Hello everyone, today we are going to solve Cognizant previous year aptitude questions. These 25 questions are getting repeated in Cognizant examination or you will be getting similar type of questions in your examination. Hi all, my name is Prateek Srivastava, founder of Online Study For You. As you are aware Cognizant has started the hiring process and The second round of exam that is aptitude is scheduled on different dates in different different colleges which is on 17th of September, 19th of September, 24th of September, 25th of September. So it is very very important for you to solve previous year question or similar type of questions.
Please do not practice the things which does not come in your examination. Now this particular PDF which we are going to solve here will be available right here in the telegram group. So I am putting all the previous year questions in this telegram group so that you can just go there and you will be able to download that particular PDF from the telegram group. And don't forget to like the video and also subscribe to our YouTube channel. Here you can see we have already started putting cognizant previous year question.
aptitude technical cognizant latest previous year question and again this video will be also there on youtube right okay anyway so let us start solving the question so friends here top 25 questions we are going to solve right from different different topics okay so each and everything will be covered in very much detail now i request all of you first please try to solve the question by yourself and then you watch the solution question number one log 3600 is equals to right okay so log 3600 is equal to now friends can i write like this so log 36 into 100 okay see there are multiple ways to do the question even you can directly write log 60 square okay now you the properties of logarithm says so if you have log a right into b then you can write log a and plus log b okay fine now here log 36 we can write 6 square and log 100 we can write log 10 square okay now so friends if we have any you know a square or cube in your argument so that will come and sit here so this will become 2 log 6 and this will become 2 log 10 okay now so friends log 10 okay log 10 will be equal to log 10 okay will be equal to 1 and log 1 will be equal to 0 this you have to keep in mind so this will become 2 log 6 and plus 2 here now let's see if we have any options right so here we have 2 log 6 plus 2 option c becomes the correct answer for this particular problem logarithm properties is very very important that you need to understand and then only you will be able to solve it right okay so question number one solution is done your answer will be 2 log 6 right 2 log 6 plus 2 now moving towards question number two if you have any doubt please let me know and also friend this kind of questions you can do in multiple way i'm trying to tell you see when we teach you know we keep in mind that what all properties we should take so that it will help a student in future as well so the you know idea of doing this kind of problems in detail so that you understand or you learn lot of things from this 25 question anyway Now question number two. So question number two is again a question from logarithm. Logarithm is a very important topic as part of your cognizant examination.
So here we have 1 by 2 log x okay plus 1 by 2 log y plus log 2 is equals to log into x plus y okay then you have to tell out of these four which will be the correct answer right okay now friends so here we have 1 by 2 so why don't we do one thing let us multiply 2 on both side on LHS also on RHS also so we are going to multiply by 2 so it will not nothing will change basically here so if we multiply by 2 then 2 by 2 will get cancelled right see 2 and already 1 by 2 is there log x plus again 2 by 2 because we are going to multiply 2 everywhere and then here 2 into log 2 and then it will be 2 log x plus y clear okay now this is cancelled this is cancelled so log x plus log y okay plus here it will be 2 log 2 and is equals to 2 log x plus y now two properties of logarithms we need to understand here the first thing is friends so if you have log a plus log b then we can write it log a b okay so this is the first thing and then the second thing friends so if we have 2 log right x okay then so this particular one now it will go as a it will go as a power of whatever available log x square now so here log x okay plus log y and this we can write log 2 so this particular will go and sit here 2 square okay then 2 square is nothing but 4 and here also log x plus y square see this particular problem is not that much lengthy i am going step by step i am telling you everything otherwise see otherwise here only you can see if you multiply by two this gone this gone and this will become two square is four so you can directly write log four x y okay and here so if you multiply by two it will become log x plus y whole square so you will be easily able to equate and solve so basically because i need to explain you here so i am making it step by step so that complete clarity you get now so log a plus b log a b log a b and c so it will become log so 2 square is 4 so 4 x y is equals to log x plus y square now friends log log is here base is same then we can equate the argument from here so here what we can do I am not left with the space. So x plus y square is nothing but equal to 4xy. Okay. Then further I will expand it here.
So x square plus y square plus 2xy. And this will come left side. So minus 4xy is equal to 0. So x square plus y square and 2xy minus 4xy is what? Minus 2xy.
So now I can write here. x square okay so just a minute x square plus y square minus 2xy is equals to 0 which is nothing but x minus y whole square is equals to 0 so here x minus y is equals to 0 x will be equal to y so option b becomes the correct answer for this particular problem once again i am telling you please don't think that this problem is quite lengthy no it is not like that okay it is not like that my dear friends okay i wanted to tell you see as soon as you see the problem right so you can see you have to multiply by 2 so this will be x y if you put 2 here so 2 square will be 4 so this will become 4 x y and here so if you multiply by 2 it will go and sit here x plus y square clear okay then if you expand x square plus y square plus 2xy this will come this side minus 4xy is equals to 0 so x minus y whole square is equals to 0 so x will be equal to y option b will become the correct answer so just 3 to 4 line you will be able to get the answer but you need to know the logarithm properties and i took you you know through step by step so that you get the complete clarity of the problem right okay now let us move towards the question number three and one thing friends i wanted to tell you if you are understanding whatever i teach in the class please do like the video and also friends please do comment see if you guys comment no yes sir the videos are good you need more this kind of videos then see that is what motivates us to make more and more videos for you all right okay so uh there is some problem with my you know uh electricity that's what i'm not coming live as soon as that is resolved i will start coming live as well for you so please do comment don't forget now question number three here is a question from the topic profit and loss so the profit earned after selling an article for rupees 650 is same as the loss incurred after selling the article for rupees 426 find the half of the 50 percent of the cost price so friends first thing you need to understand is now suppose if you buy a item at 10 rupees item means item is pen pencil all these are item okay i know you guys are now i have stopped telling anything so and selling price is supposed to 12 rupees cost price is 10 rupees selling price is 12 rupees then you are in profit so what will be profit sir it is very clear sir why you are asking selling price minus cost price that means two rupees okay now if i tell you cost price of a of an item cost price of an item is 50 rupees right and selling price is 40 rupees sir there is a loss of 10 rupees you are buying in 50 and selling in 40 so sir there is a loss of 10 rupees so loss will be cost price minus selling price right cost price minus selling price clear okay so now here there will be a loss of 10 rupees fine no problem now they are telling the profit earned after selling an article for 650 is same as the loss incurred right so cost price i assumed as x okay now so what will be the profit so profit will be selling price minus cost price that means 650 minus x rupees is equals to right profit is equals to selling price minus cost price is equals to the loss incurred after selling the article for you 426 now the loss will be nothing but loss will be nothing but cost price minus selling price and profit will be nothing but selling price minus cost price these both are equal now 650 this is in minus bring it this side it will become plus this is x that will go that side 2x now this is 6 and 527 and 6410 so it is 2x is equals to 1076 So x will be equal to 2 5s are 10, 2 3s are 6, 5 38 rupees. Now they are asking you find the half of the 50% of the cost price. Now 50% will be what?
Sir 50% will be nothing but half of this. That means 26 times into 2 times is 52 and 2 9ja. And then they are asking again half of 50%. Half of this will be what?
So 2 13ja will be... 26 2 4 jah 8 and 2 5 jah will be 10 so 134.50 option a becomes the correct answer 13 times is 26 4 into 2 is 8.5 right okay friends see once you will get some experience now then what whatever the value you got right you could have directly divided it by 4 right or whatever the value you were getting here you could have directly see if you will divide 1 0 7 6 by 8 right so what answer you'll get 8 1 jah 8 right and then 2 7 so 8 3s are 24 and then again 3 6 so 8 4 jah 32 and 8 5s are 40 so if like you know you will have some practice then all those things is not required you could have directly solved it here itself 1 0 7 6 divided by 8 will be equal to whatever we got 134.5 you but right now you understand the complete process that how we are solving the questions one by one right so right now you don't get into the complete details okay fine so i hope this particular problem is also very much clear to you now moving towards question number four so this is a question from the topic permutation and combination friends before that i wanted to tell you so if you are struggling in aptitude reasoning right then definitely this achiever batch is going to help you a lot in coding also in verbal ability also right so because there we are teaching from zero to hero so you know if you are facing difficulty here you would not have faced if you are a student of our achiever batch right so this link will be there in the description please do enroll to it the price is just 2499 for one year but you are going to learn a lot right mock test is there mock interview is there ats based resume we are providing you right aptitude reasoning verbal ability dsa coding we are doing in c++ and java both now right so lot of benefits you are going to get in this particular achievers 2.0 5 batch so I don't need to tell this right okay but anyway the link is in description you already know now how many 5 digit numbers can be formed with the numbers 1 2 3 4 5 and 6 which are divisible by 4 if repetition is allowed total how many numbers are there sir total we have 1 2 3 4 5 6 total we have 6 digits are there right okay so with the numbers 1 2 3 4 5 and you have to make a 5 right so what you have to make so you have to make a 5 digit number so 1 2 3 4 5 and this number should be divisible by this number should be divisible by 4 my dear friends okay now so if a number is divisible by 4 so if a number is divisible by 4 if a number is divisible by 4 right if a number is divisible by 4 then the last two digit of the number then the last two digit of the number should be divisible by 4 if i ask you 1 2 3 4 5 6 7 8 9 4 3 okay and then 6 4 can you tell me if this number is divisible by 4 yes sir it is very very easy i will just catch the last two digit number i will just catch the last two digit number if the last two digit number is divisible by 4 then the whole number will be divisible by 4 right okay so now if this number is divisible by 4 then only last two digit is my worry okay see at the first place i can put all the six digit at the second place i can put all the six digit at the third place i can put all the six digit the reason we can put all the six digit right the reason we can put all the six digit because they're telling repetition is allowed so if you are putting three here three can also come here three can also come here right okay so that is the reason we are going to put this so that is the reason we are going to put this particular 666 okay now friends what are the possibilities here that we need to check it now okay now so let us see how many uh you know things comes here so last digit can be four four right four four is divisible by four Last digit can be 36. Last digit can be 32. Right. Last digit can be 12. Last digit can be 56. Last digit can be 64. Right. Okay.
And then how many? 3, 3, 6. Okay. And then again, we have to see. So what can be there? So 36, 64 done.
32 is also done. 12 is done. Then 16 will be there. okay so 1 6 and then one more number should be there right so 36 okay uh 40 46 will not be there 42 will not be there okay 56 right okay fine and then 52 13 forja okay so 13 forja 52 right so 13 forja will be what 52 right so we have total 33628 so basically here there are total eight possible combinations are there now so my total number of ways will become six into six into six into eight so six cube will be 216 and if we multiply by eight right so 16 8 job 128 so 2 8 will come in picture okay and 1 will be there so 17 1 7 2 8 1, 7, 2, 8 that means option A will become the correct answer for this particular problem right so when the questions are really good right the questions are really very very good okay now let us move towards the next problem question number 5 so you will definitely able to learn a lot when we are solving this particular problems okay fine now question number 5 question number 5 says the number of ways in which eight different books can be arranged on a self so that three particular books shall not be together okay very good so what they're telling the number of ways in which now we have eight different books so now we have eight different books one two three four five six seven and eight okay so the number of ways in which eight different books can be arranged on itself so that three particular books shall not be together now friends what i will do so first i will try to keep the three books together okay first i will try to keep three books together so three books together means so three books together means so this is b1 this is b2 and this is b3 right so three books we are keeping it together okay now so friends when it is together then we will find out what will be the probab you know the ways right okay so the first thing eight books can be arranged right eight books can be arranged in eight factorial ways okay now now what are we going to do so we are keeping three books together we are keeping three books together three books together that can be anywhere here there or anywhere okay so now what we are going to do so we are going to keep three books together okay and then what we are going to do so total minus three books together okay so what we will get when three books are not together that's all three particular books will not be together now so total is nothing but eight so here we have one two three four five six actually uh the diagram is little wrong we have put nine here so let me just remove it off okay and the brush is okay so total is nothing but total we have eight okay total we have eight okay fine so one two three four five six seven eight right so this is my three books book one book two and book three now if three are together then it will look like only one for us and what is the remaining so remaining we have five okay so this can be arranged in six factorial ways because wherever these three boxes will go no it will go together see what we have done basically here so we have put them inside a box we have put them inside a box single box so that they will be always together right so that can be done in only one way and this can be arranged in five other books can be arranged in 5 factorial so 5 plus 1 is nothing but 6 factorial now this books now these books among themselves can be arranged in 3 so 3 factorial right because see book 1 will come here book 2 book 3 then again next one is book 3 can come here book 2 can come here book 1 can come here right so that will be arranged in total 3 factorial so 8 factorial and minus 6 factorial into 3 factorial will give you the answer 8 factorial will be 40, 30, 2, 0. This you have to keep in mind. 6 factorial will be 720. And 3 factorial will be 6. So 0, 6, 2 is at 12. And 42 plus 1 is 43. So it will be basically 4, 3, 2, 0. Now 0, 0. 2 minus 2 is 0. 3 minus 3 is 0. 10 minus 4 is 6. And this will become 3. 36,000.
36,000 will become the correct answer. I hope. You got to know what I wanted to explain here.
So the three books are together. So keep all the books together inside the box. That will be nothing but one.
Remaining will be five. So five factorial plus one. Five plus one is nothing but six factorial. And these boxes among themselves will get arranged in three factorial. Right.
So first you calculate eight books will get arranged in eight factorial ways. And three books together is this. Subtract it. The books will never be together.
Right. Okay. fine now question number six question number six is a very good question right see why i am telling you a very good question because you need to understand how you can solve easily with the trick okay so i will you know solve it by both the method i will tell you the basic method and i will then i will tell you the tricks okay both i will tell you here so what they are telling a reduction of 20 percent in the price of a mangoes enables a person to purchase 12 more for rupees 15 what was the price of 16 mangoes before reduction of the price now friends so suppose the price earlier was suppose the price earlier was p okay now so let us try to frame the equation so if you want to frame the equation first you need to understand how easily you can put it right okay if i tell you that you have 15 rupees if i tell you that you have 15 rupees and five rupees one mango you can get it okay or i like this you i will tell you so if you have If you have 60 rupees. Okay.
If you have 60 rupees and 5 rupees per mangoes are there. Then how many mangoes you will get? So you will get 12 mangoes. Clear. Okay.
So what they are telling. So a reduction. Okay. Now so you have 15 rupees and earlier the price was P. So how many mangoes you are getting?
That we don't know because the value of P is not known. Now they are telling. Okay.
Now they are telling the price is reduced. So suppose. earlier you had 60 rupees 5 rupees was one mango so how many mangoes you are getting 12. now the price is reduced the price is reduced the price became 3 rupees per mango then how many mangoes you will get 20. so how many mangoes you are getting more now sir it is 8. if you understand this then this equation will become very very easy friends see in aptitude no always you have to learn with very much simple values very much basic values then you will be able to solve that is the rule of aptitude so you had earlier 60 rupees 5 rupees per mango you were getting 12 mangoes earlier now the price is reduced it became 3 rupees okay 60 rupees you have so you will be getting 20 mangoes now that that means how many mangoes more you are getting sir i am getting 8 mangoes more now okay so earlier the price was p okay Now the price is reduced by 20%. Okay.
Price is reduced by 20%. That means you have to pay 80% of this value. That means you have to pay 80% of this price.
Okay. And how many mangoes you are getting now? More. Sir, I am getting 12 mangoes more.
Same thing. Whatever I explained you here now, here you are able to understand because the values I have taken is a number. So it is very, very easy for you. now when it when it p and q comes and then only the problem starts happening so this p and q we need to so this p and q we need to understand it right so this p and q we need to understand right okay fine so uh i think it is going opposite direction no so why this brush has become okay so we'll see later okay now so here this we have to solve and that will you give you some value of p so 15 you can take common you can send it that side so anyway now this is done this is two four ja and two fives are this 15 i will send that side so 1 by 4 p 5 will go here okay minus 1 by p 15 i am sending it this side 12 by 15 so this will be nothing but uh three four ja and three five ja okay fine now 4 p so take lcm okay and this is 5 minus p 4 times 4 will be equal to 4 by 5 so 1 by 4 p is equals to 4 by 5 okay so here 16 p will be equal to 5 and p will be equal to 5 by 16 so 5 by 16 so definitely i am going to use the calculator here see you do not have to use i am going to tell you the shortcut methods to do it right but right now i am going with the process right now i am going with the process so the value of p what we have got is 0.3125 okay 0.3125 i will tell you the shortcut method then only you will understand so this kind of complicated things you have to avoid and you have to learn that now they're asking what was the price of 16 mangoes before reduction of the price so before reduction was the price was this so you just have to to multiply with this 16 into point okay see even you do not have to right so even you do not have to divide this right see you have you do not have to divide this after dividing what you will get this value is not required right this value is not required that is nothing but 5 by 16 16 and 16 cancelled 5 is the correct answer so option b will become the correct answer for this particular problem now i will tell you the shortcut methods which i generally teach right in all my videos so a reduction of 20 percent 20 percent is nothing but 20 by 100 20 by 100 is nothing but 1 by 5 right that means earlier the price was 5 rupees and now there is a reduction of 1 rupees it will become 4 right it will become 4 okay now friends they are telling a reduction of 20 percent in the price of mangoes enables a person to purchase 12 more for rupees 15 that means the total expenditure of 15 rupees is not changing so this is price so my expenditure is not changing total expenditure is not changing so this is price and this is consumption right okay so because they are clearly telling that 15 rupees is not changing so price is reduced right so you will be increasing your consumption because you have to spend rupees 15 so that whatever you are going to spend that will be fixed only now so friends this is nothing but your this is nothing but your old value and this is nothing but your and this is nothing but your current value right okay so four to five right so now your consumption is nothing but four to 5 okay fine they are telling here if you see the difference i will use another pen so here if you see the difference the difference is nothing but 1 but actual is nothing but 12 so 1 is equals to 12 so earlier so 4 4 into 12 will be what 48 so earlier you were getting 48 mangoes and now we are getting how many mangoes 60 mangoes right see the difference is 1 but they are telling no the difference is 12 so one unit is because we have assumed the value here so one unit is equal to 12 4 unit will be 48 5 unit will be 60 right okay fine so they are telling you tell me what is the price of 16 mangoes before so earlier in 15 rupees you were getting 48 mangoes and now you are getting 60 mangoes so if you want to know the price of 16 mangoes earlier so divide it by 3 and divide it by 3 so 5 rupees and the you were getting earlier 16 mangoes this is what you have done after doing this equations both i explained you right so you have to know both because till then you don't understand the basic okay then you will not be even able to understand the sort tricks as well and with one particular problem with one particular problem you might not understand right all those things okay with one particular problem you might not understand the complete thing So practice is required and that is the only reason I told you, you join this achievers 2.5 batch so that you will have lot of practice and when you see this kind of questions in any of the examination, it will become, you know, it will be like, you know, you just see and tick, that's all, right, just see and tick. Now, so if I go back here, so, you know, if I go back here and if you know the concept, what you will do, sir, 20% is nothing but 1 by 5, sir.
20% is nothing but 1 by 5 the price is reducing that means from 5 it is becoming 4 sir consumption remains same it will become 4 to it will become 4 to 5 right okay 4 to 5 so the difference is 1 actual difference is sir 12 so this is 48 and this is sir 60 sir earlier in 15 rupees they were getting 48 sir then now if they want to know the 16 mango price sir in 5 rupees they will be getting 16 mango and how much time you were taking how much time you are taking you are not even taking 30 seconds but when i solved i took more than five minutes many of you are irritated that sir is taking so long sir is confusing us sir is making us confused no my intention was to tell you the basic concept how it works the trick how it works so that you get the complete knowledge okay so that tomorrow if you get a similar kind of question you will be able to solve by yourself and you don't need me okay now question number seven so question number seven now okay fine so this video is going to be a quite long 25 questions it might be for you know let's say like more than one hour or one and a half hour video so a two days work is equals to b three days work by a two days work is equals to b three days work okay that means can i get a by b ratio see this is nothing but efficiency ratio this is nothing but efficiency ratio that means a by b efficiency ratio is 3 is to 2 so this is nothing but efficiency ratio efficiency ratio okay now friends one formula i have told you so work will be equal to work will be equal to efficiency in two days okay efficiency in two days efficiency into time sir how did you get the formula whatever you want you do and you think that Students will come and able to understand right I will tell you for everything I always see math works on logic don't you don't have to remember anything suppose you can clean 10 chairs in a day okay and if I give you five days how many chairs you will clean sir 50 chairs cleaning 50 chairs is what is a work right so your efficiency is 10 chairs per day you are getting five days and you are cleaning 50 chairs So days into efficiency will be equal to work. Okay. Now in this case they are telling the same work A is able to do in two days and the same work B is able to do in. three days right okay so work is what same when the work is same my dear friends then efficiency will be equal to one by days okay it will be inversely proportional that means if you are more efficient you will take less time if you are less efficient you are not working at all then you will take more days to come cover the complete the work so efficiency ratio then what will be time ratio so time ratio will become two is to three this is nothing but my time ratio very good Now what they are telling? They are telling if A can complete the work in 8 days.
That means 4 times. So in how many days B will complete? Sir 4 times because ratio has to be equal.
If you are multiplying with a number by 4, second number also you need to multiply by 4. If you are dividing a number by 5, second number also you need to divide by 5. Ratio should be always equal. Otherwise your concept is wrong. Otherwise whatever you are doing is wrong.
So 12 days will be the correct answer. So if A can complete the work in 8 days, then to complete the work, B will be taking 12 days. Okay.
So I hope that is clear. Now, question number 8. Arraya, question number 8 is number series problem. Number series problem will be always easy.
So you have 24, you have 48, you have 51, you have 204 and then you have 209 and then you have what? Okay. So.
This looks like into 2 and then 48 plus 3 will be 51. 51 into 4 will be 204. 204 plus 5 will be 209. So it is plus 2 sorry into 2 plus 3 into 4 plus 5. Then it will be into 6 right. So 2, 3, 4, 5, 6. The only change is symbol. Now here so 209 into 6. It is very simple. so 6 9s are 54 and 6 into 2 is 12. 1254 will be the correct answer if you have any option option c becomes the correct answer for this particular problem and i am assuming that you are solving this problem by yourself first and then you are watching the solution now question number 9 is a good question of number series can you please try it out anyway i will solve don't worry about it okay fine so now let me solve it here so we have 1 okay so we have 1 we have 6 we have 25 we have 76 we have what and we have 154 right okay so friends here basically 1 into 5 is 5 plus 1 is 6. 6 into 4 is 24 plus 1 25. Then 25 into 3 plus 1 so 76. Then 76 into 2 plus 1 152 plus 1 will be 153. 153 into 1 plus 1 will be 154. That means the logic is into 5 plus 1 then 1 less into 4 plus 1 into 3 plus 1 into 2 plus 1 into 1 plus 1 sir you got the logic after you saw the question okay or you might have solved it earlier that might be your answer see uh the first thing whatever you said is true so i got the logic as soon as i saw the question the reason is friends i have practiced a lot and see who is a teacher if you practice a lot of question you becomes a teacher right teacher is nothing but he has more experience in doing something regularly that's all so anybody can be the expert but the only thing is you need to you need to solve the more questions so that's the reason here we have put lot of questions for your practice and this is going to definitely help you a lot so join this as soon as possible so that so that what happens you will be you will become perfect you will be also able to get the logic as soon as you will see the question Now next is friends next question is from the topic okay let's move okay from the topic pipe and cisterns.
So pipe A can fill a tank in 20 hours. So pipe A can fill a tank in 20 hours but because of leakage okay because of leakage in the tank the tank gets filled in 28 hours. Now so friends there is a pipe is there okay. So here pipe is there.
so this pipe A right can fill the tank in 20 hours okay that I have mentioned it here now they're telling but there is a leak but there is a leak okay but there is a leak okay and what it is doing is so the water is coming out from that so definitely if there is a leak then the tank will take time to get filled right okay so now both pipe a is pipe a is filling the water and leak is removing the water in that case 28 hours in that case 28 hours it is taking right okay so friends when you will attend my classes i will tell you either the questions of time and work or the questions of pipe and systems can be done with lcm technique take the lcm sir what is the lcm of 20 and 28 see it is 140 if you have practiced a lot but if you don't know right then what you can do is so you can take the lcm no problem so two fives are and two sevens are so five into two is 10 7 into 2 is 14 right so that becomes your total capacity right so that becomes your total capacity now one for by 20 that will give you the efficiency that means pipe a can fill 7 liter of water in one hour and if both are working together then 140 by 28 they can fill 5 liter of water in one hour 2 liter water in one hour basically 2 liter of water in one hour basically is getting removed because of this leak so friends a is nothing but 7 a efficiency is 7 and a plus l and a plus l efficiency is 5 so l efficiency will become what so a is 7 right so 5 minus 7 it will be minus 2 right but we don't take minus 2 see minus 2 shows that this is a leak this is not filling the water but instead it is removing the water so a efficiency is 7 and l efficiency is 2 okay that is the reason it is giving 5 minus sign we have to ignore minus sign is just the indication that this is a leak pipe and it is taking out the water from it right okay now so what they are telling in how many hours leakage alone can empty the completely filled tank now a completely filled the tank okay fine so total capacity is what 140 liter and we know because of leak every hour every hour two liter is getting removed so total capacity is 140 you and leak is removing two liters of water in one hour so leak will take 70 hours to completely clean or completely empty the tank so 70 hours option a will become the correct answer right friends see understanding the question understanding the concept is very very important then only you will be able to solve the question okay fine now question number 11 question number 11 says consider the sequence of five consecutive integers if the average of first three is t then the average of all five integers so my dear friends this is a question from the topic average okay so this is the question from the topic average there should not be any kind of you know confusion here now the first three integers average is t so the first three integers i am taking a minus one a you a plus one sir what is your problem sir so five consecutive integers five can see what i did is now i have this five consecutive integers like this sir why sir why did not you start with a a plus one a plus two a plus three and a plus four sir in this case we will get different answer no my dear friends see the knife right falls on apple and apple falls on knife what will happen apple will only get cut right okay so i see you should have taken only the five consecutive integers it can be this or it can be this anything you will be always getting the same answer right that i can guarantee you okay now so then sir why did you take negative you know negative whenever we see it creates confusion negative why did i take because the first three integers they are telling the first three integers they are telling their average is nothing but their average is nothing but right so their average is nothing but equal to t so if i take like this then it will become very very easy to solve the problem i will not be getting right so i will not be getting a plus a plus a so 3 a plus 3 so it will become little easy but answer you will be getting in any case my dear friends okay now Now they are telling then tell me the average of all five integers. No problem. A is equal to t now.
So t and here you will put right. okay so for 3 already we know the sum for 3 we have right 3 is nothing but just a minute so what we can do here a minus 1 so again you can put t minus 1 plus t plus t plus 1 and t plus 2 and plus t plus 3 right okay divided by 5 will give you the average okay so see 1 and 1 is cancelled so 5t plus 5 divided by 5 so it will be nothing but t plus 1 so t plus 1 will be the average option b 5 by 2 common t plus 1 will become the answer right see instead of writing all this instead of writing all this you could have also written directly 3t because i know the sum is nothing but 3a and a is equals to t so 3t plus 4t plus 5t plus 5 however you think it is easy however you can do it you start with that slowly slowly you will learn you cannot become perfect in one or two days of practice it needs like 15 days or one month of the practice to become better in any of the subject either it is aptitude it is reasoning it is variability it is coding it is interview everywhere you need practice to become perfect okay i hope this is clear and now let us move towards the question number 12. question number 12 is a question from the topic ratio and proportion okay so question number 12 is a question from the topic ratio and proportion right ratio and proportion okay fine now so the income of A is the income of A is 150 percent of the 150 percent of B and the income of C is 120 percent of income of A many people will take x here many people will take x here friends see two things which again you need to understand so x in mathematics and x in real life it will always create problem now if your x will come to your life what will happen already it was you know and now again it will okay so you know see that's the reason present became you know x and x in mathematics you know the calculation will be complicated dude so i understand see if you take x then gone what i am going to do now i am going to assume b is equals to 100 okay then a is 150 percent of b so 150 percent is what 100 into 150 by 100 it is the same value it is 150 then c is 120 percent of a so a is nothing but 150 and c is 120 percent so into 120 by 100 so cancelled cancelled 15 into 12 is 180 the value of c is nothing but 180 very easily we have calculated see sir why you are now see one more question comes sir why the i mean why are you assuming why you are assuming 100 right why not other value right so what is giving you idea to assume 100 so friends basically here we need to calculate the ratio right see the income of a is this income of d is this income of d is this so you will understand so basically here we need to calculate the ratio so when you have to calculate the ratio and when you have to calculate percentage in that case you do not have to think much okay so you can assume any value whatever you want sir one one lakh one crores one after that i don't know okay so now here a is to b is to c so what will be the ratio so it will be 150 is to 100 is to 180 101010 cancelled okay so after that it will not be cancelled okay now now they are telling so if the income of a b c together is 86 000 so a is nothing but 15 so if you will take out from if you will make a value out of it 15x b is 10x and c is 18x and total value is nothing but 86,000 so this is nothing but 18 plus 10 is 28 plus 5 33 plus 4 43 x is equal to 86,000 so 43 into 2 so x will be nothing but 2000 now what they're asking my dear friends so what is c income so bhaiya c income is nothing but into 2000 right oh sorry not here so ratio it is 18 unit so it is 2000 so 18 into 2 will be nothing but 36000 That's all simple. Option D will become the correct answer for this particular problem.
Right. So what we are doing is we are reading the problem, trying to understand how we can do it easily without involving X in the problem. And then we are solving it in a very easier way. Now, let us move towards the problem number 13. Right.
So another 12 problems, another 13 problems are pending and I am filling. hungry now okay it's okay that's okay so let us see what is the square root of okay so what is the square root of 8 plus 2 root 15 now as soon as you see the problem hands up as soon as you see the problem hands up no that doesn't it doesn't work like that see write the question and then try to think what we can do here okay see you have to find out a square root so if i ask you 16 find out the square root what you do see you somehow try to make it a square of some number right and then you say sir 4 is the answer when you can do this why not this because you have not practiced that kind of problem there is no other reason i am telling you there is no other reason because when the exams will come that time you guys will come sir cognizant video sir cognizant video cognizant video right this is how you will get placed no this will not help you to get placed you have to prepare beforehand see now everybody is running behind cognizant video cognizant video cognizant video dude this is how you will prepare no now so what we will do 8 i can write 5 plus 3 and plus 2 root 15 okay now this 5 can i write like a square root of 5 square yes i can very well write because my intention is to bring a square inside this and 2 this is square root of 15 how can you write a square root of 5 into a square root of 3 that's all now this is a square plus b square plus 2ab so a square root of 5 plus a square root of 3 a square this is under root now if we'll take it out square and this will get cancelled a square root of 5 plus a square root of 3 will become your answer right so option a will become the correct answer now also friends i am telling you if you really want to crack placement examination okay then what you do is you get this achiever batch start your preparation from today lot of content has been already added and daily we are going and adding some and the other things right this is how you will get placed okay there is no other shortcut and friends one more thing i am telling you when we are doing youtube videos for free we just need a small appreciation from your side that too if you feel the video is good don't comment if the video you don't like okay so if you don't like the video please don't comment okay and if there is any kind of improvement you let me know i will do it but when we are putting a lot of effort see behind one video it takes around you know when the video is quite lengthy then it takes around seven to eight hours behind one video so i want you to appreciate the effort which we are putting just by commenting yes the video is good we want more such video and trust me when I see your comment that you guys are liking the video and you want more videos we are I mean personally I am working very hard to bring the videos for you before your examination and I will make you prepare before your exam fine okay this is done problem number 13 is done now moving towards problem number 14 problem number 14 is a question from sorts and indices so one by this one by this one by this you have to tell what is the answer so friends 1 by a right so sorts and indices you can write like this 1 by a will be equal to a to the power minus 1 or if you have a to the power minus 1 you can write 1 by a okay then now now this you see so i said if it is 1 by a you can write a to the power minus 1 now this a to the power minus 1 i will bring it here so if you have a to the power minus 1 then you can write it a i did a cross multiplication right so Swarts and indices you should have a very good control. So if we have 1 by this then when it will go up we can write it 125 to the power 2 by 3. So the minus sign will get over. So if you have 1 divided by a to the power minus 1 you can directly write a to the power 1 basically.
If you have a to the power minus 2 you can write a square. Clear? Okay, and then plus this is 625 again if it will go up minus sign will get removed this you will get power Then you have 729 if it will go up minus sign will be removed. It will be 3 by 6 clear Okay.
Now once you do this after that friends, it is very very important for you to think see you cannot blindly solve Questions of aptitude. Okay. I don't know about variability and coding but aptitude and reasoning no you cannot solve it blindly you need to think see here we have three then this you have to bring in cube of three i mean sorry not cube of three power of three here you have four then this you need to bring in power of four here you have six then this you need to bring in power of six that's all you will get answer so this is nothing but five cube two by three and then 625 is nothing but 25 square 25 square is 5 to the power 4 so 5 to the power 4 to the power 3 by 4 and plus this is 9 cube 9 cube is nothing but 3 to the power 6 it is 3 by 6 okay now friends if we have a to the power x and to the power y so the rule of sorts and indices says it will become a to the power x into i the power will get multiplied so here 5 to the power 3 into 2 by 3 here 5 to the power 4 into 3 by 4 and here 3 to the power 6 into 3 by 6 okay so this 3 and 3 cancelled 4 and 4 cancelled 6 and 6 cancelled 5 square 25 5 cube 125 this total is 150 and 3 cube is 27 so 150 plus 27 will be 177 so option b is the correct answer okay see if you have any doubt you can let me know that yes sir here we have doubt or there we have doubt in the comment section so i at least i reply wherever you know you are stuck or wherever you say sir this is wrong so see sometimes what happens when i'm solving no some mistake we do right see because uh it's like continuous you have to speak so long and it will sometimes no it will be very much irritating actually what happens the light will go off i am recording in between right so i lose the concentration okay so that is happening regularly so i have to buy inverter and for that only i am arranging the money so once the money is arranged then i will buy an inverter and uh you know that time the live classes will be also there and the classes will be smooth right now lot of distractions will be there right so that we are working on it okay fine so question number 15 see i think you are my family member and that's the reason we share everything with you all so that you understand okay so we what you know things we are going through anyway Now this is a very good question here.
So when I saw this question right so even I took some time to think like how we can deal with this problem. Okay and let us see 7 years later from now A will be as old as B was 4 years ago. C was born 2 years ago.
The average age of A, B and C 10 years later will be 33 years. What is the present age of A? Now, if you want to solve this question easily, no, then what you do, you make a table here.
Okay. So you make a table here and in that particular table, right? So here you write present age. Okay.
Present age. Okay. And then if you'll see, they are talking about seven years later, then after seven years.
Okay. And then again if you will try to see they are telling the average age of ABC 10 years later. So here it will be 10 years right.
Okay. And then they are telling B was 4 years ago. So 4 years ago. And here you put A, B and C. Now this will make your problem very very simple.
Now let's see. So what they are telling 7 years later. Okay.
So A present age I am assuming as K. 7 years later from now A will be as old as B 4 years ago. So A present age is K. After 7 years it will be K plus 7. After 10 years it will be K plus 10. So what they are telling whatever age of A.
So A age after 7 years is equals to B age 4 years ago. four years ago so A age after 7 years will be K plus 7. Then B age 4 years ago will be also K plus 7. Clear? This if you understand is done.
Present age, that means after 4 years it will be K plus 11. After 7 years it will be K plus 18. And after 10 years, that means after another 3 years it will be K plus 21. That's all. See, present age K plus 11. After 7 years it will be K plus 18. After 10 years it will be K plus 21. right and then they are telling c was born two years ago c was born two years ago so what is the present age of c today so the present age of c is nothing but a kid only two years after seven years it will be nine after 10 years it will be 12 that's all once this table is done 90 percent of your problem is solved now the average age of a b c 10 years later 10 years later is this so the average age of ABC so a is nothing but K plus 10 B is nothing but K plus 21 C is nothing but 12 average will be total divided by number and average given here is 33 years old now 2 K plus 2 K plus so 2 plus 1 3 and 2 1 3 plus 1 4 is equals to 33 so 2 K is 33 okay divided by 3 is here I'm sorry 33 by 3 is equals to 33 so 2k plus 43 is equals to 33 into 3 is 99 so 2k will be equal to 9 minus 3 is 6 and 9 minus 4 is 5 and k will be equal to 28 that means the this value we have got 28 what they are asking what is the present age of a that is what we have calculated that's all done 28 years will be the correct answer but this was a good problem that is what i will say see here you are able to you know many things you are learning in a single problem that friends you have to keep in mind so i am not teaching you one problem i have taken the problem in such a way that you understand average you understand this kind of things like after five years after four years before three years before after four years all those things you understand okay so you this particular video is going to be one of the wonderful videos till now whatever i have done okay next next friends three children took part in racing competition in their school with the respective probability to reach the finishing point being 1 by 3 1 by 5 and 1 by 4 so child 1 will reach to the finishing point the probability is 1 by 3 you Child 2 will reach the finishing point 1 by 5 and child 3 will reach the finishing point is 1 by 4 respectively. What is the probability that at least one of them will finish the race? Okay. Now, so friends, this kind of question, it is very simple.
So the probability of the probability of at least right one will finish the race. One will finish the race. Okay.
See at least means either one person or both or all three will finish the race. Will be equal to 1 minus none finish the race. 1 minus none finish the race.
1 minus none finish the race. Now so friends child 1 will finish the race is 1 by 3. So child 1 will not finish the race. Subtract from 1. Because the total probability will be equal to 1. Because the total probability will be equal to 1. Then. Child 2, 1 by 5, it will not finish the race, 1 minus 1 by 5. Child 3, it will not finish the race, 1 minus 1 by 4. Because the total probability is 100%, 100% is equals to 1. Now 1 minus, so this will become 2 by 3. This will become, right, 4 by 5 and this will become 3 by 4. Now 3, 3 cancelled, 4, 4 cancelled.
So 1 minus 2 by 5 will be nothing but equal to 3 by 5. so is there any option 3 by 5 yes that will become your answer option b becomes the correct answer for the problem number 16. another 9 problem we have to solve question number 17 is a question from the topic probability question number uh your uh the previous one 16 was also from the topic probability so there are six green ball there are six green ball okay And then 5 red ball. 5 red ball. and three white ball white how will you draw one so white we can't draw so white i will take you know some this color so three white ball okay in a bag so in a bag this many balls are there now what they're telling if three balls are drawn randomly what is the probability that no ball is green so the formula for probability will be equal to n e divided by n s n e divided by n s that means probability will be equal to any by n s NS is total outcomes. NS is total outcome and NE will be favorable outcomes. But in your favor what you want favorable outcomes.
Now so total is what? 6 plus 5, 11 plus 3, 14. Total is 14. Randomly you are choosing 3 ball. Now that ball should not be red. None of the ball is red. If you don't want red ball, don't take from red.
No. If you don't want to eat non-veg don't go inside the non-veg hotel no simple right so if you don't want red ball then don't take from red you take from green and white three balls problem is solved now 11 c 3 so 11 c 3 the formula you might be knowing ncr will be equal to n factorial divided by r factorial into n minus r factorial right okay so 11 factorial 11 into 10 into 9 okay into 8 factorial okay i am stopping here 8 factorial then 3 factorial into 11 minus 3 is 8 factorial okay 8 factorial 8 factorial cancel then 14 into 13 into 12 into 11 factorial i am using the formula divided by 3 factorial into 11 factorial 11 11 cancelled then this 3 and this 3 cancelled now you have this particular one which we have to solve right so let me take another pen so 11 x 10 x 9 divided by 14 x 639 okay so I have done one small mistake here so 6 plus 3 will be 9 I have put here 11 so we will just remove it off here so 9C3 okay 9C3 means so this will become 9 this will become this will become 8 this will become okay so this complete part i will remove so this will become 9 this will become 8 and this will become 7 and 6 factorial and then it will be here so 3 factorial into 6 factorial right okay so let me remove this so there is no problem at all okay so 11 and 11 cancel 6 6 cancel and then this 3 and this 3 will get cancelled right so now we have 9 x 8 x 7 and divided by 14 x 13 x 12 so 7 twos are and 2 fours are okay and then 4 threes are and then 3 threes are anyway you have 13 in denominator so check the option where 13 is there so two options are there now 3 by 13 option c will become the correct answer for the particular question number 17. there is a small mistake so see you don't take from rate then what is remaining 6 plus 3 is 9 somehow i had taken 6 plus 5 is 11 that i have already corrected it so please watch complete and then comment otherwise many will tell sir 6 plus 3 is 9 you have taken as 11 okay anyway now question number next so this is a very good question wonderful question i will say so if you think it is not wonderful please solve by yourself and then you watch the solution okay fine so the tremors of earthquake were felt at the interval of 15 seconds so every 15 second the tremors of earthquake was felt the first tremor was felt at 8 59 57 and then the next was felt at and the last tremor sorry the last tremor was felt at this how many times where the tremors failed okay now so we have 10 45 12 and then 8 59 and then 57 but can we subtract this here we have 12 this is lesser than this here we have 45 lesser than this so what we will do see this is hours this is minute and this is your second now what i will do i will send one hour from here to here so this i can write nine hours okay so one hour when i will send it here so 45 minute in one hour 60 second so now this will become total 105 minute okay and this will become 12 and this will become 8 59 and this will become 57 again which we could see here we have 12 right so 12 again lesser than 57 so what i will do i will send one minute from here so in one minute how many seconds will be there 60 second so 60 second will come here 60 plus 12 will be 72 and then this is 8 59 and then this is 57 now just subtract 12 minus 7 is 5 6 minus 5 is 1 14 minus 9 is 5 9 minus 5 is 4 right and okay 9 5 14 9 plus 1 10 and this will be nothing but 1 right okay now this right so we have to tell how many tremors were felt and every 15 minutes the tremors were felt so what we will do so we we will be dividing this by 15 but this is now in our minute and second so in one hour will be 3600 seconds i am converting everything in seconds and then in 45 minute in 45 minutes how many seconds will be there so in one minute 60 seconds so 60 and plus 15 here so okay now so 3600 plus this will be six fives are 30 2700 and plus 15 now here 15 7 6 13 and 5 plus 1 6 and then we are going to divide it by 15 so 15 4 ja 60 and then 15 2 ja 30 and then 15 1 ja 15 right okay so the tremors of the earthquake were felt at the interval of 15 second the first tremor were felt at 8 59 57 right and the last tremor were felt at 10 45 12. how many tremors were felt so here the answer will become 421 and that will become the correct answer here okay so question number 19 says okay two-third of a consignment was sold at a profit of six percent while the rest at the loss of three percent okay so means two-third of a consignment was sold at a profit of six percent and the remaining and the remaining so six percent and the remaining was at a loss of was at a loss of was at a loss of three percent okay fine Then how to deal with this kind of problem? So again what you will do?
Sir x and x. Sir x and x, x and x will always, right? So x and x will always create problem.
In real life, x will create problem. In mathematics, this particular x will create problem. So what we will do? Friends, I will take a value which is, you know, divisible by 2 by 3 and 1 by 3, okay? So what I will do?
I will take 30 okay 30 now 2 third of 30 so 2 third of 30 is nothing but so why did you assume 30 you are free to assume any value there is no problem at all any value we can assume but if you'll assume a value which is divisible by 2 by 3 and 1 by 3 then it will be easy for you to calculate so 2 third of 30 will be nothing but 20 now 20 you are selling at 6 percent profit okay 6% profit means what so if you calculate 6% of 20 see 60% of 20 will be 12 so 6% will be 1.2 so this you will be selling at 21.2 right okay then 1 by 3 so 1 by 3 is nothing but 10 so this you are selling at 3% loss so 3% of 30 will be 9 but 3 sorry 30% of 30 will be 9 so 3% will be 0.9 so here loss will be 0.9 so here okay see 10 right so 30% of 3 will be what 30% of 10 will be what so 10 30% will be what so 30% will be nothing but 30% will be nothing but it will be 3 so 3% will be nothing but 0.3 so this is a loss so subtract 10 minus 0.3 it will be nothing but 9.7 okay and here what we have done 6% is nothing but 1.2 so we have added in 20 this is a profit so 1.2 21.2 so you had actually 30 rupees okay and when you sold and when you sold so 21.2 and plus 9.7 so basically you have a profit of 30 and 729 so when you had 30 rupees you got a profit of 0.9 okay so they are telling if there was a overall profit of 1080 so if there is overall profit of 1080 zero then what was the price so calculate the number of time so it is nothing but 12 into 9 is 108 so it will be 12 000 here also 12 000 so that means 12 000 into 30 so here it is 1200 right so 1200 into 0.9 so 1200 into 0.9 so this will uh if you remove it will come as 10 so it will be one zero eight zero so here also it will come as twelve hundred so 1200 into 30 will be nothing but 36 000 right so what we did is we assumed a value which is divisible by 2 by 3 and 1 by 3 you can assume 30 you can assume 60 you can assume 90 you can assume 150 120 300 right 300 will be also divisible by both right so you could have also assumed 300 right so then also it will come 200 here and it will come 100 here but in any case you will be going to get the same answer right so don't play with x and x otherwise it will always create a problem when you are going to solve the question it will become very much complicated now moving towards question number 20 question number 20 is a question from the topic mensuration okay so find the cost of carpeting a room so there is a room is there which is 30 meter long okay and 9 meter broad so it is very very clear that it is a rectangular room right rectangular room so that's the reason right that's the reason the sides are not equal so the find the cost of carpeting a room 30 meter long and 90 meter broad so what will be the area of this room sir area of this room will become length into breadth so 13 into 9 100 170 meter square now they are telling uh okay so find the cost of carpeting a room 13 meter long and 9 meter broad with a carpet of 75 centimeter so this is little tricky so carpet length is 75 centimeter but your area is in meter square so this you need to convert into meter so what you do you divide it by 100 right so it will be nothing but 3 by 4 meter right it will be nothing but 3 by 4 meter see 100 centimeter is equals to 1 meter So 1 centimeter will be equal to 1 by 100 meter. So 75 centimeter. So 75 centimeter will be equal to here it will be you know 75 by 100 meter which we have done it directly here.
Now so total area is 117 okay and the width of the carpet is 3 by 4 meter square and per meter the cost is 12.40 that's all you will be able to get the answer so this 4 will go up 117 into 4 into 12.4 and this 3 will be down 3 will divide this by 3 3 is a 9 and 3 9 27 3 3 is a 9 3 9 27 okay and then write 3 3 is a 9 and then now we have to multiply so 4 9 36 and 156 into 124 so 4 6 0 24 and 60 plus 2 62 2 6 0 12 31 and 156 so it is 4 4 13 9 1 so 193 4.4 because there is a decimal so my answer will become 193 4.4 because there is a decimal so option a will become the correct answer for the question number 20 right so fine still we have another five question to solve okay okay great now we will be moving towards the next problem so next problem is question number 21 question number 21 is find the least number which when divided by 5, 6, 7 and 8 leaves a remainder of 3 but when divided by 9 leaves no remainder. Okay, fine. so friends there is a number is there okay so there is a number is there when we divide by 5 6 7 or 8 right so it is giving a remainder of 3 but the same number if you divide by 9 it is not giving any remainder okay it is not giving any remainder that means it is completely divisible now so you find out which number is there okay so you find out which number is there right so when you will divide by 9 you will not get any remainder that means it is completely divisible by 9 so if a number is divisible by if a number is divisible by 9 then sum of numbers then sum of number should be also divisible by 9. so first option 6 plus 1 is 7 7 plus 3 is 10 and 10 plus 8 is 18 sum of number is 18 then 2 plus 3 is 2 plus 3 is 5 6 and 2 8 4 3 7 2 9 1 10 and 9 7 16 this is 24 so there is only one number which is divisible by completely divisible by 9 because the sum is also divisible by 9 so option a is a correct answer right okay anyway so this is one way we could have done already we have got the answer and now suppose if this line would have would not have been given then how we would have solved it so find the list number which when divided by 5 6 7 and 8 leaves the remainder of 3 but when divided by 9 leaves no remainder so friends if you divide 7 by 2 what will be the remainder so 2 3 is a 6 and 1 will be remainder if you don't want any remainder then just subtract 1 from 7 right so the number which you will get will be completely divisible by 6 so they are telling the numbers when we divide by 5 6 7 and 8 leaves a remainder of 3 now what i will do so if i will subtract 3 from it if i will subtract 3 from the options right if i will subtract 3 from the options that means whatever the answer will be there right whatever the answer will be there this will be nothing but so this will be nothing but divisible by this will be nothing but it will be divisible by 5 6 7 and 8 okay now the next process says that take the LCM of this and check which number it is divisible right okay but friends also you can see 5 cannot divide this 5 cannot divide this right okay then 6 cannot divide this because 6 right 6 12 is 72 6 12 6 13 is 78 so 6 cannot divide this so definitely this will be the answer okay but anyway if we'll take LCM then 30 30 into 7 into 8 so 30 into 7 is 210 okay so LCM if we'll take so 2 5s are 2 3s are 2 7s are 2 4s are this will come okay so 2 5s are 10 10 into 4 is 40 40 into 3 is 120 840 now you could see which number is divisible by 840 so definitely this will be because there is 0 at the end so this will be the correct answer see i am telling you multiple method to solve one question right so here i told you three methods right so you could have checked with five and six you could have checked by you know nine itself so you have already given the answer but additionally i am telling you so many things so that when next problem you will solve you will keep these concepts in the mind next four more problems so the greatest number which can divide this leaving the same remainder 12 in each case now friends so if you don't want remainder okay so the greatest number which can divide this uh okay and this leaving the same remainder so if you don't want any remainder what you can do so you can subtract this right so you can subtract 12 from all the numbers right and then if you divide by the greatest number you will not get any remainder right I explained you see if you have 4 and if you have 18 if you will divide 2 will be remainder if you don't want any remainder then from the number you subtract the remainder so 16 will be completely divisible by 4 same concept you have to use everywhere 6-2 is 4 5-1 is 4 13 then 8-2 is 6 6-1 is 5 18 minus 1 is 17 and 4 minus 2 is 2 6 minus 1 is 5 and 2 2 7 5 2 right okay now see greatest number means nothing but you have to calculate hcf so how will calculate hcf let us take the difference 6 minus 4 is 2 5 minus 4 is 2 oh sorry 5 minus 4 is 5 minus 4 is 1 and this is nothing but 1 8 okay so it is so just a minute okay Now here what we will do, so here 6 minus 4 is 2, 5 minus 4 is 1, 8 minus 13 is 5. So now I am feeling very much hungry, my mind has stopped working now.
12 minus 6 is 6, 14 minus 5 is 9 and 16 minus 8 is 8. Okay, fine. And then this difference we will take. So in a class I will teach you about HCF, so how do we take HCF.
Now 12 minus 4 is 8 and 4 minus 4 is 0. and 17 minus 13 is 4 so where is the minimum value so the minimum value is nothing but 512 now so basically if you want now to calculate scf then definitely the factors of this 512 will be your scf right okay so which options will divide 512 64 yes 64 will divide by how many times so it will be for uh you know 64 into 8 into 8 okay so this will divide by 8 times 120 4 will not divide 156 will not divide 260 will not divide so 64 will be one of the factors of this because 512 when you will calculate the factor so 256 into 2 then 256 is nothing but 16 into 16 into 2 right so this will be 8 into 2 into 8 into 2 so this will be the factors right so 8 into 2 8 into 8 is 64 is one of the factor so 64 will be the scf of this value and when you will divide these numbers by 64 it will give you a remainder of 12 and when you divide this number by 64 it will completely divide clear so question number 22 also it is clear friends see if you are facing some issues in understanding the basics then definitely achiever batch is going to help you right okay now friends find the number of factors of 2 to the power 8 into 7 to the power 5 into 14. see so if we have to find out the factors of this then it will be x plus 1 so whatever highest power we have plus 1 whatever the power we have plus 1 right so here 2 to the power 8 into 7 to the power 5 into 2 into 7 so this will become 2 to the power 9 into 7 to the power 6 so now the factors will become 3 plus 1 into this will be 6 plus 1 so 10 into 7 and it will nothing but 70 so the total number of factors will become 70 option c will become the correct answer for this particular problem right I hope guys you are understanding the video is little long right so almost one and more than one and a half hour but the concept should be very very clear then the question number 24 is a question from the topic percentage in an examination it is required to get 290 marks then only you will pass the exam okay fine so in an examination it is required to get 290 of the aggregate marks to pass a student is getting 203 marks and is declared failed by 12 percent of the total marks 12 percent of the total marks right so if we give them 12 percent of the total marks then he will pass right or or you can say if you give them 213 plus 87 marks then he will pass because 290 is the passing marks he got 213 that means if we give him 87 more marks he will pass or if we give him 12 percent of the total marks then also he will pass so can i say that 12 percent of the total marks is equals to 87 so 1 percent is equals to 87 by 12 and they wanted to calculate total marks so 100 percent multiply 100 on both the side okay and then you solve 4 3s are 4 25 times and 3 2s are is 6 and 29 25 into 30 will be 750 750 minus 25 will be you 725 is there any option yes 725 option c becomes the correct answer for the question number 24 right so i hope this is also very very clear for everyone now friends let us move towards the question number 25 question number 25 is from the topic cone volume related question is there so the slant height of a right circular cone is 10 meter so we have a right circular cone here okay we have a right circular cone like ice cream okay so we have a right circular cone okay like this the slant height of a right circular cone is 10 meter and its height is 8 meter and we have to find out its curved surface area so what is the curved surface area of curved surface area of a cone so my dear friends the curved surface area the curved surface area of a cone will be equal to pi r L. r is not given it's a right angle triangle so we will have to use Pythagoras theorem. Pythagoras theorem says if you want to calculate the base here then hypotenuse square minus perpendicular square so 10 square minus 8 square 10 square is 100 8 square is 64 this is nothing but 36 and 36 is nothing but 6 so this we have got as 6 now pi into r is 6 and l is 10 so this will be nothing but 60 pi right so it's in meter so meter square area so 60 pi meter square option c will become the correct answer for this particular problem friends the 25 questions which we have done in our today's video are very very important this kind of questions you will be expecting in your examination prepare hard and for the effort which we are putting please do like the video and also comment appreciate the effort which we are putting by commenting if the videos are good and trust me promise to you is we will be uploading more and more videos before your exam so that you prepare well and clear the exam thank you take care all the very very best jai hind