11th Math Binomial Expansion Important Questions for Board Exam | Class 11 Maths Preparation

Added: 2026-05-12

[00:00:00]Welcome first year Mathematics students, I have brought a long video for you all and it is a very important video, Inshallah this video will definitely come, it is done, all the videos that I am uploading are long videos, both long and short, of important questions, now after this the scene is such that I have uploaded approximately 16 videos on 16 questions, in past papers, in model papers, in guess papers, in pre boards of different colleges, the important questions, I used to make videos on those.

[00:00:25]So this has also appeared on many boards.

[00:00:27]Now what do you guys have to do? You have to understand this and if you people are facing any problem in any question, for example, if you know this question but there is some question on which you are not able to find the video on YouTube. You have to send me the picture of that question in the comment and write solve please by mfu. Do you want to write this much or solve it please, then I will solve it. fixed bugs? Now let us come to its solution.

[00:00:48]Its solution is very easy. It is extremely easy. We have to make this thing. We have to make this.

[00:00:53]What to make it from? Have to make it from this. Ok?

[00:00:55]Because I'll put a line here.

[00:00:56]Basically, we have to show this thing with the given thing that we have.

[00:01:01]Now if I look at this y, O Bhaijaan y is running.

[00:01:06]How do I stop this y? So to stop this y, I'm going to have to do a little bit of simplification here.

[00:01:11]What will have to be done? A little simplification will be required here. Are you able to understand this or not?

[00:01:17]What is the first thing we will do now? That we will remember a series to solve this.

[00:01:23]What will you remember? What series is a series?

[00:01:25]Come to the solution. We will come to its session.

[00:01:27]So one thing we need to know is the binomial series. What is?

[00:01:32]Binomial Series. Now what happens to the binomial series? Basically when you have this question given y = 3 / 2²1 okay? This square is dot one 1orial + 3 / 2 4 2 + 3 / 2 6.3orial plus so on. fixed bugs? what shall we do now? After this, if I ask you to write the binomial series, then the binomial series is 1 + x n = 1 + nx + nn - 1 2 x², that's it, we've brought it up to here. So on. Now from this so on and so on I got the idea that a question of binomial series has been given. I was given this question on binomial series. What do I have to do in this?

[00:02:25]This story which is so on, has to be ended.

[00:02:27]Because this story is ongoing.

[00:02:30]Now how will this So On story end? See if I have x to the power of 1 + x and I have n then my story will be solved. fixed bugs? Now to solve this story, the first thing we will do is add both side ones in the solution. There is forest here and there is forest here too.

[00:02:51]Why would we do that? Let me explain to you why we will add Pay One here?

[00:02:56]Let me write it down once. Then I will explain to you why we write one on both sides. Let me explain its story to you. The basic story is that if I look at this binomial series, there's one here.

[00:03:09]Next is nx. So if I get one here, what will I do automatically? This will take the form of a binomial series for me.

[00:03:18]1 + nx Now this term is of nx. Look, whatever belongs to One One.

[00:03:25]He is doing this.

[00:03:27]Ok? This term is doing it.

[00:03:29]Similarly, the next term will be belonging to him.

[00:03:31]What will the next term be like here? Plus the next term I have is nn - 1 n - 2 / 2 3 and x q + so on now if you look here also 3 here also so it belongs to this thing.

[00:03:48]fixed bugs? Did you understand till here or not? Leave the right hand side aside for now.

[00:03:51]Leave the left hand side for now. I have no connection with him at the moment. One is touching one. nx is coming in comparison to nx. n Understand this concept in comparison to this. I can make nx equal to 32² of 1serial. Did I do the right thing with nx because when I compared it, I made nx equal to 3 / 2² 1.5. Now can I make n - 1 over 2 equal to x² by adding a comma? 3 / 2 4.2Oral Who agrees with these two things I have done?

[00:04:34]Who all agree with this? Please tell me who all agree with this NX? I've made this nx equal to this first factor and this. Now I will find the value of n from here. I will put it from here to here. I will take out x. I will find the value of x and put it here. I will take it out.

[00:04:51]Brother, there cannot be an easier question than this.

[00:04:54]If you only know this one thing. It's just simplification, there's nothing else here. If there's anything else here, let me know, so I can just do it. I will write n right there. x multiplied there will become g divided by 3/2 to the power of 2.1orial is 1 and x friend and how do I simplify the question? Let me know if this can make other questions easier.

[00:05:18]No, n = 3 / 2² 4 and x = 3 / 4x. Now what value of n do I have here? The value of n came to me. If you see 3/2 to the power now take this value of n and put it here. I'll take x out from there.

[00:05:38]This is not right. And if we are facing problems in its simplification then take the value of x from there and put it here. It's your wish. This n that I have found, you can do this n in such a way that you can also find x from this question.

[00:05:51]x = 3 / 2² 1 can also be done with reals 1 and n. This is the answer to x.

[00:06:01]Pick up this x and put it here. Oh brother, do it as you wish. I have 1 minute, just name this equation. This equation is useful to me, name it Equation One.

[00:06:10]Now, I will put the x that I took out from here here.

[00:06:12]Whichever way you find easy. n n - 1 If you put n here, here also, here also, then the question may become a little difficult.

[00:06:20]2orial is equal to 2 1orial, you know norial is equal to n n - 1 n - 2 so on so if we have 2orial then it will be equal to 2 and 1 if we have 3orial then it will be equal to 3 2 1. fixed bugs?

[00:06:34]Understand further. The value of x is 3/2² 4 and 4.

[00:06:38]Meaning here 3 can be equal to 4 x.

[00:06:42]This is the first thing and secondly, what did we conclude from here that x equals what? of 3 and 4m. So the story continues the same. There is no doubt in the story. I am not having any doubt. fixed bugs? Now what is on its right hand side? Here comes the square. On its right hand side 3/2 square 2 to the power 4 16 and 2 and one will come in 2orial, so this is what I got, what did I get, 16 and 2, it is okay, why did I not make any mistake, 2 to the power 4 is 16, right 2 * 2 4 4 * 2 8 8 * 2 16, it is okay, it is absolutely correct, I understood 2 4, now we have to simplify it further, in simplification we have to find out n, n² - n / 2 is being multiplied. Give this bracket to him also.

[00:07:30]Give it to him also. 3² is 9 4² is 16 and n² is ok? This n² would not be common because then I would subtract n from n.

[00:07:39]n - 1 not taking common. Ok? And here we get 3 / 16 * 2 = 32. Now from here we have an n cut off by this n. So what will be left there is n - 1 2 * 9 / 16n = 32. Are you understanding the story?

[00:08:04]We also have to think about a little simplification because brother, the work is not easy while making a video. 9n - 1 / 16 * 2 = 32n = 32. Bhaijaan, the story will be solved further. 32 will come here. 9n n - 1 32 * 32 = 3. Because what is 32 happening here? It is getting divided. Going there the multiplier got reduced by 32. 9n - 1 = 3 Now n - 1 = 3 9 n - 1 What will be the answer?

[00:08:40]1 2 3 * 1 = 3 3 * 2 = 9 Now after this let's do some fun simplification and remember one thing that small mistakes happen brother.

[00:08:47]Then look at the next question. Now here, thankfully, I prevented the mistake. Was.

[00:08:52]fixed bugs? How did I stop it, I had released three here. So if there is any calculation mistake, please tell us in the comments.

[00:08:56]Sir, I made this calculation mistake and please send a crying emoji along with it. n = 1 / 2 + 1 n = 2 What will be the answer of LCM 1 + 2 n? 3 2 Oye Bhaijaan, I have taken it out.

[00:09:10]n We have found 3 / 2 n. Let's take the value of g 3 / 2 n.

[00:09:17]Put it here. Take out the x.

[00:09:19]Put it here. Take out the x. Put it wherever you want.

[00:09:21]I put in x = 3 / 4 n.

[00:09:25]What is the value of x = 3 / 4 n? 3 / 2 x = 2 * 1 = 2 2 * 2 = 4 3 and 2 and 3 so x = 3 and three is cut off. 1/2 Let me clarify once that x has come to me only 1/2.

[00:09:41]x What has come to me? 1/2 has arrived. Did you understand this far? Has she come this far or not? Now after this we basically have the answer of x which is 1/2, what did we have as sum of series? Now if the answer to x is one, the answer to x is 1 + 1/2.

[00:09:59]This was the sum of the series. I'll write the sum of the series up here.

[00:10:01]1 + x n 1 + nx + nn − 1 2 x² + so on. Now the value of 1 + x x is 1/2 to the power n and further the sum of the series. Now that sum of series was this and I had kept it equal to the question. That's right. Meaning it was kept equal to the entire question. I told you this sum of series, I kept the sum of series equal to the entire question. Now if I simplify this, I mean I was on its left hand side. What will come here? 2 and 2 + 1 of ^ n from here I will explain again. 2 to the power of 3 will come to n. Now n came out. What value of n did I get? What value of 3 / 2 n did I get? The value of 3 / 2 3 / n was 3/ 2. So what is x? 1/2 has arrived. 3/2 to the power 3/2 answer what did you get? 3/2 to the power of 3/2 1 min. Let me explain one thing. Let me explain this thing to you again here.

[00:11:02]This was the sum of series I had.

[00:11:04]1 + x Let me explain to you. This is the sum of the series I have 1 + x n 1 + nx + n n - 1 and 2 x² + so on question what I made was 1 + 1 1 y + 1 1 + 3 / 2² 1 + 3 / 2 3 2 42 + 3 / 2 6 2 3 plus so on. Now if we what I did here was pick up the red marker.

[00:11:43]What I did here was that I connected the first one with the previous one. The other one had established a relationship with the other one. It was like that. The third one has to do with plus. The third one had established a relationship with the third one.

[00:11:55]Same is the case with the fourth one. Now that I saw it coming to this.

[00:11:59]This is coming to be equal to this. This is coming to be equal to this.

[00:12:03]Similarly, thirdly, will the left hand side not be equal to the left hand side? Will you come?

[00:12:07]So what was on the left hand side? 1 + x to the power n. That's right. Now look, let me explain one thing to you. If I put x here and n here, then you will see that this thing will automatically be created for you. Check it. This x that I put here, what value did I put for x? What values ​​of 1 2 and n did I put in? This one. When I open them, I will open them. Of course, I will let you try it once. The value of 1 + n is 3 / 2 and the value of x is 1/2 1/2 Now simplify this a bit. What will 3 / 2 and 2 to the power of 2 become? 2 dot 1orial is equal to 1. So write it down from seven. Look, these two terms have been made here. So, the values ​​of x and n that I have calculated are absolutely perfect. Now its left hand side will become equal to its right hand side.

[00:12:55]Meaning y + 1 means its left hand side will be equal to the left hand side.

[00:12:59]Its left hand side will be equal to the left hand side of the formula. What do we do next when the left hand side equals the left hand side of what value did we have of 1 + x? This was completely solved. The value of x was 1/2 which I solved above and what is y + n? 3/ 2y+1 Now after this 1 comes its LCM 2 okay. 2 + 1 3 / 2 = y + 1 Now 3 / 2 3 / 2 which I am solving twice above.

[00:13:33]This question is very important. Look at this thing and it has come here also.

[00:13:36]Why am I doing this now? Because what do I have to get out of here? I basically want to make this thing.

[00:13:40]So what do I need to do now to create that equation? I'll have to find its fraction form. Now to finish this, that is, if I multiply its fraction form above, 3/2 to the power of 3/2, by two and here also if I multiply y + 1 by two, then what have I done on both the sides, I have squared it here, both the sides have been squared.

[00:14:02]Now after this this square and radical will be cut. So the power of 32 will be the whole square and the whole cube.

[00:14:09]fixed bugs? And from here the whole square of y + 1 will be squared. Did you understand till here? Then the square of 3 will become 27 and that of 2 will become 3 27 2 8 and the formula has to be opened on y + 1².

[00:14:23]But let's move ahead here. I think you people might be able to see it till here.

[00:14:26]I made a mistake, I should have started a little there.

[00:14:27]But no problem, it is visible here. Then we have 27 8 = y² + 1 + 2y. The formula is open. Will pick up the at after the formula. Will throw it to the other side. 27 = 8y² + 8 + 8 * 2 = 16y Done right? Then make it zero here. 8y² right? + 16y + 8 - 27 8y² + 16y - 19 = 0 Bhaijaan, we have made what we had to make.

[00:15:07]This is its session which we have proved. Now children, I just want to explain to you that whenever any such question comes in which the concept of so on comes in which the concept of so on comes in, understand what it is? That is the binomial series.

[00:15:24]What is that? is a binomial series. Now suppose there is another part of this, it is the other one.

[00:15:29]So let me explain the second part to you in a minute. There I have 1/3 of 1 minute. 1 / 3 + 1 / 3.3.6 So on. Take this forward. Now there is a shortage of forest here.

[00:15:42]One added from his side. Similarly, whatever is there on the left hand side is 2 and y, so add one there also. fixed bugs?

[00:15:49]Whose there too? Add one. Then one ad was added here also.

[00:15:52]Now this has become a binomial series.

[00:15:53]Then 1 + nx means this term is nx. Put it equal to nx. 1 / 3 From here n or x is your choice. Take out n, take out x. It's your choice. You just need to remember this series. 1 + nx and this is a very interesting series. The more I explain this series, the more I enjoy it. Now tell me whether I should solve its part two or not. Whoever says Sir Part 2 in the comment box, I will make Part 2 on that.

[00:16:19]And its question number 10 is its variant.

[00:16:24]If you say in question number 10, its part number two is very important. Part number two of question number 10 is important. We can solve that. So Inshallah Taala, I hope you have understood the question. If there is any calculation mistake somewhere, please comment to me because Bhaijaan, when I am writing here, I am not able to see the board there.

[00:16:38]When I am writing it correctly here on the copy, it is a very easy task and can be done in a jiffy.

[00:16:42]So I hope you liked the video.

[00:16:43]Subscribe for more videos, thanks. Allah Hafiz.