 Hey, so so guys, can you all hear me? Hello? Good evening to everyone. So welcome to centum R and I hope you have a notebook centum R book and pen with you Yeah, now can you hear all of you can hear? Yes, very good. So welcome guys Bring a notebook and a pencil or a pen you will be required to again solve and then answer you have taken your dinner dinner done or still pending dinner done very good very good Oh, some people haven't done it pending no problem. So we'll try to finish by nine o'clock and Okay, cool. No problem. So next Saturday, you are ready for another quiz And I have already asked can't hear you and won't respond Yes, only 50 people. No problem. Let it be history or geography history or geography. How many for history? How many Geography lots of geography people are there. Geo, okay geography, okay? geography geography, okay? Okay, okay, okay? History, okay, John. We says Prateek history to history both never and will do everything but first first what should be done geography or geography geography who's this who's so happy with geography Geography, okay, so now people are giving their voice vote Okay, very good. How about English now? I will I will be fairing pathetically bad in that so really really English is not my cup of tea any literature for that matter Yes, you can I can conduct quizzes on Sanskrit and Hindi by the way So Sanskrit was the language which I had taken in my 10th grade So I can do a quiz on Sanskrit as well as Hindi my mom was a Hindi teacher So hence that ways I have learned subject of Hindi as well So Sanskrit and Hindi and any other subject, but English English. I can't do because there are lots of Technologies in Italian. Okay. Yes, Italian. I can do No one will understand but I'll do I can do Okay, so Sanskrit is easy. Yeah, okay French no, sorry No, not at all. I can't do French Hebrew. Okay, everyone is Yes, you know mentioning some of the Teacher how to get into IIT you guys will get into IIT any which way if you really work hard from now on no one can stop you You guys are much more advanced than ahead of so many people So hence Okay, okay, okay. Okay. Now Japanese and all that now sell out so shall we start so this is uh How many 60 people are there? Okay. No problem. So Yeah, so I can wait. Okay. I can definitely wait But not beyond 8.05 because otherwise Time will be shot up with us. Okay with subject Subject is mathematics. Yes waiting time you're waiting Okay Thirds only are exponents also mixed. Yes. I'm Monisha. Correct. What what choice do I have? Anyway, I have only one choice To wait for you all to join and then we'll start Right last one minute. Maybe you see we already are in 70. I figured so everyone is there. That's nice. Good Gaming quiz, right? Uh, yes, so Okay, so 70 70 people have already joined Nice. Yes krish. I made the question I spent some good two three hours researching on how to trap you guys So that you know, but then every time I fail So you guys are much smarter, but yes questions would be, uh In that, you know, it has been designed such a way that you will get tempted to mark an answer and that will be wrong 100% so hence don't be tempted answers, you know Every answer you would be knowing but you will be tempted to mark a wrong answer So hence read the also do we have to answer against the guts feeling? No, don't don't apply gut feeling here right now All all your guts are are we not that mature to have feelings about mathematical options? So don't use gut feeling So work it out if you can't don't mark it. That's better. Okay, but then I would advise no one to just randomly mark it because it's going to be useless You know, even if you are on the top of the list of the leaderboard and all that doesn't help So the if I were you I would have done this I would have read the questions carefully took time no problem solve it And anyways, I will get some marks the some points the moment I mark it So hence the idea and objective is to learn And the questions are made in such a way that you will be tempted to mark a wrong answer point number one Point number two, there will be very close options very close options. So you my I my Uh, you know effort has has been to make sure that you are in a confusion So that because I am trying to simulate the actual Exam environment as much as possible. So Hence that has occurred to us that will occur to you as well And hence, okay, no more unnecessary unnecessary chatting in the chat box. Don't don't get distracted guys Okay, now can we start all of you All of you ready? Okay now no more discussions over chat the chat chat box is for me to see who are not able to comprehend Any particular question and then I work with them and you guys also learn how problems are solved So hence let's utilize the chat only for that All other discussion when we'll go for a pizza party. You are free to do anything any any discussion. No problem. Okay So here we start and Let's start three two and one start So the first question is on your screen Do not mark it randomly. Please Questions will be something which kill which can Trap you Okay, so you have to read the question So initial questions will be like monisha you it's better to check now. No no problem. What is the problem? There will be, you know So once you are in that momentum, you use that momentum to not do Not mark any question wrong take time. Hamstika. No problems at all dear. Please understand Yes, please take time. Please take time. We have lots of time to improve in terms of speed But once your you know habit is set in marking hastily I will not be able to mend that ever so hence from experience. I'm saying Right now. Let's let's focus only on accuracy. No problem I would be happy if out of 73 all of you get correct. That is Yes for pizza anything above 50 is pizza Okay Yes, I'll tell you there The exactly this has happened in with me. I have lost good amount of You know Okay, anyways, it's shallow. Okay Fair enough. Lots of people got it, right? Okay. Good one. Good one. Okay So those who could not could not get it. It was very simple. You had to just simply rationalize. Oh, sorry So rationalize the Just a minute So you had to rationalize the numerator, right? So how to rationalize the numerator we had discussed this But could not see the Smart people never mind. How does it matter? How does it help? So root three by seven You have to simply multiply by what was the rationalizing factor root three And you will get three upon seven root three Simple, right? Okay. No, it was very very simple. There was no big deal on on this. So me Okay, anyone any x here Any person want to get an explanation? Any further explanation? No, very good. So here is the first Oh, okay. Okay. Everyone will get lots of food. Don't worry. So harsh is On top of the list very good Very good. Right. No, not that. Okay. Very close Barat and harsh. You're almost on you exactly same I think I don't know what has uh, you know, uh Made this for her. Anyways, so let's go and go to Next question very close on if you see most of you have marked it very fast. That's encouraging. Okay Next question Take time take time. Do not do not Do not be intimidated by the question guys very simple question Very simple. Do not get intimidated and work Think and then then mark it What is that even me and what is integral cube? So which one will have an integral cube root if you find out the You know cube root of this which one will be Who or which one will give you an integer as a cube root? That was the question Harita, that's it. Ahaan. So then I understand this So which one of these will give you An integral cube root questions will not be that straightforward. Okay, so you have to be ready with such things. So In the course of let's say we have around 52 weeks in a year So in 150 plus centum hours, you will be ready for all of this this kind of this will start flowing in your blood Integral cube root can be cube root, which is integer but check Okay, so lots of people have bought it. Correct. That's encouraging So integral cube root. What is integer? What is integer guys integer is you know integer what integer is so I am not explaining that So hence basically which one of them would have given you D so let's say if you want want to find out the cube root Which one is integer that was the question out of these three Which one or these four which one is an integer? Oh, sorry. This one is three so which one Yes, we will be doing raga. We will be I'll be talking to you separately. We will be having an accelerator batch Which will be you know All all of your performances are being monitored now So hence this is why we do it never never mind. So This is where you will get an integer. Why because If you see what will this be 11 1 1 0 1 by 3 And you don't need to solve anything by the way. You have to just check which one was Uh integer. So hence this was divisible by 3 very much This was also divisible by 3. Why we had to use what? Divisibility or by 3 Yes, that is the method. So you have to add all of them See clearly this is divisible by 3 but this one is not why because 9 plus 1 is 10 not divisible Here 1 plus 8 is 9 and another one. So this is this is ruled out. This is ruled out Then what about this one? This is true. This is true the moment you saw that And option was c Right Did you did you all understand any any issue in this any problem? Yes only c is divisible right clear Very good any any difficulty guys any x any further. Okay So leaderboard Okay, so some shuffling no No, very good very good That's great Okay, okay folks. Let's go to the next question. Don't worry about the performance right now only 100 correct Next question is on your phone Now think very very carefully Read the question again twice The options have the hint of the question The options itself will tell you Which one is correct? Uh I then this will take you take you as a new entrant in the quiz. You can still participate But your scores will be lost That will take you as a new entrant Then you'll have to participate from that question onwards like that So No worries. No worries. You can you know, um Uh continue playing maybe it it would you know, it can get sorted out. I don't know. Uh Not sure the options have the answers itself See my intention is this that after few sessions you become masters of it Why Sunayana? Why nervous? Yeah, nothing world is not going to be over. Don't worry No, no, no, no one should feel nervous and other things. Just Just relax. Okay Let it be wrong. No problem. If you learn that's the best advantage Good drag up Good. Okay. So here it is the final answer and two three Okay Very good. This is like even decision. Yeah, everyone has just uh, that means most of you didn't know it now Let me explain this Now How do you really crack this see what are the questions a is to the power b by c equals k where k and a are non-zero integers many a times There will be extra information given not needed. So hence where this is where the practice comes into, you know play So b and c could be any real number. You can deploy value and see take any a a is let's say five Okay, there is no restriction on a only restriction is non-zero integer. So five is a non-zero integer B and c could be any real number. So root two by root three Let's say b and c are this is it an integer? Is it an integer? No, right? So this is ruled out This is ruled out then be any rational number. This is also ruled out. Why five to the power seven by five Is it a Right? So this is this is not true Right b by c could be any integer. Is it true five to the power minus one by two? Let's say if I took I take this Is this number an integer? No But this could be possible. See that's why I keep on kept on saying the answer is within If you mark the arms options properly, there was any any any in all of them There was no any in this Okay, so hence Correct. Okay. So these three first three are not there. So fourth. What is what happened? You understand? Hello Yeah Okay, see once again I just took examples to Disprove it. What is the question question is Anyway, so what I'm saying is It is said that a to the power b by c Is equal to k where k is what a non-zero integer A and a and k are non-zero integer. So let's take an integer. Let's say a is five Okay, and choose b and c according to the options. So b and c could be any real number So my choice of real number are root two and root three Is this an integer? No, not possible Okay, okay, then b and c could be any rational number my choice of rational numbers are Seven and five. Is this an integer? No This is also not an integer Could be third option b by c could be any integer. So five And minus one upon two I took minus one and two as b and c Is this an integer? No, this is also not an integer Yes, sir. So this is Raghava. I have a doubt it didn't b by c So doesn't this mean the simplified form could be any integer because in because in the above options It didn't b and c could be any real number. That means that it's like b and c individually But in b by c could be an integer. That means For example a b by c is two Then works Five squares or not. So this option Is the only possible option What about c C b by c could be any integer. Okay, five to the power minus two. Is this an integer? No Five upon two is an integer No, no Right and this is also ruled out Right. So you have to rule out Okay, very good. Next conceptual question. This will enhance your understanding of exponents. No problem No problem. I understood Raghava. Where did you go wrong? Okay here You have to rule out all possibilities. This is exactly the same environment of an exam People get confused and in that rush They mark wrong answers Thankfully, there is no negative marking here. Just imagine you marked and you got a negative mark It's a very difficult thing Right. Okay, next easy easy So giving you a hint easy easy So you will you will be on a roller coaster ride in the quiz easy easy Some conceptual some momentum building easy easy Go back to eighth grade Find an identity So in my this thing you will have Ups and downs highs and lows Now miss piquing his disastrous So I'll tell you a story while you are solving. So when I was writing iltj. There was an exam called prelims Okay, prelims and uh in prelims what used to happen right? Uh, they used to give us an omr seat omr sheet, which is called optical mark reader and uh, normally, uh, you know Usually the process is you solve a question and mark it bubble it then and there But there was one friend of mine Who first solved all the question? And then in the last 10 minutes, he started marking. Okay started marking So one kasi 2 kadi 3 ka a like that okay, and then He did one mistake and he just skipped one row of bubbling And so one kadi became 2 kadi One kasi 2 kasi became 3 kadi and like that one one, you know one offset And then he got negative marking total score Whole paper is gone. Exactly. So hence I I have seen him, you know almost losing his life because of this So these are scary stuff. So hence be be prepared be ready. Don't be You know overconfident at times as well very good. So most of you have got it, right? But 19 people have got it wrong as well. That is something which is concerning So I will solve why people have got it wrong So root 3 minus root 2 square you have to just use an identity a minus b whole square Is equal to a square minus 2 a b plus b square. That's it. This is what this was the game Yeah, so you didn't see the sign. This is what happened. This is what this is what happened So hence it is root 3 square Then minus 2 times root 3 times root 2 And then plus root 2 square. So hence it is 3 Plus 2 minus 2 root 6 that is 5 minus 2 root 6 Hence I said I will give you options very very close so that you know you will make mistake Okay, so a is the right answer and many people would just multiply root 3 and root 2 to find this maybe so hence root 6 So options will be very very close Why do you like sir? Why do you do like that? Why because sanvi? I don't want you but say to do the same, you know thing in a real exam Now that you have tasted it Now see sanvi is saying isn't it, you know, is it one? No, it's not one sanvi So root 3 minus root 2 is not equal to 3 minus 2 here not equal to right. So this is Okay Okay, fair enough anyone wants an explanation further on this Okay, here we go then and Read about So right now I keep on saying this statement the more you sweat in the rescue bleeding war That whole I will re-explain don't worry. Okay, so hence Okay, so here is the anyways before that. So re-explanation is you have to square this compound third and we discussed this right a minus b whole square is a square minus 2 a b plus b square Okay Okay, I understood nithya. So hence I simply deployed that here And squared or you know a is root 3 so root 3 is a and b is root 2 And using that you deploy it get the value the value is 5 minus 2 root 6 nithya clear dear Clear dear is good. Wow clear dear Okay Got it. Okay. Fantastic. Don't make such mistakes now. Okay. Here is the next question ready Many of you will lose marks in carelessness in this question I give you I give you so much so many hints, but you don't use it properly My age lies in negative numbers. Oh my god Oh that word I don't like don't don't don't don't don't do that. Please Please please all for life All for life everyone for life Okay, very good. So this is very easy again you have to be observant and Oh this miss clicking you have to use PC for best performance For this experience because there you have to actually take your mouse and then click it on Be right this thing so hence option so Raga just saw the clap. Uh, that's nice Okay, say it's not easy. My thing is convert everything into No, please connect. Please connect. Let me see. Yeah, cool So most of you have Got it, right? Okay See, uh, the only Trap was and this is a common mistake people do is that I had inverted the order here and most of you would have Yes, I'm pizza is anyways you know, uh Assured so hence, please be careful that when you do it It is root six square minus root seven square Out of temptation people just because they are habitual of you know doing such exercises So they will mark one which would be wrong minus one is Okay, okay six minus seven is one right No trap at all. Good. So now at your alert. So there is no trap for those who are alert Okay here next Prateek. I'm really sorry for that. Hey, what happened hush you miss clicked it Okay, the order has changed. Okay. Never mind. Never mind. Good. I'll if just reason and current next question for you guys here is the next question. Don't be intimidated 2020 is the year of corona virus. So hence I thought probably I should include that year In the questions as well Yes, I understand. We buy two. I second you on that. We're really depressing 2020 is also there. No monisha So part 2019 part 2020 don't get depressed guys. Don't worry You will solve the issue You will solve the issue. No problem. You guys are only hope So become good doctors later on good researchers And then be ready Monisha is saying she's stuck with her sister and hence he dating Why you get rarely, you know very rare You know occasions I am longing to you know meet my sister You know because of this we are not able to Meet her. Okay. Never mind Okay, so the final 20 seconds. I hope most of you have already answered those who have not please just Make a choice and then let's go ahead Okay Okay. Okay. Okay. So root of n plus 1 minus n Okay, time's up and here is the Oh, so there are still people who could not get it correct and I will you know explain very easily So what is this what you need to do was you have to what is the rationalization is rationalizing factor In such cases first find out rationalizing factor Okay, and the rationalizing factor is 2020 Plus root 2019 Okay, and then what simple it is one upon 2020 under root minus 2019 Correct answer was adr right, so hence 2020 You don't need to write so much and you know invest time also while you are in mcq Okay, right. So hence if you see this is nothing but Again a square minus b squared. So you will be left with 2020 Plus root 2019 divided by 2020 minus 2019 which is one Right. No, is it understood by all This this item is one So denominator is one Okay Is that fine guys Okay, great. So let's move on to the Leaderboard, okay No, actually manisha. I love writing on on this on the pencil is Uh good So yeah, good. So there is some Okay, very good. Oh, you have put up very good Nice, let's go to the next question. Oh, sorry Thankfully, I did not Display the question over there Okay. Yes. Yes, Anika correct Apple pencil they have really put a lot of effort to design that Yeah, here's the question guys Be careful Be careful don't rush through Don't rush through it Don't rush through it You might get it wrong Think about it These are called exponential equations My brain seems to be lagging Okay So Arthur what you need to do is uh Startup programs have to be closed that will make your window XP faster That is your brain faster Do not insert XP Yeah, that's true. I was I have been brought up with XP only So I am a XP generation guys my first windows, uh This thing was windows 98 And my hard drive was 20 GB and my RAM was 128 MB first computer Okay, here is the okay. Okay Only 38 people why Okay, okay, let's let's let's see what happened. How many x why what happened any x here any x Okay, got it Never mind now those who have could not Focus on the screen See if x square x to the power of minus two is 64 guys What do I know one upon x square is 64? That is what we learned So x square is one upon 64 Isn't it so x will be plus or minus one upon eight because Right x square x will be plus or minus one by eight. So hence x to the power one by three will be Plus or minus one by eight to the power one by three Right Anyways, so for me jagra. I need 80 people getting it right now. So hence plus minus one by two All of you agree with this Is this clear so far simple you should have taken a pen and a paper And then write like that and then you could have solved it now What was the question add x to the power one by three to x? Right, there are two possibilities when x is so that you know, there is no negative option here So we'll rule out the negative one So simply one by eight plus one by two was the answer because x to the power one by three was one by eight And x is one by two. So hence Hence, what do I what do I see if you add both of them? I'll get five by eight Okay. Yes, Chris will we talk about it right now? Okay Is it okay here to those who had written x? Did we use anything? Did we use anything which is beyond our understanding? No, so hence, don't worry. Let's go Okay, so uh Monisha is on top position now What is LOTR a lot of the rings a lot of the rings, okay, very good next slow slow slow Don't get trapped people at any time. That's really good Right now you should take time and solve 28 seconds. No problems with that. You should get it correct. That's the first No problem Nikita take time, but be correct. Okay. No problem. If you're right correct, then it's fine Ah through you got trapped See that was the agenda Through but so this is a normal human tendency that you know, we are the moment we see Something very tempting You forget and many a times you would have realized this. Oh still lots of variation is there Okay. Okay. Okay. Jen here here now all focus here guys. See still people are not getting it correct Oh Yes, so basically most of you have marked x Most of you are marked x x. I believe hence you have got it wrong. That was the Answer was to find out root x the question was to find out root x not x Okay, so hence if you'd have found x as four How many of you did this mistake? Tell me that you are marked for Ah see Now right Right. See hence I keep on saying that you know, please be very very careful while you are Solving it was so simple question. Just because you are tempted to solve it faster and you got it wrong Again, so but never mind. This will repeat once more so 125 to the power 3 into 1 upon 9x was the thing and this is 5 to the power 1 by 4 Right. So this is 125 to the power 1 by 3x is 5 to the power 1 by 4 Now this is nothing but 125 1 by 3 whole to the power 1 by x Correct is equal to 5 to the power 1 by 4 So this is 5 1 by x is equal to 5 to the power of 1 by 4. So all of you would have reached here and then immediately x is equal to 4 and you saw an option over here and you mark this and got it wrong. But the question was to find out root of x, right? So answer is 2 not c. Okay, learning, what is the learning? Learning is don't be so fast that you miss the bus only. Okay, here is, so you are running more faster than the train and hence you lost the train, missed the train. Okay, here it is. So new, okay, so new shuffling. Okay, now my speeding kills. Now see, now you realize it. Next question folks, ready, ready, don't be over fast. Okay, here. Now these are confusing grid structures. So hence, this is deliberately made to make sure that you are fixed or you're confused between options, right? The answer you're, so people are taking time. That means they are solving. That's encouraging. That's really encouraging. Take time, but be right. Then we'll go to a stage where we will do it faster. So we will be playing, you know, so where the timing will be reduced to 50%. So you have to answer in 50 seconds. And the question will be doubled. Okay, so people will make more wrong decisions. Okay, so this was very, very easy, very, very easy very, very easy question. So now you are warming up, but then see, okay, but still the majority are getting it correct. So I have to explain it. It was very easy guys. So yes, yeah, I can hear you, your beautiful voice, but then yeah, now, so three to the this 500 can be written as 500 to the power one by three, which is 125 into four to the power one by three. Is it? So this is nothing but 125 to the power one by three into four to the power one by three. Okay, so 125 to the power one by three is five. And this is third root of four. Beautiful. Then what, what is it is equal to k root of B, this is which form. So hence, let me not go up. So k is equal to five. A is equal to three. And B is equal to four. It's like in the childhood used to match square, whole and square peg like that kind of thing. Okay. What happened? Nice. What happened? What happened? Okay. Okay. What happened? Tell me, tell me, is it okay? All fine. All of you understood now. So what is k five a three before which option B? Okay, all those who could not answer. Give me up. Cheers. Or why comes up? All okay. All okay, guys. Okay, all of you write cheers. Cheers, cheers, cheers, cheers, cheers to all, all students participating in quiz, you know, raise all of you. Very good. Very good. You guys are doing great work. Next. No, it's not very happy. Never mind. Here is the next one. Okay, so very good. Very good. And here is the next. Monisha still on maintaining the top lead. Very good. Next. Make mistakes. Very simple, but very prone to make mistakes. People would be making mistakes. I am giving you my future prediction. They will miss this question because not because they don't know how to solve, but because they didn't pay attention to detail. Why Vibha? You don't like such. Okay, never mind. So my intention is only one thing that you guys be alert all the time and get right when you all will succeed in any of the exam. I will be the most happy person. Okay. Why do you confuse us? Because if I see it's like a cricket coach, if I teach you with only full toss balls, then when you are facing your curves and hook, you know, when you have to play hook shot, how will you play right? You'll get out, right? And then it will be a defeat of mine. What is it? You know, my effort also is lost and I get defeated. So you guys are my weapons, right? So my weapon should be sharp. Okay, so never mind. All of you would be at the same level. Just I prefer challenging questions. You will get challenging questions. Just hold on. See the idea is first to, you know, make sure that your senses are in control. So most of you are making mistakes because of that. Okay, here you see, so people think that it is easy question, but still people make wrong. I told you, right? Most of the answers are where people have marked it incorrectly because of their condition, not because they didn't know it. So this was the question. Okay, right. So what was and if I if you remember, I had told you this was simply if you rationalize the denominator and denominator, sorry, denominator, what will you get rationalizing factor was this, right? Now what route, route nine plus root eight on top. And here it is nine minus eight, which is one. So effectively it is root nine plus root eight. It was similar question, similar question, previous type, you know, question, but then I knew where you will go wrong. So this is three and this is plus two root two, root eight is two root two. Now you have to compare three a minus b root two, right? So what will be a guys? A is simply one here. One is hidden one and minus b is two. So b is minus two. Correct. So hence my dear friends, that was the intention. So easy questions are very dangerous, very, very dangerous. I have faced in my life. Hey, Agatha Christie. Yeah, come back. Nikita Garwal rocks instead of that. Now, so hence this is what is required. And hence these type of questions. Now you understand even for us easy questions, see the breakup only 19 out of 77 got it. Correct. So hence I didn't get it. Once again. Did you, did you get the rationalization part? Did you get the rationalization? I will suggest more, more good novels. Don't worry. I have a collection. I can give you 100 such novels free. Don't worry. Okay, I showed you my collection the other day, right? I have a thousand plus collection of novels. Very good novels. Okay, here, here, guys. Now, please mute, mute. Now, here. So those who could not understand once again, one by root nine minus root eight, multiply, divide by its conjugate, that is its rationalizing factor. So this should be easy, I believe. So when I do that, you will get, yep, root nine plus root eight divided by root nine square minus root eight square. Right. This is root nine plus root eight divided by nine minus eight, which is one. Okay. So hence root nine is three and root eight is two root two. Is that okay? So hence this is equal to three a minus b root two. Right. This is what it was given, right? So what could be a then? So this entity can be written as three into one plus two, sorry, plus or rather minus minus two minus minus two times root two. Right. So match a now. So a has to be one and b has to be minus two minus two. Is that clear, guys? Easy, but tricky. That's what the intention was. Right. So even easy questions, people are not getting even 50% correct. Intimidster. Next. Here is the new see lots of the only four out of top 10 got it right. That shows that how you are not paying attention. Okay. So only four out of top 10 six out of six of the top 10 got it wrong. That's surprising. That's really surprising. Next. Very easy question. But again, I know people would be takes or hate hate hate make efforts waste. Actually, I have now realized that you know, anyways, anyways, so in fact, in this question, I have myself got trapped. So hence don't worry. It happens. There is only every every question. There is something which is really challenging. So I will confess myself. I have got trapped in this question. Yes, correct. Now I realize that it was really bad question. Answer is the answer is the I will confess it because yes, yes, this was a trap question actually. But then somehow the answers I have now I realize that I you know the answer while I am marking the answer I have put it wrong. So it was very simple question. Actually, yes, answer is the race, the reciprocal of one upon five plus root two will be simply five plus root two. Is it so one upon five plus root two is simply five plus root two. There was no brainer in this. Right. Many people would have done the rationalization. Okay. So don't worry. Don't worry. Okay. Okay. Well, D is correct. So how many of you how many of you marked it D? So tell you that how many of you marked it D. So all of you marked it D. Okay. Okay. Never mind. So hence, let me see. So let me cancel this question. Okay. So I'm canceling this question so that there is no marks allotted for this. Here. Let me just do the back end. Wait a minute. Give me one moment. So reset it. Okay. Reset it. So what you guys can do is now all of you mark D as the option. Okay. So next question when it is the previous leader board. So don't worry. This is the previous leader board, previous leader board. So now next question, which will happen, you just mark it all all market D. So all of you marked D so that it's nullified. No, nullified mark mark D so that you know, so I have canceled that anyways. So all all of you marked D so that you get D. Okay. Fair enough. Your wish fulfilled. So that because there was some error, there was the option was wrong. So hence, so now fair enough, all of you are at the same platform. So everybody would have got it correct. See, there's still few people have marked it C. That's surprising. But anyways, now people are deliberately okay. Next one. So this is a this is a refreshed one. So that is canceled. Okay, so that was canceled. The 11th question number 11 has been canceled. Okay, next, ready for the final one. Here is the final question. Code is 699165. 699165. It's there on the screen. Correct guys, don't be afraid of being slow. But in the in the last not too many. That means if you are taking time, you are perfect. You are going in the right direction. At this stage, I would recommend take time. And that's all. No problem. Okay, so here is the Okay. So most of you are right. But again, not lots of people have not got it correct. Why? Why? Why? Why? Why? Why? x anyone x. So this was very, very, very simple, very, very simple. So hence, x is one upon two minus root three, which is equal to if I rationalize the denominator, I'll get root two minus root three multiplied by what you get. Or the rationalizing factor is this. Okay, is that okay? Now, this is equal to two plus root three divided by two square minus root three square a minus b a plus b is a square minus b square. So it is two plus root three by four minus three, which is one. Okay, right. And those who attended my class, I told you this was, you know, one step process. So this was root four minus root three. If you remember, this is directly equal to root four plus root three. Do you remember? We discussed this. We discussed this in the class as well. We discussed this in the class. All of you remember that if it is n one upon, but what is the thing? So one upon one upon root of n plus one minus n is simply root of n plus one plus root n. If you remember this, we discussed this in the class. Okay, so directly you could have written that as root four plus root three, that is two plus root three. Now, this is equal to x. This was x. That means x minus two was root three. x minus two was root three. And what was the question? Find out x minus two whole square. So square it, you'll get root three square. So your root three square is three. Clear to everyone? Any doubt in this, guys? Anyone? All clear? Yes. Okay. So here is the final leaderboard. Fantastic. Okay. Hey Monisha, what happened to you? You did good. Okay, but still you are. Okay, okay, okay. Wow. Wow, wonderful. Congratulations. What happened? What happened? I used to be no problem, no problem, no problem. So you checked your accuracy. Well done. In fact, the last mathematics, grade 10, you know, grade 10 Centum R also was won by a girl. Very good. Fantastic, guys. Keep it up. Very good. All of you. And you came close. No problem. Very good. Rishabh. Well done. Well done. And then Raghav. Right. Learning is even silly questions might go wrong. Srijan, you know, all of you. Good. Well done. Abhishek. Very, very well done. Krishna, very good. Okay. And then what? Groove. Very good, Groove. Vihan and Nishant and all of us. Don't worry. There were 82 people. All of you have now learned something and the learning is again, my dear friends, younger brothers and sisters, please understand this. Don't really rush through question solving at this stage. Take your time, struggle with the problem and, you know, and solve it correctly. 100% correct. Okay, guys. So, thanks for your time. I hope this will be uploaded. By the way, just wanted to make an announcement that all this Centum hours are now being uploaded as a part of this thing. You know, you can check it out in Learnys. So, this is also available. So, geography I've already uploaded. So, you know, you have to just wait for the others to be, you know, there. So, I had not published it, but anyways, so that's, I'll show you how it is. How does it look like? So, basically, here it is. Yeah. So, in the grade nine geography, grade nine geography, this thing has been now uploaded. You will get it published in today's, you know, the first two chapters this thing which we did is uploaded. So, all of them will be there. Okay. Very good. So, we'll meet on Saturday with your geography second chapter. So, be ready and let's see who wins that day. Okay. So, bye. Take care and stay safe. Buddy's all the best. Bye. We will be meeting tomorrow also. Sorry. Center MRA was talking to you guys.