PYQs on CONTINUITY| CSIR NET 2011 to 2023 | Short Cut Tricks

[@sheemanitinsan7235]

I went to many institutions and invested a lot of money 💵 but no one ☝️ taught like you …..and you taught so very well 👌 without any fees thank you so much dear sir ❤

[@yogendravishwakarma5592]

Forget wrong things only take right and good things.

[@sheemanitinsan7235]

@@yogendravishwakarma5592yes ♥️

[@aakashbhuse3170]

Because he is recognised by the top Indian scientist in the current time and recently included in the top 2% scientists in the world !!

[@sheemanitinsan7235]

@@aakashbhuse3170 absolutely 💯 right brother

[@shubhamkumartiwari2379]

@Dr.Harish garg , at 1:16:37 csir net June 2019 . Sir In this problem options (c) and (d) are also correct.

[@steel679]

very helpful sir `thankyou so much sir .

[@supriyarani2645]

Aisa content aaj tak nhi mila you tube pe... difficult topic hai isko banane ke liye bhot thankyou sir... kindly make topicwise aptitude pyq

[@himanisingh3784]

Thankuuu so much sir.your teaching style is excellent.❤❤❤❤❤❤❤kash ap hmee phle

[@goutamjana1292]

Very helpful sir . Please upload more videos.

[@pusplatasahu5738]

Superb session.....❤

[@BalajiPadhy-l8f]

Really, you are teaching Real analysis, sir; thank you so much for sharing such videos.

[@riyagoel8939]

at 35:40 how did we have discarded the unbounded option(d) .Please provide a valid justification for the same

[@dipeshvishwakarma3511]

1/1+e^x is cts, one one and bdd.

[@pulkitgaming5401]

Take tan inverse x as example

[@rnithyaraj9498]

Tku sir
Your videos very use full sir

[@Achukutty25]

My prayers and wishes are always for you sir 🙏

[@preetyahlawat2464]

How to take f(x)=1, it is not one one ..at 35:01

[@rashmimalik9769]

Bahut jyada helpful h sir ji

[@anitakaushik-be8mo]

@ dr harishgarg 41:00...a option kaise shi ho gya ...f(a ) bdd to a ko bdd kaise bol skte h ..inverse image thode hi bdd hoti h

[@imkunalkapoor]

Sir this is very helpful please upload next 2 lecture very soon please your trick very helpful in exam

[@naveenpondara4903]

at 16:11 how opt d is correct?

[@ratanprajapatirp3529]

Thanks you sir aap great ho

[@shankarkubal5259]

sir 70min, lim x tends to zero [x] is not defined, so [x].sin(1/x) cannot be continuos at 0.

[@shaswata07]

Very helpful ❤

[@RanjangamingYT7477]

34:24 you have not taking example f(x)=1 because one one function bola ha😢

[@mathematicslovers2888]

Very nice explanation, thanks sir

[@professorragavan9783]

8:17 I have a doubt in selection of option c. We neglect [-1,1] because 0 belongs to it. Similarly option C also have 0. Then why we take as a correct answer?.... Please someone explain me 😢

[@DrHarishGarg]

The given option is set not interval because 1/n, n€N given .. So we need to find the function corresponding to this set and then check it continuity.... For example, for a and b option, function is given , but for c and d , function is not defined.... That's why, first defined the function and then check... Hope it help you.

[@professorragavan9783]

Yes sir thank you ❤

[@shankarkubal5259]

sir 44 min, option D is wrong. let f:(0,1) to R given by f(x)=1/x , then A=(0,1) is bounded but f(A)=(1, inf) is unbounded

[@riyagoel8939]

37:10 how can we consider A=R in the (4) option sinceR is not compact

[@newsteplaiddown9481]

A={1} it is compact , f^-1({1})=R it is not compact

[@charitylyngdoh8912]

Thanks alot Sir 🙏

[@vandnanamdev4443]

Thank you for your efforts sir 🙏

[@yogendravishwakarma5592]

Very nice lecture sir....

[@Siyagupta52]

@50:14 option (d) is incorrect as compact set will map to compact set.
Is this correct or not?
Can someone confirm?

[@anusuiya.]

Thank you sir🙏
Sir at 43:04 image of close interval under countinous function is always closed. and range of tan ^-1x is -pi/2 to pi/2 . So how option 1 is incorrect

[@Siyagupta52]

Take f(x)=e^x , A=R then f(A)=(0,oo) which is not closed

[@shefalithakur4580]

​@@Siyagupta52 ha to in this case you take A=R which is not closed
But continuous function always map closed to closed
Compact to compact
Cauchy to cauchy
So option 1 is true here

[@Siyagupta52]

​@@shefalithakur4580continuous function maps compact to compact
Closed to closed is not true .
As take the same example of e^x

[@shefalithakur4580]

@@Siyagupta52
I got it dear thanks
Continuous not necessarily map closed to closed

[@sahanar5228]

Continuity maps Closed inteval to closed interval...but not closed set to closed ..ie ex R

[@rajkumarmanna3855]

Thank you so much sir ❤

[@SunitaPooran-bi8gj]

37:24 can anyone tell me..why sir had not taken compact subset A...why he has taken A=R

[@Dearbhanusir]

Yes A can't take R because A is compact

[@RanjangamingYT7477]

31:37 b option me continuous booa ha but greatest integer function always discontinuous at countable numbe of points how b option correct 😂

[@positivethoughts6419]

Really you are great sir ❤

[@itsyourdev5143]

Thank you sir 🙏

[@siddhusiddharthan161]

Thank you❤ sir

[@SaifAbbas-c9p]

thanks sir

[@steel679]

solid content sir

[@SanchitMehra-mf3rh]

Thanks again ❤

[@intelligencecorner609]

You are genius sir

[@ranachanda2839]

Thanks sir...❤

[@ikmathacademy5747]

Sir ode or pde bhi topicwise krwa do

[@prabavathig462]

Sir... Please... Which software you are using for screen recording this video ?

[@ASHISHKumar-zu7xo]

Please explain in bilingual. Your lecture is very useful for me. Thanks sir

[@Radharanilove-y5d]

Sir please upload the vedios of linear algebra ... inner product spaces...and orthogonal...invariant subspcaes...

[@DrHarishGarg]

Linear algebra, inner product space etc already uploaded.. Explore at my youtube channel.

[@Radharanilove-y5d]

@@DrHarishGarg ok sir thanku

[@ankitadangi1655]

Very helpful 🎉🎉🎉

[@ChandanKumar-dn9lz]

Thanks a lot sir jee .

[@PIMMATHS]

Thanks sir ji

[@nerdhayafs62525]

Please complete this topic with uniform continuity and all

[@DrHarishGarg]

Already uploaded.... See at my youtube channel.

[@professorragavan9783]

Thank you sir

[@ThoihenbaKeishamMeetei]

love you sir❤❤❤

[@anamfatima3524]

Please upload the next lecture,

[@BEGINNERMATHS]

Thankyou sir

[@vikasmehta8027]

Thanku sir❤

[@shreya2262]

Thankyou

[@parveenkumar8050]

Thanku sir

[@saikatmalla7390]

sir last request..... please upload a video on pyqs of ring theory.... 🙏🙏

[@shalinichaudhary1082]

At 7:50, c is not correct

[@thibakarrasu1786]

🎉❤

[@steel679]

😃😃

[@theexpress85]

🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏

[@dsm2905]

❤

[@anuragpandey4912]

Thank you so much sir 🙏🏻🙏🏻🙏🏻

[@celinjoseph-x4s]

Thank you sir

[@ilmaaijaz3898]

Thank you sir😊

[@amitgupta-sk4hw]

Thank u sir😊

[@chauhanpriyanka9871]

Thanku sir

[@professorragavan9783]

Thank you sir

[@ShaliniDubey-v8w]

Thanku sir

[@Anita-o4w]

Thank you sir😊

[@KalpnaDevi-xc3gx]

Thanku sir

[@ajaysuman4946]

Thank you sir❤

[@sumitsharma2926]

Thank u sir ❤️❤️❤️❤️