 Okay, so as I, I will repeat the protocols. First of all, do not rush through the questions. They are, they may not be straightforward. Then there would be some traps laid in the questions and the options. So hence, okay, so here we go. Five, four, three, two, one, stop. First question on the screen, read carefully. And then, okay, based on identities. Don't really, you don't need to click the answer somehow. Okay, mark the answer, no need. Solve and then mark. Take time, no worries, but make sure that today, whatever number of questions you do, you do it correctly, all of them. Mark at the last moment, that's acceptable, but don't mark it wrong. So the question says X plus Y is four and X dot Y, X dot Y is multiplication. X times Y is minus two. Then find the value of X square minus Y square. Take your time. I hope you have a, you know, piece of paper and a pen or pen with you. Okay, mark, very good. Calculations, no, why you should guess. Don't guess. No, no guesswork. No clue, oh my God. Questions will be tough today. So please be, please be careful, okay? Okay, fair enough. So this was the question and it was fairly simple, fairly simple. I don't know why. The moment you have, you should have seen this X square minus Y square. Move around, okay, done. Now, X square, oh, wait. Yeah, so X square minus Y square. Eight root three, eight root six is the answer. X square minus Y square. Oh, I didn't show you the answer. This is the, oh, sorry. This is the answer. Most of you have got it wrong. Okay, so let me solve it. So X square minus Y square is how much? Simply X minus Y and X plus Y. Identity, you only wanted identity. So here is the identity. Okay, next. X plus Y is anyways given, right? This value is four, no problem. You just wanted to find out, you needed to find out X minus Y and what is X minus X plus Y is equal to four. X square plus Y square plus two X Y is equal to 16, correct? Correct. So that means X square plus Y square is equal to 16 minus two X Y, which is 16 minus two times minus two, which is 20. So X square plus Y square is 20. So X square plus Y square minus two X Y will be equal to 20 minus two X Y, yes or no, right? So hence, I'm writing it here now. So this becomes X minus Y whole square is equal to 20 and minus two X Y was plus four, correct? So this is 24, right? So X minus Y will be ideally plus minus root 24, which is plus minus two root six, correct? So there was no minus sign here. So hence, X minus Y is two root six. X plus Y is four. So what is X square minus Y square? Four into two root six, eight root six, clear? Anyone didn't understand this part, okay? Yeah, wait, wait, wait a minute about again, you guys are missing the point. Why most of you could not solve is a point of concern, right? That means this is not flowing very, you know, clearly in your mind. Time was less. No, I don't think so. I don't think so. That means strategy was not there. You should have started from here. X minus Y, X plus Y, it's gone. So while solving faster, you need to find out X minus Y. In class also, we have done how to go from X plus Y to X minus Y. No, I had given you 100 seconds, nevermind. So please be careful, questions will be like that. See, was there, we didn't know in this, was there anything in this that we had? Did we bring something from our college or something? I already heard this first in the world. But I was, I'm not happy. Most of you have got it wrong. But many people have got it right. You're so good at it, you've got it right. Your voice is breaking. Sorry? Your voice is breaking. Is it fine now? Is it okay? The giant's mic is on, giant's mic is on. Is it fine guys? Hello? Sir? Who's this? Kanya. Sir, you did some step on X square plus Y square minus 2XY equals to 20 minus 2XY. Yes. So why was that? See, the idea was that I already got X square plus Y square, right? X square plus Y square was how much? X square plus 20. 20. I wanted X minus Y, right? Yes. So I can definitely find X minus Y whole square. What is X minus Y whole square? X square plus Y square minus 2XY. So X square plus Y square is 20 and minus 2XY is plus 4. That means X minus Y root square is 24. Okay, sir. Okay, sir. Got it. Got it. It's 24. Okay, questions will be on similar lines. Do not expect a very straightforward, formula-based questions. Sentom Rs will not be meant for that. You have to put your brain in maths, okay? So no mechanical questions. Okay, so let's go to the next one. Be ready. Have your pencil and paper. Need piece of paper. Start and do methodically. 100 seconds are more than enough. Here is the next question. Don't guess. Everything is related to identities. You have to manipulate. Learn manipulating. Learn observing. Hints are there in the question itself. The coefficients are the biggest hints in identity problems. Learn to observe coefficients closely and then utilize the information. Take time. No problem. So the files are there. As I told you, I'm giving you hints repeatedly. No problem. Just mark your answers. Okay? So last 10 seconds, guys. Not sure. Okay, here is... Time's up. Let's see the leader. I'm not very happy. Lots of people are still not able to get the answer. How many of you? Problem, how many? How many, how many, how many? X, X, X, X, X, X. Okay, lots of people are saying X. Oh my God. This could not be simpler than this. So hence, what is the learning observation? Observation is minus 4. Observation is X square. Observation is minus 4 X. Where do you see all of that? Okay, so this question was very, very simple. No audio. Can you see? Can you listen to me? Hello? Anush, just log out and re-log in. Oh, I don't know. I just sent that message over there because you can't listen to me. Anyways, so there you go. Just a simple manipulation would have worked. I hope you have not squared X then multiplied by 4 and then added 1. How many of you did that? This was not necessary. So don't do that. What you need to do is X minus 2 is root 3 and game over. This manipulation was required, that's it. Okay, and then simply square both sides. Okay, why do I square it? Because I'm getting this feel that, hey, there is an X square and then there is a minus 4 X as well. So this is X square minus 4 X plus 4 is equal to 3. Correct. And hence, X square minus 4 X plus 4 minus 3 is 0. Right? So this is X square minus 4 X plus 1 is 0. How many steps? How many steps? You could have done this in your mind. Right? Isn't it? So what is the learning? Math is all about observations. How much observant you are and can you recognize the pattern? This is the whole game throughout your mathematical career. Okay? Time... Come on. 100 seconds, yeah, come on. You know, 100 seconds is more than enough for any this thing. So you are now gearing up for a bigger platform. So don't expect more time. It will be lesser later on. I'm going to reduce the time later on. There must be some pressure on your mind. Okay? So here is the leaderboard. So please get accustomed to 100 seconds as much as fast as possible. It's sooner going to be 90 seconds, then 80 seconds, then 70 seconds and finally it will end up at 60 seconds. Fastest mathematics. You must be very, very comfortable with that. Okay, good. Good. Let's go to next question. Okay? Here is the next question. No one will crack under pressure. You guys are much better place than probably we and your parents' generation. So don't talk about that pressure at all. There's no pressure. Careful. This can be done in mind, but careful. Again, use of identities and manipulation. These manipulations will be required later on when we are going to discuss trigonometry. So this question is inspired from trigonometric identities. But it is very much within the ambit of algebraic identities. Why were traps ever invented? Were traps invented or they were discovered? Question mark. Was mathematics discovered or invented? Million-dollar question. Maths was discovered or maths was invented? There is no gut feeling maths. Okay? Maths was found. Math was found. Okay, cool. So, done. Time's up. Very good. Still, people are... Oh, no. Today the correct percentage is down. You need to work hard more on identities. It was as as I mentioned earlier, you need to work hard more on identities. It was as simple as when you look at the solution you will curse me or maybe yourself. So this was the question and what was it? It is simply if you cross multiply, take this thing up and multiply with this. Okay, so it is a square minus b square is equal to step number one. Count the steps guys. All the questions will be solved in three steps. That's the fun part of it. x a square minus b square is one a square minus one is b squared step number two, right? a minus one a plus one is b squared that means that means this is b into b, right? Okay? So a minus one upon b will be b upon a plus one over. Got it? Got it? Did we use something out of the world boss? So easy. But I don't say that. See, I am not trying to see these are first of all, please understand this. These are level up questions. So you guys are anyways daring enough to get into the woods without, you know, knowing much about it. So I really appreciate all of you for this. So my intention is nowhere to break your this thing, okay? Confidence. So don't say that. Then my purpose gets defeated. So these sessions are for you to expose to level up. I never judge anyone, guys. Please understand. You know, you guys are daring enough. I was so fissured. I could not ever, you know, I could not have ever sat for these kind of sessions. Forget about solving. So hence, you guys are anyways ahead. But what I am trying to tell you is these are level up questions. So hence, see, I have put in a lot of effort to fabricate them. I am not copy pasted from somewhere. Because this is what I want to introduce you to. Please understand this. So slowly and slowly, with time you will all get to that level. Okay? So hence, what learning please focus on learning. Learning is there is nothing hard in it. Was there anything hard in it? Tell me honestly, was anything which is very, very, you know, out of the world? Was it so hard question? Once you know this is just a manipulation game over. So hence, this will happen multiple number of times. It's better to be prepared than to be sorry. Okay? Let's move ahead and let's see who did well in this question. So there are only 20 people who got it correct. Right? So slowly and slowly you will it will become part of your life and then it becomes easy. So don't worry. You guys are facing this that's itself is a big thing. Okay? These are okay. So Anvi is on the first rank right now. Okay. Let's go to the next question. Put some thinking behind the questions. It is related to only identities. Only identities now here. But it will not be a straight forward. It will ask you some multiple aspects of it. Yes. Solve this again and it's getting so this one isn't this one is an easy one warming up question so that you are someone said I am breaking his confidence or her confidence that was like the purpose getting defeated. So hence bring your confidence back back. All of you can solve these. There is no intention of showing you down. Okay? So hence, please understand slowly and slowly you will come up to that level. You it's on the individual to decide whether someone was something was warming up or not. Why warm up in the middle? Because I change the question just now. Okay? Very straight forward Ashish don't write the you know don't discuss the options here. Okay anyways this was fairly simple. Most of you have got it but still only 50%. Okay? So this was again very simple very very simple question. So again it is of the form of A minus B times A plus B So what is it? A square minus B squared right? Then hence it is 10 to the power 6 squared so whatever you learned in the previous chapters should not be forgotten. So hence right? So hence it is 10 to the power 12 minus 10 to the power 10. Okay? So this is if you take 10 to the power 10 common what is left? 10 square minus 1 right? Is this clear to everyone? Right? So hence this one is 99 into 10 to the power 10. Okay? So what is the answer? 99. Okay? Clear? Let's see. So all top 10 people are continuously performing well good? Very good. Let's go to the next question again it's application of identities I have just written it in a different ugly looking fashion. That's it. When on a battlefield the bullet can come from any side so hence you must not be prepared for only one direction warfare alertness all around. You shooting the bullets will not impact much no Vishak you are receiving bullets at the same time so you must be alerted from whichever end, whichever direction it can come. So you should be prepared for any exigency. So you should be able to look things from different perspective right? You should be able to look at things from different different angles. That's exactly what this question is doing. So they will not be direct. They will ask you to go beyond a point. Okay? So again this was very very simple question in three steps it can be solved none of the questions are okay. Most of you have got it but again 50% only so here is the question which identity? Trinomial square why? a plus one sorry a plus one minus b is zero this is what you have to write. That's it and done. Then what you need to do is square both sides right? So hence a square plus one plus b square then plus 2a then minus 2b and minus 2ab this is zero isn't it? This is a plus b plus c whole square now over game is over here itself. In one step you could have written it minus 2b is equal to 2ab minus one right? Was it difficult? How many of you think it is difficult? Right? Is it difficult? Was it difficult question? See observation okay. How do we figure out that we have to do this? The catch was these two terms right? and so hence the moment you saw that and there are 2a and 2b and 2ab times are missing. So that was when it would have like that. Trinomial formula yes why not Trinomial formula is this a plus b plus c whole square I asked you to compile all of this and keep it whenever you are solving questions correct? This one was the trinomial formula but then here one it was a minus b plus 1 whole square right? Is this clear to everyone any doubt in this question? Below nothing beyond 3 steps get the maths in 3 steps is the no no one is done don't say such words if you curse yourself that means you are indirectly cursing the teacher who is teaching all of you that means you are cursing me my students cannot be done okay next now conventional questions simple easy get some points there will be mix of easy and difficult question okay very good not recording of the speed it's all there on the recording of this thing no okay come on come on very good 10 9 8 second left okay cool oh no still we are not crossing 50% today what's happening I have to do something now some more effort maybe okay why were you struggling in such questions anyone lots of you cannot do it so again whenever you get such kind of questions you know the conventional methodology is squaring right squire you will get 4 right so this is x square plus 1 by x square right plus 2 because x and 1 by x will get right so this is 4 so this 2 comes here it makes it 2 right right then what x square plus 1 by x square minus 2 is 0 and game over here itself game over right so x minus 1 by x whole square root 0 is 0 got it right x minus 1 by x is 0 so should not have faced any again see how many steps 1 2 3 right none of the questions will require more than 3 steps next oh there is shuffling happening cool and we again back identities may learning is you need to some more time never mind we will write some tests shall next question focus go by elimination eliminate elimination was the best way here hmm wonderful ok here hmm oh better performance this time what happened this was fairly again very very simple questions I don't know why are you AB what was AB in such questions breakdown into 2 parts so first part is AB right so what is AB AB is simply XY and x plus y into x minus y is x square minus y square no problem first step done A plus B let's write A plus B ok so x by x minus plus y by x minus y right common denominator what happened what c c means what what happened any any problem so this is common denominator is again x plus y times x minus y and here oh c for clear ok c so hence it is x square minus x y so this will multiply like that and this will multiply like that so this is again plus x y plus y square so this minus x y plus x y is good right so this is x square plus y square and in the denominator x square minus y square the question was AB by A plus B so AB is x y upon x square plus y square divided by x square plus y I'm sorry minus it was minus here isn't it so this this is gone so what is left x y upon correct any problem in this correct all of you yep good very good so hence let's go to leader assia board assia ok so here is the leader board and we is saying ok there is some shuffle very good now next conventional problem training zz zz zz z easier zz zz zz zz zz zz zz zz oh my god so many z's sir solve easiest one so far is it easiest one oh my god increase the bad feeling don't have bad feelings for anything yes now ok cool nice looking graph I hope our corona graph is like this only going down ok right now let's solve this was the question fairly simple again in such questions wherever a square b square and a b is given right what do you do add to a b subtract to a b ok now so a square plus b square minus 2 a b will be how much 1 1 7 minus 2 into 54 isn't it this will leave it as 9 that means a minus b whole square is 9 right that means a minus minus 3 right now what about a plus b so a square plus b square plus 2 a b you will get 1 1 7 plus again 2 into 54 which is 225 so a plus b whole square is 15 square so a plus b is plus minus 15 now you have to find out a minus b by a plus b so no negative has been given in the question so hence you take the positive once so plus 3 divided by plus 15 a minus b a plus b what is the learning if a square plus b square is given and a b is given always go for a plus b whole square and a minus b whole square correct 3 4 ok very good tambourine gang what is this why do you have gangs and all my god floor gang roof gang no one will fail don't fear when I am here ok again intentional question if you fail I fail and I generally don't fail none of you will fail none of you will fail because I don't fail so hence you will not fail henceforth you will not be I don't worry I have supernatural powers also so all all my students cannot fail guaranteed no problem I'll solve questions are very easy yes I know they are easy ok here is the so 25 people still got it nice these are very conventional problems I didn't want to put them but then I knew that you will be facing some trouble here again first thing what I did was the position usually you will say this kind of a thing so just to break that right these things I just swap the places so a square plus 1 by a square is 7 you know whenever a square plus 1 by a square is given what do we need to do a square ok go like this you want to find this out right 1 by a cube plus a cube what is this is of the form of x cube plus y cube what is the formula x plus y x square plus y square minus xy right this is the thing ok now then what is this x plus y x plus y here it is a plus 1 by a and you will need a square plus 1 by a square minus a times 1 by a correct right so 1 a plus 1 by a you need and a square plus 1 by a square you need a square plus 1 by a square already given so within this bracket this is 7 minus 1 half the problem solved you just want a plus 1 by a ok so what is a plus 1 by a a square plus 1 by a square is equal to 7 then if I add 2 to both sides I will get 9 and this will become a plus 1 upon a whole square is 9 so a plus 1 by a is plus minus 3 did you understand once again I will repeat you have to find out a cube plus 1 by a cube ok this is a cube plus 1 by a cube now x cube plus y cube what is the formula x plus y so a plus 1 by a and within brackets x square plus 1 by sorry why am I writing x square I have to write a square plus 1 by a square minus a times right right this is 1 this item was already given in your question see a square plus 1 by a square is how much 7 you don't need anything here so this bracket is 7 minus 1 correct you just needed to find out a plus 1 by a and then it's done how to find that out it was given a square plus 1 by a square is 7 ok now add 2 to both sides no problem ok so this becomes a square plus 1 by a square plus 2 times a times 1 by a 2 can be written like that and this is 9 so hence it is a plus 1 by a whole squared so a plus 1 by a is plus minus 3 that means this 3 and this becomes 3 into below difficult but learning in this question is please for God's sake I had given you this from x plus 1 by x I did in the class also converted into x square plus 1 by x square converted into x minus 1 by x converted into x cube plus 1 by x cube converted into x cube minus 1 by x cube did I not discuss this these forms right so just you have to remember also and repeat repetition is the best way done so next question need a board ok some changes very good nice very good shall let's go to the next question slow and steady wins the race I was a drummer in my college dude yes once upon a time I wanted to end up being a musician but destiny had something else for me ok fingers crossed observation will be key here yes I will solve I will solve I hope people have seen the trap there are the trap in this question tan tan tan tan wah that's amazing I hope I know you would not have seen the trap there was no this question is wrong this question itself is wrong why there is some issue in this question what was that wait a minute is it wrong hold on x is equal hold on hold on hold on yeah yes yes yes it's cube so the option was not there I will delete this from the backdrop so this question what had some issue wait where do I go I have to go to mentee just a minute give me a moment I will just a minute so that it is yes I will explain the question don't worry but let me one minute do mentee ok so one minute one minute your presentations I messed up with the x over there hence never mind so yeah I will explain don't worry explanation is spending I have not still not done it I will first remove the leaderboard this was question number 10 question number 10 hey don't whistle not appropriate question number 11 not number 10 ok so I am deleting question number 10 done now so I have eliminated question number 10 so let's go back to our presentation let's go back to sharing the screen screen started yeah can you see the screen now screen visible yeah so I have oh this so what you can do is so we can't see the screen all of oh you can't see the screen oh sorry why now visible so all of you simply mark D mark D D D quick mark the answer D D D D D ok all done why did you give you a right answer I had reset the leaderboard and then ask no problem here hardly I am chalo one question here and there will not make much of a difference right now so all of you mark D ok so I will move ahead oh there are 55 56 come on everybody ok ok ok done anyways so it should be X I had to write X cube I had written X 1 by 3 actually so that was wrong anyways so oh still people marked C and all never mind there go the explanation to this is give me a moment where is it why it is not coming just a minute ok so this was again very very simple why because you have to observe this that A plus B plus C is 4 I had purposefully written it like that and A B plus B C plus C A is 6 ok right and now it was very simple A cube plus B cube plus C cube minus 3 A B C is B plus C A square plus B square plus C square minus A B minus B C minus C A this is the formula this is the identity right so hence A plus B plus C you already know it is 4 A B plus B C plus C A is already known 6 you just needed to find out A square plus B square plus C square how to find that out simply square this one A plus B plus C is 4 so squaring both sides will get you 16 so this formula we learned previously A square plus B square plus C square plus 2 A B plus B C plus C A this is 16 no no no you don't require to start video ok so now A square plus B square plus C square will be how much 16 minus twice A B so this I am writing here A square plus B square plus C square plus 2 times A B plus B C plus C A is how much 6 is 16 so you got A square plus B square plus C square is 16 minus 12 which is 4 right so this is 4 ok now what all you now know this is 4 within bracket this is 4 and what is this minus 6 ok hence it is 4 into minus 2 which is minus 8 correct yes this is X so it was given that X to the power 1 by 3 is minus 8 so X should have been minus 8 Q that means 256 negative is it not 8 sorry what will this will be 9 no so 512 minus 512 like that so this should be the answer actually while framing it I wanted this to be X here and 1 by 3 was supposed to be here but I by mistake interchanged it anyways ok let's go to the next question here is the next question no no no no it's minus 512 it was missing correct the option was missing ok next question come on let me see how many of you can do this pizza party no problem Biba no problem simple one again ok come on downfall and why god big words Pranav where will you fall on the ground only I can never fall ok very good very good very good oh my god I was thinking that D was the answer still many people got it wrong one more question ok yes so A plus B plus C is 0 that means A plus B is minus C B plus C is minus A and C plus A is minus B and game over so this term is A square times minus A and then B square times minus B plus C square times minus C right so this is minus A cube minus B cube minus C cube that means this is minus A cube plus B cube plus C cube and we know that if A plus B plus C is 0 then A cube plus B cube plus C cube is is it right minus 3 ABC was the answer correct got it anyone didn't understand once again explanation good what happened Monisha any problem keep it on screen ok Monisha can we proceed ok last question of the evening leader board 2 only 2 people 3 people from top 10 ok very good and we still maintaining the lead that's fine last question guys very simple very simple good night sleep after this question I will repeat explanation after this don't worry those who want any explanation to any of the questions please stay back will repeat don't use calculators not needed I hope I am right don't stay awake till 12 o'clock not good if anyone wants me to wake you up let me know I have a software for waking people up here is the cool still 26 people got it right that's nice and I think you guys fell for the trap those who have so 16 there was a 2 here I hope you saw that 2 right so this is right otherwise it was very simple question so this is a cube plus b cube plus c cube minus 3 a b c divided by a square plus b square plus c square minus a b minus b c minus c a this was leading right so hence this is a plus b plus c isn't it a plus b right so a plus b plus c is 2 but there was a minus 2 also so 2 minus 2 is 0 answer was a ok so there was a in the last question sorry if you if I hurt your sentiments but then that's how life is you will have to get trained for all of that and the final leaderboard is this so this is the final one see who came on ok so Anvi maintained the lead till last very good congratulations but then I see lots of people who were last time were are not there very good Anvi from Rajasnagar is 7976 points very good very good very good then Anirudh Akshay Karun Ishika so these are the people we have already done till what polynomial didn't understand someone said something Jagarap Singh said that we have already done till polynomial but in school we will again start from number system what is the point good revision no but hey guys my request to all of you please do not disturb me just because I have got a feedback from previous batches that once you know stuff you actually you know so just observe in the class don't go all out and solve all the problems and ok so please just be grounded you don't know anything right now maintain that ok bye bye guys take care see you again on Saturday be prepared for the next quiz on remaining portions of whatever geography is there and we will start physics mostly this week onwards yep bye bye take care and enjoy your school all the best for a great year ahead from tomorrow bye bye take care I will repeat this those who want to stay back for the explanation please stay back here is the explanation this was the this one right question number 11 explanation who wanted yes yes ok a 0 a plus b plus c is 0 and you have to find out value of a square b plus c b square c plus a c square a plus b cyclical expression this is called cyclical so a is replaced by b b is replaced by b then b is replaced by c c is replaced by a a is replaced by b like that cyclical right in such cases so what do I do from here if I see a plus b is equal to minus c or not first ok then similarly b plus c is equal to minus a right and c plus a is equal to minus b now a square b c b plus c is odd a square times minus a from here b plus c was minus a so this is minus a q similarly b square c plus a will be minus b q and c square a plus b will be minus c q correct so you have to add all of them so adding all of them ooh there was some explosion by locality anyway so a q b q plus c q correct see one got it yep and now we had a conditional identity we learned what was the conditional identity if you remember if a plus b plus c is 0 then a q plus b q plus c q is how much is it clear so can't I replace this a q plus b q plus c q by 3 a b c so then it is minus oh is it now it is clear clear anyone else wants any other explanation please tell me sorry for that yeah can I do any shall I clear this off so that you can understand this properly for explanation I had done that okay is it okay understood okay buddies bye bye and enjoy your first day that's cool see you all got this no miscellaneous quiz let me see if I will I will give you two days notice if I am done with the preparation of the questions then we can do okay I'll tell you okay do you like more miscellaneous quiz huh bye see you