 So anything less than 10 seconds is usually a fluke so please okay so can we begin now Satyam? You're okay you're fine now right so here is the first question take your time and solve don't really rush through it will take some time for you to get to the answer you know already three people have marked it hmm never mind take your time 100 seconds have been given for all the questions okay so last 10 seconds I hope you have reached to the last step so options could be little confusing okay nice so let me see how was the performance oh so not everyone could get in so why you know so people got confused I told you right see most of you got confused between the two options so that's what will be tested also yeah so that's wrong so answer was answer is 40 second so the number has to be greater than okay so here so few things are very clear here first term is 30 right yeah so a is 30 and d is how much was the d if you see this is nothing but minus three upon four this is d right then you have to get first negative term so let's say nf term is first negative term and it is less than zero that's the first negative term so tn is a plus n minus one times d should be less than zero okay what is a 30 30 plus n so what is n I don't know n minus one into minus three by four must be less than zero correct this is how you have to solve it now what if you see this is 30 and minus three by four n and plus three by four should be less than zero that means three n by four should be greater than what 30 plus three by four okay so three n should be greater than what four into 30 plus three by four which is 120 plus three that is 123 right so three n is greater than 123 so n has to be greater than 123 by four am I right so far so good any problem 123 by oh I'm sorry by three yeah sorry yeah so that by three so what is this number this is somewhere equal to 41 right it is actually n is greater than 41 you're getting n is greater than 41 so n is greater than 41 so immediate number which is greater than 41 is 42 so it's most of you have a few of you definitely 22 of you have clicked this one wrong so 42 is the right answer got it so this was given because I know most of you can see almost 50% of the people would have got this till this level not 50% almost 100% of you but then at this stage you mess it up okay so n was greater than 41 not equal to there was equal to sign missing so it's got this clear right so this was a mistake because of that okay next let's go to first leaderboard now which any case is this good so next question on the screen guys take time take time it will take time so don't just mark like that 10th common term between the two apes 37 11 15 16 is and there will be close options so hence do not make mistake over there okay so last eight seconds okay three two and one okay most of you have got it correct very good so that means you found it easy so let me solve it and it was very very simple actually so if you if you see what's it what is this so first term is 37 11 here so 11 is the common term first common term right so hence you will see the the common terms will be what 11 and then the next common term can you predict the next common term will be what is the next 31 very good next common term is 31 how is it uh yeah how is this done actually so here you have to find out the first common term and the next is 31 so common difference is 20 so it will this this also will be an ap right so 11 31 51 71 all of these will be in this ap so you have to basically find the 10th term of this right so the 10th term will be how much 11 plus 9 into 20 which is 11 plus 180 which is 191 how do you find the second common term so what is the technical way of doing this is this so what is that what is the common difference here first ap has a common difference of four right and the second one has five so the common difference of this ap will be lcm of this right so lcm of four and five you have to find out this will be the common difference of the new ap so lcm of four and five is 20 okay and hence you can find out the and in that ap the new ap which has been formed the first term is 11 common difference is 20 so you have to find out the 10th term in this ap simply clear are in so whenever there is common terms have to be found out between two ap this is what you have to do so once again okay see if you look at this series let's look at this series if it is 3 7 11 15 then what will happen next is 19 then 23 27 31 okay here it is 1 6 11 16 21 26 31 right so if you see these are the common terms 11 the next common term is 31 okay so what will happen if you take out the common terms from both it will be of this this type 11 and then 31 and then next you will see 51 will be there right and how is this happening because there is a common difference d here d1 is equal to 4 and d2 is equal to 5 so it's like after the lcm number of terms lcm difference lcm of d1 and d2 is 20 so after 20 again you will get a common common term right so hence in this ap the first term is 11 11 and the common difference is 20 so hence t 10 10th term will be 11 plus 9 into 20 which is because if you see this is this will go on right 11 31 51 71 91 so on and so forth so for this ap you have to find out the 10th term so answer is 191 right so any two ap has a common term no why why do we say that let's let's say this is ap 1 3 5 7 and 2 4 6 8 need not need not be okay so let's go to the next question understood by all any difficulty here please let me know so here is the next question 64 is divided into four parts such that they are in an ap the product of first and last parts is 15 by seven times that of the product of the second and third parts find the sum of first and the last parts i hope this is easy very easy problem this should have been solved mentally this should have been solved mentally okay see you get you get trapped all of you now the thing is this question didn't require any sort of calculation i don't know you don't really read the question properly this question didn't require any sort of any calculation any calculation why because if you see 64 is divided into four parts and we have discussed whenever you have to divide into four parts and all what will you take you will take a minus 3d a minus d a plus d and a plus 3d these are the four parts yes so there are these are useless these are all useless information not required at all so just to deviate you distract you you have to simply see this and this find the sum of the first and the last parts total is how much if you add all of that 4a 4a is how much 64 so a is 16 okay and then what first and last parts is a minus 3d plus a plus 3d that is 2a so 2a is 32 over yeah that's what so hence so what is the learning there will be questions which will be distractionary in nature they will distract you yeah this distracted most of you got distracted spend a lot of time you lost focus on what was required so always always always first fix your you know target on what is what is the desired end result and then work backwards you guys the moment you'd have seen four parts you'd have thought like this but then this step distracted you all right clear so in a competitive scenario don't really work only on the method which you have learned you have to keep an eye on the end result in fact you have to keep keep the eye only there okay so nice someone has got it okay show next question you remember how to find out some of all the all the angles of a polygon yeah so last three two one and time's up could you solve this question i hope let me see okay so most of you majority of you have gotten right so this was an easy question simple direct formula and you will get it so basically there's a convex polygon and so one of the smallest angle is 120 degrees so hence it's nothing but a is 120 degree here and five and the difference between any two consecutive interior angle is five degrees so given is d five degrees okay and then we have to simply do what sum of all these let's say there are n sides n sides are there so total angle some property of the polygon n sided polygon is n minus two into 180 degrees this will be the total angle correct now what you need to do is frame an equation what is equation so n number of sides so n by two how do we know the other angles only increase the difference between any two consecutive interior angles of a convex polygon is five degrees smallest angle is 120 dude smallest angle is given smallest so all the angle will be above it right so n by two into two into a that is 120 plus minus one into five right two a plus n minus one into five this is what it is is equal to how much this is equal to n minus n into 180 minus 360 this is the equation you have to simply solve this this will end up into in what a quadratic sense if you see the first one is 120 n first term two two gets cancelled 120 n plus five n square five by two n square okay so five by two n square correct just correct me if I'm wrong and then minus five n by two so minus five by two n right is equal to 180 n minus 360 so let's eliminate the two from the entire equation so 240 n plus five n square minus five n is equal to 360 n minus 720 I can eliminate a five also okay five also so hence five four p eight n plus n square minus n minus five seventy two n and plus five one four four is equal to zero this is the equation right so hence what will it be n square then how many n's are there minus 72 n minus 48 so 24 and minus 25 25 n plus one four four this is a quadratic equation right and from the options itself you could have figured out that it is nothing but n square minus 16 n minus 9 n plus one four four is equal to zero so that means if you solve it you'll get n is equal to 9 and n is equal to 16 but why did you not mark 16 what happened Anish you are in trouble what happened Anish is saying something which side don't know right increase or decrease is not stated what is increase or decrease not stated you you are saying the angles could be 115 and 120 110 and 105 like that Anish is that your question is that your question guys Anish one by one let me clarify Anish first and then what is the doubt Anish I don't understand your doubt Anish can you hear me you still have a doubt yeah so what is the problem loads so so be it's 120 125 130 and what after 130 why would it go down oh like that oh like that okay so you are saying 120 125 120 125 120 125 like that yeah okay that is possible but then again yeah it should be mentioned difference between any two no no not like that see whenever it is said that difference between any two consecutive interior angle is like that you take the second one and then the first one difference is always taken like this in this manner later minus initial never initial minus later do you get that Anish so hence five degree is a positive angle so hence you have to so if this is the one first one and this is the second one if difference is five that means t2 is more you always take later minus initial if it was minus five then it will come down right then the consecutive will have a difference so hence it will be progressive in nature coming to why 16 is wrong 16 is wrong because if you take 16 you will get 195 as one of the last angle check it so 120 plus 16 minus minus 1 this will be the last angle right so 15 fives are 75 so 120 plus 75 is how much 195 and in a convex polygon how can a reflex angle be there do you get the point right so there cannot be a reflex angle so hence this was wrong not possible so nine good i hope you understood this all doubts cleared let's go to the next question it's mentioned here check and anyways if in a polygon there is a reflex angle it cannot you know it will be uh what do you say two arms will be crisscrossing each other okay anyways so this is good Thamman is showing real this thing but why is Thamman so come in class Thamman i will talk to you okay so do this maybe if three times the fourth term is equal to two times the seventh term the ratio of seventh and tenth term is four three two and one let me see how did you perform cool most of you have got it it was very very simple actually you don't need to do any experiment here so clearly if three times the fourth term that means three into t four is equal to uh what uh two into t seven this is the equation that means t four by t seven is equal to what two by three isn't it so what is two t four a plus three d and t seven a plus six d is equal to two upon three cross multiply you'll get three a plus nine d is equal to two a plus twelve d okay so hence you'll get a is equal to three d moment you got this you have to find out t seven by t ten c seven upon t ten what is t seven t seven is a plus six d and t ten is a plus nine d now replace or substitute a is equal to three d so you'll get three d plus six d so three d plus six d divided by three d plus nine d which is nothing but nine by twelve which is nothing but three by four is it okay now what is what is what is happening aditya what is the issue okay so yeah all clear any doubt in this this guys all clear yes any doubt in this any x no so let's go to the next question before that leader board question on board guys am am means arithmetic mean if the am between ps and qs terms of an apb equal to the am between its rs and sf terms then which of the following is correct so i'm happy that all of you are able to do this okay so in an ap again so let me yeah so ap three oh sorry this is a previous question this question is question is if the am between ps and qs term of an apb equal to am between its rs and sf terms so am between ps and qs term will be ap plus tq upon two right and the this is equal to pr plus ps upon two and now what tp is equal to let's say a and d or the parameters of the ap so a plus n sorry b p minus one d plus a plus so this two can be cancelled so a plus q minus one d right is equal to a plus r minus one d and plus a plus s minus one d so all a's will just get cancelled and we will be left with all d's will also one one d will also get cancelled if you see this one this one this one and this one all these d's negative d's will get cancelled so what do we get all d's anyways d's also will get cancelled so why only one so d one line answer is it so hence p plus q is equal to r plus s you will get which is nothing but this one right so it was very easy in this question assume that a and b and c are not equal apc are not equal majority correct but most of you are making mistakes here how many of you could not get it yep x party how many x party i like the graph okay good so many people are saying x okay so let me solve this so this is in ap then let me also use some space over here okay so what does it mean if this is an ap that means one upon c plus a minus one upon b plus c will be equal to what one upon a plus b minus one upon c plus a common difference right either okay one upon one upon a plus b minus one upon c plus a is equal to one upon c plus a minus one upon b plus c right so hence now take common denominator so i can write here let me write here so this implies in the in the denominator you will get c plus a and b plus c and in the numerator you will get simply b plus c minus c minus a is it it and here you will get again a plus b times c plus a and in the denominator you will get c plus a minus a minus b now if you see c plus a c plus a will get cancelled okay they are not zero so they will get cancelled this c and this c will go this m this l will go so it is basically b minus a by b plus c is equal to c minus b c minus b by what a plus b simple and then you need to just cross multiply and chill relax so hence it is b minus a b plus a is nothing but b square minus a square okay and this will be nothing but c square minus b square that means what a square b square and c square are in a p okay so hence yes everyone understood so this is also a common difference from b square minus c square is equal to sorry this is c square minus b square so this is also common difference okay so hence it will the moment you see such kind of a thing that for example x minus y is equal to z minus y sorry y minus z then x y z or z y x are in a p okay so always remember this kind of relationship means these three numbers are in a p whichever way x y z or z y x okay cool so let's go to the next one nice show let's go to the next one now this is gp okay so let me see how was the question we saw it on time this shows some issue okay that means only nine people anyways let me solve it some of three numbers in a p is 21 okay so obviously you know the first step what's the first step you have to take uh what numbers are a this is too light so let us say a minus d a n a plus d right these are the three terms in a p and the sum is 21 so if you sum them you'll get three a is equal to 21 that means a is equal to seven okay so what are the number terms seven minus d seven seven plus d and now what is being said uh three uh one is reduced if the second number is reduced by one that means this becomes six and the third is increased by one that means it becomes eight plus d okay so seven minus d six and eight plus d the three resulting numbers are what in gp okay so what is gp guys so i know already gp may common ratio will be same so six by seven minus d will be equal to eight plus d by six this is what we know right so hence it will give you six square is equal to eight plus d and eight seven minus d so which is nothing but 56 and eight minus eight d plus 70 so minus d uh yeah and minus d square right and this is 36 so that means d square plus d plus d square plus d minus sorry minus 20 is zero am i right so you'll get two values of d d square this is five d minus four d minus 20 is equal to zero splitting the middle term so d if you solve you'll get d is equal to minus five or d is equal to four these two values but since it is an increasing gp so ah so you got d is equal to four so you have to find out common ratio right so what is common ratio six by seven minus four which is six by seven minus four is three so two so two is the right answer got it you will not take minus four because then it will become if you take minus four it becomes minus five if you take d as minus five then it becomes 12 so it becomes half then half common ratio will not be there why because they're increasing gp is that clear below eight out okay let's go to read the board so the word term is missing here okay nf term you have to find out nf term so let's see if you are able to get this one still mixed my god that means gp is not very clear to everyone why are you who all could not do it you're struggling in gp guys struggling in gp okay here sorry this one so suppose m plus nf sum of a gp is p so you know for a gp p is equal to what first term into common ratio to the power n minus one m plus n minus one simple and and m minus one f term is q so q is equal to a r m minus n minus one simple divide these two equations divide these two equations what will you get you'll get p upon q is equal to a and a will get cancelled and r will see what m plus n minus one and then minus m plus n plus one if you divide it so that means m m one one will go so p by q is equal to r to the power two n okay so what will be uh r so you get r r is p upon q whole to power one by two n and you have to find out nf term right so what will be nf term so if you see a um sorry yeah nf term is a into r n minus one correct this is nf sum now this will be nothing but a into r so you have to basically find out a from somewhere so in terms of p so let's say from here a is equal to uh a is equal to nothing but p by r m plus n minus one okay so this is a so what is a and uh so nf sum will be tn is nothing but a so what is a p upon r m plus n minus one into r what is r p by q to the power one by two n and then minus one this is a thing right or rather what you can do is you can keep this as r only so let it be instead of that instead of that write this as p upon r m plus n minus one into r n minus one so r n minus one that means this is nothing but p divided by simply r to the power m because r n minus one n minus one will get cancelled is it so p by r m so which is nothing but p into r to the power m will be q by p four to the power one by two n and is it and m also m also because there was an m here so hence this matches with this one what was the issue why did you make mistake here uh what you found out what what was the what was the problem m instead mf term you found out mf mf term oh why it's clearly mentioned nf right so hence okay so this is this is not correct this is correct be careful i have been telling this and now by by now i think i would have told you thousand times in the last two years be careful be careful be careful be careful be careful thousand times anyways let's go to the next question okay a one a two a three a n are in ap such that a four minus a seven plus a ten is equal to m then sum of first 13 terms of the ap is this should be easy i believe simple nf term so are you able to identify trend in the questions in the the questions are not dealing with numbers numerals so to say okay there are lots of variables and lots of unknowns are more unknowns are there in the question that's how a typical comparative exam scenario would be so you'll not be getting okay these are the five seven eight nine these are the some these are the terms of ap five the sixteenth term and things like that very rarely in tough exams okay so hence you have to be and the other thing is we have not used anything which is beyond our knowledge and third thing is it also is it also involves knowledge of other topics trigonometry or geometry and things like that good that most of you have got it so i'll quickly solve this one this was not very hard so if you see this this is a four so you can directly write a four as a plus 3d okay a seven can be written as minus a plus 60 and this can be written as a plus 10d sorry 90 90 yep 90 right and this is equal to m so if you see a and a gets cancelled a one a will be left and 3 minus 6 minus 3 and plus 60 is equal to m a plus 60 is equal to m right you want 13th term so 13th term is a plus 12 sorry saying something what is 30 uh oh some oh sorry some of the first 13 terms my bad hence so yeah some of first 13 terms is how much a uh sorry 12 by 2 13 by 2 my bad again 13 by 2 first 13 terms is 13 by 2 and what else twice a to a plus 12d so it is 13 upon 2 into 2 times a plus 60 and a plus 60 was m so 13 into m right yeah i hope this one is clear to you so let's go to next question next question guys on the screen so the question says three positive numbers form an increasing gp if the middle of this gp is tripled the new numbers are in ap and the common ratio of gp is hmm let me see your performance okay wow so you guys need to revisit the topics on gp okay anyways gp and hp i hope it is covered in all all the batches right all of you have covered gp yes or no everywhere it is covered right okay never mind so if a1 a2 a3 are in ap sorry this is the previous question so go to the next one how to go about it three positive numbers form an increasing gp so the moment this is there what do you need to do it's a upon a upon r a and a are are the three numbers in gp increasing gp right you can always where r is greater than one r is greater than one because it's increasing gp if the middle term on in this gp is tripled that means 3a then a upon r and 3a and ar are in ap the new numbers are in ap these numbers are in ap ap meaning what 3a minus a upon r common difference is equal to ar minus 3a or 2 into 3a is equal to ar plus a by r so a a will cancel so 6 is equal to r plus 1 upon r so r square if you do minus 6r plus 1 is 0 this is a quadratic equation you have to solve for r so r will be minus b 6 plus minus b square that is 36 minus 4 ac minus 4 by twice a so twice a is 2 only right so this is nothing but 6 plus minus 36 minus 4 32 that is 2 4 root 2 4 root 2 divided by 2 okay so what will what will this be it will be 3 plus minus 2 root 2 but if you take 3 minus 2 root 2 then it will be less than 1 so only 3 plus sorry what yeah so d what was the right answer 3 plus 2 root 3 what did i say answer is wrong is it let me verify yeah 3 plus 2 root 2 should be there oh 3 plus 2 root 2 so oh this root is root was extra as actually this one root was extra oh sorry bad so let me delete this question wait so you all mark uh wait huh question number 11 it was right so question number 11 you are marked a so all of you should mark a i am resetting the result reset result this slide reset okay so i'm going back to this one so i have reset the result in question number 11 i could not wait a minute this was this was after 11th you know so let me reset it just hold on guys just hold on so this was 11th question yeah i have reset it now no problem so we can go back to presentation yeah so all of you just marked mark a so that you all all of you get the same score a mark it so that none of you are at disadvantage yeah so just mark a answer was 3 plus 2 root 2 but it is actually 3 so by mistake it is mentioned as 2 root 3 okay just quickly mark all of you so that i can proceed with the quiz you should say all of all of you have voted all of you have voted come on come on come on quick don't waste one minute time on this no rnd rm in the middle of anything so the best whatever is possible is done so i just need everyone to vote so 49 people still people are waiting for voting i don't know why what are they doing so they have just because of because of their parental pressure or whatever uh they have logged in and they are moving around or they are they have put some so these are all insights for us as well you know they put some speakers on their uh headphones on and they are listening to music oblivion to what's happening in the quiz so there are all sorts varieties of people are there anyways so so let's go to the next last question guys here is the question attention attention attention now there is an element of hp also i hope you understand that okay so the final 10 seconds eight seven six five four three two one i hope uh you got it correct okay this time 20 people got it so good staircase graph let me solve this one so six is the right answer correct and why is this so you know this was fairly simple a1 a2 a10 is in ap so a1 is 2 so a1 is 2 and a10 is 3 a10 is equal to 3 so you can find out b correct so what is this a10 a10 is equal to a1 plus 9d right so a10 is 3 and a1 is uh 2 so 9d so d will be equal to 1 by 9 right this is d so you can find out a4 first of all so a4 is nothing but a plus 3d so 3 into 1 by 9 which is 2 plus 1 by 3 2 plus 1 by 3 which is 7 upon 3 so this is about a4 a4 you got it next is hp let's take hp so 1 by h1 h2 h10 are in hp that means 1 upon h1 1 upon h2 1 upon h10 are in ap that is what is the definition of hp right so h1 is given 2 so here the first term is 1 upon 2 and h10 is also given 3 so the 10th term is 1 upon 3 okay now let's see common difference be d1 in this case so i can say 1 upon 3 minus 1 upon 2 or 1 upon 3 is equal to sorry first term so 1 plus 1 by 2 plus 9d1 so here it will be 1 by 3 minus 1 by 2 is equal to 9d1 right so what will be d1 so this is nothing but 2 minus 1 by 1 by 6 this is 1 minus 6 is equal to 9d1 so d1 will be equal to minus 1 upon 54 you got d1 so 10th term will be easier to find out so 10th term will be how much first term that is 1 by 2 so t10 of the inverted hp term that is ap right what t10 will be first term first term was half plus 9d so 9 into minus 1 by 54 okay so 9d1 9d1 sorry 9d1 so which is anyways minus 1 by 6 so half minus 1 by 6 will be 3 oh sorry yeah sorry so it will not help 10 is already given us yeah yeah sorry yeah so hence we have to find out it's 7 sorry yeah so how to find out it's 7 easy so t7 is half and what 6 into minus 1 by 54 this is it's t7 so what is this value this value is uh half into 6 1 minus 1 by 9 so 18 and 9 minus minus 7 sorry plus 7 7 by 18 so h7 is 18 by 7 isn't it this is h7 you have to reciprocate this term to get h7 so this is h7 so a4 into h7 is equal to a4 was 7 upon 3 into 18 by 7 which is 6 so this got it okay so this is what we have done today let's see who is the winner of the quiz so one question was wrong and here is so Meghna Meghna is the winner of the quiz is very good keep it up so Meghna, Akira, Shreyas, Pranav, Sanjana, Ariman, Aniket, Smriti, Alisha, Laksh good good guys very good nice so keep it up let's meet again with Acha how many of you would be interested in a geography quiz i just need your response geography quiz all of you okay we have i have already kind of framed the questions i will and geography quiz will be mostly open book so you have to just keep your ncrd book in front of you and you can solve questions from there okay so take care guys okay bye bye and questions on moxa okay bye bye take care see you stay safe sir when Ariman had geography quiz so it's anyways open book whenever it takes let's just participate yes i will tell you first chapter geography first chapter yes bye bye take care