PYQs on Sequences of Real Number | Fully Short Cut tricks | CSIR NET 2011 to 2023

[@faruksk399]

Outstanding sir❤

[@vermastudiesmathematics3274]

30.20 option A is not correct , it is not monotonic but its its even odd subsequences are monotonic ,both cgs to same limit.

[@preetiyadav-k9i]

shi pakde h

[@kenchappab1548]

30:09 here sequence Xn ={0,1,1/2,3/4..} these are the terms of the sequence so its not monotonic sir

[@naveendixit9304]

Ekdum sahi bola X (odd) is monotonic increasing but X(even) is monotonic decreasing and both converge to 2/3

[@anusuiya.]

Thank you so much for amazing short tricks sir At 23:10 sequence is +ive. So how we took (-1)^n as xn

[@nabilafathima3223]

Solutions are easy to understand...keep uploading sir...its veryyyyyyy helpful

[@NAWAZSARIF-n8s]

36:33 it is MCQ (Single correct) so option D will be true and C is not correct as by Bolzano Weierstrass theorem every bounded sequence of real number has a convergent subsequnce

[@kenchappab1548]

Some other yutubers solved this question they mentioned its part c question and c also correct option,

[@meghapatidar4067]

1) 5:01 every convergent sequence is bounded Bolzano theorem 2) 23:10 b option should be correct 3) 28:28 a is incorrect 4) 36:06 c is incorrect

[@dhanujpathak7655]

Yes, i thought the same as well for 23:10

[@abdulkaleem6510]

Yes I am thought the same as well for 23:10

[@Siyagupta52]

But if we take x_n=sum 1/n then b will be incorrect???

[@poojasharma-ot6ty]

Very helpful sir thanku so much 🙏

[@Euphoria-k6r]

I am learning a lot ❤. Thanks a lot Sir!!

[@ShubhamYadav-gu7ls]

Very helpful lecture ❤

[@popideb1157]

Thank you so much sir your videos are very helpful... Sir please upload Modern Algebra (Group Theory & Ring Theory) PY Questions

[@Radhakrishna11192]

Limit, countinuty, and differentiability CSIR net 2011 to 2023 complete solution please provide sir 🙏🙏

[@dipankarmedi4640]

Best teacher ever ❤❤

[@easytolearnmathematics918]

30:30 option a is not true, i.e not monotone. Please check.

[@vermastudiesmathematics3274]

Yes

[@MohdAasif-mf8tu]

Sir 24:00 question mai b) kai liyai only positive term sequence kei example Laine hai, becoz it's given in question, so therefore (-1) ^n isn't a valid example. In fact the b) option will be correct as both +ve term &-ve term series converges to same limit therefore +ve term series will be convergent i.e: {Xn}-----> same L

[@SP-zt7br]

Sir please upload video on queueing theory...

[@kenchappab1548]

36:20 sequence An={sinn} it is bounded then how to construct convergent subsequence for this sir

[@SasankaKayal-b8s]

Thank you sir ...❤❤

[@ronneysaini7763]

Thanks Sir❤

[@rkn7717]

Very helpful ❤

[@SantoshKumar-ip5ej]

Dr. Sahab great initiative but some options are wrong. E.g. see 36.15 option c is incorrect. Others questionstudents have already told

[@NAWAZSARIF-n8s]

30:33 xn is not monotone sequence as x1x3

[@Mathematician_2025]

nx are monotonic sequence Because x2n are decreasing And x2n-1 are increasing subsequence

[@dwivediclasses5186]

Very very helpful sir 🙏❤❤

[@Sudeeppradhan1999]

Thank you sir ❤❤❤

[@charitylyngdoh8912]

Thanks alot Sir 🙏

[@RanjangamingYT7477]

23:25 b option you have not taking example sequence (-1)^n given question sequence of positive term .

[@jayprajapat2016]

Thankyou sir

[@shankarkubal5259]

sir 31.45, lambda n is not defined for n=1, since denomenator becomes zero. so option a is correct

[@artography0077]

Sir @1:05:15 , series has sum log2 . So it means it is also convergent???? I dont think so because when you apply limit comparison test it is dgt...So it is not neccessary that sum is finite so as series convergent.... Please let me know I'm contemplating right or not ????

[@shivamzaveri1412]

Yes. I'm Also Thinking Like You an=1/(n+k) 1/n is dgt if n

[@shivamzaveri1412]

Are You Thinking Like This?

[@satyanarayanpruseth8943]

24.10 mn in option (a) and (b) .....you have taken alternating sequence but in question mentioning about positive real no.s seq

[@pravinkamble2757]

So if we consider as (n)...

[@Siyagupta52]

@satyanarayanpruseth8943 Take the sequence sin^2(npi)/2 . Consider the subsequce then it has two limit points 0,1 hence not convergent

[@kanikakaundal1133]

58:35 option 3 is not true please check sir

[@nabakumarborah7510]

Yes,if we choose a= -1/4 then the sequence converges to the limit -1/2 . So the statement is False for every a.

[@kanikakaundal1133]

@@nabakumarborah7510 yes then this is false bcz in same way I take -1/3

[@jayprajapat2016]

Sir statistics k topic wise theory and question

[@vickymeena-l9v]

sir is it your any telegram channel...

[@abdulkaleem6510]

23:10 par Jo sequence hai vo positive real number ki sequence hai usme hum oscillate wala example nahi le sakte

[@RanjangamingYT7477]

Thank you ❤

[@yashrajtripathi4832]

Thnk you sir

[@SuryaSharma-fb5vp]

36:00 we cannot tick option c because it is not always true ...

[@tanish6035]

At 50:58 , you cannot mark d correct by your given reason

[@artography0077]

Yes ...the reason he gave for option c is also apply for option d .. in a way , we can take common constant term and summation 1 is also dgt

[@Dearbhanusir]

Optiod d me subsequence bola h jbki c me sirf sequence bola h​@@artography0077

[@SuryaSharma-fb5vp]

23:08 b) option should be true .. given sequence is of positive real numbers ..

[@HarshSingh-uy7zh]

Take 1/n

[@imtiyazansary]

Sir at 22:40 you take an example of sequence {x_n}={(-1)^n} which is not a sequence of positive real numbers 🤔

[@DrHarishGarg]

Then consider 2+(-1)^n or other equivalent example..

[@arun-007]

​@@DrHarishGargSir it is not satisfied convergent sir pls check it again

[@RanjangamingYT7477]

30:28 a not true not monotonic

[@abhinikki1]

Dear Sir, it is my humble request to you please reply if anybody has a doubt in any question. Please Sir....please 🙏

[@vkp8548]

30.15 min. sequence monotonic nhi ho rha hai yadi x1 x2 x3 x4 x5 ... Ki value nikal kr check kr rhe hai so I think monotonic nhi hoga

[@jayprajapat2016]

Sir next video

[@mufaknr8811]

❤

[@divyayadav3377]

36.30 3 marks k question me 2 option kese thik h

[@supriyarani2645]

Ek hi correct hai

[@freethinker5670]

🪁🪁🌱🌼💐💐🌳🌳🌳

[@ravindermehta397]

Hello

[@debajitroy7300]

30:25 not option a Thank you Sir

[@RanjangamingYT7477]

Thank you ❤

[@Deliciousecipes]

thanku so much sir