Part 2 - PYQs on Number Theory | CSIR NET 2011 to 2023 | Short Cut Tricks

This Lecture explains PYQs on Number Theory
#csirnet #csirnetmathematicalscience #csirnetmaths

[@Kailash_Jangid-bt5lv]

00:02 Understanding the Euler's function for finding phi of an integer. 02:15 Key concepts in Number Theory 07:13 Calculating cardinality using set operations 09:57 Finding the cardinality of S complement 15:35 Key concept: Discarding options based on even and odd numbers 18:17 Use prime numbers as key strategy in solving number theory problems 22:54 Finding N to satisfy the given condition 25:19 Understanding the concepts of D of n, V of n, and W of n in number theory. 29:59 Choosing two numbers for composite products 32:15 In-depth explanation of D(n) for composite numbers 37:31 Understanding Prime Numbers and Divisibility 40:13 Shortcut to find the value of P using summation approach 45:19 Discussing the possibility of P and D values for given conditions 47:53 F(n) is always finite for n >= 3 52:44 Explanation of divisibility in number theory 55:21 Discussing distinct Prime divisors and pairs of positive integers 1:00:07 Understanding the Omega of n and its significance in number theory. 1:02:31 P + 2P can never be the smallest prime divisor of N 1:07:54 Even and odd numbers and their divisibility rules 1:10:24 Understanding divisibility by 2 in Number Theory 1:15:38 Discussing prime numbers, divisors, and FM definition 1:18:20 Explaining congruence and solving equations using modulus 1:23:19 Finding unique solution using modulus and gcd 1:26:01 Solving modular arithmetic equations using shortcuts 1:31:03 Solving modular arithmetic problems using shortcut tricks 1:33:41 Using number theory to find the right answer Crafted by Kailash

[@ChandanKumar-dn9lz]

@@Kailash_Jangid-bt5lv Thank you brother

[@professorragavan9783]

@45:44 We cannot choose option b, because 25 is not a prime number. So, we can choose b=2, c=3 and so a=13. it is a prime number which cannot be written as 3 mod 4. But the option B is correct.

[@navathamadha5908]

It's amazing lecture sir

[@ChandanKumar-dn9lz]

130 views 40 likes .What Sir doing for us what we are doing for him😢

[@shatruhandhiwar4265]

Apke padhane ka technique BHA gya h dear sir jitna v tarif Kiya Jaye km h big big thank you sir❤

[@selsias32]

Tq sir ..very useful video

[@simonrai7300]

Sir you are doing great job. God bless you sir. We all need to support our sir. He deserves more...

[@906mukesh8]

Thank you sir

[@gumpularamesh1440]

Superb sir🙏🙏🙏

[@mymathspartner6019]

Thanks a lot sir for your great efforts for us .

[@DrHarishGarg]

It's my pleasure

[@snehasneha8634]

Thank you so much sir 🙏❤❤

[@athirapr1423]

Thank you sir 🙏🏻

[@schelderrose1669]

Superb sir 👍

[@DrHarishGarg]

Thanks a ton

[@meremahadev9318]

sir group theory aur ring theory se related pyq's v solve kra degye.... 🙏🙏

[@evaanandkashumasti2447]

Yes sir plz

[@stevenabakash919]

Kabhi nhi karenge woh

[@stevenabakash919]

Those are not his topic

[@rnithyaraj9498]

Thank you sir Eagerly waiting for part 2 Calculation of Variations

[@DrHarishGarg]

Not possible to uploaded.... Because, not good response on Part 1

[@nandhiniguru1169]

Respected sir, your videos are very useful and way of teaching is easily understood, kindly please upload video regarding galois theory,sylow theorem

[@professorragavan9783]

Thank you very much Dr. Harish Garg sir... because of your teaching in so many previous lectures i can able to find a different ways to eliminate and select the options. Once again thank you sir

[@rajeshwarideventhiran36]

Thank you so much sir..... Ur simply great in explaining csir questions.,.,..... Respect U alot sir🙏🙏🙏

[@newsteplaiddown9481]

Tq sir

[@aslicodes9736]

Thank you sir, for this video 😊😊

[@DrHarishGarg]

Most welcome 😊... Keep liking and sharing

[@sinsiyap4036]

Great ..sir . thanks alot..

[@marubahamad1236]

Your are great teacher.

[@Diksha-eu4tg]

Thank you so much sir 🙏 its really very helpful for us ☺️

[@yashrajtripathi4832]

You are doing great work sir ❤ Thank you sir

[@DrHarishGarg]

My pleasure. Kindly share with other and like the video too

[@professorragavan9783]

@46:20 we can choose option d, with p=7 and q=11 which satisfies the given condition so that a=77 which cannot be expressed as sum of two squares.

[@Ashishyadav-id9zb]

Thankyou sir

[@DrHarishGarg]

My pleasure

[@supriyasahoo5358]

Best lesson ever

[@professorragavan9783]

@45:04 We cannot eliminate option A, for p=25 where p is prime. We can eliminate p=29 a prime and 1 mod 4 with b=5 and c=2

[@professorragavan9783]

@46:14 we cannot choose option c, because p=1 is not a prime number not a composite number also. So we can choose, p=5 and q=7 d=1 with given conditions, so a=35 which cannot be expressed as sum of two squares. So we can choose option c as a correct answer

[@Diksha-eu4tg]

Thank you so much sir 😊😊🙏

[@arijitdas24]

Sir please upload videos on ring theory and Sylow theorems pyq..

[@susmitasaha4584]

n=6 is the answer of the last question Sir please make videos on Group Theory and Ring Theory

[@sucharita2888]

Why n is 6 Plz explain

[@deepakgautam7062]

Thank you sir ji

[@MrBhupsa197604]

Thks very much dear respected sir❤❤❤

[@DrHarishGarg]

So nice of you... Keep liking and sharing

[@PujaJangra-jx6eg]

Thanku so much sir 😊

[@techmath8922]

Thank you so much sir

[@DrHarishGarg]

Most welcome

[@parulchhabra7766]

Thank you sir 🫰

[@aslicodes9736]

I watched this lecture twice 😊

[@naobaangom8416]

Thanks sir

[@krishnakantadutta5374]

Always great 👍👍👍 sir

[@DrHarishGarg]

Many thanks.. Keep like and sharing

[@sheemanitinsan7235]

Thank you so much sir❤

[@DrHarishGarg]

Most welcome

[@SanchitMehra-mf3rh]

😊😊bestttttt solutions ❤

[@DrHarishGarg]

Thanks... Keep sharing with others too

[@sureshrasu5281]

Nice thank u

[@DrHarishGarg]

My pleasure

[@parulchhabra7766]

Sir 1:16:46...both b and c are correct ..but i have 1 doubt ...in that qust they have asked necessarily true ..then only b should be correct ..i am unable to understand qust in which they have written necessarily true ,etc

[@anshikathakur7085]

You r legend

[@DrHarishGarg]

थैंक्स यु

[@anshikathakur7085]

@@DrHarishGarg sir only pyq se hmara csir net clear ho skta h?

[@DrHarishGarg]

dear... these are not only PYQs, but each video tell you how to attempt the question, how to think the question and finally how to solve the question easily. with short cut tricks. .. Once you watch all my lectures, then definitely you will qualify the exam easily...

[@anshikathakur7085]

@@DrHarishGarg yes sir but yeh sufficient h

[@anshikathakur7085]

@@DrHarishGarg maine hrr topic se related aapki videos dekhi h full short trick k sath bss tension hori h btw you r great teacher

[@ishadevi2071]

Thnku sir 😊

[@DrHarishGarg]

My pleasure

[@vikasmehta8027]

Thanku sir ❤

[@DrHarishGarg]

My pleasure always

[@mathguru9257]

Sir jee please make video on Abstract algebra ❤❤

[@menakayadav9250]

Thanku sir

[@DrHarishGarg]

My pleasure always

[@Surya-nn6zs]

a,c are answers of last questions

[@Manish-uq5le]

Thanks ❤sir

[@DrHarishGarg]

Most welcome

[@Manish-uq5le]

@@DrHarishGarg almost every video are completed from my side ,all are very helpful to understand concepts.Thanks once again🙏

[@Kailash_Jangid-bt5lv]

tq sir

[@DrHarishGarg]

Welcome

[@dandibhotlaswetha5270]

Sir, I'm having a doubt regarding the problem that you explained at 44:00 minute a=b^2+c^2 in the explanation of the first point you said that b=3 and c= 4 which implies a=25 and p= 25 d= 1 but according the option p must be a prime number but 25 is not a prime number. Can you explain that to me?

[@DrHarishGarg]

Yes.... Correct.... Now take b=2, c=5, then a =29 which is prime. Also a =1(mod 4) thus option (a) is discard again.

[@imtiyazansary]

Sir at 45:04 in the question it is given that p is prime but you take p=25, 1 how??

[@sumathinagarajan1937]

a and c are correct

[@ishujain4344]

Last ques ans is a,c

[@PujaJangra-jx6eg]

Sir please upload numerical analysis

[@professorragavan9783]

1:02:40 Sir I have one doubt. Since p>3 there does not exist anyN such that omega n=3, how can we say option A is correct. If option A is in the form >3 we can choose, but this is in the form >=. Please clarify anyone. Thank you

[@DrHarishGarg]

Because >3 satisfy for all N thus it is correct....

[@professorragavan9783]

Ok sir... Thank you

[@alokkprajapati]

❤❤❤

[@professorragavan9783]

For last question n=5 and 7

[@NitishKumar-tt6mn]

n=5 & n= 7

[@harini7083]

A,c

[@charanramaviharpasumarthi6038]

Nice sir .. thanks yu❤

[@DrHarishGarg]

Welcome 😊

[@Zeelkhokhariya]

Last que ans is option a&c

[@DrHarishGarg]

Correct... Very good

[@vibhamishra3290]

20:28 phi(n+1) =n kaise aaya?

[@DrHarishGarg]

Take n is prime.

[@vibhamishra3290]

​@@DrHarishGarg sir if we taken=3 then phi(4) =2which is not equal to 3

[@RohitKumarYadav0516]

A and C

[@DrHarishGarg]

Correct.

[@MrBhupsa197604]

A,C

[@DrHarishGarg]

Great... Correct.

[@professorragavan9783]

Thank you sir

[@amanrajput826]

Thank you so much sir🙏

[@DrHarishGarg]

All the best

[@masterkapil6214]

Thank you sir ji

[@DrHarishGarg]

Welcome

[@ragavanananth2860]

Thank you sir ❤

[@DrHarishGarg]

Most welcome

[@ektagodara5936]

Thanks sir

[@DrHarishGarg]

So nice of you

[@activeclasses458]

Tq sir

[@DrHarishGarg]

Welcome

[@ChandanKumar-dn9lz]

Thanks a lot sir for your great efforts for us .

[@DrHarishGarg]

It's my pleasure always

[@MukulThecool6707]

A,c

[@ummehabeeba9026]

Thank you sir

[@DrHarishGarg]

Welcome

[@MUTHUKUMAR-q4m]

Thank you sir

[@DrHarishGarg]

All the best

[@sujatanayak207]

Thank you sir

[@DrHarishGarg]

All the best

[@somaghosh3151]

Thank you sir

[@DrHarishGarg]

My pleasure

[@kancharlaasritha9494]

Thank you sir

[@DrHarishGarg]

Welcome

[@Ankushpra]

Thank you sir

[@DrHarishGarg]

All the best

[@Ritaya8286]

Thank you sir ❤😊

[@DrHarishGarg]

Most welcome 😊

[@anishaiqbal4808]

Thanks sir

[@DrHarishGarg]

All the best

[@a.shakila7171]

Thanks sir

[@DrHarishGarg]

Welcome