CLASS - 06 | MPTET Varg 2 Maths Practice Class 2026 🔥 | Mains Maths Complete Preparation | Jay Sir

Added: 2026-05-27

[00:00:00]What we were studying yesterday was doing polynomial questions in this manner. Today also we will do more things along with polynomial questions. But if all the children who are watching the class like it and share it once. Isn't it? Then everything will be fine. Will you also study chemistry and physics together, sir? Where does Chemistry Physics fall in your class two, brother? You will not get to see this.

[00:00:27]Let us consider the quadratic equation x² + 99x + 127, what will be its two roots? So let me tell you that if the zeros of the quadratic polynomial are both positive, then what will be the two roots? Will remain negative. Isn't it?

[00:00:48]If both are positive then what will be the two routes? Both routes are positive and not negative.

[00:00:52]One will be positive and one will be what? It will be negative.

[00:00:55]If one is negative and one is positive, what will the two roots be? Will be positive. I gave you the wrong one here. Both will be negative.

[00:01:02]And in the case of negative positive negative and negative negative, what will be one positive and one? Negative. One positive and one negative. So in case of both being positive, both will come negative. Both are negative. Option B will be correct. Both are negative. Both will be negative. Option B will be its correct answer and option C will be its correct answer. C is written on B, B is written on C. The third option will be correct. Ok? Absolutely the third option will be correct that both will be negative.

[00:01:28]Ok? You are doing class two and you are doing NTPC.

[00:01:34]Very nice son. Spectacular.

[00:01:37]Meaning the main thing is that class two will definitely come. If not today, it will definitely happen tomorrow. And that is a very good option for you. But yes, until it comes, you can give the NTPC paper. And the mathematics is such that you understand that it is Brahmastra, right? One who is good in mathematics can focus on many exams. NTPC is yours.

[00:01:54]If you are a student of Maths class 2 then you are sure to get 60 marks. For the remaining 40 marks, you have to prepare a little more for GS.

[00:02:00]You will be able to qualify the exam easily. Then you will defeat the rest of the people very well. If you are a class 2 student then you can also do it for NTPC. The next question is given. If the roller coaster is represented by the graph y = px shown in Figure 2.1, what is the type of polynomial it traces? What type will it be? So you look carefully. He is cutting at three places.

[00:02:24]This is the first point. Isn't it? If you look carefully here, it is cutting at three points.

[00:02:28]Here is the first point. Here is the second point and here is the third point. Total is cutting it to three points. So this is cubic.

[00:02:34]Option C will appear correct. is cubic.

[00:02:38]is in the form of a cube. Option C will be its right.

[00:02:40]Ok? is a cubic polynomial. Cubic is the correct answer. Option C will be its right answer.

[00:02:43]Ok?

[00:02:46]Option C will be correct.

[00:02:48]All the children who are watching the class, please like and share it once. Here is the next question for you.

[00:02:52]Solve this.

[00:03:00]I think you will see category two only in 2024.

[00:03:03]Your paper will be in 2024 only.

[00:03:05]And now in the coming time, whatever classes we will bring, we will ask only those questions which are 100% sure to be related to our exam. These questions are also related to our exam. But we will practice the questions in such a way that when we give the paper, we do not face much difficulty.

[00:03:22]We can solve that paper very easily.

[00:03:24]Ok? The roller coaster is represented by the following graph y = px shown in the illustration.

[00:03:29]Which roller coaster graph has more than three distinct zeros? So there's a zero here. If you look here, there is a zero. There are three zeros here. And there are one two three and four zeros here. Option D will appear correct. Because is a function of x. Isn't it? Here px is cutting the x axis.

[00:03:46]If y was there, we would check on y. Making a cut on x. One is making a cut. Making three cuts. Making four cuts.

[00:03:52]So the D option which is more than three will be correct that more than three is cutting in D option. The next question given to you is that if it is a cubic polynomial then which of the following conditions? Which of the following is always true. Which of these will always be correct? If the roller coaster is represented by the cubic polynomial function of x px + qx² + rx + s, which of the following will always be true? Okay son, I will shift this to the app also.

[00:04:20]Sorry, I forgot today, but from tomorrow you will get a notification on your app today itself. From tomorrow onwards, there will be classes on your app every day at 8:00 pm.

[00:04:28]Look, I have completed the entire course.

[00:04:30]I have read everything.

[00:04:32]So I will provide you the classes that will be on YouTube and for the ones you have purchased on the app, I will provide a special thing that whatever class will be there, I will also provide it in the form of a test.

[00:04:42]You will get the same taste. Ok? Done.

[00:04:47]Ok. Here it is given px + qx² + rx + s. If you look here carefully, you will see here what will be the answer to this question that if it is a cubic polynomial then p cannot be zero, so p is not equal to 0. The correct answer will be that p is not equal to 0.

[00:05:09]Option D will be correct. Which of the following is always true? For a cubic polynomial, p cannot be zero. This will be the correct answer.

[00:05:16]Option D will be correct. Now you might be thinking that every question that comes in the exam will have an answer. This is not necessary. There was a match here. Isn't it? The camera probably turned off. Let me check it in a minute. Is the camera running properly?

[00:05:32]You please wait. One minute. The camera's power supply may have gone out. So I'll check that.

[00:05:57]Come on, has the rainbow gone away from in front of you? Has the rainbow gone away? The camera has come back from in front of you, it was turned off, no problem, now you will be able to see it properly, now the rainbow must have gone away. Tell me quickly.

[00:06:18]Let's solve the next question. The next question is in front of you. If the polynomials ax + 4x² + 3x - 4 and x - 4x + a leave the same remainder when divided by x - 3.

[00:06:31]Meaning x = what will it be? 3 Keep the three values.

[00:06:37]a 3 + 4 3² + 3 * 3 - 4 = 3 - 4 * 3 + a correct so this will be 9a - a equals this will be 3 * 3 = 9 9 * 4 = 36 36 and 9 45 45 taken from 45 so 41 minus 41 and if we look here then 3 * 3 = 9 9 * 3 = 27 isn't it 3 * 3 = 9 9 * 3 = 27 isn't it 27 is cubic 27 3 * 3 = 9 9 * 3 = 27 27 - 12 15 is left if we add 9 to 15 it will become 24 so this will come out to be 26a equals 27 taken from 24 so 16 16 and a 17 will be left minus nothing went wrong. Let's look at it once again. 3 * 3 = 9 9 * 3 = 27a + 3 * 3 = 9 9 * 4 = 36 36 and 9 45 If 4 out of 45 is removed then 41 is correct. And in this we will see 3 * 3 = 9 * 3 = 27 - 4 * 3 12 means this is 15 this is a. This will leave 15.

[00:08:08]15 - 41 so this will become - 26 of a equal to - 26 / 26 26 will be subtracted from 26, the correct answer will be -1 which option will be B option -1 will be the correct answer for this option B will be -1 correct answer - 26 / 26 son, I had taken this as nine whereas this a is what is this a which will become minus when it goes there, the correct answer is -1 will be absolutely correct -1 is the correct answer. Let's move on to the next question.

[00:08:37]Here is the next question for you.

[00:08:38]Solve this. Alpha beta are the roots of this equation. It is original. Then x² + aphax + beta = 0 If alpha and beta are the roots of this equation, then what is alpha + beta equal to?

[00:08:54]If it is original then it will mean α + beta = - alpha and alpha * beta = beta from where the value of alpha comes to one the value of alpha comes to one and the value of alpha becomes one means 1 + beta = -1 means beta = -2 the value of beta becomes -2 1 + -2 this will become 1 - 8 1 - 8 means -7 Option A is correct. -7 What will be the correct answer to this?

[00:09:27]-7 -7 is absolutely correct. Isn't it? Good evening.

[00:09:30]Good evening. Welcome to all of you.

[00:09:32]All the children who are watching the class, please like and share it once. If you have not yet subscribed to the channel, please do so.

[00:09:38]Its correct answer will be option A. A will be its right answer.

[00:09:47]First, the value of alpha was calculated from the multiplication of alpha and beta. The value of alpha is arrived. From that, the value of beta was calculated. The values ​​of both alpha and beta are obtained.

[00:09:56]Then what did we do after that? Solved it by putting the value.

[00:10:00]Its correct answer is -7. The correct answer is -7. Let's move on to the next question. Here is the next question for you.

[00:10:06]Solve this.

[00:10:07]What will be the answer to this question?

[00:10:09]What will be its factors? Tell me, the value is given in front of you.

[00:10:11]What will be its factorization?

[00:10:58]Let's see what the answer will be? a² + 4b² + 4b - 4ab - 2a - 8 So we check where the multiplication matches. a * a² a² a² is happening everywhere. The match is going on.

[00:11:11]What does 4b² plus 2b * 2b become? 4b minus minus is plus. So this is correct. -b and +b this will not be possible.

[00:11:20]Meaning option B has been removed. 2b and 2b becomes 4b².

[00:11:23]2b and -2b, this D option will also not be possible. Meaning a and c have to match. The first match is over. The second match is over. 4B We need 4b, so what is 2b - 2b + 2? 4b But what is minus -b here?

[00:11:41]What will it become if we multiply -2b -2b + 2? 4b and this will become 4 * 2's 8 + 8 will give 4 means here b is matching but here we see b -b - 2b and minus and minus so this will become minus 's 8 and 2 10 this option ok this has been removed this option is 2b * 2 so this will become plus's 4b we also need plus's 4 but here minus's 4 * 2 = 8 will also come so option C cannot be the correct answer option A will be the right answer try matching all the things it will match exactly multiply in option A a * a² correct then 2b minus's 2b minus's 2b so + 4b² and minus's 4 and plus's 2 so 4 * 2 = 8 - 8 now let's multiply these by the remaining two so - ab 2ab and here a will be multiplied so + 2a after that it will be multiplied by 2b 2b * a then - 2ab correct, after that 2a b will be multiplied by 2, so - 4b minus minus + 4b, at last there will be multiplication of -4, so -4a and 4 will be multiplied, so 4 * 2 is 8, but plus is fine, at last 2a got matched with 2a, 4b² got matched with 4b², - 8 got matched with -8, if you want 4b then this is 4b plus and this is 8b plus, sorry 4b plus will not come, why will it come, it will come with minus, so because of this +4b will be left, after adding these two +4 will also be left and apart from that if you want 2a then 2a will also be left. Option A will appear correct. 2a Whatever remains, what will it be of any use? 2a whatever remains is plus one.

[00:13:23]We need minus. Plus's 2a arrived. I want minus. Option A doesn't seem to be working. So it wo n't happen.

[00:13:37]Okay, 2a and this minus 4a together. 2a plus the minus 4a will add up to 2a. It is correct. Option A will be the correct answer. A is correct. If you solve it finally, option A will come correct on multiplying. You can do this by checking one or two terms also. Well, I had checked one or two terms and ticked them.

[00:13:52]Option A is correct. Here is the next question for you.

[00:13:54]If x² + ax + b is a perfect square then which of the following will be the relation between a and b? Which of the following could be a relation between a and b? If a question of this type is given then solve it.

[00:14:06]Will the answer come? If it is a perfect square, what is the relation between a and b?

[00:14:36]OK Solve x² + ax + b Correct This is a perfect square. So when will it become a perfect square? When it's what? a² this 2ab and what should happen? b² correct? So what does this mean the value of a is? If the value of a is x and the value of a is x then what will be the value of 2b? equal to a. What will the value of 2b become equal to? equal to a. Or here instead of taking a and b, we take something else. Let's replace ab 2ab with something else because you will get confused. a and b are given here also. We took j and k so j² 2j and wrote k² here, correct?

[00:15:21]So this k² is equal to b and here if what we want is a which is equal to 2k.

[00:15:28]Because the value of j is equal to what? equal to x. The value of j equals x, so that j is equal to x.

[00:15:34]Meaning, what will 2k be equal to?

[00:15:37]2k which is going to be equal to a. Meaning what will k be equal to? a / 2 k equals to what? If we take a / 2 or k² then what will be a² /? 4 while k² is given equal to what? equal to b. So b = a² / 4 means if we multiply this then what will a² be equal to? 4b which will be the correct answer a² = 4b a² = 4b means option B will be the right answer a² = 4b option B will be the right answer a² / 4 a² = 4b will be the absolutely correct answer.

[00:16:09]If I explain this in another way.

[00:16:11]This may have seemed too typical to some children.

[00:16:13]So if I explain it in a better way then we can see it like this x² + ax + b, so if you see here then this is the square of something or the other, that is k² = b means what will be k =? b When it is written as b, then it is obvious that it will be equal to b. And this is equal to b.

[00:16:34]Meaning this will be 2ab. Isn't it? In the case of 2ab, this is the value. But what is this value equal to? equal to b. Meaning, what have we written in place of 2 b? a is written. 2b b This should be 2 b. Meaning, if we look at it, it is x + b² which should be written as ax² + 2bx or 2 bx + b correct. And what is this value written equal to? is written equal to a.

[00:17:03]Meaning a is equal to 2b and squaring on both sides, a² will be equal to 4b. This will be the correct answer.

[00:17:11]a² = 4b Option B will be the correct answer.

[00:17:14]B will be absolutely correct. B will be the correct answer. B is its correct answer.

[00:17:18]Here is the next question for you. Solve this.

[00:17:20]All the children who are watching the class, please like and share it once so that others can also join. I have done this class timing especially for you people. If you guys are not liking this time also then I will close the class. There is no problem. Then we will teach on the application itself those children who want to study on the application. If you find this time suitable then please tell me in the comment section so that I can continue teaching you at this time.

[00:17:52]D is the right answer. If q is a factor of x - 2, then this means that at x = 2 it will have the value 0 and what will 2² + 3q * 2 - 2q be equal to?

[00:18:06]0 means 4 + 6q - 2q = 0 means 4q = -4 and q = what will it become? -1 correct answer will come. q = -1 Option D will be correct. -1 What will be the right answer to this? -1 will be the correct answer.

[00:18:23]This time will be right. Ok? Let's say -1 is the correct answer. Here's the next question. This is where our geometry starts. Till now the questions we were doing were polynomial questions. Now the questions we will ask will be of geometry.

[00:18:35]After geometry, questions on mensuration will also come. After mensuration, you will also get questions on trigonometry.

[00:18:40]As long as you remain interested, I will continue teaching you. Ok?

[00:18:46]Okay son, let me fix this time for you. Isn't it? This time I will teach for regular class two. But share this link with as many children of class two as possible. Isn't it?

[00:18:57]Everyone should join. By the time the vacancy comes, I will have covered everything for you once again.

[00:19:02]Ok? Now it is not necessary that you are given such an opportunity that the paper is after 4 months or 3 months. It is possible that you may appear for the paper in just 20 days.

[00:19:13]20 In triangle ABC, angle B = 70, angle C = 30, isn't this angle? This question has not been changed till date, these people have kept the values ​​the same. In ABC, angle B = 70, angle C = 30, AD and AE are perpendicular and bisector respectively.

[00:19:29]This AD is perpendicular and AE is the bisector. The angle which is called Konardak is. What will be the angle between the two? So the angle between the two is the difference of the two divided by how much.

[00:19:42]30 out of 70 becomes 40. If you divide 40 by two, the correct answer will be 20°. The correct answer will be 20. Option D will be the correct answer. 20 will be its correct answer. What will be 20? I remember the formula. It is a good thing. If yes, I will definitely put a notification in the group.

[00:19:57]Son, if you people have not joined the WhatsApp group Mind for Academy, then you can join that as well or if you want, you can join Mind for Academy on Telegram as well.

[00:20:07]You will get it there also. Isn't it?

[00:20:09]You can get it at both places. There is no problem. You can join a class anywhere. You can join the class from anywhere. Move ahead.

[00:20:15]Here's the next question.

[00:20:18]Solve this. I'll put the link for you in the comment section.

[00:20:42]Solve the next question.

[00:20:46]NTPC Maths class will be in the morning, son.

[00:20:48]I will keep it in the morning at 11:00. I will teach you guys at 11:00 am. At that time you will have your NTPC Maths class. Ok? It is going to be confirmed at 11:00 am. The next question should be solved.

[00:21:01]Chords PQ and RS of a circle when produced meet at point O. PQ and RS are joined at O.

[00:21:07]Meaning there is a chord PQ and a chord RS which are extended and where do they meet? Found it at O. If PQ = 6. If PQ = 6 cm. Is. OQ = 8. OQ = 8. OS = 7. OS = 7. Then what will be the length of RS? What will be the length of RS? Let me tell you guys that OQ * OP = OS * OR. Isn't it? The distance from here to here and then the distance from here to here. Well, the distance from here to here is equal to the distance from here to here, multiplication. So we saw that 6 * 8 is equal to 7 * what? The sum of these two means 7 + how much? x is 7 + whatever the value of x is, the sum of these two. So what is given? 6 PQ PQ and OQ PQ and RS chords of a circle, when produced, meet at point O. Where do we meet? At O. If good 8 will become 14 son.

[00:22:16]I took these eight. 8 will become 14. One will become eight and one will become how much? It will become 14.

[00:22:20]7 * 2 = 14. So this will become 8 * 2 = 16 = 7 + x means x = 16 - 7 means what will be the answer? 9 cm The correct answer will be 9 cm. I did not add the distance from here to here. What will be the sum of 6 + 8? 14 What will be the correct answer if solved in this manner? nine. Nine is the right answer. Nine is the absolutely correct answer. Nine is the right answer. All the children who are watching the class, please like and share.

[00:22:49]Please subscribe to the channel. Join the class every day.

[00:22:51]You don't need to do anything else. There is no need to study anything, no need to make extra notes, no need to join any other class. There is no need to go anywhere else.

[00:23:01]I can provide you everything. The only requirement is to stay connected and keep preparing for class two.

[00:23:08]If you are studying for class two then you have to study only for 2 hours for class two.

[00:23:11]I will teach from 8 to 10 every day.

[00:23:13]You all should join both the 2 hour classes.

[00:23:16]All your things will be covered here.

[00:23:17]Ok? It wo n't work for 4 hours every day, son. It will last for 2 hours. 4 hours will not be possible right now.

[00:23:24]I will try to take your class for 2 hours.

[00:23:25]Ok? Here is the next question for you.

[00:23:27]Solve this. The next question is in front of you. There will be classes every day. Classes will be held daily and you don't need to study during the day. There is no need to join any other class. There is no need to do anything.

[00:23:59]You will be able to prepare comfortably in these 2 hours.

[00:24:02]10 cm And 8 cm.

[00:24:04]Two circles of radius 1 intersect each other and the length of the common chord is 12 cm. Is. A 10 cm. and one is 12 cm. Is of.

[00:24:14]10 cm And 8 cm. Two circles of radius intersect each other. And the length of the bisecting chord is 12 cm.

[00:24:22]Chord to circle of radius 10 cm. 8 cm From the length of the common tangent is 12 cm. I had made a common chord chord without making a common tangent. The common tangent is this one. What is its length?

[00:24:34]12 cm Is. Ok?

[00:24:37]What will be the distance between their centres?

[00:24:40]What will be the distance between their centres?

[00:24:42]If the radius of one is 8 cm.

[00:24:44]And the radius of one is 10 cm. So you know the formula that distance equals route over, right? Or we will take it as D. Let us talk about center distance. Isn't it?

[00:25:02]We need the center distance to be equal to the length of the common chord, so the length of the common chord has been given to us. The length of the common chord is 12 cm. And 10 cm. 8 cm Two circles of radius r intersect each other and the length of the common chord is 12 cm. Is. 12 cm Is.

[00:25:16]What will be the distance between their centres? So the distance between their centers is equal to d² - r1 - r2 squared 10 - 2? The square of 12 will be 12, which is the length of the common chord, that formula is equal to the length of the common chord, so squaring on both sides, the square of 12 is 144 = d² - 10 - 8 10 - 8 What will be the square of 2, 4 will be here, so d² will be equal to 148, what will be 148, whereas this value should have been increased, 10 - 8 10 cm 8 cm is the difference of two, the square of 2 becomes four.

[00:26:06]Where is the problem with the formula? I think this will be the formula for the distance between centers.

[00:26:16]12 square minus 10 - 8 2² 4 Yes, this will be it. Now either there is some mistake in the answer or there may be some mistake in the question. Let's look at it once again. Two circles of radius 10 cm.

[00:26:44]And 8 cm. Intersect at the length of the common tangent. 10 cm And 8 cm.

[00:26:51]Two circles of radius intersect each other and the length of the common chord is 12 cm. Is. The length of the umbilical chord is 12 cm. If so, what will be the distance between their centres? The distance between the centers so the length of the common chord equals the square of the distance between the centers over r1 - r2² so square root over r1. The square of 12 becomes 144 10 - 8 2. The square of 2 will equal 4.

[00:27:15]Four will come here and it will become 148. It will come above 12, it will come below 13. This will be some answer. I think I can answer this.

[00:27:23]Whatever the answer may be, I am not ticking it because I have some doubt on its value. The next question is before you. The square of 2 will be four only, son.

[00:27:33]How will two come? It will become the square of 2. The square of 2 times 2 will be 4, right? Here it is t² - r1 - r2 squared.

[00:27:41]So 10 - 8 is 2. The square of 2 will become four. Four will go there and join. Ok? Here is the next question for you.

[00:27:47]Solve this. The next question is before you.

[00:27:50]Tell me what answer will come?

[00:27:53]In triangle PQR, side QS QR is produced to S. Isn't it? In triangle PQR, side QR is produced to S.

[00:28:01]Triangle P Q and R extended to S. The side QR is produced to S. In that the bisectors of PQR and PRS meet at point T.

[00:28:17]Where do we meet? See you at the point.

[00:28:20]From here it is confirmed that this is X, so what will this X/ become? It will be two.

[00:28:24]This is half.

[00:28:26]If QPR = 80°. QPR = 80°. So what will QTR equal? So what will QTR equal? It will be half. I just wrote that there is property here. So it will be half. So what is half of 80? So divide 80 by two. The correct answer will be 40°.

[00:28:42]Option B will be correct. 40 Its the right answer. How many answers will come? 40° which will be the correct answer. 40 will be the correct answer. There are 40 correct answers. Isn't it?

[00:28:55]Okay, will you convert that into centimeters?

[00:28:57]So it is just a centimeter. 10 cm And 8 cm. 12 cm It is just within one centimeter.

[00:29:02]And what doesn't need to be changed at all?

[00:29:06]All things are there. The previous question has 40 correct answers. Right now it is not getting installed for the last few days. Isn't it? You are not able to take the full length test. There are many problems in the test series also. She is being improved. But the reason for the problem in that is only software problem. Even if I edit it, it gets changed again and reaches the same place.

[00:29:26]So I am improving slowly.

[00:29:27]I had asked for 4 days time. Just one day has passed. 3 more days left. I will get it done within 3 days.

[00:29:31]Ok? next question.

[00:29:35]In triangle ABC, the internal bisector of C intersects AB at point D. The sides A and B of triangle ABC intersect AB at point D.

[00:29:52]is the internal bisector of C. Here D is cutting on.

[00:29:54]Internal bisector means cutting into two equal parts.

[00:29:57]In this, AB is not equal to AC. AB is not equal to AC. AB is not equal to AC. E is such a point on CD.

[00:30:06]E is such a point on CD. E is a point on CD such that AE is equal to AD.

[00:30:17]AE will be equal to AD. What will happen to these two? Will become equal. AE will be equal to AD. Well, these two will not be equal. The other two are equal. AE will be equal to AD. will be equivalent to AED. Ok?

[00:30:34]If ABC = 50. ABC = 50°. If it is 50°, then angle CAE is equal to: So angle CAE is equal to what [nasal sound]? Angle C will be equal to? What will angles C A and E be equal to? Who should I tell this angle to?

[00:31:00]It will happen slowly son. I will start teaching from the basics. I will ask you small questions.

[00:31:03]Ok?

[00:31:07]Well, I just purchased the test series today. There is no problem. Son, you will get everything in order.

[00:31:14]Well, I did not pick up the pen in all the questions. Did n't pick up the pen in this. What will be the answer to this? Tell me. In triangle ABC, the internal bisector of C is the internal bisector of The internal bisector of C intersects AB at point D.

[00:31:25]intersects AB at point D. Ok? In this AB is not equal to AC. AB is not equal to AC. Ok? E is a point on CD such that AE = AD. AE will be equal to AD.

[00:31:42]If ABC = 50. If it is 50° then what will CA be equal to? So what will CA be equal to?

[00:32:10]If I take this to be k then this will become k and this will become 50 + k and this will become 50 + k then this will also become 50 + k. Correct.

[00:32:21]It became 50+k. It became 50+k.

[00:32:24]Both of them reached 50+k.

[00:32:28]Ok?

[00:32:52]How to call 25 BD 25 of BDC, will the answer come, tell me please check once, does anyone see any solution? Good evening. Good evening. Welcome to all of you. The internal bisector of angle C intersects AB at point D. Ok?

[00:34:00]Where is he cutting AB? Cutting at D.

[00:34:03]Hence, AB is not equal to AC.

[00:34:08]not equal to AB. We said we don't need it at all.

[00:34:10]E is a point on CD True that E is a point on CD True that AE = ED AE = AD Sorry these two are equal. If angle ABC = 50° angle AB = 50° then CAE = So CAE is equal to 50 + k.

[00:34:53]What is this 50+? k is. So look carefully. From here it becomes clear that this angle will be according to this triangle, look carefully according to the triangle, what will be this angle? This angle will be 50° because 50 + k = 50, so option B will be correct.

[00:35:11]25 The one who gave the answer is wrong. 50 is the correct answer. How much will it cost? 50 Answer will be B option 50°.

[00:35:19]Look again. Look carefully once. It is 50. I have given this. This is the angle bisector. Meaning it is half an angle. This is k. This is k. So this k + 50 + k comes here 50 + k. These two are equal. So 50 + k so this is 50 + k and this is 50 + k so this is k. This means it will be 50, only then both of them will add up and reach here. So, the correct answer will be 50. 50 will be its right answer. Ok? Not a single child gave the correct answer. And if this comes in class two paper, then I will be selected and someone else will be selected. Here's the next question.

[00:35:46]By the way, I am not giving the paper, otherwise it would have happened.

[00:35:47]Here's the next question. Solve this. This is a good question. This is a bit time consuming question. But yes you can do it. The next question is in front of you. Solve it. 50° is its correct answer. 50 is his correct answer.

[00:36:04]If there is someone who does not understand, you can watch it again. This is 50. It is given in the question. These two are anglers. So both the angles will be equal.

[00:36:13]So this is k. This is k. By combining these two we reach here. Both these sides are equal. So these two angles will be equal.

[00:36:18]Looking inside this triangle, the sum of the two interior angles is equal to the third exterior angle. This is 50 + k which has ca k, so this will be 50. Ok? So, the correct answer will be 50. Option B is the right answer. The next question is before you. Given in the question AB is 8 cm. And CD 6 cm. There are two parallel chords that are on the same side of the center of a central circle.

[00:36:37]An 8 cm.

[00:36:40]And how many cm is one? Is? 6 cm And it will be below. This is 6 cm.

[00:36:46]Ok? The distance between them is 1 centimeter.

[00:36:48]What will be the radius of the circle? Their circles have a distance of 1 cm between them.

[00:36:52]How many centimeters is it? 1 So what is the radius of the circle? So let's say this is r.

[00:36:57]What will happen here too? It will be r. And what is this? x is.

[00:37:02]This is four and how much is this? It is 3.

[00:37:06]So this becomes r² = 4² + x² or 3² + x + 1².

[00:37:15]Because r in both cases this also has radius and this also has radius. Both will be equal. So 16 + x² = 9 + x² + 1 + 2x x² will cut x². If 10 goes out of 9 and 1 10 16 then 6 = 2x and x = how much will come? 3 Correct answer will come 3. The value of x is three. Isn't it? The value of x is three. Meaning what will be the radius? So we can see the radius. Radius [nasal sound] will come here three. This is forming such a triangle. This is three and this is four. So, how much will it be? Five. The correct answer will be 5 cm.

[00:37:50]Option A will be correct. How much will it cost? Five.

[00:37:52]We need the value of the radius. The value of r is required. So r² = 4² + 3² 25 means r is equal to what? Five. The radius will become five. Five is its correct answer. All the people who gave five answers were very good. Five is its correct answer. 5 cm The right answer will come. Here is the next question for you.

[00:38:10]Solve this. The next question is in front of you. Tell me what answer will come?

[00:38:17]5 cm of the previous question. This is the right answer.

[00:38:20]All the children who are watching the class must like and share it once. Please subscribe to the channel if you haven't done so yet.

[00:38:56]Looks like I will have to pick up the pen, sir.

[00:38:58]Then the radius of identical circles is 4 cm. intersect each other in such a way that their circumferences pass through each other 's centre. Passing through each other's centre means passing through each other's centre in this manner.

[00:39:11]Then what will be the area of ​​the intersecting region? Meaning, how much area will this area be? We have to find out this.

[00:39:19]So how can you calculate this area? You can calculate this area or you will have to do it. There is no option. Or you can calculate it this way.

[00:39:34]Correct? Or take out one side, take out the other side and subtract both of them.

[00:39:42]This is the radius, this is the radius and this is also the radius. The triangle radius itself is being formed.

[00:39:46]So the angle will be 60°. This will be 60° 120°. So we calculate two arcs like this. First arc this one. We will then subtract the second arc. So there is an arc of 120°. There are two arcs. Meaning there are two arcs of 2 * 120°. 360 120 / 360 * π r² So we don't know the radius here. 4 cm If the radius is 4 then square it.

[00:40:08]What is the radius? 4² So this is the area which we calculated once completely from this side and once completely from this side.

[00:40:19]So the triangular area in the middle has come twice. Which one? If the triangle appears twice, we will subtract the triangle. Isn't it?

[00:40:26]Once I calculated the area like this and once I calculated it completely from here. If you do this and look carefully, the triangular area in the middle will appear twice. Which one? The triangular area will appear twice. So when we calculated, how many times will it go by 120? Three times. And this will become 4 * 4 = 16, 16 * 2 = 32 means 32π / how much? 3 right? 4 * 4 = 16 16 * 2 = 32 32π / 3 and subtract the area of ​​the triangle from it. So which one is the triangle? So this is a triangle whose radius is 4 cm. So two triangles 3/4a² equals 4², right? So this will be 2 * 2 equals 4 and this will be 32π / 3 - 4 * 4 = 16. 2 taken from 16 is 8, so 8 3 will be the correct answer. 32π/3 - 8 3 Option C Right Answer. 32π/3 - 8 3C option will come correct. Priya Dhakad ji gave the correct answer. Harish, Deepali, Shivani, Akash, Divya, Manoj all have correct answers. Option C is the right answer.

[00:41:26]32π/3 - 8 3 will be its right answer. Option C will be the right answer. C will be absolutely correct.

[00:41:31]Here is the next question for you.

[00:41:33]Solve this. What will be the answer to this question? If you continue attending these classes and give the tests that are given daily, then your work can still be done.

[00:41:42]Your practice will easily be covered completely by that also.

[00:42:18]Let it be given in the question that if O is 5 cm. is the centre of a circle of radius.

[00:42:22]O which is 5 cm. is a circle with radius r at the center of the circle.

[00:42:28]13 cm from O A point P is taken at a distance of.

[00:42:31]13 cm from O A point P is taken at a distance of. 13 cm from O A point P is taken at a distance of. 13 cm Is at a distance. Let's say five and this eight, then it will become 13. Ok? From this point two tangents PQ and PR are drawn to the circle.

[00:42:46]From here PQ is drawn and PR is drawn. Which one was drawn? PQ and PR then what will be the area of ​​the quadrilateral PQ PQ O and R also? What will be its area? So you can write this as 13 8 5 13 and what is the radius here? Five. So 13 5 and what is this going to be? 12 So the area of ​​two triangles is going to be equal to 1/2 base * height half base five and what is the height going to be? 12 because it is a 90° angle, so it will be divided by two, 12 * 5 60 60 cm² will be its correct answer.

[00:43:19]Option A will be correct. 60 cm² will be the correct answer. How much will it cost? 60. Because two right angle triangles are formed. One this one came here in which this is 13. This is five and what is this? If it is 12 then there is a right angle triangle and how is another right angle triangle like this, one is here and one is here, if two right angle triangles are found then it will be solved by 1/2 base * height, isn't it sir, is it a recorded class or a live class, if I read your comment then but obviously it will be live too, isn't it, it is a live class, sorry it is not recorded, it is a live class, the next question is in front of you, please solve it, no madam, yes no no no, I will not eat food. No no no, I still teach. Then I talk.

[00:44:32]Let's solve it and see what answer you get. The side of a right angled triangle ABC is ABC where C is the hypotenuse. C is the hypotenuse.

[00:44:42]This C is the hypotenuse. Let this be A and this be B.

[00:44:47]What will be the radius of the incircle of this triangle? So the radius of its incircle is a + b - c / 2. You should remember this formula directly. a + b - c / 2 means perpendicular + base - hypotenuse / 2. The correct answer will be option B. It is a direct formula. If you want to solve it, you can do so.

[00:45:07]Even after solving it, you can get your answer.

[00:45:09]Okay, the sides of the right angled triangle abc are ab and c, where c is the hypotenuse.

[00:45:15]What will be the radius of the incircle of this triangle? The radius of the incircle will be a + b - c / Okay? Let's move on to the next question. If you want to write in Hindi also, then you can write that length + base - hypotenuse divided by how much? This formula. Ok?

[00:45:39]Let's solve the next question. The next question is before you. ABCD is a trapezium where AD is parallel to BC. Isn't it? ABCD is a trapezium in which AD is parallel to BC. Meaning but obviously this must have been AD and this must have been BC. Only then ABCD will become a quadrilateral and AD will be parallel to BC. AD parallel to BC AD and DC 10 cm. Is. A B and DC 10 cm. Is. Meaning this is also 10 and how much is this also? 10 cm Where did CDE, C, D and E come from? CDE is 45°.

[00:46:14][sound of clearing throat] C D and E we replace with A. CDA is 45°.

[00:46:24]How many degrees is it? 45° We do one thing, let's take it as CD. Let's take this as D. Let's take this as A. And let's take this as B.

[00:46:37]ABCD means CDA = 45° because it looks good 45°.

[00:46:43]Then find the distance between AD and BC. The distance between AD and BC means this height has to be found.

[00:46:48]So can we apply the formula here? This is perpendicular. This is hypotensive. So sin 45 = p / h sin 45 1 / 2. It will become equal to p / 10, meaning it will become p = 10 / 2 * 2 / 2, due to which it will be cut five times. The correct answer will be 5 2, meaning which option will be there? C Option 5 2 will be its right answer.

[00:47:16]How much will it cost? 5 2 5 2 is the correct answer.

[00:47:23]Looking good. Looking good means it is looking good or it is not looking good.

[00:47:30]5 2 Its right answer will come. Option C will be correct. 5 2 Its the right answer.

[00:47:40]Proceed to the next question.

[00:47:43]Here's the next question. Solve this.

[00:47:45]5 2 is the correct answer to the previous question. The next question is before you.

[00:47:53]Okay, it looks good, so no, no, that diagram was not looking proper, that is why we changed it.

[00:48:24]Let's solve the next question. Will the answer come?

[00:48:36]Call me. You will find the class of this chapter in the old video. In this equilateral triangle whose side is 24 cm. There is an incircle whose sides are touching. Isn't it? There is an equilateral triangle whose sides are 24 cm. There is a circle inside it. The inner circle that is touching it from inside. The area of ​​the remaining part of the triangle will be equal to this. So here if we look at the equilateral triangle, what will be the area of ​​the equilateral triangle? So the area of ​​the triangle will be 3 / 4 a², meaning what is the square 24², meaning if we divide it here then 3 * 24² 576 / what will it become? 4 * 1 = 4 4 * 4 = 16 144 3 Correct. If we look at the area of ​​a circle, whose area should we look at? Area of ​​the circle because we need the difference.

[00:49:36]Area of ​​the remaining part of the triangle excluding that even incircle, then what will the radius of the incircle be equal to? So what is the radius of the incircle? Radius of the incircle. If you see here, the radius of its incircle will be 2:1.

[00:49:50]Divide the height in 2:1 and the height is 3 / 2a. So 3 / 2a means 3 / 2a means 24 / 2 1 means if we divide it by 3, then it will be 12 divided by 2 and divided by 3, 4, then the radius will be 4 3 and its area will be πr². What will the area be? πr² means π r² means the square of 4 3. The square of 4 3 means 4 * 4 = 16 16 * 3 = 48 48π will come correct 48π. What was said in the question that what is it equal to? What will be the area of ​​the triangle, the area of ​​the remaining part will be equal to, so 48π means 48 * 3.14 4 means this will become 48 48 * 2 = 96 96 * 2 = 144 144 means 100 or we can multiply it by 3.14 which will come out and here we will multiply 144 by 1.732, we will multiply it by 1.732 and tell me what will be the answer, if we multiply both then see if I will multiply then it will take time, there is a better way than this, a machine has been developed, you will not get to see that machine in the paper but right now you might not be using that machine for the work which I am doing. You might be doing this after 10:00 pm or after 12:00 am in the dark to send messages on TikTok or somewhere. Right now what I am demonstrating is using it as a calculator. 144 * 1732 so this will become 249.13 this is 12 and if we multiply it here then it will become 48 * 3.14 so this will become 150.7 150.72 when we subtract then on subtraction it will become 249.12 98.4 98.4 which is approximately equal to 95. 98.5 K.

[00:51:40]Option D will be the correct answer. D What will be the right answer to this? Option D will be correct and I have shown this by calculating it through a machine made by a scientist.

[00:51:48]So there is no chance of any mistake.

[00:51:51]98.4 is its correct answer.

[00:52:01]What option will come? Option D will be the correct answer.

[00:52:03]98.5 is its correct answer. Here is the next question for you. Solve this. Please call me. The next question is before you.

[00:53:01]If the length of the base of an isosceles triangle is 2x - 2y + 4z. Isosceles means whose two sides are equal. Isn't it? So this is 2x - 2y + 4z. And its perimeter is 4x - 2y + 6z. What will be the length of each side? What will be the length of the side of each rhombus? So let's assume this will be k + this k. 2k + 2x - 2y + 4z = 4x - 2y + 6z. This will happen there. So if 2x is removed from 2k = 4x then 2x will remain. Minus 2y goes over there and becomes + 2y. Meaning 2y 2y so what happened between them? It got cancelled. - 2y and this - 2y cancel each other out. If 4z is subtracted from 6z, what will be left of the plus? If we divide 2z by k = 2 then what will be x +? z Correct answer will come. x + z which is the right answer. x + z means option D is the right answer. x + z its correct. What will come? x + z Option D is the correct answer.

[00:54:03]D is the absolutely correct answer. D will be absolutely correct.

[00:54:07]Here is the next question for you. The next question is before you. Solve it.

[00:54:12]Will the answer come?

[00:54:41]Let's solve the next question. Will the answer come?

[00:54:47]16 Answers are coming. Tan 5x Trigonometry questions are out. tan 5x - tan = cot 5y + 20 So you know that tan and cot are complementary to each other.

[00:55:01]So what will 5x - 10 + 5y + 20 be equal to? 90 Here if you solve both of these then 5x + 5y + 10 = 90 means divide 5x + y = 80 and x + y = 80 by five, the correct answer will be 16, option B will be correct, 16 will be its correct answer, how much will it be, 16 16 its correct answer will be 16°, it is absolutely correct, I have removed the ad, son, now you will not get any ad, not a single ad will be shown right now, the correct answer will come. Will the answer come? Option B will be correct. Option B is the correct answer that one should have some special friends. Isn't it? It is said that there should be some close friends in this crowd of life. My beloved does not drink tea at night. I don't write that much poetry.

[00:55:59]But sometimes if I remember some lines then I recite them to you. Ok? Let's put this next question before you.

[00:56:04]Solve this.

[00:56:10]Now don't interpret this thing in any other way.

[00:56:13]Read it well. So that my mood gets refreshed a bit.

[00:56:15]Well, one should always remain fresh in mathematics.

[00:56:21]next question. In a cyclic quadrilateral ABCD, cyclic quadrilateral means the quadrilateral which is inscribed in the circle. ABCD is a cyclic quadrilateral ABCD. BCD at A, B, C and D is equal to 120° then ADB is equal to what? What would the ADB equivalent be? AB is equal to what is this angle? Correct?

[00:56:50]What will ADB equal to?

[00:56:52]In a cyclic quadrilateral ABCD, angle BCD, angle BD and D are equal to 120° and AB passes through the centre of the circle. Well AB also passes through the center of the circle. That's ok. We make it like this. I did n't make that line. AB passes through the centre of the circle.

[00:57:15]C and DCD B C and D equal 120° then what is ABD equal to? ABD equals what is this angle? What is ABD equal to? The question is what will ABD be equal to?

[00:57:34]If this is 120 then obviously how much will it be? If this is 60 and this is 60, then this is 90 and this is 90, then what will this angle be? 30° The correct answer will be 30°. Option A will be the correct answer.

[00:57:42]30 Its the right answer. How much will it cost? 30° which is the correct answer. 30° will be the correct answer. 30 Its the right answer. Ok?

[00:57:50]And I'll read it for just a minute. Ok?

[00:57:53]Yes. Please deliver the key to lock it.

[00:57:59]Locked it completely here. Closed easily.

[00:58:01]Ok? How much will the correct answer be? 13. Let's move on to the next question. Here is the next question for you.

[00:58:05]Solve this. The next question is in front of you.

[00:58:10]I will get all the questions repeated. I will make you solve questions of every level. The only requirement is to take regular classes. Stay connected constantly.

[00:58:38]Let if in isosceles triangle ABC, be the median of the odd side of ADBC ​​meeting at D. In triangle ABC, be the median of the odd side of ADBC ​​meeting at D in the points A, B and C. is the median of the odd side.

[00:59:00]This is the odd side.

[00:59:03]is its median. These two are equal. This became the median. In an isosceles triangle ABC, AD is the median of the odd side meeting BC at D. This is the median of the odd side. DP is the angle bisector of ADB. DP is the angle bisector of AD and B.

[00:59:22]DP is the angle bisector.

[00:59:25]Meaning this angle and this angle will be equal to DP. Ok?

[00:59:30]And PQ is a line parallel to BC meeting AC at Q. This is a parallel line PQ drawn parallel to BC [sound of clearing throat].

[00:59:42]What is the measure of PDQ? Then what will be the measure of PD and Q?

[00:59:48]What will be the value of PDQ?

[00:59:50]What will be the value of this angle?

[00:59:53]What will be the value of P good PDQ?

[00:59:55]What will be the value of this angle? 1 minute let me back this up a bit.

[00:59:59]What will be the value of PDQ? PQ means you have to find the angle with the value of this angle.

[01:00:05]Tell me, it is not possible to calculate such things anyway. So it is simple that such a value will come which is a fixed value and mostly what I am thinking is what will be 90°?

[01:00:17]Right answer. If you want to solve the rest, you can do it.

[01:00:19]This is x and this is x. Because what are these two arms? Is equal. This is x and what is this? Now let's talk further about x, this is the angle bisector. Meaning what will these two angles be? Will be equal. Isn't it? And this is a parallel line. So we can also do it according to the parallel line.

[01:00:54]is the median. Ok?

[01:00:56]And this is the center point. What is this arm and this arm? Is equal.

[01:01:01]is the angle trisector of PDP. Let's see what will be the answer if we tick it directly then it will be 90 but we are trying to solve it by solving PDQ. Isn't it? 90° However, its answer can be made directly. But we will try to solve it as to how we can solve it. So if this X, both its sides are equal because it is an isosceles triangle. So this is x. This will be x. It became average. After that he said that this is Konak. This line is the angle. So is Konak. This means it has an angle and it is an angle. Secondly, both are equal lines. So this will be a 90° angle. How much will it be? will be 90°. So this is the angle. Meaning it will be 45 and how much will it be? 45 correct. It will be 45, it will be 45 and it will be 45, 45. After that we will talk about the next thing.

[01:02:15]These two are parallel lines. So it is a parallel line. This means it will also be 90.

[01:02:20]And if this is 90 then this will be 45. This will be 45.

[01:02:23]Ok? This became 45. This 45 on that side 45, this 45 becomes 90. Now the angle on this side is left.

[01:02:32]What will this angle be?

[01:02:58]Okay, this 90 and 45, how much will this be?

[01:03:01]135 90 and 45, so it should not be 135, it should be complete, it will be complete only after adding it, how will we know this angle with just this much, and this 45, okay, if it becomes 45 45 90, then it will be complete 90, it is not possible to find out this angle, it will be 45 plus, it is confirmed, if it is 45 40 plus then it will be 90. But if we search somewhere, we will find it.

[01:03:32]90 is its correct answer. If we look for it, we will find it. It will be made somewhere or the other in some way or the other. Yes, it is confirmed that it is 45. How was this 45 confirmed? It's a full 90. If it's angled then this is 45 and this is 45 from 90.

[01:03:42]This line and this line are parallel. This is 45 on this side, so this will be 45. The sum of the three angles of a triangle is 180°.

[01:03:51]This will not solve it. Do you see any other way? Do you see any other way? Do you see any other way?

[01:04:00]not visible. It will be 90. Option B will be the right answer.

[01:04:13]We ticked for now. We can find the rest of the solution. The next question is in front of you, solve it. Well, have you lost your voice? Is the voice coming or not? She must be coming now.

[01:04:24]Let's stop our last question where we have solved it here.

[01:04:29]I did not tell the solution to this. The answer is 90.

[01:04:31]This is where we stop the class.

[01:04:33]I will conduct further classes for you tomorrow.

[01:04:35]I have many more questions which we will address and somewhere the children have just come to know about the class, so gradually other children will also join us in the class and you will keep getting classes continuously. Ok?

[01:04:44]If you have not joined the Twitter channel yet, then join it. You will find the Telegram channel of Mind for Academy.

[01:04:49]From here you will get PDFs of all the classes. You will get information about the classes. You will get information about the course.

[01:04:55]What time tomorrow? Every night at 8:00 pm. Every night at 8:00 pm. Meet at 8:00 pm.

[01:04:59]Classes will continue uninterrupted. Ok? That's all for today.

[01:05:03]Yes, I will also enter the question number.

[01:05:05]So see you in the next class. Till then take care of yourself. Study well.

[01:05:08]Jai Hind, Jai Bharat Mata ki Jai.