2028 AL Theory EM Special 1 Hour | Day 2

Added: 2026-05-10

[00:00:06]If you need me to if if there's any issues that you need to discuss, you can discuss with me now. Okay?

[00:00:15]Just come towards the stage and let's discuss.

[00:02:20]Okay.

[00:02:21]So, let's start the extra session.

[00:02:24]Let's start the extra session.

[00:02:27]And again, I repeat, it's okay to leave in the middle of the session. Okay. It's okay to leave in the middle of the session. If you have transportation issues or anything, you can leave in the middle of the session. Okay, let's start. And anyways, you would get the recording. Okay, and I'll repeat uh pay attention now everyone pay attention.

[00:02:53]Uh I'll repeat this session is not mandatory and again understanding is also not necessary. Okay, you just have to keep trying to understand because this session is done to train speed and quick understanding. So if it is not there at the moment, you would find it hard to understand but it's okay. Okay. So just try to understand but if you are not understanding it's okay. That's the whole point of this session. Later with time you would understand or you would figure out how to think quickly. Okay.

[00:03:28]So let's start the additional session.

[00:03:31]Let's start the additional session. Pay attention everyone.

[00:03:37]Online students you can find the additional question tute. It's mentioned at as hard question t or something like that uh from the resources section.

[00:03:51]No not that one.

[00:04:02]Wait, we'll make that available.

[00:04:17]Provide that in the group quickly. Yes, sir.

[00:04:23]M.

[00:04:47]Okay. Which up to which question did we discuss last week?

[00:04:57]48. I think we skipped one or two questions in the middle, right? Okay.

[00:05:10]Is it available now?

[00:05:14]Put them in the groups.

[00:05:17]Okay. Online students, you can find the T in the groups. Okay. You can find the T in the groups. Okay?

[00:05:25]If you if you still can't find that from the groups, put a message on the Zoom chat. Put a message on the Zoom chat if you can't find it in the group.

[00:05:40]Okay?

[00:05:48]If you are not in the group or if you can't find it in the group, put a message on the Zoom chat.

[00:06:38]Well, did you provide that in the group?

[00:06:40]Okay, now you should be able to find that in the group. Quickly add that to the resources. Pay attention. Pay attention everyone.

[00:06:48]Uh let's start from uh did we discuss question 11 and 12? Did we discuss question 11 and 12?

[00:06:57]Yes. Right.

[00:06:58]Okay. So then uh let's uh I'm not going to do questions in the order. Okay. Pay attention. I'm not going to do the questions in the order.

[00:07:10]Uh cuz some students asked some questions.

[00:07:13]So I'll prioritize those questions too.

[00:07:16]Let's start with uh maybe question uh 16.

[00:07:23]Question 16.

[00:07:29]There's a system like this. Pay attention everyone. Pay attention everyone.

[00:07:39]There's a shape like this.

[00:07:43]There's a shape like this. This is four.

[00:07:45]This is five. This is three. Okay. So now pay attention everyone. Stop talking. Pay attention. Stop talking.

[00:07:56]Okay. Now, uh they need us to find the area of this shaded part. Okay. They need us to find the area of this shaded part. If this is a, if this is f, okay, I can get uh the area of this part. Area of this part can be taken using what?

[00:08:19]Area of this part can be taken using af. Total area right? AF means the total area AF minus 4 + 5 + 3 right the remaining parts are 4 + 5 + 3 got the idea total area is pay attention stop talking total area is a f - 4 + 5 + 3 okay so uh area equals Now this should be my main concern right let's take this as x this should be my main concern x - 12 right clear okay so I either find a way to find the area of this one okay or I either find a way to find this total area okay ideally most probably finding the total area would be easy if I find the total area I subtract sub four, five and three. I subtract four, five and three. Then I get this area.

[00:09:28]Clear? That should be the target. Okay.

[00:09:30]So now um like they have given me these three areas. So I can try something like this. Uh like let's put some unknowns into this. Let's take this as maybe uh B. Let's take this as B.

[00:09:49]This as C.

[00:09:52]this as D, this as E. Okay, clear.

[00:09:58]Now I can write the given areas. Right?

[00:10:01]Now I can write the given area. So the whole point should be using the given equations, find A and F, then get the answer, right? Clear? If you can use these given areas, create some simultaneous equations, find A and F, then you have the answer, right? That is the target, right? Clear? So uh let's create the required set of simultaneous equations. Then this area is four. This area is four.

[00:10:34]That is given as 4.

[00:10:42]4 = what? 4 = half 4 = half a into b. Right? 4 =/ A into B.

[00:10:54]Then 5 = half 5 = half C into D half C into D clear. Next 3 = half is it available in the resources now?

[00:11:13]Half 3 = half F into E. Half F into E. Clear?

[00:11:21]Pay attention. Okay. So now 4 =/ A B 5 =/ CD 3= half FE. Okay.

[00:11:34]You write the area of this, area of this and area of this. Clear? So now you have a bunch of simultaneous equations. What you do is you use this somehow find a and f then you have the answer. Right?

[00:11:48]Clear? That should be the target. Okay.

[00:11:50]So now Okay. So now and F right targets are af that means uh I can write uh here using this I can write using this I can write uh b= 8 / a right I can replace b I can replace b using 8 / A okay I can replace B using 8 / A and uh now B is not necessary now right my whole point is try to find A and F okay so remove as many unknowns as possible okay remove as many unknowns as possible okay that should be the target okay now uh E E can be removed again.

[00:13:17]E is equal to what?

[00:13:20]Six of F. Right? Now E is also written using six and F. Okay, clear. Now uh C and D.

[00:13:31]C and D. How can I write C and D?

[00:13:35]Uh I can use something like this. See F equals what? f= F = C + B. Right? F= C + B. Right? Clear? F= C + B. So I can find C. Why? C is what?

[00:14:03]C is F - B. Right? C is F minus B. Here B is 8 A.

[00:14:12]B is 8 A. Now C is also written using FN A. And uh again here A equals A= Here A= E + D. a= E + D. Okay.

[00:14:34]So now uh D is the only unknown remaining. D= A - E, right? D= A minus E. What is E? E is 6 / F. So now all the unknowns, right? All the unknowns are written using F and A, right? I mean, you can't always figure out what is the final target or you can't always get the final answer. But what you can always do is just keep a step towards the final target. Okay? Keep one step towards the final target. You know that your final target is finding A and F or multiplication of AF. Okay? So just remove as many unknowns as possible and bring A and F. Right? Okay. That should I mean you just what we do is we just break a larger question into smaller questions. Okay. So now the smaller questions is Okay. Now the smaller question is what? Smaller question is breaking things down.

[00:15:40]I mean now the smaller target is not finding the answer. Smaller target is writing everything using A and F. Right?

[00:15:48]Clear. Now there's one equation that we didn't use this. Right? Clear? One equation that we didn't use. So let's use that two. Why? Still there's too many unknowns. Right? Still there are too many unknowns. So we would use the remaining uh equation. 5 into 2 is 10.

[00:16:07]5 into 2 is 10. 10= CD. Right? 10 equals CD. Okay. C is this. C is this.

[00:16:19]F - 8 / A.

[00:16:22]F - 8 / A. That is C. Clear? What is D?

[00:16:27]This is D, right? A - 6 of F A - 6 of F here. Okay. A - 6 O F Ah.

[00:16:39]Now what? Uh now we can solve right?

[00:16:42]Why? Here I have 10 = AF a f - 8 / a a f - 8 / a. Here I have a f - 6 / f af - 6 / f. Right? Clear? So now uh you have uh I can get this af and multiply it to this side. I have 10 10 you take this af to this side. You have 10 AF equals You have 10 AF equals AF - 8 AF - 6. Right? Clear? You have 10 AF= AF - 8 AF - 6. Clear? Now you have an equation of AF. Just solve that. Right?

[00:17:38]You just have an equation of AF. Just solve that. Clear? That's all you have to do. Okay? So now uh just let's try to expand this uh you have let's take a as x okay no point of going through a lot of trouble writing a and f again and again 10 10 af means x equals x equ= here x - 8 here x - 8 here x - 6 right clear here x - 8 here x - 6 here 10 x right so it's all about finding x now right okay so let's solve this uh let's expand this 10 x = 10 x equ= uh here x² Here x² here - 8 x - 6 x which means - 14 x then 8 and 6 48 right 8 and 6 + 48.

[00:18:58]Now what?

[00:19:01]Uh now let's solve for x.

[00:19:04]Uh let's keep zero in this side. x² you take this guy to this side. Then uh 24x + 48 24x + 48 clear. Uh so can we solve this?

[00:19:26]This is not my area.

[00:19:29]Can you solve this? Yes. Do we have a nice answer for this? I'm not good at this stuff. You know how to solve this kind of stuff, right? Yes. Right. Can can you can we solve this? Break this into two parts quickly.

[00:19:58]So now you can find the paper. Okay. It is available in the resources section.

[00:20:02]Okay. It's available in the resources section of the webinar.

[00:20:07]Check the resources section of the webinar. Now you can find that and available in the groups too. Okay, it's available in the groups too.

[00:20:21]Can we yes or no? I mean at least yes no. Can we solve this easily? That means do you get nice answers for this or not?

[00:20:31]If no, we can find a different method.

[00:20:34]No. Okay. If no, I mean you have this equation, right? I think my calculations are correct until this point, right? I'm not sure about that. - b + or - b ^ 2 - 4 a c over 2 a. I mean this is the only result, right? Okay. I'm asking for the last time, can we solve this or not? No.

[00:20:58]Then we have to use this, right? Okay.

[00:21:00]You know this, right? This was in grade seven or somewhere like that. Okay. So, uh - b means 24 plus or minus 24² - 4.

[00:21:15]A means one here, right?

[00:21:18]A means 1.

[00:21:21]C means 48.

[00:21:24]C means 48 over 2. A means 2. Right? Clear? Ah, so I'm going to use the calculator. Uh, okay.

[00:22:01]So we are getting uh 12 plus or minus 4.6.

[00:22:08]So you know that you are getting two answers for a quadratic equation, right?

[00:22:12]Okay, you're going to get two answers, right? Cuz it's a x² equation. So you're going to get two answers, right? Now what is the area?

[00:22:23]Required area is this.

[00:22:26]Required area is this. And a f is x.

[00:22:31]af is x. Clear?

[00:22:34]So x is what? Here 12 + - 4<unk> 6 - 12. Right? Here you have a - 12. Clear? Uh so 12 and -2 cancels out.

[00:22:49]You have plus or minus 4<unk> 6. Area can't be negative. So the answer is 4<unk> 6. Okay. Clear. area can't be negative. So the answer is 4<unk> 6.

[00:23:00]Anyways, clear got the idea? Clear? So you can write these things later. Okay?

[00:23:06]You can write things later. Anyways, the recording would be available in the group. And not understanding is okay.

[00:23:12]That's the whole point of this session.

[00:23:13]Okay? You should not understand. Okay?

[00:23:20]Let's go to question 15.

[00:23:26]Let's go to question 15.

[00:23:36]I think my calculations are correct, right? That's the part I'm not sure of, but it should be right. We have 12 cancels out with 12. It's nice. So, I think should be correct.

[00:23:47]Okay. So, let's move forward.

[00:23:51]Question 15.

[00:23:54]You can write things later. We can't allocate time to write things now.

[00:23:59]You can write things at home. Okay? You you would anyways get the recording Okay.

[00:24:34]15.

[00:24:38]Question 15.

[00:24:42]A road connecting two towns contain a bridge over a river crossing the road.

[00:24:47]Somewhere between the towns, two cars travel from one town to the other at a constant speed v_sub_1 everywhere on the road except on the bridge where they travel at a constant speed v2 in the pre in the graph is shown variation is separation between the cars with time.

[00:25:07]Question 15. What is speed v_sub_1 of the cars on the road? What is speed v_sub_2 of the cars on the bridge? What is the length L of the bridge? Okay.

[00:25:20]So now uh they have given me a graph. Okay. They have given me a graph. It is the gap between cars with time. Pay attention everyone. Stop talking.

[00:25:35]It is the gap between the cars with time. Okay. Gap between the cars with time. So it goes like this.

[00:25:45]then like this then like this and when I'm discussing one question don't keep trying to understand the previous one okay you would lose both okay so uh I mean it's okay not to understand that's why we are allocating a separate time okay so it's okay not to understand but keep keep listening okay just don't focus on the previous question don't just don't wait and try to understand the previous one just focus on what I'm discussing now okay cuz it's all okay it's not going to affect your result or a anything like that. So just don't worry and keep listening what's happening here. Try to focus. Then later you would improve the ability to understand things fast. This is 10.

[00:26:28]This is 30.

[00:26:31]This is 80.

[00:26:35]This is 100.

[00:26:37]Okay.

[00:26:39]Pay attention. Stop talking.

[00:26:42]Now here like uh it's a nice question actually.

[00:26:49]There's a road.

[00:26:54]There's a road and there's a bridge.

[00:27:01]Initially both vehicles are moving in the same speed in the road. Okay. Same speed. V1. Pay attention.

[00:27:09]Both vehicles are moving in the same speed on the bridge.

[00:27:14]Sorry, on the road. That's why their gap stays constant. Okay? That's why they pay attention. Stop talking.

[00:27:25]That's why their gap stays constant, right? That's why their gap stays constant at 500. Clear? Their gap stays constant at 500 continuously. Clear? Now what? Now all of a sudden at a place like this, this vehicle is here.

[00:27:48]So this is the bridge.

[00:27:53]This is the bridge.

[00:27:57]At a place like this, now this vehicle, it enters the bridge. Okay? This vehicle enters the bridge.

[00:28:08]Clear. It enters the bridge. But this one still on the road. Still on the road. On the bridge.

[00:28:19]On the bridge. They moves slowly. Right?

[00:28:23]Vehicle moves slowly on the bridge.

[00:28:25]Clear?

[00:28:27]So as a result, gap starts decreasing. Gap starts decreasing. Why? This vehicle is moving faster. This is on the bridge. So they have a difference in velocity. Clear?

[00:28:42]They have a difference in velocity. So their gap keeps decreasing.

[00:28:48]That is the part from here to here. See that is the part from here to here.

[00:28:53]Okay.

[00:28:56]Then after a while what happens? After a while, the vehicle that was following the first one, it enters the bridge.

[00:29:09]That means after a while the second vehicle enters the bridge while the first vehicle is still on the bridge. Okay, clear. So after that their gap again keeps constant. Now it is 200.

[00:29:25]Now it is 200. Why? Gap kept decreasing from 500 to 200, right? Gap kept decreasing from 500 to 200 because when this guy was moving slowly on the bridge, this one was moving faster, right? It kept decreasing. Now it is 200. Now it is at a 200. But it is 200 constant. Why? It is 200 constant because both vehicles are on the bridge at the moment. Clear?

[00:29:54]Both vehicles are on the bridge at the moment. Clear? So they are maintaining a constant gap. After a while, what happens? After a while, if this is the end of the bridge, okay, the first one gets out of the ridge.

[00:30:12]First one gets out of the ridge while the other one is still on the ridge.

[00:30:16]Clear? So the first one now starts moving faster because on the road they can move faster. Clear? So their gap starts increasing again. This is where that starts happening. Clear?

[00:30:30]Yeah. Their gap starts increasing.

[00:30:33]Clear? Then after a while, after a while both gets out of the bridge. Again the velocities become constant. Okay? Again the velocities become constant and velocities become equal. So the gap keeps increasing. Again become constant and continue. Clear? So this is what happens in the question. Okay. If you understand the situation now you have the answer. Okay. Clear? If you understand this situation now you can come up with the answer.

[00:31:04]How? I mean uh Pay attention.

[00:31:31]Attention. Now the thing is this.

[00:31:35]What was the gap between them? The gap between them was 500. Right? Then this guy entered the bridge. This guy entered the bridge at this point.

[00:31:49]He entered the bridge at this point.

[00:31:51]Right? Clear. He entered the bridge at this point. Clear?

[00:31:58]Then within this time, it took this time. It took this time for this guy to reach the bridge. Right? Clear? So at this moment, what is their gap? It's 500. Right? Initially their gap is 500 right clear. That means this vehicle took 10 to 30 20 seconds to go through this 500 and enter the bridge. Right? Clear. This vehicle took 10 to 30 from here to here. from here to here. That means 20 seconds it took to go this 500 m and enter the bridge.

[00:32:47]Right? So now you know the answer for V_sub_1. What is the answer for V_sub_1?

[00:32:53]We know that velocity equals displacement over time. We know that velocity equals displacement over time.

[00:33:01]Okay. Here displacement over time.

[00:33:05]Velocity equals displacement over time.

[00:33:09]And this displacement is 500. Pay attention. This distance is 500. Clear?

[00:33:17]This is 500. And it took 30 seconds to go there. Right? It took 30 seconds to reach the bridge. Right? So it's 500 over. Sorry, 20 seconds. 10 to 30. It took 20 seconds. Right? So velocity is displacement 500 took 20 seconds to bridge that you get 25 m/s that is v_sub1. Okay that is v_sub_1 clear.

[00:33:51]Next.

[00:33:53]Next. V_sub_2. Finding v_sub_2. How can we find v_sub_2?

[00:34:00]Pay attention. How can we find V2?

[00:34:03]Within this 20 seconds?

[00:34:06]Within this 20 seconds. Clear? Within these 20 seconds, their gap felt from 500 to 200. What is the reason? That means their gap decreased by 300.

[00:34:19]Their gap decreased by 300 within this 20 seconds. What is the reason?

[00:34:27]What is the reason?

[00:34:29]Reason is the velocity difference, right? So we know that we know that velocity into time equals distance, right? Velocity into time equals distance or displacement.

[00:34:42]Okay? Velocity into time equals displacement. Now their velocity difference is V_sub1 minus V_sub_2.

[00:34:49]Right?

[00:34:51]Their velocity difference is V_sub1us V_sub_2.

[00:34:54]Okay? With this velocity difference, they moved 20 seconds. With this velocity difference, they moved 20 seconds until the second one entered the bridge. Within that 20 seconds, their gap felt from 300. So velocity difference into time is equal to 300. It accounts for 300 m. Clear?

[00:35:19]Due to the velocity difference between them they are gap decreased by 300 m. Clear? Okay. That means velocity difference into time means the difference between their distance it felt by 300. Clear? Ah. So you get v_sub_1 minus v_sub_2 equals here 15.

[00:35:47]Okay. V_sub_1 is 25 - V_sub_2 = 15.

[00:35:52]Okay.

[00:35:56]V_sub_2 = what? V_sub_2 = 20 - 15 means 10.

[00:36:04]V_sub_2 is 10 m/s. Clear? V_sub_2 is 10 m/s.

[00:36:10]Clear?

[00:36:12]We got V_sub_1 and we got V_sub_2. Okay, clear. That means if you are running with a velocity of 5 m/s, if I'm running with a velocity of 10 m/s, okay, within 1 second, I would run 10 m. Within 1 second, you would run 5 m. So, our gap will be increasing by our gap will increase by 5 m. Right? So, that means our velocity difference is 10 - 5. Our velocity difference is 10 - 5.

[00:36:46]With that velocity difference, if we run 1 second, our gap will increase by five or decrease by five. Clear? With that velocity difference, if we run 2 m 2 seconds, our gap will increase or decrease by 10. Clear? Clear. This is relative velocity. So don't worry, there's the entire lesson called relative velocity. Okay? There we are going to learn this in a more structured manner. Okay, this is I mean you I mean the theory explanations are well structured. Okay, that structured nature do two things. Okay, it improves your theory learning ability and the skill set destroys your fast thinking ability.

[00:37:29]Fast thinking ability and ability to understand something different. Okay.

[00:37:33]The structured learning do two things.

[00:37:36]Gives you a very nice and clear understanding about theory which is good. Destroys your destroys your ability to understand something when it is scattered which is bad. Okay. So this session is for that. Okay. Improving your ability to understand something when it is not well structured, when it is not well explained. Okay. It takes a lot of time to improve this. Improving theory knowledge easy. Okay, improving theory knowledge within the 3 hours in our class it's easy. It's not a big deal. This is the hard part. Okay, so don't worry if you understand. It takes a lot of time to improve these kind of skills. Okay, structured skills. It's very easy to improve. Okay, these kind of unstructured stuff. Okay, this is about the brain. Okay, it's really difficult. Okay, yes. So, it's okay not to understand. Try to understand the maximum proportion possible. Okay, if it is 20% it's okay. After 2 3 months it would improve to 30%. After like 5 6 months it would improve to 70%. Okay. So here if I try to explain things well structured first teach the theory then the question theory then the question then again this is going to be useless.

[00:38:47]Okay. So this is not structured for a reason. Okay. Uh let's move forward. So I know the velocity v2 10 m/s. Now what?

[00:38:58]Now what? Pay attention. Pay attention.

[00:39:02]Uh I mean actually this session is the whole point of this session is protecting you guys from what happens from our educational system. Okay.

[00:39:19]Clear? The session is the main target of the session is in the future we would come up with entire sessions like this.

[00:39:25]Okay. 3 hour sessions, 4 hour sessions, 5 hour sessions like that in the future.

[00:39:30]So this is entirely protecting you guys from the destruction happens to your brain from our education system. Okay, clear. Our education system is the worst education system in the world. Okay, clear. You learn theory, theory, theory, theory, theory, you have no ability to understand things faster. You can't understand real world scenarios. Why real world scenarios are scattered?

[00:39:53]Nobody teach you a theory about a real world scenario and give the problem. No, real world scenarios pop up. Okay, then you have to somehow solve that. But you don't have that ability. Why? You don't have past papers for real world scenarios. So, so it is a problem with the educational system. So, this is we protecting you from educational system.

[00:40:12]Okay? Let's move forward. We can't do that in theory class. Okay? Cuz anyways you move, you have to move in the system. Okay? Let's move forward. Pay attention.

[00:40:28]Okay, let's move forward. Uh, next.

[00:40:32]Length of the bridge. It's easy. Length of the bridge. What is this point? What is this point?

[00:40:41]This point is, pay attention. This point is, stop talking everyone. This point is uh you enter the bridge.

[00:40:51]This point is you enter the bridge. The first vehicle, first vehicle enter the bridge. Okay?

[00:40:59]And this is where the first vehicle gets out of the bridge. Right? This is where the first vehicle enter the bridge.

[00:41:05]Second vehicle enter the bridge. Both moving in the bridge. First vehicle goes out of the bridge. Clear? So from here to here.

[00:41:14]From here to here. Clear. From here to here, it's the time that the second first vehicle was in the bridge. Right? Here the first vehicle enters the bridge. Here the first vehicle gets out of the bridge. So that means all together from 10 to 8 it is 70 seconds. Right?

[00:41:35]From 10 to 8 it's 70 seconds. Right? Uh so you are in the bridge for 70 seconds and your speed on the bridge is 10 m/s.

[00:41:45]You have the answer right? Okay, clear. Got the idea.

[00:41:54]Distance equals or displacement equals velocity into time. The first vehicle stays in the bridge for 70 seconds.

[00:42:03]First vehicle stays in the bridge for 70 seconds and it moves in the bridge with a velocity of 10. So the length of the bridge is going to be 700 m. Okay, length of the bridge is 700 m. Let's move forward.

[00:42:25]Yeah, I asked you to try question seven, right? Let's try that. It's a very it's a very lengthy question. So, let's try that question seven. It's lengthy but I mean someone asked that question and I think I last week skipped that right. I think I last week skipped that and asked you to try. It's a lengthy question but let's try to finish it.

[00:42:53]Uh Okay, pay attention.

[00:44:05]This is the radius 4.

[00:44:08]They asking this area, right?

[00:44:12]They asking this area, I think. Okay, they're asking this area.

[00:44:17]Uh so I would be able to do this quickly because uh I did this in Monday class.

[00:44:24]Okay. But it took a lot of time for me to think analyze this in the Monday class too. Uh the method I came up with may not be the best answer. Okay, there may be better method but I tried for a while. I have to do that in the class time within 1 hour. Okay, I tried for a while. So that was the method that popped up on my mind first. Okay. So, I went I moved forward with that. But I'm not sure whether this is the best method. Okay. I think there should be a better method than this. But I don't have enough time to figure out.

[00:45:02]So, you can go home and figure out. You have nothing to do, right? You Okay. So, uh I started drawing triangles like this actually cuz there's no other way out.

[00:45:15]just make things more understandable.

[00:45:20]That means uh this is a method. This is the method actually used in Olympia maths and stuff.

[00:45:32]If the shape is complex to analyze, if the shape is complex to analyze, break it into shapes that are analyzable.

[00:45:42]the shapes that you already know. Break the shape into circles, triangles, rectles, right? Break the break the shape into squares, rectangles, uh circles, half circles like that.

[00:45:59]Okay. So, let's break it like this.

[00:46:06]Now, pay attention.

[00:46:09]I'll quickly do this cuz it takes a bit of time for this. This is the center of this circle, right? Pay attention. Stop talking everyone.

[00:46:19]Stop talking.

[00:46:22]This is the center of the circle.

[00:46:25]This radius is four. This radius is four. Right? This radius is four. This radius is four. So you should understand that uh again this is four again the radius right three equal circles this is the center of this circle this is the center of this circle right so this is four cuz it is the radius this is four cuz it is the radius this is four cuz it is the radius right so these two sides are equal okay so if I get that triangle out. If I get the triangle out, it is 4 cm, 4 cm, 4 cm, and 60, 60 and 60. Okay, a very simple triangle. Okay, so you know how to get the area of a triangle like this, right? You can somehow figure that out, right? You can get the area of a triangle like this. uh write the height h height h and uh maybe use sin 60 sin 60 sin 60 = h / 4 right from this triangle sin 60 = h / 4 sin 60 = h / 4 clear h / 4 then h = 4 sin 60. If you don't know the value of sin 60, it's okay to keep it like this.

[00:48:01]But I'll write the value of sin 60. Sin 60 is <unk>3 /2. This you have to remember later. Okay. Sin cos tan values of 30 45 60 90. These you have to remember. Let's think about that later. We have better problems at the moment. So this is 2<unk>3.

[00:48:25]This is 2<unk>3. Pay attention. Height is 2<unk>3. Clear? So I know the area of the triangle now, right? Area of this triangle is half into base. Base is 4. Pay attention.

[00:48:45]Into height into height, right? Into height. Height is 2<unk>3. Pay attention everyone. Stop again.

[00:48:56]Height is 2<unk>3. Clear? So you get 4 <unk>3. You get an area of what? 4 <unk>3. Clear?

[00:49:09]You get an area of 4<unk>3. Clear? Ah.

[00:49:14]Now what? Now uh moving forward from this point now I know the area of this triangle.

[00:49:25]Okay, nothing is solved now. But I know that uh this is a non shape. Okay.

[00:49:45]Okay. Pay attention now.

[00:49:50]Uh, now the next part. This one I can find. Okay. This part I can find. This area. Pay attention everyone. This area I can find how how can I find this area?

[00:50:07]Uh this is 60°. Pay attention. This is 60°.

[00:50:13]Okay.

[00:50:15]So this is I can't remember the name we mention use for this. A part from a circle. Okay. Okay. It's a part from a circle. This one, this this it's a part of a circle, right? Okay, there's some kind of a name for that, right? Uh sector. Okay, so it's a sector. Okay, so uh you know that if I I'm going to find this area colored in blue color that area I'll mention as A2 that can easily I I mean I can easily get that. What is this total area?

[00:50:57]You know that uh total area of a circle total area of a circle is pi r² p<unk> r² okay that is for all 60 360° of the circle right that is for all 360° of the circle right then how much for 60 then how much for 60 here. Okay. If you get 10 mangoes for five rupees, how much? One rupee. Okay. It's p<unk> r².

[00:51:34]That means the total area of a circle total area is for 360° se sector. Do we have a 360° sector? No.

[00:51:44]Right. Okay. It's a circle, right? Then what? Then how much for 60° sector? Got the idea? You divide this by 360 multiply by 60. Okay. Clear. So that is the area of this part. That is the area of this part all together. Clear? Clear.

[00:52:05]You subtract this triangle. You subtract this triangle. Then you get this small part. Right? So what is the triangle?

[00:52:13]Triangle is 4<unk>3. Right? Triangle is 4<unk>3. Clear? Ah. So you subtract 4<unk>3.

[00:52:22]You subtract 4<unk>3. You get this small part. Okay. Now what? Pay attention. Now what? Now you have the answer. Okay.

[00:52:34]Why?

[00:52:36]You need these two, right? You need these two. So that area you can get by.

[00:52:44]Let's tell that area as a dash. What is the area of this full circle? What is the area of this full circle? Pi R². R means 4².

[00:52:58]Pi R² is the area of this full circle.

[00:53:02]You subtract four triangles. 1 2 3 4 and eight parts like this. 1 2 3 4 5 6 7 8. Clear?

[00:53:16]Clear. From this full circle you subtract 1 2 3 four triangles. Okay. So this minus four triangles. What is the area of a triangle? This right area of a triangle is this. Clear minus minus you have eight sectors. They are not sectors actually. You have eight pieces like this. Okay? You have 1 2 3 4 5 6 7 8. You have eight pieces like that, right? Okay. Eight pieces of this.

[00:54:02]Clear? So, you put A2 here. Uh, you have the answer. Clear? Okay. Here we are not here we are not learning how to do a question. Okay. just ways of thinking.

[00:54:16]Okay, ways of decoding problems. Okay, this is not about this question. This is about how we decoded these complex shapes into much understandable shapes.

[00:54:29]These are concepts. Okay, don't take these as questions. Understand these as concepts. Okay, we have 1 minute left.

[00:54:37]Wait.

[00:54:41]Uh anyways this time would be increased little by little. Okay. Let's wait until you get results and all.

[00:54:55]Okay.

[00:54:57]Then you get a like some kind of a boost when you get the result. So we can increase the time then you won't feel that.

[00:55:05]Um so I need everyone to pay attention.

[00:55:11]I need everyone to try question 24.

[00:55:14]Okay. Which you won't understand.

[00:55:17]Uh question 24. Some students may have done this in uh all levels. Did you have that fish eye in all levels? No. Right. No.

[00:55:30]Right. I don't think so. Okay. Pay attention.

[00:55:40]Pay attention.

[00:55:42]Question 24. I'll explain you a certain amount. You can go home and try to understand this and try to get answers.

[00:55:53]Uh you know that pay attention. Pay attention. I'll give you a rough guideline on how to handle this.

[00:56:08]Everyone stop talking. Pay attention. A rough guideline.

[00:56:16]Like some rays going like this will refract like this according to which law you did low levels. Which law? Stell law right?

[00:56:32]Some rays going like this after a certain point what will happen to them?

[00:56:37]They will go along the surface. What is this angle?

[00:56:42]You again did all critical angle right that you know right yes or no critical angle was there right okay assume that there's a fish here okay okay did you know or do you know reversibility of light I think yes if light goes in a certain path path it returns in the same path.

[00:57:14]Yes.

[00:57:15]So this ray will return in this path.

[00:57:21]This ray will return in this path.

[00:57:24]Clear?

[00:57:25]Again this ray this ray will return in this path.

[00:57:35]Okay. So if this is a fish, what is happening here?

[00:57:42]What is happening here? Assume that this is a tree.

[00:57:47]Assume that this is a tree. What is happening here is seen here.

[00:57:53]Just that ray bends here.

[00:57:57]What is happening here is seen here.

[00:58:00]Something happening here is seen here.

[00:58:04]Okay. Another tree here. Pay attention.

[00:58:06]Stop talking.

[00:58:09]Another tree here.

[00:58:12]Okay. Another tree here. That ray coming from this tree. It would return like this. So for the fish, it would be seen here. Clear? So for this fish, everything happens would happen in this circle. Right?

[00:58:28]Okay. For this everything happened in the world. Everything happened in this world above okay would be seen in a small circle okay you can check this okay in the pool okay don't die but I mean you can check okay clear everything happening in the world okay is been I mean it looks like everything's happening in this circle okay so for a fish for a fish when it look above Now everything happening above water is seen only in this circle. Clear? Cuz light bends here. I need you to find the radius of this circle. Okay? Now it's really simple. Okay? Got the idea. I'll explain this again next week properly.

[00:59:20]But I mean I just needed you to I needed to establish a small guideline on how to try this. So let's meet next week. Uh let's meet next week.

[00:59:36]New students give your information to our invigilators.

[00:59:41]And that's all actually