 on your screen guys please take your time while solving it don't really jump on to any conclusion not straightforward solve this question it's not straightforward first question is good people are taking some time to solve that's nice so tough options are tough okay so oh no oh no that means you you you when you look at the solution you will be I don't know let me let me express the solutions or okay cursing don't curse me very very easy now learn learn only seven people could get it but then see intensity will go up intensity will go up so please brace for you know all that so hey they go how to solve this one now look at look at the screen all of you now understand how to how to do it so it was this expression given and there was a hint in the question itself that there is a power three okay so power three is there so you have to cube it but then cubing directly will not help you have to write this can I can I do that can I do that this is what you have to then what you need to do is you need to cube both sides right right so hence now don't see this is now no no chatting in no chatting right now then you lose the purpose we all lose that purpose the question is that these kind of questions will be there it is very much within your syllabus or whatever you can call it it's related to cubing of binomials which we have studied you could not get it at the right moment and hence someone who would have done these kind of problems will be ahead of you so I don't want any of my students to be like that so no one should be ahead of you guys so please pay attention how these problems are solved mathematical manipulations you have to learn so nothing beyond this we are going to do right don't you know how to cube how do cube cubing is first term is x cube second is minus one by three whole cube so let me write a minus b formula is a cube minus b cube minus 3 a b a minus b right this is the formula for minus b cube I am going to use only this right so x cube minus this then what minus 3 times a which is x in this case is 3 to the power 1 by 3 correct and then a is x minus 3 1 by 3 right and on the right hand side what will you get you will get 3 to the power minus 1 right nothing beyond this then what x cube minus 3 minus what will this be 3 x 3 1 by 3 and see x minus 1 by 3 to the power 1 by 3 was nothing but 3 to the power minus 1 by 3 did you understand this step this was a crucial step from here this step was very crucial x minus 3 1 by 3 is equal to 3 okay so the moment you see this I wrote this and the problem is solved okay see what will this be x cube minus 3 minus 3 and this entire quantity is 1 3 to the power 1 by 3 into 3 to the power minus 1 by 3 okay so minus 3 x is equal to 1 by 3 multiply entire thing by 3 what will you get 3 x cube minus 9 minus 9 x is equal to 1 okay so what is 3 x cube minus 9 x is equal to 10 right 3 x cube minus 9 x is equal to 10 correct below all good all good understood so hence hence instead of how do you ace these kind of questions how do you ace these kind of questions first stay calm because if your mind is restless you will not be able to solve and trust me friends exam conditions are exactly like these panicky you know and you are you know your hands will have full of sweat and all that don't panic and if you lose focus you lose it yep there will be okay let's see how many of you got it because you are you lose focus because you keep on your focus is on chat box hence if your focus is on the question you will be able to solve did we use anything which you didn't know 1 by 3 this is 3 to the power minus 1 more cubing both sides did you understand I cubed both sides LHS RHS both sides so the person who asked who asked this question did you get it yes I got it yep okay next let's see the leaderboard first leaderboard only seven got it mostly people that I've guessed I believe okay so freedom Jhagrav okay good nice okay very good let's go to the next can be good next question what or no what irrespective of that you must know how to solve the question the do those who are if at all there is a bot it's his call how does he want to plan for his life okay for her life hmm solve this this shouldn't this should be easy very easy question now first was the eye opener next is this should be very easy year 2020 is there any role of this 2020 year 2020 please read it carefully signs are traps okay let's see what is the oh no oh no why what was that many people did not see the sign negative sign did did you did you already do not see the sign this sign did you see the sign those who could see the sign it was very easy it was so easy did not see easy most of you so that 20 people who have not got it they have made this mistake these be option be those who have written be because too many numbers so here is where you have to you didn't need to do anything when you saw that question this is a this is be so if you are this is again a and this is again be so the question is a minus be whole square minus a minus a plus be whole square this was the question right so a square plus b square minus 2 a b right minus a square minus b square minus 2 a b so the answer is minus 4 a b right minus 4 a b and a was x to the power 2020 b to the power 2020 everywhere these two terms were same so there was no difference at all only difference was minus 4 4 minus 2 2 ruled out ruled out ruled out minus 4 a right so so our doubt where did you get the minus 4 so minus 2 a b plus minus 2 a b add did you get it now clear yes all all clear everyone clear on this this was so simple only identity to be used was this if you are not careful with the sign then obviously it is going to give you some pain right silly mistake again say sorry if each one says each one should say sorry to each one say sorry all of you those who made mistakes say sorry say sorry come on right don't repeat this problem or issue again okay but when you say sorry feel also today eat half a chapati less why right or tomorrow do the dishes mom tomorrow or clean the mop hey what is that clean the floor mop the floor a little bit more right oh you finished it Harita finished eating so her her punishment is she will mop the floor of her room everyone who made a mistake your punishment okay chalo next so eat eat don't don't cut down on your eating do some extra physical work so Jadoo look out Jadoo at your home next question okay so this was the new then we can we is leading why God can we how come you're on top great maintain it and who else is not that behind Russian Tarun Krithika Risha Nishant Rishabh Dima he and Jagra let's go to the next question what is 26 26 is what observe the more you observe so many people are 26 how come observe observe observe observe identity trap observe identity trap observe identity trap observe identity guest there are guesses are generally correct when you look at the solution you will laugh at yourself and again I will make you say sorry very easy see the questions will not be straightforward in my centum are don't expect questions to be straightforward I will make who's who's this oh no why answer is 125 no answer is zero zero was the answer zero was the answer zero was the answer zero and it was so simple our question 61 beautiful number a prime number 61 is equal to x minus 4 x square if I would have written you written given you like this you would have cracked in no time is it if I would have given you like this you'd have cracked it no time so this is x cube minus 4 cube so can we repeat this so I simply took this term and multiplied here simple so won't the given expression look like this right and this would be simply 61 is equal to x cube minus 64 so x cube is equal to what 125 isn't it isn't it so x is 5 if x is 5 x minus 5 is 0 how many how many how many steps say sorry again can't talk back right sorry say sorry those who did not get it say sorry sorry to everyone apologize yes you should apologize and one more floor to be mopped tomorrow and send me pictures while you are mopping the floor those who made the mistake okay no keep your words please mop the floor tomorrow half half of your house how did you know people get it wrong because I also got it wrong when I was in your age so I know you are like me so you will make the same mistake okay next next question before that okay very good very good very good folks that means you are paying attention if at all if you're not guessing it you just stay focused only on that screen where the question comes if you you know who's saying who's and what is it yes sorry someone is saying something anything any problem guys can we proceed yes now you understand practice makes a woman perfect okay so please hence so many worksheets there on the learnest okay next obviously man and women both from one issue asked to hence I said women women are already perfect see Arushi is bang on target great stay stay perfect always but still some bit of practice will improve your status let's solve this one so that dot dot dot means all those terms are continued for example 100 minus 99 times 100 plus 99 99 minus 98 99 plus 98 then 98 minus 97 right all there is this is series series of such some that dot dot dot means it continues till that so I hope you got it through say easy easy ZZZ ZZ ZZ ZZ ZZ region says easy ZZZ ZZ nishant easy ZZ so number of ZZ sir sir but do you see ABCD option no sir I don't see that I'm reload reload don't worry about your course it will be there reload solve solve solve solve solve sir again if you if you when I solve this again I will make you say sorry so macho don't expect straightforward questions please put some thoughts behind it some thoughts very easy very very easy very very easy see most of you have got it cool that's nice that's nice that's nice very good you have to just observe observe what is this identity is this an identity yes or no identity what is that identity 100 square minus 99 square okay next next term what is plus 99 square minus 98 square here itself the you know trick was and it would continue till minus 3 square plus 3 square minus 2 square plus 2 square minus 1 is it and beautifully this is going going gone gone gone gone gone gone gone and what is left 100 square minus 1 square so this is 1 double 0 double 0 minus 1 so 9 9 9 9 is equal to 9x so x 11 11 11 right got it so why 9x why 9x because here is 9x okay sir trapped that it's trapped okay cool so answer is right right clear no doubt no doubt any problem in this quiet question no doubt say sorry those who could not get say sorry sorry to everyone overlooked 9x Nitya so you are here in Centaur traps all around come on shallow good Tharon is fastest as well as highest okay next after this question after this question now the question has been displayed I'll take the doubt again no focus on chat whether you finish early or late world doesn't care you please solve and get it correct corona is not going to go back go back just because you got it right or fastest please try to solve and save the world 10 years down the line no chat focus on the question no chat raga whether it is easy or not no one will right now I can see lots of people are distracted no chat no chat here all of you just focus solve once 30 seconds are left then you can chat focus many people are getting distracted because of that chat itself I can understand so focus focus focus focus guys listen easy or hard stay away from chat telling you focus focus not focus focus now you can chat no many people have this issue of while solving they will see a who what is the world doing people are involved in more than what the world is doing rather than their own stuff so right okay easy question it is very very easy I hope most of you have valid oh still 23 people got the sign incorrect ha ha ha sign incorrect very easy again very very easy a minus root t you root 2 you have to just do this the moment I saw 5 okay the moment I saw 5 I was tempted to take it on the other side anyways I'll square okay now square 2 plus 3 got 5 minus 2 root 6 a square sorry plus 2 root 6 so a square minus 2 root 6 and 1 2 3 step over 1 2 3 step over right where are we using some out of the world formula here yes I know you made a mistake with sign I know that's where that's why I gave these questions I have taken some 9200 minutes preparing this so that you guys are aware but every time we are seeing that my efforts are going down the day don't get depressed so if I am not depressed you can't be depressed okay I wanted everyone should get correct option but then never mind show like don't worry don't worry stay spend time but then every time you make a mistake you have to say I have to realize then otherwise there's no problem there's no improvement realize realize that right okay next I should tell me frankly have we used anything which is beyond your learning have we used anything which is beyond your learning everything is within the scope of whatever you have learned you're just not focusing enough never mind chalo next question again fresh start don't look at look at the question and then just solve the order of the terms will be changed it will be shuffled just to check whether you lose cool or not that's what the test is about so situation would be at worst you have to make it align to your comfort and that you can do so no no no don't take extreme steps your dinner and all should not be skipped you should rather oh my god oh my god oh my how many if you got it right very good now see this was again very very simple question I don't know usually in the textbook you will see the question would be given like that right this is the format textbook correct but then I deliberately change it like that so that you become a little uncomfortable okay and that's where they will be testing you okay so x minus 1 by x is root 3 so hence you have to simply do what square game over no nothing more am I right so what is this x square then plus 1 by x square minus 2 is 3 so what happened hold on hold on hold on hold on hold on hold on don't don't write so much I won't be able to read that much correct now simple you have to simply subtract for right done is that problem out of your knowledge was this problem out of your knowledge so where is the problem where is the problem see everything you know right it was so easy right now so you have to just again problem lies within you know the fact that you are not again don't be impatient take time don't worry again no problem don't get depressed and all you will get another chance similar question Tanya saying these questions are not good at all so why do you keep such questions no it's not about your cerebellum brain and IQ and all that it's about focus and attention and you know just concentration nothing else you can all solve it okay chalo next question silence now focus okay okay which identity was which identity was used which identity oh most of you have got it correct that's cool nice who do you are you know randomly mugged oh my god never mind so there was an identity here there are cubes can you why do you see yes why do you guess don't guess 1 0 2 4 cube minus 512 cube minus 512 cube right is that understood so yep this is the denominator is this much now can anyone tell me what kind of identity is this what I need you have anyone on what is a cube plus a plus b plus c is 0 right what is a 1 0 2 4 what is the minus 512 cube twice because there was 2 d r did you not notice hence hence right okay what is this oh my god someone is screaming like anything okay so a b and c the meme oh is it I see so then don't you think this is 3 what what is what was the identity guys if a plus b plus c is 0 then what happens to a cube plus b cube plus eq it becomes simply 3 a b c correct so hence it will be simply 3 times 1 0 2 4 times minus 512 times minus 512 why because they were are adding up to 0 see 1 0 2 4 plus minus 512 minus 512 is 0 okay so 3 into 2 to the power 10 and then 2 to the power 9 into 2 to the power 9 the minus sign will get minus into minus plus correct so this is 3 2 to the power 28 this is in the denominator guys what was in the numerator 3 so what is this 2 to the power minus 28 and hence 2 to the power minus x is 2 to the power minus 28 so x is 28 below did we use anything again beyond your was it so so bad that you have to scream like that don't scream your vocal vocal box will get ruptured even if it is mean oh okay well why last 2 of them so where do you get these questions from ma'am I make it myself clear I think you forgot sir is an alien come on folks don't don't just be like that so hence the the thing is not now but sooner you understand my thing is that you know don't hide it like that in life will the traps tell you that hey here is here am I come avoid me I should I should identify the trap and tell you hey here is the trap that's that's what we don't have an adult brain like your don't tell us where the trap is usually only adult brains are equipped to face the trap yes sir okay she gets all you'll be trained sir make options easier see still people are but you learn are you learning or not next time when similar questions are there in any of these platforms will you be able to do it yes or no yeah that's the main objective dear forget about whatever is happening okay so learn learn learn again this requesting one and all please learn again the same thing here same identity so I hint I'm giving you hint also same identity now solve the identity which are you which we used the identity which we used in the previous question same identity here deploy it get the value quick oh no little sim similar identity so I'll correct myself similar identity not same the theme remains the same there was a condition the condition remains the same oh come on don't get demotivated it's easy are a Baba I actually let me tell you one story then do you know I have failed in computer science exam in my 11th grade did I tell you this story in my 11th grade I was I had failed in computer science exam so hence this don't take it as demotivating I didn't know I guess tell me computer exams are like the easiest exam and that too I failed just imagine how dumb I would have been computer science is what extended sir B&D option are same oh is it sorry so anyone but that was not correct anyways B&D was same huh very hard correct but that was not the option so you could have guessed it okay sir my thing kicked me out of the question 30 seconds before it ended oh I'm really sorry for that so was this question again similar yes or no how many of you got it 25 people got it actually no problem okay so yes any how many of you didn't get it again this was very very simple the moment a square plus B square plus C square is there which identity comes to your mind the identity which comes to your mind is a plus B whole plus C whole square right so this is a square plus B square plus C square plus what twice AB plus BC plus CA see even if you are not getting it correct don't worry these problems you are learning no different types of problems that's cool that's that's at least that is some take away from the session so please at least focus how are these problems approach that so the moment I see this problem I the moment I see these three squares I am tempted to use again again guys guys guys please then the purpose gets defeated please requesting all of you then the purpose gets defeated so we need to learn different types of varieties of questions and you know just imagine in 10 days time you learn 120 different types of varieties of question is it something which is really good to learn so you your database is going up so please at least that is one advantage right now look at now no no no here here here Arushi again then please requesting guys guys guys requesting all of you focus the main main agenda is oh then we again stop stop stop no one was like that I told you right I failed in my grade 11 okay so hence nothing is correlated like that you this is outright insulting please don't do that can can I have some focus then the winner when we are losing the losing the plot please don't do that okay here now focus focus come again come you know come come come to the screen guys so they go a plus B plus C whole square is equal to this I have to find this one learn the method no how to approach so I have to find this out right so a plus B plus C has to be there now if you see a plus B plus C is coming out to be 0 how first a is 10 by thousand right B is minus 6 by thousand and C is minus 4 by thousand so if you add all of them it is going to be 0 so this is 0 so this is 0 so what does this mean a square plus B square plus C square will become minus twice see if you want all simple simple questions kindergarten questions I can get those questions also but then the idea is to make you learn here not to make you feel happy that you are able to solve all the questions that's also there but then here yeah so you can calculate if you can calculate faster but see isn't a square plus B square plus C square is this minus twice AB plus BC plus CA so simply minus 2 AB was 10 by thousand B was minus 6 by thousand okay then B was minus 6 by thousand C was minus 4 by thousand and then plus C was minus 4 by thousand and this was 10 by thousand right isn't it so what is this sum then minus 2 minus 60 by thousand square then minus plus 24 by thousand square and minus 40 by thousand square right so hence what is it minus 2 times minus 76 by thousand square correct so hence it was times 76 by thousand square which is 152 by thousand square and someone had pointed out that two options were same correct these two options were same right and you could have seen that it could not be thousand in the denominator either this one or this one it would be correct and you could have guessed by the options also right you can guess by options how a is so big so a square this quantity has to be this quantity has to be greater than 0 why all our squares sum of square is always greater than 0 so this is ruled out anyways isn't it sum of three squares can it be negative never so hence it has to be either this or these two you could have guessed that these are same so obviously ruled out so you could have done this way as well okay so 25 people got it correct let's see the little board cool so Nishant is leading oh Kaveri great good work next chill very easy question again there is no role of 2020 no no I did not do it purposefully I had some other maybe why it was by mistake so while see framing the option is more difficult than the question because it has to be near right near the actual one I think there's some problem on my and it again oh you are on a mobile phone or a PC PC you can try mobile but then you lose but then try doing both try participating through both okay good majority of you 50% of you have got it correct right again five not five 2020 were just to distract you it was very easy question right so you have to basically find out this this is nothing but 1010 minus x1010 and this is one upon x1010 plus x1010 right so you have to just find out these two individually multiply get it get the answer okay how to find that out square this hence this was given square it what will you get you will get x1010 plus 1 by 1010 plus 2 is equal to 4 right so hence x1010 plus 1 by x1010 is equal to 2 so this item is no problem but what about minus you have to get minus so square both sides again so you'll get x 2020 plus 1 by x 2020 plus 2 again is equal to 4 correct so that means x 2020 plus 1 by x 2020 minus 2 is 0 and that's where the fun lie right so this is x1010 minus 1 by x1010 whole square is 0 game over right so this guy is this guy takes it down this is 0 is it clear clear what is it it means what ywt what is ywt okay all clear anyone any difficulty understanding playing with the same format see lots of question we have discussed of this former if x minus 1 by x is given how to go to x plus 1 by x word is what is eat eat eat means what never mind chalo what expression of enthusiasm oh my god chalo next okay so who's leading oh kaveri is kaveri is leading good good good great very good well done well done next next question this I have done in class at least in my class I have done if you don't get it then I'll have to fast for one day if indranagar hsr kormangala people and raja negar also we did yes if you guys are not able to do this then I'll have to stay hungry for one full day as a token of penance penalty I have to inflict on myself I don't want to obviously I want to eat daily why would I want fast no one wants to eat you know fast but then for penalizing for some misdeeds you have to take you have to observe fast it's healthy at times once in a while you should do it don't eat salt that day eat only fruits but not for kids you are not you're healthy it's what we people self hate is known who's saying I'm hating you have to hold yourself accountable for all your misdeeds and hence go through the penalty I hope you remember this question very simple see an obvious answer also okay so last three four seconds very good okay now oh no heart breaking heart breaking so you just remembered the answer so are you going to fast now I love to fast no yes so but then the result is totally opposite so I think most of you remembered the answer and you marked it but I am not confused yeah so I had some devil in you know intent in my mind yes so I had in the class in the class I had given you the reciprocal of this and I just flipped it yes I just flipped it why because some difference has to be there okay so it is very easy again don't wait me Ashish now if you see again numerator let's take numerator first so clearly a plus b plus c is adding out you know you know the you know the identity right a cube plus b cube plus c cube is equal to 3 a b c when a plus b plus c is 0 and both in numerator and denominator it is coming out to be 0 so numerator is 3 a minus b b minus c c minus a and denominator is 3 a square minus b square b square minus c square c square minus a square correct so hence if you see the denominator is nothing but this 3 and this 3 will go so a minus b b minus c c minus a divided by a minus b a plus b b minus c b plus c and c minus a c plus a correct right so hence gone gone gone gone gone so what is left 1 upon a plus b b plus c c plus a so don't remember answers you are not supposed to become robots okay chalovi next leaderboard as a next quiz pukka easy more question easy one okay no traps next math squeeze more number of question easy ones right you remember the answer okay got it nice next more number of questions but very very easy chinnu munnu questions next quiz man let's keep around 20 on bane ga karolpati type question general awareness general awareness in mathematics questions okay general general awareness in mathematics for example which is greater 11 is greater or 9 is greater right sample questions ah they go correct answer very good so these kind of questions okay you have to you have to answer in five second each each question five second rapid fast hundred questions in one hour very easy hint again can you see there is a cube are very easy our cube cube it is cube cube the answer the the this thing itself is attracting cube it is cube a cube a cube was the hint ah most of you have got it that's nice so the hint was very this was hint cube so that means you have to use and you know binomial cube so simply a minus root 3 is equal to 1 right and then cube both sides so this is a cube then minus 3 a square root 3 see second term plus 3 a root 3 square c third term minus root 3 cube is equal to 1 right so this is what was asked for a cube minus 3 a square root 3 plus 9 a correct which is equal to this item will be equal to 1 plus root 3 cube is 3 root 3 okay so what is x 1 what is y 3 so what is x into y 3 right was it difficult how many steps did I write anyways 3 and how to solve such questions cube was the hint either it could be binomial cube or a trinomial cube trinomial cube anyways that's exactly my purpose here that I want I want to drive this point to all of you that mathematics is about exploration it's not about who won the first battle of panipat you have to explore it's not you know only fact okay shallow never mind after sometime you'll guess to it you'll you'll be sorry you'll be used to it so don't worry the purpose is to learn right or just only you know if I give you easy question you'll always been but that will will you you know learn anything by that mechanism so hence last question of the evening folks ready very very simple to end the question very very simple to end the session simple question to end the session very very simple question which of the following is or are a prime number so identities are also used to prove but whether a particular number or expression in numbers the prime or not so identities come in handy so big numbers are prime or not you can very easily say if they are in particular format that's the learning learning is not whether I got it correct or not this is the last question of the evening yes only elimination no when I'll solve this you will you'll see hint is prime numbers do not have factors okay oh no oh no oh no oh no none of them are prime numbers yeah none of them are prime numbers because this is 200 minus 1 200 plus 1 so there are factors and this is anyways even even even all are even so this is an even number how can this be prime and this one is 10 to the power 3 square minus 3 square can be written as 10 to the power 3 minus 3 times 10 to the power 3 plus 3 all of them have factors this is there are two factors there are even means two is a factor this is a factor this is a factor all of them have factors yes obviously composite but let's say it was question like prove that that's a subjective question PRMO 19 to the power 4 plus 4 is this a prime number yes or no how would you know is this a prime number 19 to the power 4 plus 4 is a prime number yes or no right how do you know it's not a prime number then if using the if you go to learn this I have given you one identity I don't know whether you have learned this in learners I have a video on this sophie germain identity if you see this you will be able to prove that this is not a prime number correct this was our regional matter it's in identities algebraic identities it was asked in rmo around 1900 something in 1990s it was asked regional mathematics olympiad 1990s okay prove that some weird let's say any prime number let's say 101 to the power 4 plus 4 is not a prime number okay like that so how to prove something is not a prime number just factorize it okay so answer was none of them how to prove something to be a prime factorize it prove that there are factors okay you can write rmo from eight onwards okay so here's the final leaderboard okay so jagrav finally again good jagrav is back with his potent potential weapon okay uh never mind okay okay okay so good nishant great shivam kaveri and abhishek abhishek or what then srijan roshan and harsh harsh harsh is there and rishabh and vihan great good work guys okay good very good so did you learn something something or not sir next time give easy questions next time what easy questions why why do you want easy questions only only then can you become a person like you become much better than me oh wrong wrong examples and benchmarks oh this is exhausted by eight o'clock sir what will get into our mind ah that's all that's good i i i can i can take that point yes i don't want to do folks i want to do it early but i have no choice so please keep learning the 12 questions which we call today weren't a little different and i my intention is to keep you exposing to different you know keep you you know uh let's say exposed to different different types of questions so that's what the intent is i hope it is helping you all thanks guys and thanks for attending the session so let's meet again tomorrow in the class with hsr folks bye bye take care and stay safe bye do some exercise thank you sir bye bye bye bye thank you do some exercise make it in back three things bye bye take care thank you thank you thank you bye bye bye momisha take your learning learning please remember the learning guys how many people i think around 70 odd so please keep learning keep learning learning is the key whether you win or not secondary learn learn learn learn learn learen learn thank you sir bye sir bye bye take care thank you for that by who's this sony sir we roshan oh roshan oh roshan thanks roshan thank you bye bye bye bye take care