

[00:22:51]Let's go yes let's write next one last question I am taking circle paration ka yes A B C D E & F A B C D E & F are to be arranged are to be arranged at a round table at a round table in how many ways is na in how many ways E is always E is always in between D and F E is always in between D and F. Let's see what suits you?

[00:23:55]You solve it and tell me the answer. You don't know me.

[00:24:00]I don't know.

[00:24:22]Some people are saying wrong six. Some people are saying 36. Here's what Princey says: 12. So what answers have we received so far? One too has come. A six has come. A 36 has come. A 12 has come.

[00:24:39]What are online students saying here? 12 6 2 12 6 What do you say? There are 12 answers. Equally [laughter] yes. Tell me how did you solve it? Tell me.

[00:25:02]Which three did you group together, okay, so they form a group, yes, then these are three, so plus one they become four, okay, why did you do -1, tell me, n - 1 is the formula, it is over, six came, these 2p2, why can you move D and F here and there, can you do it with E or not, why ca n't you, it is fixed, it should be in the middle, right, for this you can move D and F here and there, right, what condition will come, 2p2, which two you are moving here and there, like Akshay Kumar's reel, F and D, right, 2p2, so 4 - 1 means 6, 2p2 means 2 * 1 means 2 6 * 2, what will be the answer? 12 [laughter] has arrived. Friends, have you understood? For which different answers came.

[00:26:29]I don't know how he got 36. I had brought six different answers. Six Six who brought it. I think they didn't interchange D and F. All three were interchanged. So what went wrong with you then?

[00:26:43]So, you are telling me what wrong people did? If something goes wrong in life, contact Kamal. What's wrong? He will tell you. [Sound of clearing throat] So [laughter] yes, I understood, did you understand, online students, have you all understood this circular permission, okay, so you have understood the circular permission, so now I am taking you to one last part, we will finish it, we will finish the chapter, I mean, take two questions. Maximum times two questions came.

[00:27:32]Dharma is asking why you did not do 2p2 in the previous question? Because where was the f needed? On the right side. If it is moved here and there then it will go to the left side of FE.

[00:27:42]Not allowed. Is it or not? Let us speak.

[00:27:49]These two can be interchanged.

[00:27:50]D E F No D and F can be interchanged.

[00:27:54]Yes, what would you say, where is the facing, what difference does it make?

[00:28:04]Why? But send him to the mental asylum.

[00:28:13]So you go to the protest, yes, yes, go to the protest there, you will be beaten by the police [laughs] then you will come to the line like this [laughs] come on, if there is some problem in life, then you will have to contact him, you will take him along, why should I say that I will fight alone?

[00:28:45][laughter] Okay, let's move on to the next concept.

[00:28:53]Giving headings in your notebook. Questions related to digits Questions related to digits are important. Ah, questions related to digits may come in the exam. I mean, look, the permutation is a simple one that we have done till now, simple means that there was variety in it also, but where there is a simple arrangement, combination means selection, where yesterday we saw a lot of questions that there should be at least two boys. There should be exactly two boys.

[00:29:35]A particular boy has to be included.

[00:29:37]One particular boy has to be excluded. I have become like that type. Then today I saw variety in Circular of Permutation. Now this is the last part question related to digits. Now write a question in it.

[00:29:48]Then I will explain to you in detail what varieties can be there in it.

[00:29:52]Note down the first question. How many three digit numbers? How many three digit numbers can be formed? How many three digit numbers can be formed.

[00:30:18]Using digits of Using digits of decimal number system Using digits of decimal number system If If first sub question Repetition of digits Repetition of digits is allowed.

[00:30:52]And second sub question repetition of digits is not allowed.

[00:31:06]Ok? First understand this completely. Ok? Then you can ask the next question yourself.

[00:31:11]But understand the first question very well. Firstly, the wording used in the question is digits of decimal number system.

[00:31:20]This means where to get the digits from 0 to 9? All these digits from 0 to 1 2 3 4 5 6 7 8 and 9 are called digits of decimal number system.

[00:31:38]Right? Ok?

[00:31:40]So how many digits do you have available? It is 10. 10 zeros are considered, 1 2 9 is not there, so 0 is 10 digits. Now how many digits number do you have to make? Three digit.

[00:31:53]So my suggestion is that you should mark as many places as the number of digits you want to make.

[00:31:59]1 2 3 equals. Ok. Now there are two cases. One case is repetition of digits is allowed. And there is a case where repetition of digits is not allowed. Ok? Now listen to me. What am I saying? First of all, check whether there is any restriction given in the question? That means the number should be less than 400. Hey look here crazy, look here, everything is going on for you. Isn't it? Is it less than 400? Do you need more than 500? Have you given any such condition? Not given. But the condition is not given in the question. Still I am saying that there is one restriction.

[00:32:43]What is that restriction?

[00:32:46]We cannot put zero in the first place.

[00:32:49]Why? Why can't you keep it? For example, if I write 0 25 like this, will it become a three digit number or a two digit number? Will it become a two digit number? 0 25 means it would have been 25. If you put zero first then it has no value.

[00:33:04]So we cannot place zero at this place.

[00:33:08]So you can place any other numbers.

[00:33:10]So tell me, first place can be filled up in how many ways? Nine Ways.

[00:33:15]What numbers will work? 1 2 3 4 5 6 7 8 9 equals. So here I am writing nine.

[00:33:22]Friends, understand one thing. This number nine is not written. This is the number of ways.

[00:33:29]These are the methods. You can place any one of these nine numbers.

[00:33:32]Equals now repetition of digits is allowed.

[00:33:40]What this means is that if I am just talking about an example, let's say. I make up the number 455 is it allowed? Yes. This same digit is coming. But what did I tell you in the question? Repetition of digits is allowed. Equally so first place filled up with nine ways. Call me second place.

[00:34:00]What numbers can you keep? You can keep any one. You have no restrictions.

[00:34:05]So you can keep any digit from zero to n.

[00:34:08]So these will be 10 ways. And in the last place again put any digit 10 ways.

[00:34:14]How does it matter? So these will also become 10 ways.

[00:34:16]So first place pe 9 ways and second place pe 10 ways and third place pe 10 ways. So what will be the total numbers? There will be 93 digit numbers. If repetition of digits is allowed then no.

[00:34:40]Now let us look at the second case: Repetition of digits is not allowed. So the restrictions of the first place will remain the same.

[00:34:50]Why would Nine Ways have such a restriction on the first place? Zero cannot come in the first place. You can keep it for later.

[00:34:57]So Nine Ways will come in the first place.

[00:35:01]How many ways can we fill up on agreed par other place? Second place nine. Why Nine Ray?

[00:35:11]One digit has been used. For example, I placed five first. Let's accept it.

[00:35:15]So how many are left now? Nine numbers. So second place can be filled up in nine ways.

[00:35:22]Now tell me the third place.

[00:35:25]Third place third place at why at two digits got reduced one digit went to the first place one digit went to the second place then how many eight 10s were left with us so the last place can be paid up in at that is correct then the answer will come 9 * 9 * 8 means 648 at first I understood it to be equal let's do its variety now let me tell you the next questions everyone is done till here question to how many four digit numbers how many four digit numbers can be formed using digits [nasal sound] 1 2 3 4 5 6 if if first question repetition is allowed second question repetition is not allowed.

[00:37:09]Ok? Now listen to me. In the previous question I told you that the digits of decimal number are 16. This means that all digits from zero to n were available. Not all digits are available here. Which ones are available? 1 2 3 4 5 6 Only these six digits are available. The first question is Repetition is not allowed.

[00:37:30]How many digits number do you want to make? How many digits number do you want to make? Four. So mark four places. 1 2 3 4 Okay?

[00:37:40]First Place Can Be Filled Up in How Many Ways Say.

[00:37:45]How did you answer the first place, tell me out of how many, six, oh six, but in the previous it was written as nine, so there was zero there, there is no zero here, so you can use any digit out of six, 6 * second case six, how can you use any six, you can repeat it any number of times, there is no problem, so 6 * 6 * 6 * 6 what is the answer, 1296 is matching, see, and second repetition is not allowed 360, how can you give the first place six, way, second place pi pi, why one is reduced, right, we cannot use the one that was used, so one is reduced, then four and one is reduced, then three and one is reduced, what will be the answer, is 360 added, is it added, is it added, everything is added properly, yes [nasal sound] should I tell you the next one? Write how many, now I will put restrictions. Now the condition is yes how many?

[00:39:01]How many three digit numbers?

[00:39:06]How many three digit numbers less than 400 How many three digit numbers less than 400 can be formed using digits These digits are 0 1 2 3 4 5 If If Repetition is not allowed I am giving only one case.

[00:39:51]Repetition is not allowed.

[00:39:57]Ok? Listen, now listen carefully. How many digits number do you want to make? of three. So mark three places.

[00:40:04]1 2 3 Now there are some conditions in the question. What is that condition? Less than 400. Well, when will the number be less than 400?

[00:40:19]Meaning, what all first?

[00:40:23]Which numbers can be used with the first digit? 1 2 3 That's all Zero ca n't do. Why? If it becomes two digit then zero cannot work.

[00:40:36]Is it clear? The forest can move. Yes. Meaning, let's assume that I made such a number, 125 is it less than 400, it will do.

[00:40:44]If I create a number like this, 243 will work. If I make a number like this 315 will work.

[00:40:52]What does it mean? That I can keep one, I can keep two in the first place.

[00:40:59]Otherwise I can keep three. Made 4 05.

[00:41:02]Will it work? No, it will be bigger than 400.

[00:41:05]Then in the first place we have 1 2 3 meaning first place can be filled up in three ways. Three ways. What are these three? Three, this number is not kept. There are three ways.

[00:41:18]Those are the ways. Equal now second place. Second place. Repetition is not allowed. Second place.

[00:41:28]fi how? How is Fi? Correct. Brother is right. But how?

[00:41:33]What are these three? What are these three?

[00:41:37]Why won't zero work? Yogesh is speaking. Hey, if you put zero here then it will become a two digit number.

[00:41:41]So what has been said in the question? Three digit numbers have been spoken. Isn't it? Yes. Hey, listen to me. Yes. Why would Five Ways come in second place? I need the reason for this. At least one number has been used. Any one number out of 1, 2, 3 has been used, right? Let's assume that we have used that two, how many five zeros are left, so it works, any one of the five digits in the middle is equal and one is reduced, now the last place is 4, yes [laughs] but you understood it well, 60 is correct, take the next question, let's do the last question.

[00:42:44]3 * 5 * No wait wait 1 2 3 * 6 * 6 would come is 3 * 6 * 6 is there or not now let me get that done how do I get it done wait wait wait wait yes yes write how many how many four digit how many four digit even numbers how many four digit even numbers can be formed using digits 1 2 3 4 5 6 seven if first case repetition is allowed and second case repetition is not allowed.

[00:44:03]Okay listen, now the first case is the case of repetition allowed. Tell me how many digits number you want to make. Let's see how to do four 1 2 3 4. Let's see.

[00:44:21]I don't know what the answer is. I will calculate it and see.

[00:44:25]A Tell me what are the restrictions in the question? I need an even number. When does even number mean even number? Any number?

[00:44:33]Even number is required at the end. So in the end either it will be two, or it will be four or it will be six. If we keep 1 3 5 7 at the equal end then it will become an odd number.

[00:44:45]Equal to what? So tell me Last Place can be built up in how many ways?

[00:44:50]Three ways. Correct.

[00:44:53]Now is there any restriction for the remaining numbers? No. So what else will come for this? When repetition is allowed 7 because seven digits are available.

[00:45:05]You can repeat any one. 777 1029 Are you getting the same answer 1029 Let us now look at the case of Repetition Not Allowed. Even in Repetition Not Allowed, the last digit will come from three ways only.

[00:45:27]Now how will the remaining people do it?

[00:45:31]One use has been made. Let's assume it's over.

[00:45:34]Then six are left, then five are left. Then four remained. So 6 * 5 * 4 * 360 is 360 plus what? Did you understand the whole chapter? Commutation and combination done, now repetition is allowed, so how many times can we take the digit? Can you take it any number of times?

[00:46:14]Urmila, you will have to look back then.

[00:46:24]Why did you keep three? You didn't keep number three, you fool. That is a three way thing. If I ask you 1 2 4 6 is it an even number? Is this an even number or not? Is this number an even number or not? 2 1 4 4 2 Is it an even number. Yes.

[00:46:49]2 5 3 4 Is it an even number? So who decides the even number? Last place. So what will you do with the last place? If two does n't work, then four doesn't work, if six doesn't work. So last place can be filled up in three ways. And you have not kept number three. That is a three way thing.

[00:47:12]Equal to what? did you get it? Yes.

[00:47:26]In Repetition Not Allowed. Hey, this number went to the last place. You have a total of seven, right? So repetition is not allowed.

[00:47:33]What does it mean? The number kept decreasing one by one.

[00:47:35]Whatever has been used cannot be used again.

[00:47:37]Then one number was placed at the last place.

[00:47:40]Then how many are left? Six left. Then another one less five from six. Then one less four. Like this 6 * 5 * 4 done, understood now, okay yes friends, now everything else is done, now only the last part is left, Calculus, the weightage of Calculus is approximately six marks, but it is a difficult part, means as compared to the first eight chapters, now the remaining three chapters are difficult. So it depends on you whether you want to do it or not.

[00:48:25]My job is to teach, so I will teach.

[00:48:28]Ok? So don't do any of this in it. A. Generally, I think you will get the hang of it in the first three or four sessions. There is no problem in that. Whether you have a maths background or not, it will not be a big deal. But the next part is a bit difficult, genuinely I mean how it is actually that he needs a lot of practice and its weightage is less as compared to the amount of practice he gives or the time he has to devote, so you have to decide as per your wish, you think that no sir, I will be able to do it, I will do it, we have time till December so we can manage it, then definitely do it and you think that no sir, I am not able to do it now, okay then leave it, then it is fine, yes because I am like this, that chapter is such that if someone is not able to understand, even if I bang my head 10 times in front of him, he will not understand, then that is unnecessary, your mind will get spoilt and mine will also get spoilt, it is better to leave it, but at least you can give it a try, whether you attend it or not, you will understand after a limit, if you do not understand then yes, understood?

[00:49:48]Meaning there is nothing like that. But but how is it for him that you have to work very hard from your side.

[00:49:53]Yes, I mean how are the other chapters that if you work hard enough then it can be done. There is double the hard work involved in that. It is like that.

[00:50:04]Ok. I was not scared at first. Meaning I am telling the truth.

[00:50:10]Why scare me now? Now you will say that if I say there is a ditch here, then what will you say, are you scaring me sir? No, whether you want to cross that ditch or not is your choice, there is a ditch [laughs] so it is your choice, my job is to teach, so I will teach you, don't talk about protest, protest, protest, work hard brother, work hard, don't protest in life, work, do that work, you have done that work, then you do n't see anything else in the rest of your life, what other people are doing, what they are not doing, so you work hard as per your own way, put efforts as per your own way, rest whoever wants to do what, he will keep doing it, you don't need to follow anyone's footsteps. We will make our own path. Simple, right? Yes. Will work hard. Don't think about the rest.

[00:51:21]You give your 100%. The result will be in your favor. Ok?

[00:51:31]Siddique is saying keep working. If the paper gets leaked, all the hard work will go to waste.

[00:51:36]Now whether the paper is leaked or not, if you work hard then you will pass, can anyone stop you from passing, then why are you thinking so much, whether the paper will be leaked or not, the system people will take care of it, if you do not work hard from your side then you will definitely fail, then you will have to see how the paper gets leaked, but if you work hard then do you need to think about the rest of the world, do you not need to think, you should do your own work, so do not take much tension, do your work, Kunal, what is he doing [laughs] or not, Tanvi Agarwal, oh there are many such questions in the module, such type of questions do not come in the exam because there is time restriction in the exam.

[00:52:29]Many such questions are given in the module.

[00:52:31]However, I mean, I have solved all the MCQs in it. There are such questions in the module which are for reference only, understand that if they keep asking such big questions then we will be done, then it means there will not be 50 questions in 60 minutes, so you do not need to worry about it. Okay done, okay, okay Siddique, I have sent it from my side, whatever needs to be uploaded, I have sent the PDF from my side, now Rudra's work, maybe he uploaded it in some other folder, has anything like this happened to you with the Pro batch? He told me that he had put some things in another folder. Meaning, along with the lectures, he has also uploaded the PDF of whatever has happened.

[00:53:37]Well, you must have done well.

[00:53:40]Okay, I have sent it from my side. Now that is his job. He will do it. Okay Aryan, there is no need to worry.

[00:53:53]When I make you do past exam papers, you will understand what type of questions come easily in the exam and they can also be solved easily. So no need to worry about it.

[00:54:01]Ok? Karan, please look at that again. Ok? Come on, yes.

[00:54:07]Ok. Okay friends, that's enough for today.

[00:54:10]See you tomorrow with new chapter new concepts. Bye-by take care.