 Okay, good evening everyone. I'll start with the session now. Can you see the screen all of you? Good evening everyone. Can you see the screen now, all of you? Okay, fine, fine. So what we need to do is, today's topic would be to identify geometrical patterns and seating arrangement. Now, can you guys hear me? Is the screen clear now? Hear me? Is the screen clear now? Okay, fine. So what we have to do today is, we have to do geometrical patterns and in geometrical patterns, as you can see the first question, the first question tells me that account the number of squares 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 figure would be given to you and what we will do is, in that particular big figure, 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. Okay, I give you question number, I give you question number four without telling anything. Try to solve question number four and try to give me answer for question number four. Okay, if you are saying B, if you are saying D, if you are saying some other answer, the problem is nobody asked 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. Whosoever 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 the right option to do it. If you have not named the vertices, that's not the 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, I am solving question number 4. 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, I have not marked 3 vertices here. 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 ADF is a triangle. So, you write like this ADJ, you write ADF. Similarly, one triangle here, first calculate the smaller triangle. So, 1, 2, 3, 4, 5, 6, 7, 8, 9. So, you can write like this, what 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 1, 2, 3, so 12 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, so if I look at this square, inside the square, how many triangles are there? It's something like this. Let me make a square for you. The square is something like this. So, I have to calculate how many circles are there. So, what I have named this, I have named this DIE, I have named this JFL and I have named this GKH. 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 1, 2, 3, 4, then a bigger triangle this, 5. Now, if I look at this half, 1, 2, 3, 4, so 8, a bigger triangle this, so 10, 5 here, 5 there, 10, then this triangle would be taken, so 11, this triangle would be taken, so 12 and this is F. So, what I am writing here, name would be JGF is one triangle, GFK is another triangle, FKH is another triangle and FLH is another triangle, then this bigger triangle which is GFH. Similarly, on the other side, I have, let me write here, let me write here, this is DJDF, then DIF, then IFE, then FEL and then I have this bigger triangle which is DFE, so 5 here, 5 here, 10, then I have this triangle, so this triangle I am writing here, DFG, then I have this triangle which is EFH. So, how many triangles here? I have 12 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 ADZADF, now I will have triangle from this side, I will have triangle LEC and I will have triangle, the bigger triangle here which will be EFC. 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 12 here, 5 here, 5 here and 2 here, so I got different triangles as 12 here, now what I will do is, I will try to find out triangles with the help of different lines of the square, so one triangle is here, So, till now I have identified 12 here, one here and the second one is here and the third one with A and this is the third one, so 3 here, then what I will do, 1 here, second here and third here, so 3 here, then this triangle is 1, this triangle is 1 and then the complete triangle is 1, so 9 here, 12 plus 9 is 28. Now what I will do is, I will, in this particular square, I did not take 4 triangles, the 4 triangles would be 1, which I write here GBD plus, then what you do is, you take from this side which is DEF, then what you do is, so 12 plus 9, 21, 23 I have identified, the triangle is getting bifurcated, so this particular triangle itself remains a triangle, so that becomes nearly 25. 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 12 particular triangles, then from the triangle itself there would be 2 components, which will be, suppose I name this I, I name this B and I name this O, I name this, let me name it ACBEGHKFJ, so what happens is, 12 simple triangles would be, as I told you, this side, this side, this side, what I have already told you, so there would be 12 simple triangles, now from 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, so 12 simple triangles like this, now what happens is, if I start taking 2 components of the triangle, so if I take 2 components of the triangle, 1 component here, 2 component here, 3 component here, 4 component here, so that becomes 4, 1 component here, 1 component here, 1 component here, that becomes 3, 7. Now what happens is, 1 component here, 1 component here, that becomes 9, so 12 plus 9 is how much, 21. Now triangles which are made of 4 components, so 4 components is IBD1 component here, the 2nd one is BDG, the 3rd component is DGI, 4th component is GIB, so GIB, then 5th component is ACO, the 6th component is COE, so 6 components from another place, so 12 plus 9 is 21, 21 plus 6 is 27, and 1 bigger scale which is ACE, so 1 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 will 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 2 questions from here. 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, 2 components, squares having 2 components are B, K, O, J, then K, O, B, F, this is half half, so this is 1, this is 2, this is 3, this is 4, so J, O, I, H, and F, O, H, G, so these are the 4 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, GI which is visible here, so most of the people will write 5 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 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 3 or separated into different number 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 muzzled 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 4 components, so why 4 components, 1, 2, 3, 4, these 4 components gives 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 will 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 3 here, you should understand that 3 lines together, 1, 2, 2 lines are fixed and 1 line from this side, 1, 2, 3 are giving me 3 particular squares, so what I will 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 3 into 3, 9 squares I will have, if you want me to write names of all 9 squares, if you are not understanding please write it in the chat box, I will write it, then I will take squares with 9 components, so you should understand that 1 component, 2 component, 9 component, how this is going, this is 1 square, sorry 4 components, so this is 2 square, this is 3 square, so what is happening, 9 component means 1, 2, 3, 4, 5, 6, 7, 8, 9, so how many squares will I get, I will get 4 squares like this, so 9 component, this I can write it for you, it is A D S P, this is the first one, the second one is B E, what is this, this is T, so B E T P is the second one, now let me go here, so you will have F I X U and the fourth one I am writing here, it would be G J Y V, so 4 here, so 16 here, 9 here, 4 here, so 16 plus 9 plus 4, so with 1 component I have taken, with 4 component I have taken, with 9 components I have taken, after 9, 1 square, 2 square, 3 square, what is left out, 4 square, 4 square is equal to 16 which I am getting here, so that is how you come to know that whether you are left out with any square or not, so 16 plus 9 plus 4 plus 1, 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 2, Dan you are giving me 9, few are giving me, Siddhas is giving me 9, 9, 9, 9, 7, 9, 11, different answers, let me wait for this, let me wait for this, I give you 2 more minutes to answer, ok still the same story, 9, 11, 9, 11 going on, let me solve this question for you, so what will I do, I will 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, 4, so I have to calculate something where 4 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, that 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 remains 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 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, 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, 11th 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 you. 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 CD, okay, most of you are saying CD, 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 colour all together, 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, 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 1, 2, 3, 1, 2, 3, so how many of them, 1 on the top, 1 on the bottom, so how much you get, 2 here, the top one is, I am not writing but I am naming it B, C, D, and A, E, F, these are the 2, so 2 I have written here, now 16 inside, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16. So 2 plus 16 with one component I am 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 am not making anything from this top and bottom anymore. So the concept of triangle will come 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 am naming it once again B, G, H, A, and M, so how many triangles do I have here, try to understand, I have already made this small triangle, 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 will keep on shifting one vertex anticlockwise, so ABG now I am 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, AB is altogether a different triangle, so how many of them I am getting here, I am 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 of four into four, 16 I will 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 am adding this component and this component, here I am 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 am 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, so I am adding one, two, three, four, four components here and I am 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 am 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 am 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 this lens 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 will solve question number five, we will not solve question number five, we will solve question number nine now, Ok I have started getting answers of this question, most of you when you are 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, Ok let me solve this question for you, a lot of time, let me mark it, 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 and O, E, F, B, L, A and M, F, G, so M, F, G, so how many of them I got, I got 8 of them, so this was triangle from single component, from 2 components, how many of them I am getting, so from 2 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 2 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, A, H, you could have identified the other part also, which is J, H, G, so how many of them I have, 6 components I have here, then so with 1 component I had with 2 components I have, can I do it with 3 components, so by 3 components I mean 1, then 2 and then 3, so B, K, I looks out to be one particular triangle, so by 3 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 3 components, J, E, G, so 4 of them, with 4 components can I have one, so if you look at the bigger one, so 1 I have never counted this, 1, 2, 3, 4, so with 4 components I have C, D, E and I have here A, J, G, so A, J, G, so 4 here and 2 here, so 8 plus 6, 14, 14 plus 4, 18, 18 plus 2, 20 and the biggest triangle that I never took was 1, 2, 3, 4, 5, 6, with 6 components I have B, K, F, so this is one of them, so maximum how much I am getting here, I am not taking here, I am getting 21, I have not counted the parallelogram, so 21 is the right number of triangles, I hope you all understood it, now I will have to mark it once again because I have made everything A, B, C, D, E, F, G, H, I, J, K, L, M and O, now for parallelograms what I do, for parallelograms 1 component will never give me parallelograms, so 2 components, so let me start from here, you look at here 1, 2, 3, 4, so C, D, K, B is giving me 1 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 am getting B, I, H, A, so I am getting here B, I, H, A and similarly I, F, H, G, so I am getting I, F, G, H or H, G, whatever you say, so how many of them I am getting it, 4, similarly I can get it with B, K, J, A with 3 components, 1, 2, 3, so on the other side, so B, K, J, A is 1, 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 am getting here, 4, 1, so these are with 3 components, with 4 components, how many of them I am getting, so with 4 components, 1, 2, so I will get B, F, 1, 2, 3, 4, so I will get B, F, G, A, I will only get 1 with 4 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 1, 2, 3, 4, 5, 5 components, so with 5 components I am getting C, D, J, A on one side, so on other side also I will 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, 4 you are getting and then you have 2 more left out, which is C, E, F, B, so sorry, you have 4 more, 2 more left out which is C, E, F, B, how many components here, 1, 2, 3, 4, 5, 6 with 6 components, so you have with 6 components, 1 of them here and then you have C, E, G, A, so C, E, G, A which has 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10 components, so 1 of them here, so how many of them, 4, 4, 8 and have I left anything else, so I have left N, J, N, B, okay I have left this, these 2 I have left here, so 1 and 2 here, so N, J, L, B is one of them and then N, O, M, I is one of them, so 2 more here, so these are the direct ones which I left here, so 6, 2 plus 4 plus 4, 4 plus 4 plus 1, then 4 plus 4, then 1 plus 1, 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 will 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, so I will 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, 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 will 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, are you done, the first one looks easy, first one I am getting a lot of answer as A, okay a lot of people have not given me the answer, so I will wait for their answer, because there are 2-3 parts of this question, so first one is A, give me answer of the second one, 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 2 lines facing each other, let me make 2 lines facing each other, these are the 2 lines in which 8 people are sitting together, each line has 4 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 2 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 am making 2 different conditions, on the other side look at here opposite to C here is C and there are 2 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 3 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 am just getting once again, H is not here, H is somewhere here, so H is just on the right of G, so H would be here, so I am 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 B, A, sorry 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 FA, A is on the right of F, that's a wrong answer, GA is the right answer because on the left of G, this GA is the right answer, now let me go to question number 4 and let me solve it for you, so question number 4 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 GF facing north if you look at here, FA, G, H are facing north, only one option is there which is H and question number 5 is in which of the following pairs seems, 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 and B, 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, 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 6, that's not a problem, once it has been identified that what needs to be done, you can do question number 2, now solve this question, question number 7 to 11. So I am getting a lot of answers, 7, 8, 9 I am getting here, so a lot of people have given me answers for 7, 8, 9, now let me solve question number 7, 8, 9 for you, 5 girls are sitting on a bench to be photographed, Sema 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, Sema is to the left of Rani, so if this is Rani, this is left, this is right, so I will write here Rani, then Sema 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 Sema and other, so who is sitting immediate to the right of Rita, immediate to the right of Rita, Mary is sitting, question 8, who is second from the left, so from the left is this side, so Sema is second from the left, so option is D, now question number 9, what's the answer, question number 9 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 will have to solve it, solve question number 11 now, today I will leave by 7.45, what's the answer of question number 11, most of you are saying question number 11 the answer is B, okay 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, okay 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 2-3 more minutes, solve question number 12-13 both, okay 2 more minutes, I am 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, the answer is there, question number 13, I have only got 2-3, 4-5 answers, 13-8, okay let me solve this question for you anyway, what has been told in the question that EFGH IJKN, it means that 8 people are seated around a square table, 2 on each side, so here is the square table F, G, H, I, J, K, so it's not actually in this order, so there are 3 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 will 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 2 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, sorry, once again give me a moment, 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 will have to make 2 other possibilities and I am making those 2 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 am 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 4 different cases, in all 4 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 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, so 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 2 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 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, 1, 2, this case is not possible, this is left, if somebody is facing centre, 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 2 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 1 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 3 lady members, so 3 lady members are 2 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 3 lady members, 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 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 is the answer, question number 16 is how many persons are seated between K and F, so K and F from all 3 sides, from all 2 sides, 3 people are seated, so answer here would be 3 people, now try to understand if there would have been a scenario where from this side 2 people would have been seated and from this side 3 people would have been seated, the answer could have been cannot be determined, I am taking option 3 here, why because from both the sides 3 people are sitting over here, so that is why answer is 3, 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 will send it to you so that you can do it at your place, so I hope you understood the session and I am getting doubts only from 1 or 2 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 will publish the paper in class pro or in the group, the 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 will let you know the timing, I will let you know the format in which the test would be done, mostly it will be a 50 question test because we have only done 3 topics or 4 topics, so please send the answers to me and I will 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