 not going to wait for anyone. We are now starting okay so all of you are ready with pen and paper questions will be of application of mathematics in different subjects it could be math it could be physics as well. So all of you are ready okay so bring a piece of paper and pen okay and that will be helpful so yeah so ready guys I am starting okay we are not ready going to wait for anyone people don't come on time we'll have to suffer start okay so here is the first question on your screen guys right so use quadratic equation to solve this okay take your time and solve in methodical way don't rush through the questions so this is called an infinite ladder application of yeah please mute your mic direct application of quadratic equations I hope you know how to solve these so this is the similar type of questions are in nested surge in this those who have studied capacitor I believe some of some batches have studied capacitor there also it can be applied nested or infinite ladder they have to just put the code Nandini that would be good enough there is absolutely no other way how it can be joined you can you have to wait for the next question so time to attend all the questions no problem let it be let it be so yeah so last 20 seconds I hope done by now so there is some kind of trapped in the question also or in the option so please be careful and please put your mic on mute please put your mic on mute most of you have got it wrong that means your physics concepts also are dicey okay here who is on unmute so I can see who else is there there is Pranav CHK 10 please put your mic on mute yeah it distracts and why should I think he's not able to okay so uh why yes so uh why could you not solve this have you not discussed this in the class have you done it in physics yes or no right so yes so you could have tracked it by options itself right very very easy you know the option itself gave the answer so you need to be smart you can't really only put in a lot of efforts to solve questions it the only uh you know uh missing of this r here gave a lot of so r was missing him right and this is the answer okay and how is this solved this is how it is solved so whenever you have such kind of infinite ladder what do you need to do just give me a moment for that yeah so whenever you have such infinite ladder you need to use the repeatability for your own benefit so this was the circuit and here direct application of quadratic equation if you don't know quadratic equation you'll not be able to solve it so this was the scenario right this was the scenario that in so let me draw it once and then yeah and then it repeats it repeats like that so what you can do is what you can do is you can see there is a pattern which is repeating so hence this is repeating this whole thing is repeating isn't it so yes so what do we do here so let this is point a and this is point b you have to fit in a equivalent registering here isn't it so how to do that so equivalent resistance or the equivalent circuit could be this all our r and let's say the equivalent r equivalent a b right this is b this is a point let's say after all this mathematics you put an r equivalent here okay so hence if you see now r equivalent itself is repeating right is the circuit here to everyone this is why is the circuit here this is how you have to you know use the pattern right so this pattern is repeating so hence the r equivalent can be inserted here itself now it was very very simple r and r equivalent are in parallel so the next equivalent circuit is this so a b this is r times r equivalent by r plus r equivalent correct this and this one is r right so hence now this r and the other one is in series so hence the total r equivalent so anyways you had this as r eq between a and b so what will be r equivalent it is nothing but r plus r r equivalent by r plus r equivalent is that equation clear to everyone so this is nothing but r equivalent minus r is equal to r times r equivalent divided by r equivalent plus r okay then simply cross multiply this one so you'll get r equivalent minus r and r equivalent plus r is equal to r times r equivalent isn't it so then what this is nothing but r equivalent square minus r square is equal to r times r equivalent right is it okay guys so what will this be this is a quadratic equation in r equivalent this is what my purpose was to tell you that such infinite ladders are solved using quadratic equation so this is my equation okay so once this is the equation you know how to solve this use quadratic formula minus b plus minus under root what is quadratic formula so those who want to revise here is the quadratic formula for roots b square minus 4ac by twice a this is the third we are doing it if you still need to remember these formula then you are on a wrong track so hence r equivalent is simply minus b that is r plus minus b square what is b square r square plus 4ac that is 4r square right divided by 2 a so 2 so it is r plus minus r root 5 by 2 we can't have negative resistance so if you see you have to drop the negative sign why negative resistance is not allowed so hence it is r common 1 plus root 5 by 2 tell me anyone who didn't understand please remember this kind of circuit and it is also advisable to remember the concept or the result please remember result also root 5 plus 1 by 2 is the r equivalent what is the variable here r equivalent is variable sneha mack this is variable okay is that understood by all any doubt in any of any of the steps please tell me I will again repeat but your focus should be on accuracy again repeating most of you are very distracted your only focus is on leaderboard which is not really helpful okay so this was the question those who could not see the question was this was the question so those who came late please don't come late join on time every time okay so that we can finish early instead of delaying the process is that okay guys clear give me a why if you have understood this question so please remember this result as well so but don't you know blindly put it everywhere but remembering always helps it reduces some time of yours so good but I am not very satisfied out of 50 people only 15 that is 30 percent of people could get this answer that's really not good that is and someone pointed that it was done in the class as well so okay so here is the first leaderboard so don't really you know get hooked on to all this positioning and all doesn't help in long run please focus on whether you are getting into or getting the right solution every time or not next question please be ready pen and paper pencil focus lesser time right answer minimum value of fx defined by fx equals 4 sin square x minus 4 sin x plus 100 is so trigonometry you need to understand you need to understand quadratic equations you need to understand polynomials all three concepts applied into one so there is no point asking which topic and all in my center mars the topics will be totally mixed next time you can expect a chemistry question with mathematics as well so hence take your time and you know you might have been told about how to find out maximum value of something minimum value of something you would have seen polynomials in polynomials we have discussed this and there is trigonometry of course so you must know some bit of trigonometry as well okay last 20 seconds and the options are very very obvious the option itself will tell you what is correct what is wrong so hence one way is always to evaluate all the four options okay last four three two one and up times up and uh sad it is very very sad lost most of you are not able to now you must be thinking that these questions are not regular in our cbsc curriculum and all that so all these questions are are directed towards your comparative exam so none of your regular questions will be there in any of the comparative exams you are preparing for okay so uh why was this question difficult when i will solve it you will say that it could be done very easily look at this solution now any anyone who uh who would like to comment on how to solve this one no again if you always that's exactly why i wanted to uh you know d minus d by 4 a is one minus d by 4 a is one but then don't remember the you know you don't need to apply formula all the time that's where i wanted to draw your attention all of you have this mindset of finding the right formula yes complete the square is the right this thing right you differentiate it need not you did not so again you are killing a mice using a nuclear weapon that's not required it was simple question if you know the squares are always greater than equal to zero so if you look carefully this is four sine square x minus four sine x and you just needed to complete the square plus one plus 99 isn't it hundred could be written like that this is nothing but two sine x minus one whole square plus 99 now any square has minimum value of zero right it cannot go beyond zero can it go beyond zero can square be negative no so the minimum value of this particular quantity is zero so what will be the minimum value of the total quantity zero plus 99 so answer is 99 how difficult was it how difficult it was it so hence you know uh if you do not pay attention to such things and in fact in the last centymar whenever we did it we had a problem where we wanted to complete the square this is so effective a tool those who are saying i differentiated and use this and that they're used with you know wasting that much that tool right don't waste tools these are so it can be asked in question exams like kvpy very much or ntsc so they just want to see how much aware you are about the properties of square or let's say you know are you observant or not now in none of the textbook you will see someone saying what in in theory somewhere there is a theory saying squares are always positive have you seen this line or always greater than or equal to zero equal to zero this is observation none of the textbook will write this statement ever or they will teach you in theory so don't expect such things so you have to be observant and use it let's see the leaderboard only 17 it's very very pathetic okay so some shuffle good the top 10 at least get the right answer that's good very good let's go to the next one okay next question now again it will you will not find these questions in your textbook apply your mind apply the knowledge it's an application application based question so there are now two quadratic equations if you look carefully should be the following equation not equations s is extra sorry for that following equation there's only one equation here studied polynomial is a mix of polynomial as well as quadratic as well as concept of equations concept of roots concept of roots you have done in last grade grade 9 again reiterating there is no syllabus questions from previous grades will be mixed up in ntsc especially it will be mixed question so remove the fear of syllabus from your mind everything is in the syllabus i hope this should be correct for most of you let me see okay so the final okay all right so at least majority of you have got it correct still many of you how many of you could not get it i could not understand so you must be thinking how to apply the you know the discriminant rule and all that stuff is it so you have to apply for both the yeah anyone who could not or was there any positive time guys was it lengthy what is going on so anyone can just now tell me what where is the issue what happened and why would you little more time there was no requirement of more extra time why because if you see the roots of this equation actually in my mind i was i was initially giving you the bi quadratic equation it was something like that but then i realized that maybe you will not be able to solve it so hence i just gave them gave it in a factored form correct so both this and this will never be zero both the factors cannot be zero both the factors cannot be zero why because if you check the discriminant d of this minus d minus one oh sorry i have to do only d d is b square minus four ac so one minus four minus three for this also minus three for this also discriminant is minus three so both the quadratic equations will have no roots whatsoever so how can their product be having roots how can their product be having roots right so hence there is no real root but does that mean they have no roots at all no they have complex roots there is no equation which doesn't have any roots every equation will have some root or in fact you know this that the number of roots of a equation is nothing but degree of the polynomial do you know this or not do you know or this do you know this or not so what is the degree of the polynomial which is appearing on the left hand side of the equation what is the degree four four the degree of in the left LHS is four why because x square will get multiplied by x square to give you x four the term so degree was four so obviously it will have four roots what are the nature of roots we'll see later so four roots are sure so this was ruled out and none of them are real why because both of them have discriminant less than zero both of them had discriminant less than zero so all four had were complex roots so this was the answer right four roots but zero real roots no they we don't call call it only one root aniket it is called real and equal so question is x square minus one is zero right or x minus one whole square sorry this one x one minus whole square is zero right as only one root you are saying right no we say that the two roots are the two roots are coincident okay sitting on each other right so any equation if it has a degree three polynomial it will have three roots if it has n degree polynomial it will have n roots complex or real that is decided by different or various other parameters is that okay concept clear okay yes or no very good so learn this now these are see my intention is to expose you to higher level of questions which are now asked in exams like kvpy and nkc so still manageable with your knowledge but kvpy for next year you will be writing so you need a little bit more exposure to different varieties of questions so be ready for such questions yes there will be easier ones as well so very good ananya anish abhipsa sneha shavita adit aniket adan aditi keep it a base very good now next question is again related to physics and application of quadratic equation let me see how many if you remember the concepts and secondly this is very important concept with respect to ntsc let me see how many of you recall it because ntsc is syllabus now those who ask for syllabus ntsc actually prescribes grade 9 and grade 10 science maths and social science syllabus in ntsc sat papers if you have forgotten it you better start revising it but yes the idea was to use quadratic equation here let me see the reforms okay most of you have got it how many of you could not understand the question there was some trick or some you know the question was not that straightforward so did you understand the question so body even is when it is thrown up okay so when a body is thrown up with some some velocity okay so it goes up and attains the maximum height so let's say this is the maximum height okay and then what happened yes difference between roots correct aniket and what happens it goes and comes back this is the journey so there will be two times in the journey when it will have the same height always remember when a body is thrown up and comes down there will be exactly two times t1 and t2 right from the start when it will have the same height h okay you had to just find out t2 minus t1 this was the question so a body of mass 1 kg why was this 1 kg given just to distract there was no need there was no need okay but vertically upwards with a velocity of 14.7 why was this number given 14.7 because it goes by 4.9 so you can divide 14.7 divided by 4.9 is 3 yes so that was the catch so if you if you start calculating over there you will miss the bus you will you should remember 4.9 can multiples 4.9 9.8 14.7 19.6 at least this much you must remember these are our multiples of no sorry not 19.6 it is yeah 3 and 4 yes correct 19.6 only right no you should remember these and it becomes very easy now so what is u initial velocity was 14.7 all in meter per second okay g is how much 9.8 meter per second square so you have to write h h was how much it's given how much was h 9.8 it could not be easier than this 9.8 is ut 14.7 t minus half into gt square 9.8 into t square is it this is the equation did you get this equation if you get this equation done this was the equation how many of you got this equation do you remember this or not you remember the formula ut is equal to yeah sorry what are the three equations of motion all of you would have forgotten it u plus at s is equal to ut plus half at square and v square is equal to u square plus 2 ac whenever you get time revise right equation of motion right so hence if you divide all through by 4.9 what will you get you will get 2 is equal to 3t minus t square this is the equation so this is t square minus 3t plus 2 is equal to 0 so t is equal to either 1 or t is equal to 2 these are the two times so you have to find out t2 minus t1 what is t2 minus t1 Anish why was it so difficult how much time did i take did i write something which is beyond your scope below any anything i wrote on the screen which is not known to any one of you present in this quiz right now then what is the problem you understand where is the problem now so these are all tricks my friend please now when you're solving problem you should be able to retain facts little bit of retention can reduce your effort is that clear to everyone give me a why if you are okay with whatever we did so far okay please learn the idea is to learn not to secure first position in this every week's centum are that's also there but not at the cost of your accuracy levels guys shallow next question please on your screen pay attention this will be if you have done oh sorry before that okay good show next question is going to be little tricky so don't lose hope as well as patience now you'll say we have not learned how to solve a cubic equation but you don't need to if you know what is some of root what is product of root use the concept of polynomials so i've used the concept of polynomials in equations where in sum of roots and product of roots are to be okay so good most of you have got it correct i don't know how many of you actually solved it okay here is the solution so you know sum of roots what is sum of root guys minus b by a so 16 upon 3 correct let's say alpha beta gamma are the roots some of the roots taken two at a time okay will be how much c by a so 23 by 3 and product of root alpha beta gamma is minus d by a in this case so it is how much minus 6 upon 3 so 2 okay alpha beta gamma is 2 do you get that all of your tear on this yes or no is it so now what is given if the product of two roots of the equations is one two roots is one that means let's say alpha beta is one so you get gamma gamma is two okay gamma is two gamma is two that's so gamma is two so hence ruled out but there it unfortunately two is here also here also here also okay and now what clearly this is ruled out why is this ruled out can anyone tell me a is ruled out why is ruled out because if gamma is two and alpha beta is one yes either that alpha beta was one so one by two cannot be the either of alpha and beta in any ways we had alpha plus beta plus gamma is 16 upon three so now you can solve these two equations to get alpha and beta isn't it so you can check alpha plus beta now is or alpha plus beta plus two is 16 upon three and what else alpha beta is one and this is how much gamma common alpha plus beta is equal to 23 by 3 yes is that okay below any any difficulty in such in these two equations oh it's lagging now it's it's fine these two equations and then you have to solve for alpha and beta simple so alpha plus beta wait a minute there is some lag okay alpha plus beta is 16 by three minus two which is 10 upon three okay and alpha beta sorry yeah so now either you can see from the options which alpha plus beta is 10 by 3 so if you see this is clearly the one so two was one and three plus one by three was 10 by three so you can solve from here as well so option was D let's say you wanted to solve it methodically then if alpha plus beta is 10 by three and alpha beta is how much one it's given so what will be alpha minus beta so if you remember your ninth grade identities it will be alpha plus beta whole square minus four alpha beta I don't know how many of you remember this so this is nothing but hundred by nine minus four which is hundred minus 36 by nine under root which is root over 64 by nine which is how much eight upon three alpha minus beta is eight upon three so alpha plus beta is 10 upon three and alpha minus beta is eight upon three some them you'll get two alpha is equal to 18 by three which is six so alpha is three if alpha is three beta is one upon three is that clear was it difficult was any part of this question not known to you yes no any part of this question not known to you sir I was not aware a little bit lengthy no so I told you in your there are two approaches to solving one is you eliminate quickly so I eliminated actually I did not solve full laksh did I solve full I would have guessed the answer by half solving it yes that's what you don't need to solve fully who is asking you to solve fully right so in your competitive environment you can just find two and find that alpha plus beta is 10 by three that's it and you are done correct so this is how you should have solved it never mind let's go to the next one this is a leaderboard okay so ananna is maintaining it very good let's go to the next question guys very good again pen paper knowledge and careful approach you remember this question was there in your polynomial test similar yes ananna is shared screen is very much shared code is 599388 if you have missed it re-login in moxa ananya without logging out from mentee re-login in moxa only these questions doesn't require any pen and paper also if you are aware let me see so this is the result oh my god so again how many of you could not understand the question itself what happened here what was the problem I need to know tell me tell me your issues individual issues forget about the leaderboard what's happening you can unmute and say annish acceleration due to gravity what does it mean g what is g okay unmute and say if anyone wants to share or discuss anything it was very simple how many of you did not know how to attempt it how to attempt it we told you right in any polynomial equation sum of root is nothing but what is sum of root in any polynomial equation is negative coefficient of x to the power n minus 1 divided by coefficient of x to the power n right what you call as minus b by a in this case what is minus b by a what is a a is 100 what is b what is b in this case yes so b was 0 if you noticed it b was 0 right so what is minus b by a 0 so sum of roots so 90 how many roots are there in this equation how many roots are there 100 roots are there very good so 100 roots are there so 99 roots custom plus let's say one root is alpha 99 roots let me write it here so 99 roots plus let's say the 100th root is alpha is 0 right and sum of 99 roots is given how much is that k so k plus alpha is 0 so alpha is minus k is it it how much difficult was it how much time um didn't see 98 that's what the question would be okay so hence careful right it was purposefully 99 was removed because i know most of you will get tempted because you know the concept but carelessness and doom so answer was b minus k right on track very good others please what up next question people are playing the quiz just to participate 12 people cannot mark the answer by glitch they're just here to press some key here and there thumb bola they're playing thumb bola guess work doesn't work like that my friend you're ruining your own prospects if you're doing that you you are feeling that it is millisecond because multiple people at different locations are just pressing some key here and there it's not because of a glitch all the time if that was the case then everybody once in lifetime they would flip you know face the glitch during the quiz itself so stop blaming that and start working out here is the oh my god why for 20 why did you go for see guess this told that all of you are guessing all of you are guessing how many of you guessed it tell me frankly i'm not going to judge you tell me frankly how many of you guessed it and he gave gupta guess everyone guessed why why did you guess so far what is there to guess they go now let's say this this question is there in kbpy next year very much possible very very much possible so how would you solve this you will guess and then get a negative they go why no not required see huh time see the moment i solve this you will say oh my god it was not so the all the questions are designed so it cannot be some lengthy question picked up from somewhere and is given to you no i have solved these questions also so they go what you need to do was you can observe the what are they so sorry let me what are these things the highlighted one what what what do you say about this what are they root over x by a and root over a by x what is that what are they in each other to each other they are very good so hence let's say it is 2 y plus 3 by y is equal to b by a plus 6 a by b can i say that can i say that so what is y in this case y i am writing as under root x upon a remember this okay can i say that now what let's let's frame the equation quickly how much time does it take to write this as is equal to b square plus 6 a square divided by a b right or not quickly solved like that okay so what now 2 y square plus 3 plus b square sorry minus b square plus 6 a square by a b times y is 0 yes or no can you show the question question is on the screen okay is this okay so the equation is 2 y square minus b square plus what 6 a square by a b times y plus 3 is equal to 0 below y all all is correct yes now what is the question product of roots right product of roots will now tell me if y1 and y2 are the roots of this equation what is y1 y2 what is y1 y2 3 by 2 very good what was y1 y1 was x1 by a what was y2 x2 by a yes or no yes or no this is equal to yes or no so if you see what is this under root x1 x2 by a is right so x1 x2 under root is 3 by 2 a so square both sides how much below was it lengthy understood now you understood questions will be like these they will not be straight forward at all so stop you know being in that comfort zone start coming out stop being in that comfort zone of under root so all of you are in this comfort zone alpha is minus v plus under root b square minus 4 a c by 2 a n beta is minus v minus under root b square minus 4 a c by 2 a that's it your life revolves around this that should not be the case yes now i hope you got the message next so very good yes make now after this one solve this now easier questions harder questions are gone oh no so let's see this is very straightforward see 13 people have already marked it so 13 people are having glitches 14 people now within 10 seconds of the question this way okay last 10 seconds okay okay very good let's see oh equal to easy huh but she got it correct yes very good so it was easy for only 14 people that side okay that's sad now so my dear friends how to solve this product is one yes aren't undone correct so you could have guessed by that as well so clearly this was ruled out this was ruled out only this and this was left oh i'm sorry i'm sorry i'm sorry i'm sorry here is the screen okay so as r n was correctly saying product of the root is how much one is it alpha by beta into beta by alpha is one so obviously product of root is for any equation is how much c by a for a quadratic equation now c by a here clearly is not one here also here also it is not one b by a only cases are this one and this one c or b or d so you'd have eliminated either of them you could have guessed what 50 percent of probability of getting it correct anyways but now how to so how next what about the next one so alpha plus beta by alpha beta is the sum isn't it alpha plus beta yeah signs of some also that's fine so now i'm sorry i'm what happened to this some of the root oh sorry alpha sorry so it is alpha square plus beta square by alpha beta okay now as you are mentioning sign of this thing also will be true so this is greater than zero isn't it is this is this quantity greater than zero you agree alpha square plus beta divided by alpha beta alpha beta oh no it's not given you can't say you can't say no you can't say why can't you say because i don't know about l n n whether they are positive negative whatever correct so alpha i don't know about alpha beta i know about this being one but anyway so how to solve alpha square plus beta square you know already so alpha plus beta is how much in this case minus m by l by the first equation provides that yes that's what so alpha plus beta is how much minus m by l and alpha beta is n by l so alpha square plus beta square plus two alpha beta will be how much m square by l square right so alpha square plus beta square you'll get alpha square plus beta square is equal to m square by l square minus two alpha beta hence it is m square minus l square minus two alpha beta is how much two n by l which is nothing but m square minus two nl by l square by here it itself you would have got it that there is a negative sign so this is ruled out okay so here itself was good enough indication that some of the roots of the new equation is going to be m square minus two nl by l square this is alpha square plus beta square divided by alpha beta where alpha beta is two nl sorry whatever uh two n by l alpha beta was n by l n by l okay so hence it is nothing but m square minus two nl by nl this is why some of the roots of new equation so hence clearly here is the and nl goes and multiplies by x square n like that right so you can do it in your mind itself is that understood anyone didn't understand this question come on tell me quick anyone didn't understand this one quick quick quick quick all of you understood then say why very good now the rest of the four questions are very very simple all the intensity we were there in top eight questions now i don't want any one of you to make mistakes this is now level down okay so all the top eight questions are gone these are very very simple questions word problems shall mix of come on now none of you none of you should be getting it wrong none of you should be getting it wrong so it was very simple question guys i hope you have got it correct cool i was expecting a to be more the same but then most of you have got it correct wrong unit so one of you one of those three is use s that's add see here is where you lose marks in very very easy question how many of you think it was difficult how many of you think it was difficult was it difficult guys by any standard no right so by increasing the speed of car by 10 kilometers per hour the time of journey for a distance of 72 kilometers is reduced by 36 minutes so let the speed be v okay and it is now increased by 10 right and the time is reduced by so let's say time is t t hours it takes t minus 36 minutes means 0.6 hours and this is equal to 72 did you get this equation and v t also is 72 am i right are these the two equations you got guys quickly tell me is this is this is this the two are these the two equations you bought guys confirm so t is equal to 72 by v always eliminate the variable which you don't want right so i don't want t i will eliminate t now what is this vt if you expand the equation vt minus 0.6 v plus 10 t minus 6 is equal to 72 this is the equation yes or no vt minus 0.6 v plus 10 t minus 6 is 72 right so hence what do i do vt is anyway 72 this goes correct v2 vt vt and 72 goes so hence now this becomes minus 0.6 v plus 10 t that is 720 by v minus 6 is equal to 0 am i right guys tell me just check if there is any error v square plus 720 minus 6 v is equal to 0 right so hence this is i am just multiplying by minus 10 6 v square plus 6 v 60 v sorry and this will be minus 7200 am i right is equal to 0 so v square plus 10 v minus 1200 is 0 that means this is v minus 30 v plus 40 i am just splitting the middle term and writing quickly 0 this cannot be true because this will make negative velocity so v is 30 got it clear so there was no ish scope of any error here but still people have made it okay never mind okay so ananya is leading the pack and sneha is just next very good next yes make that towards the end i will show you don't worry again very easy one now all the questions are easy all the four questions would be easy i hope you get it correct by the way this is not even a quadratic equation i just realized grade nine people question speed distance time oh my god oh my god oh my god these questions are difficult then we need to teach you quadratic for instance once more right what is this a peacock is sitting on top of a pillar so make a pillar of solid screen pillar right which is nine meter high so nine from a point 27 meter away from the bottom of the pillar this is the thing this is 27 kilometers sorry 27 meters there's a snake so here is snake s here is peacock p this is four okay all right now what seeing the snake the peacock bounces on it if their speeds are equal at what distance from the hole is the snake caught so obviously snake cannot fly so it will crawl and come here okay let's say here is the s dash new position and hence the peacock was very smart calculated properly and it flew along this line is it p s dash now p let's say both had velocity v so this is vt this is also vt yes or no velocity was same time taken will be same okay what is this let's say this is x this is 27 minus x correct now you have to solve only for x you wanted x that's it so if you see vt is equal to 27 minus x and vt square is equal to nine square plus x square am i right my fibro square so hence what will happen vt square is how much so i can write this as 27 minus x whole square is equal to nine square plus x square see it is not even quadratic not even quadratic quadratic equation so if you expand this you'll get 27 square plus x square minus 54x is equal to nine square minus or plus x square so this x square and this x square both v and t are in v is velocity t is time so v into t is distance isn't it velocity was same time taken for both will be same because they started together they reached together so time taken was same so hence if you see what will this be 54x is 27 square minus 9 square so x is 27 square minus 9 square is 27 minus 9 27 plus 9 divided by 54 which is 18 into 36 by 54 so 18 thrice 12 so x is 12 but it not even quadratic equation okay let's see five more five more minutes guys sorry still we started on time still we delayed okay because we are explaining to everyone okay never mind shallow next so towards the end i purposefully kept easier questions so that you get a good night's sleep also one more dutch very good so it was yes i think you could have done trial and error as well okay so this should be okay good so still people are struggling never mind quick quick explanation so this is nine times three x okay let me explain methodically so this is three x into three square plus one by three to the power x is ten correct this is a thing so three square is nine so nine times three to the power x plus one by three to the power x is ten this is methodical i will tell you the shortcut also so let y be three to the power x so it is nine y plus one by y is ten so nine y square plus one is equal to ten y quickly right so what is this nine y square minus ten y plus one is zero so nine y square minus nine y and then minus y plus one is zero so nine common y sorry nine y common y minus one minus one y minus one is zero so y is either one or y is one by nine correct what was why three to the power x so three to the power x is one that means three to the power zero and three to the power x is either three to the power minus two one by nine is three to the power minus two so what is x x is either zero or x is minus minus two right so b you could have deployed the options itself and you could have checked it x equals to zero we'll make it one and this is nine nine plus one is ten so zero would have given you some kind of so zero was definitely there and there is no zero everywhere anywhere so this would be the answer right so you check zero get it satisfied that means then is there is no zero anywhere else so b is the answer so it was hardly 10 seconds sum never mind let's go to the leader board and the last question of the evening oh my god what happened to these stalwarts you got it wrong how come okay here is the last question of the evening what i want to do what did you do and term is such that you forget no problem aditya you will realize now yes now you got it now see people are smart that's good right right the options were clearly you know this is the last question come on very good right so it was not to be solved at all so some people have caught it so 30 hours and 10 hours this was the catch but good that you were trying to solve so difference was 10 hours so obviously all these are ruled out right so hence it should be 25 and 15 but anyways just in case you want to solve it it's like this because not every time there will be objective time now two taps together can fill a tank in 93 by 8 hours 93 by 8 is 75 upon 8 okay so in one hour 8 by 75th portion of the tank will be filled 8 by 75 isn't it in one hour in one hour this much tank will be filled by both of them now let's say individually the larger pipe takes lr's and the smaller diameter pipe takes lr's so in one hour 1 by l and in one hour 1 by s these are the rates of the smaller and the larger and this put together is 8 by 75 you have to just solve this and also l minus s is 10 it's given so the moment you write this you get the option and it's correct right or if you solve this one you can you can also put 25 and 15 here also to get 8 by 75 so you can validate otherwise you have to get up you have to solve like l is equal to 10 plus s and then it is 1 by 10 plus s plus 1 upon s is equal to 8 by 75 form a quadratic equation and solve for s you will get s is equal to 15 okay do i need to solve this quadratic equation all of you understood this all cool right understood or not any problem in any of the 12 questions which we discussed what is the learning of the day guys learning of the day is there is nothing which is beyond this syllabus for point number one so just yes i will come to that make now just give me one moment remove this mental blocks all of you that hey i need to prepare for this syllabus this exam that exam and all that all what have been taught is the syllabus hence forth so you must be ready anytime so you have to develop that kind of flag is that fine so i just don't want to give you syllabus of this and only solve some uh regular questions here and there no in my centrum hours in mathematics expect questions could be from anywhere and all of them will be aligned to competitive exams like everybody and in pc okay second is yes second one is uh in in competitive exam be careful about the options okay be careful about the options third if there is a mcq question it has to be solved easily you can if you're taking time that means you're going in wrong direction period so these are the learnings of the and then yes don't miss on the units don't miss out on the signs don't say i forgot i could not see 98 99 and all that that you cannot afford no unforced errors guys now final leaderboard and then i will explain to megna as well the question number seven okay so ananya i believe is the top position very good congratulations so akshay adan sneha and what akshit aniket and then who yanesh naina shobhita and neha very good guys keep it up i want others also to you know uh tell me frankly how can i help you more so that i can align my listening to your requirements please let me know individually also please text me on moxa you can tell me send worksheets which worksheets there are lots of worksheets already available on learn is please solve all of them level one level two whatever okay on complex questions okay right is that okay bye bye take care megna just wait i will solve the yeah megna you're there megna yeah megna tell me okay bye guys take care yeah so do you have a mic megna you can speak then it becomes easier for us to connect bye bye take care guys yes megna no you're not there are there uh excuse me sir can you hear me yes is it megna oh yeah sir i got the explanation i just wanted the picture of the question so can yeah oh okay no problem no problem yeah bye bye take care yeah that's it thank you sir bye