 questions will be easy it will be confusing at times now now no no more discussions on the chat box because let's you know once this quiz starts then we can start talking right now all it's monologue from boring boring feature just mute your mic all the time guys so yeah okay so let's begin okay so we are going to start the quiz anyone wants to join later can join later five four three two one go first question on your screen take your time don't mess this up first question take your time it's not easy easy but confusing take time and then solve x to the power minus 16 divided by x to the power minus 8 divided by x to the power minus 6 divided by x to the power minus 4 chain division I don't see no trap sure see my job is to make you aware now if you can see better if you can't see that's also better so hence no worries so 50 people have already almost all of you have marked it okay so I have given 100 seconds last time people were asking about more time yes done everybody 68 people have mark their answers oh there are 70 I did never knew this okay cool maybe some someone in Romania Yugoslavia doesn't exist Belarus Romania they are also playing minty cool so okay so here is first answer hmm I hope okay most of you have got it correct but lots of you have not got it correct why is that I don't know so let me explain yes it was a very simple question actually so you had to just put the brackets at the right places so you can start like that you can start like that right so hence it is x to the power minus 16 right upon x to the power minus 8 upon x to the power minus 6 and then this will become into what what what into x to the power minus 4 correct this is the first one then the second one x to the power minus 16 upon x to the power minus 8 in 2 one upon x to the power minus 6 and one upon x minus okay so this will continue like this and it is extra power minus 16 divide by extra the power minus 8 into x to power minus 6 into x to the power minus 4 right so this is nothing but X to the power 8 plus 6 is 14 plus 4 18 so 18 into extra power minus 16 okay so let me write it here so it is extra part 2 okay so good right is that clear to everyone it was just your 7th 8th grade stuff no more no technology here no trap nothing warming up game okay so let's go to the next one and the first leader board of the evening first leaderboard okay so Burger Rishabh good name I liked it good so Czech Republic see Czech Republic I and R is also there that's nice okay who who's who's Czech Republic I and R by the way but he's really Czech Republic person never in hello let's go to the next question guys don't get trapped so the mix of Serds and identities almost all the questions will be like that mix of Serds and identities so we'll play a lot with them you hate Serds hate is a very deadly word don't use that word please you can say you dislike Serds that's better and yeah don't hate anything yeah dislike is better okay come on come on guys there's a trend there's a pattern there are the numbers are very specific set of integers I hope you have noticed that so that will help you that will help you right so there's a pattern in the numbers I hope you could observe and that could give you the answer in what I am observation is very very necessary not sure don't worry easy answer is easy me confused don't be confused me 222 wait one oh wait what is that pattern pattern yes okay okay six five four three two one time's up okay so oh my god lots of people who have got wrong answers okay why did you get it wrong very easy it was this was a question I don't get how to find this out so you know if you square all of them square all of them that's the identity I was talking about see if you square all of them you get root 11 square that is 11 plus 3 plus 2 times root 33 you didn't need you didn't require to calculate that's why we are learning search and identities you square the second one you will get 12 plus 2 plus 2 root 24 and third one 13 plus 1 plus 2 13 now tell me what is the answer see that's what I was repeatedly telling you repeatedly telling you 11 plus 3 14 12 plus 2 14 13 plus 1 14 so the rational parts were all equal the deciding factor was the irrational part which is highest root over 33 and if square is highest square root will also be highest you understand you stand understand now all of you those who mentioned X so how to compare Serds you don't need to find the value if you want to compare two Serds X and Y you can square them and compare as well okay if required cube them and compare no problem you are learning identities anyways sorry square root the difference between 11 and 12 is much smaller than 2 and 3 how does it matter Raghav see did we violate any issue any mathematical law here we didn't write so square root you don't really calculate anything you don't need to calculate anything here always remember if X and Y and Z are positive numbers XY and Z are positive numbers then and let's say X is greater than Y than Z then X square will also be greater than Y square is greater than Z square okay okay so very good clear to everyone or not what did we learn in this question very very important quiz is at one place but learning is right what did I say if you have to compare Serds you can square or put into cubes or whatever and compare no problem okay so it was very simple question but then you did not see the trick learning is apply the knowledge okay very good some bit of shuffle never mind lots of more questions to go next question please again a deep breath all of you you guys are you know very impatient a deep breath make a promise to yourself you don't need to market fastest no worries very careful very very careful you know what is our rationalizing factor that factor which when multiplied with this number makes the number rational okay what is a rationalizing factor that number which you multiply the given number with the product becomes a rational number so that's called rationalizing factor so be very careful the keyword called the smallest so that means there could be many rationalizing factors as I had discussed in classes also I think wherein you can have multiple rationalizing factor for the same same irrational number use that concept what is rationalizing factor quick question so there is no square root there is a cube root please be careful by the way this was asked in NTSC examination guess work going on yes I will I will explain everything don't worry let everyone let everyone answer Prateek don't be late okay so here is the performance of all of you oh see lots of people are studying how many of you don't know what is the meaning of rationalizing factor you know rationalizing factor all of you Anika doesn't know rationalizing factor so they go tell me before we get into this question what is the rationalizing factor for root 2 can anyone tell me rationalizing factor for root 2 will be no root 2 root there could be so many rationalizing factor they may not be one so root 2 could be one itself okay minus root 2 can also be 2 root 2 can also be right 3 root 2 2.5 root 2 5 by 6 root 2 all are there right all are rationalizing factor why are they called rationalizing factor because if you multiply them each one of each each of these pairs you will get a rational number base right if you multiply all of them you will get rational numbers isn't it that's called rationalizing factor now what was the question here the third which is given here is 63 car one third root so 63 to the power 1 by 3 what is 63 9 into 7 to the power 1 by 3 what is 9 3 square to the 7 1 by 3 what is now you open it so it is 2 upon 3 8 to 7 1 upon 3 this is your root over one third of right 63 cup power 1 by 3 now you have to multiply with something some box here so right it becomes a rational number what should be in this box is the question smallest number so if you want to make it rational see this is this is a third how can you make 3 to the power 2 by 3 rational hold prasam wait so now this is 3 to the power if you multiply this by 3 to the power 1 by 3 it will become rational is it and 7 to the power 2 by 3 if you multiply this together now these two together won't you don't you think the result is a rational number right so the this is the rationalizing factor smallest rationalizing factor and what is it basically so 3 into 49 to the power 1 by 3 which is a root of 147 got it all of you got it give me a thumbs up if you understood this why why why why why okay so good so you know solving question is a very you know good technique or good way of learning very good so don't worry you learn something you know learnt about rationalizing factor today very good so oh my god lots of reshuffling happened jump next let's go to next question and now simple one use of identities using identities in search again I have given you this type of search if you remember it okay okay don't worry don't worry everything is fine voice though who was this good voice great someone's younger sibling very good come on guys silence and people are taking time I clearly see our you know remarkable difference in your behavior I you if you if you remember you used to mark the answers within 5-10 seconds initially now you guys are taking time that's sign of you coming to the terms of the world world would require you to be calm compose and solve with utmost focus I am pretty sure I got this one we are in ninth so my more you guys are the people on whom we our future depends yes boy correct correct boy got it okay oh no I'm still not very happy only 30% of the people are getting it correct why what happened what happened what happened why did you make it it was very simple very very simple right so X is 5 plus if you didn't notice this is 25 plus root 24 and time and again I have told you hey don't do that please then becomes difficult to interact run up no how would I know who's asking question don't do that please they go all of you all of you focus on the board so root 25 plus root 24 what is the recipe program of this what is one upon X simple you have to change the sign and it will become root 25 minus root 24 correct and this one you remember this one or not we talked about this so many times if you have n plus 1 plus under root n this is equal to one upon root of n plus 1 minus right so many times I have given you this trick so hence one upon X will be simply this right and one upon X square will be simply this right and the other one if you see is nothing but root of 25 plus root of 24 square and you understood Monisha is that understood this step is understood to everyone below I'll again explain don't worry until unless everyone is understood clear everyone is clear everyone has to be clear none of you should be right now you expand using the identities you know so this will be 25 plus 24 minus 2 root 25 root 24 and this will be 25 plus 24 plus 2 root 25 24 correct this will just disappear and 25 plus 24 25 plus 24 is 98 yeah yeah okay so you have to be a little bit of more patient and cautious okay next leader board see turn up hence close answers will be there in the option that there was one odd answer as well 99 but I checked it out and put 96 deliberately I knew these things you're going to do okay so next who's turn around turn is from which which batch which group it is turn who's turn by PR open to put your name otherwise I will not be able to identify school name has to be there okay next is this option A and C are the same no they are not what happened not all if you if you if you look at the solution you will be just beating yourself up okay a lot many people have got it correct but okay yep I don't know how to solve this one anyone what to what is to be done yet anyone anyone anyone those who got 31 people got it come on so we can make X root PQ or you instead of that multiply LHS of all multiply RHS of all see what will you get so you'll get XYZ equal to PQR plus minus that was the catch guys XY X square Y square Z square multiplied all of that what will you get PQ into QR into RP so P square Q square R square simple isn't it so that means XYZ square is equal to PQR square correct that means XYZ is equal to plus minus PQR right so XYZ by PQR is what plus minus one or PQR by XYZ this one is plus minus one is it it so plus minus one to the power XYZ whatever is the XYZ value you'll get either plus one minus right okay now don't don't worry Prateek let it be let be don't really play with your names there okay okay clear all of you give me a thumbs up if you got it so did we apply any out of the world technology over here nothing it was just observation multiplication solution done okay next let me see what's the standing now yes ania identity is but there was no identity here in this there was no identity but you want identities then later on coming in coming good okay very good let's go to the next question you wanted identity you wanted identity okay wish granted extremely easy okay you guys have not expanded it centermars are always online Zagreb centermars are always online okay okay okay okay good most of you have got it correct oh amazing that's fine that's good but then I hope you didn't expand it did you expand anyone expanded it so you don't need to put anything here yet it was very simple actually so P minus 2 is root 3 this is what you had to do that's it that's it you didn't need to find p square then 4p and nothing like that so you simply this one would have done this and then square it right so what will you get p square minus 4p plus 4 is equal to 3 correct then oh no idea no discussion p square minus 4p plus 3 will be 2 simple one liner one liner you could have someone is yeah so hence many people have done this 2 plus root 3 square minus 4 times 2 plus root 3 plus 3 yep most of you would have done this but you didn't require it right in Ahaan buddy I will tell you more I have a full I can give you at least five books one class very bye don't worry there are lots of projects lying with me okay isn't it plus 3 on this side yes but then the question was to find p square minus 4p plus 3 so you have to take one outside right so this was 3 plus 1 so this was 2 plus 1 so you cancelled one from both sides so that 4 became 3 so 3 will become 2 correct oh right now so hence this if I would have given you p square minus 4p plus 4 then it was it was like a piece of cake for all of you and hence I deliberately changed it to 3 the question was p square minus 4p plus 4 okay so jagra people are impatient about their results only no learning only the leaderboard okay chalo my mind so very good very good so here the learning was not on the expansion the learning was on whether you could see that structure over there okay next don't okay what good still a lot of people have made it made me mistakes okay very easy one it is so you have to simply you know I had actually I had made it simple there was a product here but I thought it will take time for you so I prime factored myself to know I factored it to a large extent but anyway this is 3 to the power m into 2 to the power n and if you see this is nothing but 2 into 9 into 9 into 27 so yes so it is nothing but 2 to the power 1 and 3 to the power 2 into 3 to the power 2 into 3 power 3 which is 2 to the power 1 and 3 to the power 7 so clearly m is 7 and n is 1 right now put here 3 to the power 7 divided by 3 to the power 2 which is 3 to the power 5 which is 243 right any problem here no problem I guess this was fairly simple okay so actually I could not get this time too easy yes now everyone will say easy now you guys are fairly equipped with the knowledge okay let's go to the next question see Praveek Raghav is laughing lol why are you saying lol Raghav lol there should be mix of easier ones in teachers smell a trap here okay yes integers are very much part of rational numbers don't worry sorry didn't understand what was the question see that is asking if you get yourself as fastest will it be a mandatory that you will be in the leaderboard no if you are already there around top 10 11 then then it will make sense if you are having some bit of gap then no so the top 10 are ahead then can't do anything it's cumulatively the board not only the question after the question after every question it just adds up your previous points no trap yeah all of you got it correct very good but still many people are wrong it was so easy very simple very simple right so this was if you could have noticed this a square is 2 and b square is 3 simple there there there will be irrational parts why when we expand it you'll get terms like 2 times root 6 here minus times 2 root 6 and all that okay it's very easy see but then you should now yeah good that you are no problem so let's go leaderboard oh no what happened I do says why this is so difficult square root I told you how to find out square root didn't I it's there on sentimentist special you know specific we video is there dedicated video is there okay okay never mind chalo so last five second guys answer was okay time's up it's 49 okay most of you have got it correct that's nice and it was very easy you have to find out you could have guessed it but then let's say if you don't know then you can say that this is root a minus root b square okay so hence it is 7 minus 4 root 3 square it you get a plus b minus 2 root a b we done so many times right so a plus b is 7 see that's it so square a plus b square was asked you understood this part this part understood jagra world on buddy hold on with patience right all all of you understood so this is simply 49 okay shallow mix yes I can read Monisha identities Tanya here it is Nishant self for the trap Shivam you guys are so funny oh my god oh my god this is surprising what happened totally upsetting result what happened guess work why you have to square both sides right my both sides so what will happen you will get 12 plus a root 2 is equal to 2 square into 2 plus 2 square minus 2 into 2 root 2 into 2 right so hence if you see this 12 and this hole will go because that is also 12 so a root 2 was minus 8 root 2 so a was minus 8 no problem right and minus 8 to the power 1 by 3 code is 109 to 7 so minus 8 to the power 1 by 3 trapped how many got trapped right see understood this is going to happen in your exams buddies please understand this see every every centum are I'm telling you this but I'm glad that it is going it is coming down the number the amount of mistakes you are doing is coming down but still you know I in the beginning of the session itself I told you that you can expect some traps okay yes that was that was the thing right so hence what you know your focus is to get ABC or D somehow and in that in that journey you forget everything around you and that's the problem okay and this is going to be a the regular pattern now I am with these questions I am trying to remind you again and again don't do that don't do that don't do that okay very good dhagrav is doing great good so next question okay Monisha let's go to next question guys 11th one beware beware only when you get it right that will be easy till that point it is last question answer was minus 2 I believe one of that yeah minus 2 I will see what happened this is very easy don't be depressed depression and all you guys should not be using the terms like that don't use words like depression sad if you become depressed and sad then we are gone no hope in life then we we are dead if you don't have hope in life then we are dead buddies don't don't think like that so you're talking to a dead man 14 year old saying life is so sad no come on chalo cheer up and this one is very easy this one is very easy right so most of you have got it okay very good so cool right so how to do it very simple it is m so it is nothing but if you check this is a to the power 1 by n hold to the power 1 by m the roots if you remove the roots it will be something like that and to be power mn minus 1 upon a to the power minus 1 is simply a to the power 1 this is the peak okay now so what will happen this is 1 by mn to the power mn minus a which is a minus a which is 0 most of you got it correct so that's nice okay so let's go to the leaderboard let me see the performance okay jargrab is maintaining the leads I'm sorry like every single question I've been observing he gets 990 is it I don't know I have no clue I have no clue he only can tell you 9 oh my god seriously this is too fast how did you do even in the previous two questions that is some data point okay let me analyze how is that possible yeah within okay water but how do you how do you do this as I want to know this okay can you really do this but for that what you need to do this is beyond beyond my understanding okay so you must have some kind of is running a board what will the board do what will figure out the this thing okay I'll analyze the maybe use the browser add on so how does it help you must click one of these ABCD right and unless you how do you know that this is the right answer that for that you need to know the right answer first okay I'll figure it out don't worry I also have got some bit of brains so let me see but then I don't jagrab is there jagrab so I need to understand if really I'll see all the you know previous this thing as well never mind so anyways how does it matter you guys should be focusing on whether you are learning or not in a quiz like this you can do whatever you want but in the actual quiz the real life problem okay child last question of the day nice data point you don't need to guess very easy question again patience I will explain Kandahar don't worry what's up you very wrong oh my god why why did you get wrong right so it was if you if you solve this one okay 3 to the power 5x and then 81 square what is 81 square guys 9 square square square and 729 is 9 cube is equal to 9 to the power 7 unit yes right so and in the denominator you have 3 to the power minus 5 y okay so hence what will happen this is 3 to the power 5x plus 5 y the this 5 y will go up is equal to 9 to the power sorry into 9 to the power 7 is equal to 9 to the power 7 so 9 to the power 7 9 to the power 7 goes right so what do I get 3 to the power 5x plus 5 y is equal to 1 right and 1 can be written as 3 to the power 0 right so that means 5x plus 5 y is 0 okay so that means x plus y is 0 okay that means x square minus y square will be x minus y times x plus y it can be written as one also what what can be written as one Tanya it understood so x plus y is 0 then entire quantity will become you guys you know lost patience here after this that's where you so what you would have done is you would have written x is equal to minus y right and then then also x square and x is minus y so you could have done this also x equals to minus y let's say so then you deploy this here what will happen so x is minus y right so minus y whole square minus y square is 0 yes so these are the learnings see I keep on telling you and I'm telling you from my experience guys it's not that I enjoy making you fall in trap you can win a quiz by cook and by cook unfair means and all that but then once you go to the other side of the you know boundary then it becomes very difficult to exist so lots of people you know clear these exams like jay and all by some kind of mechanism learning mechanical learning and all that but he would be astonished to know that in IITs a lot of them fail in the first year a lot of them to that an extent that the government has to convert their b-tech degrees into BSE degrees so that they get a degree at least okay yes so please understand that right so don't really you know go behind getting into the top most position here doesn't happen doesn't work if you become top most for you know get top post position in our pool of 60 70 odd people would not help right so you have to right now is the time when you have to learn and gain the knowledge and apply where it is required okay so hence I keep on emphasizing on forget about leaderboard and all that okay so you guys are doing good right now and it's very you know heartening to say that earlier you used to do within 10 seconds 15 seconds 20 seconds at least way you know oh sorry sorry something just just to conclude that don't really rush through have patience and you're going good okay very good so jagra again is never mind so jagra gets it whatever if he's really getting it then congratulations to him if he's doing by something some other means I don't know