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

[@faruksk399]

Outstanding sir❤

[@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

[@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

[@nabilafathima3223]

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

[@poojasharma-ot6ty]

Very helpful sir thanku so much 🙏

[@anusuiya.]

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

[@easytolearnmathematics918]

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

[@vermastudiesmathematics3274]

Yes

[@dipankarmedi4640]

Best teacher ever ❤❤

[@Euphoria-k6r]

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

[@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

[@popideb1157]

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

[@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

[@ronneysaini7763]

Thanks Sir❤

[@abdulkaleem6510]

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

[@SasankaKayal-b8s]

Thank you sir ...❤❤

[@jayprajapat2016]

Thankyou sir

[@Radhakrishna11192]

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

[@charitylyngdoh8912]

Thanks alot Sir 🙏

[@rkn7717]

Very helpful ❤

[@RanjangamingYT7477]

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

[@dwivediclasses5186]

Very very helpful sir 🙏❤❤

[@RanjangamingYT7477]

Thank you ❤

[@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

[@shankarkubal5259]

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

[@yashrajtripathi4832]

Thnk you sir

[@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

[@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

[@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

[@SuryaSharma-fb5vp]

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

[@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?

[@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

[@SuryaSharma-fb5vp]

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

[@SP-zt7br]

Sir please upload video on queueing theory...

[@jayprajapat2016]

Sir statistics k topic wise theory and question

[@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

[@mufaknr8811]

❤

[@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

[@freethinker5670]

🪁🪁🌱🌼💐💐🌳🌳🌳

[@jayprajapat2016]

Sir next video

[@abhinikki1]

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

[@divyayadav3377]

36.30 3 marks k question me 2 option kese thik h

[@supriyarani2645]

Ek hi correct hai

[@RanjangamingYT7477]

30:28 a not true not monotonic

[@ravindermehta397]

Hello

[@debajitroy7300]

30:25 not option a Thank you Sir

[@RanjangamingYT7477]

Thank you ❤

[@csirnetmaths0]

thanku so much sir