Toughest Question In JEE Advanced 2021 | 80% Students Ne Galat Solve Kara 😮

In This Video, Let's solve the toughest JEE Advanced 2021 question of Definite integration.
According to the official data of JEE Advanced, this question was solved wrongly by most of the students.
It was so a tough question that almost 80% of students solved it wrong.
The solution to this problem is given in many books but there's no in-depth solution available.
Today in this video we will see a very detailed solution to this JEE Advanced problem and you will learn a lot of concepts as well with this.
Let's check out the complete solution.
We are coming up with a series of important questions and concepts related to the JEE Advanced 2023 examination.
Stay tuned with ‪@BHANNATMATHS‬
#jee #jeeadvanced #iitjee #iitjeequestion #definiteintegration #integration #jeeadvanced2021 #jeeadvanced2023 #amansir #amanmaliksir #amansirmaths #iit #jee2023 #jee2024

[@BHANNATMATHS]

Check out Bhannat Maths On Instagram (@mybhannatmaths) - bit.ly/MyBhannatMathsInstagram

[@prixiusnecrolance]

More convenient approach: derivative of 10x/x+1 is always +ve from 0 -> 10 matlab 10x/x+1 is always increasing. Good video!

[@MathsPlusbyCPSir]

You are right dear , it is not the toughest.. check this link for some tough problems . kzbin.info/www/bejne/l5WvaHmwnLiCra8

[@HarshitSharma.45]

Yes it's more simplest

[@divyanshurajput3586]

yes it was bit lengthy

[@goutamboppana961]

but the thing its an integer question so you still kinda have to do the procedure

[@adityachaurasiya3836]

We should use 10/1+1/x. Ise se sare results easily milenge

[@Subhalin]

I think it's the most easiest question in paper if one has completed understanding in greatest integer function and breaking the limits of integral into different small limits

[@adityasart2644]

Pucha kisi ne kisi ne pucha

[@BeastGamerZ007]

same goes with modulus function ...

[@Subhalin]

@@adityasart2644 kisi ne tumara opinion pucha?

[@rushilsoni8392]

i think its click bait thats why.... not even possible that 80% got wrong...as it is mains lvl and people are able to solve it there too.

[@ris518]

Exactly.. probably most of the people made a calculation mistake or something

[@विशालकुमार-छ7त]

For integer values inside gif function ---> 10x/(x+1) = n^2 x = n^2/(10 - n^2) Now put n = 1,2,3,4,... Till n = 3, x will come out to be positive, but at n = 4, x is negative, which is not within integral limits. Simply split the gif function at each values.

[@kalimudinansari7993]

Ye to mohit tyagi sir ke style wali approach hai..!

[@satyampandey890]

6:10 13:39 Summary of How to Approach Question

[@suyashrawat5343]

Sir I have not taken such depth of this question at that time thanks for the valuable depth🙏🏻

[@Riversarelife143]

This was the most Easy Question actually. Interestingly The Function was increasing in the provided domain , so we just needed to open the greatest integer function by putting the value of y = 1,2,3,4.

[@Ganesh2168Xvjti]

Bhai tumhe yah sab kese ata he

[@MathsPlusbyCPSir]

You are right dear , it is not the toughest.. check this link for some tough problems . kzbin.info/www/bejne/l5WvaHmwnLiCra8

[@beastgoesdesi]

​@@Ganesh2168Xvjtipadhoge toh aa jaega bro😊😊

[@allukachallu154]

👍 agreed, I did it within like 2 min and that too is much time for such easy question 😅 Jee advanced has asked very very tough questions than this one but bhannat sir always ignore such questions and pick up easy questions 🙄

[@Riversarelife143]

@@Ganesh2168Xvjti Bhai Sarcasm Me puch raha ya sach me 😅😅😅

[@godson200]

I did this wrong I remember. But still I got 2k rank in jee advanced 2021. I guess this can prove you that solving 1-2 questions wrong is not worth it if u get more positive marks.

[@yatharth1305]

Didi aap kaunse IIT mai ho?

[@godson200]

@@yatharth1305 ladka hu bhai. Hyderabad

[@anuragpotter3691]

Sahi h easy question is relative. I strive to get a rank as good as you😅

[@aditsaini5094]

are bhai tum yaha bhi me jaha jaata hu aap dikh jaate ho prabhu

[@iusepc2317]

​@@godson200 bhai aap sab log apne naam me apna iit kyu likhte ho?

[@tanishq6628]

I used a totally different approach to solve this correctly. But that (linear/linear) was new for me, thank you so much for this information sir.

[@Summer69384]

Did u substitute x=tan2theta???

[@tanishq6628]

@@Summer69384 No actually I calculated the range of the stuff inside GIF [.] , and then plotted the graph of the whole using the range & calculated the respective values of 'x' wherever the range gives an Integer. And hence calculated the area under the curve(Rectangles).

[@Summer69384]

@@tanishq6628 bro😶

[@tanishq6628]

@@Summer69384 BRO🙂

[@TheHellBoy05]

@@tanishq6628 yh. when i obtained the gif graph i directly calculated the area of the blocks under the function.

[@TheMathBoy-wp9ei]

I was not aware of linear graph till now ; I did it using normal approach Thanks sir for an easy approach

[@amitapatel7464]

Same buddy

[@coreconceptclasses7494]

kzbin.info/www/bejne/oWbTeZmjlLSlkKssi=vI6mTATqPzN2hRQi

[@Sn28sept]

Graph was good but not necessary. If i put X=10 which is upper limit then we get 100/11 which is greater than 9 and thus function becomes 3. So it is evident that function can't attain values more than 3. Put X=0 lower limit thus we get functional value 0. Tbh I was completely unaware about linear/ linear graph still solved it. Anyway approach was nicer than mine.

[@dabs7739]

he used the graph to find out that the function was increasing. yeah there are other methods to find whether a function is increasing but i personally feel a graph in this case was the easier method

[@wm14690]

Bro how did u know weather the graph was increasing or decreasing..I don't think u can just put values like that without knowing

[@ishitagoyal18]

@@wm14690 it could be judged with derivative i solved this question before in less than time without using graph

[@Ashish21_]

Same question in my shift 30 jan 2024 shift 1 Only limit was changed that was from 0 to 9

[@VIHANXY]

Sir that gp+circle question was the toughest

[@avgjoe550]

No, i was most logical i.e. most suited for adv ( and still tough though)

[@manojchaudhary2780]

No the hardest question is of aod + integral chapter from jee advanced 2021 paper 2 . A paragraph type questions with various symbols and two questions asked in it in which each option is a full question.

[@avgjoe550]

@@manojchaudhary2780 yes, that was🥶🥶🥶

[@sanchitmukherjee2410]

i think the paper 1 probability single correct qn was also on slightly tougher side. I myself attempted JEE Adv 2021, mujhe woh kaafi mushkil laga tha saare cases cover karne mein

[@sohamkurdukar5443]

fun fact : aise karte karte sabko saare jee advanced ke questions ek ek karke toughest lagte hai 😂

[@pratyushdayal852]

I gave 2020 jee adv I had curiosity to solve it before watching whole video😅😅. Frankly speaking Solved this in less than 2.5min Even after gap of 3 yrs. Just wanted to tell my juniors to keep practicing the basic concept. IIT sets the paper only to check ur basic concept clarity by give question which visually seems to be tough but actually requires basic. Best of luck jee 2023😊

[@adityapatel87092]

Abhi kis iit mehi

[@raghavsikarwar10f46]

Chal be lodu aagye hero banne

[@ludicrousreality0]

Where are you now brother

[@satyampandey890]

It means you had practised a lot or revised the concept in between!

[@achintya-7]

This is not basic man

[@avigorai1644]

Simple 2 min solution Integral 1/9 to 2/3 of 1 + integral 2/3 to 9 of 2 + integral 9 to 10 of 3. Make 10x/x+1=1, 4,9 you will get

[@pushprajbhardwaj4820]

I'm a Master's student of Physics but I still enjoy solving the integrals whenever I come across some problems like this. It reminds me of the JEE preparation days.😂 Later learnt many different forms and methods of integrals. The joy of integrals. This preparation you guys are going through isn't just for getting into IIT, it's more than that, which will stay with you entire your Life. Thanks

[@higherthangods]

Exactly, my 1st year of BTech is gonna finish in 1 month, still I'm here revisiting the last year, the precious JEE days. One hell of a time it was.

[@Kanishk43329]

​@@higherthangods which college?

[@higherthangods]

@@Kanishk43329 IIT Kanpur

[@Kanishk43329]

@@higherthangods great ⁠•́⁠ ͜⁠ʖ⁠ ⁠•̀⁠ 😀

[@gouravgupta1639]

Chup

[@Physicslover1729]

Amazing and beautiful question sir ❤❤❤ Mere se to nahi ho paya kuch naya sikha ki graph kaise banaye!

[@arijitsen1947]

This was not the toughest, but it is a good question indeed

[@dibyabratabhattacharya3346]

i am a neet student but i have always taken interest in math and I had literally no idea that you could do these kind of sums in this way and how easier it became when the hyperbola concept came into play. never fails to intrigue me

[@vikasgupta9218]

What about 7th may going to use maths in bio😂😂😂😂

[@dibyabratabhattacharya3346]

@@vikasgupta9218 you see i was forced into neet so i'll not give up on my love for maths and i dont even expect anything from neet this year so

[@অভিযাত্রী]

​@@dibyabratabhattacharya3346how did it go

[@dibyabratabhattacharya3346]

@@অভিযাত্রী 586 aa rha

[@অভিযাত্রী]

@@dibyabratabhattacharya3346 🤩

[@sumantabanerjee8287]

Detailed explanation! The most brilliant part was the graphical analysis of the function. 👍😊

[@ayushdey5494]

Yes but I think it was useless

[@Its_now_ORnever]

​@@ayushdey5494yes as we can see that by differentiating the function it is a always positive value that implies it is increasing

[@atridevbhattacharya5050]

Thank you sir for explaining the solution of this question

[@nuranichandra2177]

Excellent problem and equally elegant solution

[@orangesite7625]

I'm shocked ki mei ne kiya(10+ min) but I think it is because now I have confidence but after going to exam I will lose it😭

[@me_ayushj]

bhannat smjh me aaya sirji ❤

[@AmanAgrahari-zl8hl]

Ashish Agarwal sir ne ye question bahot easiest way mein Kiya hai,bs fn ki range [0,10] ke bich mein hai and fn ki maximum value nikal lo √100/11 =3.something kuch ayega

[@ashishVlogs393]

In school level we are not taught such approaches that's why coaching is required in jee preparation

[@bharatiyainnovator3185]

Yeh bilkul bhi difficult nahi tha..sirf GIF mai break karna tha.. Aise sawal toh module ke mains section mai hote hai

[@neerajgogate5596]

sir could you please make a video on "how to mathematically prove that the shortest distance b/w any two pts is along a straight line joining those two pts and not any other curve ?"

[@aaaaaaaaaaaaaaaaaaaaaaaaaa1992]

Came in JEE mains 2024 30Th january morning

[@AdityaJee-us1pq]

I am not boasting, but I was in 11th when I saw this for the first time, and solved it in the first attempt. I myself was confused about how I did it.😂

[@adityakumar2159]

aapki toh achi percentile aagayi hogi 😢

[@AdityaJee-us1pq]

@@adityakumar2159 Are nahi 😅 main to abhi 12th me aaya hoon. 2024 me doonga

[@SamarpanSadhu]

par how integration toh 12th mai padai jaati hai

[@AdityaJee-us1pq]

@@SamarpanSadhu Jab differentiation padaa tha tab basic sa integration bhi seekh liye tha. Aur vaise bhi physics me integration batate hi hai kya hota hai.

[@SourishRoy-ge8jp]

@@AdityaJee-us1pq NICE BRO

[@shanimaurya2474]

Sir please bring this like session solution , approach for jee adv problem

[@Jee-kk7jd]

Salute to sir efforts, with such a valuable efforts

[@soumitrachakravorty2812]

Excellent explanation ❤❤❤.

[@Dineshsohaney]

Literal defination of halwa see here are two approachea 1. Use defination of gif that it is not defined on integral values so we can find x by i 1 i2 i3 2. Graph approach

[@manojchaudhary2780]

Sir I have solved this question without your solution 😊 this question is not that much hard. I think in exam pressure students made mistake in this

[@An_ony_mous]

That's the reality bro. The actual test is whether students can handle pressure or not. It's not about the questions.

[@arjunbhosale9967]

Same bro n yea true the pressure is unconvievable ... That's y I just practice most difficult papers so that atleast the ease of level will comfort me

[@manojchaudhary2780]

@@An_ony_mous yes bro you are right. As these types of questions in jee mains 2022 are harder than this one

[@khushwant6875]

BHAI INCRESING FUNCTION SOCHA THA KI NHI

[@MathsPlusbyCPSir]

You are right dear , it is not the toughest.. check this link for some tough problems . kzbin.info/www/bejne/l5WvaHmwnLiCra8

[@realkanavdhawan]

This Greatest Integer Function is also called as Floor Function in mathematics and programming Floor[2.3] = 2 Floor [0.5] = 0 Floor [0.9] = 0

[@SukeshKumar-ti5gq]

Sir please make a video on how to attempt or approach maths problem

[@shamaagrawal48]

😂 I haven’t even studied definite but solved it in 30 sec Its very easy. So ironical how we mess up these in paper

[@Its_now_ORnever]

Simply we had to find first derivative of that function which is always positive that implies its a increasing function

[@Devhes]

I took a slightly different approach, instead of using graph method because I am dumb and didn't know how to draw graph for linear/linear function, I just differentiated the function inside the root and got 10/(x+1)^2 and put the minimum value of x in the given domain, which is x=0 and got that the function is approaching 10 as maximum, took root of it and then proceeded the same way you did, after about 3 minutes of calculation I even got the correct expression, then forgot that I had to multiply by 9, simplified and got 20.22 and reported the nearest integer 20🥲🥲.

[@adityajain6270]

Sir depth samjhane ke liye graph toh bna diya aapne but uski zarurat nhi thi matlab simple function ki range nikal lo vahi se sabh kuch ho jana

[@sanataniofficialhindu]

Because it is increasing function we can easily solve it by putting the values from 1,2,3,4

[@sambhavgiri4007]

Easy question tha, bas check karna tha when the function broke continuity, that's when [√10x/x+1] = Integer

[@aarush552]

Sir if 1⁰=1 and 1¹=1, then we can say 1⁰= 1¹ Therefore 0 = 1 How plz explain (Student of 10th class)

[@AdityaJee-us1pq]

Ispe HC verma sir ka ek video hai vo jaake dekho.

[@anuragpotter3691]

Excluding 1 hoga...

[@shivapandey8958]

Fun fact- atleast no of comments/2 AIR are present here😅

[@SathwikDonthu-nf2po]

Easy way draw graph mark integer points and get rectangles and find area

[@ADITYAKUMAR-xj8xk]

Sir maine ye solve Kiya wo bhi pyq mock test me pehli baar me hi Feeling confident 😮 Becoz Im weak in maths😂

[@friakii]

Chalo at least 80% had the guts to attempt it sir!!

[@gautamgoyal7397]

sir, aap vishwas nhi karoge mere JEE Mains 2023 1st attempt mei maths mei mere 2/100 and ab 2nd attempt mei 23/100 ban rhe aur mujhe thoda mathsphobia bhi hai but mai such bolunga mere liye ye wala querstion hardest nhi bulki easiest tha. Maine aapka video pause kara aur exact 4:47 mins mei ye question solve kara with right answer with my own developed hit and trial method instead of your Hyperbola method and I also I didn't know that Linear/Linear logic. So it was also surprise for me. btw love ur videos❤❤

[@namanraikwar4555]

Thank you sir 🙏🏻🙏🏻

[@Its_Ari24]

Happy to solve it with knowledge of graphs only😊😊...I don't even know integration and all...Even sir did it similarly...

[@AmanAgrahari-zl8hl]

Are yrr ye to bahot aasan tha , Ashish Agarwal sir definite integration mein karwaya tha,mujhe to pata bhi nahi tha ki ye advanced ka hai

[@ajaybishnoi4967]

Awesome solution sir g.

[@honestadministrator]

At 0

[@suprabhat54321]

Superb solve Sir

[@arunsingh-ny7uh]

Sir aaap aise hi advance aur jee ke questions laate rahiye ❤️❤️❤️❤️❤️❤️❤️❤️

[@atchaya5532]

Sir I have a doubt I get 34 percentile in maths 87.97 percentile in physics 97 percentile in chemistry Overall 90.41 percentile In Feb 1 morn session 2023 Am i eligible to write jee advance

[@atchaya5532]

@@horny_emoji Are you saying That i am not eligible sir

[@anuragpotter3691]

Yep youare

[@aravpratap61]

Is question ko x - fractional x me likh ko then seprate kar lo fractional of x ka period is 1 so periodic vali property laga do the it is cake walk

[@a_minor]

si GINT wale sawaalo pe aur video laaiyega, mujhko unhi me problem hoti h. Ye wala sawaal bhi helpful tha.

[@amitapatel7464]

SIR meine bas range nikala and range mein dekha ki y not equal to root10 hai and then jaise aapne kiya vaise kiya ❤❤

[@white444ytfanclob7]

You are best teacher ❤

[@saisharan2687]

Wow I have Solved This Question in 2 min Im Lucky or I have deep Concept i don't knew i just solved after pausing it by seeing thumbnail and later i skipped to last and saw answer was Correct 🥰😊

[@akashkumarsaha5191]

Thank you sir for your concern

[@Programmer-f2x]

Sir ye increasing function hai isse hum directly values put on krke b toh Infer kr skte haina jaise aapne 1,2,3 daalke show krra??? Without graphical analysis..

[@kamlakshsambyal3890]

Sir please Indefinite Integration aur Definite Integration oe ek aur series bna de please.

[@thevisious_slayer]

Sir agr koi jee mains iss saal clear kar leta hai but advance nhi toh agle saal agr jee advanced ke liye attempt krne ke liye kya phir se jee mains Dena padega yaa direct jee advanced mein baith skte hai based on previous year jee mains percentile

[@Amaan_khan334]

No bro tumko firse jee mains dena pdega next year adv. ke liye

[@jaymishra5218]

Graph ka toh koi use hi nahi hai idhar f'x always +ve hai dikh raka hai toy increasing function hai Aap toh phaltu me deep ja rahae hai ...sab itna deep chale jate hai aur jyada steps ho jata hai phir mistake ka chance bhi badta hai isliye 80% ka galaf hua

[@Mathlover22969]

Utna bhi nahi tha......maine phehle hi dekh liya derivative karke jo function increasing hai in [0,10] and the functional value after taking sq root will lie from 0 to 3 and something then greatest integer so 0,1,2,and 3value lega....so at first I have found at which points 1,4,9 these occurs and broke the interval into 4subintervals and easily solved the integral......everytime har questions graph se nahi karna padta....kuch senses ke use se bhi ho jata hain

[@mono7891]

Man, you have head full of hair ----- By the way, you are a wizard. You made this problem look so easy. I am impressed. Good job!!

[@souryasanyal2894]

sir aap bahut achha parate he, love from bengal

[@siddhardhachaitanya4560]

Extraordinary, Mind blowing, super, fantastic

[@vipinbhatnagar8752]

Please do not cross or stand in front of the black board. A teacher should stand on one side and explain. One can go to the other side only when writing something on that side.

[@omkarshrimali7]

It's been 7 Years, since Kota Coaching, still able to solve is an achievement I guess ?

[@tanishqgoyal7180]

sir ek doubt tah... kahi par pi diya ho to usshe 180 degree manne ya 3.14...

[@pragyankalita7831]

Sir, itna mehnat karne ki kya hi zaroorat thi.. simply 91 × 2 kar dete, 182 answer 5 seconds mein mil jaate.. brain ko use karna seekho.. work smart, not hard.. question mein diya hi hua hai value of 91= ?.. simply multiply by 2

[@syedsaaduddin4124]

91 ku 2 se multiply karne hai bolke khaab padta kya?.. Why should I multiply it by 2?

[@ashishkumar9408]

Yeh teacher apne apko sabse bada gyani aur Einstein samajhta hai apne apko.itna ghamand nahi karna chahiye..

[@ayan6535]

ye to first try m hi bn gya😬😁

[@shubhamg9495]

Took me more time to solve the arithmetic than to evaluate the integral. This is a very easy problem.

[@parvsheth5078]

I am surprised most people did this wrong..... very simple question

[@ShubhamSingh-xs6ei]

bhai yeh tow itna easy tha- tf ek hi baar mein answer aa gaya

[@shrawon3605]

Honestly speaking NO This was NOT the toughest... In fact it was one of the easy questions in that paper.

[@UnknownGhost97]

182 is the correct answer but can I write the answer as [sqrt(100 - 10log 11)] using logical method

[@Rex_07_sudo]

Sir ye official data milta kaise hai jisme ye pata chalta hai ki kitne % baccho ne question kara hai?

[@jitendrasng421]

Sir plz prove this inequality in complex numbers : | zk + zk − 1 | ≤ | zk | + | zk − 1 | ≤ 2

[@chatrughanprasad7778]

Nice explanation Sir

[@vaibhavjain4066]

Sir y = 10x/x+1 kyun li hai and y=√10x/x+1 kyun nahi li hai

[@anubhavmishra295]

y^2 = 10x/x+1 liya he

[@vaibhavjain4066]

@@anubhavmishra295 bhai thanks for your reply but sir ne y=10x/x+1 liya hai. Kindly check once more

[@anubhavmishra295]

@@vaibhavjain4066 ha sir ne likha nhi he lekin graph y^2=10x/x+1 ka hi he, sir may have mistakenly written that

[@ADITYAKUMAR-xj8xk]

Wherever we see greatest integer or fractional part we make intervals where is discontinuity

[@chinmaysrivastava4836]

hamne sahi se kar liya sir 🙏💖

[@maths123umer]

Cool hai aman sir...

[@Vsufhuvvjf]

I am your big fan because you provide me track for survive in class 11

[@s.psingh230]

Great 👍👍👍👍👍👍👍

[@sarveshdubey2528]

Awesome sir

[@harshmalviya1737]

just put 10x/x+1 = I and bring x in terms of I which would be I/I-10 and then start putting values of I for 1,,4,9, ( square values ) after 9 you would see that it become negative x become negative . but we need integration till 10 just . So we need not to worry . Fir to jhandu baam question hai yaar .

[@utkarshgautam4620]

Thank you sir, aapne itna hard question ese smjha diya jese Nana ji kahani suna rhe ho...❤😄

[@productionofscientificandt7320]

I AM STUDENT OF CLASS 9TH, PHIR BHI AAP SE PADH ke ye sawal 3 minute me bana diya thankyou sir

[@shivagarwal9378]

Pretty doable question imo... Haven't seen the paper, but pretty sure there were more difficult questions than this

[@procodemaster356]

I have done in first attempt it is not a tough,but a fundamental question...

[@udaychauhan395]

I gave jee advanced 2021, and during the paper i was able to do it in first attempt 😀 i don't think ki ye tougest tha

[@ravisinha2165]

Sir aapka jee k liye new batch kb se hai admission🙏 process btaiye

[@potu6534]

Sir thank you very much 😊