on the vlog it has been a while I'm sorry about that but life has just been busy, manic, hectic I've been taking some time out all that jazz so yeah but anyway I'm here with some updates. Firstly Merry Christmas to everybody I hope you all had a happy holiday whatever you were doing however you were spending it and a huge happy new year to everybody 2023 I hope is going to be even better than 2022 I know 2022 was very very tough for some people out there obviously with the pandemic was still going we've got the NHS in crisis everybody's going on strikes the war in Ukraine poverty is happening out there homelessness is rising there is so much chaos and it feels like the world is going backwards right now instead of forwards but I really hope amongst the chaos you have found some peace joy and kindness throughout 2022 I know I have I've been very very fortunate I have to say and I feel guilty for feeling like that because I know people have struggled and actually 2022 for me has been a really good year all in all so what have I been up to lots of different things a lot of you know that I had a job change back in January I left GP and I was doing many other things so I can kind of tell you what I was doing now so I started off in January I left GP and I became a disability assessor working from home I can't name the company or anything like that obviously because of confidentiality reasons and we sign a waiver and stuff like that when we started that's why I couldn't really tell you anything about my role or vlog about it and that sort of thing which was really frustrating because vlogging is what I do and I like to share my experiences and my journey with everybody anyway I yes was a disability assessor working from home there was a number of reasons I wanted to do that it was going to give me more time to do the other things that I love so I'd also started with a private transgender healthcare company I was seeing transgender patients there was somebody that made a comment on one of my videos of my new job update that said they were very disappointed that I'd left GP and gone elsewhere and I was a wasted nurse please please please don't say that to anybody don't say that to anybody out there that wants to develop their career and do more for patients especially a vulnerable group of patients and obviously this person didn't realize that I was still seeing patients and I was still out there doing what I love they clearly don't know me they don't follow me on socials they don't know anything about my life to make that comment which is really really sad because I was actually seeing patients and I was making a massive difference to the trans community through doing that so yes please don't judge anybody for the career developments or the roles that they go into every single nurse is valid no matter what area you go into so never give up keep going guys don't let anyone put you down so yes alongside my two jobs I was doing at the time I was doing my disability assessment seeing transgender patients as well as my second role and then I was also setting up my own website called GC Health I'll put the link below if you want to have a look but it's just to help share education information and materials and things like that resources for people that want to care for trans patients so I've set the website up now it's still a work in progress don't get me wrong it's very basic but there's some resources on there about transgender patients and guidelines and resources and things like that so please have a look and hopefully that there'll be a use to you if you are caring for trans patients another add on to that was myself and George my partner if you don't know my partner George you should all know George by now we set up some webinars to deliver to students and healthcare professionals and different organisations charities that sort of thing anyone who wants it really about transgender healthcare and just given all of the educational advice knowledge and things that we have combined together me as a nurse George is a transgender man himself and together it just works really really well to give that information out there to people um so we've been doing that as well alongside of things so actually I've had three jobs going since January another thing that happened this year was I got engaged in case you didn't know I know I don't know what way it goes I'm sure I shared the story though before um but you don't know yes we got engaged so that was amazing next up my book I've been telling you for ages about my book I is finally underway it's been way too long it's been frustrating long process I started this book as a student nursing 2018 this book was finished like a year ago it was done it was finished uh sent it to the editors um and it's just been a really long process to get it finalised um I'm not too sure why the editor um has been very very slow they haven't been well and things like that so it's been a really really slow process from the minute I handed it in to this stage which is the editing stage I have a book cover ready they've showed me the chapters and what they're going to look like it looks amazing they've sent me the first six chapters yesterday to edit them and look at the edits that they've made and make any changes there was one reference actually that wasn't in there it's a good job they're looking I don't know where that reference went I think it's to do with um when I was submitting the book they wanted it all chopped up into different chapters and then the reference split up and put on each chapter and nobody had told me that at the start so at last minute before submitting I had to completely dismantle the whole of my book which was just on a word document and then a separate one for the references um I had to dismantle it all and rearrange it all so I think in that process somewhere that reference has just got removed somewhere and I've had no no doubt in the next six or seven whatever chapters there's going to be other little bits that are missing as well so but it didn't take me too long it took me a couple of hours just to go through all the six chapters make sure I was happy with everything do the little edits that they wanted um yeah it's that them six chapters should be good to go I think and yesterday when they sent me the chapters to edit I thought I'd just do a little video so you can see what I had to go through just to make you feel included in this book because this book is for you all of you and this is to help everybody you know through your nursing journey from start to finish it's going to be that you know applying to university from the get go all of the tips and advice for that personal statements interviews everything all the way through first year second year third year newly qualified nurse life and then some bonus bits at the end about lgbt and disabilities and people of color bane communities that sort of thing is included in it there's loads of different areas in this that's going to really really hopefully help manage sort of different patients as well as yourself and get you to where you want to be and just give you a little bit of a hand if you need it so here is the little video that I posted yesterday for you sorry this is going to be a little bit of a whoosh uh vlog uh but this is the video I did yesterday just to show you what's going on with my book so this is kind of how it comes um with all edits and notes and things like that so I'm just going through all of this this is one of the chapters and then I was just sent this just to see like the layout what it's going to look like uh the font and things like that um and I quite like this I like the layout I like how that looks so I'm happy with that I know how exciting is this this is so exciting um I really really hope that it helps so many people out there because nursing is tough this course is tough um and since writing the book the course has changed as well but all of the aspects that's in this book is going to be useful it's really done in a generic way so that if the course does change and things like that all these points will still be relevant so things like assignment writing how to structure an assignment and that sort of thing that's all in there you can apply that to anything um things like placement advice placements aren't going to really change much you're still going to have the same process replacements and and there's also ward specific placements as well that I've put in in there community primary care all the help and advice that I could think of to help you through it's all just really a survival guide to nursing and hopefully it's just I'm so excited for it even if it just helps one person out there my job is done with that book the only thing I worry about with the book is I don't know what the price is going to be and I don't think I have a say in it because it's with the publisher and the publisher has to set the price for how much it's cost to develop and the editors and the images and um the quality of the book and all of that I'm really worried that it's going to be a bit hefty because I know that books with publishers nursing related books can be a bit pricey sometimes so I'm hoping I'm going to get one some free copies to give away to people two I might have a say in the price I don't know I haven't asked the question I need to find out but hopefully I will have a say in the price because I want to make it affordable for everybody I'm not here to make money and even if I do even even with the money side of books I'm literally getting 5% I know so you get 10% of book sales I've split the the percentage with Annmarie Dodson those that you that don't know Annmarie she was a lecturer at my university as a student she wasn't my personal tutor or my personal lecturer but somehow the universe brought us together and we did a lot of charity work Snowden was with Annmarie bake sales that we did and all of that and she just became like family to me after I left university I still saw Ann we still did stuff together we still go to a house and things like that and meet up for lunch and catch us up and things like that so yeah she's become like family uh Annmarie she's almost like a mother it's lovely so yeah so she is getting 5% so we're splitting the costs she wrote one of the chapters in the book anyway what I was getting at was even whatever price it's set at I'm not going to make much money anyway I'm not really bothered I didn't write this to make money I wrote this book to help students and help people and that was my main aim of it it's not about money to me so if I can put it for as less money as possible that would be great anyway this video is getting to be really really long so my final update of 2022 is uh have a new job I know I've just listed 101 things that I do but I have a new job I saw another job come up and I applied for it it was for an assistant lecturer role at university and I know so many people have said to me even as a student onwards all through my I've been qualified for almost three years now and everyone was saying oh you make a great lecturer you'd be a really good lecturer why don't you go into lecturing and I was just like oh I'm not sure I could do it I love teaching I love education I love helping students I'm very very passionate about student nurses and the future of nursing so I knew it was something I would love and something that I would like to apply for and something that I'd love to do but the reason why I had doubts in the back of my mind was um I have a fear of public speaking and people think that's crazy because I do youtube vlogs and I'm really active on social media and stuff like that and people think I'm this extrovert person when I'm really really not I'm actually a massive introvert and the thought of standing in a room with eyes watching you and speaking has always terrified me and I knew that from a student nurse from the get go however as a student nurse I realized that I really loved education and I wanted to do more to educate others and stand up and speak and things like this so I knew I had to get over that fear somehow so I pushed myself and I went to spoken conferences I did um I've done guest lecturing and things like that just to get me used to it just to sort of try and help the fear I mean don't don't get me wrong I'm still terrified but it's not as bad and I can calm those nerves now and I can get over it and I can just enjoy it hopefully um but yes I anyway applied for assistant lecturer role that was a very long story around about way um at university and I'm ecstatic I I'm still absolutely buzzing I've been in the role for three weeks now we've just had a week off for Christmas technically it's four weeks um but I'm just absolutely buzzing like I mean I'm in the pinch me moment because I was like I never thought I would get this I don't know why I think it's that just that self-confidence um imposter syndrome that sort of creeps in and you say no I'm not good for this role um and actually I got it and I'm going to be doing the leadership module which is amazing I'm really excited to be on the leadership module I'm going to be I've been given the task of setting up a diversity section and delivering that so I'm really excited because obviously I love diversity I love spreading awareness for trans health and things like that and it's something we really really need in university for student nurses to give the best care possible to their patients we need diversity we need equality so I'm really really excited to be setting this up and getting it out there and just hopefully making change to the future and I'm not a hundred percent sure how much I'm going to vlog about it just because I'm very wary now that I'm on the other side I'm on the educating of confidentiality I'm very wary of giving things away that I shouldn't be and I've always been wary of things like that anyway even as a nurse I'm probably not going to be vlogging at university itself one because I don't want to give away where I'm working so I think a lot of my vlogging is going to be possibly from home from this view um I might take you around um I might do some vlogging at university we'll see what happens and how things go and progress and things like that um I know I'll be sharing some bits on Twitter because the university is very active on Twitter so I'm going to be doing a lot of twittering um so if you're on my twitter have a look go and add me and I'll add you back and all that jazz but we'll see we'll see we'll see what happens I'm really excited though um I'm at home the minute I walked through that door on the first day I was home so yes that is it for 2022 um there has been some highs there's been some lows of 2022 you know I've changed a couple of jobs we've got our cat Isaac who some of you have seen on social media on my previous youtube vlog um we've had a proposal but then there has been some lows as well we've had some unfortunately some family members that have passed away uh my my own dad as well has been very very ill this year um and I'm hope he's going to make it through 2023 um but yeah but we have had some lows but we have to try and focus on the positives of 2022 and the good things that have happened whilst recognising that we do have low points in life but it's really really important that we we recognise the struggles we recognise those low points we have our moments you know we cry we get under a duvet we kick we scream do whatever you can to just release that emotion that you're feeling and then rebuild it rebuild it and move on in a way if you can because you have two options in this life you let something eat away at you and every single day passes by anyway or you try and change things if you can and alter things and try and create a positive environment instead for yourself and keep going and I know that probably sounds really really harsh and I fully understand that sometimes you can't change things sometimes it's just the way it is um but we can change how we react to things and how we move on and just dealing with it the best we can with what we've got so on that happy note um I hope you all have an amazing 2023 and wishing every single one of you so much love joy happiness good health as well and just let's make 2023 even better than 2022 happy new year everybody


The Cavalcade of America, sponsored by DuPont, maker of better things for better living through chemistry, presents James Craig with Bula Bondi in Joe Dyer Ends a War. Nowadays, many of DuPont's peacetime better things for better living are vital materials of war, for instance, fire retardants. Engine coverings, life preservers, and the clothes of workers in war plants are made safer with chemical fire retardants manufactured by DuPont. Tonight, Cavalcade brings you a story of America, a story that foreshadows the fulfillment of an ancient promise, peace on earth. Will the promise at last be kept? Will men of alien lands and creeds now learn at last to live and work together and settle their disputes and solve their problems in goodwill and in peace? It happened once here in our own country, so perhaps it can happen for all the world. What happened here once in America is the background and inspiration for tonight's original radio drama, written by Victor Wolfson. James Craig will soon be seen in Metro Golden Mayor's Lost Angel. Cavalcade presents James Craig as Joe Dyer and Bula Bondi as Joe's mother. In Joe Dyer Ends a War. In the little town of Lebanon, Connecticut, Joe Dyer and his mother ran a farm. It is spring, morning spring of the year 1782. You finished your chores early this morning, son. Joe, I'm talking to you. Huh? Oh, what'd you say more? Joe, what in the world would matter with you?  Now, what is it? Ma, do you figure you could manage your farm with young Sy? Hmm, your brother's only 14, but I suppose we could manage? Why? Ma, I'm going away. Oh, you don't say, Joe Dyer.  I guess so. Sure. And where do you think you're going? If you don't mind my asking. Oh, Connecticut's opening up some new land down Pennsylvania way. Tain't far and they tell me it's good rich land. Oh, do they now? Mm-hmm. Pass me a shirt, Ma. Joe, there are folks that say that land along the Susquehanna don't belong to Connecticut. It belongs to Pennsylvania. There are people down at the state capital at Hartford say to belong to us. Joe, don't go. I don't care what anyone says. There's got to be trouble down there over that land sooner or later. Well, maybe. Maybe there ought to be trouble. Joe. Ma, there's only one way to get land, and that's to take it. That's how we got this whole country. That's what this revolution was all about. There'll always be that kind of trouble. Not between neighbors, Joe. Not unless somebody goes out and makes it. I'm sorry, Ma. But I'm going down there to the Susquehanna to get us a farm. So that's the way it was with Joe Dyer and a lot of other Connecticut men. They went down there to the Susquehanna to get them a farm, to stake out new living room, to clear the land, to cut the timber. Stand back, Si. Here she comes. Yep. Timber. That's the way it was along the Susquehanna. The men from Connecticut clearing the land, cutting the timber, building new homes. The men of Pennsylvania are watching the new arrivals and wondering, questioning themselves, questioning the men from Connecticut. That's a real solid house you're building there, stranger. Yep. Aimed to live in it quite some time. How many more of you fellas coming down from Connecticut? No, no. Many's got gumption, I guess. You got a deed to this land, have you? Sure. Sure I got a deed. Got my rifle. Guess that's about as good a deed as any. As the way it was along the Susquehanna, the Connecticut men clearing the land and building, the men of Pennsylvania watching and mistrusting, and the long frontier rifles standing ready by the cabin door. There, Ma. There she is. Land-sake, seems like you built it in no time. Come on in. I'll show you around. Pretty, ain't it? It's a wonderful house, Joe. A good, strong house around us, and we'll be ready for anything. In case anything happens. What do you mean, Joe? In case anything happens. Oh, you hear that? Thunder. It could blow up a storm, Ma. A man needs a good, strong house when it blows up a storm. Well, someone's at the door, Ma. Well, I'll go. No. Come here, Si. Joe, Dyer, whatever's the matter with you? You'd think we were out in Indian country. You're so jumpy. Never you mind, Ma. And you stay here, Si. I'll sneak around the back door and see who it is first. Have you heard anything down at the trading post? What's Joe Acton's a strange for? I don't know, Ma. There's a sign down there says for all settlers to be on the lookout. The lookout? What for? Just me, Joe. Come on, Josh Higgins. It's all right, Ma. You can open up. It's only Josh Higgins. Come for a friendly visit. In all this thunder and lightning? Josh Higgins, I'm glad to see a living soul beside my own two boys. Come on in. Thank you, ma'am. That thing's over at your place, Josh. Well, the funniest thing. Night before last, a brush fire started up. Any damage, Josh? No, it didn't get the house or nothing. That was two days ago. Well, this storm had just broke. Put out another fire. Only this evening. Oh, I see. What do you see, Joe? What's the matter? Ma'am, I can't figure out how two fires just got started like that same hour a day and all. If it wasn't for this rain, this last fire would have got the house sure. Looks like it's high time we got together on this, Josh. I kind of thought I'd go down to the trading post and see what the others can make of it, if you know what I mean. I know what you mean. Yeah. Want to come along? Yeah. Yeah, I sure do want to come along. Go on, Joe. Now tell us. It's about these brush fires. They're happening awful regularly and at awful peculiar times. And I don't think they're happening by accident. They want trouble. I say give them trouble. That's the ever man stand by his rifle from tonight on. And if we catch any Pennsylvania men sneaking around our cabins, I say shoot. And shoot straight. And keep on shooting. Down along the Susquehanna, the rifles weren't standing by the door anymore. They were carried to the fields and to the trading post. They were always ready at the hands of watchful men, Connecticut men. But that same night in a tavern in eastern Pennsylvania, there were other men meeting. Other men with rifles at their hands, anger in their voices. The men from Pennsylvania. No, no, listen to me. Listen to you Maxwell and see our land. Good Pennsylvania land taken over by settlers from Connecticut? No. We can't let that happen. That's not our land. Listen to me. Dear Hill. What do you mean? That land is our land. We didn't clear it. We didn't build on it. They did. The Connecticut men. These 13 states of ours are going to be a big country someday. And that's the way they're going to get that way. But men of every state clear in the land. Building on it. Not by fighting each other the way you fellas want it. When are we listening to him for? I've been up in that region over the Poconos. More Connecticut men are clearing the land, building houses. They'll be putting in seed before long. And we'll never be able to root them out. Once they're settled, I say we go up there now and burn them out. That's such a thing as law, men. There's no such law to cover steel in a land of one state from another, Maxwell. You, being law-wise, should know it. I'm in favor of going up there now. Tonight. Yeah. Come on. The storm clears. It's a warm night. The men from Pennsylvania come up along the Susquehanna on horseback. 30 men from Pennsylvania galloping in the spring moonlight. They turn north suddenly away from the river. Up to the new lands, the men from Connecticut are settling. They come to the woods just outside Joe Dyer's place. I'm glad to stop raining. It's drying off quick. Now, all right, men. After you start over there to the northwest, and the others go down the creek there, closing on either side, see? William and me will go right up to the house.  Yeah, we'll wait five minutes. Come on, let's go. Come on, William. The two men start for Joe Dyer's house across the moonlight clearing. The others separate and surround the place from the woods, starting a brush fire. They started that fire too soon. We've got to hurry.  Who's there? Get the boy over the head, Jimmy, strong as an ox. I got the woman, come on. Now we'll take him to Eastern and hold him for a few days. That'll teach him to steal other folks' land. All through the moonlight night, the men from Pennsylvania go from place to place, cleared and settled by the men from Connecticut, burning their places to the ground, kidnapping any settlers they can find, taking them back to Eastern. All through the night, the burning went on. In the morning, the settlers from Connecticut looked over the smoking ruins, charred forests. Well, nothing's left of it at all, Joe. They say this land belongs to them. And we say this land belongs to us. There are people down in Philadelphia that tell them they're right. And there are people in Hartford that tell us we're right. What are we going to do about it? My house has burned the ground too, Joe. And mine. What are we going to do about it? They got my mower and brother. They burned my godfrey. Have we a government at home to protect our rights and stand behind us? Or haven't we? It's war. That's what it is. Right, Joe. Then let's make our government stand behind us. And if the people of Pennsylvania want war, let the people of Connecticut give it to them. The affidavits sent by our settlers explaining the situation, and very well too. I pass these down the tables so the others can read them. Has there been any bloodshed, Your Excellency? The affidavits mention none. But there's been destruction, serious destruction. The lives of our settlers have been threatened. Some of them have been thrown in jail. The question we have to decide, gentlemen, is whether to send a regiment of our soldiers to the Susquehanna. Pennsylvania, of course, will answer by sending a regiment of her own. There will be bloodshed. I realize that. That's what makes the situation so serious. Your Excellency, I've been in favor of bloodshed. This issue must be decided once and for all. Now, just a minute, Mr. Curtis. Let's not be hasty. No, Your Excellency. Mr. Curtis is right. Our claims to that territory are perfectly clear. Our sovereignty as a state has been threatened by Pennsylvania. We must take decisive action. I agree. Yes, immediate action. Send our regiments. Gentlemen, gentlemen, please. Yes, come in. Oh, what have you got there, Willis?  A communication from the state of Pennsylvania. Excuse me, gentlemen. Gentlemen, I have here a communication from the governor of Pennsylvania, who's sent with a full approval of his legislature. I beg you to consider it with an open mind. What is it? Let's hear it. Gentlemen, the governor of Pennsylvania requests that we submit our dispute to a court of law. A court of law? He suggests that instead of resorting to our regiments, which, as he says, will determine nothing but who is the strongest, he suggests instead that we hold a trial to decide which state is the rightful owner of the land near the Susquehanna. A trial? Certainly an unusual suggestion. Are we to give up our sovereignty to a court? Why, what does he take us for? No, refuse the offer, I say. I say accept it. And so do I. I, for one, am unwilling to bear upon my conscience the responsibility of sending a hundred or a thousand young men to their deaths. While there remains the slightest hope that such a calamity might be prevented. With your permission, I shall so inform the governor of Pennsylvania and that we are ready to submit our case to trial. You are listening to Joe Dyer ends the war starring James Craig with Bula Bondi on the cavalcade of America sponsored by Dupont, maker of better things for better living through chemistry. In our story, which took place just after the American Revolution, the threat of open war has flared between the states of Pennsylvania and Connecticut over a boundary dispute. And as our play continues, the governors of the two states have agreed to submit their differences to a court of law. And along the Susquehanna, among the Pennsylvania men, among the men of Connecticut, like Joe Dyer, news of the impending trial spreads like wildfire. If they decide against us, we all got muskets and shots, ain't we? Well, Tom's right.  We sit there facing the judge in the court. They don't dare decide against us if they can read what's in our minds. Now, wait a minute, men. Wait a minute. Don't, Joe. Don't, Rylan. They're like dry timber, and it won't take much to set them afire. Maybe that's what'll have to happen more. Now, listen, men. Listen, I've got a better plan. I want you to stay right here, right on this land of ours. Now, wait a minute, wait a minute. You stay here in case the verdict at that trial goes against us. I want you to start in building a blockhouse. I want you to start in getting ammunition. I don't care where you get it from. Joe Dyer, what are you saying? I'm saying we're keeping that land no matter what the verdict is. That's right, Joe. Josh and me and a couple of others, we'll go down to that trial and keep our eyes on that court. If they decide against us, we'll let them know what we're going to do about it. I guess that's the judge coming in now. He looks like a fair-minded man. I don't matter how fair-minded he is, all matters as he decides the case in the favor of Connecticut. Joe, how can you say that when you know how much trouble there might be up there in the wilderness? That's how this country is going to be made, Ma. Folks like us starting trouble in the wilderness. I declare this court in session. First, I want to emphasize that this trial is of the utmost importance. The peace of two states, and consequently, the whole union, depends on the amicable and final settlement of this dispute. Your members of the court have an awful responsibility, not only to the states involved, but more than a month. The arguments, proofs, and testimony of witnesses go on. They have to do it. I submit an evidence the following charter in favor of one William Pan. I surveyed the lands along the Susquehanna under the terms of the original charter, and it is my consistency. All I know is we went down there and settled. I think Connecticut, they said it was our right. The aforementioned treaty with the aborigines at this area in question states most unequivocally that the land was ours. They knew it wasn't their land. They're not settlers. They're squatters. They're worse than that. They're thieves. That, sir, is a lie. And finally, the last of the evidence was in. Gentlemen, all testimony and evidence on behalf of both claimants having been duly submitted, I declare this trial concluded. You will retire to consider your verdict. The court is adjourned. Well, how do you think it looks for us, Joe? I don't know. But I'd better have a little talk with that judge. I've got an idea. Say, Judge. Yes, what can I do for you? Just wanted to have a little talk with you, Judge. Kind of private. Well, all right. Come right in here, please. Do you need your musket for this talk? Connecticut men generally keep them with them at all time, Judge. I see. Now, what is it you want to talk about? I want to talk about the verdict of this trial, Judge. I want to know how it's going to come out. Oh, great heavens, Lady. I don't know that. That's what's being decided now. You mean you don't have anything to do with it? I know. Those men that you saw at the trial are the only ones who'll render the verdict. And maybe they're the ones I want to talk to. What do you want to talk about, son? I want to tell them what's going to happen in case they decide wrong. Oh, I see. Um, tell me, son, did you fight in the revolution? I was in Valley Forge. I was no summer soldier if that's what you're driving at. Oh, what were you fighting for, Valley Forge? I was fighting for my farm, for my land up in Connecticut. Is that all? Well, maybe not. What else? Well, I was fighting so mean my neighbors could have a say in what was going to happen in this country. So nobody could come along and tell us what to do, just because he had soldiers in his back and a sword in his hand. I was fighting for that, too. Yes, but you wanted to go with a musket in your hand until that court had decided, is that right? I'm fighting for my land. That's all. Son, that isn't just a group of men that has some power of you that they don't deserve. Any power they have, you gave them. You even thought to give it them. The verdict it renders will be your verdict. And that is why it will be a true verdict. But, Judge, suppose they decide against us. My boy, something has happened in this country that has never happened before in all history. For the first time, men have established a system of government of which their public and private problems can be solved by reason, not by superior force, in peace, not by the sword. And today, that system is on trial. And the whole world will watch to see whether it can succeed or whether it must fail. If it succeeds, perhaps someday the nations of all the world will follow us on that path toward peace. And if it fails, that will be your failure. For what those men decide today will affect us only for a little time. But what you decide will affect the future course of all mankind. Will the clerk please bring with the decision Monday, 30th of December, 1782. The members of this court are unanimously of the opinion that the state of Connecticut has no right to the lands in controversy. And that all the territory lying within that charter boundary of Pennsylvania, and now claimed by the settlers from Connecticut, do of right belong to the state of Pennsylvania. It was night when Joe Dyer arrived at the clearing where his new house had once stood. The men from Connecticut had been building the stockade feverishly all night long. They were men in arms. What's the verdict, Joe? You look glum enough so I can almost guess it. It's against us. We're standing on land that don't belong to us. Well, let them just try to put us off it.  We're ready for them, Joe. No, no, listen, men. We've got to abide by the decision of that court. Joe, what are you talking about? By nothing but the musket in our hand. No, no, listen, men. Future Americans are going to look back on us in the way we settle out disputes. And I don't want them to think we settlers from Connecticut didn't know how to live by the American idea. The brotherhood of man and all. We've got to abide by the court. No, by no means. No, now listen. You don't understand. That's what we've been fighting for in our revolution. That's what a lot of men died for. So we could decide things fair and free and equal. Every man the same as every other man. That's something the whole world has been trying to do ever since the beginning of things. And that's what we are going to stand by today. I'm going back to Connecticut. Who's going with me? I'll go with you. I'll go too. Sure, I will. I'll go. Come on, you go. That's good. And we'd better get started. Because we're in the wrong here. And that's the only way to make it right. And all that night along the rutted roads of Pennsylvania and New York, one could see the wagons of the settlers from Connecticut headed homeward from where they came from. In the lead were Joe Dyer and his mother.  Judge sure made a mighty impression on me, ma. You know, son, it takes a big man to start a war. But it takes a sight bigger man to end a war like you did. You know, I can't forget what that judge said. How someday maybe the whole world is going to be like us 13 states, living in peace, settling things peaceful like we did. Yes, son. I'd sure like to be there when that day comes. When that day comes, a wish which is echoed in the heart of every American. In presenting tonight's play, it is the hope of all that this lesson from America's past may help to set a better pattern for the future between the nations of the world. James Craig will return to the microphone in a few moments. Meanwhile, here is Gain Whitman speaking in behalf of DuPont to pay a tribute to the women of 1943 who, like the pioneer mother in our play, are gallantly serving America. More than 17 million women in the United States are now employed, according to the Bureau of Census, most of them in industry. By and large, women are carrying this great part of the load of wartime production out of patriotism. They were needed, and they answered the call. Many of them have husbands or brothers or sweethearts in the armed forces. They want to back their men in the fight, and they want to have some money saved when their men come home. They're buying war bonds. Many of these soldiers in slacks are in industry to stay. They like it, and the American industry likes them. They're proud of their work. They're careful and painstaking. Last but not least, they are good industrial housekeepers, keeping their machines and work benches as clean and orderly as they keep their homes. So far as the chemical industry is concerned, twice as many women are working for the DuPont company as there were a year ago. 36% of the employees of DuPont and its associate companies are now women. That's more than one in three. Women are making tests and analyses in DuPont laboratories. They're operating lathes and punch presses, even two-ton cranes in DuPont machine shops. There are women doctors, inspectors, janitors, blueprint file clerks, production line workers, still operators, truckers and textile operators. Fitting the job to women makes it unnecessary in many cases to fit women to the job. Platforms are raised, chairs are adjusted, overhead electric hoists do the heavy lifting. These women in wartime jobs wear safety goggles and safety shoes like men. They lay aside the frilly dress or piece of costume jewelry that might catch in a machine. But they want industry to treat them as women, and industry does. It took World War I to liberate women and gain recognition for them in the world of business. It has taken World War II to demonstrate that they have an important place in American industry as well. And despite the great number now at work, industry can use many more. The DuPont company welcomes women workers. For their patriotism, their determination and the splendid record they have achieved, we salute these millions of new recruits to industry, including those who have come to DuPont, maker of better things for better living through chemistry. Now here is the star of tonight's cavalcade, James Craig. Thank you, ladies and gentlemen. I'm sure I speak for Miss Bondi and the cavalcade players when I say that tonight's drama brought all of us the hope that international disputes may be settled as we learn to settle the troubles between the American states in the early days of our country. Our big job right now is winning the war. And we all must do all we can for victory. But in a greater sense, we're working for the day when world states will settle their troubles without force of arms. Next Monday evening, cavalcade will present Edward Arnold in 12 Desperate Miles, based on the Saturday evening post article of the same name by Bertram B. Fowler, a tense, exciting story of our merchant marine in action, telling for the first time on the air how the battered old merchant ship Contessa played a unique and important role in the African invasion operations. DuPont invites you to be its guest again next week when cavalcade will present Edward Arnold as Captain John of the merchant ship Contessa in the dramatic story of 12 Desperate Miles. James Craig appeared tonight by courtesy of Metro-Goldwyn-Mare in whose production, Lost Angel, he will soon be seen. Tonight's musical score was composed and conducted by Robert Armbrister. This is James Bannon sending best wishes from cavalcade sponsor, the DuPont Company of Wilmington, Delaware. The DuPont Company.


Hydrogen sulfide, H2S, a gas produced by bacteria in the gut, plays a critical role in regulating many physiological processes throughout the body. It can act as a neuro-protectant against diseases such as Alzheimer's disease and traumatic brain injury. This article was authored by Bindu Deeppaul and Andrew Piper.


Hello everyone. We are once again back in our video series where we are providing the solutions to the questions given in the exercises of Arihan's book. So we have covered the two exercises of sequence and series chapter. So today we are going to start the next exercise, exercise number three. So let's proceed. So here comes the exercise three, question number one. The fourth, seventh and last term of GPR, 1080 and 2560 respectively. The first term and the number of terms in GPR. Okay. So let's proceed with the given information. It is given that the fourth term is 10. Okay. So a fourth term is 10. The seventh term is 80 and the last term or we can say the nth term is 2560. Okay. So since this series is in GP, let's consider it as AAR, AR square up to AR raise to power n minus 1. So we can consider these terms in GP. So as per given information, the fourth term is 10. So what will be the fourth term? The fourth term will be AR cube. AR raise to power 3 is equal to 10. And the seventh term, the seventh term will be A into AR raise to power 6 is equal to 80. So substituting the value of R cube in this second equation, let's consider this as equation one and this as equation two. So we can rewrite the equation two as A into R cube whole squared is equal to 80. So A into R cube can be replaced by 10 by A. 10 by A square is equal to 80. From here, we will get the value of A. So this will be A into 100 by A square is equal to 80 or 1A will be cancelled out and A will be 100 upon 80. That is nothing but 5 by 4. So we got the value of A. What is A? A is the first term of this GP. So since we got the value of A, we can easily derive the value of R also. So put the value of A in equation one. It will be 5 by 4 R cube is equal to 10. From here, we will get R cube is equal to 10 into 4 by 5. So this is nothing but 8. So R comes out to be 2. So we have find out the value of A and R. Now it's turned to find the value of N. So use this information. Our nth term is equal to 2560. So nth term of a GP is given by A R raised to power N minus 1 and this is equal to 2560. So put the value of A and R in this. So this will be 5 by 4 2 raised to power N minus 1 is equal to 2560. It will become 2 raised to power N minus 1 equal to 2560 into 4 upon 5. Cancel out this 512. So 2 raised to power N minus 1 is equal to 42048. So this 2048 can be written as 2 raised to power 11. So N minus 1 is equal to 11. From here we get the value of N as 12. So total number of terms in the given progression is 12. So the first term and the number of terms. So the first term is 5 by 4 and the number of terms is 12. So option number C is correct. Okay. So let's move forward to the next question. What is our next question? Okay. Question number 2 is saying that if the first and the nth terms of a GP are A and B respectively, and if P is the product of the first N terms, then P is square is equal to. Okay. So it is saying that P is the product of first N terms. So let's consider the GP as A, A, R, A, R is square, A, R, Q, dot, dot, dot up to. Nth term that will be A, R raised to power, sorry, A, R raised to power N minus 1. So this is our product P. Now the question is asking to find the value of P is square. Okay. So if you see this P can be simply written as A raised to power N since there are total N terms and R raised to power 1 plus 2 plus 3 up to N minus 1. Right. So this can be further simplified as A raised to power N into R. What will be the sum? 1 plus 2 plus 3 up to N minus 1. This will be nothing but N, N plus 1 by 2. So it will become this minus 1 plus 1 will be cancelled out. This will become N into N minus 1 upon 2. So R raised to power N, N minus 1 upon 2. So this is our P. Now the question is asking to find the value of P square. So let's square it on both sides. It will become A raised to power 2 N into R raised to power N into N minus 1. Now we can further rewrite as A raised to power N, sorry, A is square into R raised to power N minus 1 whole raised to power N. Right. So further we can split this A square as A into A raised to power N minus 1 whole raised to power N. And this can be written as A into this A raised to power N can be written as B because the Nth term is given as B. So this will become A into B raised to power N. So this will be our value of P square. So this is our answer. A B raised to power N. So option C is correct. So this question is done. Let's move to the next question. Question number three. It is saying if A1, A2, A3 are three successive terms of a GP with common ratio R, the value of R for which A3 is greater than 4A2 minus 3A1. Okay. So A3 should be greater than 4A2 minus 3A1. Okay. And A1, A2, A3 are the three successive terms of a GP. Okay. So A3 can be written as A1 into R square. This should be greater than 4 into A2. A2 can be written as A1 into R minus 3A1. Now we can divide this left hand side and both sides. We can divide both sides by A1 since A1 is positive. Okay. And the equality sign will remain same. So divide both sides by A1. It will become R square is greater than 4R minus 3. Let's take this thing to the left hand side. It will become R square minus 4R plus 3 greater than 0. So this is quadratic in R. And we have to find the value of R which will satisfy this inequality. So let's factorize this. Let's factorize this quadratic equation. So it will become R square minus 3R minus R plus 3 greater than 0.   Now we have to find the solution shape for this. So this is an inequality. So first let's draw the critical point. So critical points are 1 and 3. So for the values R greater than 3, this whole thing will be positive. For the value between 1 and 3, it will be negative. And for R less than 1, both these factors will become negative and overall it will be positive. So the value of R ranges from minus infinity to 1 union 3 to infinity. Or the same thing can be written as R less than 1 or R greater than 3. So this is our solution shape.  So option C is correct for this question. This is clear to everyone. So let's take the next question. Question number 4. Question number 4 is saying if x2x plus 2, 3x plus 3 are in GP, then the fourth term is looking simple only. x2x plus 2 and 3x plus 3. These terms are in GP. So we have to find the next term or fourth term. So since these terms are in GP, so 2x plus 2 upon x should be equal to 3x plus 3 upon 2x plus 2. This is nothing but common ratio. We can write common ratio as 2x plus 2 upon x. We can write common ratio as 3x plus 3 upon 2x plus 2 and both these are equal. So cross multiplying we will get 2x plus 2 whole square is equal to x into 3x plus 3. So let's open it. This will become 4x square plus 4 plus 8x is equal to 3x square 3x square plus 3x. So let's take everything on one side. It will become x square plus 8x minus 3x it will become 5x plus 5x plus 4 is equal to 0. So we can further split the middle term and factorize it. It will become x square plus 4x plus 6 plus 4 is equal to 0. Taking x common it will become x plus 4 plus 1x plus 4 is equal to 0. So x plus 1 into x plus 4 is equal to 0. From here we are getting the two values of x. x is equal to minus 1 or x is equal to minus 4. So these two values we are getting. x is equal to minus 1 or x equal to minus 4. But what the question is asking? The question is asking for the fourth term. So let's take x equal to minus 1. When x is minus 1 what will these terms become?  And the third term will become 3 into minus 3 plus 3 is 0. So actually this is not in GP because in GP no terms can be equal to 0. So x equal to minus 1 is rejected. x equal to minus 1 is rejected. Now let's take x is equal to minus 4. So taking x is minus 4 our terms will become minus 4 comma 2 into minus 4 will be minus 8 plus 2 that will become minus 6. 3 into minus 4 will be minus 12 plus 3 means minus 9. This is in GP. So now we have to find the fourth term. So what will be our fourth term? So let's find r first. So r will be minus 6 upon minus 4. This will become 3 upon 2. So our fourth term will be r into third term or this 3 by 2 into third term or third term is minus 9. So this will become minus 27 upon 2. This is nothing but minus 13.5. So this is our fourth term minus 13.5. So option D is correct. Option D is correct for this question. So it's done. Now we can move ahead to the next question, question number 5. This is the question number 5. It is saying in a sequence of 21 terms, the first 11 terms are in AP with common difference 2. And the last 11 terms are in GP with the common ratio 2. If the middle term of AP is equal to the middle term of GP, the middle term of the entire sequence is okay. So let's create one sequence that is A1, A2, A3 up to A11. Then this will go up to 21 terms. So our 21th term. So this is our sequence. Now the question is saying that the first 11 terms are in AP. So these first 11 terms are in AP with common difference of 2. And it is also stating that the last 11 terms. So last 11 terms means what? It will start from A11 and it will go up to A21. So these last 11 terms are in GP and for which the common ratio is 2. So this is the given information. And one more thing is given the middle term of this AP, the middle term of the AP is equal to the middle term of GP. So what will be the middle term of this AP? Like total terms are 11. I am considering only this first 11 terms of AP. So total terms are 11. So our middle term will be 6th one. Our middle term will be 6th one. This will be the middle term for this AP. And how can we represent this 6th term? 6th term can be represented as A1 plus 5D. And what is D for this AP? D is 2 for this AP. So A6, we can write A6 as A1 plus 10. This will be our 6th term or the middle term of the AP. Now what will be the middle term of this GP? Look this A11, this 11th term will be actually the first term of the GP. This 11th term will be the first term of the GP. And similarly here also the total number of terms are 11. So the 16th term. So 16th term will be the middle term of AP. Like this middle term of GP. This will be the 16th term. So A16. And how can we write A16? This we can write as A11 is the starting term. And the common ratio, common ratio R raised to power 5. So our 16th, A16 or the middle term of GP will be equal to A11. And R is given to, so it will be into 2 raised to power 5. So this will be our middle term of GP. Now question is saying that both these terms are equal. Both these terms are equal. So we can equate this. So equating this, both these terms we get A1 plus 10 is equal to A11 into 2 raised to power 5. We can write it as 32. Okay. Now can we find the value of this A11? Yeah, we can find because this is the last term of the AP. This is the last term of the AP. So we can write this A11 in terms of A1 so that we can find the value of A1. So this will become A1 plus 10 is equal to and what will be the A11? A11 will be A1 plus 10d. 10d means what? 20. So A1 plus 20 plus 32. Am I doing something wrong or what? Okay, okay, okay. This will not be plus, this will be multiplied, patient side. Right. So this A1 will be written as A1 plus 20. Multiply it by 32. Multiply it by 32. So we get A1 plus 10 is equal to 32 A1 plus 32 into 2, 64, 640. From here we get the value of A1 as this will become 31A. Let it write completely 31A is equal to 10 minus 640 that will be minus 630. Okay, from here we get A1 as minus 630 upon 31. So this is our first term. This is our first term. Now we got the first term of the sequence. Now what we have to find? We have to find the middle term of the entire sequence. Okay. So for entire sequence, the middle term will be this A11. Right. Middle term of the entire sequence will be A11 and A11 is nothing but A1 plus 10 times of D. So A1 we got this is minus 630 upon 31 plus 10 D is nothing but 20. So simplify it. It will become 31 this minus 630 plus 31 into 2 will be 62. So this will become 620. So finally we get minus 10 upon 31. So this will be A11 and A11 is the middle term of the entire sequence. So this will be our final answer minus 10 upon 31 option A option A is correct. Okay. So we are done with this question also. Let's have a look to the next question. Question number six. It is saying three distinct numbers x, y, z form a GP. In the order that the number 7x plus 5y, 7y plus 5z, 7z plus 5x form an AP. The common ratio of GP is okay. So it is saying that x, y, z form a GP. So let's write it x, y, z is in GP.  These terms are in AP. Now we have to find the value of common ratio of this GP. Okay. So since these three terms are in AP, we can write it as 7y plus 5z minus 7x minus 5y. This is the value of D. We can write it as D equal to this.  So this will be 7z plus 5x minus 7y minus 5z.  So take all the terms to one side, we will get this 2y plus 7y, it will become 9y, 5z minus 2z. It will become 3 plus of 3z then minus 7x minus 5x that will become minus 12x is equal to 0. Now it is divisible by 3 I think, so we can write it as 3y plus z minus 4x is equal to 0. So what we have to find actually, we have to find the value of common ratio of GP. Okay. So what will be common ratio of this GP? Common ratio of this GP will be we can write it as y upon x or we can write it as z upon y. This will be the common ratio for this GP. Okay. So let's divide this equation by y. So it will become 3 plus z upon y minus 4 times x upon y, this will be equal to 0.  And what is this x by y? This x by y is actually 1 by r, right? I am taking this to this side. 3 plus 2 upon z upon y is r, so 3 plus r minus 4 by r is equal to 0. So let's solve it. It will become 3r plus r square minus 4 is equal to 0. Or 3 square, sorry r square plus 3r minus 4 is equal to 0. Further we can simplify it as plus 4r minus r minus 4 equal to 0.  So r minus 1 multiplied by r plus 4 is equal to 0. From here we are having two values of r, r is equal to 1 or r is equal to minus 4. r equal to 1 or r equal to minus 4. So there is no one in the option. So we will go with the option a that is minus 4. So minus 4 is correct answer for this. So this question is done. Now let's move to the next one. Question number 7. The sum of in terms of the series. One series is given here 11 plus 103 plus 1005 plus dot dot dot. This is going up to infinity. No, this is going up to n terms. And we have to find the this sum of n terms. Okay. So this 11 can be written as 10 plus 1. And this 103 can be written as 10 square plus 3. Similarly this can 1005 can be written as 10 cube plus 5. Now this series will go up to n terms in the similar fashion. So let's write it separately. So we can write it as 1 plus 3 plus 5 plus 7 up to n terms and 10 plus 10 square plus 10 cube plus 10 raise to power 4. This is also going up to n terms. So we know the value of the first n odd numbers that is equal to I think n square. Okay. Let's we can find the value also. So n terms. So what will be the sum? It will be n by 2 2 times of first term to a plus n minus 1 into d d is 2 here. And what will be this? This is a GB with common ratio 10 and the first term as first term as 10 first term as 10 and the common ratio is 10. So we can write this sum as a raise to power n minus 1 upon r minus 1. Okay. So this will become n square. I know because this plus 2 minus 2 will get cancelled out. This will become 2 n in the bracket. It will become 2 n. 2 n square upon 2 plus 10 into 10 raise to power n minus 1 upon 9. So this will be our answer. 10 by 9 10 raise to power n minus 1 plus n square. Yeah. Option C is correct. So let's move to the next question. Question number 8. Increasing GB the sum of the first and the last term is 66. The product of the second and the last but one means the product of the second and second last one is 128. And the sum of the terms is 126. So let's collect the information first. What it is given in the question. The sum of the first and the last term. So let's assume a GP first.  Okay. So we have considered total n terms. So the sum of the first.  This is the first information we got the product of the second and the last but one. I think this mean second last only. So the product of the second. What is the second term? This is a r into second last one. What will be the second last one term? That will be a r raise to power n minus 2. So a r into a r raise to power n minus 2 is given as 128. This is the second information we got. And what is the third information? The sum of the terms is 126. So what is the sum of this GP? Sum of this GP can be given as a into r raise to power n minus 1 upon r minus 1. This is given to be 126. So these three informations we are provided with. What are the unknowns here? If we see a, r and n. So three unknowns, three equations. So definitely we can get a solution from this set of informations. But how to retrieve it? Let's check it out. Let's go ahead with this equation too. Let's go ahead with this equation. So from equation 2 we can see a square. We are rewriting this equation too. So a into a a square r raise to power n minus 2 into r. This will become r raise to power n minus 1. And this is equal to 128. So from here we can get r raise to power n minus 1 as 128 upon a square. Now we can use this thing. We can use this value of r raise to power n minus 1 in the equation 1. So putting this value in equation 1, what we will get? Whether we have write it, wrote it correctly or not? The sum of the first term and the last term. The first term is a, last term is a, r raise to power n minus 1. That is 66. Okay, let's try it out. So this will become putting the value of this in equation 1. We will get a plus a into 128 upon a square is equal to 66. It's working. So a one times a will be cancelled out. It will become a square a square plus 128 is equal to 66 a. So let's take this 66 a to the left hand side. It will become a square minus 66 a plus 128 is equal to zero. So we can split this middle term 64 into two. Yeah. So a square minus 64 a minus 64 a minus two a plus 128 is equal to zero. Take a common from here. It will become a minus 64 take minus two common from here. It will become a minus 64 is equal to zero. A minus two into a minus 64 is equal to zero. From here we are getting the two values of a either a is equal to two or a is equal to 64. These two values we are getting is equal to two or a is equal to 64. Okay. So let's check it. So we know from here we know our race to power in minus one. So our race to power in minus one is equal to 128 upon a square. Now when a is equal to 64 we will get our race to power in minus one is equal to 128 upon a square. That means 64 into 64. This will go two times this will become one upon 32. And if we take a is equal to two this our race to power in minus one will be equal to 128 upon two into two. So four three two. So our race to power in minus one will become 32 when when a is equal to two and when a is equal to 64 it is becoming one upon 32. But one thing we have to notice here it is an increasing GP right. The question is saying it is an increasing GP. So if it is increasing GP or must be greater than one. But from here we are getting are less than one when we are putting a equal to 64. So this implies that R is less than one. So this option is we have to reject this one. So A is two. This is confirmed that A is two. This is the accepted value. Now if A is equal to two we are having our race to power in minus one is 32. What are the other informations we are provided with? We have not utilized this third equation yet. So let's take this third equation in the room. So third equation is saying A into our race to power in minus one upon R minus one is equal to 126. Okay. So we can write. So put this A equal to two here. We will get two into our race to power in our race to power in can be written as from this we can write our race to power in upon R. This will become our race to power in minus one. This is equal to 32. R race to power in can be written as we can write our race to power in is 32 R. So replace our race to power in by 32 R minus one upon R minus one is equal to 126. We are getting something. Okay. From here we can find the value of R. So this will become 63. So 32 R minus one is equal to 63 R minus 63. Right. So it will become 63 R minus 32. 32 42 52 62 31 R. 31 R is equal to 63 minus one 62. So R from here we get RS two. So we got the value of A. We got the value of R also is also equal to two and R is also equal to two. Now what else we have to find? We have to find the value of N. Right. The number of terms in the series. So let's utilize this equation. R race to power N minus one. From here if you see, let me go downward. Okay. I'm changing the color of the pin. R race to power N minus one is equal to 128 upon A square. Now we know the value of R and A. So put that it will become two raised to power N minus one is equal to 128 upon A square. A square means four. So this will become four, three, two. So two raised to power N minus one is equal to 32. We can write it as two raised to power five or N minus one is equal to five. So N equal to six. So total number of terms in the given progression is six. This will be our answer N equal to six. Whether yeah, option A, it's given in the option A. So option A is correct for this. So this question was a bit lengthy, but okay, we have done it. Let's move to the next question. This is board number eight. So I have to go to board number nine. Okay. Here we are. If S1, S2, S3 be respectively the sum of N, 2N and 3N terms of a GP, then the value of this expression S1 into S3 minus S2 divided by S2 minus H1 whole squared. Okay. So what is S1? S1 is sum up to N terms. Okay. What is S2? S2 is sum up to 2N terms and S3 is sum up to 3N terms. So we have to find the value of this S1 multiplied by S3 minus S2 upon S2 minus H1 whole squared. Okay. I think this question, mechanical type, let's say, let's calculate. We have to do work on this S1, S1 sum of N terms. So sum of N terms of a GP, we can write it as A into r raised to the power N minus 1 upon r minus 1. This is sum up to N terms. What will be the S3? S3 sum up to 3N terms. So it will be, A is the starting term of the GP. Okay. So it will be common. So A into r, r will be also common because this is the same GP. So r raised to power, only difference will be in the power of r. That is r raised to power N, total number of terms. It will be 3N here. r raised to power 3N minus 1 upon r minus 1.  And what is there in the denominator?   And this, total car, fully square. Right? Okay. So do, we can do one thing.  Now, let's take A upon r minus 1 common from these two terms. Okay.  And in bracket, it will be r raised to power 3N minus 1 minus of r raised to power 2N plus 1. Right? Similarly, take A by r minus 1 common from this. So it will become r raised to power 2N minus 1 minus r raised to power N plus 1. And this will be a square. So we can see here, these things will be cancelled.  So these things got cancelled. So we are left out with, we are left out with r raised to power N minus 1. Here, this minus 1 plus 1 will be cancelled. Similarly, this minus 1 plus 1 will be cancelled. This will become r raised to power 3N minus r raised to power 2N divided by r raised to power 2N minus r raised to power N. So we can do one thing. We can take r raised to power 2N common from this bracket. And from denominator, we can take r raised to power N common. So let's take it r raised to power N minus 1. If we take r raised to power 2N common from here, it will become r raised to power N minus 1. Right? And if we take r raised to power N common from here, it will become r raised to power N minus 1. Yeah, whether I have done something wrong, wrong, wrong. Okay. These things, this square will come. So if we take r raised to power N common here, it will be 2N and this will be square. So r raised to power N minus 1, r raised to power N minus 1, 2 times in the numerator. This will be cancelled and this r raised to power 2N and this r raised to power 2N will also be cancelled. So this will become 1 finally. So it was earlier looking a bit so much what you say. Difficult, but finally we got rid of it and we got answer as 1. So option A, option A is correct for this. So we are done with this question number 9. Let's move ahead with question number 10. So question number 10, if mod A is less than 1 and mod B is less than 1, then the sum of series. Okay, one series is given and we have to find the sum of that.  Right, because dot, dot, dot is in continued fashion. So we have to find the sum of this series. So what can we do? Let's open the bracket first and see what we are getting.  So whether we are getting anything convenient. So 1 plus B plus B square. Okay, let's write it as 1 plus. Now take the terms having only B. So we will get this B. We will get this one we have already taken. So this B, B square, B cube and further it will be B4 also. So B plus B square plus B cube plus dot, dot, dot it will go up to infinity. Now take the terms which are having A. So if we take that then this we will cover AB, AB square then AB cube. Okay, so this will become B plus B square plus B cube plus dot, dot, dot up to infinity. Now similarly take the terms having A square.  Okay, so first term is having B square then B cube and it will continue in the similar fashion. Similarly, the terms with A cube will also come. And seeing the pattern I can realize that it will be having the terms B cube plus B4 plus B raised to power 5 within the bracket. Similarly, A raised to power 4 will be having B raised to power 4 plus B raised to power 5 plus B raised to power 6 and this series will go on. Right, so what can we do further? This is the GP and we are given that mod B and mod A are less than 1. This is the sum of GP for infinite terms. It will become the sum of GP up to infinite terms A upon 1 minus R. Okay, so what is A here? Means first term is B and 1 minus R and the common ratio is also B. So this we got from here. From here what we will get? This is also some up to infinity terms. The common ratio is this. So this first term is B and common ratio is also B. So this will be 1 minus B. Similarly this A square and B square upon 1 minus B plus A cube into B cube upon 1 minus B plus dot dot dot this will go. So what we are getting now? So this will be 1 plus B upon 1 minus B, let it be as it is. I think I am able to see something. In all these terms I am taking 1 upon 1 minus B common. So what will be remaining terms? What will remain in the packet? It will be AB plus A square B square plus A cube B cube plus this will continue up to infinite terms. Right? So 1 plus B upon 1 minus B plus 1 upon 1 minus B and we can write this sum of infinite terms of this GP as AB upon 1 minus what is the common ratio here? AB. So first simplifying this take 1 minus B and 1 minus AB as LCM. So this will become 1 minus B into 1 minus AB plus B into 1 minus AB plus AB. So let's open the packet.  So minus B plus B got cancelled AB square minus AB square minus AB plus AB cancelled. So we are left with 1 upon 1 minus B into 1 minus AB whether this is there in the option or not. Let's check it out. 1 upon 1 minus B 1 minus AB 1 minus B 1 minus AB yeah. It is there. Option C is correct. Option C is correct for discussion. So I don't know I approached through this method. If anyone have some alternative or any shortcut method please come to me and like we can discuss on that. So let's close this question here only. So let's move to the next one. Question number 11. Okay. It is saying if the sites of a triangle are in GP and its larger angle is twice the smallest then the common ratio are satisfies the inequality. Okay. So. Triangle is there. So triangles have three sites and for considering three numbers in GP we prefer taking A by R, A and A by R. So here we assume that A by R like this. Let's assume this side as A by R. This side as AR and this as A. So we can do that and what then the common ratio are satisfies the inequality. Okay. Let's consider A by R as the smallest side smallest side and this AR as the largest side. So since A by R is the smallest. So angle opposite to it will be less. Right. So if I'm taking this as theta and angle opposite to this AR since this is the largest side we have considered. So it will become two theta. Right. Its larger angle is twice the smallest. So it will become two theta. Now we have to find the value of R. We can apply sign rule for this triangle. That is A by R upon sin theta is equal to AR upon sin two theta. So this will become A by R sin two theta is equal to AR into sin theta. So this I'm cancelling this A with A it will become sorry. So R square will become sin two theta upon sin theta. Now we can write sin two theta as two sin theta cos theta upon sin theta. So cancelling this we get R square is equal to two cos theta. So we got R square as two times of cos theta. Now the maximum value of cos theta can be one. But cos theta we get cos theta one at theta is equal to zero degree. So theta cannot be equal to zero degree since it is angle of a triangle. So theta cannot be equal to zero degree. So R square should be always less than two. So R must be less than root two. So R maximum we can say R maximum must be less than root two. Now while considering this right while considering this sides of the triangle R must be greater than one. Why? Because if suppose we consider R less than one suppose we take R is equal to half. So what will be our sides? Our sides will become A upon one by two A and A into one upon two. That is two A A and A by two. But we have assumed that this is the smallest side but now it is becoming like largest side. So our assumption will be wrong. So hence R must be greater than one. So where should R lie? R should lie between one and root two. So this will be the range of R. This will be the range of R. R must be within R must be greater than one but less than root two. So option B is correct. Option B is correct for this question. So we are done with this. Let's take the next question. It is saying if A x cube plus B x square plus C x plus D is divisible by A x square plus C then A, B, C, D are in A, B, G, P or HP or none of these. Okay. So it is saying that A x cube plus B x square plus C x plus D it is divisible by A x square plus C. Right? Divisible means what? It is completely divisible. Means remainder will be zero in this case. So let's divide it by our long division method. Take x. So it will become A x cube plus C x. So plus C x. Now let's subtract it. It will become zero. B x is super will come as it is. It will become zero. And B x square plus D will remain. Now what we can do? We can take it as B upon A. B upon A. Right? Then only A is it. So B upon A. So B upon A into x square will be, let me write this side. B upon A into A x square plus B upon A into C. So it will become B x square, B x square. This A will be cancelled and B C upon A plus B C upon A. Now let's subtract it. This will be cancelled. It will become D minus B C upon A. Now this is the remainder, right? But the remainder should be zero here. Because question is saying this, that this cubic polynomial is divisible by this A x square plus C. So since this remainder must be equal to zero, we can write it as D minus B C upon A is equal to zero. Or A D minus B C is equal to zero. Or we can say A D is equal to B C. So suppose we are having four terms A B C D. So let's take these are in GP. Okay? So B upon A must be equal to C upon B and that must be equal to D upon C. So okay. So this cross multiplying we get A D is equal to B C. So since A D equal to B C means these A B C D are in GP. These are in GP. So this is the answer. So option B is correct. This result we got, right? A D equal to B C. Now we have to check it whether it is in AP or GP or HP. So I just gone with this assuming that these are in GP and we got the correct relation as we derived from the required condition. So these are in GP. A B C D are in GP. So moving to the next question, question number 13. It is saying if R N denotes the RRR up to N digits where R is equal to 1, 2, 3, up to 9. And A is equal to 6 suffix N then B equal to 8. N C equal to 4 to N. So R N denotes number R. This will be written up to N times, like N digits are there. Okay. So we can write 6 N as 6, 6, 6, 6, how many times?  We have to write this 6 N times. So this will be our 6 N and this is equal to A. As per question, this is equal to A. Okay. And what is, and it is also saying B is equal to 8 N and C is equal to 4. But in foot it is written 2 N. So 2 N times it will repeat. This B will repeat, this 8 will repeat N times as it was repeating in 6. But C will repeat 2 N times. Okay. First let's solve this A. Then I think we will get some idea. So take 6 common form here. Like then things under the bracket, I mean within the bracket can be written like this in digits. So 6, this number can be like, we can rewrite this number in the bracket as 10 raised to power 0 plus 10 raised to power 1 plus 10 raised to power 2. How many times? 10 raised to power N minus 1. Because total, how many digits are there? N digits. So it's starting from 0, 10 raised to power 0. So it will end, so it will end at N minus 1, 10 raised to power N minus 1. So this is GP actually, right? So this is GP having 1 as the first term and 10 as the common ratio. So 10 raised to power N minus 1 upon 10 raised to power N minus A, R raised to power N minus 1 upon R minus 1. R is 10, 10 minus 1. So this is our A. Let us simplify it. So it will be 6 into 10 raised to power N minus 1 upon 9. Okay. So I think in the similar fashion we can find the value of B also, right? So B will also become, B will become instead of 6, it will come 8 and rest all things are similar only. So 8 into 10 raised to power N minus 1 upon 9. So this will be the value of our B, right? But in C, C the digits are repeating up to 2 in terms, right? So we can write C as 4 into, the only difference will be instead of this N, like 2 N will come, right? So 10 raised to power 2 N minus 1 upon 9. Rest all things will be same only. So this will be the value of B and this will be the value of C. Okay. Now what the question is asking? Then A square plus B plus C equal to 0 or A square plus B minus A equal to 0, A square plus B or A square. Like everywhere in every option A square B is there. So let us first calculate it. A square plus B thing. Like this A square plus B because it is common to every option, no? So let us check it out. So what will be A square? A square will be 36 into 10 raised to power N minus 1 upon 9 is squared. So this will be A square and B. B is 8 into 10 raised to power N minus 1 upon 9, okay? So we can take 4 into 10 raised to power N minus 1 upon 9 common. We can take this common. So what will we left out with? 4 into 9, right? So this will be 9 and this thing is squared so it will come one time. 10 raised to power N minus 1 upon 9. And plus 8. So we have taken it will be 2, okay? I think I am doing right. So 10 raised to power N minus 1, okay? So this 9 and 9 will be cancelled out. We will have 4 into 10 raised to power N minus 1 upon 9 into this will be 10 raised to power N minus 1 plus 2. This will be plus 1. So it will be 4 into this A minus B A plus B. So A square minus B square we can write it as. So A square like 10 raised to power 2 N A square minus B square minus 1. The things in the numerator I have written here and 9 will be as it is. So I think this was the value of C which we have. Yeah, it is there. Value of C 4 into 10 raised to power 2 N minus 1 upon C. So A square plus B is equal to C. This is equal to C. Means A square plus B is equal to C. This is the relation between A, B and C. This is our answer. A square plus B equal to C. A square plus B is equal to C. A square plus B equal to C. So option B. Option B is correct. A square plus B minus A equal to 0 or A square plus B equal to C. So we are almost close to this, to the end of this chapter. So 0.427 recurring. 0.427. 27 are repeating terms. Represent the rational number. Okay. So suppose this is the value of X. This type of problems we used to do in like class 10. In first chapter, I think real numbers. So let's multiply it by 10. Why multiply it by 10? Because non-recurring figures are only one figure is non-recurring. So I'm multiplying by 10. So it will become 4.27. And now multiply by 100. Let's suppose it as equation 1. Now multiply it by 100. So it will become 1000 X is equal to 427.27. And consider it as equation 2. Now subtract equation 1 from equation 2. It will become 990 X is equal to. This will become 427.27 minus 4.27. So this will become 424. So 990 X is equal to 424. From here we get X is equal to 424. This will be 423, you know. 423. So 423 upon 990. I think it is divisible by 9. 9. 4 times 36. 6 into 3. That will be 747 upon 110. So option B is correct. Now coming to the question number 15. This is the last question of this exercise. So we are at the end. Let's do it quickly. If the product of three numbers in GP be 216. So three numbers in GP. So we prefer considering number as A by R, A and AR. So the product of these numbers are 216 and their sum is 19. So let's take the product A by R into AR is equal to 216. So AR will be cancelled out. It will become A cube is equal to 216. So A we will have as. So A is 6. Now their sum is 19.  So A is 6. So sorry. 6 by R plus 6 plus 6R is equal to 19. So taking R as LCM we will get 6 plus 6R plus 6R is equal to 19R. So it will become 6R is square plus 6R minus 19R it will become minus 13R plus 6 is equal to 0. So we can break it as 9 and 4. So 6R is where minus 9R minus 4R plus 6 is equal to 0. Take three are common. So first two terms it will be 2R minus 3 6R is where minus 9R. Okay. And take minus 2 common from here it will be minus 2. This will be 2R minus 3 is equal to 0. So 3R minus 2 into 2R minus 3 is equal to 0. So from here we get R is equal to 2 by 3 or R is equal to 3 by 2. These two values of R we are getting. So what it is asking then the numbers are. So okay when R is equal to 2 by 3 our GP will become A means 6 upon R 2 into 3 comma 6 comma A into R. R is 2 by 3. So it will be 9 comma 6 comma 4. Okay. And when R is equal to 3 by 2 I think it will be opposite to it. Let's check it. Our GP will become that means terms of the GP will be A 6 upon R is 3 into 2 comma 6 into 6 into 3 by 2. So it will be 4 comma 6 comma 9. Yeah 4 comma 6 comma 9. So the numbers are 4, 6 and 9. Option A is correct. So we are done with this exercise. Actually the number of questions in this exercise was 15. So it took a long time but we tried to summarize it like close it as early as possible. So anyhow the length of the video will be more but can't help with that. So okay we are closing this session right now and we will meet again. Okay. Bye.