SIMPLIFICATION PART 1 (सरलीकरणभाग 1 )

सरलीकरण , यह गणित  एक महत्वपूर्ण भाग है जो की परीक्षा मे 5 - 10 अंक का आता है। अब हम 

सरलीकरण की कुछ ट्रिक्स पढ़ते है-

1) अभाज्य संख्या : वह संख्याएँ जो स्वयं से और 1 से विभाजित होती  है, अभाज्य संख्याएँ  कहलाती हैं।  (उदाहरण  2,3,5,7,11.13...)

2) प्राकृतिक संख्याएँ : सभी पूर्ण संख्याएँ प्राकृतिक संख्याएँ कहलाती हैं। 

( उदाहरण : 0,1,2,3,4,5,.........)

3) BODMAS: कोष्ठक (Bracket), विभाजन  Division), गुणन (Multiplication), जोड़ (Addition) और  घटा 

इस नियम के अनुसार पहले कोष्ठक हल करेंगे उसके बाद विभाजन करेंगे उसके बाद गुना फिर उसके बाद जोड़ और अंत मे संख्या को  घटाएंगे। 

[ उदाहरण : (10/2)*6+5-3]

4) सभी पहली N प्राकृतिक सँख्याओं का योग : N(N+1)/2

उदाहरण : 1+2+3+.....+50 = 50(50+1)/2 = 25*26 = 650 

5) सभी पहली N प्राकृतिक संख्याओ के वर्गों का योग  : N(N+1)(2N+1)/6

उदाहरण : 1²+2²+3²+……10² = 10(10+1)(2*10+1)/6 = 10*11*21/6 = 385

6) सभी पहली N  संख्याओ के घणो का योग : [N(N+1)/2]²

^{उदाहरण :} 1³+2³+3³+……8³= [8(8+1)/2]²  = (4*9)² = 1296

7) सभी पहले N विषम संख्याओ का योग  : N²

उदाहरण : 1+3+5+7+9 = 5² =25

8) सभी पहली N सम  संख्याओ का योग : N(N+1)

उदाहरण : 2+4+6+8+10 = 5(5+1)= 5*6 = 30

9) अनंत तक वर्गमूल (जोड़): √x+√x+√x+√x+ …..∞ = ?

इस प्रकार के प्रश्नों मई संख्या को दो भागो N (N +1) मे विभाजित करते है और बडा अंक प्रश्न का उत्तर होता है। 

उदाहरण  √20+√20+√20+√20 …..∞ = ?

 20 = 4(4+1) = 4*5 , बडा अंक 5 इस प्रश्न का उत्तर होगा।

10) अनंत तक वर्गमूल  (घटा ): √x-√x-√x-√x- …..∞ = ?

इस प्रकार के प्रश्नों मई संख्या को दो भागो N (N +1) मे विभाजित करते है और छोटा अंक प्रश्न का उत्तर होता है। 

उदाहरण : √30-√30-√30-√30 …..∞ = ?

30 = 5(5+1) = 5*6 , छोटा अंक 5 इस प्रश्न का उत्त्तर 

11) अनंत तक वर्गमूल (गुना ): √x*√x*√x*√x* …..∞ = ?

इस प्रकार के प्रश्न मे दी गई संख्या ही प्रश्न का उत्तर होती है। 

उदाहरण : √12*√12*√12*√12 …..∞ = ?

उत्तर  12 होगा। 

xxx−−x√−−−−−−

October Last week One liner Points

*World post day - 9october and theme " innovation integration  inclusion"
* Old path white clouds--- buddha book - Thich Nhat hanh
*Batukamma festival 9 days - telangana
* Disaster risk reduction(unisdr) - new Delhi India pm
* Nobel piece ( narvey) - Juan Manuel Santos ( Colombia President)
* Fark Gorilla - Colombia
* Honorary consul of germany - BVR Mohan Reddy
* First platinum green airport - IGIA'S T3
*UK Shadow cabinet- Shami chakravrthy
* Doordarshan-  Ignou - Gyan darshan
*Young voter - Facebook
* F1 Japanese grand prix - Nico Rosberg, germany
* Indo Pak border(4) announced to seal till 2018
* Mental health day ( psychological fist aid) - 10 Oct
*Internal energy agency with india- UJALA SCHEME
* Vizag steel ambassador- PV Sindhu
* US lifted eco sanctions- Myanmar
* Lalima abhiyan in Mp-  Anemia
* Int Geeta festival- kurukshetra, Haryana Pranab Mukherjee
*Book "Half lion - how PV Narsimha Rao transformed India"- Vinay Sitapati
* China's new ambassador to india- Luo zhaohui (LZ) replaced Lae yucheng
* President of press club of India - Gautam Lahiri
* CHINA Open women's singles - Agnieszka Radwanska
*World no 1 chess player Hou Yifan defeated by Indian player Harika Dronavali

4th Bimonthly Policy Rates, September 2016

REPO RATE - 6.25%
REVERSE REPO RATE - 5.75%
BANK RATE - 6.75%
M.S.F. - 6.75%
C.R.R - 4%
S.L.R - 20.75%

*All rates have been decreased by 0.25% except C.R.R.

List of New Appointments September, 2016

List of New Appointments in 2016 : September Month

1. Abid Riaz Qureshi - Federal Judge (US) [1st Muslim to be nominated]
2. Aishwaryaa Dhanush - United Nations Women’s Advocate for Gender Equality and Women’s Empowerment
3. Ajay Singh - President, Boxing Federation of India (BFI)
4. Aleksander Ceferin - President, UEFA (Union of European Football Associations)
5. Ali Bongo Ondimba - President, Gabon
6. Alka Sirohi - Chairman, Union Public Service Commission (UPSC)
7. Anandi Ramalingam - 1st Woman Director, Bharat Electronics Limited (BEL)
8. Anoop Kumar Sharma - CMD, Shipping Corporation
9. Anuradha Rao - MD & CEO, SBI Mutual Fund
10. Arun Goyal - Additional Secretary, Goods and Services Tax (GST) Council
11. Ashok Chawla - Chancellor, The Energy and Resources Institute (TERI) University
12. BHVS Narayana Murthy - Director, Research Centre Imarat (RCI)
13. C.K. Asnani - CMD, Uranium Corporation of India Limited (UCIL)
14. Chennamaneni Vidyasagar Rao - Governor, Tamil Nadu
15. Deep Kumar Upadhyay - Nepal's envoy to India
16. Diane Gujarati - Attorney to the US District Court bench (New York)
17. Dilip Kumar Mandal - MD & CEO, IDBI Asset Management Company (AMC)
18. DR Soni - 19th General Officer Commanding-in-Chief
19. Emma Walmsley - CEO, GlaxoSmithKline (1st woman to lead a major global pharmaceutical company)
20. Girish Chandra Gupta - Chief Justice, Calcutta High Court
21. Hamid Baeidinejad - Iranian ambassador to the UK
22. Hiroshi Nakagawa - Chairman, Isuzu Motors India
23. J. Satyanarayana - Chairperson, Unique Identification Authority of India (UIDAIU)
24. Jacob Martin - Head Coach, Baroda Ranji team
25. Jayant Purushottam Gokhale - Director, Syndicate Bank
26. Jeffrey DeLaurentis - 1st US Ambassador to Cuba
27. Jim Yong - President, World Bank (2nd Term)
28. Junaid Ahmad - Country Director (India), World Bank
29. K.K. Aggarwal - National President, Indian Medical Association (IMA)
30. Lee Jae-yong - Executive Director, Samsung Electronics Board
31. M.S. Sahoo - Chairman, Insolvency and Bankruptcy Board
32. M.S.K. Prasad - Chief Selector, BCCI
33. Michel Temer - New President, Brazil
34. Monika Kapil Mohta - India's Ambassador to Sweden
35. Nadia Murad Basee Taha - Goodwill Ambassador, United Nations Office on Drugs and Crime (UNODC)
36. Nawazuddin Siddiqui  - Brand Ambassador, Samajwadi Kisan Beema Yojana
37. Nicholas Hopton - UK ambassador to Iran
38. Om Prakash Kohli - Governor, Madhya Pradesh
39. P.V. Bharathi - Executive Director, Canara Bank
40. Ravi Reddy - Head, International Society for Blood Transfusion (ISBT)
41. Ricky Ponting - Brand Ambassador, Tasmania
42. S S Mallikarjuna Rao -  Executive Director, Syndicate Bank
43. Sachin Tendulkar - Brand Ambassador, Kerala government’s campaign against drugs and alcohol
44. Sakshi Malik - Wrestling Director, Rohtak university
45. Sanjiv Singh - Chairman, Indian Oil Corporation Ltd
46. Sunil Godhwani - CEO, Religare Enterprises Limited (REL)
47. Suresh Subramanian - Head, Biocon Branded Formulations (India)
48. Urjit R Patel - 24th Governor, Reserve Bank of India (RBI)
49. V. Shanmuganathan - Governor, Arunachal Pradesh
50. Virat Kohli - Brand Ambassador, Punjab National Bank (PNB)
51. Wasim Bari - Manager, Pakistan cricket team