 own question. Don't really just hit any option. Okay, so I think we can start now. Here we are starting 5, 4, 3, 2, 1, 0. First question. Take your time and then answer. Then respond. Don't really rush through. No point rushing through. And all questions will require knowledge of identities. Nitya will have this, but this week or next, definitely. Someone's mic is not on mute. Okay, so I hope this is done. Easy question, not big deal. So if you remember the identities properly, it will be done very easy. Right? Guys, again, all these questions are distraction. Can we, you know, restrict our questions related to the topic, you know, which is going through right now? Okay, all questions, that's where the distraction starts. Focus on the question. That's it. Okay, so last three seconds, and it should be very, very easy. Right? The factors of X minus Y. So most of you have got it correct, but they're not all. Not all have got it correct. Why is that so? So let me solve it and tell you how to do it. This was again a conditional identity. This identity was if A plus D plus C. Yeah, so if A plus B plus C is 0, then then a cube plus V cube plus C cube is equal to thrice ABC. Last week also, I told you the moment you see three cubes added together, to add them up first. Okay, so if you add them up, you are getting zero, isn't it? So that means ABC here are X minus Y, Y minus Z and Z minus X. Right? So this particular thing is equal to this. So obviously, this is not true. This is not true. This is not true because there is a plus, plus, plus, plus. Right? So only answer was this. Yes, I have changed the sign a little bit, but that doesn't take away its property that it is a factor. Right? Clear? Okay. Now, again, if someone doesn't know the code, no one is writing the code on the screen. If you want to participate in the quiz, please come on time. Period. Okay? This, the only 28 people have got it. Why? Because the only problem is you guys are not paying attention. Right? So please remember the code 91792. No one is going to write the code in the chat. I will write the code if at all someone is logged out. Is that okay? Because all of you are very much distracted, focused on the question and nothing else. If you want to improve your accuracy, guys, so please listen to my advice. Right? Okay. So no one does any chatting. Pranav. Okay. So all of you, if it is relevant to the question, please put it there because what is happening is I'm missing the messages, which are, you know, people are asking me questions. Okay. No, no, I don't want you to be sorry, but please your, this performance is because of distraction, guys. Distraction. Please stay away from distraction. Focus on the questions you will do good. Trust me. Next question. Before that, the leaderboard. So this is good. Very good. Who's football? Who's football? See, I'm telling for your own benefit, guys. Please understand. I have suffered through this distraction. I don't want you to repeat my mistakes. Please. So who's football, by the way? Okay. Anyways, who's over it is next question. Attention. Do not get distracted. Focus on the question. Leave the world where it is. Just focus on the question and you will be able to solve it. Forget about the world now. Since options are little confusing. So if you don't pay attention, there is where you lose the question. Right? So it could be easy for someone could be very difficult for someone, but if you really pay attention, I keep on telling you repeatedly, there must be some way of improvement and that is only through cutting down on your distractions. Right now, all of you have a lot of potential, but I see again, Rishabh, what does this mean? Why did you even post it here? Why? But everyone knows everyone here. Else, right? It's not YouTube chat. Come on. Let's be focused. No focus. You will get to, you know, do the same mistakes again and again. No improvement. Let's try to improve now, improve our accuracy and speed slowly. No problem. Please stay focused. Okay. Let me see the response. See, can you see the performance out of 64 only 25? I've got it correct. So for 14 plus 16, 30 and 39, this majority of the people are not able to perform. And main reason is destruction. You can, you know, check yourself. Okay. So this was very, very simple question. You have to just expand and add. Right? So what was a plus b cube? A plus b cube is simply a cube plus b cube plus 3 a square b plus 3 a b square identity. Correct? And what is a minus b cube, a cube minus b cube minus 3 a square b plus 3 a b square. So if you remember this, these two identities, it's done. Okay. So hence, if you see the identities are very, very straightforward, there is nothing to lose here. But if you give attention to something. So in this one, you can observe that b and b are there in both. So it'll be two b cube and the only option with two b cube is a. My friend, one piece of advice. Till you reach the, you know, mock test level. See, I have 1000 tricks of solving it in two seconds. I can tell you that first as well. But now is not the time. Okay. See, we have done probabilistic approach of solving J papers as well without knowing anything. Still you can crack big jam if you have real little bit of sense of how to mark a paper. But that doesn't make us really knowledgeable. So hence, right now at your age, if you have to, you know, adhere to my advice or if you have, you know, take my advice, go methodically. I will tell you 1000 ways of shortcuts. Right now method, method is more important. This is not an MCQ quiz. This practice is this particular session is for give you more and more practice and exposure. Okay. So this is two b cube and three a square b simply. So you can take b common in fact twice of both. So this will be six. So two b common and then and b square plus three a square. Right. I really appreciate those who can do. Yeah, you can you can do shortcut method as well. But as I told you last class, the learning comes when you brood over any problem. My dear friend, not by getting an correct answer. Okay, this will happen in my class. At least I will tell you repeatedly that brood over the problem, think over it, get insights. It will help you more. Okay. Anyone that didn't understand this question, anyone didn't understand this question below x all okay. Right. So this one is which one, which option is correct? First one. Learning should be the key guys. Winning and losing is not this is not the final end game. So good. Take your time. Focus on the question. You will be able to solve it again repeating all of you have enough potential. Just take your distraction under control. That's it. So next question. Let the world go to hell. Focus on your own solution. You will get it right. I have a belief you will get it right. Focus on your own work. That's it. So you have to just combine the terms and get the answer. That's it. Four terms are there can be paired up. If you hit the right pairs done, hit the right pairs and be very observant while picking up the option because options could be very close and raga. If you want to eliminate after you have done it, please analyze the question like that as well. So what to do if one information is missing? That's learning part of it. Someone's mic is unmute. Please put it on mute. No, I've given 100 seconds for every good. Very good. If you're confident, good enough. When you have more time, think about it that, you know, whether you can solve it in some other method or right. See, even so that's the problem. What do we do? You're getting a point now. This is what I did. But it's giving me wrong answer. Oh, is it showing a wrong answer? Did you miss click? Are you on a phone? No, I'm getting wrong answer. So I went for me. Okay, maybe some Never normally doesn't happen. So you clicked on these, you're sharp. Anyway, still a ticket. We can't really do anything right now. So the answer was D. This is how you solve it. This was very, very simple. So no worries if you've got it wrong. If you have learned the purpose is solved. So a square a minus B from the first two terms. And then you can take out B square and a minus B from the second two term. So a minus B, a square minus B squared. So a minus B, and this can be written as a minus B and a plus anyone didn't understand this one. So if you go by the elimination method, you can see this is a what is this? This one was a cube plus B cube formula. Okay, but then there are two extra terms. So this is anyways ruled out. If at all you have to do like that. Okay, and then this one, this one, though, there is no formula. They all are positive terms. You can see like that. What was was mentioning that is also a, you know, method to crack it. So hence, if you see all our positive terms and there are two negative terms here. So this is also ruled out. This is what ruling out you eliminate. Okay, and yes, there were these were the two closed options for which if you really had that, you know, knack of multiplying. So you have multiplied a and a you'd have got a cube. But if I have multiplied B and minus B and plus B, you'd have got minus B cube. So this is also ruled out. Did you understand this way? This you understand this particular methodology. So if you don't know anything, let's say, if you're not able to find out the answer. So what is this? This multiplied should give you this particular result. But is it so a times a times a will give you a cube and B times minus B times plus B will give you minus B cube, right? But there was plus B cube over here. So this is also ruled out. So only thing is D. Okay, the leaderboard. So maybe some glitch. Sorry for that. But unfortunately, I don't control the hold. So hence, kindly bear with me. Okay, no problem. Next question. There are lots of questions. Don't worry. Next question on board. Again, you have to pay attention, guys, please requesting everybody. You have learned this in the previous grade on itself. Only thing is there is one upon X square. Instead of X square, you can split the middle term. There are two ways of solving this question. At least I know two ways. There could be more if you can come up with a new one. Split the middle term messed up science. That's where turn off my requests again and again. See who what to do messed up with sign. Yep, how many of you are totally, totally unaware of this? Now you can respond in the chat. Totally not knowing. Yep, it was very, very simple question. Sorry, sorry, sorry. Sir, I'm not B, but it's showing up. Are you sure? Because I got this on chef. Oh, I don't know why this is happening because otherwise it never happens. Okay, anyways, if you've got it correct, then good enough. Nice, nice, good, good work. Okay, here are two ways. Now again, learn two ways. So my objective is not to click one of ADCD. I will learn one of techniques how to solve this. So there are two ways of doing it. How many of you those who solved correctly? Okay, those who solved correctly, how many of you use the middle term splitting? Anyone use middle term splitting? Yep, two people. For me. Yes. So it was easy by splitting the middle term. So one is split the middle term. What to do? One by x square. And you have to just ignore that this is something x square, right? And this is you can write five by x minus one by x minus five and game was over. This is what you have to do. So one upon x, you have to take common one upon x plus five, then again minus one one upon x plus five. So one upon x plus five and one upon x minus one three step solution. Okay, three step solution. Now, deliberately the here the signs were opposite because here is where the human brain actually faulters, right? Deliberately I had put minus sign in this and then put minus sign here as well so that the brain get should get confused. This is practice. So you must do all this. No problem. Right? Learn, learn, learn again. Right? Second method. What is second method? Second method is identity is method. How I am seeing one by x squared and there's a four. So mouth watering. Why? Because I will do this. x square four by x plus four minus nine. Can I like that? Can I write like that? Yes. Why is this important? Because if you look closely, this becomes an identity. What is that? One by x plus two whole square minus three square. Right? So now what? A plus B A minus B. So one by x plus two minus three one by x plus two plus three. Right? So what will this be? So let me write it here. This is equal to one by x minus one one by x plus five. Got it? So the same problem can be done in two different ways. That is learning. That's what I call as a doubt. Yes, please go ahead. How did you get that one one by x square plus four by x plus four minus nine? What is minus five? I am writing minus five as four minus nine. Can I not do that? Okay, got it. Thank you. Why did I do that? That's more important. That's more important. Why did I do that? Is more important. So that you could get squares? Yes. So that I can complete this square and there is another square. So difference of two squares will give me two factors. Got it? So this is applying so many times. Okay, so learn fair enough. Good. Good. There is this is the okay. So in the top three, top 10, only a few people could do it. Three people. Never mind. Next question guys. Again, stay calm, focus on question. Even if you miss click or get it wrong by glitch or technological problems, don't worry. Did you learn the question or not? Is the important thing? Sure. Next question. Now these are questions which are giving you glimpses of higher order sums. So hence, you have to think through. Again, I'm telling there are two methods of solving it. Addition and subtraction of same terms in an in algebra is is used many, many times. So in the previous question also, I added four and subtracted four. Monisha, I don't give up. Okay, hint for everyone. No, no, no, you can do it. No, you don't require hint. The answers are there already. The answers are there on the screen. Answer is there on the screen. So why are you saying that? Now, those who have marked it correctly, already you'd have got it. Right? So don't worry. Let others also come up to the same level. Come on. Hello, trial and error method. Anyone has done two proper channel. Good. So if you don't know, you can do that. Then again, focus should be on good that most of you have got it. Correct. You can have simply stuff. How many of you did not understand the question only? Did not understand the question? Right? So the thing was, what are the positive if this particular thing is zero? Now, this is a precursor to something called equations that you are going to learn next. So I just stress the saturation a little bit more. And yes, if you do elimination, you can just put the values. So what value of a will make the zero value of a polynomial or let's say, right? Yes, you can do trial and error. So you put one cube minus seven times one plus six is zero. So one is definitely a solution. One is definitely a solution. Isn't it? So this is ruled out. This is ruled out. Correct. Now you can check minus two and two similarly. Okay. So what is that a cube is? I will give you the formal method also, but let's say if you are doing like this. So let's say if a is two, then it will become two cube minus seven times two plus six. Anyone, anyone did the formal way? Anyone solved it through solid in front of solid informal. No, not trial and error. Let's say if options were not given, options are not there. Oh my God, this is happening more number of times now. Anyways, now, now listen, listen, forget about technical glitches, guys. I really can't help it in that because I have no control over minty actually. So now understand this, forget about wrong or right. Now, did you understand how to approach if the options are not given? As a first thing first, did you understand this method trial and error? Anyone didn't understand trial and error? Anyone didn't understand? Anyone didn't understand trial and error method? What did you do? You simply put the values of h a in this given equation and you saw whether LHS is equal to RHS. LHS is equal to RHS. You just check that, right? This is what many of you have done, most of you, right? Now the formal method I have to, when is something zero? Yes. Now look at the explanation, AQ minus 7A plus 6 is zero. Now those who have done lots of splitting the middle term, so 7 is giving you some hint, 6 is giving you some hint, okay? So what is that hint? I know x square minus 7A plus 6. I can split, yes, region, right? So but then x, sorry, not x square, but there is no a square. What to do? There is no a square. What to do? I will add and supply. That was the trick. AQ minus a square plus a square minus 7A plus 6, right? And then a square common a minus 1 from the first two terms. And this is, if you split the middle term, you will get this, is equal to zero. Again, you can take commons A minus 1 and what is this? A square plus A minus 6 is zero, right? Here itself, you will get the solution, one solution. Okay, when? Okay, let me first, can I factorize this further? I can factorize this further. Yes or no? What are the factors, right? You can factorize further. So how A minus 1 and a square plus 2A minus, the other way around, minus 2A plus 3A minus 6 is zero. Namrata, I am just factorizing. Are you understanding factorization? Factorization is what we have discussed. I am just factorizing, splitting the middle term again and again, right? Now what is this then? A minus 1 and again take common A minus 2 plus 3A minus 2 is equal to zero. That means A minus 1, A minus 2 and A plus 3 all are zero, product together. Oh, don't switch on the video please. Okay, right? So hence what will be, when is these three together zero? When all of them are zero, product of three terms are zero, when is that possible? When all of them are zero, right? Okay, so what will it be? A is equal to 1, A is equal to 2, A is equal to minus 3, formal method. Yes, when any of the term is zero, Nikita, correct? No. Product of three terms is zero, only when one of the terms is zero. So hence, these are the three values. Okay? Come on, next. Next. Pay attention, guys. Okay, Anush, the code is on your screen. I hope you got it. Come on, next question. Focus again and you will be able to solve. Next. Did this question last? Sentimental. Again, there are three cubes. Okay, where are you going Siddharth? Don't go anywhere. Stay here. Vihana. Stay here. Solve. Don't go anywhere. Get confused by the given condition. The given condition suits your purpose if you know the condition. Conditional identity. Sorry, I did not know that through less goo. L-E-S-G-O-O is a term used to describe one's joy. Let's go. Let's go. Okay, okay, let's go. Where do you want to go? Don't go anywhere. Okay, very good. So majority of getting it correct, but then I told you in the very first question, the hint was there. This question was there in the first question also. See, same thing. Same thing. Same thing. Same thing. Same thing. Only thing was you have to see what is the hint. Hint is again there are three cubes and this three times something, sign something. This is conditional identity. Conditional identity. What conditional identity AQ plus BQ plus CQ minus three ABC is zero if A plus B plus C is zero. Right? And which is true. So let's say this is the given condition. If you see this is A plus B plus C is equal to three X. That means X minus A plus X minus B plus X minus C was zero. That is what the condition was written in a different format. That's it. So if this is true, that means this entire thing is zero. Did you understand? This is understood. Right? Right? Anyone didn't understand. So we use conditional identity. Conditional identity again. AQ plus BQ. By this time now you must be able to in fact predict that there are three cubes and there's a three ABC term. It has to do something with conditional identity. Isn't it? Right? Okay. What happened, Rishabh? What is wrong? Is it my solution is wrong? Rishabh is saying it's wrong. Rishabh? Yeah. Oh, for me. Okay. So never mind. Lead a board. Excuse me, sir. Yeah. Who is this? Rishabh? I don't understand what he did. After what he said. I don't understand what he did, sir. Three. A plus B by A plus B plus C by X is three. So then I can say this A plus B plus C is three X. So three X is X plus X plus X. Now take A and pair up with this X. Take this V and pair up with this XE pair up with this. So you'll get X minus A plus X minus B plus X minus C to be zero. Right? Why did I do this? That's the basic question. Question is because I wanted to prove that this plus this plus this is zero, then the entire thing gets resolved or get reduced to zero. Okay. Understood? Next question. Now this can be done without piece of paper. Just pay attention and understand what a factor could be. No pen and paper required. You can observe and mark it. Understand the multiplication process. Factors are being multiplied. Which one will not suit this case? That's the question. What happens when factors are multiplied? Hamzika, don't give up. Try multiplying. You don't need to multiply everything. Only a few things can give you the answer. It's like a doctor. I have lost my voice box actually. Off late. My voice is not this. Dead. Oh my God. So much of... Don't say so many hard words. If I tell you the solution you will laugh occurs me maybe. Equal. Okay. Never. I had to just see this should match this right after multiplication. It should match after multiplication. So what will be the first term multiplied? This to this. Px into Px square plus Rx square. What will be the power of x here? Five. Right? This one. Here also you will get x to the power five after multiplication. But here was the problem. You will get x to the power six. x to the power six. But there is no x to the power six here. Correct? You understood now? So this looked intimidating. But it's not. Right? This is the correct option. This also if you see will lead to x to the power five after multiplication. Is it okay? Right? So what I'm saying is for this question you just needed to multiply. See what is factor guys? Please understand what are factors? Factors are nothing but if you multiply you'll get back the original expression. So hence if this was to be factor that means this into this first term will be this when you open the brackets. So the power of x will be five in that case. What will be in this case? Again x to the power five. But in this case if you multiply after opening the brackets you will get x to the power six. Right? Now this x to the power six is missing in the given expression. So how can this be a factor? This cannot be a factor. Okay? So hence see what the option. Right? Understood? All of you have understood or not? Yeah. Okay. Next question. If you get time please go through this problem solving session again and again if possible. If you get time some you know fast forward it and watch the question. Okay. Next one. Let's go. Simple application of apply the identity. I'm giving it now now that you're saying that you are not getting the answers. There's an identity which is pretty much evident over there. There's a cube so you can figure out which identity I'm talking about. Mute. Someone's mic is on mute. Please mute. Hamzika got it. Okay. Anush got it in 35, 33, 40 second. Haritha Hamzika says Hamzika is not happy. I don't know why. Sriram said 26. Radha says 58. Kamal says slow. Slow gang. Slow gang means by my god you talk in so many acronyms. People who are slow. People's. Okay. Okay. Slow gang. See. Boss I am a basic person. I don't understand such. I don't ever do DD but DD. Is it C? Answer is right. Yeah. It was very easy. Was it really big? Because this is simply 3.7's cube. The moment there is a cube and there was fire in a fint boss. In a fint. In a fint. So this is 3. This is 0.7 cube divided by 3.7. So are you explaining it on the blackboard? Your screen is not showing. Now it's okay. So 3.7 into 0.7 plus 0.49. Isn't it? And then there was a minus one. Now a cube minus b cube is equal to a minus b a square plus a b plus b square. Is it? So a cube minus b cube divided by a square plus a b plus b square is equal to a minus b. Yes or no? So I have to just find out a minus b. A was 3.7 and b was 0.7. So you will get 3.0. Right. And then but this was not the correct answer because there was a minus one. So minus one. So 2. Correct. I'm holding Karyan. Right. Got it guys. Easy. Very good. Thank you for appreciating a very bad song. You should win a Grammy. No, no, no. I don't want a Grammy. I want you to clear some good exam and then I want to get into you in times of India. Okay, next. This question is rocking question. Use of identities. I'll give you a hint also. Those who know arithmetic progression, if at all you have learned, you can do that. If you haven't used identities, square of difference of squares a square minus b square form. Easy. Oh my God. Sriram has cracked it. Nice. I really feel happy when someone says it is easy. That means all's fine. Good. Misclick. You guess. Tanvi. Unsure. Unsure. a square minus b square. Giving you another hint. Once again. A square minus b square is the no problem. No problem. I'm exposing you to different varieties of higher level questions because now if I tell you that this question was asked in a KVP by exam, then you will say, Oh my God, so I am eligible to write. No, without AP also you can solve it. That's the fun. That's some of all odd numbers. Your school level is easy. No, so you should be elevating yourself up. Why do restrict only? Yeah. This was so easy. If you'd have noticed something that three can be now look carefully, learn this process, learn this, learn this, learn this. Three can be written as three into one. Right? So this can be written as two. Sorry. So you can write this as two plus one and two minus one below. Right or wrong? Similarly, five can be written as five times one is equal to and write this here as two square minus one square. Similarly, five can be written as three plus two, three minus two. So it can be written as three square minus two square. Similarly, seven can be written as four square minus three square. Go on like that till you reach 199 or let's say 197. 197 will be 99 square minus 98 square and this will be 100 square minus 99 square. And then you simply add all of them. It was all getting added, right? Getting added. Add all of them. Add all of them. What will happen? This two square, two square will go. Three square, three square will go. Four square, four square will go. 99, 99, 98 all gone. What is left? 100 square minus one. Right? This was X. Right? So what is X plus one? 100 square. So what will be root of X plus one? This question was asked in Kishore, Veggiani, Prachan, Yodhna and if a ninth grader can crack it, then you understand. Understood? What is the level of the question? Okay. This is the method. Another method is arithmetic progression. You have not learned that AP. So if you want to learn the formula, sum of n terms of an AP is n by two twice a plus n minus one d. This is a formula for AP. What is n? n is number of terms. Right? What is a first term? What is d? Common difference. So in this case, what is the difference between the term? Two. Difference between any two consecutive term is two. So d is two. A is three and n is how many? How many n? n is 99. 99 terms are there. Right? But this you will learn next year, not now. I think we will be learning this year itself but in a regular. Please show the equation. This one. So this is sum of n terms. Thank you so much. Sum of n terms of an AP. What is an AP and all that? We'll discuss. If you're interested, you can go and check my learnings videos. It's there. Okay. Now again, again, again, guys, please. Right? So we will discuss all of this. So that method you didn't require in this case and you solved it. Next question. What's the d in the equation? Common difference. Difference between two consecutive terms. So in this case, two. Next question. Oh, sorry. Just click this. Oh, never mind. Shallow. Next letterboard you'll see. We'll have to close this. Again, this question I gave you in the last centymar. If you are still not able to do it, then I failed. I gave you in the last centymar. Remember, please, because you still don't get it. Then I failed in last seven days. I have just simply replaced A, B, and C. In the last centymar, it was A, B, and C. And most of you have got it correct that time. Please. If you don't get it correct, most of you, then I will be sleepless today. I will have to do something. Fasting. Yes, fasting. Satyagra against yourself. I don't like to. That's why I do Tanvi. If you want to punish yourself, you do something which you don't want to, right? So that's why some people appear bright until you hear them speak. Do you get this pun? Oh, my God. It's not heavy. GDRNR9. GD. Dhruv Desh Pandey. Okay. Oh, very good. Thanks, Dhruv. They got nine, only nine people. Oh, my God. Fasting. All of you deliberately made it wrong, no? So that you know that this teacher is really boring. Let's make it, make him fast. Right? Very funny. Who was that by the way? Right? So you guys. Sorry. It was me, Tanja. Oh, come on. Tanja, you made me fast. Yeah. It was so simple again. Two and three, two minus three, three minus five and five minus two. All of them are adding to zero. Again, same question repeating. Cube. A cube plus B cube plus C cube. What will that be? Three ABC if A plus B plus C is zero. So this is three times two minus three in the numerator, three minus five and five minus two. And similarly in the denominator, it will be three times two square minus three square, three square minus five square and five square minus two square. Is it? Yes, I did that, but I, okay. Sorry, I did not get it. See, what did we discuss so far? A cube plus B cube plus C cube minus three ABC. Is what? If A plus B plus C is zero, what will this be? If? Three ABC. Yeah. So this becomes A cube plus B cube plus C cube becomes three ABC. A plus B plus C is zero. Now say A is two minus three and B is three minus five and C is five minus two. Are they not adding up to zero? Yes. A plus B plus C is equal to zero. That means this will hold. Right. That means two minus three whole cube plus three minus five whole cube plus five minus two whole cube will be equal to three times two minus three, three minus five, five minus two. Is it? Yes, sir. Similarly if you apply it into a denominator, you will get three times two square minus three square, three square minus five square and five square minus two square. Is it? Is it numerator? Is it denominator? Can you explain the questions in class because there are seven questions left after this? So those who want to leave can leave, no problem. Those who want to stay will complete the quiz rather hardly five more minutes. Come on. Stop the quiz rate. Like we completed it. Yes, I will complete it anyways. Yes. Okay. So is that understood? Is that understood? Right. Seven more questions. Thank you, sir. Only eight questions are eight seconds are given for those questions. So don't worry. It will be over in one minute time. Okay. So this is three into again, if you simply move forward, then it will become three, two plus three, two minus three, three minus five, three plus five and five minus two, five plus two. So this, this, this will go right. So what is left? This three and three will go. So the only thing left will be one upon five into one upon eight. How did you know that A plus B plus C was going to be zero? It is coming, adding up, add all three, you'll get zero. Two minus three plus three minus five plus five minus zero. Okay. Yeah. So this is X. So 56 X will be multiplied by 56. This will go one upon five is the answer. Yep. So you could also simplify the, from the three into two minus three into three minus five into five minus two divided by three, you can also simplify it from there. Yes, why not? Right. You can, you can calculate. No problem. Oh, okay. Iman Shu and Krishna, two people got it. Correct. Very good. Chalo, Maika is on. Now easy questions on board. Chalo, I will give you some respite. Oh, I hope if you remember, I had discussed this in the class. Good Monisha. Come on, back up. Come in top 20 of 15. This I have discussed in the class. If you don't remember this, at least I have tried to explain it in the class. Or even if you don't know, you can simply square after this. After this question, one more and then we will quickly finish it. Don't worry. Just give me five minutes. There go. At least you will gain one thing. No, what is that? You are now aware that these kind of questions also exist. So even if you just go through the solving process, that will be good learning, even if you're not able to participate. See, variety of answers are coming. I will quickly explain. If A plus B plus C is zero, I had explained this in the class, is it it? Did I not explain A plus B plus C is zero? Square both sides. It will be zero. So A square plus B square plus C square plus twice, AB plus BC plus CA. You must have, you have to remember the identities. Otherwise, how will it be? So that means A square plus B square plus C square is equal to minus two AB plus BC plus CA. Right? Right? Now, what was the question? A square plus B square is always an even number. Yes, it is an even number. Why? Because there's a factor of two. Right? And AB plus BC plus CA is always greater than zero. No. Why? Because this is always greater than zero. I discussed this in the class. Okay. And this is minus two into something. Why is this greater than zero? Because all our squares, all our squares, it has to be greater than zero. So minus two times something. So something has to be less than zero, negative. Right? So minus two times something negative. So something is negative. But here it is greater than zero. So that is wrong. So one only. Right? Okay. So let's, let's go and quickly finish it off. Only nine people got it. Correct? See, if you are, you know, if you're afraid of tricky questions, then my dear friends, we will have to do something about it. Easy question. Again, I have discussed in the class. If you have paid attention when we were discussing all these satirization and other things, you would get it in one go. RNR and what? RNR and there was a peculiar identity I discussed about. It's there in our Lernist platform as well. Yeah, Krishna remembers. Good. Thank you. So my effort is not wasted. Sophie Germain. And you can just come to my Lernist videos. There's one very, it's there. You can check there. But it's there in your normal textbook as well, but they have not mentioned the name. They have used it. They're not mentioned name. Nice. So lots of people, right? That's nice. Good. So Sophie came to your rescue. So you have learned this very good. So Sophie Germain was A to the power four plus four B to the power four. Right? Yep. Yep. Whenever this is there, this is always, this can be factored. How? It is A plus B whole square and plus B square. And then finally into A minus B whole square plus B square. This is the identity. So it can always be factored like that. Here, B was one, right? And this was four into 16, which is two to the power four. So B was two. Right? So I saw both of them by just replacing A and B with like a number. You don't need to. You don't even need to go to all this. The moment you saw this form, this was not a prime. It will never be a prime. Any X to the power four plus four, Y to the power four is never a prime because it has two factors, this factor and that fact. Okay. So if you want to learn more about Sophie Germain, please visit once. Now, rapid fire round starts. Okay. All ready. Only eight seconds will be given to you. You have to mark two and false. Be ready. And five such questions are there. Okay. So you have to just see the question. See the question and all set mute your mics. You are going for rapid fire. Easy. Only dependent on identity and your common sensical. Okay. And here we go for the next question. See eight seconds only, only eight seconds. Okay. Cool. So this is just to revise your identities. Oh my God. Good. But then that as well, this we will be doing rapid fire to revise easy concepts. Okay. You will not be given time. Only revision next leaderboard. So if you have revised it properly, you will get it in the shortest possible time. Otherwise, you have to revise more. That's the intention. Okay. Next question ready. So you get more than eight seconds. Actually, one of the questions gets displayed and then. Okay. Very good. Let's see. Very nice. Cool. That's cool. Right. Okay. Oh my God. Very close. Good. Maintain that up. Monisha is in top. Then you were in top 20 or something. Right. Oh, good. You breezed it. Very good. Next. Patience. Everyone is able to mark it. Okay. Why? Why? Why? Oh, I have to fast. Oh no. Sad. So it was so easy. That's what. See what question and panic situation does to humans. Was it easy? Do you want to see the question? Oh no. How can you make sure? This was a question. The two was plainly missing. The factor two AB two BC two CA was totally missing. So you could not have made that mistake. Oh my God. Okay. Never mind. So next. Okay. See when panic attacks, what happens? Good. Next. Eight seconds. Let's see the. Oh my God. Oh my God. This is. Oh my God. Now it summarizes the entire quiz. It summarizes the entire quiz. That's a lot less than eight seconds. Sorry. Sorry. I didn't get you Monisha. Come again. It was a second. We're not sufficient. Was it not sufficient? I'm saying it is so easy right for all. This was the catch. It is true only when A plus V plus C is zero. That's it. I think she meant to say it feels a lot less than eight seconds. Oh, I see. The other way around. Right. So see now you get the summary of the quiz. Summary of the quiz. Summary of the quiz is we need to work more on these identities. More practice is to be required because basics itself. Are questionable. Okay. Nice. So how to get my head started walking. Last question. We will hear. I will finish this on your note. Good. Thank you. At least now I have some easy question again. All were even powers. So you cannot have right. Okay. Good idea. So what about the three question quiz? Ha ha. Just next after this. So don't go. Just mark that. So here is the final quiz. It's like a just a survey. Okay. So very good. So I think who wins. Vihan Singh in PSHSR. Very good. Congratulations. Just a minute. I will I will come complete this. Yes. Do this, please. Please. Mark, mark, mark quickly so that all of you done. Come on, come on, come on. Mark your answers. Thank you. So I am going to the next one. I don't think anyone else is going to vote. Okay. Next question. You can mark more than one option. Come on, everybody. Mark it. Mark it quick. So this gives me some indication as to what I should be prepared for. Okay. Very good. Thanks a lot for all for this. All this. Okay. And nice last one is this. Let's see your creativity. So I'll share these results. Don't worry with you as well. So that we are on the same page. Right. You can only one word you can use. Or you can use two. Two. My God, so long. I hope you understand what this means. It means the more the number of different people are writing the same word, it will be in bigger font. Okay. Yes, I can leave. Sorry for bothering you for so many minutes more. I am really sorry for that. But then I need to just get some direction. Okay. Very good. Thanks a lot guys. Thanks for your time and thanks for the feedback as well. I will work on this. Thank you. No problem. Don't worry. I will try to thank you reduce the what do you say the level. But then my thing is you think don't worry about the difficult level guys. You will get trained on all of this. Thanks for your time. Bye-bye. See you. Bye-bye. Take care. Thank you, sir. Okay, sir. Bye-bye. Thank you. Take care. Good night. Don't go out. Stay at home. Yes, I'm going to fast.