 What we have to do today is we have to do geometrical patterns and in in geometrical patterns as you can see the first question the first question tells me that account the number of squares in in the given figure now how do we solve this kind of question So basic idea about this kind of question is that we have to identify number of geometrical patterns like squares in the given combined square so a bigger number would be given to you and sorry a bigger figure would be given to you and what we will do is in that particular big figure we will identify we will identify how many squares are there how many rectangles are there depending on what question is telling us to do so in this particular case what happens is that let me identify a small question for you ok I give you question number I give you question number 4 without telling anything try to solve question number 4 and try to give me answer for question number 4 ok if you are saying b if you are saying d if you are saying some other answer the problem is nobody asks me how to solve this kind of questions and I also didn't tell it now I am asking a few questions I would like you to give me an answer about that how did you count it how many of you counted the number of triangles and squares without naming the vertices here there are many vertices how many of you just type this answer in the chat box how many of you tried to count out the number of triangles and the number of squares without writing the names of the vertices and by writing the names I mean a b c d e f g h likewise whoever has written I did like that has also given me I don't know the name because the name has been given as irrational good if you have done by naming the vertices that's that's a right option to do it if you have not named the vertices that's not a right version to do it so try to understand how I will solve the question so to solve this question what I will do is I will start marking suppose this is a this is b this is c this is d this is e this is f this is g this is h so to do this kind of question you always have to mark the vertices after marking the I have not marked three vertices here so so this g h this is i this is j this is k and this is l so I have marked several vertices over here now you have to calculate how many triangles are there and how many squares are there so if I calculate triangles calculate the number of triangles starting with a so you find that adj is a triangle you also find that you also find that adf is a triangle so you write like this adj you write adf similarly one triangle here first calculate the smaller triangle so one two three four five six seven eight nine so you can write like this what you will you will do is you will write the names of the smaller triangles you will have better idea now how many triangles you are leaving here you are leaving one two three so twelve triangles you are leaving here and then you will go for the bigger triangle so what is the bigger triangle adf is a bigger triangle now if you look at this square the square is something like this so I have to calculate how many triangles sorry circles are there so what I have named this I have named this di e I have named this j f l and I have named this g k h now how many triangles are there so if I start writing the names of the triangle the number of triangles would be if I look at this half in this half the number of triangles would be one two three four then a bigger triangle this five now if I look at this half one two three four so eight a bigger triangle this so ten five here five there ten then this triangle will be taken so eleven this triangle would be taken so twelve and this is f so what I am writing here name would be j g f is one triangle g f k is another triangle f k h is another triangle and f l h is another triangle then this bigger triangle which is g f h similarly on the other side I have let me write here let me write here this is d j d f then d i f then i f e then f e l and then I have this bigger triangle which is d f e so five here five here ten then I have this triangle for this triangle I am writing here d f g then I have this triangle which is e f h so how many triangles here I have twelve triangles here and is there any other triangle which I am missing out so likewise how many triangles I have here so if I include this I have written here a d z a d f now I will have triangle from this side I will have triangle l e c and I will have triangle the bigger triangle here which will be e f c what I am trying to do is what I am trying to show you over here is that how do you count the triangles and to count the triangles what I do is first I find out the square the procedure is first I have taken the square in that square I have tried to identify how many different triangles are there I got different triangles as twelve here five here five here and two here so I got different triangles as twelve years now what I do is I will try to find out triangles with the help of different lines of a square so one triangle is here so till now I have identified twelve here one here and the second one is here and the third one with a and this is this is the third one so three here then what I do one here second here and third here so three here then this triangle is one this triangle is one and then the complete triangle is one so nine here twelve plus nine is twenty eight now what I will do is I will in this particular square I did not take four triangles the four triangles would be one which I write here G B D plus then what you do is you take from this side which is D E F then what you do is so twelve plus nine twenty one twenty three I have identified the triangle is getting bifurcated so this particular triangle itself remains a triangle so that becomes nearly twenty five now what happens is in this particular square let me it's just muddled up now let me just clear the idea for you because everything is getting muddled up so what happens is first I draw this square in this square I found out twelve particular triangles then from the triangle itself there would be two components which will be suppose I name this I name this B and I name this O I name this let me name it C B E G H K F J so what happens is twelve twelve simple triangles would be as I told you this this side this side this side what I have already told you so there would be twelve simple triangles now from one two three four five six seven eight nine ten eleven twelve so twelve simple triangles like this now what happens is if I start taking two components of the triangle so if I take two components of the triangle one component here two two components here three component here four component here so that becomes for one component here one component here one component here that becomes three seven now what happens is one component here one component here that becomes nine so twelve plus nine is how much twenty one now triangles which are made of four of four components. So four components is IBD, one component here. The second one is BDG, the third component is DGI, fourth component is GIB. So GIB, then fifth component is ACO, the sixth component is COE, so six components from another place. So 12 plus 9 is 21, 21 plus 6 is 27 and one bigger scale which is ACE, so one scale here. So you get how much? You get 27 plus 1, 28 triangles. Now let me calculate squares for you. If you are not understanding, let me know. I repeat it once again for you. Don't worry if you are not getting these kind of problems. If possible, we will do only one type of question which is geometrical patterns because this is very very important. You will get at least two questions from here. So if you are not getting it, please let me know. Suppose this is B, this is K, this is D, this is J, this is O, this is F, this is I, this is H, this is J. So what I get is two components, squares having two components are B, K, O, J, then K, O, B, F, this is half-half. So this is one, this is two, this is three, this is four. So J, O, I, H, and F, O, H, G. So these are the four squares that you have in the half components. The other square which is difficult to find out over here is that square is try to understand. If you look at here, if I remove everything here, one square is B, D, G, I which is visible here. So most of the people will write five squares. The one square which is difficult to find out over here is, you look at this, this if I mark as C, this as B, this as D, and this as O, this particular square is very difficult to find it out over here. Look at what I am doing on the screen and where I am finding out the square. So this particular square C, D, O, B makes my sixth square. So the answer would be D over here. So this is how we have to solve the question. I will give one more question and let's do the first question now. All of you, let's do the first question now. If you are not understanding, let me know. I will repeat once again. See, I was not looking at the chat. It doesn't matter whether it was 30. How do you count 30? Okay, let me solve this first question for you because most of you have given me the answer. Now let me mark it. So this is A, this is B, this is C, this is D, this is E, this is F, G, H, I, J, this is K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y. Suppose something like this. Now I have marked everything. Now the first thing that I always do is my approach is that if I start counting the components, most of the time I forget to add the bigger square. So my first thing to do is I write the bigger square at the first. So I write A, E, Y, U as the first square so that I don't forget about it. Second approach is then going into component. If I get into component 1, 2, 3, component means see this particular square has been separated into three or separated into different numbers of a square by various lines. So try to understand the square is formed by separation of one line. What do I mean by separation of one line? So this line BG here and FG here. Similarly, with BG you have one more separation which is CH. If you move to CH, there is one more separation which is DI. If you move to DI, there is one more separation into EJ. So this is in column direction or in vertical direction. In horizontal direction, if you look at AB, the next separation is FG. If you move to FG, the next separation is KL and likewise. So this is called one component. So by one component, I am getting 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16. So I am not writing names of all because I started writing names of everything in the last question and it became muddled up all the way. So one component, you have 16 squares. One component means it is made by lines which are adjacent to each other. So you look AB, FG are adjacent to each other. Now I will remove this adjacent line both vertically and horizontally. So how many squares I am getting? Now I will write the names. So third, made with four components. So why four components? 1, 2, 3, 4. These four components give me one particular square. So what is the name? ACMK is first one. Then what I do? This particular line I shift here. I will not take this adjacent one. I take this one. So the second one is BDNL. I will not take this one. I will go here which is C E O M. So three here, you should understand that three lines together. One, two, two lines are fixed and one line from this side, one, two, three, are giving me three particular squares. So what I do? I will keep this line as it is. Instead of this line, now I will take this line, then I will take this line. So how many squares we will have? I will have three into three nine squares I will have. If you want me to write names of all nine squares, if you are not understanding, please write it in the chat box. I'll write it. Then I will take squares with nine components. So you should understand that one component, two component, nine component, how this is going? This is one square, sorry, four components. So this is two square. This is three square. So what is happening? Nine component means one, two, three, four, five, six, seven, eight, nine. So how many squares will I get? I will get four squares like this. So nine component, this I can write it for you. It is ADSP. This is the first one. The second one is BE. What is this? This is T. So BETP is the second one. Now let me go here. So you will have F, I, X, U and the fourth one. I'm writing here it would be GJYV. So four here. So 16 here, nine here, four here. So 16 plus nine plus four. So with one component I have taken, with four components I have taken, with nine components I have taken. After nine, one square, two square, three square, what is left out? Four square. Four square is equal to 16, which I'm getting here. So that's how you come to know that whether you are left out with any square or not. So 16 plus nine plus four plus one, how much it is, it comes out to be 30. So how much you get? You get 30. So 30 is the right answer. Now let me go to another question. So solve question number two. Dan, you are giving me nine, few are giving me, Shethish is giving me 9, 9, 9, 9, 7, 9, 11 different answers. Okay, let me wait for this. Let me wait for this. I give you two more minutes to answer. Okay, still the same story, 9, 11, 9, 11 going on. Let me solve this question for you. So what will I do? I'll start marking it. So this is A, this is B, this is C, this is D, this is E, this is F, this is G, this is H. I don't think I have left any particular edge for you. Now what do I have to calculate? Quadrilaterals. Quadrilaterals require how many different edges or how many different sides? Four. So I have to calculate something where four sides are there. So try to understand how I do it. Try always start from marking those quadrilaterals, which are very, very obvious in nature. So you look at here, there is a trapezium here, almost looks like a trapezium, A, B, C, D. So the first and the most obvious one which looks in front of me is A, B, C, D. Obviously A, B, C, D, opposite to it would be A, D, E, F. This was the most obvious one which I marked, which I marked. Now look at here, there is a rectangle made over here which is looking very, very obvious, which is A, B, D, E. So I have written A, B, D, E. Now if I have written A, B, D, E, why not instead of going from D to E, there is a direct line going from D to F. So it means that it makes the quadrilateral. So this was my third one. The fourth one is A, B, D remain same, but from D there are two lines. So D I have written, now I write D, F. Now if I make, if I saw A, B, D, F, you come, you know that this D, F has two parts. So if you start from D, you can go till F. If you start from D, you can stop at H also. So instead of writing A, B, D, F, I can also write A, B, D, H. So this is the fifth one. The exact story from the other side, from the different side. So I will write C, D, H, A. So sixth one would be C, D, H, A. Instead of writing C, D, H, A, I can write C, D. Instead of stopping at H, I can go till F. I can write it C, D, F, A. Now from D there are two lines. So D, F and D, E, I have only taken D, F. So I will write eighth one as C, D, E, A. This is my eighth one. Now let me stop from, I started from A, then B was included. Then I went to C. Let me start from D. So if I start from D, I have ninth one as D, E, A, G. So D, E, A, G, tenth one as D, E, A, D, E, A, C, D, E, A, C. So D, E, A, C. Is D, E, A, C included anywhere? No. So these are the three things. The next one can be D, E or sorry, the next one can be, next one can be D, E, A, F which I have written over here. So how many I have written? I have written 10. Eleventh one can be D, H, A, G. So D, H, A, G, the middle one. So there are how many quadrilaterals I have added? I have added 11 quadrilaterals. This is the answer for me. Now solve question number three. Was there something repeated? I am looking at here. What was repeated? You are saying D, E, A, C was repeated. Okay. I look at it at the end of the class. Don't worry. How many of you are done with this? Let me check. Somebody is saying C, somebody is saying D, somebody is, most of you are saying C, D. Okay. Most of you are saying C, D. So C is the right answer here. So let me solve this question for you. And by marking different things, this is A, this is B. Let me start marking it from somewhere else. Let me mark it with a different color altogether. So that A, B, C, D, E, F. Now what do I do? G, H, I, J, K, L, then these ones. M, N, O, P. So marking is done. Now again, in this kind of question, the concept of components come. So if I talk about components, I will start with most obvious one. And the most obvious ones are generally made with the lines which are adjacent to each other. So one, two, three, one, two, three. So how many of them? Two on the, one on the top, one on the bottom. So how much you get? Two here. The top one is, I'm just, I'm not writing, but I'm naming it B, C, D and A, E, F. These are the two one, these are the two. So two I have written here. Now 16 inside. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16. So two plus 16 with one component, I'm getting 18 different. So how many components? One component or this is simplest triangles. So how much do I get? I get 18. Now, if I take any one of them, now concept of triangle is gone in top and bottom. I'm not making anything from this top and bottom anymore. So the concept of triangle will come only in, only in this small square. So let me make one square for you and let me check how many different triangles do I make. So I'm naming it once again B, G, H, A and M. So how many triangles do I have here? Try to understand. I will, I have already made these small triangles. So I will not take adjacent lines. You look at here, I will take the first one that I write is A, B, G. This is the first one. The second one that I write is, I have started from this particular vertex. I'll keep on shifting one vertex anti-clockwise. So A, B, G, now I'm starting here. B, G, H, this is a different triangle. So B also covered. Let me go to G. So G, H, A is a different triangle and let me go to fourth. H, A, B is altogether a different triangle. So how many of them I'm getting here? I'm getting four different triangles and I have four such squares. So this is square number one then two then or rectangle number one, two, three, four. So in first rectangle, I got four different triangles like this. If I have four different rectangles, so four into four, 16 I'll get. So 18 simplest triangle I got, 16 I got with the help of two components. Two components means one plus two two components added. So I'm adding this component and this component. Here I'm adding this component and this component. Now can I get, by adding three components, one, two, three, you know, you cannot get different triangles but by adding four components you can get it. So you look at here from, I'm making it here. It's like this. So it's something like this and what is this? This is A, this is B, this is G, H, this is I, J and if you look at this, this is one particular this. So I'm adding one, two, three, four, four components here and I'm getting A, G, J as one of my triangles and one is exactly opposite to it. So you look at here A, G, J is one such triangle. So one, two and three triangles upwards and three triangles downwards. So how much I'm getting here? Six. So 18 plus 16 is 34. So 18 plus 16 plus 6 is equal to how much? It is 40. So I'm getting 40 triangles over here and let me go to squares. Now how many squares? So try to understand, let me read the question. Okay. So to do this question, we have to assume that these, these lengths are same. So one square is this, this is B, this is G, this is H, this is A. So B, G, H, A is one triangle and I have four, sorry, one square. So I have into four, so I have four such squares. Where are other squares? So other squares are, you look at here, this I named as M, this I named as H, this is N. So other squares are here, M, G, H and N. This is A, this is H. So M, G, H, N, then one square is here, this is the second square and this is the third square. So four squares, I have counted this vertically and four squares like this. So four plus three, how many squares here? Seven squares. So answer is C, which is 40 triangles and seven squares. So question number four, we have already done. Now we'll solve question number five or we'll not solve question number five. We'll solve question number nine now. Okay. I've started getting answers of this question. Most of you, when you're writing answer, please write the question number also so that I can identify which question you are answering. So people are saying B, few people are saying D, B, D, everything is going on over here. What do I have to find out? I have to find out triangles and parallelograms. Okay, let me solve this question for you. A lot of time. Let me mark it. So this is A, B, C, D, E, F, G, then this is H, I, J, K, then this is L, this is M, this is N, and this is O. So I hope I have marked all the yes, I have marked everything. Nothing is left out. So if I have to identify triangles, I will always start with the simplest one. How many simplest triangles you can find it out? So simplest triangles would be K, J, N, and K, J, O. So K, J, N, let me write here because the maximum number is 21, so should not go beyond, we can write it, K, J, O. Then where do you find the other one? The other one is C, N, B, these are the ones difficult to identify. So C, N, B, and then you have on the other side O, E, F. So O, E, F. Then you have here J, I, L, and then you have J, I, M. And after J, I, L, and J, I, M, you have smaller ones, B, L, A, similar ones as this C, N, B, N, O, E, F, B, L, A, and M, F, G. So M, F, G. So how many of them I got? I got eight of them. So this was triangle form single component. From two components, how many of them I am getting? So from two components, I will have one component here, C, D, J, this vertical one, so C, D, J. And on the other side, I have E, D, J. Similarly, N, K, O, joining these two components. So N, K, O, then I have here J, L, M. Then I have the below one, J, A, H. So as I write J, H, you could have identified the other part also, which is J, H, G. So how many of them I have? Six components I have here. Then, so with one component I had with two components I have, can I do it with three components? So by three components, I mean one, then two, and then three. So B, K, I looks out to be one particular triangle. So by three components, I have B, K, I. Then I have K, I, F. Then I have from the other side. So from here, so I can have triangles such as C, J, A from this side. So C, J, A. And on the other side, I have J, E, G. So three components, J, E, G. So four of them. With four components, can I have one? So if you look at the bigger one, so one, I have never counted this. One, two, three, four. So with four components, I have C, D, E. And I have here A, J, G. So A, J, G. So four here and two here. 8 plus 6, 14, 14 plus 4, 18, 18 plus 2, 20. And the biggest triangle that I never took was one, two, three, four, five, six. With six components, I have B, K, F. So this is one of them. So maximum how much I'm getting here? I'm not ticking here. I'm getting 21. I have not counted the parallelogram. So 21 is the right number of triangles. I hope you all understood it. Now I'll have to mark it once again because I have made everything A, B, C, D, E, F, G, H, I, J, K, L, M, N, O. Now for parallelograms, what I do? For parallelograms, one component will never give me parallelograms, so two components. So let me start from here. You look at here one, two, three, four. So C, D, K, B is giving me one parallelogram. Similarly on the other side, D, K, O, E is giving me, no, not D, D, K, E, F is giving me once again. Just D, K, F, E is giving me. Then where am I getting? I'm getting B, I, H, A. So I'm getting here B, I, H, A. And similarly I, F, H, G. So I'm getting I, F, G, H or H, G, whatever you say. So how many of them I'm getting it? Four. Similarly I can get it with B, K, J, A with three components, one, two, three. So on the other side, so B, K, J, A is one. Similarly K, F, J, G is the other one. Similarly C, J, I, B is the third one. C, J, I, B is the third one. And the fourth one would be J, E, F, I. So how many of them I'm getting here? Four one. So these are with three components. With four components, how many of them I'm getting? So with four components, one, two, so I will get B, F, one, two, three, four. So I will get B, F, G, A. I will only get one with four components. Now there are other parallelograms also which are they, these parallelograms are, if you look at it very carefully, the parallelograms are like this. This line, this line, this line, and this line. So how many components? There are one, two, three, four, five, five components. So with five components I am getting C, D, J, A on one side. So on other side also I'll get, which will be D, E, G, J. Then if you start from here, you will get C, J, H, A, C, J, H, A and J, E, G, H. So how many of them you are getting? Four you are getting. And then you have two more left out, which is C, E, F, B. So, sorry, you have four more, two more left out, which is C, E, F, B. How many components here? One, two, three, four, five, six, with six components. So you have with six components one, one of them here. And then you have C, E, G, A. So C, E, G, A, which has one, two, three, four, five, six, seven, eight, nine, ten, ten components. So one of them here. So how many of them? Four, four, eight. And have I left anything else? So I have left N, J, L, B. Okay, I have left this, these two I have left here. So one and two here. So N, J, L, B is one of them. And then N, O, M, I is one of them. So two more here. So these are the direct ones which I left here. So six, two plus four plus four, four plus four plus one, then four plus four, then one plus one. How many of them I get? I get 17. So 21 and 17, this is the right answer. Okay, so we have done enough questions like this. I'll post this sheet on the WhatsApp group. You can solve questions on this basis. Now let me move to another particular topic which is seating arrangements. So this is the first question. One thing that you need to make clear in your mind is in seating arrangement, what happens is you have to look at the direction in which the objects are facing. Why? Because always it would be written that A is sitting right to B, B is sitting left of C. How does the direction in which the objects are facing matters is like this. Suppose if they are facing on north side, so if I say that A is sitting left of B, I'll first mark B and if the person is facing this side, left would be this side and right would be this side. So A has to go somewhere here. But on the very opposite, if somebody is facing south, so in that particular case, what happens is I say that A is sitting left of B and somebody is facing this side, left becomes this side. So A would be sitting here. So you always have to look at the case where the direction of, I mean direction in which objects are facing are identified by you. Always remember if no direction is being talked about in the question, like if the question doesn't tell that in which direction objects are facing, the default direction is north direction. If in the question you are not able to find out or the question does not specify explicitly that which direction the objects are facing and again repeating, you have to assume that the objects are facing north direction. But if in any question it has been given to you that the objects are facing east direction, then you have to apply that particular concept. So if somebody is facing east, this is my east. So this becomes my left and this becomes my right. So if B is sitting here, A would be somewhere here and likewise. So that's how you have to focus on seating arrangement questions. Now if there is any extra thing, I'll help you out in the question. So this is the first question of seating arrangement. First read the question and then try to solve the questions. Oh, let me solve this question for you. Enough time. So what happens is, how many people are there? A, B, C, D, E, F, G, H are sitting in two lines facing each other. Okay. Let me make two lines facing each other. These are the two lines in which eight people are sitting together. Each line has four persons. A is sitting between G and F and facing towards north. So this side is facing towards north and this side is facing towards south. So what has been told to me? So it has been written in the question itself that A is sitting between G and F facing towards north, opposite to C. So who is sitting opposite or exactly facing C is A option would be D option. So A would be here somewhere sitting between G and F. So two options A, G and F on this side or G and F on this side. Now if G and F has been given, don't only take that G can be on left hand side and F can be on right hand side. It has not been given clearly. That's why I'm making two different conditions. On the other side, look at here opposite to C. Here is C and there are two conditions here B and D or D and B. Now try to understand H is on the right hand side of D. So if I make three people sit like this, H would be either here or H would be here. So if I keep H here and I keep D here, D becomes left of H. H is just right of once again. I'm just getting one second. H is not here. H is somewhere here. So H is just on the right of G. So H would be here. So I'm just writing it down. So it would be like this once again. This I misread it. So if H is on the right of G, H would be here. So my final answer would be on this side, it will be F, A, G, H. This is something like this and C is sitting between D and B. Here, you don't know whether B is sitting on the right of D or D is sitting on the right of B. So answer would be B or D. You don't know here. Option would be D option here. Now the next one is in which pair of the following second person is sitting at the left of the first person. So if I take F, A, A is on the right of F. That's a wrong answer. G, A is the right answer because on the left of G, this G is the right answer. Now let me go to question number four and let me solve it for you. So question number four tells me who is facing north. So you know that in facing north, C is not there, B is not there, E is not there. Only H is facing north because G, F facing north if you look at here, F, A, G, H are facing north. Only one option is there, which is H and question number five is in which of the following pairs C. So if you look at here, if you identify D on the side, there should be one option here, none of these because what he is doing in this question is that he is taking the question as it is. If he is saying C is sitting between D and G, he is assuming D to be here and B to be here, which is not the right case, even if it has been written in the solution of this and as B is sitting here, it has been told that B is sitting opposite to G. But from my experience, this is absolutely wrong. You have to take two cases. So you always have to take two cases. If none of these is not there as in this case, then you can assume that D is here and B is here. So if none of these option is not here, then I am assuming that D is here and B is here. So B and G would be opposite. Then in second question, you will have to say that D is sitting on the right of C, but this is not a right logic to do it. You always have to make two different scenarios. So these are the questions. Now, similarly, you can solve question number six. That's not a problem. Once it has been identified that what needs to be done, you can do question number two. Now solve this question. Question number seven to 11. So okay, I am getting a lot of answers. Seven, eight, nine. I am getting here. Okay. Okay. So a lot of people have given me answers for seven, eight, nine. Now let me solve question number seven, eight, nine for you. Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Vindu. Mary is to the right of Rani. Rita is between Rani and Mary. Very, very simple question. No information has been given in which direction they have been facing. So I will assume that they are facing north. Seema is to the left of Rani. So if this is Rani, this is left, this is right. So I will write here Rani. Then Seema would be on her left and to the right of Vindu. So here is Vindu. Rita is between Rani and Mary. So here is Rita and here is Mary. Because I cannot put Rita somewhere here because already Seema and other other. So who is sitting immediate to the right of Rita, immediate to the right of Rita, Mary is sitting. Question eight, who is second from the left? So from the left is this side. So Seema is second from the left. So option is D. Now question number nine, what's the answer? Question number nine tells me who is in the middle of the photograph. Rani is in the middle of the photograph. Who is second from the right? Rita is second from the right. Question number 11 is altogether a different question. So you'll have to solve it. Solve question number 11 now. What's the answer of question number 11? Most of you are saying question number 11, the answer is B. Let me check what is question number 11. Yes, the answer is B. As most of you are getting it, let me not waste time by solving these questions. Solve this question. This is the last question. After this question, we will break for the day. Done. Only few people have replied. So take some two, three more minutes. Solve question number 12, 13, both. Okay, two more minutes. I'm not getting a lot of answers like I got in the other questions. Question number 13, 12, people are giving varied answer. Somebody is saying D, B, C. Every answer is there. Question number 13, I have only got two, three, four, five answers. 13, A. Okay, let me solve this question for you. Anyway, what has been told in the question that E F G H I J K N, it means that eight people are seated around a square table two on each side. So here is the square table E F G H I J K. So it's not actually in this order. So there are three lady member, they are not seated next to each other. Okay, J is between L and F. G is between I and F. H is a lady member. It's second to the left of J. F is a male member, which is seated opposite to E, a lady member. So how many of them are lady member? I have identified H is a lady member. I have also identified E is a lady member. And there is a lady member sitting between F and I. So that I'll get after putting out the sitting arrangement. Now try to understand it J is sitting between L and F. So all the sides are same. Now on any side, these two positions are different. So try to understand I make different possibilities. So if J is sitting here, then L can be here, F can be here. If J is sitting here, then L can be here and F can be here. But you can say that if J is sitting between L and F, why can't I interchange the places of L and F? So for that, I'll have to make two other possibilities and I'm making those two other possibilities. So for this first case, when J is sitting here, F can be here and L can be here. And for this, I'm making a possibility here. So which is like this that when J is sitting here, L can be here and F can be here. Now I have four different cases. In all four cases, I try to identify which one is suitable for me and which one is not suitable for me. So G is between I and F. So G is between I and F. So in this case, G sits here, I is here. In this case, G sits here, I is here. And in this case, G sits here, I is here. In this case, just G sits here and I is here. Now what has been told, H is a lady member which is opposite to J. Now in this particular case, already opposite to J, I is sitting. So this particular case is not accepted to me. What about this case? In this particular case also, J is opposite to J, I is sitting. So this particular case is also not accepted to me. So I have only two cases left out, this and this, which tells me that if J is here, so what is opposite to J? Let me read it once more. H is a, no, did I read something wrong? H is a lady member which is sitting second to the left of J. So I perhaps read the wrong thing. One second guys, question reading mistake. In front of you, I am making this mistake. In exam also, you can make this mistake. I mean, I also used to make this. H is a lady member who is sitting second to the left of J. So if J is here, one, two, this case is not possible. This is left. If somebody is facing center, for J, this will be left, sorry, this will be right and this would be left. So this is left. So H is a lady member sitting to the left of J. H can be here. Now for J again, left would be here. So if you look at the second place here, is not accepted. So this is gone. Now H is a lady member. What is left of J is only, there are two places left out. Now how many places are left out? So this case is already rejected. So see in this case, opposite to F, H is sitting. So this is not possible. So I have only one case left out now. So which is E, F, I, J, K is not here. So I will put K here. So now let me find out the answer which among the following are three lady members. So three lady members are two. I have already identified H and E. So the third lady member is sitting between F and I, which is G. So it comes out to be G is third lady member. There is no such option here. So answer would be none of these. So this is my right answer. Now let me go to 13th question. The 13th question tells me about which of the following is true about J. So lady members are now finalized, three lady members H, E, Z. So J is a male member. That is correct. Position of J cannot be determined. That is also wrong. So A is the correct answer that J is a male member. Now question number 14, which of the following, who among the following is seated between E and H? So between E and H, between E and H, K is sitting. So answer would be none of these. See, here cannot be determined is there. I am cutting this and I am writing it none of these. When I will send you the answer, it will be corrected there. So it will be none of these. Question number 16, what's the answer? Question number 16 is how many persons are seated between K and F? So K and F from all three sides, from all two sides, three people are seated. So answer here would be three people. Now try to understand if there would have been a scenario where from this side, two people would have been seated and from this side, three people would have been seated. The answer could have been cannot be determined. I am taking option three here. Why? Because from both the sides, three people are sitting over here. So that is why answer is three. Remember, I am again repeating if from left side and from right side number of people are different. Hence the answer would be cannot be determined in that case. So this is what it is guys for from today's session. I hope you understood everything. If you have any doubt, do get in touch with me. So these sheets would be sent to you by tonight and you can solve it at home with answers. I'll send it to you so that you can do it at your place. So I hope you understood the session and I'm getting doubts only from one or two students. I do believe that most of you who are solving these questions also please don't leave the session now. I am planning a test on Friday, the coming Friday. So I'll publish the paper in class pro or in the group the paper test paper would be given to you and you will have to send me the answers. So one test would be planned this week, coming week on Friday sometime, Friday, Saturday, Sunday before the next class. Your test would be there. I'll let you know the timing. I'll let you know the format in which the test would be done. Mostly it'll be a 50 question test because we have only done three topics or four topics. So please send the answers to me and I'll let you know your answers. This is very important to track your progress in NTSC classes. So that is how it is. So thank you so much for joining the class and I hope you enjoyed the class. I hope everything you could understand. Thank you so much. Thanks for joining the class.