 Anirudh, Anirudh, waiting for Anirudh to confirm. Sorry, brother, you have to join now as the quiz progresses. Okay, so here we start. Three, two, one, go. So the first question on screen, read carefully and then answer. Okay, all of you will have to continuously put your mics on mute. Okay, so now they have changed, it seems. Okay, so the first answer is, okay, so still people are doing, do it. Come on, come on, come on. Yes, they have redesigned it. They have changed many things actually. We are also trying to adapt with that. Yeah, so now you don't get to see how many people have already voted. So that's good. So you don't know how many people have voted, right? So just relax and solve, focus on solving the question. Yeah, less pressure, good. Okay, so first question was very easy. It was based on your last grade concepts on linear equations. Okay, so here is the, lots of people have made a mistake. Why, but lots of people have made a mistake. 28, right, why? Why did you, didn't read properly? I told you. So this was the question. There cannot be any distance between two intersecting lines. If you see, X is zero and Y is equal to eight are intersecting lines. They are nowhere parallel, okay? So X equals to zero is Y axis. And Y is equal to eight is X axis and eight, yeah. So what is the distance between this line and this line? Right, silly, right? So what is the right answer? So you have to check first of all which are parallel lines. So these are parallel lines and these were parallel lines, right? These were parallel lines. X equals to minus one and X equals to nine. So X equals to minus one is this line and X equals to nine is this line, somewhere like that. So total distance is 10. So this is not correct. Only Y is equal to five and Y is equal to minus three is. Any problem in this one? Yeah, so don't expect linear equations question to be only solving linear equations. You must have the concepts clear of Y and how do we study linear equations? Anyways, done, shall we proceed? So the first leaderboard, yeah, okay. Very good, so Aniket Gupta. Okay, so nice, here is the next question. All of you would have got your, yeah. This thing, there is someone called Volcani and I don't know who. Anyways, next question to you. Someone's mic is not on mute, can you just mute it? Otherwise I'll have to just change the window, okay. So which of the following doesn't represent a line? Take your time, it will require some bit of thinking. Sorry guys, can you hear me? Just give me a confirmation, can you hear me? Yeah, thanks. Okay, so here is, okay, fine enough. I hope all of you would have answered this. Okay, very good, let's see. Lots of people have made a mistake, yes. So D was a zero equal to zero form, so you should have identified that. So basics, struggling. This is clearly a linear equation, no problem, right? What is a linear equation? AX plus BY plus C is equal to zero. This is a form of linear equation where A cannot be zero, B cannot be zero, right? And A, B and C can be any real number. A, B, C are real numbers, right? So this is very well, very well satisfies this one. This one also satisfies, you just manipulate. This one also is a linear equation because this is 4.5X plus zero Y plus one equals zero. So this one is very much a linear equation. This one is not a linear equation. Why? Because this is zero X plus zero Y plus zero equals to zero. This is that form, why? You would have learned in ninth grade that one upon two minus root three is equal to two plus root three. If you rationalize, you will get this one. Okay, one minus two root three, rationalize. The denominator, you'll get two plus root three. So that means two plus root three X and one minus two minus root three X are same thing. Okay, so this is zero X. Similarly, two minus root three Y and two plus root three Y are same thing, zero, zero. Right, so they just get canceled. So hence this equation is of the form of zero X plus zero Y plus zero is equal to zero and this cannot be linear equation. See, in the very basic question, how many people have got it right? Sir, is it wrong to say that the reason is that there are irrationals in the denominator? No. What did I say? A, B, and C are real numbers. It could be anything. A, B, and C, there is no restriction on A, B, and C. The only restriction is A and B simultaneously cannot be zero. Both of them cannot be zero, right? And this was the only option where both A and B was becoming zero. So hence irrational numbers are allowed. Irrational numbers are very much allowed in linear equations, okay? Is that okay? Only the powers, power will be only one, right? The power of the variable has to be one, right? There is no ambiguity in that. Okay, fair enough. So basics, clear your basics. Okay, next question. Before that, the leaderboard. Okay, right? So, good. Nice, let's go to the next question. Read carefully and then answer. Don't jump on answering. Read each one of them, each of the options. Take time and solve. Read each question very, very carefully. Each question will have some bit of information. So if everyone would vote together, then we can proceed. Nevermind, take your time and try also to think, even if you're marked by others, or is there any possibility of other options to be true or incorrect or correct, whatever. Last 15 seconds, yes. So let's see how many of you actually got it correct. X axis is not zero slope line. Aren't all true? Okay, aren't all true. So those who have marked B, why did you mark B? Can anyone unmute and say? All of you can hear me, correct? Hello, are you able to hear me, guys? Oh, yes, sir. Yes, sir. Hello, can you hear me? Yes, sir. Yeah. Okay, guys, I think I am facing some issue. Just give me a moment. Just a minute. Who do I, yeah, okay, fair enough. Okay, yes, so here is the solution. First of all, so two lines may intersect exactly at one point. Yes, possible. This is very much possible. This is what we are learning at time to find out the solution, right? Okay, X axis is the zero slope line. What is the slope of X axis? Zero, this is very much correct, right? Right, and two lines, if at all they will intersect, they will intersect exactly at one point. There is no ambiguity in that. Okay, there are infinitely many solutions to a linear equation in two variables. Yes, wait a minute. So this is the, if two lines are not parallel, they will intersect at a point, not necessary. Not necessary. Why? Why? Because if you take two intersecting lines and just displace them in vertical direction. Okay, or imagine like that. In your room right now, there are two lines, right, which are one line at the roof and the other line is on the wall, like that. So when they are not coplanar, this is possible, right? When they are not coplanar, this is possible. Okay, did you get this second point guys? If two lines are not parallel, yes, obviously. Did I say this is 2D? Why, Anish, in which case it is not, Aditi, in which case there are not infinitely many solutions to a linear equation in two variables. I am talking about only one linear equation in two variables. Why are you assuming a Cartesian plane? Did I say anywhere? I'm just talking about two lines. Have we ever, are we even talking about any planes, anything we have given? No. Why are you assuming? I said which of the two lines is not correct. Okay. So two lines, if they are not parallel, need not intersect. Okay, when is that possible? When they are in two different planes. So imagine a line on the roof of your room and one line on the floor of the room, right? Even if they are not parallel, they will never intersect. Okay, so hence, V is the option. See, in the three very basic questions, we have not got into solution part of the linear equation so far. They will add some distance. Now who started the video? I don't require the video. Please turn it off. Yep, please, yeah, anyways. So, sir, they will add some distance. Never mind here, if two planes are coplanar, two planes are parallel, right? Imagine, as I'm telling you, imagine a line on the roof, another line on the floor. They are not parallel, let's say. And they will never intersect, is it? Sneha, is that clear? Sneha, is that clear? Yeah, Aniket, any issue here? Any problem? Anyone need to understand? Okay, let's move ahead. Okay, let's go do. So most of you did it wrong. X axis is very much zero slope line. There's no slope in that line. Okay, so change, shuffle, very good. R n single, keep it up. Next question on your screen. Someone has his mic on mute. Can you please request you to mute it? Who is this? Aniket Gupta, your mic. And yeah, Aniket Gupta, mic mute. So you know this is basically a question related to consistency of linear equations. It was very, very simple. Okay, that's nice. So fair enough, okay? So only 22, again. That means you need a lot of lot of practice. So I have to put another test on linear equations for all of you. Because, okay, so why? What is the rule for two equations to coincide? Two lines to coincide. It was A1 by A2 is equal to B1 by B2 is equal to C1 by C2, correct? This is the rule for coincident lines. The only one which satisfies is this one. See, the factor of 2.5 is there. Sorry, 1.5, yeah, four into 1.5 is six. Yes, correct? So this is the four parallel lines. Parallel lines, sorry, not parallel. Coincident lines, coincident lines. These are coincident. So people are making mistakes there. Please remember your rules, right? So if A1 by A2 is not equal to B1 by B2, then they are intersecting lines, just to intersecting, just to give you a, you know, recap. And A1 by A2 is equal to B1 by B2 is not equal to C1 by C2 is parallel lines. These are the three rules. Okay, please remember. So it was very simple question. I don't know why many people have not marked correctly. So here is the leaderboard. Okay, let's see. So some reshuffle, cool. Okay, nevermind. So let's go to the next question. All set, read the question carefully again. As I'm telling you, questions will be a little tricky. The wordings will be tricky. Oh, so option D has none of these. D option has come up, like some typing error is there. So D option is none of these. So now you are saved. So one out of three is correct. Again, infinitely many solutions. I just gave you the rule in the previous slide. Okay, let's see. If time is too much, then everyone should get it correct. Okay, see, let's see. See, even if with 100 seconds given, all of you have made the wrong. Most of you have made it wrong. What is the point of having lots of time? Yep, all of you got it, correct? How many? See, why? All of you have marked six. What was the question? I told you, read the question carefully. How many values of C? They are not asking value of C. They're asking how many values of C are there, right? And all of you have marked the value of C, right? So hence the questions will be right like that only. So you guys don't understand. I keep on saying, I keep giving hints. Keep giving hints that, you know, read the question carefully, read the question carefully, but no. See, you got trapped, right? This is how you will get trapped. See, both the options are there. These are the real exam scenario. Both the options will be there. You will be solving very easily. System of equation has infinite many solution. Y, six upon 12 is equal to three upon, what? C, is it? So you will find C is equal to six. Okay, C is equal to six. And then you will see the option. Oh yes, it is there. Click it and go. But then question was, how many values of C are there? So only one value is there. So answer is A, clear? Understood. Learning is learning. My mother tongue is Hindi. So I will give you one. All of you would have read Hindi sometime in your life maybe. This, do you understand this? Right? Yes, one more. Correct. So hence the, Ananya you understood. Saadani, Adi, Durgatna, Adi. So you guys are on that track. It's like a cricket match. If you take away your eyes from the ball, gone, bold, right? And lost the match. So hence concentrate. And these are the types of questions which will be there to test your temperament more than C, only 12. This is so surprising, right? Anyways, see lots of people have got it wrong. In the leaderboard itself people have got it wrong. So that shows that where is your focus. Anyways, let's go to the next question. Again saying, read the question very, very carefully. Again the same rule, but I don't know whether again, you are paying attention to the minute details. I hope this time also you will take time and then solve it. So why time has been given is solve and check again whether you have done it correctly. If option 1.5 was there, many would again make a mistake. Okay, so you understood the theme now, right? Questions and knowledge base will be very a sound. You will be knowing everything. Very rarely you will miss. It's not Olympiad question. Olympiad is where you don't know the question only. How to solve it. But in most of the competitive exams it will be like, you know it, but you would. Okay, so here you see again, lots of distribution happening. Again very few people are able to base it. I don't know what, okay. So you have forgotten the, you know, the, this thing. Okay, so hence if you see, this one was k plus one x. So you have to simplify this first, right? So hence it is k plus one x, right? Minus three y plus six equals zero. And the second equation is three plus k x minus six y plus 15 is equal to zero. Isn't it three? What is three? K is equal to one. K is one, right? So you have to do what? K plus one by three plus k should be equal to three by six. Okay, three by six. So what should be the value of k? K is equal to one. We'll satisfy this. Isn't it? You can, you can solve, right? Six k plus six is three nine plus three k, okay? So that means three k is equal to three. So k is equal to one, right? So when I was framing this question, I did not put this minus x on the right hand side. I was putting it zero. So hence I put minus kx also here. Yeah, understood Aniket Gupta. I told you, this is what will happen. This is exactly what is going to be there, right? So hence now you know the purpose of centimars. Anyways, it will help if you now curse yourself that, hey, when will I, you know, set it right? Okay, so eat one chapati lesser today, tonight, next. Oh, miss clicking can happen, Surya. So really, really can't help you there, buddy, sorry. So here is the new leaderboard. Okay, let's go to the next one. Again, for God's sake, read the question thoroughly. Read the question thoroughly. This should be done by all. So hence if everyone votes, so we can proceed. Just confirm once you're done. So I'll request all of you to mark your answers if you're done, but again, spend time. That would be better. Questions would be easy, but they would be tempting you to do wrong activities. So hence the only idea is to improve your, improve your, what do you say, consciousness. But this is very simple question, no? Very easy one. Okay. Okay, very nice. So, so why is this session conducted is to give you a taste of unconventional approach towards problem solving. So don't really bank on only your, you know, Adi Sharma's and RS Sarval's and NCRT's for the basics. Okay, here is the explanation. Very simple it was, right? So AM is equal to BL. So AM is equal to BL. It will give you A by L is equal to B by M. And BN is not equal to CM will give you B by CN, right? CM, yeah. So B by M is not equal to C by M, right? And this is possible only when they are parallel lines, right? So it's basically satisfying A1 by A2 is equal to B1 by B2, but not equal to C1 by C2. Isn't it? So when that is true, then it has no solution. Clear? Any question here? Any problem? Anyone? No. Let's move ahead. Okay. Lead a board. Hmm, most of you did it right. Very good. Okay. So let's go to the next question. Okay, I don't know if you are able to see this. So let me show you here. Which of the following graphs represent the line two X plus four Y equals to eight and three X minus four Y is equal to 12. Now I can't give you plotting a graph question here. So I have done the other way around. I have two graphs and then you have to find this out. It's a bit so that I could know who or how. Okay, so how much time is left? 20 seconds. What is the code? Someone code is 80548. Okay. So this was, okay. Most of you have got it correct. That's nice. Yeah. So how to solve this one? Again, it was very, very simple. No time consuming. It will not be time consuming at all. That means, no, that means you have not implemented it properly. How to, you know, very easy. See, two X plus four Y. I hope you have not solved these equations. No, you don't need to do anything. Put X equals to zero. What is Y? Y is two. Yes, that's it. Correct Sneha. So X is zero, Y is two. So first point of the first line is zero comma two, right? Next put Y is equal to zero. So you'll get X equals to four. So four comma zero is the another point. So these two points are on the first line. There are these zero comma two. Zero comma two is here. This one and four comma zero is also here. So this one option is there, definitely. None of the other options are. This one also is there, right? So out of these two only have to check A and B. Okay, then go to the next question. Next equation, three X minus four Y is 12. Put X equals to zero again. You'll get Y is equal to minus three. And put Y is equal to zero. You will get X equals to four. So four comma zero and zero comma minus three are the other two points. So four comma zero is here and zero comma minus three. So A is the answer, how much time? So the question need not, you know, you didn't require to solve them. But you have to, Momita, you can do. You can do, but then one has positive, one has negative. So don't you think you can get stuck here also? One has positive, one has negative intercept here also. So there are more such options, Momita. Momita is saying can we check these slopes or Y intercepts and one has positive. Okay, so you can eliminate. You can do that. Oh, I was thinking of slope. Oh, you're talking about Y intercept. Yes, you can do that. Yes, you can do that. Yes, you can do that. You find out the, right? Yeah, that also can be done. So for precise, you know, points. So if only A has Y negative, okay? So you're finding Y intercept. So Y intercept is found by putting X equals to zero in both. So what you are doing is put X equals to zero in both. So X equals to zero if you put, for first case, Y is two. And for second case, Y is minus three. Yes, the only option is this, correct? You can do that. Yes, that was faster than. Nevermind, so let's go to leaderboard. Okay, so this is the new standing. Nevermind, let's go to the next question. Require you to solve it. This will require some solution. Some solving has to be done. Very simple question, I think. This is a typical question. But then yes, I have not asked you the direct solution. I have now I want to also check whether you have retained whatever you learned in previous grade or not fair enough. So I think most of you would have got it correct. Oh, again, some spread is there. Why in this, what was the problem? We had to just solve it, right? So use elimination and solve, that's it. Or if there is any other method, let me know. So it's very two X minus Y plus three is equal to zero. And this was three X minus seven Y plus 10 equals to zero. So what I'll do is I'll multiply this equation by seven. Correct, so that Y can get eliminated. So 14 X minus seven Y plus 21. No, how are you doing that? How are you doing that? But then, you know, you never know, yeah, it's basically, it will take same time instead of, you know, so it will give you very quickly answer also. So subtract it, you'll get 11 X, 11 X, and plus 11 is zero, so X is minus one. So when X is minus one, you can find out Y. So Y is nothing but two X plus three. So which is one. So minus one and one, how much time does it take? So minus one and one is in second quadrant. So try drawing graph when the graphs are complicated. For example, if you have now learned polynomials also those who have learned, if I give you this, Y is equal to X square minus three X plus one equals to zero and Y is equal to two X square minus five X plus two equals to zero. Let's say these are the, sorry, not equal to zero. These are the two graphs. Then where, then you have to plot, you know, then exactly, you know, one way is to plot the graph and check, right? But then here it was linear, simple, 30 seconds. Never mind, but still most of them are not able to get it. So that's concerning. See, in the top 10 also there are lots of shuffling happening. So that means you have forgotten now a month old. So we discussed linear equations in the very first few weeks. So hence I think you have forgotten many things. Anyways, next question. So this, these kind of sessions will help you. Results are here. Okay, never mind. I hope you have done the basic calculations properly. Okay, so very good. So three, two, and one, let me see how many of you have. Okay, so still lots of people are getting confused. How many of you got it correct? Just give me a confirmation. Anyways, I have the result, I will check back. Okay, very good. Very good. So even if you don't know this particular form, you could have done it very easily by using trigonometry maybe, that can come into, you know. So what is this line? First of all, let's draw this line. So four X plus three Y is 12. So if put X equals to zero, you will get Y as four. So zero comma four, so this is one point. And if put Y equals to zero, you will get X as three. So the other point is this one. So the line is like that. So this is three, this is four. Isn't it? And you have to find out this perpendicular distance P. Okay, so clearly let's say this is theta. This will be 90 minus theta, so hence this will also be theta. I hope this is understood by all. You found out X and Y intercept hypotenuse area and height. Ha, that is also correct. That's also, so half into, that's actually easier. Half into four into three. So hypotenuse is five, no problem. Half into five into P. Area will be same, correct? The two ways of doing it, one is area method. This is area method. Find out the area. So area is half into four into three, base into height. And hence, yeah, that's also cool of guessing. So hence you will get P is equal to 2.4. There is no, no tau, what does it mean? Ah, right, so hence be careful. Correct, advertise has a point. Are in, there is none of these also. So hence you have to check the answer anyways. Okay, so 2.4 is one way of doing this is like this. Another way of doing like that would have been three upon P, or P upon three. P upon three is cos theta. P upon three is cos theta. And P upon four is sine theta. Check from your trigonometry, right? Correct, no? P by three is cos theta, P by four is sine theta. Square and add. So P square by nine plus P square by 16 is one. Why? Because sine square theta plus cos square theta is one. So this is another way. So you'll get P square common. One by nine plus one by 16 is 25 upon nine into 16. I'm doing the fast calculations faster. So this you can figure out yourself. So P square is equal to nine into 16 upon 25, isn't it? So P is three into four by five, which is 2.4. Either way, this way also, or those who know, those who know the equation of a line, the third way of doing it is any equation of a line, let's say X upon A plus Y upon B. Or no, you don't use this one. You'll get complicated results. So there is another, which we had probably, area method again, yeah. See area of, so let me complete the third method first. So third method, which I'm talking about is there is a typical form of a linear equation where you can convert it. Yes, how does it, how does this form communicate? So there's a, you know, it's called the perpendicular from the origin and the line form. So there's a typical form where you can convert any linear equation, which you'll learn in next year, coordinate geometry. So that way, that method I'm skipping. I'm just telling you the area method once again. So area of the triangle, which triangle, A, B, C is what? Half into A, B into B, C. And this is also equal to half into A, C, which is hypotenuse into the P, perpendicular P. So what is P? Half, half goes. So P is simply A, B into B, C upon A, C, right? So three and four, you knew. So by Pythagoras theorem, this was five. So apply three into four by five, 2.4. Clear? Alisha, right? So I hope this is clear too. Everyone, let's go to the leaderboard and then the next questions. Okay, okay, okay, okay. So many people didn't get this correct. Why? And you took so much of time also. Very good, next one. No problem, next question. And Rose downstream at 12 kilometers per hour. I know, I hope you know what is downstream. So going along with the stream and upstream at eight kilometers per hour, that is going again, the stream. He doubles his speed in still water and rose 72 kilometers upstream. In T minutes, T is equal to last 10 seconds. I hope this should be not that tricky. Fair enough. So let me see how many of you have, today I'm getting a lot of mixed responses. I don't know why. So there's no clear, but people are just guessing or why people have marked A or C? So D is very less, why can ignore, but A and C, why? Okay, so how many of you could not solve this in time? Time was lesser or what happened? Anyone? Out of time, okay. Anyone else who struggled in this question? Any other struggle here? So it was very easy question actually. See a man row downstream. So let's say V1 is speed in still water. So I told you, right? Immediately after reading the question, so we read it, a man rows downstream at 12 and upstream at eight. Obviously upstream will be lesser, so verified. He doubles his speed in still water and rose 72 kilometer upstream. So I need to have upstream speed. No, you can't, you don't need to assume anything. So speed of initial still water, V1. V1 is the speed in still water. V2 is speed of water itself, right? So V1 plus V2 is 12, correct? And V1 minus V2 is eight, big deal, right? So sum to V1 is 20, so V1 is 10. Correct me, V1 is 10. Then V2 is two, he doubles his speed. So doubles means 20 now. Doubles his speed in still water, so he's now 20, but he's going upstream. So his speed will be 20 minus two, 18 kilometers per hour. And he covers 72 kilometers. So how many hours? 72 upon 18 is four, four hours, no problem. Yep, so 72 by 18 is four, right? So four hours, 240 minutes. Okay, so 240 minutes is the right answer. So 21 of you. Anyone who didn't get this? All clear? Actual speed much faster. No, I mean sir, here we can assume actual speed much faster. That's the question. So is the real speed average of upstream and downstream? Yes, so for any V1 minus V2 is A, let's say, and V1 plus V2 is B, right? So if you, two V1 is A plus B, or very good point, A plus V by two, arithmetic mean. Not visible, what is not visible? Who? Am I, am I audible, visible? Guys, yes, Aniket, yes, I am very much visible to everyone. So, yes, Anirvan, oh, board, oh, sorry. Yes, so good point raised by Momeda, that in case of, but only in case of constant velocity, constant velocity, Momeda, if there is some acceleration happening, then you can't see it say that. Okay, so hence upstream and downstream. So, yeah, so the still water velocity is nothing, but the arithmetic mean of upstream and downstream velocity. And the catch was that I had given you upstream. So hence you have to subtract this two again, which many people have missed, and hence the problem. Okay, next. Oh, out of 10, five people got correct. That's surprising. Okay, next, last one. Question of, last question of the day. The largest angle of a triangle is twice the sum of the other two. The smallest angle is one fourth of the largest. The largest angle is, trial and error is faster. Actually, this question need not require any solving. This question need not require or didn't require any solving. No solution was, no solution was, no solving was required, actually. The first line itself, no, you don't even look, you know, so most of you have got it correct, actually. So you don't need to look at the options also. So this is a useless information. So I have deliberately added that. So you have to identify which one is useless information. So the smaller angle is one fourth of the largest. We'll take away some time. Some people would have been involved in taking X and Ys and all that. This itself was over. So largest angle of a triangle is twice the sum of the other two. So even if you would have taken X and Y and Z, so X plus Y plus Z, you know, is 180. And X is given as two Y plus Z. So even if you have taken this for the sake of doing it, so you'll get X plus this Y plus Z can be written as X plus X by two, 180. So clearly X is 120 degrees, okay? So this one is the, so there will be, what is the learning? Learning is there will be questions which will give you unnecessary information as well. It happens in most of the competitive exams. So hence, whether you are able to screen off or siphon or, you know, shift through the data, right? The largest angle is, many a times people will go back to this again. Why, if the largest angle is asked, why is this statement given? So it also checks whether you are confident enough of whatever you're doing, right? So this is the correct answer. Thankfully, most of you have got it right, but not all, that's surprising again. But anyways, yes, so that's the question. That's what the intent of the question, Aryan, so that the examinee get confused. So they will deliberately try to confuse you because otherwise, anyways, so understood all these questions, question again, yeah, here is the question, right? All these questions were deliberately made to trap you. Trap in the sense, why do I keep trap? You know, why do I do this? Not that I get some sadistic pleasure here, but you guys, from my experience, I know most of the errors happen at this stage only in the sense last stage, calculation stage, not reading the question properly, and overconfidence, yep, and not checking your answer again and tempted to, and especially in MCQ based exams, what happens is, you are tempted to bubble that round circle over there. Temptation is quite high, and you have to learn how to control that temptation as well. And hence, by practice only, it is possible. So hence, every centaur with me or with anyone else, we will try to fall, we make you fall in the trap so that you learn, learn, learn, and eventually come as a winner, okay? So don't get disheartened if you are making such silly mistakes here, but then do please learn and raise your consciousness more and more. Fair enough, so the last leaderboard of today is this, and let's see who was the person who got the first position. So I think Aniket Bhukta retains his first position followed by Aidan Aditya and then Suresh and then I, then Arun Singhal, Vivao Anish, Pamesh and Mahabal. Very good guys, keep it up. Keep the learning intact, congrats, congrats to everyone, but you could not get anywhere closer to 12,000. So that's something also is, the total marks was 12,000, you got around 8,000. So around 66% of marks you have got. So hence, think about it. Okay, very good guys. So let's meet again. By the way, next week we are going to conduct one geography center, maybe on Monday itself. So be ready, right? Geography, first chapter. You have to just read through. Yes, it's on mentee and it will be an open book quiz. So you can keep your book with you, okay? Keep your book with you. 10th grade, first chapter geography, which is going towards NTSC, okay? So hence, yeah, like this only, like this only. It will be like this only. So you will be having the book soft copy, first chapter, whatever it is, check it, okay? So keep the copy, keep the copy of the book with you and you are allowed to see through or go through the books, go through the internet, Google it, whichever way. And let's see if you can solve geography problems then, okay? On Monday. Bye, take care, enjoy.