 We will start the session in next two minutes. Good evening, everyone. We'll start the session in the next two minutes. OK, so I've got only 14 people out here, which is still not full strength that we get. So no issue, we'll start the session. So a few people have suggested to me that they did not understand. I'm starting the class. Few people have told me that they have not understood the portions of dates and calendar that I was discussing that day. So I am just revising it for some time. So try to understand the first thing that we need to understand is concept of odd days. So what do you mean by concept of odd days? If any number of days have been given to you, if 200 days has been given to you and somebody is asking you what is the number of odd days in 200 days, so you divide this by seven. Odd days means those days which are not part of any complete week. So it means that to find out odd days, I find out number of complete weeks. And whatever remainder is, that is my odd days. Remender in case of what? In a week, seven days are there. So I divide 200 by seven. It goes two times. This is 14, and this is 60. It goes eight times. This is 56. And four is my remainder. It means that in 200 days, 200 days, I can write as 28 weeks multiplied by seven days plus four days, which is nothing but four days. Four days are those type of days which are not part of any week or any complete week. So number of odd days are equal to four days. So this is the first concept. The second concept that we need to understand is what is a leap year and what is a non-leap year? So a leap year. Leap year has two categories. First, century year and second, non-century years. So a century year has to be divided by 400 to be a leap year. Keep on writing these things. Those who did not understand. And a non-century year has to be divided by four to be a non-leap year. Then I have to be a leap year, I'm sorry. Then non-leap year. So any year which is not divided by four is a non-leap year. Now next concept is number of odd days in a leap year and non-leap year. So in a non-leap year, 365 days are there. I divide it by 7. So I get 52 here. I get 364 here. And I get 1 as remainder. So it means that 52 weeks have been completed. So 52 weeks have been completed. It means that you check the calendar in your mobile or somewhere. First January, whichever day is there, that is considered to be first day of that year or first day of first week of that year. So suppose it starts with Wednesday. If one year, first January starts with Wednesday, it means that first day of the week or first January is Wednesday. So if first day is Wednesday, second day would be Thursday, then Friday, then Saturday, then Sunday, then Monday, then Tuesday. So here the week is complete. So if a week starts with Wednesday, it completes with Tuesday. So this is 7th January, which would be Tuesday. So 8th January, from 8th January, second week would start and that also would start with Wednesday. And 14th January would be Tuesday and likewise. So what will happen? Every week of that year will start with Wednesday and end with Tuesday. So if 52 weeks have been completed, it means that 52nd week will start with Wednesday and it will end with Tuesday. And one day is odd day. So if one day is odd day in that particular case, one day means last day, 31st December would be odd day. It means that 31st December is the only day which is not part of any complete week. So if 31st December is only day which is not part of complete week, it means that 30th December is the day which is last day of completed week. So 30th December would be Tuesday. Then 31st December would be Wednesday. So 1st January would be first day. So that is why I told that if a non-leaf February comes in between, so I'll have for same date, I'll have plus one day. You can understand from this that for a leaf February, it will be plus two days. So this is one rule. Then another rule that you need to take care of is that repetition of ears. So a leaf ear repeats itself after 28 years. Second, I see a lot of people are leaving. Let me tell you, this is only for 10 minutes and I'm gonna teach a lot of new things. So those who are leaving, please have patience. A lot of people have not understood these things. They have written to me. That's why I'm repeating all these things. Now we did that N plus one. Here it repeats itself after six years. N plus two after six years. And N plus three after how many years? It came out to be 18 years, I think, 13 years, I think. Let me check it for you. 2007 was N plus three. So suppose it is Monday, 1st January, eight would be Tuesday, nine would be Thursday, 10 would be Friday, 11 would be Saturday, 12 would be Sunday, 13 would be Tuesday, 14 would be Wednesday, 15 Thursday, 16 Friday, 17 Sunday, 17 years Sunday, and 18, it would be Monday. So it will be 11 years. So six years, six years and 11 years. So this has been done. You need to know only this thing. For months, it has to be only number of odd days you have to complete, sorry, count. And for same day, you have same date, you have to increase it by number of odd days. So like if 15th January is Monday, so 15th February would be what? So which month I'm crossing? In between 15th January and 15th February, last day of January is coming. January is of 31 days, so it will have three odd days. So if it will have three odd days, Monday plus three is equal to Thursday. So 15th February would be Thursday likewise. So solve one question. I'm giving one question. First, June 2019 is Saturday. What would be first September? Not September, let's take it. First January, 2050. So what's the answer? Okay, a lot of people are giving the answer Wednesday. I've got one answer on Saturday. Let's see what happens. I'm giving you one or two more minutes. Okay, if you are giving me Friday, again, if you are giving me Wednesday. Okay, so let me solve it for you. How I'll do it is, first Jan, my process would be like this. First Jan, 2019 is Saturday. So first June, sorry. So first June, 2020, it would be Monday. Why it will be Monday? Because Feb 2020 is coming in between, which is a leap February, leap year, so hence plus two. So 2020 plus 28, because 2020 is a leap year. 2048 would be Monday only. So first June, 2048 is Monday. So first June, 2049 would be Tuesday. Now let me go month by month, I'll have to go. So first July, I'm crossing June, so plus two. So this gives me Thursday. First August, so this gives me plus three, so Sunday. First September, so I'm crossing August 31st month, so plus three, Sunday, Monday, Tuesday, Wednesday, so Wednesday. First October, plus two, so Friday. First November, plus three, Monday. First December, plus two, Wednesday. And first January, Wednesday plus three, so Thursday, Friday, Saturday. So first January would be Saturday, so answer is Saturday. So all of you who gave Wednesday as the answer, removed your answer, I don't know how suddenly you got answer, okay, you all are not in this. First, let me give you some odd date. 18th May, 2019 was Saturday, so I'll tell you this. Suppose first January, 1901 was Monday. What would be, or 1910 was Monday, then what would be? 1920 was Monday, then what would be first or not first? What's the date today? 25th May, so what would be 25th May, 2019? Okay, one answer is Wednesday, Monday, Wednesday, I'm getting two answers, that's it. That's why I changed the date. I'll give random dates for random days. I know a lot of people are checking Google for answers. Monday, Monday, Thursday, Wednesday, Wednesday, good. I wanted these kind of scenario. Now look at here, a lot of time has gone for this question. I'll solve one more question like this and then I'll move to clocks. So, first Jan, 1920, it itself is a leap year, so it is Monday, keep on adding 28 to it. I add 28, one time I get 48, this is 1948. Then I add 28, I get 1976, then I add 28, I get 1994, and then I add 28, I get 2012. So it means that anywhere 28 into four is, how many times I've added 28? 28 into three is once again, have I done any mistake? So I've added one, two, three, four. So 19, 20 plus 28 is 48, 48 plus 28 is 76, 76 plus 28 is, no, this is wrong. 76 plus 28 is not 1994, it is 2004. So here we have a calculation mistake and here we will have a calculation mistake. So this is nothing but 2004 and plus 28 will give me 2032. Now, I have given you a scenario where either you have to go forward or you have to go backward. So 2004, it means that try to understand how I'm doing it. I will go for 2004, 2004, first January is Monday. So first January 2005 would be equal to what? Can anyone tell me? It would be Wednesday, because February 2004 is coming in between. So if it is Wednesday, I know that N plus one year repeats itself after six years. So first January 2011 would be Wednesday. Now I know that 2011 is N plus three kind of year. So it will repeat itself after 11 years. So first January 2022 would also be Wednesday. Now let me come back from there. So first January 2022, this is a very difficult question which I posted. So which will be Wednesday. So first January 2021 would be Tuesday. First January 2020 would be Sunday because February 2020 is coming in between. First January 2020 I have got. I have to come to 25th May. So if you want, you can write first Jan 2019 that would be Wednesday. So I'm sorry, that would be Saturday. And then you can move forward if you have problem with moving backward. So Feb would be Saturday plus three Tuesday. Then March would be because this is non-leap. So this will be Tuesday. April would be plus three. So Tuesday plus three is Friday. Then May would be plus two Sunday. So May first would be Sunday. So May first would be Sunday. Airth would be Sunday. 15th would be Sunday. 22nd would be Sunday. So if 22nd is Sunday, 25th would be Wednesday. Answer is Wednesday. Whosoever is getting Wednesday, that is the right answer. Okay, now let me move to another topic. Let me just check how many questions we have solved. Okay, so now let me teach you clocks. So next, okay, solve this question. This question is very famous. The question is 24 hours. How many times hours hand minutes hand will meet each other? I have not taught you this, but I want you to attempt this. Okay, I'm getting all kinds of answer. Somebody has said two, three, all these are not the answers. I've got only one, two correct answers still now, which is 22. How it is 22? Look at here. I'm writing a statement. Suppose let me make a clock for you first. A clock looks like this. And at 12 o'clock, it is somewhere like this. It is somewhere like this. Yes or no? So this is the scenario of 12 o'clock. So at 12 o'clock, hours hand minutes hand meet each other. Now I'm making a statement. I'm saying that hours hand minutes hand meet each other at every 65 is to five by 11 minutes. Now write it down and let me know. Do you want to know the derivation of it? I don't think you should know the derivation of it. But if you are interested, then I'll show you. Otherwise, because it's derivation is dependent on physics, I mean, relative motion of physics and all these things. So if you want to know, I'll tell you how to do it. Otherwise, if you can remember that hours hand and minutes hand meet each other after every 65 is to five by 11 minutes, that will suffice for you. So let me know, do you want to know the derivation? If you want to know the derivation, I'll do the derivation. Let me know in the comment box. Let somebody know me whether you want it or not. What are you guys doing? Okay, don't comment them. So try to understand. Okay, one person has said yes. Look at here what happens. Try to understand at 12 o'clock, suppose this is like this. This is my minutes hand and this is my hours hand. Now, look at the speed of minutes hand. Minutes hand take travels 360 degrees in one hour. So it means that in one minute, it travels 360 divided by 60, which is six degrees. So minute hand will travel six degrees per minute, speed of minutes hand. Speed of hours hand would be, it travels 360 degrees in 12 hours. So if it travels, so in one hour, it will travel 360 by 12. So that comes out to be 30 degrees. So in one minutes, it will travel 30 by 60, which is equal to half degrees. So speed of hours hand equal to half degree per minute. So it means that I am making a statement, which is speed of minutes hand is greater than speed of hours hand. So you will find that at 12 o'clock, it is something like this. And at one o'clock, it will be something like this. So minute hand will travel complete one round and hours hand will travel only this from 12 to one. Yes or no? Now try to understand, in any clock, 12 numbers are written, one to 12. So between two numbers, between two consecutive numbers, angle would be equal to 360 by 12. So how much it is? 30 degrees. So this is how much? 30 degrees. So try to understand, I'm making one statement. I want, after this statement, I want confirmation from all of you whether you understood or not. I am saying that between 12 o'clock and one o'clock, there, I mean at 12 o'clock, hours hand and minutes hand are meeting each other. But as soon as this minute hand leaves here, means after 12 o'clock and till one o'clock, minute hand would always be ahead of hours hand because speed of minute hand is more than hours hand. I'm again repeating it. At 12 o'clock, this is the condition. Both of them are together. But what will happen? As soon as they start moving ahead from 12 o'clock, as the speed of minute hand is more than hour hand, hour hand will never be able to catch minute hand and in that particular scenario, till one o'clock, they will not be able to meet each other. It means that hour hand will never be able to catch minute hand. So at till one o'clock, I mean, once they have met at 12 o'clock, they'll not meet till one o'clock. So it means that they are not meeting for a period of one hour. Is that clear to all of you? Yes, no. Okay, all of you are saying yes, so I am moving ahead. Okay. Now try to understand. Again, I'll ask again, I'm trying to do something. Now at one o'clock, what is the distance between minute hand and hour hand? At one o'clock, distance between minute hand and hour hand is 30 degrees. I am not counting this distance in terms of radius because I don't know the radius. The only thing that I know is angular displacement between them. So at one o'clock, angular displacement or angular distance, whatever you call, between minute hand, hour hand is 30 degrees. Now try to understand. If minute hand has to catch this hour hand, so what will happen? First minute hand will have to overcome these 30 degrees, which is the initial distance, but it will not catch it up at one o'clock. Look at my statement. I'm making a statement. Minute hand will catch hour hand. T minutes, I'm assuming that. Let's assume that minute hand will catch hour hand. T minutes after one o'clock. So what will happen? Just try to understand. If it is catching hour hand after T minutes after one o'clock, so in T minutes, hour hand will move how much? T minutes, hour hand will move. Try to understand, look at the speed of the hour hand. It is moving half degree per minute. So in T minutes, it will move. In T minutes, it will move P by two degrees. So I'm writing here, this becomes T by two degrees and minute hand is meeting hour hand here. So this is my hour hand and minute hand is coming and meeting over here. So what will happen? Minute hand after one o'clock, it is meeting after T minutes. So in T minutes, minute hand will travel 60 minutes. This 60 minutes should be able to cover this 30 degrees initial distance plus T by two degrees, which has been covered by hour hand in the T minute after one o'clock. So what I'm trying to say is that, that 60, which is the angle traveled by minutes hand after one o'clock should be equal to 30 degrees, which is the initial distance, initial angular distance plus T by two. This T by two is angle traveled by hour hand T minutes after one o'clock. So what I get is, I get is 60 minus T by two is equal to 30 degrees. So 12 T minus T by two is equal to 30 degrees. So 11 T by two is equal to 30 degrees or T comes out to be 60 by 11, which is equal to T comes out to be five is to five by 11 minutes. So five is to five by 11 minutes after one o'clock. After one o'clock, five is to five is to five by 11 minutes are needed. But when did they meet? Did they meet at one o'clock? No, they met at 12 o'clock. So from 12 o'clock to one o'clock, they have not met. They are meeting five is to five by 11 minutes after one o'clock. So after 12 o'clock, they'll meet after 60 minutes from 12 o'clock to one o'clock and five is to five by 11 minutes from 11 o'clock. So it comes out to be 65 is to five by 11 minutes. So that is why I told you that our sand and minutes hand will meet each other after every 65 is to five by 11 minutes. Now, tell me if you understood this thing or not, otherwise I'll explain once more. Okay, so what I'm trying to understand is, sorry, what I'm trying to tell you is that after one o'clock, suppose they meet after T minutes, if they meet after T minutes, so our sand and minutes hand will not stop at one o'clock. If they are meeting after T minutes, it means that our sand will move for T minutes and minutes hand will move after T minutes. So in T minutes, our sand will move how much? In one minute, it is moving half degrees. In T minutes, it will move T by two degrees. So it means that from minute hand, already it is 30 degrees away and it is moving T by two degrees away is more. So this comes out to be 30 plus T by two, which means that if minute hand has to meet it, minute hand will travel 60 degrees. In T minutes, if they are meeting after T minutes, minute hand travels six degrees per minute. So they will travel, minute hand will travel T into 60 degrees in T minutes. So this 60 has to cover up 30 degrees the initial distance plus T by two degrees, which the R hand has traveled after one o'clock. So how much it comes? It comes out to be 60 minus T by two. So it means that 11 by two comes out to be 30. So T comes out to be five is to five by 11 minutes. It means that after one o'clock, it is meeting after five is to five by 11 minutes. So after 12 o'clock, when it will meet, 12 to one is 60 minutes and after one o'clock, five is to five by 11 minutes. So 60 plus five is to five by 11 comes out to be 65 is to five by 11. Hence, R hand and minute hand meet each other after every 65 is to five by 11 minutes. Now you understood? Yes, no. Okay, now you solve the question, R hand and minute hand will meet each other after what time? How many times? Now you solve my first question and give me the answer. Now you tell me the answer 65 is to five by 11 minutes. Give me the answer of the question, how many times R hand and minute hand will meet each other in 24 hours? Okay, so all of you are getting 22. The answer is also 22. Now next formula is angle between R sand and minute sand. So it is theta is equal to write these values, write this formula. What is theta? Theta is angle between R sand and minute sand. H is equal to R's value and M is equal to minute's value. Okay, so now the question is, question is find the angle between R sand and minute sand the angle between R sand and minute sand at 340. Okay, now the question is, look at here. If I put value of H is how much? Value of H is three, value of M is 40. So if I put here 30 into three minus 11 by two into 40, this comes out to be 90 minus 220, which is nothing but minus 130. And if I put this value, this is nothing but 11 by two into 40 minus 30 into three, which is equal to plus 130. So which one to accept minus 130 or plus 130? You can accept anyone. If it is coming out to be negative, ignore negative. So try to understand when exact time is given, the shortcut is when exact time is given. Theta is asked, use any formula if negative sign found, ignore it. Then try to understand, I'm giving you second question. What is the second question? Between four to five, at what time theta would be equal to 90 degrees. Can you please tell me any one of you, can you please tell me once again, can you please tell me what would be the value of H here? Look at here how to solve this kind of question. You guys are not doing it properly. Theta is equal to 30 H minus 11 by two M or 11 by two M minus 30 H. So what is theta? Theta have given as 90. So always remember shortcut is when theta and H value given, here H were between four and five, any time you will say as four o'clock that many minutes. So H value is four here. Theta and H value given, use both formulas. So I'm using here 30 into four minus 11 by two M, 11 by two M is equal to 120 minus 90, which is 30. So M is 60 by 11, which is five is to five by 11. So it would be 90 degree at four o'clock, five is to five by 11 minutes. And if I use this formula, so then 90 is equal to 11 by two M minus 30 into four. So 11 by two M is equal to 90 plus 120, which is equal to 210. So M is four 20 by 11, which is equal to 38 is to two by 11 minutes. So one second, 38 is to 11, 30, 93, 90, 88, 20. So 38 is to two by 11, two by 11 years. So 90 degree angle is formed at two times between four o'clock and five o'clock. One at four o'clock, five is to five by 11 minutes. And second four o'clock, 38 is to two by 11 minutes. Solve another question of this type between five o'clock to six o'clock at what time 80 degrees angle is formed. I've got a few answers, I'm waiting for other answers. So I have to understand, I use both formula. What both formula? So it is theta is equal to 11 by two M minus 30 H or 30 H minus 11 by two M. So I put 80 here, 11 by two M and H here is five, so 30 into five. This is nothing but 150. So 11 by two M is equal to 80 plus 150, which is equal to 230. So M is 460 divided by 11. This was four times and two zero, so which is one, 41, nine by 11. And on this side, I get 80 is equal to 150 minus 11 by two M. So 11 by two M is equal to 70. So M is equal to 140 by 11, so which is equal to, it goes one time and then three zero, so two, so 12, eight by 11. So the timings are five to 12, eight by 11 and five is to 41, nine by 11. Don't convert this into 13 and this into 42. That is a wrong answer. It has to be exactly in the same form, five, 12, eight by 18 and five, 41, nine by 11. Okay, next question. So let me go to the sheet. Solve this question 21. Okay, I'm getting a lot of answer as C 180. Try to understand. Remember this, T minutes are sand, speed is equal to half degrees per minute. So for T minutes, it will be T by two degrees. So nine o'clock to three o'clock, nine o'clock in the morning to three o'clock in the afternoon, it is six hours. So six hours means six into 60, 360 minutes. So how many degrees? Degrees would be equal to T by two, which is 360 by two, that is equal to 180 degrees. So answer is C here. Next question, 24, 25, 26. A lot of people are giving answer 24 C. Okay, so I'm getting a lot of answers. Let me solve it. This question number 25, four adds is same as the last previous question that we solved. So five PM to nine PM, I'm assuming here is four hours and plus quarter past, it means that plus 15 minutes. So four into 60 plus 15 is nothing but 240 plus 15, which is 255 and divided by two groups, me 127.5. So answer here is C, absolutely no doubt about it. Next is in a clock, the angle between hours and minutes hand at five, 10 minutes. So when I say that, I have already said that when theta has to be found out, I will use any formula and if negative comes out, I'll ignore it. So theta is equal to 11 by two M minus 30 H, which is 11 by two into 10 minus 30 into five. So this gives me nothing but 55 minus 150. So this comes out to be minus 95, I'll ignore this. The answer would be here. So next one is, yeah, the director came to the office to attend a meeting at 15 minutes past 12 and he came 25 minutes before his tenure. Who in turn was late by 30 minutes to the meeting? At what time was the meeting supposed to start? So 12 minutes past, so 12, 15 p.m. Director came, Steno came, he came 25 minutes before his Steno. So Steno would have come plus 25 from here. So he could have come at 12, 40 p.m. And he was 30 minutes late, the Steno was 30 minutes late. So it means that meeting was about to start at 12, 10 p.m. So answer over here is C. So that's the answer. You can see what kind of questions are there which are very easy if you know the formula and you can solve all these kind of questions in the examination. Now let me check if there is any other question left out. So I'll question number 13 and 14, two questions and then we'll wrap up this. Okay, 13 C people are saying 14 Bs, few people are saying. One answer is 13 C also, okay, 14 B, 13 C. Question number 13. So in question number 13, what happens is 340. So 11 by 2m minus 30 H is equal to 220 minus 90. So this is the answer, 830, so 30 H minus 11 by 2m. So 30 into 8 minus 11 by 2 into 8, 30. So this is nothing but 240 minus 165, 165 which comes out to be 75 degrees. This is the answer. So you all have got mostly right. So when you go for your exam, remember these things. I'll share the sheets with you. Let me check what is there in another sheet. Okay, so this is easy, please solve it. This is change of sign, solve some, there are eight questions, solve these eight questions, then we will solve question number one and two. There is nothing to be done here, this is board mass. I hope you know board mass. If you don't know board mass, let me know, I'll teach them. And here there is no board mass. Here only D mass has to be done because bracket enough would not be there. So first change the sign and then apply D mass. How many of you have started giving me the wrong answer? One, B, E, C, everything is coming. Okay, so in this question, always remember all four signs are here. Multiplication, division, addition, subtraction. So multiplication sign varies, multiplication means division. So as soon as I see multiplication, I replace it with division. Now division means plus. So I write plus 15. Plus means negative, so I write minus five. And negative means multiplication, so I write two here. And then I solve it. So first I do division, 15 divided by three is five. Plus 15, then I do multiplication minus 10. This comes out to be 20 minus 10, that is equal to 10. First answer is B. Second answer, question number two, answer a lot of you are giving me, E you are giving me, so okay. So here division sign is there, division means plus here. So 20 plus 40, negative signs means division. So 40 divided by four. Multiplication signs means negative, so minus five and plus means multiplication, so six. So 40 divided by four is 10. So 20 plus 10 minus five into six is 30. So this is 30 minus 30 is zero, so two D is answer. So that's the solve question number three and four. Once we are done with this sheet, we will wrap up the session today. Okay, take one more minute and solve it. Four D and three B, that is the answer. Okay, so first one over here is multiplication. Multiplication stand for addition. So 20 plus six, then division stand for subtraction. So six minus six and multiplication stands for addition. So then again I add four. So how much it is? This is nothing but 24, three B is the answer. Here, 12 division stands for where is division? Division means negatives, 10 minus two. Negative, where is negative means multiplication? So two into 15, plus means division three and multiplication means plus, so five. So 10 minus two into 15 divided by three is five, plus five. So this is nothing but 10 minus 10 plus five. So this is 10 minus five, which is equal to five. Answer is five, four D. Question number five, if you solve, there are three more questions. Question number five is, so where is P? P stands for multiplication, so seven into three. Y stands for subtraction, so minus six into five. And there is no X here. So should I assume this to be X for multiplication? I'm assuming this to be X because without that the question will look, let me check. So six plus five. So first bracket needs to be solved, 21 minus six plus five is nothing but 20. So answer is 25, answer is D. Then let me go to question number 678. So this is question number 678. Just solve it quickly so that we can wrap up the session. Question six D, question seven. Seven D, I'm getting eight A or B people are saying. Okay, take one or two minutes of time to solve all of them. I've not got all the answers for question number eight. Okay, question number eight. Okay, most of you have replied question number eight. Question number seven, also people have replied. Question number six, also they have replied. Okay, let me solve these three questions for you. So, so positive means division. So first of all, positive only is there. So nine division three, division means multiplication. So three division four, negative means plus. So plus eight, multiplication means minus. So nine divided by three is three. Three into four plus eight minus two. So this is nothing but 12 plus eight minus two. So 12 plus six is equal to 18. So this is the answer. So D is the answer, question number six. Then question number C plus seven. Plus means multiplication, so five into eight. Negative means division, so eight divided by four. Multiplication means minus, four minus two. And division means plus, so this is nine. So five into eight divided by four is two. Minus two plus nine. Five into two is 10. 10 minus two plus nine is equal to 19 minus two that is equal to 17. So answer is D over here. And question number one second, eight. Question number eight is a plus means divided by. Divided by means plus means divided by. So 12 divided by six, divided by means minus. So six minus three, minus means multiplied by two. And multiplied by means plus, so plus eight. So 12 divided by six is how much? Two minus three into two plus eight. So this is 12 minus six, sorry, two minus six plus eight which is 10 minus six that is equal to four. Eight answer is A. So this is what I wanted to cover in today's class. I'll share these sheets with you by tomorrow morning or by tomorrow evening. You just solve it with the answer sheets and we will meet next week with something new. So please keep on solving QODs. I will, till now I know names of most of you who are joining the classes regularly. So let me check out the list of QOD that you are solving it or not. It is very important that you solve QODs. It's very, very important that you keep in touch with Matt Sylevus together. Also for SAT, I'm not finished that you guys have started writing bye and thank you. Did I say bye and thank you? Why is so much in hurry? I'm not finished now. For SAT Sylevus, Karnataka Medium 9 10th, social science book needs to be mugged up completely. Start with 9th and then go to 10th. Total nearly 300 pages are there that you need to mug up. So if you start from today by July 1st week, you should be able to finish it. If you read five pages daily, so start reading that Karnataka Medium book. Your SAT portions would be completed. Anyway, I'm completing your math portion and I hope you are solving it from your TMH, Magrahill books, Magrahill book and the QOD question which we keep on sending to you. So Matt and SAT together only will make sure that you get selected for NTSC. If you are solving only Matt and not SAT, it is guaranteed that you will not get selected in NTSC. So there is no point solving only Matt or only SAT. It has to be combination of both. Last year the cutoff was 153 marks out of 200. So you can understand that what kind of competition it is and what kind of scoring people do. So Matt will come only for 100 marks. Out of 100 maximum you will score 85 to 90. Those who will have a very great day will score something between 90 to 95. Still you have to score nearly 80 marks in SAT for your selection. So 80 out of 100 is very good score in SAT and for that you will have to put in a lot of hard work. And the first step in that direction would be to mark up grade nine and 10 books of Karmatka Mood syllabus social sciences. If somebody don't have it, please ask it on your group. We'll post it on there. I understand this has already been posted. If not, if somebody does not have access to that particular book, post it on the WhatsApp group you'll get it. So that's it for today. I hope you are taking care of your NTSC part also apart from your school. School and one thing which I have observed from the last year is that when the school reopens people just lose their enthusiasm for NTSC in the midst of grade 10 syllabus and unit test and all those things. So make sure that you have this thing in your mind that unit test would be there, other test would be there and you will have to cope up with both unit test and the preparation of NTSC. So don't lose track of any one of them. Your time management should be in such a manner that you are in touch with NTSC at all the days till the time you write NTSC. That is when you are gonna be selected for NTSC when you are serious about it. If you are leaving it for 15 days all your preparation that you have done for the last three months will be wiped out. You will have to start a press again. So which will not be a good sign in that particular scenario. So that is why it is very important that you keep on practicing both math and side part of NTSC and that is what is important and that is what will decide whether you are getting selected in NTSC or not. If you are preparing for it, prepare it for it wholeheartedly with this thing in mind that you will have a lot of pressure for your board examinations also in between. So you need to have a good time management, a good strategy to cope up with both the things, NTSC as well as your board pressure. So please don't let your enthusiasm die down just because school is open and you are busy with school curricula and your homework and all those things. Please have at least half an hour to one hour for NTSC daily and that will suffice. So that is what my idea behind cracking NTSC is. So thank you so much for joining. Let's meet next week. Thank you. Thank you so much.