11th Class Math Exam Questions 2026 | Important Board Questions | MFQ Academy

Added: 2026-05-12

[00:00:00]Greetings. This is a very important question for first year mathematics students. This is a very important question. You will see that this will definitely appear in the paper.

[00:00:07]I took this question from the model paper. And I am sure it is such an easy question, there is only one small formula.

[00:00:14]You all have to remember one word in this – neglected.

[00:00:16]You people have to keep this word in mind – neglect. Ok? What does the word neglect come from? From neglect. fixed bugs? I mean remember this. Now what they say is that the meaning of 'ism' should be understood or ignored.

[00:00:25]What to ignore? Brother, you know I have this question from chapter number 7.3.

[00:00:31]We study one of its formulas, binomial expansion. Meaning, if you remember the binomial series, what is the formula for the binomial series? If you guys remember a little bit in which we read 1 + x n = 1 + nx + nn - 1 2 x² + so on. fixed bugs? Now he tells me what you have to do is if x is so small. x is so small that it is square and its square and higher powers, meaning square and higher powers are neglected, neglect this. Show that, is this equal to this or not? So when the word neglected comes, he is saying that x is so small. So when is x small? when x is itself.

[00:01:16]So x itself is x small. So I put n - 2 / 2 x² into this formula because it comes with x². All the terms beyond this have to be neglected.

[00:01:27]What all that needs to be done? I have to neglect it. So the formula I have is basically if I look at my formula, it's 1 + x n = 1 + nx, okay? This will just happen. If I apply flowers then I have to apply only this formula.

[00:01:43]Because what will happen to all these terms in future? It will be neglected. It will be cut.

[00:01:47]I don't want to put any term of x². So if I look at my question, what is it? 2 + x ^ 1 / 2 power will be changed to ah exponential form 1 - x 32 and we will use brackets and this bottom factor will be brought up to the top 3 + x ki ^ -1 and we have to use approximation and what does it have to be equal to? 2 3 and 1 - 19 12 and x we ​​have to bring this equal to this.

[00:02:15]fixed bugs? Now kids, it's a simple concept. It's a simple concept. What we have to do is try to make 1 + x n.

[00:02:24]Ok? To factor out every x, if I have 2 + x to the value of 1 2, what do I need to do to make it this? I am just explaining this to you here. I will have to take two common ones. The remainder of 1 + x / 2 will be 2 ^ 1. Are you getting the point?

[00:02:41]I am just explaining to you how we can take it in common. Whenever something comes out, the thing inside gets divided.

[00:02:47]Meaning that this one has two but this one does not have one. Understanding this thing again Understanding this thing again. When I took two common from both of them, from these two terms in this factor, this and this, this and this, then here there was two, but one came in its place.

[00:03:02]But this x didn't have two, so it was divided by two. Now after this the simple thing that will happen is that 2 to the power of 1/2 will be divided and 1 + x / 2 to the power of 1/2 will be divided.

[00:03:12]Similarly, this concept has to be implemented here.

[00:03:14]2 to the power 1/2 common.

[00:03:18]What will I have left inside? Who all have understood that 1 + x / 2 to the power 1 2.

[00:03:24]fixed bugs? I hope everyone has understood.

[00:03:26]Then 1 - x 32 and close the bracket. Then from this outer term also we will get power-1 common to 3. Inside 1 + x / 3 to the power of -1 because he doesn't have that thing. And we have to make the thing on the right hand side.

[00:03:43]fixed bugs? Did you understand this?

[00:03:47]What was the purpose of doing this? So that we have 1 + x to the power. So we can make that equal to 1 + nx.

[00:03:52]We have to make each term of 1 + x n arbitrary. We have to make the inevitable into inevitable. What will we have after this?

[00:04:01]This to this power of 2 is not working at all. 1 minute, this two to the power of 2, I take it out.

[00:04:10]And from there to the power of 3 -1 because both of these, both of these, you guys can see. Were being multiplied.

[00:04:16]fixed bugs? And if this term comes from bottom to top then that will also be multiplied. If this term comes from bottom to top, it will also get multiplied. So that three, that three will also come in the beginning, power of 3 -1, now only three people will be left inside the bracket.

[00:04:29]a + x / 2 to the power of 1/2 will remain.

[00:04:33]A - x to the power of 3 / 2 will survive and a + x / 3 will survive ^ -1. And approximation right hand side as it is. Right hand side as it is. Now 2 to the power 1/2 means square root. fixed bugs? And the power of anything is becoming minus when it goes up and becomes plus when it comes down. If you look on the right hand side, I have this thing ready.

[00:04:54]Now I come to my concept.

[00:04:56]My concept is that we will apply this thing on 1 + x / 2. 1 + nx Now understand one thing here for a minute. 1 + x / 2 to the power 1/2 This will replace 1 with one.

[00:05:12]Ok? 1 will come in place of one. x will be replaced by x 2 and n will be replaced by 1 and 2. Did you understand this? Now what do we do to get 1 + okay? Brackets have to be put on. I will close the bracket by replacing 1 + n with 1 2 and replacing x with x2.

[00:05:27]Similarly, the same work has to be done inside this also.

[00:05:29]1 + But here instead of x there is -x and 1 + nx 1 + n n is 32 and x is I have -x and bracket closed. Ok? And do the same thing with the third one. 1 + -1 and x. x / 3 and close the bracket.

[00:05:48]Who all understood this?

[00:05:50]Everyone understood this. One and two etc. all the things.

[00:05:52]Now we have squared 2/3 approximation equal to that side as it is.

[00:05:58]This thing has to be made. This isn't a frequent place, so this is how I'm doing it.

[00:06:01]Square 1 + x / 4 Close the bracket. fixed bugs? 1 - 3x / 2 is it ok? Bracket close. and 1 - x / 3 close the bracket. I have three factors generated here. How many factors have been generated? Three factors. You guys might be seeing I think here.

[00:06:21]1 - 3x / 2 1 - xy Now we have to multiply these three factors.

[00:06:27]And after the approximation on the other side of equal, that term as it is came.

[00:06:32]Now the square is 2/3 right? Bracket. Now we have 1 + x / 4 as it is. I will multiply these two.

[00:06:42]So I will use a bracket here.

[00:06:44]1 1 - x / 3 - 3 - 3x / 2 and minus and minus plus 3x² / 6 But remember one thing here, this thing will be neglected. This thing will be neglected.

[00:07:05]What will happen? This thing will be neglected.

[00:07:07]Because he told me that you have to keep neglecting every term of x², every term greater than x, including x², x, x, including x4. That has to be neglected.

[00:07:20]So I should neglect every term. There is only one formula for this question. 1 + nx becomes just 1 + nx ok? And the term x² will be neglected.

[00:07:30]Square 2 Bracket 1 + x 4 1 - x 3 - 3x 2 Bracket Close I understood that she had been neglected. Now this is going to multiply by this and the right hand side as it is right hand side as it is squared 2 3 1 - x 3 - 3x 2 okay? + x 4 - x multiplied by x is x² 12 Neglected but I will write it down. - 3x² 8 Now this term and this term have been neglected.

[00:08:11]Neglected got cured. What do I have left? Equal Approximation.

[00:08:16]Right? This has been neglected.

[00:08:18]What do I have left after this? Square 2 3 brackets.

[00:08:21]fixed bugs? 1 - x 3 - 3x 2 + x 4 and the approximation on the right hand side squared 2 3 and 1 - 19 12x here we go. Now I have squares 2 and 3 as it is bracketed 1 - 3 2 4 what will be the LCM of 3 2 4? The LCM of 3 2 4 will be 12. Now 12 becomes its LCM. -12 What happened to it?

[00:08:51]LCM is done. Bracket approximation right hand side as it is. fixed bugs? 1 - 19 and 12 and x now 12 LCM because I did not take one, hence I did not take one here it is already one. There is already one on the right hand side.

[00:09:03]So 1 - Okay, remember one thing from here. This minus is coming out, it creates a big issue. You take the minus from here in this step. So when the minus comes out, this will become a plus and this minus will become a plus minus. Now divide 3 by 12, then 4x, divide 2 by 12, then 6x and divide 4 by 12, then - 3x, meaning multiply by the one above, these are matters of very small classes. So 2 3 1 - 12 as it is 4 + 6 ah sorry this will come 2 12 this will come 18x multiplied by the one above 18x 4x + 18x 22x 22x - 3x 19x bracket close approximation square 2 3 1 - 191 and x Now if we look at this, did we get equal to the right hand side or not? The approximate answer on the right hand side was exactly equal.

[00:10:05]By neglecting. By doing what?

[00:10:08]By selecting our answer we have got it accurate.

[00:10:11]Just by using this formula you have to save four marks of the question. How many marks? Four marks save in your exam. So I hope you have understood.

[00:10:21]Tell me when you want to do a life scene. And remember the code of life. MF Q 224. fixed bugs? When you comment on this to me, when I get 100 comments on this, I will get the entire book marathon solved within a day and important questions and if I get 30 questions then I will get a total of 30 questions solved, if your paper is not solved within 30 questions then tell me that Sir the paper is not solved, I will get those 30 questions solved, there will be such questions and I will get it done through an easy method, so remember the code MF Q 224, thank you very much Allah Hafiz