A Perfect Question From Calculus for IIT-JEE ADVANCE (2022)

[@Abhi-kr6df]

Now this is one of my most favourite que. 7:46 and that'll be all

[@manamtiwari]

I was thinking to actually put the function in it , but now I just want to ask how can we come upon this idea in exam . Though it was an amazing approach , sir can you make a series in which you cover most of these types of outside the box problems approach

[@l1mbo69]

we need to telescope a pi (ie multiplicative) series but here we have two terms in the numerator, so we should try to convert that into one trigonometric term and try to get the next in the denominator (so that it cancels with the numerator of the second term). Now thing is whatever manipulation you do, taking x/3^k as theta, any attempt to convert it to any other trig term will always have angle in terms of theta. But since indice of multiplication is k, we note that for each next term theta is 1/3rd the last. This heavily prompts us to think about the sin3A and cos3A formula and then we just proceed with the given solution.

[@manamtiwari]

@@l1mbo69 thanks buddy got it , nicely explained:)

[@funkyjunky845]

Better leave such type of qs unless you have prepared for International Mathematics Olympiad.

[@prajwalzagade4916]

@@funkyjunky845 exactly bro…these type of questions are for people who have finished syllabus in 10th only and are only doing revision 🤣or for people who can solve all jee main level integration questions…

[@peculiari6425]

I just saw this full approach on this channel. It's really amazing how he solved it kzbin.info/www/bejne/gnjUfYFop7qderc

[@missfly4406]

Couldn't we directly do this by observing that this function would be non-differentiable at points where the function inside the absolute function becomes zero. That is, speaking for ||x-2|-1|, those points would be 1,2 and 3. And as for the |x.f(x)|, it would be zero when f(x) is zero, since x can't be zero. And so, without actually simplifying the function, you could just check at what values of x belonging to 0 to 3π, cos(2x/3^k)=(-1/2). And simply speaking, this is only possible when 2x/3^k is 2π/3 or 4π/3 as you don't want x to exceed 3π, and since increasing k from 1 will only increase the value of x. So the only possible scenario is when k=1, and x=π and 2π. And I didn't even have to fuss about f(x) :)

[@debajyotichatterjee1891]

Exactly what I thought. That way also it seems to work

[@aasthaiitbombae5750]

same here dude ; I did in the exact same wayy

[@imsahil16]

Did the same

[@linxuser897]

Just a small correction, the angle 8pi/9 is also possible.

[@missfly4406]

@@linxuser897 You'll need x=4π for that. But x lies between [0,3π].

[@atultiwari9528]

Absolutely genius of you. Loved how you recreated the function from scratch, I was confused on why you were writing the sin3x formula but everything got clear when you said to put ø = x, x/3, x/3^2...... Absolutely genius sirji, I learned a new approach today

[@ketankukde1248]

Amazing problem sir I have a request that can you put some problems of coordinate geometry (for adv 2022) in this similar manner . Hoping that next video would be on coordinate geometry 😊

[@mandirabasu2170]

When u will want to play ( 2 cos theta +1 ) into factors u will see that 3 sin x - 4 sin^3 x And then as, the function proceeds with 1/3 GP that's how , u can easily predict sin 3 theta formula. Yeahh , Nevertheless nice problem. It can be featured among the hardest 5-6 questions of jee advance 2022.

[@shourya3099]

You're building my concepts stronger thank you

[@arjitasharma2153]

Thank you sir for discussing these kind of questions Nice explanation 😊😊

[@samarthchaplot2998]

sir i did this que by myself and i felt ao confident when my ans matched with urs. although, i did not find f(x) in the simplied form , i just found where individual modulus were non differentiable.

[@aswin7482]

IIT Delhi welcomes you😌

[@lordpain4945]

1:24 According to bodmas rule you can't just subtract 3-2=1 first .when 2 is already in the multiplication with (1-cos theta). If I m wrong explain me.

[@utkarshdwivedi6983]

are bhai, pehle multiply kra hai fir subtract kra hai

[@lordpain4945]

@@utkarshdwivedi6983 I got it thanks

[@tanishsukhija6128]

This is real advanced. Want similar channel for phy chem if anyone knows specifically for phy.p.s. thanks for such type of questions sir. Doing great for many students out there. 🥰

[@anilmangawa4566]

physics galaxy "Advanced illustrations" for physics 👍👍

[@aniketpal5189]

Highly recommended Phys 1.physics with vinay uppal 2.indian school of physics Chem 1.chemiit vishal Maths 1.Maths unplugged 2.Rz maths

[@ishan__001]

@@aniketpal5189 sb bta de

[@ad2793]

Also Physics sirjee janardhan Physics with ambarish Free Inorganic course by Parth Chopra bhaiya on their website

[@vaibhav5839]

@@aniketpal5189 bhai kyun kyun kyun competition badha raha hai

[@sakshamraj1333]

Tbh, if questions like these come in exam Then it is one of those questions you will actually leave to save your time.

[@parthkapoor1754]

why did u start from sin3x what gave u that hint and how will we be able to attack the ques. in similar fashion

[@sharanhuli9527]

Ya I also have send doubt

[@premrajthakur]

1Man he solved a lot of problems in his life , 2 when ever the term 1+2cosx will come you have to proceed from sin3x wala step .

[@sharanhuli9527]

@@premrajthakur is it so...? Can u pls tell me few more like this 💔 bro

[@premrajthakur]

@@sharanhuli9527 bro , gb sir tell his concept thoroughly ❤️,..

[@parthkapoor1754]

@@premrajthakur ohh okay..actually I haven't done these type of questions where Series is in mult. thats why...thx bro

[@dhruvdengada3490]

guruji aur guruji ke saare problems are OP :)

[@krishgarg2806]

Once we get 1+2cos2x = sin3x/sinx, we can convert the product into a telescopic product, and directly get sinx/x

[@keshavgupta3698]

The question is amazing

[@bijaykumarpanda7325]

The solution is great, but you can just check where cos(2x/3^k)=-1/2, so 2(3pi)/3^k>=2pi/3: only possible value of k will be k=1. So 2x/3= 2pi/3 or 4pi/3, therefore x=pi, 2pi.

[@dhruvdengada3490]

waah sir dill jitliya iss problem ne ! :)

[@lokaranjanpanda7038]

I have done the reverse first split cos 2x in hiher powers and then use 1-cos^x and the multiplued sinx/3^k and divided the all the terms get canceld after that i have just slacked from the limit part then see the sol

[@shorya_ss]

Nice question.. Core advanced problem.. Momerised the approach 😁😅.. Bring more such problems

[@tipsfluent7354]

im a 9th grade student, and im weak in maths, but after seeing this probelm...its like i can solve my whole guide

[@Rajeev25514]

Superb 👍

[@ayushparwal2004]

Good question bro

[@AnjaliSKyadav]

Thanku sir🙂

[@krrishbansal2275]

i like this approach but this is not easy to think of it we can simply put f(x) in first and just analyse it we will find that only two points in 0,3pi the first xf(x) is not differentiable .this will come only for k=1 as for other ones the range will be crossed. when u will solve u will get 2x/3=-1/2 which is 2pi/3 or 4pi/3 answer will pi and 2pi and for other expression it is easily calculated

[@goravgupta9334]

Marvellous

[@subhrayanbarman1654]

Good question

[@gauravahuja7803]

Thx

[@neelshah9043]

It's almost impossible to proceed a question like this in ongoing examination😅

[@hiltoneditz-w4b]

Tru dat

[@OmMallick-07]

That is really a brainstorming question

[@anirbanchatterjee8145]

yes i think intelligent person will also struggle with these kind of questions in jee adv and will most probably leave it as it will not give him that much value for his time

[@i3wm724]

@@anirbanchatterjee8145 Yep , its pretty stupid to solve these qs in the exam unless you are mridul agarwal

[@harshit3133]

@@anirbanchatterjee8145 such que can neither be done by an avg student nor by a topper , ig even teachers will struggle at first. Que like this can be done only by the lucky ones who have already practiced it and know the approach of it

[@extraterrestrialbeats3590]

is there any chance one can find f(x) either by using continued cosine series formula or by taking log on both sides and converting product into summation?

[@cutegirlakanshabag2449]

Thank you so much sir 😊

[@arjunso2665]

Thank you sir for this amazing question. Sir please upload such questions in this month. Also, I request you to please tell us the source of these advance level questions so that we can refer more...pls sir 🙏🙏🙏🙏

[@sharanhuli9527]

Yes siir. Pls

[@NitinKumar-dd6kv]

Due to these types of questions in jee advanced .. now one was born till in the history of jee advanced who had scored full marks ... 😅😂

[@sanjaijee7157]

Thanks a LOT!

[@neutron417]

Here after pratham bhaiya's video!

[@T22-t3z]

Exactly same question was in allen adv test

[@geetapandey9956]

sir i converted it inot cos3theta and almost everything got cancelled except 3 and

[@physicsbyabhijit.6740]

sir you said that you will teach more miscellaneous series for summation of binomial coefficiants...pls sir expln it

[@lildreamer8421]

Literally such a brilliant and satisfying question. Not easily approachable in the beginning but gets progressively easier once you get the first step....but then again only 0.1 percent will be able to solve this question in exam. And at the end its all about who can think about that first step that's where your iq plays a role

[@Ash-rx5wl]

The solution will indeed involve converting the cos2theta function into a fraction of sines. However, the approach u took, starting with sin3theta, it's impractical in the sense that a human brain won't be thinking like that. There are hundreds of formulae in trigonometry, there are so many different "types" of problems in calculus, human brain won't come up with that unless they have seen the solution. So instead we can just directly start from the function itself and write cos2theta in terms of sine and we'll get the same thing.

[@jignashah8120]

I think it's a perfect question to leave🙄😅

[@vishalsai6903]

op in the chat guys

[@subhrayanbarman1654]

It came in Fiitjee Aits today

[@harshvinayak9849]

sir this question appeared on AITS part test advanced paper 1 for students giving jee advanced 2023 . I solved it and got it right

[@04_144]

In which chapter?

[@tanishk2005]

This is really awsm approach.. but Exam ke un 3hrs me ese approach nhi chamkte ...🥺🥺😞😞😭😭😭😭

[@ayushmishra7082]

Sr how we know to solve the function from sin3¢ i can not get this part only

[@vidhanp482]

This solution is elegant but wastes too much time. You can just check for which values 2 cos(2x/3^k) is -1/2 within the interval. And we take k=1 because any k bigger than 1 would require an x larger than the bounds to satisfy the 0 condition(2cos(2x/3^k)=-1/2.)

[@amanshukla118]

Thank you sir for giving such problem approach I was doing through integrations Sir can you please share a pdf of such problems in telgram?

[@deepanmaitra4018]

Thank GOD the JEE days are over

[@anurag_gautam00]

Thanks sir 🙏

[@themathworm4984]

I have a problem for you from Olympiad 2019 It says, Let Z be the set of integers. Determine all functions f:Z→Z such that , for all integers a and b, f(2a) +2f(b)= f(f(a+b)) I will request you to solve this..

[@itsRakesh]

I'm glad it wasn't asked yday in the JEE Advance 2022. But how come this was recommended to me after the exam ?😂

[@ayushdoglaaurharamihai1002]

Bhai itna lmba kya kr rha h seedhe 1+2cos2x / 3 ko 4cos²x-3/3 likh k cosx multiply divide krdo telescope ho jayega product cos3x and cosx

[@Time..traveller]

Bhai kaise toda explain karoge

[@ayushdoglaaurharamihai1002]

@@Time..traveller bhai ye bhi ni bn rha to dub k mrr ja

[@iitianladka8712]

Sir konse book ka question hai please reply

[@longsteinpufferbatch4949]

Jee moment.

[@yashasvipandey4397]

Sir how will we know to use sin 3 theta and simplify it?????

[@NitinKumar-dd6kv]

By doing lots of questions bro ...

[@vikask2512]

Baba re Baba Starting kya ho rha hai pta hi nhi chal rha tha

[@Maddy_2206]

Had to take a little bit of hint but then did it nice problem

[@zuro181]

Where do you find all these questions?

[@m.s.mohamedwaseem1935]

just seen this becoz question seems intresting but i not ubderstand to solve it

[@NewbieCommentator]

Sir how is x=2 making the whole modulus zero?

[@varadthube4851]

Its critical point of inside mod.....you can also find it by graphing it

[@hiltoneditz-w4b]

Or u can see that |x-2|-1 = 0 so |x-2|= 1 That means x-2=1 and x-2=-1 So x=3 and x=1

[@NewbieCommentator]

@@varadthube4851 yes i got it..graph is symmetrical about x=2 and there is a cusp

[@steroid17]

Niiceee

[@vv_ryder2819]

Which didn't came

[@Kathan_]

i am in 10th what am i doin here

[@gouharmaquboolnitp]

7:46 good place to stop 🙂

[@tanmayvishwakarma8861]

after mathango best for maths may be better than mathango

[@geetapandey9956]

is better than mathongo notmay be cant u see the level but only negative thing is that very few qs so cant quench my thirst of solving tough problems

[@tanmayvishwakarma8861]

@@geetapandey9956 behen this channel has great concepts but mein jaha se padha hu use hi acha bolunga na obvious si baat he

[@geetapandey9956]

@@tanmayvishwakarma8861 han ok tanmay mai jaha se ppadhi hu wo bhi sir kafi achche qs lagwae hain kai bar in sir keuar meresir ke qs match ho jate

[@tanmayvishwakarma8861]

@@geetapandey9956 pandey ji vaise aap up se lag rhi he

[@geetapandey9956]

@@tanmayvishwakarma8861 yes

[@yuva980]

@ Jee simplified

[@Heloobehappy]

Job still missing 🤣🤣🤣🤣

[@vempatisridhar7448]

♥♥♥♥

[@AnkitSingh-mv1oi]

❤️

[@devilbruu8304]

Ye kya hai

[@Cool_Guy6867]

Hi guys, How are you? I have nothing to contribute here

[@kbstreams5140]

Ye gate jaisi dikhne wali cheej kya hai

[@devilbruu8304]

Isse jindagi mein kya milega

[@ravinder6840]

First comment

[@jameyatesmauriat6116]

No enough explanation, just copy and paste

[@pri012]

It's not that much hard....almost done 90% of the question

[@priyanshrawat442]

Wtf was this question

[@l1mbo69]

we need to telescope a pi (ie multiplicative) series but here we have two terms in the numerator, so we should try to convert that into one trigonometric term and try to get the next in the denominator (so that it cancels with the numerator of the second term). Now thing is whatever manipulation you do, taking x/3^k as theta, any attempt to convert it to any other trig term will always have angle in terms of theta. But since indice of multiplication is k, we note that for each next term theta is 1/3rd the last. This heavily prompts us to think about the sin3A and cos3A formula and then we just proceed with the given solution.