How are you all? All of you who have come to watch this video are very excited to prepare for the railway exams. If you are a little excited, then it is obvious that I will be 10 times more excited than you. And we had announced the free practice series of the railway on this YouTube channel, Maths Concept King for all the students of the railway.
And today we are going to upload the first lecture in that series, Number System. You know that the most favourite topic of railway is number system and simplification Most of the questions are in depth and number of questions are asked from these two chapters So I have asked almost all the exams of railway whether it is group D paper, NTPC paper, RPF sub inspector, RPF constable paper, JEE paper Best 50 questions I have given and these are 50 must do previous questions of railway. I will give you some homework questions as well. Okay my friends, you have to watch this video from start to end. You will get a very good revision and here you will learn some unique and fresh things of number system.
This video is very beneficial for those who are preparing for any railway exams. You can give a railway paper for a year or a year and these videos will always be helpful to you. Along with the railway, constable police, the children who prepare for the police can also take help from these videos.
Their level of exams is almost the same. I will also give you the PDF of all these questions. And you will get the PDF on our telegram channel. The link of the telegram channel is in the description.
The name of the telegram channel is Maths by Gangadhar Pratap. The notification bell of all our videos is on the right side. you will get the PDF of all the previous courses if you want to download all the previous courses of Railway then I have also uploaded it on this channel if you get the notification of C.D.S. then we have made this video yesterday so you will get the free PDF of all the exam notifications, videos, and previous courses ok, let's go along with this we have the series of the long videos of Railway We have started a series of shots on this channel, Maths Concept King, where I upload daily best questions of the railway. Two, one in the morning at 10 o'clock and one in the evening at 5 o'clock. We have uploaded 8 best questions so far.
If you give me 1.5-2 minutes daily, you will keep watching from this channel, then your two questions will be revised. You will learn two concepts. And the good thing about these shorts is that I also give you homework here. Okay?
We have started with the first question of the railway. And I don't tell you the fake trick of irrelevant calculation just to make the kids happy. I tell you the same things that actually come in the exam. Okay kids?
Let's start. The best 50 questions series of the railway number system. The best 50 questions series of the best 50 questions.
Part 1. In this single video, I will ask you all the questions. Okay? Take a copy pen. No need to make notes. You will understand once you watch the video.
Because it is not very difficult to ask in the railway. Okay? Let's start, kids. The first question is, The number of 6 digits is divisible from 4, 7, 3, x, y, 5, 125. How many such 6 digits are there? then how many 6-digit numbers will be made?
For this, you should know the rule of 125. The rule of 5 says that the last number of any number should be divided by 5. The rule of 25 says that any number will be divided by 25 only when the last two numbers are divided by 25. Similarly, the rule of 125 says that any number will be divided by 125 only when the last three numbers are divided by 25. 3 numbers are divided by 125. For example, I have written 67913750 Will this number be divided by 125? So, you will say, sir, the last 3 numbers are 7500. 125 is divided by 6 times. 125 times 6 is 7500. So, this number will be divided by 125. So, in the same way, here is a question that this number is divisible by 125. So, the last 3 numbers are 6500. should be divided by 125, my dear brothers.
So, what can I take? But my compulsion is that unit rate should be 5. So, I can take 125 in the last 3 points. I can't take 125. If you take 125, then in the end, it will be 0. It will be 5. So, I can take 125, 3, 375. 125 can't be taken as 500, 125 can be taken as 5, 625, 125 can be taken as 7, 875, right? If I keep 8, 7, 5 at the end, it will be deducted from 125. 125 is 8000, this is the number of quadrants, nothing is possible in the future. So I can keep only the last three digits, that is, I will have four numbers like this.
In this way, I can make four different numbers. The answer to the question will be 4. Okay, we have cut the options. See, the next question. Here, the options are also given.
Along with every question, what is the source of the question? In which paper has it come? In which shift has it come?
In which date has it come? This is also written in detail, my friends. Okay.
You will get all these questions in our railway books as it is with solution. Railway Mathematics Complete Practice Book. 4000 questions, you will get it in that.
The bad thing about railway is that it gives the same question 15-20 times. So I have to ask you one question only, so that you can learn it quickly. 99.75 and 0.02554, how many numbers are there on the right side of decimal point?
The question is very scary. In the question he is asking that, If I calculate them, then after decimal, how many numbers will come to the right side of decimal? Now, as I ask you, as I have calculated 0.71 in 0.3, then what will you say?
Tell me, how many numbers will come after decimal? Then you will say, sir, 3 and 3 is 7, so it will be 0.219. After decimal, there are two numbers, yes, one number. After decimal, there will be three numbers. Is it correct?
So you will say that here after decimal there are two numbers and here after decimal there are five numbers. When I will do their calculation, then after decimal there will be seven numbers and many children will mark seven. Seven is wrong, it cannot be greater than seven. You will say that why seven is wrong? You missed something, my dear brother.
as soon as 5 to the 2 is multiplied by 0.5 like I have to multiply 0.05 by 0.2 so tell me how much will it be multiplied? so you will say sir 5 to the 2 will be 10 this will be 0.010 although this 0 has no meaning in 0.010 means after decimal how many numbers are there? only 2 numbers are there whereas how many numbers should have come? only 2 numbers should have come what is wrong?
As soon as 5 is with 2, it will be 0 at the end and we don't count 0. Here also it is the same. This number 0.02554 does not cut from 4. Because it is 54 at the end, this number is cut from 2. Because it is 75 at the end, this number is cut from 25. 25 means it cuts from 5 too. Means here... 1, 2 and this number is cutting from 25, here 2, 5. Now 1, 2 is coming here 5, 2 times but 5 and 2 will be a pair of 1. Here 1 is 2, 2 times 2 is not coming because 54 is only divided by 2, 4 is not divided by 4. So when 1, 2 and 1, 5 will be a pair then in the end it will be a 0. So in the end it will be a 0 which we will not count so in their number 6 will be a number. 6 digits will be.
We will answer the good question asked in the railway. Which of the pairs in Nimrin is not a twin prime? Which of the pairs in Nimrin is not a pair of twin abhazhas?
First of all, you have to learn the concept that what are twin prime, that is, twin abhazhas? Prime numbers are those numbers which are either divided by 1 or by themselves, like 5. 5 is either divided by 1 or by 5, like 11. 11 is divided by 1 or by 11. But what are twin prime numbers? Twin prime numbers are such two prime numbers Such two prime numbers which have two differences Such two prime numbers which have two differences Which have two differences We call them twin prime For example, there are 5 and 7 which are twin prime For example, there are 11 and 12 13, twin prime, there are 2 prime numbers 17, 19 these are all twin prime, now I will tell you 23 and 29 although 23 and 29 are both prime numbers but there is a gap of 6 in between so these are not twin prime So, there is a gap of 71-73 in twin prime. There is a gap of 2 in twin prime. But, is this the right answer?
The first answer is that 133 is not the prime number. 133 is deducted from 19. 19-7 is 133. When 133 is not the prime number, then how can we make a pair of 131 as twin prime? So, this option is wrong.
C option will be the answer. Next. The question is, what is the answer to the paper of group D?
The result of two positive exponential numbers is 552. If the small number of these two numbers is denoted by x, then which of the following is the equivalent of x? To find out the answer, the answer will be similar. Very good.
Two consecutive integers have a product of 550. They have a small number x. You tell me, there is a small number x. There is a gap of 1 in consecutive numbers.
1, 2, 3, 4, 5, 6, 7. If there are two consecutive numbers, there is a small number x, then the big number will be 1 more, x plus 1. And what did I give in the question? I gave their quality, so I will do the quality. What will be equal? 550. So can you make a question from here?
equation. Not even a small number. x square plus x equals to 552. When 552 comes to the left side, then minus 552 equals to 0. This equation will be made.
You will use this equation. C option is correct. Don't think that I am asking you one question and it comes only once in the paper. No.
It has come at least 10 times in the paper. Sometimes it will be 560 instead of 552. Let's move on. Question is from RRB Group D paper. What is the double of the largest number of two digits and the triple of the smallest number of three digits?
You should have knowledge only then you can do it. The largest prime number of two digits is 97. The smallest prime number of two numbers is 11. Next, you should know the biggest prime number of three numbers. The biggest prime number of three numbers is 997. The smallest prime number of three numbers is 101. So, in the question, the biggest prime number of two numbers is 97. The biggest prime number of three numbers is 2. 997 triple's sum is what?
I have asked you. Okay? So, look, it is approximately 1000. 1000 is 3000. And it will come around your 100-200-232. Options are quite far.
So, I have done it. Only one option was around 232. First option is correct. End of the talk. I could match even one number.
When a number is divided by 234, then 36 is left. What will be the result if we divide that number by 13? This is the question of RRB Junior Engineer's paper.
It seems like a trick that some number is N. It is said that when a number is divided by 234, the result is 36. It is said that the number is not the same number. I have considered the number N to be divided by 13. So, what will be the result of this?
So, what do you have to check in such a question? Is it 234 or is it 234 children? So, 13 times 13 is 10, so it is 13804. So, it is a factor of 234. So, don't do anything. The number is 36 when it is running from 234. What will happen when it runs from 13?
You run 36 from 13. So, it is 13. 13, 26 will go. What will be left? 10 will be left.
That means 10 is the answer to this question. If suppose 234's factor would not have been there. Suppose here it would have been 17. Then the answer to this question would have been there. Cannot be determined.
Can't know. Okay, kids? Okay. We will move ahead. Question is, If 19's power 300 is divided by 20, then what will be the result?
19 to the power of 300. This is the question. Look, my dear brother, this is 19 to the power of 300. I have to give it a share. So, 19, write the number above in relation to the number below. You can write 19 as 20 minus 1, 19. And its power is 300. I have to run from 20, what will be the result? You know that when I run from 20 to 20, then the whole part will be run, the result will be minus 1. And what is the power of minus 1 here?
300 even power. If we even the power of minus 1, then... So what will be the final answer? 1. And the answer to this question is 1. If suppose in the question, instead of 300, 343. This question would have been 343. Then what would be the answer to this question?
Then you would say, sir, if we add the power of minus 1, then the remainder will be minus 1. Minus 1. But we have to tell the answer positive. If the result is negative 1 after dividing by 20, then to make the negative remainder positive, we will add 20 to the divisor by dividing by 20. So the answer to the question will be 19. Let's move on. How many numbers are not a group between 87 square and 88 square? This question is so amazing. From the paper of group D.
Okay? How many numbers are not in the group between 87 and 88 square? Tell me one thing, now there is no group between 87 and 88 square.
Now there is no group, my friends. I will tell you that 3 square is 9 and 4 square is 16. Tell me, will there be any group between 3 square and 4 square, 9 and 16 or not? Now there will be no group between 9 and 16. Yes, it happens that what comes between 3 square and 5 square?
Which number square comes? So, you say, sir, 4 square. Means, he is making you mad in language. How many numbers come between 87 square and 88 square?
There are no numbers. First of all, there is no need to have any number in between them. There will be many numbers between them, which will be integers. Means, I have to find out only that 87 square and 88 square.
square ke beech aane wali kitni sankhyaan purankay, in ke beech kitni sankhyaan aati hain ab concept samjo, jaisa mai aap se puchu ki 5 aur 8 ke beech me kitni sankhyaan aati hain 5 aur 8 ke beech me kitni sankhyaan aati hain to aap kaoge sir, 2 aati hain, 6 aur 7 2 sankhyaan aati hain kaise pata lagaogay, to aap kya kaoge sir, last wali me se pehli wali ghatao, lekin last me se pehli wali ghatao ge to, to 3 aara hai There are only two numbers in between. So, we have to subtract one more. There are two numbers between 8 and 5. This is the trick we have to use here. How many numbers are there between these two?
Because all the numbers between these two are all integers. And there is no square between them. There will be no square between them. So, what will you do?
From the last number, you will subtract 87 squares from 88 squares. But you will get one square. We have to reduce it.
Now tell me, isn't this the algebra formula? a square minus b square, a plus b into a minus b. How much will a plus b be? 165. Tell me.
What will a minus b be? 1. And if we do minus 1 from this, then 164. The answer to the question is 164. Where is it? Option number b is correct. I will move forward.
Next question. Find the value of d. Look at the question.
So, the question of NTPC is what is the value of D? Tell me quickly. Yes. Find out the value of D if 1 to 1 6 minus 3 to D is equal to 8 to 8. If my friends this number is less than 8 to 8, then tell me the value of D. What does the 8th rule say?
That the last three numbers should be less than 8. Now suppose I kept 4 my friends. Instead of D, I kept 4. so first thing is if 4 out of 6 is reduced then 2 2 2 will come, this is wrong if suppose I have kept d command 2 so if 2 out of 6 is reduced then 4 will come, this is also wrong this d and this d should be same, this is also not if I have kept d command 6 then this will come 0, this is also wrong means if 3 options are wrong then this one should be correct 8 if I reduce 328 out of 1216 then what will come 888 will be the answer. 888 is less than 8. 111 times means 8 is the answer. Use the option.
Question number 10. The question is good. If n is a natural number, if n is a natural number, So, the question is, from whom will n cube minus n always be divided? If n is a natural number, then from whom will n cube minus n always be divided?
See, kids, many kids keep a value put and see that they will keep 1, 2, 3, and check. There is a chance of a mistake. If n is a natural number, then from whom will this number always be divided? If you see from here n is common In bracket only n square minus 1 will be left What is n square minus 1?
n square minus 1 is n minus 1 into n plus 1 n minus 1 into n plus 1 This is the number basically If you see carefully, these three are consecutive natural numbers The smallest one is n minus 1 n minus 1 1 plus n will be n then 1 plus n will be n plus 1 the smallest 1 plus n is n 1 plus n is n plus 1 these are 3 continuous numbers and the number of 3 continuous numbers 3 continuous numbers will always be factorial 3 factorial 3 means 3 2 9 6 1 m 6 3 continuous numbers will always be divisible by 6 b option answer is You will say sir what are you teaching? There is a concept my friends. Write it from here.
Product of Product of I am writing in English. I will not come in Hindi. Product of any n consecutive number.
Any n consecutive number. Any n consecutive number. Always factorial n. always is divided by the factorial n any constant of n numbers always is completely divided by the factorial n we will listen again any constant of n numbers is always divided by the factorial n the question came in the railway So, the result of any four natural numbers will always be different from any other. So, the result of any four natural numbers will always be different from any other.
But, the guarantee is that it will be 24. Okay, kids, you will understand the concept. The question is number 11. The question is, after dividing 1597 by a number, what is the result of the result? The answer is 21. Please read the answer.
Comeridos do. Whenever we divide a number by a divisor, suppose quotients are divisible and divisible is the answer. So what will be the number?
The divisible is equal to divisible times divisible plus divisible. This is a simple concept, everyone knows it. I also want to use this concept here.
When we divide this number by a definite number, divisible is 55. Quotient comes as 55 and the remainder comes as 21. Find the denominator. What is the number? 15979. I have asked you for divisor. Quotient is 55. Reminder is 21 plus 21. You have to use this concept.
Okay, children, you will say, yes, sir. When 21 goes here, then 159. How much will it be? 50. Equal to D times 55 Tell me If you want to run from 55, then 55 times 2 is 110 495 is left If 55 times 2 is 99, then it is 295 So your answer is 290 The answer to the question will be See, the same questions come in the railway Most of the questions of the railway They are one liner One liner Remove this one-line logo If ABCDE is a number of numbers in the left to right column, then find the number.
So, ABCDE is a number of 5 numbers. It is written from left to right. That means, first it is A, then B, then C, then D, then E. This is the number of 5 numbers.
So tell me what will be the number? We will answer it quickly. Listen carefully.
First let's understand the basic concept. For example, I wrote a number in front of you of 73 of two numbers. 3 is the number of Then the number is made. 350 plus 4 is 354. This is the basic meaning. There is no multiplication between 3, 5, 4. 4 is 1 times, 5 is 10 times, 3 is 100 times.
This is the only thing that can be written in short. This is the way of writing 354. If you have this number ABCDE, which is written from left to right of 5 numbers, then what will it mean? This means that I can clearly see this option.
1 in the first number will be 1, 10 in D, 100 in C, 10 to the power of 3 in B, 10 to the power of 4 in A. So, B option is the correct answer to this question. Meaning, the basic questions come in the railway. You have to practice these, children.
Next question. Question number 13. Which number of the number is in the group A? In the group A. The square root of which of the following number is irrational? Irrational means a parime sankhya means asant dasam lav.
Which does not repeat any pattern again and again. Okay my friends, in which no number is repeated, whose exact meaning cannot be written, whose fraction cannot be written. See my friends, whose fraction is in a parime.
If you write any perfect fraction, whose fraction is in a parime. square number of the work value. For example, my friends, 256. 256 is a perfect square number. If we calculate its work value, 16 will be easily calculated. If you calculate a non-perfect square number, like under root 2, root 2 is not a perfect square number.
So, 2 under root, a peri, number will come. 1.414, a prox will come, my dear friends. Basically, I have to tell you that which number perfect square not which number is not complete if number is complete then its under root will be easily solved rational number prime number and if number is not complete like under root 2 3 4 2 3 5 7 if we solve their under root then rational number will be solved so my dear brother i can tell you that this number can never be perfect square in the end 0 after 0 4 if you square any number with zero at the end, then at the end, it will be double zero. It is not possible that in any number, the first number is zero, then it is not zero.
This perfect square can never be made. Perfect square can only be made when zero is coming at the end, then it should come twice, not less than two. This number is never complete, so its divisible number will come in a prime. A option is its answer.
This is the correct answer. The sum of three distinct prime numbers is 40. There are three different numbers of odd numbers. What is the quality of these odd numbers? There are three different odd numbers. Who comes together to get 40?
What is the quality of these odd numbers? So I have to find out the odd number. See children, there are three prime numbers.
My dear, 40 comes after this. 40 comes after T. Listen to me.
Children, understand this. Now I have to find out the three numbers. Okay? My dear children, what is 40? 40 is a sum number, an even number.
It is a sum number. It is the one which is divided by 2. Do you know what is the number of numbers which is either divided by 1 or by itself? Like 2 is a prime number because 2 either cuts from 1 or 2 itself cuts from 2. After 2 there are 3 prime numbers, 5 are abhaya numbers, 7 are abhaya numbers. 9 are not abhaya numbers because 9 cuts from 1, 3, 9. Abhaya numbers have only 2 qualities. 11 cuts from 11, 11 is my friend's abhaya number, 13 is all abhaya numbers.
Meaning all abhaya numbers, all prime numbers are odd except 2. Do. He is the only prime number who is even. which is a sum number and also a divisible number, that is only 2 so 40 is coming with 3 divisible numbers if I take odd numbers of 3 divisible numbers divisible number, divisible number and divisible number then you should know that divisible numbers will be added to 3 divisible numbers we will add odd to odd, odd number will be even number even number If we add odd numbers then we get odd number But we need a even number when any number is even So we need to add odd numbers to odd numbers to get even number If we add even number to even number, then only it will become even number. So, it is my compulsion that I have to take one even number from these three prime numbers. And one prime number is even, 2. That means, the other two prime numbers will be odd and their sum will be 31. 31. Sorry.
Their sum will be 38. 38, 2, 40. Okay? If we add two odd numbers, we get E1. If we add even numbers in E1, we get E1.
This is the logic behind this question. Now you tell me what will be the other two prime numbers? Now I have to guess from here. If I consider 3, then it will be 35. But 35 is not a prime number, so my guess is wrong. If I consider 5 as the next prime number, then it will be 33. So, I have to add 5 and 3. and 33 is wrong.
If I consider it 7, then I have to take 31. 7 and 31 is 38. 7 and 31 should be 38. And these 7 and 31 are the absolute numbers. That means my guess is correct. There is no formula for absolute numbers. You just have to apply the formula and the answer is there. Here you have to guess common sense, hit and trial.
So, we have found out that 2 abhjai numbers are 7 and 31. These are 3 abhjai numbers. If we ask them the value of these numbers, then 2 times 7 times 31 is 2satya 14. 4 times 4 is 4. So, the answer is 434. D option is correct. Good question, we will move ahead. The question number is 15. Many questions come in the railway from divisibility rule.
If the number of 8 parts is divided by 3x, 5x, 4x, 7x, 9x, 4x, 88, and the number of 8 parts is divided by 9, then the maximum probability of 3x plus 2y minus z is ask you maximum possible value maximum possible value what can happen see my dear children this number is divisible from 88 this number is divisible from 9 its maximum maximum will come when x maximum is y maximum is also maximum and z is minimum minimum should be reduced children this number written in front of you this a 88 means 8 times 11. 8 and 11 are both equal. If a number is less than 88, then that number should be less than 8 and less than 11. We don't know the rule of 88, but we know about 8 and 11. If this number is less than 88, then it should be less than 8. And the rule of 8 says that the last three numbers should be less than 8. The last three numbers. The last three numbers are 9y and 4. What should I keep in place of y that it gets cut off from 8?
What should I keep in place of y that it gets cut off from 8? You can write 9y4 as 800 plus 1y4. We will add 100 something in 800, that's why it will be 900. What does 900 mean? It means 800 plus 100 something.
If we subtract 800 from 9Y4, then we will have 154 This number is cut from 8 Means we should only cut this number from 8 So what can I put instead of y? 0 104 will be deducted from 8 Then next 4 144 will also be deducted from 8 Then 184 will also be deducted from 8 Means y will have 3 values 0, 4 and 8 The smallest value of y is 0 104 is deducted from 8 Then next 4 will be added In the middle, we will add 4 in 0 144 is deducted from 8 18 times 184 is also deducted from 8 23 times But If I want to get maximum value of this expression, then the maximum value of y is 8. The maximum value of y is 8. So, here I am forced to take the value of y as 8. Now, children, this number is also less than 11 along with 88. Now, you know the rule of So, add up. 3, 5, 8, 7, 15 plus y. 3, 5, 8, 7, 15 and I took 8 out of y's maximum value. 8. 3, 5, 8, 7, 15, 15 and 8, 30. Now, add up the ones that are coming in place.
x, 4, 9, 13, 4, 17. 17 plus x. So, I... We have added the values at the location and the place. Now their difference, their difference should either be 0 or 11. And see what is x, y, z, these are all single digits. The value of x, y, z will be between 0 and 9. It cannot be greater than 0 or 9. The range should be between 0 and 9. So if I want to make this 0, then what value of x will I have to take? 17, 6, 30. Means, if I take the maximum value of 8 from here, then the value of x will be 6. 17, 6, 30. From 17, 30, we will reduce 0. So, the value of x is 6. Now, I have to find the value of z.
Children, if this number is divided by 9, then the rule of number combination 9 is that number combination should be cut from 9. Number combination, find 5, 4, 9. After that, my friends, 9. After that, 2 and 1. 3 and 3, 6, 2, 8, 1 plus z is here 2 and 3, 3, 6, 2, 8, 8 plus z is here 5, 4, 5, 9, 9 is cut This is digital sum Any number will be cut from 9 only when its digital sum is 9 So what value of z can I take from here? 1 z command 1 is here, z command 10 can also be taken 8, 10, 18 also have digital sum 9 But dear students, the value of Z cannot be 10, you can only take 1. So Z command 1 has come, we keep this value here. 6, 36, 18 instead of X, 8, 8, 2, 9, 16 instead of Y.
18 plus 16, 34 Z command 1. We will subtract 1 from 34, 33. The maximum value of this will come, we can see B option, 33. This was a very good question of CGL level which has come in the railway. It won't be a light question, children. Let's move on.
The question is, if the number of 5 numbers is 688XY, if this number is 11 and is divided by 21, then what is the value of 8X minus 3Y plus XY? This question is also being asked in SSE in 2020 and 2021. This question has come in the paper of group D in 2022. It is a very popular question and I will tell you its best trick. What is it? If the number of these 5 numbers 6, 8, 8, 11 and 21 are divisible, then it can be seen that this number of 5 numbers is less than 3, 7 and 11. It can also be given. So what is its meaning?
Because the number of 3 and 7 is 21. It also gives. Children, if this number is less than 11 or less than 21, then this number 11 times 21, which means 11 times 21 will be 210 and 231 should also be less. This number 688XY, this number should be less than 231. If it is less than 11 or less than 21, then it will also be less than the value of 1121. This means that I have to calculate the value of 231. a multiple or a quantity which is near to it.
Near to it. Near to it means 6 double 8 I want to see a multiple of 231 that is close to this number. This number is 68000. If the number of 231 is close to 688XY, then the double of 231 is 462. If I multiply 231 by 3, then it will be 693. But this is a 3-digit number.
This is a 5-digit number. Let's put 2 zeros. I can tell you that this number is 231 multiple. And I have reached near it. I have reached near 688XY.
Although this is 688XY. This is 693. This is 693. This is 3 00. This is more than 500. In 800, 500 will be added then 300 reaches that means I have to reduce it I have to reduce it so much that here 8 comes what to do do any number of 2 to the 31st in the multiple of the 2 to the 31st is the best way to do it is the shortest method but the mind will have to apply a little more if I reduce 2 to the 31st from this then children it will remain 6 9 if I double 2 to the 31st If I subtract 462 from this, then 2 out of 10 is 8, 6 out of 9 is 3, 4 out of 12 is 8, 6, 8, 3, 8. 6, 8, 8, 3, 8 is such a number which is a multiple of 2 to 31. This number is less than 2 to 31 by 300 times. This number is less than 2 to 31 by double. If I subtract them, then this number is also less than 2 to 31. 32 means 11 and 21 will be deducted. This number is 68838. The number was 688XY.
Means 3 is written in X and 8 is written in Y. X is 3 and Y is 8. I asked you, keep it here. We will keep 3 instead of X. 3, 8, 24. We will keep 8 instead of Y.
8, 3, 24. And how much will X into Y be? 3, 8, 24. Right? All this has been cancelled out.
24 questions are answered. B option. Very nice question.
Good question. Next. Question number is 17. See, number system questions are more.
You keep watching that I am asking you mostly question of number system. Okay. If P is an unbounded number and P divides the square, then So P will not be divided necessarily from these four options. First of all, P is a prime number.
Why does this number P divide the square? If P is a prime number, why is it dividing the square? Why does P divide the square? will divide Q as well.
Will divide Q as well. P will divide Q as well. No, understand. For example, I have taken 7 as a prime number. 7 is a prime number.
Now, 7 is a prime number. 7 divides 21 square. 21 square is 441. 441 will be divided by 7. But, why will it be divided?
Divide will happen because this number 21 already has 7 hidden in it. If I take its unroot 21, then also it will run from 7. Meaning if Q square P is run from 7, because P is prime number, so it is possible, then why will it run from 7? If Q is running, then Q will run 3 times. Q will run.
If Q square P is running, then Q square twice will run. But Q square P is running. Q plus 1 P will not be able to be divided. Because if 21 7 is being divided, then it is not necessary that 1 plus 2 will be divided by 22 7. It is not necessary. So, B option will be completely wrong here.
Technical and easy questions. Children, if you don't understand anything, then take an example. But you will be clear about your own things.
The question is, when the next number system gets... 43 is divided by x, so the result is x-5. When 43 is divided by x, the result is x-5. If x is a natural number, then how many solutions will x have?
Same to same question came in UP Constable's paper too, my friends. He said, when 43 is divided by x, the result is x-5. If x is a natural number, then how many solutions will x have?
Look, my dear brothers. 43, my dear children, when we divide 43 by x, then the cease-fall that we have told is x minus 5. I have assumed that when we divide 43 by x, then why did it divide? Children, if this is the case, then what will 43 be? You tell me what will be 43. So, what will be the value of 43? Divisor into quotient, that is, x into q plus remainder.
remainder is x minus 5 this is the rule if minus 5 goes there then 43, 5, 48 will be equal x common and bracket will be q plus 1 why? because xq plus x is x common if I want to get the value of x then the value of x will be 48 divided by q plus 1 48 divided by q plus 1 this will come Now in the question, I said that x is a natural number. x is a natural number.
x is a natural number. Natural numbers are 1, 2, 3, 4, 5, 6, 7. These are all natural numbers, my dear children. Now tell me one thing.
When will x natural number come? When it is completely divided by 48q plus 1. That means the lower number, the lower number q plus 1. If it is completely divided by 48q plus 1. If I take the lower number as 37, then the number will not be equal to 48. So the lower number Q plus 1 will have to be taken in such a way that it will completely run away from 48. So the lower number I can take is 48. If I run away from 48 to 48, my dear, will X1 come? Hey kids, what will be the value of X?
1 will come. But here is a problem, my dear. The problem is, you have to see this too, that when we run away from 48 to X, then the final result X-5 comes.
X is a natural number. If the final result X-5 comes, see, the final result can never be negative. The final result should always be positive or zero.
The final result can never be negative. That means, the value of x will either be greater than or equal to 5. The value of x cannot be less than 5. If you take the value of x as 2, then the final result will be 2 minus 5 minus 3, which is wrong. So, I am forced to take the value of x as greater than 5. So, tell me what you can take from the lower number.
You can take the lower number as 1. If you take the lower number as 0, then 48 divided by 1 is 48. It is possible. You can take the lower number as 2. 48 divided by 2 is 24. It is possible. You can take the lower number as 3. 48 divided by 3 is 16. It is possible. You can take the lower number as 4. 48 divided by 4 is 12. It is possible. You cannot take 5. because 48 divided by 5 will go to decimal not possible you can take 6 my friends 48 divided by 6 if I take 6 from the lower number then the value of x will be 8 is it possible?
if you can't take 7 then you will take 7 from the lower number 48 divided by 7 will go to decimal if you take 8 from the lower number 48 divided by 8 the value of x will come So, X will be equal to 6. It is possible. You cannot take 9, my dear. It will go in decimal.
You cannot take 10. You cannot take 11. You can take 12. If you take the lower number 12, then X will be equal to 4. 48 divided by 12 is 4, which is not possible. That means, you can take the value of the lower number. 1, 2, 3, 4, 5, 6. You can take the value of the lower number.
You can take the value of the lower number. You can take the value of the lower number. So, X will also get 6. C option answer is C.
The lower number, which means, Why can you consider 6 different plus 1s? So x will also have 6 values, if you take the lower number 1, then you can take the q as 0, suppose you take quotient 0, then it can go 0 times. So 48 will come, 2 people will come, 24 will come, 3 people will come, 16 will come, 12 will come, my friends, and here 6 will also come. If the value of x is greater than 5, then the total x is 6. Next question. Question number 19. Then a dangerous question of remainder.
Remainder questions are very common in the paper. It is said that 16 results are left when a number is divided by a denominator. Let's read the question.
If we divide a number by a factor, then the final result is 16. If we divide the double of the same number by the same factor, then the final result is 3. Find out the value of that factor. So, suppose that I have taken a number N and you divide a number by a factor D. Suppose that there is a number N When you give a number a divisor, then the result is 16. If you double that number, if you double that number, my dear, listen carefully.
If you double the number, you will give the same divisor, you have doubled the number. So remainder will be double, the result should be double 32. The result should be 32, my dear brothers. Listen to this, children.
If you divide a number by D, then the result is 16. If you double the number, and divide the double by the same divisor, then if you double the number, then the result should be 32. But in the question, how many results are left? 32 results should have been there. But actually, I got 3 results.
What can I write 32? I got 3 results. I can write 32 as 29 plus 3 is 32. That means I got only 3 results.
That means where did 29 go? This 29 is completely divided by the divisor. Divisor is a divisor of 29. Divisor is a divisor of 29 which has divided 29 into 3. The result should have been 32 but only 3 was left. So, the divisor of 29 is a divisor of 29. Divisor of 29 is neither 23, nor 53, nor 51. It is 29. This is the answer. option se kar lenge.
Waisa bhi aap jaante hain ki jab aap kisi sankhya ko divider se d se bhaag karte hain to bhaag dene par sesphal soli aata hai. Sesphal hamesa bhaag dene wali sankhya se chota hota hai. Jaisa mai kisi bhi sankhya ko 7 se bhaag dun sa poch 7 se. To kya bach sakta hai sesphal ya to 0 aega, 1 aega 2 aega, 3, 4, 5, 6 7 se bada thud na aasakta hai sesphal.
The number of the divisor is always smaller than the number of the divisor. If I am dividing by D and the divisor is 16, then the divisor will be 16. It will be bigger than 16 and the quality of 29 will be different. There is only one answer and only one option. Very nice question.
Let's move on. The question is, if a number and its reciprocal is 7, So, which number can be given from the given options? You can check this question by checking the options.
This question has come in the RRB group D paper. It is a good question. I am asking you the same question which is a little different, a must-do question. I assume that any number is X. So, what will be its reciprocal?
1 times x. So, in the question, it was said that some number and its reciprocal is 7. So, what can be the number? So, children, if I either use algebra or I make it a double-digit. If I multiply by x, it will be x squared.
plus 1 equal to 7x. This will be the equation. If I bring 7x to the left side, then x square minus 7x plus 1 equal to 0. This is a two-dimensional, quadric equation, which you have to solve by using the Sridhara Charay formula. You know the Sridhara Charay formula.
x equal to minus b, minus minus plus 7, plus minus, under root b square minus 4ac. minus 7 square 49 minus 4ac will be 4 minus 4 49 minus 4 is 45 divided by 2 from here x will have 2 values 7 plus minus 45 is 9 times 45 9 under root 3 7 plus minus 3 root 5 divided by 2 means this is not the answer 7 should be positive 7 root 5 will not come, 3 root 5 will come, D option. One number is given, 7 plus 3 root 5 divided by 2. This is the answer. Basic question is, we will do it, children. Next question.
Make it fast, fast. One number of two numbers is equal to 7 times the number of its numbers. One number of two numbers is beta.
And this number is 7 times the number of its numbers. The number changes by changing the place of the numbers. The number is 18 times less than the original number.
Find out the property of the number of the number. The question is from the paper of group D in 2022. Whenever children see such questions, they become emotional. They start solving the problem that the number of the number is x and the number of the number is y.
And they start making big questions. 90% of such questions are done with the help of options. They have said with a little bit of mind that one number of two numbers is equal to 7 times the number of numbers.
Means that the number of two numbers is equal to the number of numbers. The number of two numbers is 7 times the number of numbers. And the new number of numbers is less than the original number. So the number of two numbers is 7 times the number of numbers. So the number means 7 is a multiple.
What is the number of 7 times the number of 2 numbers? 14. But the opposite of 14 is 41. So 18 is not less. After 14 comes 28. 21 is 12, so 9 is less. Next is 28. 28 is 82, so 18 is not less.
After 28, 35 is not less. Next is 42. 42 is 24. If I convert 42, then it will be 24. If the number is 42 and the number is 24, then the number will decrease from 42 to 24. 18 is less, yes it is less. If we subtract 24 from 42, then we get 18. So, I am satisfied. So, I will throw a palm and a hand and I will immediately catch the number. The number of numbers is 7 times.
The number of 7 will be a multiple. I checked 7 times 2-4 times. It is set at 42. It means that the number is 42. If we change 42, then we get 24. If we change the number, then we get 18. The number is 42. The number is 4 times.
My friends, this is the answer. D option. And you can see the number is 42. Question solved. Mind your head.
Find out the number of 42 columns. The question is from RRB NTPC's paper. The white question of NTPC is in front of you.
So what is the trick to find the number of factors of any number? It is 4200. So find the absolute value of this. What can you write 4200? 4200 x 100. 100 is 25 x 4 is 100. 2 square is 4. 4 x 25 is 100. What is 4200? 6 x 7 is 4200. 4200 is 6 x 7 is 4200. 2 x 3 is 6. 7 x 7 is 4200. This is what happens.
Okay? Now my dear children will see here, when 2 square is equal to 2, then 2 cube is equal to 3. into 5 square and 7 I have done the unbiased division of the bialystic means I can't break more than this I can't break 5, 7, 3 now you have to pay attention to the powers here 2 has 3, 3 has 1, 5 has 2, 7 has 1 you have to find out the division of this to find out the division of this, add 1 to the power add 1 to 3, add 4 to 3, add 2 to 1, add 3 to 2, add 2 to 1, add 1 to power and multiply this is the total number of factors of 4 to 8, 24 to 48 so there are 48 factors of 4 to 42 Okay kids? If I give you some extra information, find the number of odd factors. If you had asked for the Vissam quality of 4200, tell me Vissam. How much is the Vissam quality of 4200?
That means, the one which has two. Then also you have to apply the same technique. Listen carefully my dear children.
If you have been asked for the Vissam quality, then only you... You have to focus on this portion. Take out 2. You have to focus on this portion.
You have to focus on this portion. Even numbers... Visham means that if there is not 2, then ignore even 2. You have to focus on odd. Add 1 in power. Add 2 in 1. Add 3 in 2. Add 2 in 1. So 2, not 2, 4...
4 tia 12 hai toh 42200 ke visam gunankhand ki sankhya 12 hai Mujhe lagta hai yeh concept aap bohot achi tarike se samajhge hongi aage How many prime numbers are included in the factorization of? Yeh sankhya di huye iske gunankhand me kitni abhajja sankhya hai samil hai Kabhi kabhi galat language bhi bol deta hai ki iske kitne gunankhand abhajja hai Jabki sahi language yeh hiye jo likhi huyi hai how many prime numbers are included in its number. So kids, what you have to do is, first break it more. 6 can be broken more. 6 means 2, 3, 6. Power is 7. So the power of 2 will be 7 and the power of 3 will be 7. Similarly, 35 means 5, 7, 35. 5 will be a cube and 7 will be a cube.
And we can't break 11, 11 has 10 power. So, dear children, we have done this. We have to break it till the end.
Ask how many odd numbers are there? How many odd numbers? Whenever it is possible, Ask how many odd numbers are there? So, just add the power.
7, 7 is 14, 14, 6 is 20, and 10 is 30. You just have to add the number 30. 30 will be the answer. There are many more questions in the previous episode. You just have to add power. 30 correct answers.
We will move on. Okay. See, guys. There is a question in the railway.
A question from group D paper. This question came in 2022. I am only paying attention to delivering content. Only to teach.
You will not get any reason to talk in this class. I am recording at night. Class at 11. Okay, brother. I have been studying all day and my mind is full of thoughts.
I don't know what I am saying but still Explanation to the point will be the concept to the point. Okay Most of the questions that come in the railway The ones who check the statement, which is right and which is wrong, that too in the number system. Which of the following statement is not correct? Which of the statements is not right?
That means three will be right and one will be wrong. There are only four single digits. prime numbers.
Only four one-digit abhazhya numbers. Two, three, five, seven. That means God has made only four single digit prime numbers.
Absolutely right. Second, there are infinitely many prime numbers. There are infinite abhazhya numbers in the world.
Absolutely right. Numbers are infinite. You can find infinite abhazhya in them too. One abhazhya number has only two qualities.
Absolutely right. One abhazhya number has two qualities. One is infinite.
One is the number itself and the other is 1. All the numbers are odd. This one is wrong. All the odd numbers are not odd. One odd number is such that two are even.
So this is wrong. He has answered the fourth question of the same question. The fourth option is wrong.
Next. Which of the following options below gives a pair of co-prime numbers? Which of the following options below gives a pair of co-prime numbers?
Do you know co-prime numbers? There are two numbers which have nothing in common except 1, whose highest common factor is 1. For example, 5 and 18 are co-prime pairs. 5 and 18 have nothing in common except 1. I will tell you that 25 and 32 are co-prime numbers. Nothing is common in 25 and 32. But I will tell you that 36 and 82 Is this a co-prime number? No.
Why? Because there are 2 common pairs in 36 and 82. These are not the same numbers. Which of the following equations is a co-prime pair? 196 and 343. 196 is a square of 14. 343 is a cube of 7. I can see that there are 7 common pairs in both. This means that this is not a co-prime pair.
These are not the same numbers because both have 7 common. 161 and 192. Son, I have been seeing the mountain of 161 since childhood. And who does 192 cut from? 4. 4, 4, 16 and 3, 4, 8, 32. That means nothing is common in both of them.
23, 7, 4, 48 are not common in both these numbers. That means these two numbers are different. And I have to check like this. I will check by removing their HCF.
Either you check by removing HCF or check by dividing by this way. These two are not common in both. So these two will be different.
Next. Which of the numbers is 4400? 4 options are given to you.
Which of these 4 numbers is completely divided by 44? Do you know the rule of 44? No.
But you know that 44 is 4 times 11. If a number is divided by 44, then it should be divided by 4 and 11. If a number is divided by 4, then it should be divided by the last 2 digits. All the options are divided by the last 2 digits. Now I have to check 11 because all these numbers are divided by 4. 11. Is it being divided by 11? You will understand the rule of 11 very well. Add the numbers of sum and addition.
1, 5, 6, 6, 3, 9. 5, 2, 7, 2, 9. So the difference between 9 and 9 is 0. This number is divided by 11. This number is being divided by 11 and 4 so it will be divided by 44. So, the options of 1 will come, which means that both these options have been removed. Now, see, with 1, it is either 4's pair or 3's, why should I check the second number? I check the third number. 1, 6, 7, 4, 11. 5, 9, 14, 4, 18. 1, 6, 7, 4, 11 and 9, 4, 13, 5, 18, their difference is 7. Difference should either be 0 or 11 multiple If the difference is 7 then this number will not be deducted If it is not deducted from 11 then this option is wrong So I will get this option right If 3 options are wrong then 4 should be correct This number will be deducted from 11 1, 6, 7, 9, 16 5, 9, 14, 2, 16 Difference of 16, 16 is 0 This number is deducted from 11 Next question is, if PQ is a two-digit number, then who will be the one to be divided by PQ minus QP?
If PQ is a two-digit number, then why PQ and QP are opposite numbers? How will their difference be divided by 9? Why PQ is a two-digit number?
What will happen my friends? 1i is 1 times 2i is 10 times if it is pq then what will happen? 10p plus q and when I change its numbers then what will happen? 10q plus p now when I take their difference then what will happen? 9p minus 9q 9 into p minus q my dear children you will say sir means any number and the difference of number obtained by changing its numbers always 9 times something will be 9. 9 times 9 will be less than 9. If this question is already in NTPC, next year this question will be asked, is it plus or plus?
So, what will be the answer? 11. Means, any number of two numbers, and the number obtained by turning its numbers, the number of numbers will always be less than 11. Any number of two numbers, and the number obtained by turning its numbers, the new number will be, their yoke is always 11th part ok children if you are enjoying in asking questions then along with the video share the video like the video and also comment 61, 62, 63, ... what will be the number of 1 in the result of 69 see the number of 1 depends on the number calculation of 1 continuous numbers 61, 62, 63, 64 65 49 x 51 x What is the unit digit of this number? So it's not like we keep doing the whole number, after 59, 51, 53, 55 5 is coming Now all these are odd numbers, not even numbers Now, how many times 5 is equal to 5? 5 will be 5. 5, 3, 15, 5. 5 times 1 is 5. 5 times 5 is 45. How many times you multiply, if you multiply in the odd number of 5, then it will be 5. This question is suitable for the future year.
Okay? Yes. We will do the next question.
Assume that x is equal to 55 power 100, 55 power 101 plus 55 power 102. So, which part of the numerator What prime number is not a factor of x? So first you have to solve x. Base is same as 55. So from here 55 power 100 common will come.
55 power 100. What will be left in bracket? If we take 55 power 100 common, then 1 will be left. This will be left as 55 power 1. And this will be left as 55 square.
By the way, what is 55 square? 25 and 5's next number 6 is 3025. 3025 will come if I add 55 in 3025, then how much will it be? 3080 if I add 1 in 80, then 3081 will come Clear? Now tell me If 11 comes in 55, then it will be deducted from 11 In 3081, my friends, 8 and 9, 3, 12, see it is also deducting from 3, what does it mean?
3 times 1027 3x1027 means this number is also cutting from 3 in 55 it is coming 11 and also cutting from 11 now we have to check from both 71 or 79 tell me is this number cutting from 71 if I see it will go from 71, how much will be left once 317 will be left so from 71 my friends So, this number will not go from 71. And you will not be able to run from 71. So, it is running from 79. How much will be left? You will be left with 237. And 237 will be deducted 3 times. So, it is 79 x 13. 79 into 13 is there. So this number is divided by 13, divided by 3, divided by 79, divided by 55 power 100 but 71 is not there.
It is divided by 79 too. The answer to the question will be A option. Many such questions come in the paper. Next. Which statement is correct out of the number?
In Group D, such questions are very common. We will read each statement. 1 is a prime number. Wrong. 1 is neither a prime number nor a composite number.
1 is neither a positive number nor a negative number. Because negative numbers have two qualities. Composite numbers or positive numbers have at least three qualities.
1 has only one quality, so 1 is neither a positive number nor a negative number. All prime numbers except the number 2 are odd. Leaving aside the number 2, all the negative numbers in the field, this statement is correct.
Apart from 2, all the prime numbers 3, 5, 7, 11, 13, 17, 19, all are odd. This is correct. I didn't have to ask the truth. That's it.
I will not check further. I don't have time to check. Next. How many prime numbers are there in 21,600 numbers?
perfect square how many quadrants are complete group very good 21,600 how many quadrants are complete group number of factors very good first children do prime factorization 21,600 sorry 21,600 is 6 cube and children 100 is 25,400 means 2 square times 5 square children this 6 is equal to 2 3 6. 6 cube means 2 cube times 3 cube. 2 3 6. You will say, yes sir, it is great. Now you tell us that 2 cube and 2 square will be 2 power 5. Into 3 cube times 5 square.
Yes, children. In the question, I have asked you how many complete groups are there? This is a very small number. Even if it is a big number, we still use this trick. Full group means numbers whose power is even number.
In which the power is 2 multiplied by 2. So whenever such a question arises that the quality is full group, then add 1 by dividing the power by 2. What do we do to check the quality? We add 1 in the power and multiply it. If I want to find out the perfect square, then I will divide by 2 and add 1. If I divide 5 by 2, then it will go 2 times, not 2, 4. If I add 1, then it will be 3. When I divide 3 by 2, it will go 1 time. If I add 1, it will be 2. If I divide 2 by 2, it will go 1 time. If I add 1, it will be 2. So it will be 2 2 4 3 12, meaning power divided by 2. 5 is going from 2 to 2.5, but not 2, but 2. 5 will run from 2 to 2, will run twice.
Add 1 to 2, 3. 3 will run from 2, will run once, add 1 to 2. 2 will run from 2, will run once, add 1 to 1. 2, 2, 2, 4, 3, 12. This is the answer. If suppose he would have asked, how many Gwankhand Poon Ghan are there? Perfect.
cube. How many factors of 21R600 are perfect cube? So in that case we would have divided power by 3. We would have divided by 3 and added 1. Did you understand the point?
It is simple logic. We will move ahead. The question is, the paper of NTPC 2021 is great. When a small number divides a large number, then we have a partial 6 and partial 8. 5 final results. The difference between two numbers is 1540. Tell me the smaller number.
This question has also come in the means of CGL. When a small number divides a large number, neither I know the small number nor the large number. Let's assume the small number is x and the large number is y.
What is said in the question? When we divide the small number by x, we divide it by the large number, then we get 6 final results. And the final results are 5. 5 comes. So this means the big number will be 6 into x 5. This will be.
The difference of both numbers is 1540. Difference means, it is a general thing. I have considered the big number as y. If we reduce the small number from the big number, then 1540 comes. This is what the question is saying.
If you ask me a small number, then put 6x plus 5 here instead of y. You have to subtract x from 6x plus 5 equal to 1540. Okay, children. We will subtract x from 6x, 5 will be equal to 1535. We will run away from 5. x equal to 5 is 15, 0 is 5 is 7, 35 is 307. then 307 will be your small number. B option is correct. There was no much courage in the question.
We will move ahead. Again, another question from the NTPC paper has come. Which is a statement-based question.
Do it and tell me, children. I have compiled very good and wonderful questions. Questions are compiled in the day, recording is done at night, upload on channel, it takes a lot of hard work.
The amount of hard work we are doing for you, you also do a little bit. Share these videos with your friends as much as possible. I had taught UP Constable for free on YouTube.
I will teach all the chapters of the railway till the end. From algebra, geometry, trigonometry, everything. Don't worry my friends, absolutely. Okay?
Okay? We are practicing chapter wise, then I will also solve mock test for you. It will be very interesting, children. Which statement is true? First, every complex number can be expressed in the form of real number.
Every complex number can be expressed in the form of real number. First thing to understand is what is the real number? Real numbers are those which can be written on the number line. From minus infinite to plus infinite, all the numbers that come between them, minus infinite to plus infinite, all of them are real numbers.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, minus 5, pi, 2 times 3, 0.7, 0.6, all of them are real numbers. Imaginary numbers are imaginary numbers, my dear brothers, imaginary numbers. Ya, Nicky? The numbers which have no meaning in Mathematics and can't be written on the number line. For example, under root of minus 2. What does under root of minus 2 mean?
It means a number whose twice multiplication equals minus 2. No, it's not like that. Under root of minus 7. Can you find the under root of minus 7? No, you can't.
There is no number in the world whose twice multiplication equals minus 7. All of these are imaginary numbers. And friends, the under root of minus 1 is called iota in short. So, the complex numbers in Hindi, it means real plus imaginary. Real, plus a imaginary number is called complex number.
Means, if any number of this form is a plus iota b, then the number will be a complex number. For example, my friends, 5 plus 3 iota is a complex number. How? Because, my dear children, we can say that 5 is a real number and this is an imaginary number.
The combination of these two is a complex number. Okay, you will say, sir, it was fun. So, in the question, he said, every complex number can be expressed in the form of real number? No.
Wrong. Any complex number can be written in the form of real plus imaginary. It cannot be written in the form of real number. The sum of the numbers can be written in the form of real plus imaginary number.
It cannot be written in the form of real number. It cannot be written in the form of real number. Wrong.
Question of the day. Let's do this first. Every integer is a natural number. Every integer is a natural number.
See kids, natural numbers are positive integers. 1, 2, 3, 4, 5, 6, 7, 8. Meaning positive integers, financial integers. 1, 2, 3, 4, 5, 6, 7, 8. These are called natural numbers.
So in the question it is saying that every integer is a natural number. No, integers are also negative. Negative numbers are not natural. Zero is an integer and zero is a plural.
Zero is not a natural number. So this statement is also wrong. Every real number can be written in the complex form. Every real number can be written in the complex form.
Yes. Every real number is an integer. Every real number can be written in the complex form.
Every real number can be written in the complex form. This is also correct. This is also correct, every real number is an integer, this is wrong C option only will be there Any real number can be written as a complex number For example, I have written 7 7 is a real number, you will say sir How will you write it in the form of a complex number?
You can write 7 as 7 plus 0 iota This is done So my friends can write it in the form of real plus imaginary Boom Means we can write every real number in the form of sum, but not every complex number in the form of real number. It will be wrong my dear children. It is not necessary that every real number is integer. 7 plus 3 is also a real number, and pi is also a real number, but they are not integer.
This statement is also wrong. A very conceptual and deep question has been asked. The next question is in front of you, tell me.
Another question from NTPC. Atul did the initial number and then reduced 15. Atul reduced 15 first and then did the interval. If both got the same answer, then what was the number?
Children, either you solve the question by assuming that the number was X. Like this. That if the number was x, then what did Atul do?
He squared the first number, and then reduced 15 out of it. But what did Atul do? He reduced 15 out of the first number, and then squared it. Both of them got the same result. Both of them got the same result.
So tell me, children, what is the number? I can take this question from options, or I can solve it. Both the ways are left to me. Whichever you...
you want to do that, my friends, because what will come equal to X square minus 15, son, what is X minus 15 square, X square minus 30 X plus 225, 15 square is 225, this X square will be cut, this minus 30 X will come there, equal to minus 15 will go there, join 15 in 225, 240 30 to 240 is 8 times, x is 8, which means the number is 8, so it is also easy. If I check each option, then also it will be done. Both the ways are fine, tell me. How many numbers are there between 200 and 1000 that are divided by 7?
You tell me. How many numbers are there between 200 and 1000 that are divided by 7? Tell me one thing.
How many numbers are there from 1 to 1000 that are 7 parts? I am telling you the best trick. How many numbers are there from 1 to 1000 that are 7 parts?
Give 1000 as 7 parts. How much will it be? 7 1 7 3 will be left, 7 4 28 2 0 7 2 9 14 142 142 numbers. There are 142 numbers from 1 to 1000 that are 7 parts. Tell me, from 1 to 200 How many numbers are there that are divided by 7?
So children, divide 200 by 7. So 7 x 2 is 14, 6 x 0 is 7, 8 x 8 is 56. I have been asked, if I subtract this between 200 and 1000, then from 1 to 1000, there are 142 numbers that are divided by 7. and between 1 to 200, there are 28 numbers which are cut from 7 so if I will do minus, what will I get? 200 to 1000 I will reduce from 1 to 200 so between 200 to 1000 I can say that 142 minus 28, there are 114 numbers between 201 to 1001 which is your If we divide by 7, the answer will be C option. C option will be correct. This is the best way to ask such questions. 200 to 1000. 1000 is not less than 7, so we will ignore it.
Okay, let's move on. When we divide one number by 7, then the result is 4. What will be the result of dividing the number by 7? So, children, we have considered the number N. The question is that when we divide a number by 7, then the remainder 4 comes.
If we divide the square of that number by 7, then what will happen? I just explained the concept to you. The action number will be in the remainder. If you square the number, then the remainder will also be square. The remainder will also be 16. But if you divide by 7, then you can't get 16. If you divide by 7, then you can get 1.11 lakh students are connected to this you go to the shorts in this daily I upload shorts conceptual questions daily 3 shorts as I understood today 2 questions of NTPC right multiply by 4 plus 2 of 42 whose example is this what property is there in it you subscribe to this all children who are watching this video Pause for a while and subscribe to this channel.
Every kid should recommend and share. Because on YouTube, there is no better channel than this. Because we work hard on this. Daily you will learn new questions, new concepts and you will also get a homework question.
All kids must subscribe to this channel. Now let's move on to the next question. There is a number of 7 numbers, which is 11th part, where a is a single digit.
What is a common? This number is 11th part, a is a single digit, a common. If it is 11th part, then calculate the number of numbers.
6, 8, 14, 3, 17, 17, 2, 19. Now calculate the number of even places. 7, 4, 11, 11 plus a. This difference should either be 0 or 11 or any multiple.
If I make this difference 0, then what will I have to take as 1? 8, 11, 8, 19 is there. If we subtract 19 from 19, 0, then 1 is equal to 8. Okay, son? Okay.
This will be the answer to this question. There was no courage in the question. We will move ahead.
Which of the numbers given below is not a perfect square number? Which number is not a perfect square number? is not perfect. That means, out of these options, 4 numbers are perfect square, not 1. You don't have to find that.
So, first look, it's not like I will find their root. No. Look carefully, you will find out.
This number cannot be perfect square ever. Any perfect number any perfect number The unit digit of any number of the plural can only be seen and you can tell. The unit digit of any number of the plural cannot be 2, 3, 7 and 8. It cannot be.
This is the concept of the question which has been used in this. You should know. There is one more concept.
If we square any number, the last two digits will be the same. Right? They will be the same.
The last two digits of the square of numbers from 1 to 25. For example, 1 square is 0, 1, 2 square is 0, 4, 3 square is 0, 9, 4 square is 16, 5 square is 25, 6 square is 36, 7 square is 49. So, these two numbers of any number can come at the end. 9 square 81, 11 square 121, so the last two parts can be 2 and 1. I am saying that the last two parts of any plural number cannot be 31. 12 square 144, so the last two parts can be 4 and 4. This is another rule, you keep this in mind, let's move on to both the rules. Now, one more question of RRB NTPC, I read the question, I mean... It is a question of options.
There are 3 numbers in one number, whose value is 18. The middle number is equal to the value of the remaining 2 numbers. If the number of numbers is reversed, the number increases by 297. What is the number? The number increases when it is reversed.
3 numbers, value 18, 4, 6, 7, 8, 18, this is also 18, all of these are 18. The middle number is equal to the other two numbers. 8 is wrong. 8, 5, 10 is wrong.
4, 5, 9 is right. 6, 3, 9 is right. There is one answer from these two.
The middle number is not equal to the other two numbers. 8, 4, 6, 10 is not equal. In these two, the middle number is 4, 5, 9. Now, it is said that turning the numbers makes the number 297. If I turn its numbers, it will be 594. This is 297. This is 99. This question is very dangerous.
And I have already put all the good questions of factors. The number given is 2 to the power of 3 times 3 times 3 times 5 times 4 times 7 square. How many factors are 50 parts but not 100? How many factors are there that are 50 parts but not 100? That means I have to find those factors which are 50. Odd multiple 50 to 150, 250 to 350 So my dear friends, you first subtract 50 from this What is 50?
25 times 50 So subtract 2, 5 square subtract 25 Then what will be left my friends? Like I subtracted 2 times, so 2 to the power 3 will be left 3 to the power 3 will be left 5 to the power 4, so 5 to the power 2 is taken out, so my friends, what will be left? 5 square will be left, and into 7 square. This is what my dear children have come.
Listen carefully. Now this number is 50. Now if you multiply 50 by this, then all the factors will be multiplied by 50. But I want to see that it is less than 50. 50 is the factor but not divisible by 100 The thing to understand is that if you multiply 3 by 50, then you get 150 50 will be deducted but not by 100 50 will be multiplied by 5, 50 will be multiplied by 100 50 will be multiplied by 7, then 50 will be multiplied by 100 But if you multiply 50 by 2, then the factors will be less than 100. This is the logic behind this question. If you multiply 50 by 2, then the factors will be less than 100. will be less than 100 means if I multiply 50 only in this only factor will be less than 50 only 50 will be divisible what is the method of taking out factors I just have to pay attention to this add 1 in 3, 4 power is 2, add 1 in 2, 3 add 1 in 2, 3 means 3, 3, 9, 4, 36 is the correct answer which is C option this is a very good question If you want to find out the multiple factor of 50, then first find out 50. There is a special condition here, we have to check it. Let's move on.
What is the ratio of natural numbers of 5 to 14? Look kids, do you know the concept? If I do 1 cube plus 2 cube plus 3 cube dot dot dot from 1 to n, I do a cube of the weights of 1 to n, which we call sigma n cube in short, then its formula is n into n plus 1 divided by 2 square.
This is its formula which you should know. and formula based also, many questions have come in the railway said, the sum of natural numbers from 5 to 14 so children, it is not that I write the sum of all numbers and then add them I can do that too, but what is best, what I asked in the question 5 cube plus 6 cube plus dot dot dot at last 14 cube, he asked me is The problem is that the cube of 4 numbers at the beginning is missing. Right? So, kids, what can I write?
I can write that from the sum of 1 to 14 numbers, I will reduce the sum of 4 numbers at the beginning. Will the logic come or not? From 1 to 1 cube, if I add the numbers up to 14 cubes, and I reduce it from it, I get 1 cube. plus 2 cube plus 3 cube plus 4 cube I will reduce the sum of 4 numbers of the beginning cube you will get the thing asked so in such questions you have to use this logic here still less numbers if there are more numbers then do this now 14 cube my friends put formula sigma n cube n into n plus 1 divided by 2 square minus 4 times 5 divided by 2 square. Okay, kids, you will say, yes, sir.
2 to 14, 7 times will go. 15 to 7, 105. What is 105 square? You know that any number at the end of 5 comes, then its square is 25. And in 10, 11 will be added, 110. What will come, son? 10 square 100. So, I will subtract 100 from 11,025. If I subtract 100 from 11,025, then 10,925 will be the answer to the question.
And this is the correct answer. We will move ahead, my friends. Learn the yoke of all natural numbers less than 85. Learn the yoke of all natural numbers less than 85. So, my friends, learn the yoke of all natural numbers less than 85. What are the even numbers? 2 What are the even numbers? Those which are less than 2 2 4 6 8 10 12 14 16 And the even number less than 85 is 84 I have asked for their yoke Okay So I am writing you the concept Sum of First n even number First n Sum of all numbers First I n sum sankhyaon ka yog.
Pehli n sum sankhyaon ka yog n into n plus 1 hota hai mere piyare bachyo. Pehli n sum sankhyaon ka yog n into n plus 1. Pratham n sum sankhyaon ka yog n into n plus 1. Agla conceptive mai likh raha hu. Sum of first n odd number. Pratham n visham sankhyaon ka yog. Pratham n divisible numbers first n divisible numbers n square as I asked you first 25 divisible numbers first 25 divisible numbers you will directly say 25 square 625 this is sum of first n even numbers n into n plus 1 what is this my friends 2 is 2 4 6 8 10 12 14 is 84 this is bar These are 42 even numbers.
These are the first 42 even numbers. And the first 42 even numbers will be N x N plus 1 which is 42 times 42 times 1 which is 43. And when we multiply 42 by 43, So, how much will be in the end? 2, 3, 6. 6 will be in the end. I can also do the multiplication. The answer to this question is B option.
These are two concepts. You should know directly in the number system and average. Both are used. Next question is from RRB NTPC paper. What is the combination of those two smallest natural numbers which have exact 7 factors in each?
This is a very difficult question. Try to understand. What is the sum of those two smallest numbers which have exact 7 factors in each? Exact.
They are the two smallest numbers. See, whenever we take out the number of factors, we add 1 to the power and multiply. See, what is 7? 7 is 6 plus 1. We add 1 to the power and multiply.
Right? And then I don't have any way to multiply 7. See, kids. The smallest number whose exact 7 factors are 2 to the power 6. How many factors are there in 2 to the power 6?
We will add 1 to the power, so it is 7 factors. The smallest. After that, 2 is the smallest. The next smallest is 3 to the power 6. I cannot do anything, my dear brother. I have no other way.
If we add 1 to 3 to the power of 6, then only 7 factor will come. 3 to the power of 6 also has 7 factor. So, 2 to the power of 6 is 64. And 3 to the power of 6 is 729. If we ask you about their yoke, then their yoke will come. If we add 729 to 64, then 793. D option is the answer.
This option is correct. It is a good question. It is going to take a lot of time. 7 What is the sum of the square of all two digit number which is completely divisible by 4?
So, what is the number of two parts divided by 4? 12, 16, 24, and 96. We have asked the sum of any square. We have asked.
This is what I have been asked. Ok kids? See, this is a very difficult question. Tell me the sum of all the squares of all two numbers.
These are the numbers of two numbers which are divisible by 4. Kids, let's do this. If I take 4 square common from these, then what will be left? 4 is 12. 4x4 is 16, 4x5 is 20 and at the end of the formula, we have 26x16 square You will say, Sir, either I will use formula to find its value There is one way Or I know that if 4 square is 16, then whatever answer will come will be from 16. If the answer is from 16, then it will also be from 8. If I take out their yoga, then the number that comes from 8 will be 300. 300 does not cut from 8. The last 3 numbers should be cut from 8. 324 does not cut from 8. 220 does not cut from 8. So the answer of the question can be cut from 320 to 8. So, sometimes even if you use your brain, there is no need to use the formula everywhere.
Okay, let's move on. So, the difference between the place value of 2 and 3 in the number 1, 2, 8, 9, 3, 5. What is the difference between the place value and the local value? One is the place value and the other is the face value. Face value is like 2 has face value of 2 and 3 has face value of 3. Whatever we are talking about digit, that is its face value. Face value of 5, which I will ask you in this number, what is the face value of 9?
But is 25 a prime number? It is never. It means that the straight part is true but the opposite part is not true. All the numbers can be written in 6n plus minus 1 form. But any number written in 6n plus minus 1 form is not necessary that it is always prime.
prime number. So, the real method is to learn to find the number of abhaya. The best concept is used in big questions.
See 323. Which prime number is near the square of 323? So you will say sir, the square of 19 will be bigger, 17. The square of 17 is 289. Does this number separate from 17? 17 x 17 is 15 17 x 15 is 17 17 x 17 is 15 17 x 15 is 17 If this number is not from 17 to 19 then it is not a prime number This prime number should be either from 1 or from itself 715 It is near the prime number square. So you will say, Sir, this is 23 square 529, after 23, the square of 29 will be quite big, 23. It cuts from 23, 23 is 79, no, it does not cut from 23. Then check the next, 23 to the next 19. After 19 is 57, my friends, you will save, no, it is not cutting from 19. After 19, the next one will be 77. Does it cut from 17 or 17.64? No.
Sorry, why am I checking so much? If it is 715, then it cuts from 5. If it is 715, then it cuts from 5, my friends. 143. If a number is cutting from 5 or 143, it means that this number is not prime number. 513. 513 is near the square of prime number.
So, it comes near 513. 23 square 529 does this number cut from 23? 23 to the 2nd is 46 no after 23 comes 19 does it cut from 19? 19 to the 2nd is 38 after 38 13 is left yes it cuts from 19 19 to the 2nd is 38 after 38 my friends 13, 19, 7, 7, 13 anyway its number combination is 5, 3, 8, 1, 9 its number combination is 9 so it will cut from 9 so this prime number nahi hai, ye prime number nahi hai, ye bhi nahi hai, to jo chautha number bache ga, wo prime hoga hi hoga, baat khatam. Ye tarika hai, aani ki aapko har ek sankhya pe mehnat karni padegi, koi trick nahi hai, sawal ki.
Chalaiye. Agla sawal hai, 8 se bade aur 69 se kam, ke punang ke beech abhajye sankhyaon ka yog kya hai? 8 se bade aur What is the sum of prime number smaller than 69? So, what are the prime numbers bigger than 8?
17, 19, 23, 29, 31, 37, 41, 43, 47, after 47, 53, after 53, it will come, it is 53, after 53, 69 comes, so these 8 bigger and those 60 small prime numbers their yoke is sum so it's not like there is a formula for sum of prime numbers no so how will I sum them, it's a difficult task I see only one number here one number is different from all options so why should I add all of them I should not add only one digit 1 3 4 7 11 2 is done 1 3 4 7 11 2 is done 2 9 11 is done 1, 3, 4, 9, 13, 3, 3, 1, 4, 4, 7, 11, 1, 1, 1, 2, 2, 3, 5, 7, 12, 2, 2, 3, 5. In the end, 5 will come. This is the answer. Let's see again.
1, 3, 4, 7, 11, 1, 1, 3, 4, 7, 11, 1, 1, 9, 10. 10 is done. So, 0 is done. After 0, 3, 9, 12, 2, 2, 1, 3, 3, 7, 10. This is also 0. 1, 3, 4, 7, 11, 1 is done and 1 and 3, 4. 4 will come.
364 answer. I did something wrong. 1, 3, 4, 7, 11. 11 has 1, 1 and 9. 10, 0. Then after 0, 3, 9, 12. 2 and 1, 3. 3, 7, 10, this is also 0. 1 and 3, 4. 4, 7, 11. 1, 1 and 3, 4. 4 will come. A option answer.
The question is over. The question is, if x is a positive even number, then how will this number be divisible? x to the power of 65 minus x.
This is the question. If x is a positive even number, then how will this be divisible? Look, this is a very difficult question.
X is a profitable sum number. That means, X is a number that is divided by 2. So, it is always cut. If I take X common from here, then the bracket will be X to the power 64 minus 1. Tell me, what is X, kids? X is an even number. Even number.
Into. Is it? Now, what is this, my dear kids? What is this?
This is x to the power 64 minus 1. x to the power 64 minus 1. Okay. Listen carefully. It means it will be odd number. What can we write x to the power 64 minus 1? We can write x to the power 64 minus 1. We can write x to the power 32 plus 1. And x to the power 32 minus 1. Can we write this?
Can we write this, my dear brother? You will say, yes, sir, absolutely right. Now, this is x to the power of 32 minus 1. We can break it again.
x to the power of 16 plus 1. 16 minus 1. We can write 16 again. 8 plus 1. 8 minus 1. This series will continue. Now, I have said that this will always be divisible by whom? You tell me.
This will always be divisible by whom? I want to tell you quickly. Look, it is a dangerous question, my friends.
I know one thing, that here x is coming. When I will factor, x to the power of 8 minus 1, when I will keep on doing this, and it will be factored. So, x to the power of 8 minus 1, x to the power of 4 minus 1. x to the power of 4 minus 1, x to the power of 4 minus 1. Again, it will be a factor of x to the power of 4 minus 1. and I can write x square minus 1 as x minus 1 into x plus 1 that means these three continuous numbers will be formed in this see, x is there if I factor it, then 32, then half, then 16, then 8, then 4, then 2 x square minus 1 will be formed, I will keep on factoring and x square minus 1 is x plus 1 into x minus 1 now x is an even number if x is an even number, it is less than 2 If x is an even number, then it will be less than 2. Next number will be 1. If I take 4, then it will be 3. That means, once 2, once 3 will come.
I have taught you that 3 continuous numbers have been formed. And the quality of 3 continuous numbers will always be divided by If it is divided by 6, then the answer to the question is A option. It has to come. Okay.
But there is a special thing hidden in this. There is a special thing hidden in this that x1 is an even number. We will pay attention to this. X is an even number.
And if I take X command 2, then my dear friends, this will come 1 and this will come 3. This will be cut from 6. If I take X command 4, then this will come 5, my friends. This will come 3. This will also be cut from 6. If I take X command 6, then 7 will come, my friends. And this will come 5. This means that no matter what you do, if you want to cut from 6, then only 6 will be the answer.
Only 6 will come, my dear friends. Okay? And there are no chances of it being true.
Let's move on, students. Between 50 and 100, how many sets of infinite numbers are there? And when you add them, you get infinite numbers. The question is from RRB Junior Engineer's paper. This question is great.
Between 50 and 100, how many sets of prime numbers are there? There are so many pairs of numbers that you will get only prime numbers after adding them. Tell me one thing, All the prime numbers between 50 and 100, 53, 59, 61, 67, all these will be odd numbers.
All the prime numbers between 50 and 100, all the odd numbers will be the odd numbers. You will say, yes sir, there will be odd numbers. What a and how many sets are there which have prime number if I add any odd number then 53 and 59 are prime numbers but these are odd numbers if I add them then there will be an even number and even number can't be a prime number except 2 if I add any 2 numbers then there will be a bigger number than 2 and even number will be 2 always comes with odd number means if we add any two numbers then there can never be prime because always comes with even number which will not be prime so there is not even one set answer is zero very very good question my friends this was asked in front of you next question is children will you make it tell me How many factors of these are even? How many factors of this number are even? This is the question of RRB NTPC paper, children.
Now see, how many qualitative sums are there? Even factors are asked. What is even?
Even means, the number which is divided by 2 is called even. So, you take out 2 from here. First, you take out 2. What will be left? 2 to the power of 6 times 2 to the power of 7. I took out 1 and 2. 2 to the power of 6 times 1 times 3 times 4. Railway people are very kind. They do direct prime factorization and give 1 times 5 times 7. Here comes my dear children.
You will say, yes sir, it was very good fun. I have to take out my dear students from here. How many factors are even?
Now I will multiply 2 in any of these. So all the factors will be even. Means I just have to count how many factors are there in this set.
Add 1 in power, add 1 in 6, add 1 in 4, add 1 in 5, add 1 in 3, add 1 in 4. 7 has power 1, add 1 in 1, add 2. So 4, 2, 9, 8, 5, 4, 7, 8, 2, 8, so 280 is the answer to this question. B option becomes absolutely correct. Let's move on to the next question. Which number is divisible from 11 in Nimr? I have asked you this question, dear children.
Solve this question and tell me in the comment section. If you have watched the lecture till here, then I will have to solve this question and tell you in the comment section. Every child who is watching this video lecture, solve this question and tell me in the comment section. And this is the last question of today's class. Last question of this video lecture.
Tell me, kids. And you will get many such questions. In the equation given in the equation, what will be the highest value of x and z? Highest value of x and z.
Tell me, kids. If this equation is satisfied, then consider X and Z as the highest. Tell me one thing, listen to me quickly, my dear brother.
If I add 7 and 8, then Z is equal to 6. How can it be? If we add 7 and 8, then if I add 8 to 8, then it will be 16. That means the value of Z... 8 should be there.
Z's 8 is here. Z's 8 is here. Means these two answers should not be there. Z's value should be 8. And if I take Z's value as 8. 7 and 8, 15, 16, 16 then the result will be 1. So, it will be X plus 1 and this Y and this Z. I have taken Z's value as 8. So, this X plus 1 and this Y then what will happen?
This X plus 1 will happen. In the middle, my friends, this Y is I don't know the Y command in between And this is 8 What should be equal? If I had got 1 result, then this is 2 If I can't get 2 by adding these, then I'll make 12 If I can't get 2 by adding these, then I'll make 12 If I make 12, then the result will be 1 So 9 and 1 is 10 8 is 18, 7 is 25 will be 25. If I make them equal 12, 1 is x plus 1, this is y and this is 8. If I make them equal 12, then 12 will be 2 and the result will be 1. So 9 and 1 is 10, 8, 18, 7, 25, 25 is written.
Now tell me one thing, I want to take the highest value of x and z, then do y as lowest, do y as minimum, 0, take y as 0, lowest. 8 and 1 is 9, so I will write the value of y as 0, 8 times 1 is 9 and 3 times 2. So, let's take x command 3 and z command 8. The answer of D option question will be x value 3 and z value 8. 8 times 1 is 9 and 3 times 2. My dear friends, this is a very conceptual question. And with this, best 25 questions of railway number system are over.
All these questions of railway will be found in this book, complete practice book. This book has 4000 plus questions From which I have solved the best 50 questions of today We will upload the PDF of this book on our Telegram channel Link is given in the description And I will give you extra 10 questions for your practice The student who wants to practice with the book of Railways can order online How did you like this video lecture? Do tell me in the comments Share this video lecture with children who are preparing for the railway as much as possible. So that they can know that a series is going on here. Okay students.
Now after number system, the next part will come. In that we will discuss simplification, questions of simplification. Thank you very much for watching this video. Bye.