Hello students, today we have brought it for you, like a few days ago I had uploaded a video on the sample paper of class 10th, so I had told in that video that if you want the solution of this paper then If you comment , I will make a video on it, so there were some similar comments from students, Sir, we need the solution of this paper also, okay, so I am making a video on the solution of this paper and those who had just commented, those comments are yours. You will come on the screen. Okay,
if you have not seen the sample paper of Maths yet, then I have made a proper video on it, the link of which will be found in the description and also you will get all the topics of Science, Hindi, English, SST, etc. You will find the links of the videos of the papers in the description, go and watch them from there because there are many such questions which come from our sample papers only. Okay, so before starting the solution of the paper, let me tell you this. The video which is the solutio
n of our class 10th Maths Sample Paper 2024 is part two of the video. Okay, in this part I am going to give you questions from 11 to 20 and if you have not seen this part yet, then that video is already there. It has been uploaded, you will find its link in the description and also on the button above. It is okay if you go and watch that video and you must share these solution videos with your friends. It is okay with as many of your friends as possible. Share, it's okay and if you want the solu
tion of any other paper, then you can comment in this video, I will bring a video on the solution of that paper as soon as possible. It is okay if you are new on our channel and want to know about the same method. If you want to see the solution of more papers then you can subscribe our channel and most importantly press the bell icon on all so that whenever I upload a solution video, its notification can go to you first. Okay, so start. Now let us see the part two of the solution video of Maths
Sample Paper 2024 of Class 10th. Okay, now let us see its 11th question. What do we have to know about the polynomial 4 y + 8 y? We have to find the zeros and which will be its zeros and What we have to do in between the coefficients is to check the correctness, okay, we can do this check only when we have what will be the zeros, so first what is it, we will find its zeros, then I will tell you how to find it, okay, so this is the solution. If you have 4u + 8u equal to 0, what will you do from
here, 4 u will be taken as common, our u + 2 = 0 will be left in the bracket. Okay, so one of us will come from here 0 and the other one will come to us u + 2 = 0 and this two of plus will go there, what will happen to minus then u is equal to minus two, so what we have is two zeros have come, one u is equal to 0 and one u is equal to -2, okay The first one we call alpha, the second one we call beta, okay, whatever is its zero power, we accept it, alpha beta is okay, so this is what we have extr
acted here, now further we will know the relation between its zero and coefficient. We have to check the authenticity, what is there in this, we have two steps, what we do in the first step is the sum of zeros, our formula is alpha + beta will be equal to minus k b / a and the second one we have the product of zeros, that It happens that we have alpha beta = c / a. Now for this we need the value of a and b, so where will we get it from this quadratic equation, then a will be equal to 4 and b wil
l be equal to 8 and c will be equal to 0. Okay, this is also written here in front of you. Now here what we have is, once we find the sum of zeros and once the product, okay, now we see that further we get the sum of zeros, we have alpha plus beta and these are equal. It is our whose minus k b is our a k alpha and if you see here, the first value we got was zero and the second one was minus two and over there too what was we got we had b eight and minus there formula I have given the value of a,
we got four, if we cut it from there then here also minus will become two and there also minus two will make it equation number one and second formula is we have alpha beta of the product = c / We will multiply the zeros we had with a by each other, we will get zero here too and the value of c we have is zero and if we convert the value of a to four from here too then we will get zero. If both of them are equal, we mean that We have to check the truth, they will be correct, if they come differe
nt then our test will be wrong, from equation one and two we will say, in the question it was said that check the truth, okay, so we have done this. Now let's see its next question. In the 12th question, we have been given such two numbers. Find two numbers whose sum is 27 and what is the product. 182. Okay, so we do not know which are those two numbers whose sum is 27. So what will we do, here we will take the first number as x and our second number will be taken as 27 - If we subtract from , t
hen our second number will come. Okay, now the first condition is done and in the second we have given that the product of the two numbers that we have is 182. So first, we have considered x and second, is 27 - _ Like I told, another number will come and the equation will be formed like I told, then we will solve this quadratic equation, so what we have here is that we will have two values of x, one will come x is equal to 13 and one will come our We have x equals 14. Okay, so let me tell you
that one will come, we have x equals 13 and one will come Because 27 is my 13 means that which will be the answer, he has asked the numbers whose sum should be 27 and their product should be 182, then which are such numbers 13 and 14 are correct and it has given us the calculation here. You look from here and write down what is here, it will not be 21, how much will be here, it will be 27. Okay, when you note it on the copy, keep it in mind, now let us see the next question of this, it has been
given to us in the meaning of the 12th question. Find the value of k and we have been given a quadratic equation and we have also been given a condition here that how should the root be equal to us, we have given this condition, so first of all what will we do? Standard form of quadratic equation. Okay , now you should know the standard form, so let me tell you that a, a, b, a, c, is equal to 0, then by comparing, we will find out the value of a, b and c. Okay, now how much will the value of a b
e? Two more. We will get the value of b, k and c will be our three, okay, what are these values, we will use them further by applying the condition, okay, let's see, as you can see here now, then what will we do here. Will put the condition. We have been told that how should the roots be equal. Now you should remember this condition. There are three such conditions. Questions can come on any condition. It is given here that if the roots are equal then its condition is b s - 4ac = 0 This is given
to us, here abc2 = 24 and what will we do from here, 24 k will come in the root and from here we will take out the value of k, that will be our plus my 2 √6, okay this is our answer. If it will be done, then we have removed it. Okay, now let's see its next question. In its 13th question, we have been given. There are three red and five black balls in a bag, so we have to remove any one ball at random from this bag. So we have to tell the probability that the ball is red and the second point has
been given that the ball is not red, so we have to find the probability of both of these. Okay, now let me explain to you what I want to say, question first. What do we have, we have a bag and in it we had five balls i.e. five black balls, so we have made that also, okay, now we will see what will be our total results in this bag, okay how many will come, that is, eight balls, that is, there are eight balls in the bag. So any C can come out, black ball can also come out and red ball can also co
me out. Now let's see the solution given to us is that the number of red balls in the bag is three and what is the number of black balls in the bag. If it is five, then how many balls do we have in total, that is, how many balls are there in the total bag, a total of eight balls, that is, how many possible outcomes will we have, it will be eight, okay, now we have because we have the formula. That is the favorable outcome divided by the total outcome. Now we have to find out in the first point t
hat what kind of ball is red, then how many outcomes of it being red do we have. If there are three red balls, then the outcomes we have, how many outcomes can there be, then we have three. Will we calculate the probability here that what kind of ball p should be red? Favorable result divided by total results is favorable result. We have three and total results, we have eight, so the answer will be 3 by eight. Okay, similarly we have to find the second point that The ball should not be red. Now
if it is not red then what will it be? If it is black, then how many black balls do we have? Five and how many total balls are there? Eight, then the answer will be 5/8. Well, one, you can find out in this way and One, you can also find out in another way, I will tell you further, like if any event is to happen, then what is its probability, one, either that event will happen or it will not happen, okay, now here we have to find out what kind of ball it is. Whether it is red or not, now what do
we have in this question? If we find out the probability of having a red ball, then we will subtract one from one. The probability of being red is fine, how is the ball, it is red. If we subtract it, then what will we get that the ball is If we come up with the probability that it is not red, then its answer will be 5/8. Okay, so it is given to us here. Okay, and these are probability questions, these are very easy questions and mostly it will be either someone with ball or There must be someone
with cards of cards, one of these comes in the board. Okay, so you must prepare such questions. Okay, now let's see its next question. Let's see its 14th question. What is given to us in this that in the following table, the values of x and y Find the value, okay, we have given the terms in this, given the frequency and given the cumulative frequency. Okay, so let me tell you once what we are going to do in this question. Okay, what will we do? Here is a cumulative frequency. We have calculat
ed and given an accumulation frequency in the question. We will compare both and find out the values of It is in front, okay, here we have given the terms, we have given the frequency and we have written down the cumulative frequency which was given to us in the question, this cumulative frequency, we have calculated it from our side, okay, now how do we get it, whatever is the first term in the frequency. Let's write it down in the accumulation frequency. What do we do after that? To get the
second term, add its second term here, then it will come to 6 + x. Similarly, if we add the third term here, then we will get It will be 24 + 6 + 73 + _ _ The accumulation frequency this time will be equal to this accumulation frequency because they have given us this accumulation frequency and we have calculated it, so they will be equal to each other, similarly, what will we do from here, we will find the value of x, we will get the value of x that is 20. How much will 20 be? Similarly, what w
ill we do here? Here is one y and one here. We have calculated the value of 58 + xx, so the value of y will be 78. Okay, now you can see these values by placing them in the above accumulation frequency. You can check whether your answer is correct or not. Like if you put 20 here then 20 + 6 will be 26. So 26 is coming here. Similarly, if you add 20 to 58 here then it will come to 78. And if you add 15 plus to 78, your score will be 93, that is, the answer you have found is correct, it is an ea
sy question, whether it is accumulation frequency or finding mode, finding median, finding mean, easy questions come from this chapter. And the calculation is also very easy, okay , but only if you know its formulas, you can do it. Okay, now let's see its next question. Now let's see its 15th question. In this, we have been given to prove that from the external point. We have to prove in this that what is the length of the tangents drawn to the circle and are they equal? Okay, listen once more
to what is written in it that what is the length of the tangents drawn to the circle from an external point and they are equal. We have to prove, okay, there should be no confusion in such two theorems, okay, first let me explain to you from the picture, what we have been given and what we have to do, one, we will consider the external point here, which we have. And let's assume that we fast, okay, now from this external point p, we have drawn two tangents, one at p and one at pb2, okay, so let
us prove this, you keep this in mind, now we will see that Solution: This is the solution in front of you, whatever is given in it, first write that there is a point p outside the circle with center o and from point p we have drawn two tangent lines to the circle, just like I explained to you while making the picture. It is written here and we have to prove that P is equal in pb3 and also in science. So you must make a picture and bring it. If there is a picture in that question then it is ok.
Now here we will create this O point, we have made it . What is it, a is also mixed with p, p is also mixed with b, okay, we have composed this, now let's start its proof, now we have a theorem, this theorem will also be in your book, okay, check it from there, otherwise. A screenshot of that theorem will now appear on your screen, along with the statement and diagram, it is okay to see that theorem from there because the same theorem is going to be used in this. The theorem is that the radii of
our circle are the tangents. But what are perpendiculars? Okay, this is also our proof. If you see, here we are directly using the theorem. Here o is what is what is on our p, what is perpendicular and p is what is of our circle. If there is a tangent line, then I can write that oa04 is perpendicular, so here also our angle will be 90 degrees, so from here we will write that o p will also be 90 degrees, okay now let's see. Further, if you look at the diagram, you will be seeing two triangles, o
ne o A and the other o P. Okay, what will we do with these two triangles, we will prove congruence and after doing congruent proof, what we have to prove from CPCT is that this The tangent lines, what will be their length, will be equal, from there we will prove them, okay you will see that here, so here we have taken triangle AO and triangle b, what will be in it, what is the radius of the circle, okay and second op0 degree . If we do the proof of then we will write that angle o A will be equal
to angle o Then we will write here that hence triangle AO will be congruent Triangle b is correct Bi is correct by whom R is correct By AA Have we proved them to be congruent? After proving the given congruence, we can say to CPCT that p will be equal to pb2, we have proved that here, okay, so there are two such theorems, you prepare both the theorems and go, whether it is board or pre-board, okay now. Let's see its next question. Now let's see its quarter question. In the 16th question, you mu
st be seeing the diagram here and we have been given in the question that AA is parallel to C, B and L is parallel to S and we have to prove that A up A will be equal to / A k Okay, this is also an easy question, you should know Thales theorem, okay, if you know Thales theorem then you will do this question. Okay, so now let's see its solution. So you will see two triangles in the picture. You will be seeing a first AC and a second AC. Okay, we are going to prove it with these two triangles. Fir
st we will write here for A. Let me draw it here and show you, this is our triangle, ab and c, this is a parallel line. Done, m and l are given to us in the question that this m is parallel to which bcmlcane.in. We will make it from the second triangle. Now let's see that second, we have this triangle, we will make it once ad and c. Here we have been given n and in the question it has been said that l is parallel to which cd3 theorem will be applied. Okay, so here we will get ann.com. Then by so
lving both the equations together, we will prove that which we get. In the question, we have to find it, okay, let's see that, first we had found out in triangle AC that m is parallel to bc1, we had made A/ bm1 of C. Now our Thales theorem also has another name, basic rational, okay, we will call it basic. They are also called rational, it is okay if the basic rational is written somewhere, then there should be no confusion in it, okay, in its place you can also write Thales theorem, there we to
ok the second one adc12, now if you see in equation one and equation two, then you will get this If both the values appear to be the same then we will write from one and two that A/ bm1 is ok, I will show it to you right now, it is the same, here also what I told you is still written, now what will we do in reverse. Okay, because we have to come up with the answer, for that we will have to apply a trick here, only then our answer will come, first what we will do is reverse it i.e. b we will ta
ke it up and what will AD also do if we take it up then we will write inverse. Okay, so here we'll take the inverse, left and eddy will go over us, then What we will do is by adding one on both sides, if we add one on both sides, then bm1 equals n/A + 1. Here we will take the LCM which will come to our A and on this side A will come to our side, AD will be equal to our A. Okay, if you are in the paper now. Let's see what we have, we have to prove its reverse. Okay, our answer is already there. I
f you look at it in the question, then according to it, what would have come now is the reverse. Now you will notice that at one place we had reversed this question. That is, if we had taken its reciprocal, then what would we do? We will write again on taking the reciprocal, what we had done at that time was that we had taken the lower number to the top, we would invert it here, what is our M here, what is below it? What will we do if we do it above then A/A and similarly if we do A here then A
up A is okay, this is what we had to prove, the same is okay and this is our important question, whether it is pre-board or board, it is okay in both. This question is asked a lot, so you must have done your pre-boards, so you must prepare this question for the board. Okay, now let's see its next question. Now let's see the question of 1.25 or I have given us the question, if you have 1.25 question. If you know, then you can do that or whatever, it is okay, you can do this, but this is a questio
n of which or that, it is easier, okay, I will make you do it, like what a diagram has been given to us here, you can see here. Must have been and it is written in the given figure if DC is similar to triangle o and we are given that angle b is equal to 125 ° and angle cd is7 ° we have to find two angles one is angle d and one is to do d Now what will we do? Let me first tell you here what we are going to do, after that I will show you its solution. First if you look, here you will see a line do
and b and its o b was o b and here What is like a perpendicular which is our C and this angle is given to us 125 degrees Now we know if it is a straight line then what is the sum of the angles on the straight line 180 then what will we do angle d plus angle b is equal to 180 b We have given the value of 'O' from here we can find out the value of 'O' and we also have to find it here. So from here we will find the value of 'O'. The first answer will come from here and we have to find it in the se
cond one. Now you will see one here. A triangle will be formed which will be our d c and o okay and we have given y 70 degree and this value of o we will have calculated above this and we have to calculate d c d co this is what we have to calculate ok so now we know What is the sum of the three angles? It is 180. If we know two angles, then we will find the third angle. Okay, this is an easy question. If you have read the chapter, after looking at the question, you will tell the answer. Okay, no
w I will show you the solution. I have given its solution in front of you, so the same is written here as I told that two angles are equal to 180, we have to find d, then we will take the second angle to the other side i.e. b, so here we have d which we have to find. We will get that angle by how much it will be 55 degrees. Now after that it was said that we will form a triangle OC, so the same is written here and what is here, we will write the value which we have to find out, d will be equal t
o what is the sum of the three angles. If it is 180 then we will subtract the remaining two angles from 180, then we will also know how much is 55°. Okay, so these two angles were asked from us, angle DC and angle OS and we have solved both of them here, okay easy. The question is just what are your formulas? You should have the formulas ready. There are main formulas in Maths that if you remember the formulas then you can ask any question. It is okay if you do not remember the formulas. You can
not do any question. You cannot do any question. You will be able to do it, okay, now let's see further, don't write this, this is what has been asked of us in the question, no, okay, this is too much, I have spared you a little in this, he has only asked the question till now, so you tell this much answer, now we will see it. Next question: In the 17th question, we have been given that if the sum of seven terms of an AP is 49 and the sum of 17 terms that we have is 289, then here we have to tel
l the sum of n terms. Okay, now this question To do this, you should know the formula for the sum of A A terms. If you know then you will understand this question in a second, but if you do not know the formula then you cannot do it, so first I If I could have told you its formula, our sn2 would be 2a + n - 1 * d. This is ours. I have said that the sum of the first seven terms is 49, so what will we do? We will put seven in place of n, wherever our n is. Okay, so we will make an equation accordi
ng to that and the second one has said that what is the sum of the first 17 terms, ours is 289. In the second time, we will put 17 everywhere here. Okay, so we will have an equation from here and these two equations will be in terms of a and d. From there we will solve it by any method, whether it is substitution, Braj factorization, elimination, you can solve it by any method. We will find out the value of a and d because we need the sn2 value of a and d. Okay, so now let's see its solution. No
w let's see its solution. We have given it here first . s7 means that if we want to find the sum of the first seven terms then what will we do like I told that s7 will be equal to 49 and s1 will be equal to 28 89 Now what will we do from here, we will apply the formula which I told, first we will find out for whom seven. For , if we put 7 in place of n then s7 = 7/2 2a ps in the bracket will come there 7 - 1 * d and s7 is given to us here how much is 49 given here and we will put its value 49 49
will be equal to 7 /2 is equal to what will be left here 2a P 7 will go to one how much will be left 6d Now what will we do Here we got our a 2a + 6d From here what will we do if we take two common then here will be our a + 3d Okay and here we If you look at it, we have 7/2 going on in the multiplication, so both of them will be cut off from each other, so here we will be left with 7 in the bracket, a + 3d and from this, our 49 which is 49 will be cut off seven times, okay, so we will have the
equation Will go to a a p 3d bar 7 Okay, we will make this equation number one, now we will find the second one for 17 terms, so here it will come s1 bar 17/2 in the bucket 2a p 17 -1 * d So the sum of 17 terms is given to us. 289 will be equal to 17/2 and here it will be 2a p 16d, so here also we will do the same as we did there, 2a ps is given here as 16d, so what will we do from here, we will take two common, it will come in the bracket a. P will go to 8d eight times and what is left for us h
ere is 17/2, we will subtract 2 from two and from the 17 here, we will subtract 289 from it. 17 times, this will become an equation: a + 18d = 17. We will make this equation number. Now we will solve it by any method and find out the values of a and d. Okay, so I will show you how to solve it here by one method, so first we will write the second equation, that is, we have aa p 8d equals 17 and which we have We have another equation, they will write a ps 3d equals 7 and now what will we do, we
will change its sign, it will be cut, from here we will get 5d and from here we will get 10 and from here we will get the value of d, that is, d. We have got the value of a. Now we will find the value of a by placing the value of d in the first or second equation. I will show you that. Now we will keep a in the first equation. What is the value of d. We have 2 then 3 * 2. 7 then a is equal to 7 - 6 so what is the value of a and okay, we have got the value of a and d. What will we do from here, w
e will find the sum of n terms. Okay, so I also wrote the formula for the sum of s terms. s will be equal to n b 2 in bucket 2a ps n 1 nadi This was the formula, now we have to find the sum of nn terms, then we will leave n in place of n and will put the value of remaining A and D, then n will be the value of A in the upper bracket. If we have one, then two will come, and only plus will come. Now here n has to remain in place of n and the value of D has come to us. Okay, now I will solve it furt
her and show you this value. Keep this value in mind, okay. So now our value was n + 2 and our 2 plus was left in the bracket. Now our n was -1 * 2. So if we multiply inside t, we will get 2n - 2. Cut the plus one from the minus one. Ours will come to n b 2 * 2n Now here 2 to 2 will be cut, how much will we come to n squared. Okay, so what we had to find was the sum of n terms, how much will come to n s. The whole question was just dependent on the formula, okay so. You must remember the formula
s. Okay, if you want a video on the formulas of the entire book, where you can get all the formulas in one video, then you can comment, I will make a video on that too, okay if. If you want then you can comment. Now let's see its next question. Now let's see its 18th question. Prove that Sa a / 1+ ca + 1+ ca / Sa a is equal to our whose 2cc a. Like we take LHS and we have to do RHS proof, so in this we will take LHS and come up with the value of RHS. Okay, so now let's see how we will do that,
so this is the solution in front of you. what here We will write down the value given to us which is equal to LHS. What will we do after that? Here we will take LCM, then our LCM will be sa a, 1 pk a, sa a, sa a will be deducted, then above will be 1 pk a. Whole square i.e. it is written there twice. If plus k 1 p k a is deducted from 1 p k a then it will come here sa square a i.e. it is written there twice and in the next line it is written here twice. What will they do now ? Here, our formula
has to be in the hole square of 1 p k a. Okay, that is our formula for the hole square of a p k a. Okay, so we will put this formula here. Let's look further, now square of 1 + c s a + 2ab i.e. 2 * 1 and ca and sin2 a, we are going on, okay now our formula is sin2 a + c s a, its value is 1 so one, we have Here, if it is from the first, then 2c a is left, we will write it and here the value of sa sa + ca sa a has come, it is ok and it is going on in our system, our 1 p + ca * sa is ok, what will
we do next? Here 1 and 1 will become 2 + 2c a and upon us we will take 1 + ca * sin2 common, our left over 2 will be 1 + ca and upon us we will have 1 + ca * sinc-sind. This is what we had to bring to LHS so that We can say that LHS is equal to RHS, so we have proved it here, okay and from the eighth chapter, two to three questions keep coming in the board every time, so prepare this chapter properly and now let us see its solution. The question So or Me also comes from the eighth chapter. Prov
e that sa a + ca times square p ca + se a times square it is equal to 7 + tan2 a + cot2a. Okay, so what is there in this also, we will move on by taking LHS and We will do the RHS proof. Okay, let's see the question. Now how will we do it? Here, if you look at both, the same formula as above has to be made for the whole square of a + b which I told you above, then we will apply the same a s + b s. + 2ab Okay, now let's see its solution So this is its solution in front of you What we will do from
here is take LHS and put the formula here i.e. sa sa a + cc2 sa aca Okay, similarly we will put it in the second c s a + to s a + 2c a * secc2011 And what we did here was that we had written 1 / s a, then our sign will be cut off from this sign and similarly here we will write cos2 a + to s a + 2c If ca is deducted from a , then we will get sin2 a + cc2. Okay, now we have cosec2x formulas here, that is why I am saying that you must know the formulas. Okay, you can do the entire paper only becau
se there is a formula in every question. Okay, so you should know the formulas, so I have written here that cca175 will give sa s a + quot sk a plus from here one is left and from there 2 is left so 1 + 2 and from here k sk a p 1tan s a + 2 Now from here, we will write these number ones on one side and our angle ones, we will write them on one side. Next, we will write the number ones on one side and the angle ones will come on one side because Here our formulas will be created, just like the fi
rst formula you will be seeing here is sa sa + ka squa, what is its value, on one side we will come and on the other side it will come cot2a + tan2 a, so here its value will come our one which we have also given the formula. It is written that one and we will add all these 2 2 4 and 1 5 and 1 6 This is six six and one How much will it be Seven more will come + cot2a + tan2 Had to be done in RHS Okay so this is ours Okay And both of these are important questions, okay, no such new questions come
in the board, the important questions keep getting repeated again and again, okay, so you should prepare properly for this chapter and I will also give you exercises. Let me tell you that your 8.4 is correct according to the book because what is your 8.3 has already been deducted. Now the 8.4 we call is 8.3 and for those who have new books, it will be 8.4 in old books and for those who have new books. It will be 8.3 in the books of those who will be booked, it is fine, so you should prepare for
it in the right way because in this, there are at least 10 to 12 questions in this, so in this way, you should prepare all those questions and repeat the same questions every time. They keep happening, you can come in the question of five marks and also in the question of four marks, it is okay, so you must prepare and go, okay, now let us see its next question, now let us see its 19th question, in this we have been given some utensil . Khokale is in the shape of a semi-circle on which the Khoka
le cylinder is superimposed, okay let me tell you here what it means, we have a semi-circle and what is that also like? What is Khola, we have placed a cylinder on top of that hemisphere and what is that cylinder like? Khola, it is okay and we have given the diameter of the hemisphere, we have given us the total height of 13 centimeters, we have placed this vessel. After which I will give you the solution, its solution also starts from here, first let us see its picture, it has been given to us,
first of all, he has said hemisphere, what has become of our hemisphere, what is a cylinder placed on this hemisphere? The center has been planted i.e. it has been placed, it is okay, we have got a shape which is a semi-circle and what has been placed on top of it is a cylinder, okay and we have been given the diameter of the semi-circle which is 14 centimeters, it is also written here which is the diameter. And we have been given the total height of this vessel, its 13 cm is fine, so this vess
el is of this type, now in the question we have been told that we have to find its internal surface area, okay how can we find it, first what will we do, which will give us We have given a semi sphere, we will find its surface area, then what will we do? We will take out the surface area of the given cylinder and what will we do with both of them, we will add them because what is the vessel made of? It is made of a semi sphere and a cylinder. So if we add the surface area of both then the ar
ea of our vessel will be found. Okay, so now I will show you the further calculation of how we will do that and you keep in mind the whole of what I have just explained. We have been given the diameter of the sphere. Now what will we do with the diameter? We will first find out the radius. Our radius will be 7 centimeters. Now you should know what is the surface area of a hemisphere. Okay, so that area is 2. Pa a square is okay, so here we will put 22/7 in place of 2 pi and r, we have just c
alculated, okay, what is our r of the hemisphere, seven, you must be seeing above, then we will calculate its value and find out the value of the hemisphere which we have. Its area will be 308 cm square. If there is area then we will put square there. Okay, now it is our turn to find out the surface area of the cylinder. Okay, now you should first know the apparent area of the cylinder. Let me tell you what it is. So what is the surface area of the cylinder? 2 pi r a. Okay, so in place of
2 pi we will put 22/7 r which is the cylinder we have. You can also see it in the picture which is the cylinder we have, it is superimposed on the hemisphere i.e. Okay, so the diameter of the hemisphere will be the same as the diameter of our cylinder, so the diameter of the cylinder will also be the same and the radius will also be the same, that is, the value of r has also been found. We need this from somewhere. h is fine, so it means what is the height of the cylinder, so we have to find the
value of h from somewhere. If we find the value of A, then we will put it in this formula. Okay, so the value of h, I will tell you how to find it. If you care, I have . What was its total height? The total height of the vessel was told to be 13 centimeters. Now here we have been given a semi-circle and its radius has come to us as 7 centimeters so the total will be 7 centimeters so we have to find out this value. Okay, so what will we do? If we subtract seven from 13, then how much will we get
? That is, the height of the cylinder will be 6 centimeters. Okay, now we have got all the values, so we will put them in the formula and get the answer . Let's see, then I had told you how we will find its radius, then after that I have also explained to you how the height has been calculated. We will apply the formula: 2 Pa a A 2 * Instead of Pa, we have given the value of 22/7 r. How much we have come near 7 cm. After 6 cm, we will calculate from here , the answer will be our 264 cm square. L
ike I told in the beginning, to get the total area of the square, if we add both of them at the end, we will get it. The internal surface area of the vessel will be equal to the one which came first, the surface area of the hemisphere plus the surface area of the cylinder, we will add both, one came 308 and the second came 264, so the total of the vessel will be 572 cm square, right. So this is the utensil that was given to us, what is its surface area, how much is it 572 cm square, okay
now let's see, we have given us this or that, now this or that has given us that find the area of the shaded part in the given figure if The radii of the two central circles with center o are 7 centimeters respectively. We get 40 degrees, so you must be seeing this shaded part in the picture. We have to find its area, this is the easiest question, I will explain it to you here, if you see the picture, you will be seeing such a shape, first you will see a small shape o b d, so this is our smal
l radius segment given to us . Is 7 centimeters and the second one let me show you the second one is O A and C. It has given us 14 centimeters. You should know what is the area of the radius segment. So you will subtract the area of the larger radius segment from the radius of the smaller one. The area of the segment will be equal to the area of the shaded part. Okay, so first let me tell you what is the formula of the radius segment. So our formula for the radius segment is Theta / 360
* Pa r squared. This is our radius. The formula of the segment is if it is a large radius segment then we will put r for it and if it is a small radius segment then we will put r as the weight. Okay, so we will see its solution further. Now its solution is in front of you. Here we will write the radius of the big circle r = 14. cm, the radius of the small circle is r = 7 cm and the angle given to us is 40 degrees. Now what we will do is to find the area of the shaded part, we will write the ar
ea of the sector aoc-2 and apply the formula th / 360 * pa s i.e. That the value of r is kept here Capital - Th / 360 Pa r Square What will we do now From here Th / 360 * Pa will come in the bracket r S - r S We will put the value of theta 40 A 360 * Pi will come to the value of 22 /7 and the value of Kapil r will be square of 14 - square of 7 So what will we do from here, we will subtract zero from zero 4 1 4 and 4 * 9 36 * 22/7 will be square of 14, we will subtract 166 from that. How much w
ill seven become 49 then how much will we get 147 Then what will we do from here after calculating we will get 154 / 3 We will divide what is by 3 and we will get 154 so we will get 51.3 cm This is the shaded part that we have. What is its area? 5133 cm square. Okay, this is also an easy question. In this also you should know all the formulas. There are many formulas. It is a cube, it is a cuboid, it is a radius segment, it is a circle. Okay, there are many such formulas. Do you know these formu
las? It should be there and if you want this complete video on formulas also, then you can comment, I will make a video on that too, you will get the formulas of the entire book in one video. Okay, now let's see its next question. In the last question of this video, it is given to us that in what ratio the line segment connecting the points minus 3 10 and 6 -8 is divided by the points minus 1 6. Okay, now after reading this question in your mind. We should know what to find out from it. Okay, it
has been mentioned in it, in what ratio it divides, so they are our m1 and m2. We have to find the value of these two. Okay, so for this I have made a picture in front of you. So that you can understand it easily, first point we will assume q which is given to us as minus 3 10, second we will assume r which is given to us as minus 6 aa. Okay, these two points are on any line segment. What is this point? is connecting to each other which we have named p and that is our one minus k 1 6 Okay, so w
e have to find the value of m1 and m2, now we can do this question in different ways, I will show you that. Let me tell you here that the ratio here can be done by assuming m1 and m2, like I have kept the values of m and 1 here, you can also do it by assuming these values or you can also do it by assuming k and v. Okay, so here. But what is we like m1 up m2 we have to find and its value we have assumed m and 1 so here we will find the value of m, small it the value of m and put it here in fr
ont of m1 / m2 so when we from here If we do the calculation, we will get the value of m1 and m2. Okay, I will tell you that further but you should know what is the division formula, the ratio one is fine, what is the formula to find out its x coordinate. And what is the formula to find the y coordinate, okay, I will tell you both those formulas first, so to find the x coordinate, it is that Okay, this is what we have to find the coordinates of the Will come in m1 + m2 Okay, now we find the coor
dinates of point p, we get a coordinate of point p. We have given in the question and we will find one coordinate from our side and compare both the coordinates which will give us the values of m1 and m2. Well, what do we get only by comparing the value of either x or y? Values of m1 and m2 are found, okay it is not necessary to compare both, okay you can compare any one of the two, okay I will tell you further, so it is calculated here and is written here. Let us assume that the point p div
ides the line segment joining bucket minus 1 6, q minus 3 10 and r 6 minus a, as I told you, and I have given both the formulas. These are for x and for y and here the value of x1 y1 Let 's consider the point and these as x2 and y2 okay and y are our coordinates of We will keep all the values, you see them from above, I have kept all the values here, so the coordinates of my pxy here will be 6m - 3 / m + 1 and the second y coordinate will be - 8m. + 10 / m + 1 Okay, now this is our Okay, like
we will compare What is the coordinate? 6m - 3 up m psv and here we will see our one number - 1, it will go here and also I will multiply it by its minus, so here it will come 6m - 3 and here it will come minus k a. And what will I do now, I will put the terms with minus k and m on one side and the terms with numbers on one side, let's do that next, we had 6m left on this side and if we bring the minus cam here on that side, it will become plus km and On that side, ours was -1 and on this side,
our minus three was left, there we will take plus three and we will be left with 7m, and on this side, we will have two, that is, what is the value of m, 2/7, okay. The value of this m will be equal to m1 up m2 whose m up we will put this value there. Okay, now let's see further m1 up m2 will be equal to m up 1. We have calculated the value of m 2 ratio 7 up 1 this. If the forest turns and goes up, what will be the value of m1 and m2? 2 ratio 7 m1 = 2 m2 = 7 i.e. the point which is p minus 1 6 d
ivides both those points i.e. what does that line segment do in 2 ratio sa It is ok, that is, we had to find the value of m1 and m2, we have found it here, ok and in this method too, there are many abstract questions, the main ones are the formulas, ok, then you should prepare the formulas very well, only then you can get good paper. It's okay, if you don't remember the formulas then how can you give the exam? It's okay if you know the formulas then if any question comes in front of you, if you
do it from the book then formulas are the main thing. If you have the formulas then it's good. The thing is, if you do not know the formula or do not have it with you, you cannot find it even in the book, then you can comment in this video that Sir, please make a video of the formula and give it to me, okay, I will within a few days. I will make a video on the formula, okay because you will get all the formulas in one video and your questions from 11 to 20 have been completed, as I had told in t
he beginning of this video that in this part only There are going to be questions from 11 to 20, I have made you do all of them here. I am not bringing the entire paper in one video because the video will be very long due to which you will have problem in watching, so I What is it, I am dividing it into parts and bringing it. Okay, Part One has arrived. If you have not seen it yet, you will find the link in the description and on the button above, you can go from there and watch Part One. Part T
wo is this. It is about to be uploaded and part three is coming soon. Okay, and share the parts of these solution videos with your friends too. Okay, because they will also need the solution of the sample paper. Okay, so you can also share part one and part one. Also share this as much as possible with your friends, it's okay and What have I got for you, which is your science sample paper of 2024, I have already uploaded the video on its solution, if you have not seen it yet, then you will get i
ts link in the description and you will get it on the button above there. You can watch the video by going to this page and you can also share that solution video with your friends because there are many such questions which come from our sample paper, okay, you can watch all my new videos. You can know only when you have subscribed to the channel, so first of all you subscribe to the channel and most importantly press the bell icon on all right then you will be able to know that my new videos a
re coming. See you in the next video. Till then please like our videos and comment. Tell us how you liked this video, whether it was helpful for your exam or not. Okay and wait for the next part [ Music].
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Sir kya aap abhi sutron ko likh sakte hai 10 th ke