So today we're going to talk about the seven red flags you're with emotionally broken man Now really quickly before I get into the topic today. I want to share with you a Instagram reel I got just moments ago From a friend and it was a female comedian. I believe she's a very young millennial I think she's in her 20s or early 30s and she was giving a recap of her dating Experiences for 2023 and I think there were like seven or eight different Experiences she had and she was going one by one of saying how you know, like one guy was late One guy wanted to have sex with her one guy was you know, just emotionally vomiting his problems I mean, she just went from one after another after another and Made me think about the fact that there are just a Significant percentage of emotionally broken people now when we say the words emotionally broken. Let's reframe that Let's just say emotionally unhealthy. We could say wounded. We could say Emotionally constipated we could say emotionally unavailable. There's a variety of different You know words that we could use but there certainly seems to be a significant percentage of people who are struggling in the dating marketplace Whether it's men or women but today we're going to talk about men because my audience is you ladies, okay? Now I can speak from personal experience because I was an emotionally wounded person after going through a significant divorce Or why should well, I guess every divorce is significant, but after going through a divorce and certainly after I'd actually lost my corporate High-paying corporate job. I found myself Actually in a very weak place in my life and why this is so important to talk about is where we have to look at Where does brokenness come from if we're going to use the term brokenness? What's the root cause? That causes someone to be broken We usually for men in particular. It's oftentimes an identity crisis number one or a fear of Supporting themselves. That's another one. And by the way, a lot of women experience both of these as well Maybe there's a contentious divorce like I talked about maybe there's a contentious relationship with an ex whether it's an ex-spouse and Ex-lover but there's contention. Maybe somebody's got some challenges with their children all of these experiences can weigh on us emotionally and When something weighs on us emotionally it makes it very difficult to lean into a healthy happy relationship Because I want everyone to recognize that a healthy happy relationship needs a foundation needs a foundation And if the ground underneath a person and I don't I'm not I'm talking about women as well as men If the ground underneath you doesn't feel solid both in your physical world, but also in your emotional world It's gonna make it very difficult to lean into a healthy happy significant relationship See we're we you know Well first off here in the United States, you know the number one emotional health wound is I'm not good enough and To add to that. I'm not lovable. I'm not likable. These wounds play significantly into the Personality in the behavior or let me reframe that to the behaviors people operate in in the dating realm and so, you know one of the things I Constantly constantly continuously espouse in my videos is the importance of learning To vet a person to vet a person in fact earlier today and tomorrow this video is coming out I interviewed dr. Tyese Gibson ice Gibson She wrote the book learning to love and by the way, there's a link below to get a copy of this book She's a attachment love Specialist and we're talking about the stick six stages a relationship and she was at the end of the video We emphasize the importance. I mean we over emphasize the importance of really doing your due diligence doing your vetting in The early stages instead of getting sucked into what's known as the honeymoon phase because the honeymoon phase is the lust It's the limerence. It's the dopamine. It's the oxytocin. It's the testosterone. It's the an estrogen it's the you know the attraction game It's the men are you know the your chivalrous and they do all these they love bomb you and all this kind of stuff That's in the honeymoon phase But the reality is is you could be falling for an emotionally constipated person an emotionally broken person So if you need some support, you see this link that i'm pointing out right now johntonasley.com forward slash coaching By the way, there's a link below in the description as well. My whole Coaching is centered around learning discernment. Okay with that said I'm gonna say something that I feel like is a little bit unfair But you might feel like this resonates I think a significant percentage of men don't value women the way they were once held in higher regard See sadly we live in a very myopic world. It's very tunnel vision. It's all about me I think we are the byproduct those of us the baby bonomers and the gen xers are a byproduct of it's all about me So people operate very myopic means tunnel vision And in that tunnel vision, I do believe there's a significant percentage of men that don't value women and what makes this worse Is these broken wounded constipated men? We'll choose women as rehabilitation centers I had one woman say to me jonathan.  He'll be better if I hold enough space. He will change You know as loving and as compassionate as that is it's at your own expense So Before I get into the seven and I'm about to get there in just a second. So just bear with me for just another minute or two I want everyone here to recognize that A relationship is an incubator. Do you know what an incubator is? It's where you you you incubate Look up the word. I I don't know how to properly define this. Uh, maybe hey google What does incubator mean? Here's the definition of incubator an enclosed apparatus providing a controlled environment for the care and protection of premature or unusually small babies Okay, well, I wasn't I was thinking of the the incubator in a in a lab. Okay, but not for children But it's a it's a space.  That's the incubator piece And sometimes it's done on an individual basis Sometimes you're helping someone else grow and sometimes two people grow together. Okay But most of the time since they don't work out most of the time you have to ask yourself What positive things did I learn about myself in this relationship? How have I healed from this relationship? What was good about this relationship? And what am I most grateful for because if you can dive into This experience with a positive mental attitude you have a greater chance of relationship success All right So I want you to put your binoculars on for a moment because we're going to talk about these red flags that we want you to spot well before You give your heart away to a guy and while it's it's It's not as easy as I say it's easier said than done Let's just put this let's put this out there and let's see where where it incubates. Okay So number one This is the most obvious your time together is all about sex This female comedian I was talking about Hmm, excuse me. I ate a grape earlier and there's a grape skin stuck at the roof of my mouth Oh, that's gross. Okay. Um, she was talking about the guy that was only in it for sex.  So if it's mostly time centered around sex You know or if he's pushing sex really early on if he's pushing pushing pushing Chances are he could be an emotionally constipated emotionally unavailable or emotionally broken man Number two He doesn't open up to you Meaning he avoids personal question. He avoids and he even avoids talking on the phone Now that's not a guaranteed red flag, but let me get into this a little bit Excuse me for slurping You know It's interesting how many women I talk to clients or you know clients of mine or perspective clients how They're in relationship with men who will share very little personal information They're there now we could argue that men are taught to be stoic and they're not supposed to be emotionally expressive You know what? That excuse no longer flies anymore. Yes, that is what we're we're learned But you know what if you've been around the block a little while It's time guys that listen if there's any guys listening It's time to tap into your emotional intimate side And if you're unwilling to most likely the reason is remember I talked about the ground underneath you isn't solid We're swimming in the sea of a lot of emotional dysfunctionality because humans are living in a rather dysfunctional structural world in their life So it's no wonder that their emotional life is equally as chaotic because their physical life is chaotic meaning We've got a lot of people especially in midlife going through a contentious divorce have a contentious relationship with an x Maybe their x is in a relationship with another person and that person is a problem. I mean you know You've got multiple families to deal with I mean we're dealing with a lot of emotional stuff that most humans didn't deal with You know hundreds if not thousands of years ago So it's no wonder We're swimming in a sea of dysfunctionality But if he doesn't open up and share personal things with you that's usually a red flag He's an emotionally broken man number three He doesn't ask about you after the hunt phase Okay, what's the hunt phase jonathan men are hunters and they love the chase Yes, we men are hunters and we love the chase ladies Do you honestly believe that we're running around with our bow and arrows going? I want a relationship I want a relationship.   So you must just just lean back Play hard to get that's all you need to do because once he captures you it's love I mean like what fantasy land are these people living in? Like hunting really equates to relationships ladies. You got to get like you got to let go of that narrative And by the way as men age we midlife men We're old. We're tired. We don't like hunting. We'd rather by the way, we're so used to you know Grubhub and instacarts and you know uber eats, you know So let go of that fantasy that we went by the way to the extent that we love the chase No, we love sex and when we get it If we stop asking about you after the sex phase after the hunt phase That's a pretty big sign That he's probably incapable of going any more emotionally deeper with you Let me share with you quickly a story after my divorce. It was nine months after I moved out of the house I met a really fantastic woman We're friends to this day social media friends anyway and um And and I said I'm ready for a relationship. I'm ready for a relationship. You know what she said to me Jonathan, you're not ready for a relationship. You're broken. I'm like no. No. I'm ready. I'm ready Sure enough three months into dating I'm like I put the brakes on She knew it was coming. She even said I knew it was coming. She goes. I knew you weren't emotionally ready to be in something deeper See, we're we're emotionally capable of expressing how amazing you are and how wonderful you are because we're amped up on dopamine we're amped up on testosterone We're amped up on getting our rocks off But at the end of the day once we've gotten past this If we don't ask about who you are past this phase It's a pretty solid sign that he's most likely emotionally constipated number four He doesn't protect you I don't mean on a physical level. We most men are Chivalrous from that perspective, but we don't you know broken men don't protect you on emotional level Meaning if they're broken, they're not looking out for your best interest See a true emotional grown-up is understands that words matter So when someone says, oh my god, you're the most amazing person on the planet. You're so wonderful I could see myself getting married to you. Oh my god. We're so we should go on a trip together. This is so amazing That's not being mindful of your feelings. That's only that person expressing what they want It's not a fair assessment Of how he feels about you and if he's truly a protector, he's going to be an emotional protector See we weren't trained to be emotional protectors We're we're we're again We live in such a myopic self-centric world that where most humans are only focused about themselves And I think being a true Protector is protecting someone's emotions But Jonathan men are provider protectors You guys got to let go of this narrative as if assuming it means emotionally cavemen never dealt with emotions or we or well I'm I'm going to suspect cave people where this whole narrative comes from Provider protector comes from cave people cave people didn't deal with emotions Okay, so don't superimpose that that's what it means. Okay We're talking about imprinting this hundreds if not Millions of years old. It wasn't emotionally speaking Only an emotionally evolved person is protective of your emotions Number five you've never met his friends That's a pretty good sign That if you haven't met his friends folks if you haven't met his family and friends That's that's a gigantic red flag and remember red flag Means asked deeper questions. You could call it a deal breaker But I would venture to say well, I want to be clear red flag means ask more questions Deal breaker means no red flag means ask deeper questions If you haven't met his family and friends, that's a bad sign number six He doesn't go out of his way for you Let's say you're sick and you need some support. Maybe you're moving He doesn't go out of his way to help you. Maybe you've got a professional issue going on Maybe you've got something going on with his children and you need just a little bit of support He doesn't go out of his way in other words.  All of a sudden they're busy. I'm busy busy busy busy busy busy busy busy It fascinates me how busy somebody becomes After they've been physically while they're while they're on the hunt phase. They're available available available available They're texting. They're calling. They're doing everything See vetting a person requires going deeper than the surface and you have to pay attention to someone Who it's certainly a red flag if he's not going out of his way He's in his myopic world and not vested in your world and last but not least number seven He puts off Or avoids conversations about exclusivity Or about any conversations about the future folks Some of you are in relationship for years and you haven't talked about what's going to happen in the future That's a no. No folks don't waste years with someone if you're not the minute to the minute ladies the Penis goes inside the vagina. This is the time to have critically important or maybe before But have some critically important conversations about what you both want but most importantly What does commitment look like for you and what does a significant relationship look like for you? Well, I just want to take it slow. Let's just have it casual. It just needs to be slow By the way, anytime you hear that That is a red flag. He's an emotionally constipated guy because a constipated men Can't dive into emotions And so as I share these seven red flags my real Point I want to stress with everyone Is there a lot of people hurting? There are there are a lot of people hurting and it's sad, you know, emotionally speaking And if you're hurting emotionally, maybe it's not time for you to be put yourself out there But certainly pay close attention to where someone is at in their life because if they're hurting Your job is not to be his rebuild rehabilitation center Women are not a man's rehabilitation center. Is this sinking in is this resonating? Please let me know and if it is post a comment below I'd like to hear your thoughts as always if you found value in this video Please hit that like button. Please share this video Please subscribe to my channel and hit that notification bell so you can be notified of new videos as well All right, it's time to ask questions. If you have a question Right, there's a little chat box in the Write the word question and post the question thereafter Or there's a little dollar sign the chat box. You can purchase a super sticker super chat All of the money's from the super sticker super chat goes to a scholarship fund in the name of my son connor asley That's a picture of him right there in the little woody outfit It's my son who passed away over five years ago and his honor we donate to causes like the hoffman process And insight institute just to name a few and again, there's a little dollar sign our goal is $50 tonight Let's get $50 donate. I think we got 40 the other night. Let's get 50 tonight Oh, and if you'd like to join the hot seat, there's a link right here Who's brave enough to join the hot seat tonight? We had some fun last night. I'd love to have you join as well All right, lisa's in the house What are three good vetting questions to ask someone great question? Okay. Well first This is where my coaching comes in but i'm i'm a big proponent of asking what does commitment look like for you What does a relationship look like for you? And lastly, um, find out about their past relationships. I mean those are three really critically important questions And I think, you know, it's interesting when I interviewed Tyce Gibson Um, who wrote the book uh learning love. I'm just getting started on this book. I'm really enjoying it There's a picture of her. She's gonna be in my video tomorrow. So there's her her Her youtube channel is called the the the personal development school But um, oh fuck. What was I going to say about her? Um We were just talking about the importance of vetting. So um, anyway be on the lookout for that video. It's coming out tomorrow Oh, oh so about important questions She thinks uh have two to three important questions that you want asked in the first five days So I well, she didn't say five dates, but I'm I'm going to super impose this So your first couple critical dates make sure you have two or three important questions you want answered I like doing it all up front, but I'm unafraid to do that. Um, but that was what she recommended. Okay All right a beach lover's in the house with a five dollar super sticker Let's get the ball rolling now. We need 45 more dollars or is it four 45 Thank you for the love I appreciate it. Uh People are talking about dogs. Okay stop that I need questions here. Oh When is it appropriate to meet family and friends? I think if two people begin a physically intimate relationship, that's the time to connect I mean certainly you can do it before physical intimacy But certainly by the time two people are physically intimate You should be getting to know more about this person at a deeper level So whether it's before or shortly thereafter folks, you can't be afraid to dive in Folks this do you know our current dating model is just a strung out version of friends with benefits That's all dating is really just a strung out version of friends with benefits Most of you find yourself In friends with benefits And sometimes you don't even know that's what it is and sometimes you're not really friends Situationships or casual relationships. I would say 80 percent of all Non-married couples in a relationship excluding those living together are in casual relationships. There's no real clear direction Let's stop that stop that stop that. Okay All right What does this say? What is the brand name? What brand name is that shirt? Oh, I think this is a bugatti or something like I think it's uh bugatti or something like that I can't see it right now. Where's let's see. I can't Here hold on since someone asked can you see it? I think it's bugatti. I'll check it out later. But that's a weird question magic entertainer. So Uh something like bugatti or something like that. I got it the Nordstrom's rack. Okay Uh, let's see what else Uh, bum bum bum bum. Well, we got a bashful group. Come on somebody magic entertainer Why don't you have some nerve and join the hot seat tonight or marcy join the hot seat or beach lover join the hot seat Come on. Let's have some fun tonight. We did last night. Otherwise, this is going to be a very short live stream Um Vila says how long does it typically take for a man to be emotionally available after a divorce? There is no one size fits all um, it's mostly predicated on the um amount of personal development work that he has done to be ready for something like that um, so Anyway, great question How melt melissa. Okay. There's a link. I just point posted in the chat box if you want to join the hot seat There's the link. Okay. So melissa. Let's see if you're brave enough to join Click that link. It will be fun um You know I'm going to come back to this question How long does it take for someone to be typically emotionally available? So after my divorce I would say let's see two thousand five Six seven eight nine ten. So I went down the rabbit hole for about five years And I began crawling out of the rabbit hole for the next five years. So I would say men Okay, alison armstrong talks about the tunnel Where's my book the queenscope? Alison armstrong talks about the tunnel The tunnel and I I'm going to say the average tunnel for a man that that that hero's journey Could be up to 10 years sometimes even 20 years Wow, jonathan, that's so long. Well human, you know, you have to really Decide that to work on yourself and it takes years of peeling back the layers to find yourself in a position To be able to learn emotional expressiveness. So yeah, um Melissa says I want to but I'm in my jammies. Oh, it's okay. Melissa. Who cares? Um, but I'm gonna say it took it took me a good 10 years to get just Just appeal a lot of the layers and many of you I'm gonna say probably find yourself in the same place. So anyway, great question. Thanks so much Hey folks, we've got a bashful group tonight. So I think we'll have a short live stream for tonight unless we get some good questions coming in um I know we're talking about my shirt. I appreciate that. I appreciate that. Melissa will do this next time Folks, I'm gonna give one more or 30 more seconds if we don't have a good question coming We're gonna wrap up for the evening Um, come on. Give me something good to talk about other than my shirt. Okay Um, McCoy says I think I'm finally healing from my late boyfriend and what went on. That's good to hear Uh Miss fischer says why do men play the Hot cold game. Is it really about sex even if they tell you over and over again? They want forever We're swimming in a sea of emotional brokenness. That's part of the reason most humans aren't really that aware of who they are on the inside and it's no wonder Um, you know, we're seeing a lot of hot and cold hot and cold is a person who who isn't really attuned to themselves That's my perception anyway. So great question. Thank you so much Why can't two broken people help each other heal? Both people have to want to help Both people have to want to heal if they want to heal The problem is once they heal they go and find someone new So they look like a bright shiny penny to someone new It's not your job. Listen if you need work Do the work so you can show up in a relationship where you don't need to be with another broken person to make it work Okay Mary Ann says I'm finding time going faster since my divorce. Do you agree? Well Yeah, because I want you to think about when you're one year old And you go from one to two. That's 50 percent of your life When you go to two to three, that's a third of your life when you go three to four That's a quarter of your life. So time does move faster. I think as we age. All right, jill. Oh, hey jills in the house Hey, how are you? Hi guys Um, I do have a question and it's like for real. Okay. So, um, the guy that I was telling you about last week Okay, so he's he's kind of been like a little bit like I'm inviting everybody a quick recap Okay, so recap. So a friend of mine introduced me to this guy. He's pretty spectacular. We've been out a few times like breakfast but um, no no intimacy yet, um And um, I've invited he's like said, oh, let's get together a couple times and then I'd say Yeah, sure, that'd be great. And then I invite him to something and he'd say, oh, I have surgery I was gonna be kind of late. I'm gonna be tired So he's kind of like said yes and then pulled back And then the friend that introduced me, um, apparently he said to him like, look, you're gonna lose her If you don't like get serious about how do you feel about her? The triangulation which I don't care for but whatever and What triangulation? Well, because she's like talking to him and then she's asking me, you know that thing Okay, got it. Um, so like I was saying, um, so she apparently he was she said, well, yeah He's really really interested. He's really he really he sees you as like the lifetime partner And so then he's like, well, so so immediately she said, well, you better move because she's gonna move on And so then like within minutes apparently I he sent me a text and just said he got covid today or yesterday or something So we couldn't get together today But he said I'm gonna get a PCR test. I'll be fine by Friday And so I'm like, okay, but then I'm going like, well, should I just be pulling back a little bit? I mean, I feel like it's like he's been sort of distant a little pulling but he's been kind of hot and cold And I'm hearing things like he really he was divorced 18 years ago and he Is still pretty bitter about it. He was real I think I told you this is interesting because you always say, you know, whatever however their answer is about their x He was like, oh, yeah. Well, it was really difficult a lot of financial situation, but um, you know, it was, you know It is what it is, you know, and then he kind of he played it down So I thought well that was good, but according to my friend he was he's still it's like she said It's like it happened two years ago and he's really upset about it And so I'm wondering I'm just seeing remember we talked about like that how charged is the charge, you know I think this is a real big charge and I'm wondering my my intuition is going like Run but I don't know if it's me saying my intuition saying run or if it's me being scared of getting hurt again Should I should it's interesting and by the way, um, just for everyone listening the reason why I let jill uh I'm gonna use the word ramble, but you didn't ramble um that I allowed you a little more Latitude and sharing the story I remember a place the word ramble because many of you women when you talk to me you ramble All I hear is what what what what what so thank you for being articulate here. Okay with that said, um Is it your intuition or fear? That's why I'm at wanting to figure out is So, you know what you think about this for a moment and let's just play with this for a second Does it matter? Oh No And why doesn't it matter? Because it would be the same end result Yeah Well, if you're in fear Okay, if your intuition says run you run, okay, or when we say run just we'll say pass or next. Okay That's the intuition saying that okay pass or next but you're going well is this fear. Okay, so if it's fear What is the fear telling you? It's gonna he's going to he's always busy with work like he's he's even gonna get more busy because he's trying to build his business up here again and he in surgery and so If this is the best if this is the best he's gonna do like I mean in terms of like he's showing up as much as he can Time out time out. Okay. Is that fear? Or is that a rationalization? Could be a rationalization. Yeah, because you're just rationalizing what's going on So what let's go back to the fear if you're afraid. What are you afraid of? I'm afraid that he is going to take me for granted at some point because right now It's like, oh, she'll always be there and then I can just work and not and not have to worry about things Is that fear? Yeah, it's like the fear of being being Not important to him. Okay. By the way, I want to give props to brian for the $20 super sticker Thank you for the love brian. We appreciate it That means we're only 25 dollars away from our goal tonight. Okay, so thanks for the love So jill If it's fear or intuition does it matter? I guess it does because I need to figure out whether if it's if it's fear I need to work on what i'm afraid of Okay, and maybe it's nothing Okay, so Are you afraid of him or are you afraid of putting yourself out there? I'm not afraid of putting I put myself out there. Okay. I'm working. So really This isn't you sabotaging anything then no no, it's your really it's most likely Your intuition that's going beep beep beep beep beep And then what we do is we rationalize it. We make up stories. Okay to to validate that fear and then we start thinking Oh, I'm sabotaging this experience instead of just going, you know what something doesn't feel right And you know what I don't need to figure it out I just what and to the extent that you pull back you disengage from investment Okay, and then if he reengages investment then you go, you know what do I really want to do this now? Here's where the ego comes back and says hey, I'm in Buenos Aires.  What's the definition of insanity again?  Well, some that's a that's a great phrase But then someone else came up. You just never know. Okay.  Okay, but we hold on to these one time that it might happen In fact, she even talked about it and drew Barrymore talked about it in the movie. Um He's just not that into you. So, um You know when we really if you really want to live in flow, okay, you've been following mac con, okay? Yeah, love it. You really want to live in flow than just living your into trust your intuition You don't need to make up stories about what's going on. Just go, you know, it doesn't feel right I'm just gonna disengage Okay, because this feels like so much just like discomfort like dis ease like this just like oh Not disease but dis ease this. Yeah. No, I got it It's like oh one minute. I get a text the next minute.  I'm just curious Oh, I like that. I mean, it's a it's it. You know what?  I'm sorry. It's a it's a passive aggressive comment, but it's you know, I mean, I don't I think there's a deeper situation with him is that he lost a lot of money in his divorce And now he's trying to make up for it. I think subconsciously he he's He's punishing himself a little bit because he he did he did it happened and it's a long story But I think that's what's happening and so he's working excessively and You literally Can say you know what I've observed from you It's just an observation. I have tell me how this lands with you Literally say exactly what you just said because I don't remember it verbatim And see how he responds to it Oh, oh, right like duh like just straight up right say what it is Let me just keep it to myself. Oh, yeah, that's a great idea What do I have to lose nothing? Yeah, you got nothing to lose Thanks. All right, jillie. That's great. Appreciate it.  I'm in my pajamas. So you need to get it on here All right, melissa wants to get in your pajamas and join us. Thanks jill big hug. Bye. Good night everybody. Good night All right, so let's see what we got here Valerie Why does a ghoster return then disappear again?  Okay, let me give you an analogy. This is a crude analogy, but where's the picture? There's callin right there my son callin Okay I think he was 14 years old Halo had just came out and they were having a midnight halo is a video game for those who you don't know Halo's a video game and they um, and it was on sale at best buy, but it didn't come out till midnight So what people did is they waited in line to get the game and it turns out we got there at like three in the afternoon Okay, midnight right three in the afternoon. There was already 20 people in line By 1159 there was 3000 people in the parking lot. I mean it was like a football field long 20 people deep Or 20 people wide. Okay, and he gets this video game And he's all excited He's just excited. He's playing the game playing the game playing the game Until he stopped and put it up on the shelf It calls me up dad. It was a new game called duke nukem Gotta get it. Gotta get it midnight. This was at game stop.  He says yeah when i'm bored I'll just pull out it pull it off the shelf and play it See, okay. How's this relate? Played the game got bored put it up on the shelf See men who ghost Always think you're like the video game on the shelf I could just go pluck it at any time and put it back in the in the in the game cartridge.  That's why they do it. Just my perception on that anyway um Anyone wants to join the hot seat and ask me a question about that, but that's my response to that um pest says American men and women are as Are as too spoiled when war breaks out our soil You will see the focus switch to total survival good men will rise to the top like cream till then You know the minute that happens i'm fucked because i don't you know listen i i don't know how to i don't know how to fight I was never prepared. I don't know any survival skills.  It's just the reality of life That's my perception of that anyway um Jill says thank you for allowing her to rant you're very welcome. Hope you provided We provided some value for you um Ardley says Jill Collins connections Thank you for sharing your emotions of having a man who puts you first is important Then listen to it if it's something you prefer amen All right Ardley says well my goodness jonathan asley. This is powerful insight. Thank you so much. I appreciate that Thank you. Thank you Um, there was a personal question that came up earlier one question. I asked why while dating is how many Would you handle zombie apocalypse?  I'm just very aware of who I am as a person. I was never trained Most guys were never trained, you know where we might have some basic survival skills But most of us have not been trained um I saw this earlier question come in personal question By the way, if you have any personal questions, you're more than welcome to ask towards the balance of this video How much are you spending per month for dating apps? I'm so old-fashioned. I'm struggling at the idea, but how um by idea how Well, anyway, okay, so I paid let me just give you exactly what I paid I joined bumble and hinge and I paid the 99 dollars for a six month So that's uh 200 dollars divided by six. That's about 35 dollars a month for that I joined match.com. I got a discount. Um, I paid 30 dollars a month I guess, you know 28 dollars a month for that. So now we're at 58. Is that right 58? 60 and then I joined millionaire match, which is another 38 60 so roughly I've invested a hundred dollars a month in my prospecting I mean, that's by the way, that's nothing hundred dollars a month to invest in your love life is nothing So, um, I don't think that's a lot to spend. Okay. That's just my perception. Anyway, all right Diane is in the house and she wants so she's gonna be live with us Hey What's uh, what's what's going on there? I'm with my family. Okay. Well, we can hear that Are you just saying hi because I want just saying hi, that's all okay Well, can I reach into and give you a big gigantic shot the mirror? Sure. Thank you. All right. Thank you for joining. We appreciate it Wasn't that sweet she came on just to say hi that's very sweet. All right um Jonathan, what are your thoughts about? Layer bonding and how to heal what's layer bonding most influencers talk about it from a standpoint of shame towards women who no longer have hymen prior to marriage Hey google What is layer bonding? Oh Hair bond pair bond. Okay. What are your thoughts about pair bond? I just saw by the way. I'm reading it properly. It says layer bond pair bonding Uh, what are your thoughts on pair bonding on how to heal most influencers talk about it from standpoint of shame um Hey google What is the definition of pair bonding? According to wikipedia in biology a pair bond is the strong affinity that develops in some species between a mating pair Often leading to the production and rearing of offspring and potentially a lifelong bond Hair bonding is a term coined in the 1940s that is frequently used in sociobiology and evolutionary biology circles Okay, so I I'm all for pair bonding I just don't understand the balance of the most influencers talk about it from a standpoint of shame Towards the women who no longer have a hymen. I don't get that rose. I mean, I just don't know what influencers talking about so I apologize i'm not um I don't know how to respond to this because I don't know what those influencers are talking about so um But pair bond and well to me. Okay, so I said i'm for it. Let me be clear what I am for I am all for conscious relationships intentional relationships. I'm all for two people you know co-creating a significant relationship together that leads to um Leads to either living together or getting married. I'm a big proponent of that I'm just a big advocate for that. So to that extent. I'm um very all for it.  We're in the midlife category We got all broken hymens here and we got vaginas that have pushed out a baby most of the time. So, um I'm just that you know just not that interested in what a bunch of 20 gen z's are talking about Okay, um pump pump pump pump I'm the one who said in a profile. You must like women as people you said that was cynical why I'm the one who said in my profile.  That's almost a that to me is a cynical statement. Okay. I don't know the necessity for it Like why do you need to put that you must like, you know, you know, you must like women like Do you like do you think people that hate women will read that and go? Oh my god I shouldn't reach out to her because she only wants she only wants a man who likes women I mean a person that's a woman hater is not going to see it. So it's a to me It's both moot, but it's also meaning that you've been hurt by somebody who you believe doesn't like women and now There's a projection of that Miss leila you may disagree with me. I'd be curious to hear what other people think about what I say is that cynical is that Or what's the value for doing putting that up? I'd be really interested to hear what other people say about that um so anyway, um Women are more emotional than men true fact women and men are different and humans are complex differing journeys body chemistry exactly Uh, oh, yeah, by the way lisk. Oh, she brings up a good point Actually, a woman hater will take that as a challenge.   So why There's no benefit. There is no benefit of putting that on your profile. Okay. That's just my opinion Paul tree says it's just negativity in your profile. You're right, jonathan. Thank you Um, that's kind of my take on it. It's kind of cynical You know, it doesn't it doesn't serve you it won't benefit you but You can disagree with me. That's okay.   Thank you for being you carrying on. Thank you so much Um, arly says and by the way, these are other people saying this. Uh, miss leila Uh, jonathan, it came across as being cynical to me as well. The misogynistic will definitely take this as a challenge Not that you want them to take it on as a challenge. So, okay, good. We got that covered Okay, why are you guys talking about circumcising women? All right. We're we're in the united states. I don't believe that happens arly goes on to say Yes, conscious relationship co-creating a significant relationship leading the marriage is what I want as well. Amen Um, windy says as long as you're open to lean jonathan, you will serve Okay, I don't know what that means, but thank you all right Come on. Let's oh, we just got a new member. Melissa just joined. Okay folks Right next to the video There's a little spot. Wait, let's open up a video here um Um jonathan asley will turn down the volume so you don't hear this but right next to one of my videos There's a little There's a little join button you can join Oh, wait, you can join somewhere.  There's there's a join button. Okay, you can join the membership here It's only $2.99 a month. It supports our cause. It allows me to do what I do We're stoked that melissa join. Let's give her some props Love to anyone who joins tonight. I'm just going to give a shout out of a lot of love. Okay Chrissy says Uh jonathan, thank you for the analogy of your son with uh games He would put on the shelf that aha light turned on Turned on with that. I'm so happy Chrissy that turned you on There's taja a lot. Okay. No as people jonathan No as people jonathan. I don't know what that means But I think you're referring to the thought that I thought it was sigin cynical. I guess you don't but that's okay We're all by the way folks we all get to do what we want to do well to some extent. I I do believe Um do what you want to do so long as you're not doing harm to another that's kind of my philosophy anyway Um Jess says I don't see it on my phone. Um, just there's a space to join The membership.  Um It's underneath it's right next to my name or something like that, but it says join. Okay Okay List says something just must like women as people as opposed to women as objects Hmm. I'm still not a fan of that but that's certainly a little bit. Um That's a little bit more direct. There's no doubt about it. Uh, that's a little bit more direct River chick Question confront a ghosted you've been dating on and off for four years Okay, folks, that's not a question or a ghost or confront Confront a ghost or who you've been dating on and off for four years Folks, why do people look at I I am guilty of a non-again off-again relationship Can I tell you what the definition of insanity is? During the same thing over and over again expecting a different result Oh How crazy are we humans? I'm guilty of it Oh list wants to say it's right next to the subscribe button on my videos to join Uh Hardly says join is between the name and the subscribe button folks. We'd love it if you join we'd love to have some more love I'll give you some props tonight okay, um Um McCoy says I've always say don't put anything out there that might Seem to challenge for people who like causing issues. You will get what you you know, it's interesting I was reading when I prepared my hey, do you guys want to hear my uh bumble profile? Okay, let's okay. Let's have some fun here Um because I wrote something and I asked one of my girlfriend She goes oh that's kind of passive aggressive when I say girlfriends a female friend of mine, but I will read you my Profile from bumble. Do you guys want to hear it? Okay? About me okay, here's my about me page. Okay For the past five years after losing my son I've been on a deep exploration to find out who I really am beyond fear and ego A journey of self-love speaking a marriage-minded woman who wants to explore the depths of love I go on to say um Swipe right if personal development and spiritual practices are important to you Including plant based journeys to explore deeper consciousness and expand to the divine and I go on to say a non-negotiable You must have connection with source or spirit And a desire to heal from childhood wounds and adult traumas basically to grow Emotionally as a person and as a couple And pro and con of dating jonathan. Okay, here's a pro and con Pro high emotional IQ and good relationship skills con. I like to process everything That's my bumble profile. What is my uh hinge profile say I'll just read that because it's kind of the same but slightly different Uh, oh you you're gonna like this I'm looking for someone who's ready for a fully committed relationship Where we can spend three or four days and nights a week together doing shared activities Hobbies mutual interest spending time with family and friends traveling together teamwork building skills both in our personal and professional life Intimacy both physical and emotional intimacy where we can either move in together or get married I would like someone who wants those same things Is it you let me know So that's the recording in the hinge profile.  We're a fit as a sapio sexual I'm attracted to an inquisitive woman who's interested in expanding mutual consciousness personal development And spirituality are my jam my love language Words physical touch and quality time as a leo. I love words of adoration What can I say? I like my main stroke with words and touch quality time as well with an empty nester or no children That's my profile Um Anyways, I thought I did you find that interesting. I'm curious to hear Uh, one of our facebook members says can we copy that? Okay, if you join for those that are in my group called midlife love mastery There's a link below to join my private group where you can have direct access to me on a regular basis through a facebook page and um And a once a month webinar in fact will be holding our our monthly q&a call next week I will cut and paste My profile on I will put it on the midlife love mastery page. So in the link below join midlife here folks here If you want to join midlife love mastery Join my vip group go to jonathan asley dot com forward slash midlife love To join my private group jonathan asley dot com forward slash midlife love to join my private group and you can have direct access to it there Jill says that's very interesting Kia says I would love to come across those profiles sapio sexual Yes, for those that don't know what sapio sexual means it's people that are intrigued with the mind and the way people think Uh vila says I love it great profile. I like it interested too. Ardly says I love it um, elissa says whoo Trista says that's cute Hey folks I appreciate the love tonight. You guys have been fantastic. Um It's been an hour. I've been great It's been a it's been a privilege to allow me to share with everyone tonight. I hope you found value in this I'd like to hear your thoughts post a comment below. I'd like to hear what you thought about it I do my best to read all the comments as always if you find value in my videos Please hit that like button. Please share this video. Please subscribe to my channel and hit that notification bell as well All right, we're gonna wrap up this video as I always do first. I've given myself a big gigantic job at the bear hug I'm gonna reach into the camera and give you a hug of love if that's okay I'm gonna ask you to turn to someone a pat a teddy bear a pillow and give enter them a hug of love Because hugs are a great source of love and let's face it. We could all use more love in our lives I want to thank mccoy and our facebook group members and liske and biva and kia and ardly and jill and melissa our brand new member and trista and river chick and b and Tal yet taja And by the way, thanks for that brave question. I really appreciate it sharing your truth. We really appreciate it Anyway shirt fire, uh, let's see who else marianne and uh beach lover and jess and uh, liske everyone big hugs Thanks a bunch wishing you a fab evening. Take care. All right, you be well


Hello, good afternoon. Welcome to the J main problem solving session. So those who have joined in the session I would request you to type in your names in the chat box so that I know who all are attending this session Moreover just a brief up on what are these topics that I'm going to talk about today So we are going to talk about trigonometry with special focus on properties of triangles We are also going to talk about topics related to permutation combination and a bit of coordinate geometry So many of you had requested me to hold a session on these three topics so this topic is exclusively on these Problem solving for these topics only So those who have joined in the session, please type in your names in the chat box. Hello. Good afternoon, Vaishnavi All right, so let's get started with the very first problem of the day The number 24 factorial is divisible by Which of the following options? Rotten, Sondarya, Shruti Those who have written computer science exams yesterday hope everything went well Good, good to know that. Again, let's try to solve all the questions that you see today well within three minutes The lesser the better. Yeah, so I'll wait for response to come at least from three of you before I start solving the question Anyone? Okay for this question, I'll just give you a hint We all know that coefficient of any prime number P in n factorial is given by the formula GIF of n by P, GIF of n by P square GIF of n by P cube and so on till we start getting zeros correct Now look at the numbers that we have over here all these numbers if you see They're all made up of the prime factors 2 and 3 correct So try to see or try to find out What are the what is the exponent of the prime number 2 in 24 factorial and what is the exponent of the prime number 3 in? 24 factorial Okay, and let's say to see which of the following options is the best fit option for 24 factorial to be divisible by so if I talk about e2 e2 of 24 factorial that would be 24 by 2 24 by 2 square 24 by 2 cube 24 by 2 to the power 4 and beyond that there's no point going because I'll start getting zeros after that Right, so that will be around 12 6 3 plus 1 Right, that's going to be 22. So from 24 factorial we can extract The prime factor to 22 times Okay, let's talk about the exponent of the prime number 3 in 24 factorial so that will be 24 by 3 24 by 3 square which is 9 24 by 3 cube that would start becoming 0 correct So that will be 8 plus 2 only which is 10 So I can write this as this into 3 to the power of 10 correct, okay Now if you see we can make a 6 maximum of 6 factor can be made maximum 10 times so option 1 cannot be correct Okay Now let's try to make 24 Okay, to make a 24 I would need a 8 and a 3 correct, so we know that 24 is made up of 2 cube and 1 3 correct now Given that I have 2 to the power 22. I can extract a maximum of 2 to the power 3 7 number of times And of course 3 can also be extracted 7 number of times and we would be left with 1 2 and of course 3 3's right, but anyhow, this is going to be 24 to the power of 7 into 54 you can call it that means I can always extract 24 to the power 6 from this because if this number can divide if this number can divide 24 factorial so can 24 to the power 6 can okay, so option B is definitely going to be the right option So I am going to stop here because just a single option correct question. Is that fine? Hope you all have recalled this formula, which is useful Yes, option B is correct Kushal. Absolutely Let's move on to the next question. Now simple one find the value of 35 c8 Right plus summation of 42 minus rc7 from r equal to 1 to 7 and summation of 47 minus hc40 minus h From s equal to 1 to 5. I think this is an easy one because you have done this in the very Initial part of your permutation combination chapter Let me remind you once again. We are going to focus mainly on permutation combination Solution and properties of triangles Including a bit of trigonometric equation as well as a bit of coordinate geometry with special focus on circles So how many of you are writing the GMN exam on April 8th morning session? Anybody who's taking it on April 8th morning session. Oh Great. Okay. So just two of you. Yes guys are waiting the answer for this So we have been given 35 c8 and This is going to be 41 c7 40 c7 39 c7 38 c7 37 c7 36 c7 to 35 c7 Okay, and here we have we can actually write this term as 47 minus sc7 So that's going to be 46 c7 45 c7 44 c7 43 c7 till 42 c7 Okay Now the formula that I'm going to use over here is the Pascal's identity this says that Ncr minus 1 plus ncr is n plus 1 cr right So if you club the terms 35 c8, which 35 c7 Okay, so these two terms are going to generate 36 c8 Correct. So I'm going to get 36 c8 So 36 c8 and 36 c7 is going to give me 37 c8 Right, then this will give you 38 c8 39 c8 40 c8 41 c8 42 c8 43 c8 44 c8 45 c8 46 c8 47 c8 so answer is 47 c8 which is going to be your option number D. Is that fine? So, please do not forget this very famous and useful identity on binomial coefficients ncr minus 1 plus ncr is n plus 1 cr Great, so first one to answer this correctly or Spurik Well done. Let's move on to the next question number three 18 guests have to be seated half on each side of a long table for particular guests desire to sit on one particular side and Three others on the other side the number of ways in which the sitting arrangement can be made is which of the following Okay, anybody else So far this site has responded All right, so let's discuss this So first of all, let's say the four particular guests want to sit on that side where you have round chairs Okay, so let's say four guests want to sit on this side and Three particular guests want to sit on that side where you have square chairs Now you are not choosing them. They have already mentioned that there are some particular guests Okay, and one particular side. So you are not choosing them because they have already been decided correct yes or no now let's say these four guests have sat in these four chairs Right, so obviously we have to fill the side. Let's say I call this as side a and side b So I have to fill the side a with five more guests correct and out of 18 Okay, let me make let me make three guests also sit on this side So let's say this chair is gone this chair is gone and this chair is gone now out of 18 4 plus 3 that is 7 have already been seated that means 11 of them remain and Let me start by filling The side a of the table. So I need five more people to make it a set of 9 So I can choose it in 11 C 5 right and Whatever people remain they can be sent to the side B So if you want you can write 6 C 6, but this is immaterial because that's going to be water Okay But on each side we can now arrange the nine guests who have who are seated So side a the nine guests can be arranged in nine factorial ways side B also nine guests can be arranged in nine factorial ways and Therefore your answer is going to be option number B Okay, let me tell you this is your Adi Sharma question. It's a very simple one. Let's take another simple one The number of arrangements that can be made with the letters of the word Mathematics in which all the vowels come together Okay, remember the vowels are a e a I in this So a e a I So M M T T H C S so these are the vowels. These are the consonants So how many arrangements can be made with the letters of the word mathematics in which all the vowels come together very easy question I think you should be all able to answer this within 30 seconds Okay for C Oh B, okay Anybody else sigh perfect kushal. Okay, mostly people are going with B So this we are going to apply a string theory. We're going to tie this up So we have one two three four five six seven eight alphabets But out of that, I think two M and two T's are repeated And not only that you can make an inter arrangement of the vowels that can be done in four factorial divided by two factorial because two is repeated So that's going to be eight factorial nine four factorial by two factorial two factorial two factorial guys Let me tell you these are all very simple questions. I think they all come in the beginning itself later on you realize Questions are becoming slightly more difficult So you have to save your time and energy in these questions Again a simple one Question number five the letters of the word random are written in all possible orders and these words are written out as in a dictionary Find the rank of the word random Again should not take you more than 30 seconds Okay Alright, so let's slide down the number these letters in alphabetical order, which will be a d m and oh, okay A d m and or that's the alphabetical order in which you can write this the number of words beginning with a that would be five factorial But D also is five factorial with m also will be five factorial with n also five factorial with o also five factorial right So it's almost five times five factorial. That's going to be 600 Okay, now let us begin with our the first word will be Okay, our a random also start with our a so we'll have our a d and For that that will be three factorial words then our a M That also will be three factorial words then our a n Random also starts with our a n. So I have to fill the next one in order. So our a and d Okay, random also starts with our a and d right So I have to fill the next in order So our a Nd is gone. So next word will be m o. That's one and then our a and d o m That's another one. So let's add them up. So that's going to be six plus six twelve twelve plus two fourteen So the rank of the word random is going to be six one four that's option a very simple simple question and Most of you have done these type of questions before as well Next let's talk about this question question number six the sum of all five digit numbers that can be formed using 1234 Five when repetition of digit is not allowed. So we have to find the sum of all digits Some of all five digit numbers Okay anybody else All right, so let's see a five rated numbers. So how many of these numbers will end with a five? We all know four factorial such numbers will end with a five How many of them will end with a four again for factorial? How many of them will end with a three again for factorial and with the two is four factorial and with the one will be four factorial correct? So if you add all the units digit That's going to be one plus two plus three plus four plus five into four factorial right So that's going to be 15 times 24 15 times 24 is going to be 360 This is just the sum of the numbers or some of the digits in the units place right In a similar way can I say some of the digits in the tens place will also be 360? But since they are occurring on the tens place, they will have a place value of 10 correct, so you'll have 360 as the sum of the numbers in the units place Same would be true for the sum of the numbers in the tens place But I will be multiplying it with a 10 because of its place value of 10 So in a similar way we'll have 10 square That's the sum of the numbers in the hundreds place then 10 cube Right the unit 10 hundred thousand and this will be 360 into 10 to the power 4 Right right, so this is going to be my sum Okay, so this is going to be three six zero followed by four zeros and Again, we'll have three six zero followed by three zeros Again, three six zero followed by two zeros and finally three six zero. So that is going to be zero Six, I'm sorry. I think yeah, I made a mistake here. So there'll be a three six Double zero over here and three six zero. So zero six nine nine nine nine three That's going to be option number D in this case so yes Option D is correct and the first one to get this correct was Saundariya. Well done Let's move on to the next question The number of triangles whose vertices are on the vertices of an octagon But none of whose sides happen to come from the sides of the octagon Okay, this is a question number seven for you. So Please mark your response against this Yes, exactly. So they are made out of the diagonals Okay Okay, so I have changed the answer Kushal says see What about others? Okay, so first of all if you don't have any restrictions how many triangles can be formed So number of triangles without any restriction that would obviously be eight C three, right? Right. So you have to choose three vertices from eight of the vertices Right, that's eight C three Now let's subtract those cases where I find alpha I form such a triangle which has one side common Okay, which has one side common With the octagon. So first of all I can choose one side itself in eight C one way, right? Okay, so let's say I choose this side. Let's say I choose this side Okay, now exactly one side when I say one side means exactly one side Okay, now for the rest of this vertex I mean two of the vertices are already fixed for the remaining vertex. I cannot choose seven and four Correct. So I have to choose one from eight one two or three that can be done in four C one way Right. So I can say a total of 32 triangles would be such that it has exactly one side common with the octagon Sounds good Now what are the total number of triangles which has got exactly two sites? Let me not use the word exactly over here. It's just two sites Okay Now in that case you have to choose two continuous locations Right, so you can choose one two three. I can write it down one two three two three four three four five four five six five six seven six seven eight Seven eight one correct. So let's count it one two three four five six seven and I can also have eight one two Right, that's eight. So altogether eight such triangles are possible So now what I have to do is I have to do one Minus two minus three to get exactly those many number of triangles which has got no sites common with the octagon So that's going to be eight C three eight C three is going to be eight into seven into six by six Which is going to be 56. So 56 minus 40 is going to be answered and that's going to be 16 So option number D is correct next again a simple question question number eight the number of odd proper devices of Five zero four zero all right. So first. Let us factor is five zero four zero Okay, so five zero four zero can be factorized as two to the power four Three to the part two into five into seven now if you want all the factors to be odd, you should not select any factor to right So it's like selection of None or more objects from Three five and seven which are present in these following quantities. So think as if you have Two threes present you have one five present and you have one seven present and you have to select None or more from them So how many ways can I select a three I can select either one or a two or none So there are three ways to select a three Okay, that is nothing but two plus one In a similar way the number of ways to select a five will be one plus one a number of ways to select a seven will be one plus one Right, you understand why an additional one is over here because you may not even select it. So that's one more case right But let's if you don't select any one of all you are actually selecting one and that's actually Not a proper divisor. So I have to subtract the one So the answer is going to be three into two into two minus one. That's going to be eleven and That's going to be option C. That's correct. Is that fine next There are five balls again back to back the ninth question on permutation combination There are five balls of different colors and five boxes of colors same as those of the balls the number of ways in which The balls each one each in a box could be placed as that exactly one ball goes to a box of its own color Okay, okay, most of you are going with 9b. So let's say we have Boxes of these colors Okay, and even balls of the same color right violet indigo blue green and yellow now the question says the number of ways in which The balls one in each box could be placed says that exactly one ball goes to a box of its own color That means only one ball goes to the box of its own color Rest all the balls are in different color boxes. That means no other ball can go to the Box of its own color right? So it's very obvious that let's say I choose a ball which I want to send in the right color Let's say V goes into V That means the rest four should be deranged correct, so we have to derange these four balls and We know the formula for derangement. That is equal to n factorial 1 minus 1 by 1 factorial Plus 1 by 2 factorial minus 1 by 3 factorial and so on till minus 1 to the power of n 1 by n factorial, correct, right? So these four balls can be deranged in This way, which is okay So first two terms will actually get cancelled so 1 by 2 factorial minus 1 by 3 factorial plus 1 by 4 factorial that's going to be 12 minus 4 plus 1 that's going to be 9 ways correct for each of these nine ways Right each for each of these balls there are nine ways to derange the others So your answer is going to be five times nine. That's going to be 45 Option C is correct. I is nobody got this correct Surprisingly, is it clear now? So your answer is just five d4 d4 is nine. That's going to be 45 next 10th question The number of ways of number ways to give 16 different things to three persons ABC so that B gets one more than a and C gets two more than B is This should be easy Absolutely, so let's say a gets x items B gets x plus one items and C gets x plus three items together. They should be 16 items So it's very obvious that three x plus four should be 16 So three x is 12 so x is four Right, so a gets four items five items and seven items correct So the number of ways to distribute is 16 C4 Into 12 C5 right if you want you can do 7 C7 as well Right, that's just going to be 16 factorial by 4 factorial 5 factorial 7 factorial That's going to be option number a It's a less than 10 second problem guys Let's now take up some problems on Trignometry find the values of x satisfying this trigonometric equation Okay, again, the best way would be to just put these values Pi by 3 pi by 6 pi by 2 pi by 4 etc and see which of them satisfies Okay, but however if I have to do this in a rigorous way I would first try to convert cos of 2x as 2 cos square x minus 1, okay and Let me bring these terms out to the left-hand side so this will become negative of root 2 plus 1 by root 2 Times root 2 cos x minus 1 okay equal to 0 right Now this itself can be factorized as root 2 cos x plus 1 times a root 2 cos x minus 1 You can take root 2 cos x minus 1 as common correct and you'll end up getting root 2 cos x plus 1 minus 1 minus So this gives you root 2 cos x minus 1 times 2 cos x minus 1 equal to 0 So your cos x can be 1 by root 2 or your cos x can be half But in the question it is said that cos x is not half So this is rejected So we have to write the general solution for cos x equal to half, which is x equal to 2n pi plus minus pi by 4 and belonging to integer An option number D becomes the right option in this case Let's move on to the next Question number 12 if the value of this determinant is 0 then b is which of the following Okay So let's expand this first.  So this is 0 So 1 plus cos of 2b is 0 Right, that means cos of 2b is negative 1 And in that case b is nothing but A odd multiple of pi Right, so b is going to be 2n plus 1 pi by 2 and belonging to integer Again, this question is just a 15 20 second question not more than that Let's move on to the next one question number 13 The smallest positive value of x and y satisfying x minus y is equal to pi by 4 And cot x plus cot y is equal to 2 You can look at the options and then you can see where you are getting that x minus y is equal to pi by 4 That would be a better way to solve this Yeah, it's a super simple question Option b only satisfies it, but let's say if you're to solve this rigorously. How will you solve this? Now assuming none of these is not an option. Okay, then only you can take this chance so basically if you know x is equal to uh y plus pi by 4 you can place it over here. So that becomes cot of Y plus pi by 4 plus cot y is equal to 2 Now we all know the formula for cot a plus b That's reciprocal of tan a plus b So we all know that it's going to be Tan a plus tan b by 1 minus tan a tan b So this is going to be 1 minus tan y by So let me just write as this is possible So that will become our 2t minus t square plus 1 is equal to 2t square plus 2t 2t 2t will go off. So you'll have 3t square as 1 that means T is going to be plus minus 1 by root 3 So the smallest positive value will come when you have tan theta is plus 1 by root 3 So theta has to be 5 by 6 or in fact you can say y has to be Y has to be 5 by 6 So that's only given by option b and y is 5 by 6. That means x has to be 5 5 by 12 So option number b is correct Let's move on to the next one question number 14 The number of values of x satisfying the equation mod of sine x is equal to sine x plus 3 in the interval 0 to 2 pi Absolutely, there would be no solution because Even if you take sine x as positive you'll get 0 equal to 3 if you take sine s as negative We'll get minus 2 sine x equal to 3 which cannot be possible because it's giving you sine x is equal to negative 3 by 2 zero solutions next question number 15 The number of values of theta in the interval minus pi by 2 to pi by 2 such that theta is not n pi by 5 For n is equal to 0 plus minus 1 plus minus 2 tan theta is tan 5 theta As well as sine 2 theta is cos 4 theta Yes any response Okay kushal Anybody else these type of any response Okay, so let's discuss this First of all if you look at this equation This as good as saying tan of theta into tan of 5 theta is equal to 1 That's tan theta or 1 minus tan theta tan 5 theta is going to be zero Which clearly implies Tan of 6 theta is undefined correct That means 6 theta has to be a multiple odd multiple of 5 by 2 this has to be an odd multiple of 5 by 2 right So if I just start with plus minus pi by 2 Okay So 6 theta is plus minus pi by 2 implies theta is plus minus pi by 12 I can also afford to take uh plus minus 3 pi by 2 that will give me plus minus 3 pi by 12 And I can also afford to take plus minus 5 pi by 12 because I have to maintain the interval of theta to be minus 5 by 2 to pi by 2 So these are the possible angles in this interval for which tan of 6 theta will become undefined Let me write here as an odd multiple of 5 by 2 Okay, plus minus or you can say 2 n plus plus 5 by 2, okay Let's talk about the second one So sin of 2 theta this I can write it as 1 minus 2 sin square 2 theta Okay So it's 2 sin square 2 theta Plus sin 2 theta minus 1 equal to zero Okay I think this can be factorized as 2 sin 2 theta minus 1 times Sin 2 theta plus 1 Okay equal to zero Which gives you two possibilities one is sin 2 theta is half and other is sin 2 theta is negative 1, right? Now sin 2 theta is half means 2 theta can be 5 by 6 Right, okay It can be 5 pi by 6 correct Minus pi means it can be Minus pi by 2 and it can be 3 pi by 2 Okay, but again 3 pi by 2 will exceed so I'll have to drop it Correct So theta can be pi by 12 5 pi by 12 And minus pi by 4 So I think these are the three values which are common to Or just two values are coming Minus pi by 4 is common No minus pi by 4 is not common So kushal, how are you getting three values? Yeah, so ideally there should be only two answers Do let me know if I'm missing out anything Pi by 12 is common So this is common Oh, I'm sorry. Sorry. Yeah So minus 3 pi by 12 is minus pi by 4. So yes, all the three values are common. That's why option number d is correct Okay Well, this was also an easy one, but should not take you more than three minutes Let's start with some problems on properties of triangles Consider a triangle a b c let a b c denote the length of the sides opposite to vertices a b and c respectively Suppose a is 6 b is 10 and the area of the triangle is 15 root c square units a c b is obtuse And r denotes the radius of the in-circle then r square is So this triangle is not drawn to a scale. Uh, remember the c is an obtuse angle Okay So what do I need over here? I need the in-circle radius. So which is known to be delta by s correct Hope everybody knows the properties of triangle basic formulas correct Now, how do I know s? I know a I know b But I don't know c So unless until I know c, I cannot know this right Now first of all, I'll use the Information given to me that the area of the triangle is 15 root c square units. That's half 10 into let's say I call this angle as c for the time being so half 10 into 6 Sign c is going to be 15 root 3 correct That means sign of c is going to be a root 3 by 2 So c can be 60 degrees or c can be 120 degrees But I will reject this because it has been categorically mentioned that c has to be an obtuse angle. So c has to be 120 degrees correct once I know my c Let's say I want to know my small c I can use the cosine rule cos of c is equal to 10 square plus 6 square minus c square by 2 into 10 into 6 And cos of 120 is negative half So that's going to be negative 60 Is going to be 136 minus c square correct So c square is going to be uh, if I'm not wrong 196 196 means c is going to be 14 So this is 14 s is going to be 15 So r is going to be 15 the root 3 by 15. That's going to be root 3 So r square is going to be 3 and hence option number c is correct Surprisingly only one of you could solve this Let's talk about the next question Question number seven Yes, can you see this we know Okay, so Maria says option c Okay, so let's discuss this. So first of all Let's take this condition into our account So this is 3 sin a cos b is equal to cos a sin b right And this is already given to us one fourth So I can say sin b cos a is given to you as one fourth Now if I just have to write the formula of sin a plus b That's nothing but sin a Cos b plus cos a sin b That would be going that would be Going to be one by four plus three by four. That's going to be one in other words a plus b is going to be 90 degrees Which implies c also has to be 90 degrees Which clearly means it's a right angle triangle at c right Again an easy one. Let's move on to the 18th question In a triangle a b c a d and b are the medians drawn to the angular points a and b respectively Angle d a b is twice of angle a b e is equal to 36 degrees each ad is six units Then the circum radius of the triangle is Okay Anybody else Guys, can you all see the screen? Okay, so let's discuss this So it's obvious that this angle has to be uh, 54 180 minus 54, which is going to be 126 degrees, correct Let's say this point is your centroid that is g We all know that a g is two third of ad So let's apply sin law Or sin rule On triangle a g b So can I say a g by sin 18 degree will be equal to a b by sin 126 degrees In other words, I can say a b is equal to sin 126 degrees By sin 18 degree into a g a g is two third ad and ad is six Correct. We have been given ad value as six over here, correct So this becomes four times sin 126. Now, what is the value of sin 126 degrees? Sin 126 degrees is nothing but Cost of 36 degrees, right? We all know the value as root five plus one by four correct and sin 18 degree This is root five minus one by four So it'll be four times root five plus one by root five minus one Correct. This is the value of a b is that fine Now if I know a b that means I know small c And we know that circum circle radius is c by sin of c correct Which is nothing but If you drop the factor of two from here, that's nothing but this And c is your a b So it's going to be two times root five plus one By root five minus one cosec of c cosec of c So let's rationalize the denominator over here. So that will become two times root five plus one the whole square by four By four means two cosec c That's five plus one going to be six six plus two root five by two cosec c That's going to be three plus root five cosec c That's going to be option number b is correct So let me see who all I've got the right answer No, nobody has got the right answer guys, what's going on Properties of triangle no wonder people who are facing difficulty in this because you don't know your basic formulas And what is the approach? So please do practice this in the coming week, especially people who are writing on 8th of april next question That's question number 19 for the day if the in radius of a circle inscribed in an isosceles triangle whose one angle is 2 pi by 3 is root 3 then the area of the triangle is Always make a diagram first So it has to be ab equal to ac And let's say without loss of generality. I consider this to be 120 degrees Yes, anyone Okay, so it's very obvious that this angle is going to be 30 degree and this angle is also going to be 30 degree Okay, let's call these sites as uh, let's say A Okay, so the area of this triangle Is going to be Half into a into a into sign of 120 degree. That's going to be root 3 by 4 a square now Let's say the other side is x Okay for the timing Can you apply sign rule over it? So if you apply sign rule, I'll get x By sign 120 degree is equal to a by sign 30 degree right That means 2x by root 3 is equal to 2a Which means x can be written as root 3a right Now what is in say in circle radius in circle radius is given as delta by s So delta you already have root 3 by 4 a square S is nothing but the semi perimeter semi perimeter will be a plus a plus root 3a by 2 So by 2 means 2 will go up Correct and this r value is given to us as root of 3 So root of 3 is going to be root 3 by 2a 1 plus root 3 So root 3 root 3 goes off. So a is going to be 2 plus 2 root 3 and x is going to be 2 root 3 plus 6 But I don't need that actually because I just have to find out the value of area So area is going to be root 3 by 4 a square that is going to be 1 plus root 3 square and 4 will go off So that's root 3 plus This is going to be 4 plus 2 root 3 Hope everything is fine so far x is root 3a that's fine. So a plus a plus root 3a by 2 delta by s is root of 3 So I'm getting the answer for this as 6 plus 4 root 3 6 plus 4 root 3 is not in the options Let me just quickly cross check a plus a plus root 3 a by 2 2 goes up, okay, that's 2a Okay, I got the mistake. I got the mistake. This has to be 2 over it a small mistake Yeah So let me just Yeah, complete this again. So a is going to be 4 plus 2 root 3 a is going to be 4 plus 2 root 3 So this will be root 3 times 2 plus root 3 square That's going to be root 3 times 7 plus This is going to be 2 into 4 root 3 So it's going to be 12 plus 7 root 3. That's going to be option number c Is that fine? Guys, nobody is answering that means you are very underconfident about this chapter So needs much practice in this Let's take another one Length of two sides of a triangle are given by the roots of this equation The angle between the sides is pi by 3. Find the perimeter of the triangle Okay, Purvik, what about others? All right, so let's discuss this So let's say we have this triangle abc Okay, so let's say I have been given these two sides b and c And the included angle here is 60 degree So from this I can say b and c Are the roots of this equation. So b plus c is 2 root 3 And bc is going to be 2 Correct If I use the cosine formula cos a which is b square plus c square minus a square by 2 bc I can actually write it as b plus c the whole square minus 2 bc minus a square by 2 bc Okay, cos a is going to be half b plus c is going to be 2 root 3 2 root c square is going to be 12 minus 4 minus a square By again a factor of 4 Right So 8 minus a square is going to be 2 so a square is going to be 6. That means a is root 6 Which clearly means the parameter of this triangle, which is a plus b plus c is going to be root 6 times root 6 plus b plus c b plus c is already known to us as 2 root 3 So yes option number b is the right option in this case The first one to get this correct was Purvik Next question number 21 If c1 and c2 are two circles touching each other and the coordinate axis is And if c1 is a smaller if c1 is smaller than c2 And its radius is two units Find the radius of c2 Yeah, that's correct. So I've drawn because touching the coordinate axis is Okay, so This is the diagram as of now Uh for for that Purvik you need to solve a lot of problems today. What I'll do is I will Send you some dpp's on the properties of triangles Okay, and request all of you to complete those dpp's After that you'll feel confident about the topic. Okay, so size says 21 c is the right answer. What about others? So guys, it's very obvious.  That's going to be nothing but 3 plus 2 root 2 Correct, so the answer is going to be 6 plus 4 root 2 Option number a is going to be the right option in this case Is that fine now the same question can also be framed as There is a circle And from a point on the director circle Okay, two tangents are drawn and there is circle which touches the circle and these two tangents Correct, what is the radius of the smaller circle? They can ask you this question in the same way remember director circle Basically is the locus of the point somewhere you can draw Two perpendicular tangents so it becomes the same situation So irrespective of whether they state coordinate accesses or a point on the director circle from where you're drawing two tangents The situation doesn't change All right, let's move on to the next one Question 22 Find the image of this circle in the mirror 4x plus 7y plus 13 equal to 0 Okay, let's discuss In this case, what will happen the radius is not going to change in the image. Just the center is going to change Correct So first of all, I would like to know the image of the center which is minus 8 comma 12 About the line 4x plus 7y Plus 13 equal to 0 Okay So we know the formula. Let's say the image is x 1 comma y 1 So and let's say this point is a comma b. So I know the formula Or let me say p comma q and let's say this line is ax plus by plus c equal to 0 So x 1 minus p by a is equal to y 1 minus q by b is equal to negative 2 ax 1 by 1 C by a square plus b square correct So x 1 Plus 8 by a a is going to be 4 y 1 minus 12 by b b is going to be 7 is minus 2 ax 1 ax 1 is going to be minus 32 sorry uh ap Not ap and aq Yeah, so ap is going to be minus 32 bq is going to be 84 plus 13 by a square plus b square that's going to be 16 plus 49 So let's calculate this value over here So minus 32 plus 84 would be 52 52 plus 13 is going to be 65 65 by 65 that's going to be negative 2 only So x plus 8 is going to be negative 8 So x is going to be negative 16 Or x 1 is going to be negative 16 And y 1 is going to be 12 minus 14. That's going to be negative 2 So your center of the image circle would be at minus 16 comma minus 2 correct So these two cannot be your answer okay So minus 16 minus 2 means only option a will work fine over here Because even c cannot be your answer So absolutely correct Purvik option number a is the right option in this case Is that fine? So you can actually distinguish from the centers only so no need to go into the exact equation next question number 23 if 2 comma 4 is a point interior to this circle and the circle does not cut the Accesses at any point then lambda belongs to which interval okay Most of you have given the answer as b. Let's discuss this out See first of all If you see the center center of this circle is at 3 comma 5 Right And if it doesn't touch the coordinate accesses means radius has to be less than 3 Right and what is radius? Radius is going to be under root of 3 square plus 5 square minus lambda. So this has to be less than 3 Correct that means 5 square minus lambda has to be less than 0 that means lambda has to be greater than 25 correct Now secondly, it's given that 2.4 point is interior to this circle That means s1 should be less than 0 s1 is when you put the point in place of x and y So 2 square plus 4 square minus 6 into 2 minus 10 into 4 plus lambda should be less than 0 That means 20 minus 12 minus 40 plus lambda should be less than 0. That means lambda should be less than 32 So combining these two conditions, I can say that your lambda lies between 25 to 32 That means option number a is going to be correct Okay, so I think the first one to get this correct was Sondarya Absolutely, okay Let's move on to the next one That's question number 24 Can be a straight line passing through origin and l2 with a straight line x plus y equal to 1 If the intercept made by the circle on l1 and l2 are equal then which of the following equations can represent l1 Okay Anybody else Okay, so let's figure out the center and the radius of this circle So this circle center is at Uh half comma negative three by two correct And radius will be one fourth plus nine fourth mine. There is ten four. That is five by two under root correct now l2 is given to us And l1 let's say Is a line whose equation is y equal to mx right Now on any circle What is the length of the intercept? Let's say this is the radius Okay, this is the distance of the line Of center from the line So it will be two under root of r square minus d square correct so let's say from this circle The sorry from this line the distance of the center is going to be five by two minus If you put the center over here, it will be half minus three by two minus one by under root of two whole square Into two is that fine? So this is going to be two times Five by two and if I'm not mistaken this is just going to be uh two by That is root two square root two square is going to be two So this is going to be two into one by root two. That's going to be root two itself right so The intercept made by the circle on this line is root two And it's given in the question that The other line y equal to mx will also make the intercept of the same length So let's find out the length of the intercept made by y equal to mx per c. Sorry y equal to mx onto this circle So let me just erase everything and start with the basics. So y equal to mx So this is going to be a Half comma negative three by two so the distance will be Minus three by two minus m by two mod Under root of one plus m squared correct This will be the distance So root two will be two times under root five by two minus This I can write it as m plus three by two under root m square plus one square Okay So let's solve for m in this case So this will become half is equal to five by two minus m plus three whole square by four m square plus one Okay, so that's going to be negative of Two so plus two Is equal to m plus three whole square Okay By four m square plus one So this is going to be eight m square plus eight and this is going to be m square plus six m plus nine That's seven m square minus six m Minus one equal to zero and this is factorizable This is factorizable as seven m plus Okay So your m value can be one or your m value can be negative one by seven So it could either be line y equal to x or it could be light y is equal to one negative one seventh of x So I think option b is the only option that satisfies both these conditions So option b is correct and the first one to give this answer is Purvik So question number 24 No, sorry before that Kushal gives the answer 24 option b is the right option Let's look into question number 25 Okay Okay, yeah again, it's a very simple question guys you just have to Appreciate the fact that if you draw a tangent at a point Okay, let's say I draw a tangent at negative three comma zero Correct And is another tangent at four comma one So this is minus three comma zero. This is four comma one Okay, so we know that the normals to these lines will actually pass through the center Right, this will be a center So what are the normal to this line four x minus three y equal to negative 12 So four x minus three y is equal or plus 12 equal to zero the tangent the normal to this will be of the form three x Plus four y plus k equal to zero Now I can find the k by putting this point So this point if I put I'll get minus nine plus k equal to zero. That means k is going to be nine So the normal is going to be three x plus four y plus nine equal to zero in a similar way if I have to find out The normal to three x plus four y equal to 16 So it'll become four x minus three y plus some lambda equal to zero put the point four comma one So lambda is going to be negative 13 So the other one is four x minus three y negative 13 equal to zero So let's see where do these uh Lines meet By the way, if you look at those points itself the center is minus one comma Sorry one comma minus three One comma minus three does it satisfy this? Let's check. Let us satisfy both the equation. Let's check So one comma three satisfies this Uh one comma minus three. Oh, it also satisfies this. So basically let's not go any further No, in fact the second one also gives you the same answer. Okay, then in that case, uh, I have to also find out the radius So negative one comma sorry one comma negative three distance from To this point is going to be Two square plus three square under root Okay, that's going to be uh root 13 Right So So c is going to be So r is going to be under root of g square plus f square minus c so root of 13 Is going to be root of g square. That's one square plus nine minus c So it's very obvious that c is going to be No, everything is fine Minus c is going to be this. Yes. C is going to be 13 Is equal to 10 minus c Why am I getting the answer as? Oh the point is one comma Uh, this point is one comma three One comma minus three. Yeah So in that case my radius is slightly incorrect. So this will become a root of 25 which is going to be five. Yeah Yeah, in that case my c will come out to be c will come out to be 25 is equal to 10 minus c is going to be negative 15 So in that case option number a is going to be the right option Okay Well, great. So let's move on to the next one The angle between the pair of tangents drawn from a point p to this circle is to alpha Then find the locus of the point p Okay, just a second No, I think it's visible Yeah, can you see now everybody? So this circle has a center as minus two comma three And what is the radius radius is going to be under root of 4 plus 9 minus c So that's going to be under root of 13 minus 13 cos square minus 9 sine square That's going to be two sine alpha Okay Now if I want to find out the locus of h comma k Can I say this is root of s1? So sine of alpha would be in fact tan of alpha would be In fact, you can take sine of alpha also. You don't have to go into root of s1. You can take sine of alpha as r divided by distance of h comma k from 2 comma 3 you can write it as h plus 2 the whole square And k minus 3 the whole square right So let's substitute so your r is equal to sine of alpha to two sine of alpha So If I replace here with two sine of alpha Sine alpha sine alpha you can just cancel it off Right, so it's as good as saying h plus 2 the whole square plus k minus 3 the whole square is equal to 4 Right generalizing it you get x square plus 4x plus 4 plus y square minus 6 y plus 9 Okay, you can just cancel off this 4 So x square plus y square plus 4x minus 6 y plus 9 equal to 0 That's going to be your option number d D option is going to be the correct answer Okay, great. So first one to get this correct is sine here We don't have much time. So let's move on to the next one. That's question number 27 The angle between the tangents from alpha comma beta to this circle I'm sure this is going to be very easy question Done Yeah, that's a very simple question So from alpha beta Okay, you're drawing two tangents What's the angle between the tangents? So connect the center This is going to be your r r is nothing but your a Right, this is root s1 So tan of theta is going to be A by root s1 So theta is going to be tan inverse of a by root s1 So the angle between the two tangents will be two theta So the answer is going to be twice of tan inverse a by root s1 That's option number b. That's correct. Absolutely. That was a sitter. So let's move on to the next one That's your question number 28 for the day So from a point a one comma one on the circle Two chords a b and a c each of length two units are drawn find the equation of the chord bc Okay All right, so the center is going to be one comma one. Sorry two comma two, correct And you're drawing chords each of length two units Radius is going to be root of two correct So let's say I have These two chords a b and ac They are of length Two two units each Yes now If you see the diameter Okay, that would actually be containing your b and c because The radius is going to be two root two So that's going to meet the Pythagoras theorem two square plus two square is going to be two root two square Isn't it So from this diagram you can make out that actually your bc is the Diametrically opposite ends of this particular circle right, okay And not only that they the center and this basically are perpendicular So the line from the origin The line from the origin is containing the point one comma one as and the center both That means this line Bc is perpendicular to the given line y equal to x so this has to have a slope of negative one So line having a slope of negative one and passing through two comma two the equation will be This which is nothing but y minus two is negative x plus two that means x plus y is equal to four Correct And another quick way is to see which of the given line satisfies two comma two so only this This doesn't satisfy two comma two does it No, this doesn't satisfy two comma two This also doesn't so only be satisfied so common sense also says b is going to be the right answer So I just show you do the longer way in case You need it but in such cases you can always first check Which of them contains the center the moment you realize bc is your diameter is that fine All right, so let's move on to the next one. That's question number 29 for the day Two concentric circles of which the smallest is x square plus y square is equal to four have a difference in radii as d The line y equal to x plus one cuts the circles in real points Then d lies in the interval. Is it done guys? Okay anybody else So I think this line will always cut this in real points because if you substitute your y as x plus one You get something like 2x square plus 2x minus c equal to zero, correct And if you find the discriminant b square minus four ac that will be four Plus four into two into three That's always be positive, right? So it'll always have real roots Okay Now let's say the other circle is x square plus y square is equal to two plus d square Okay difference in radius is two. So two plus d square So in this case if you try to substitute x with x plus one y with x plus one you end up getting this So that's going to give you two x square plus two x Plus one minus two plus d the whole square equal to zero Now the discriminant of this will be b square minus four ac minus four ac This should be greater than zero That means one plus twice of two plus d square should be greater than zero Yeah So I can write this as d plus two the whole square. I think I did not take this one into account. Okay, this one will also come So this expression will slightly change. Yeah So b square minus four ac will have one minus two plus d square Okay, this should be greater than zero If I greater than equal to zero let's take Okay, this so one minus twice of one minus two plus d square should be greater than zero Right So two times two plus d square minus one should be greater than zero or divide by two And write it as root two square so that you can complete the square here itself So I can write this as two plus d minus one by root two And two plus d plus one by root two should be greater than zero Correct So d must be greater than the greatest and lesser than the least So d must be less than minus two minus one by root two and d must be greater than One by root two minus two So that is only given by option number a in this case. So option number a becomes the right option Okay, I think only poor we could answer this Okay, so without much waste of time, let's move on to the last question of the day If the lines this and this are diameters of the circle of radius 49 pi square units then find the equation This is super simple because you have been given the two diameters Obviously they will intersect at the center And radius is given as seven So just the last question before your j main exam for maths Simple one just complete it In fact, just see which of the points satisfy both the equations minus one comma one. Does it satisfy minus one comma one? No, it doesn't this is One comma minus one One comma minus one one comma minus one. Yes, this satisfies So it will have At least minus two x plus two y term and radius is seven. So radius is seven only when you have one plus one Minus of 47. So that will be minus of minus 47 under root So option number c becomes the right option. Okay all right, guys, so This might be your last session of maths before your j main exam But we'll definitely come back after j main with j advance questions Right and those questions would be of much much more difficulty level than the questions that we are doing right now A couple of things before your j main exam Please revise your chemistry very well because chemistry is going to be the game changer Okay Maths of course you need to do Couple of mock papers just time yourself out. Don't try to overdo it Because maths is quite dicey in competitive exams. So Even though you may put a lot of hard work. It may not fetch you know, um The same amount of marks which chemistry or physics may fetch So just revise your formulas. Of course today you saw that you guys were not comfortable with properties of triangles So just solve around 30 40 odd questions Well from any standard book, in fact, I will send you some dpp's also on that and that that should be fine You just have to get a hand of the formulas That means you should know your small r in terms of capital r r1 r2 r3 know the uh area formulas Right, what are the relationship between the x center radius and the in-center all those things should be known to you the basics And do not make silly mistakes. That's the worst thing that you can do If you are getting an answer correct and by mistake you mark the wrong answer That is the worst thing that can happen to you. So be very very careful Read the entire question papers can the entire question paper before you start attempting it I think this time you would have known which button is Is uh supposed to be best so that you see the entire paper. So please do look at all the questions and start with the confidence boosting questions the easier ones Okay, and you guys you should always start with your favorite subject Right So you may have more sessions on physics and chemistry, but for maths. This is the last session before your j e main exam We'll meet after the j e main with uh sessions on j e advance Meanwhile over and out from my side Thank you and all the best