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

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

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

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

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

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

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

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

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

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

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

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

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

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

Outstanding sir❤

Very helpful sir thanku so much 🙏

58:35 option 3 is not true please check sir

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

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

Best teacher ever ❤❤

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

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 ????

Sir statistics k topic wise theory and question

36.30 3 marks k question me 2 option kese thik h

Thank you sir ...❤❤

Thanks Sir❤

Thankyou sir

Sir please upload video on queueing theory...

Thnk you sir

thanku so much sir

Very very helpful sir 🙏❤❤

30:25 not option a Thank you Sir

🪁🪁🌱🌼💐💐🌳🌳🌳

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

Sir next video

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Hello

Very helpful ❤