Short Trick on Centres of Triangle in Geometry

In this article we will discuss about the various centers of triangle. In SSC CGL exams 1 or 2  question generally come in exam from this chapter.

There are four centres  in a triangle triangle:

• In-centre
• Circum-centre
• Centroid
• Ortho centre

In-centre:

The point of intersection of the all the three angle bisectors of a triangle is called as In-centre

The distance of the in-centre from the all the three sides is equal(ID=IE=IF=inradius “r”)
In-radius (r)= Area of triangle/Semiperimetre=A/S
∠BIC = 90 +∠A/2
∠AIC=90+∠B/2
∠AIB=90+∠C/2

Circumcentre:

The point of intersection of the perpendicular bisectors of the three sides of a triangle is called its circumcentre.

The distance between the circumcentre and the three vertices of a triangle is always equal.
OA=OB =OC=R(circumradius)=abc/4A
∠BOC=2∠A
∠AOC=2∠B
∠AOB=2∠C

Location of circumcentre in various types of triangle:

Acute angle triangle: Lies inside the triangle
Obtuse angle triangle: Lies outside the triangle
Right angle triangle: Lies at the midpoint of the hypotenuse.

Orthocentre:

It is the point of intersection of all the three altitudes of the triangle.

∠BHC=180-∠A
∠AHB=180-∠C
∠AHC=180-∠B

Position of orthocentre inside the triangle:

Acute angled triangle: lies inside the triangle.
Obtuse angle triangle: lies outside the triangle on the backside of the obtuse angle. Orthocentre and circumcentre lie opposite to each other in obtuse angle triangle.
Right angle triangle: lies on the right angle of the triangle.

Centriod:

• It is the point of the intersection of the three median of the triangle. It is denoted by G.
• A centroid divides the area of the triangle in exactly three parts.

Medians:

• A line segment joining the midpoint of the side with the opposite vertex is called median.
• Median bisects the opposite side as well as divide the area of the triangle in two equal parts.

Some important tricks are as follows:

(1)In a right angle triangle ABC,∠B=90° & AC is the hypotenuse of the triangle. The perpendicular BD is dropped on the hypotenuse AC from the right angle vertex B,

BD=AB*BC/AC
AD=AB²/AC
CD=BC²/AC
1/BD=1/AB² +1/BC²
(2)The ratio of the areas of the triangles with equal bases is equal to the ratio of their heights.
(3)The ratio of the areas of two triangles is equal to the ratio of products of base and its corresponding sides.

Area (Triangle ABC)/Area (Triangle PQR) =AC*BD/PR*QS
(4)If two triangles have the same base and lie between the same parallel lines then the area of the two triangles will be equal.


Area of Triangle ABC= Area of Triangle ADB
(5)In a triangle ABC, AE, CD  and BF are the medians then
3(AB²+BC²+AC²) = 4(CD²+BF²+AE²)
6)Sum of  any two sides of the triangle is always greater than the third sides.
(7)The difference of any two sides of a triangle is always less than the third sides.

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Friend's This Page is translated through Google Translator So there may be some problem in few Questions.

 1.) नेताजी सुभाष राष्ट्रीय खेल संस्थान किस शहर में स्थित है?
 -Patiala 

2.) किस धार्मिक शिक्षक ने बद्रीनाथ (उत्तर), द्वारका (पश्चिम), पुरी (पूर्व) और श्रिंगेरी (दक्षिण) में देश के चार कोनों में चार गणित स्थापित किए?
    -एडी शंकराचार्य

 3.) मोबाइल फोन के पिता के रूप में कौन माना जाता है?-मार्टिन कूपर4.) गायत्री मंत्र को किस हिंदू भगवान को संबोधित किया जाता है?-Surya5.) सभी तत्वों में कौन सा तत्व जरूरी है?
 -Hydrogen

 6.) 'बिज़नेस एट द स्पीड ऑफ सोचा' किताब किसने लिखी थी? 
-बिल गेट्स

 7.) मानव शरीर में कौन सा अंग पित्त पैदा करता है?
 -Liver

 8. डायमंड और ग्रेफाइट किस तत्व के आवंटन हैं? 
-कार्बन

 9।) टेस्ट पारी में सभी 10 विकेट लेने वाले एकमात्र भारतीय क्रिकेटर कौन हैं?
 -एनल कुंबले

10.) भारत के राष्ट्रपति बनने की न्यूनतम आयु सीमा क्या है?
 -35 साल 

11.) किसने काल्पनिक चरित्र हैरी पॉटर बनाया?
 -जे के राउलिंग

 12.) किस विटामिन की कमी स्कार्वी का कारण बनती है?
 -विटामिन सी

 13.) रक्त के थक्के के लिए मानव रक्त का कौन सा घटक जिम्मेदार है?
 -Platelets (thrombocytes)

 14.) महिलाओं को चुनाव में वोट देने का अधिकार देने वाला पहला देश कौन सा था?
 -न्यूजीलैंड 

15.) हिंदू पौराणिक कथाओं के अनुसार, जुड़वां बहनों रिद्धि और सिद्धी किस भगवान की पत्नियां हैं?
 -गणेश

 16.) कौन सा वैज्ञानिक 'मेन्लो पार्क का जादूगर' के रूप में जाना जाता था?
 -थॉमस अल्वा एडीसन

 17.) 6 अप्रैल 1 9 0 9 को, उत्तरी ध्रुव तक पहुंचने वाले पहले व्यक्ति कौन बने?
 -रोबर्ट एडविन पेरी

 18.) भारत के पहले परमाणु रिएक्टर का नाम क्या है?
 -Apsara

 19.) किस मुगल सम्राट ने दुनिया के 'अलमगीर-विजेता' का खिताब संभाला?
 -Aurangzeb

 20.) महात्मा गांधी ने भारत में अपना पहला सत्याग्रह किस स्थान पर शुरू किया था?
- बिहार में चंपारण

21.) जब एक चींटी एक व्यक्ति को काटती है, जो रासायनिक उत्तेजित करता है जो इसे इंजेक्ट करता है?
 -फॉर्मिक एसिड 

22.) भारतीय संविधान की 8 वीं अनुसूची में, आधिकारिक तौर पर कितनी भाषाओं को मान्यता दी गई है?
 -22

23.) भले ही भारत 1947 में स्वतंत्र हो गया लेकिन दमन और दीव एक यूरोपीय उपनिवेश बने रहे 1961. किस देश ने इस पर शासन किया?
 -Portugal

 24.) अंतर्राष्ट्रीय नागरिक उड्डयन संगठन (आईसीएओ) का मुख्यालय है?
 -मॉट्रियल कनाडा)

25.) डकवर्थ-लुईस विधि किस खेल से संबंधित है?
 -क्रिकेट

26.) वयस्कों की सामान्य हृदय गति क्या है?
 -72 बीट प्रति मिनट 

27.) महाराजा में एलोरा में कैलाश मंदिर किस राजवंश के शासकों द्वारा बनाया गया था?
 -Rashtrakuta

 28.) रिजर्व बैंक ऑफ इंडिया (आरबीआई) से ब्याज दर क्या है जिस पर बैंक उधार लेते हैं?
 -रेपो दर 

 29.) अंतर्राष्ट्रीय तिथि रेखा, एक काल्पनिक रेखा जहां एक दिन पूर्व या पश्चिम की यात्रा के रूप में बदलती है, किस देशांतर से गुज़रती है?
 -180 डिग्री

30.) प्रसिद्ध निबंध 'अनटो द लास्ट' किसने लिखा था, जिसे बाद में 'सर्वोदय' के शीर्षक के तहत महात्मा गांधी द्वारा गुजराती में अनुवादित किया गया था? 
-जॉन रस्किन

31.) केंद्रीय रेलवे का मुख्यालय है?
- मुंबई 
32.) व्हीलर द्वीप, भारत की मिसाइल परीक्षण सुविधा की साइट एकीकृत टेस्ट रेंज (आईटीआर), किस राज्य में स्थित है?
 -ओडिशा

33.) भारत के राष्ट्रपति को अपना इस्तीफा किससे संबोधित करता है?
 -उपाध्यक्ष  

34.)रूस के अलावा, किस देश का क्षेत्र यूरोप और एशिया दोनों महाद्वीपों में स्थित है?
 -तुर्की 

35.) 'चिकित्सा के पिता' के रूप में कौन जाना जाता है?
 -Hippocrates 

36.) हिंदी के बाद, भारत में दूसरी सबसे बोली जाने वाली भाषा कौन सा है?
 -बँगाली

 37.) खैबर पास, मध्य एशिया और दक्षिण एशिया के बीच एक रणनीतिक पर्वत पास, जोड़ता हैपाकिस्तान किस देश में है?
 -Afghanistan 

38.) 29 अगस्त 1988 को, जिब्राल्टर के स्ट्रेट्स में तैरने के लिए कौन सी भारतीय महिला दुनिया की पहली महिला बन गई?
 -तीती प्रधान

39.) पाकिस्तान का पहला राष्ट्रपति कौन था?
 -इस्कंदर मिर्जा 

40.) भारत की पहली 11 वीं सदी के यात्री ने 'ताहिक-ए-हिंद' और 'किताब-उल-हिंद' किताबें लिखीं?
 -एल बरुनी 

41.) उच्च तापमान पर फिलामेंट्स को संरक्षित करने के लिए, बिजली के बल्बों में कौन सी गैस भर जाती है?
 -Argon 

42.) 'द फोर नोबल ट्रुड्स' और 'नोबल एटफोल्ड पाथ' किस धर्म के आधारशिला हैं? 
-Buddhism 

43.) बेकिंग सोडा का रासायनिक नाम क्या है?
 -सोडियम बाइकार्बोनेट

 44.) वॉशिंग सोडा का रासायनिक नाम क्या है?
- सोडियम कार्बोनेट

45.) किस भारतीय शासक ने अंग्रेजों को कोहिनूर हीरा की खोज की थी?
 -दलीप सिंह

46.) 'ज्ञानदर्शन' किस भारतीय खुले विश्वविद्यालय का एक शैक्षिक टीवी चैनल है?
 -IGNOU

 47.) कौन सा शहर सालाना चार ग्रैंड स्लैम टेनिस टूर्नामेंटों में से एक विंबलडन टेनिस चैंपियनशिप का आयोजन करता है?
 -लंडन 

48.) किस यूरोपीय देश को 'आधी रात सूर्य की भूमि' के रूप में भी जाना जाता है?
 -Norway 

49.) मानसून से भारत को इसकी बड़ी बारिश मिलती है?
 -उथ-वेस्ट मानसून

 50.) एक राष्ट्रपति के दौरान अमेरिकी राष्ट्रपति कितने साल तक सेवा करते हैं?
 -चार वर्ष 

51.) बांस पेड़, खरपतवार या घास है?
 -Grass

52.) कौन से स्ट्रेट भारत को श्रीलंका से जोड़ते हैं?
 -पॉक स्ट्रेट्स 

53.) भारत के प्राणी सर्वेक्षण का मुख्यालय है?
 -Kolkata
  
54.) भारतीय संविधान के किस लेख में 'अल्पसंख्यक' शब्द प्रकट होता है?
 -आर्टिकल 29

55.) नालंदा विश्वविद्यालय और विक्रमसिला को नष्ट कर दिया गया था?
 -बखतियार खिलजी 

56.) किस सम्राट ने 'सुलाकुल' के विचार का प्रचार किया?
 -Akbar

57.) उपनाम 'सात बहनों' को भारत में दिया गया है? 
-7 उत्तर-पूर्वी राज्य 

58.) योजना आयोग के नवीनतम अनुमानों के अनुसार भारत में 2011-2012 में गरीबी अनुपात क्या है?
 -21.9%

 59.) उपस्थिति के कारण मानव रक्त प्रकृति में चिपचिपा है?
 -रक्त में प्रोटीन

 60.) शुद्ध पानी का पीएच मान है?
 -7

61.) आल्प्स सबसे ज्यादा और व्यापक पर्वत श्रृंखला प्रणाली है जो पूरी तरह से निहित है?
 -Europe

62.) पेरिस के प्लास्टर बनाने के लिए किस खनिज का उपयोग किया जाता है?
 -Gypsum 

63.) दुनिया में सबसे बोली जाने वाली भाषा है?
 -Mandarin

 64.) विटामिन की कमी के कारण टिकट क्या होता है?
- विटामिन डी

 65.) दुनिया का सबसे लंबा रेलवे मंच किस राज्य में है?
 -वेस्ट बंगाल (खरगपुर)

 66. सौर मंडल में किस ग्रह का नाम रोमन देवता कृषि और फसल के नाम पर रखा गया है?
 -शनि ग्रह 

67. अंतरराष्ट्रीय क्रिकेट में पहला बल्लेबाज कौन सा ओवर में 6 छक्का लगा सकता है?
 -शेर्शल गिब्स (दक्षिण अफ्रीका)

 68.) एकमात्र महाद्वीप कौन सा है जिसके माध्यम से सभी रेखांश रेखाएं गुजरती हैं?
 -Antarctica 

69.) भारत का पहला स्वदेशी नागरिक विमान है?
 -Saras

70.) अंतरिक्ष में चलने वाला पहला इंसान कौन था?
 -एलेक्सीई लियोनोव-रूस 

71.) रिज़र्व बैंक ऑफ इंडिया (आरबीआई) के गवर्नर के रूप में नियुक्त किया जाने वाला पहला भारतीय था?
 -C.D. देशमुख 1943 में

72.) किस मौर्य शासक ने अलेक्जेंडर के जनरल सेलेकस निकेटर को हरा दिया और क्षेत्रों को प्राप्त किया काबुल और बलूचिस्तान?
 -चंद्रगुप्त मौर्य 305 ईसा पूर्व में

 73.) जिसे 'गटर के संत' के नाम से भी जाना जाता था?
 -मदर टेरेसा 

74.) भारत में सबसे पुरानी पर्वत श्रृंखला है?
 -अरावली रेंज

 75.) संयुक्त राज्य अमेरिका की राजधानी, वाशिंगटन डी सी किस नदी के किनारे स्थित है? 
-Potomac

 76.) उत्तरी अमेरिका का सर्वोच्च पर्वत शिखर है?
 -माउंट मैककिनले 

77.) कौन सा हार्मोन आपातकालीन हार्मोन के रूप में भी जाना जाता है?
 -Adrenaline

78.) किस भारतीय स्वतंत्रता सेनानी ने नारा दिया 'दीली चलो'? 
-सुभाष चंद्र बोस 

79.) निर्विवाद निर्वाचित होने के लिए भारत का एकमात्र राष्ट्रपति कौन है?
 -नेलम संजीव रेड्डी 

80. वयस्क मानव कंकाल में कितनी हड्डियां हैं?
 -206 हड्डियों

81.) किसने 'सापेक्षता सिद्धांत' का प्रचार किया?
 -अल्बर्ट आइंस्टीन 

82.) 15 वीं शताब्दी में, किस इतालवी यात्री विजयनगर साम्राज्य का दौरा किया?
 -निकोलो डी कोंटी

 83.) भारत में एक राज्य के राज्यपाल बनने के लिए न्यूनतम आयु सीमा? 
-35 साल 

84.) किस सिख गुरु ने गुरुमुखी लिपि विकसित की?
 -गुरु अंगद

 85.) यूनेस्को की विश्व नेटवर्क सूची में हाल ही में कौन सा स्थान 9वीं भारतीय रिजर्व बन गया है?
 - ग्रेट निकोबार बायोस्फीयर द्वीप रिजर्व 

86.) दुनिया में पहला मानव हृदय प्रत्यारोपण ऑपरेशन किसने किया?
 -डॉ। ईसाई बर्नार्ड

 87.) पहले चीन युद्ध किस देश के बीच लड़ा गया था?
- चीन और ब्रिटेन

 88.) वर्ल्ड रेड क्रॉस मनाया जाता है?
 -मे 8

89.) फिल्म और टीवी संस्थान भारत किस स्थान पर स्थित है?
 -Pune 

90.) वायुमंडल की कौन सी परत अल्ट्रा-बैंगनी विकिरण को प्रतिबंधित करती है?
 -ओजोन परत

 91.) डीआरडीओ का पूरा रूप है?
 - रक्षा अनुसंधान और विकास संगठन

 92.) भारतीय सेना के पहले भारतीय प्रमुख सेना कर्मचारी कौन थे?
 -Gen। के.एम. करियप्पा 

93.) जीएटीटी का पूरा रूप क्या है?
 -शुल्क और व्यापार पर सामान्य समझौता

 94.) फ्यूज तार का पिघलने बिंदु उच्च या निम्न होना चाहिए?
 -कम 

95.) भारत में सबसे बड़ा गुरुद्वारा है?
- अमृतसर में गोल्डेन मंदिर 

96.) संयुक्त राष्ट्र संगठन (यूएनओ) का मुख्यालय किस देश में है? 
-यूएसए (न्यूयॉर्क में)

 97.) उपकरण जो पानी के नीचे एक पनडुब्बी से पानी की सतह पर वस्तुओं को देखने के लिए प्रयोग किया जाता है कहा जाता है?
 -Periscope 

98.) जी -15 का आर्थिक समूह है?
 - तीसरे विश्व राष्ट्र

 99. बच्चों में पिट्यूटरी ग्रंथि से अत्यधिक स्राव के परिणामस्वरूप?
 - बढ़ी ऊंचाई 

100.) व्यक्तिगत रूप से दो नोबेल पुरस्कार जीतने वाले एकमात्र व्यक्ति कौन हैं?
 -डॉ। लिनस पॉलिंग

Most Important 100 One Liner Question's for SSC CGL-2018

Most Important 100 One Liner Question's for SSC CGL-2018

Hello Reader's Today We are Posting 100 Most ImportantGeneral Knowledge  Question's For SSC CGL-2018. These Question's are Mixture of all Parts of General Knowledge means It contains Hisory, Polity,  Science, Geography, Economics, Current Affairs and all other Important Parts like Books and authors ,Important Days, etc.
IF you wants to download these Question's as PDF you can dowload it from the Print and PDF link given below the Related Posts.

 1.)In which city is the Netaji Subhash National Institute of Sports situated?

 -Patiala

2.)Which religious teacher established four maths in four corners of country at Badrinath (North), Dwarka(West), Puri (East) & Sringeri (South)?
    -Adi Shankaracharya

3.)Who is considered as the father of Mobile Phone?
-Martin Cooper

4.)Gayatri Mantra is addressed to which Hindu god?
-Surya

5.)Which element is necessarily present in all acids?
-Hydrogen

6.)Who authored the book `Business at the speed of thought' ?
-Bill Gates

7.)Which organ in the human body produces Bile?
-Liver

8.Diamond and Graphite are allotropes of which element?
-Carbon

9.)Who is the only Indian cricketer to have taken all 10 wickets in a Test innings?
-Anil Kumble

10.)What is the minimum age limit to become the President of India?
-35 years

11.)Who created fictional character Harry Potter?
-J.K.Rowling

12.)Deficiency of which vitamin causes Scurvy?
-Vitamin-C

13.)Which constituent of human blood is responsible for blood clotting?
-Platelets(Thrombocytes)

14.)Which was the first country to give women the right to vote in elections?
-New Zealand

15.)According to Hindu mythology, twin sisters Riddhi and Siddhi are wives of which God?
-Ganesh

16.)Which scientist was known as 'Wizard of Menlo Park'?
-Thomas Alva Edison

17.)On 6th April 1909, who became the first person to reach the North Pole?
-Robert Edwin Peary

18.What is the name of India's first nuclear reactor?
-Apsara

19.)Which Mughal emperor assumed the title of 'Alamgir'-Conqueror of the world?
-Aurangzeb

20.)At which place did Mahatama Gandhi start his first Satyagraha in India?
-Champaran in Bihar


21.)When an ant bites a person, which irritating chemical it injects?
-Formic acid

22.)In the 8th Schedule of the Indian Consitution, how many languages have been officially recognised?
-22

23.
Even though India became independent in 1947 but Daman and Diu remained a European colony till
1961. Which country ruled over it?
-Portugal

24.)Headquarters of the International Civil Aviation Organisation (ICAO) is in?
-Montreal (Canada)

25.)With which sport is the Duckworth-Lewis Method associated?
-Cricket

26.)What is the normal heart rate of adults at rest?
-72 beats per minute

27.)Kailash Temple at Ellora in Maharahstra was built by the rulers of which dynasty?
-Rashtrakuta

28.)What is the interest rate at which banks borrow money from Reserve Bank of India (RBI) called?
-Repo Rate

29.)International Date Line, an imaginary line where date changes as one travels east or west across it, passes through which longitude?
-180 degree

30.)Who wrote the famous essay 'Unto This Last', which was later translated into Gujarati by Mahatma Gandhi under the title of 'Sarvodaya'?
-John Ruskin

31.)Headquarters of Central Railway is in?
-Mumbai

32.)Wheeler Island, the site of India's missile testing facility Integrated Test Range (ITR), is situated in which state?
-Orissa

33.)To whom does the President of India address his resignation?
-Vice-President

34.
Apart from Russia, the territory of which country lies in both Europe and Asia continents?
-Turkey

35.)Who is known as the 'Father of Medicine'?
-Hippocrates

36.)After Hindi, which is the second most spoken language in India?
-Bengali

37.)The Khyber Pass, a strategic mountain pass between Central Asia and South Asia, connects
Pakistan to which country?
-Afghanistan

38.)On 29 August 1988, which Indian lady became the first woman in the world to swim across the Straits of Gibraltar?
-Aarti Pradhan

39.Who was the first President of Pakistan?
-Iskandar Mirza

40.)Which early 11th century traveller to India authored the books 'Tahqiq-i-Hind' and 'Kitab-ul-Hind'?
-Al Beruni

41.)To preserve the filaments at high temprature, which gas is filled in the electric bulbs?
-Argon

42.)'The Four Noble Truths' and 'Noble Eightfold Path' are the cornerstones of which religion?
-Buddhism

43.)What is the chemical name of Baking Soda?
-Sodium Bicarbonate

44.)What is the chemical name of Washing Soda?
Sodium Carbonate

45.)From which Indian ruler did the Britishers aquire the Kohinoor diamond?
-Dalip Singh

46.)'Gyandarshan' is an educational TV channel of which Indian open university?
-IGNOU

47.)Which city annually hosts the Wimbledon tennis championship, one of the four Grand Slam tennis tournaments?
-London

48.)Which European country is also known as the 'Land of the Midnight Sun'?
-Norway

49.)The India receives its major rainfall from which monsoon?
-South-West Monsoon

50.)How many years does the US President serve during one term?
-4 years

51.)Bamboo is tree, weed or grass?
-Grass

52.)Which straits connect India to Sri Lanka?
-Palk Straits

53.)Headquarter of Zoological Survey of India is at?
-Kolkata

54.)In which article of the Indian Constitution the word 'Minority' appears?
-Article 29

55.)University of Nalanda and Vikramsila were destroyed by?
-Bakhtiyar Khilji

56.)Which emperor propaged the idea of 'Sulahkul'?
-Akbar

57.)The nickname 'seven-sisters' has been given in India to?
-7 North-Eastern States

58.As per the latest estimates of the planning commission the poverty ratio in 2011-2012 in India is?
-21.9%

59.)Human blood is viscous in nature due to the presence of?
-Protein in blood

60.)pH value of pure water is?
-7

61.)The Alps are the most highest and extensive mountain range system that lies entirely in?
-Europe

62.)Which mineral is used to make the Plaster of Paris?
-Gypsum

63.)The most spoken language in the world is?
-Mandarin

64.)Rickets is caused due to the deficiency of which vitamin?
Vitamin-D

65.)World's longest railway platform is in which state?
-West Bengal (Kharagpur)

66.Which planet in the Solar System is named after the Roman god of agriculture and harvest?
-Saturn

67.)Who is the first batsman in international cricket to hit 6 six in an over?
-Herschelle Gibbs (South Africa)

68.)Which is the only continent through which all longitude lines passes?
-Antarctica

69.)The first indigenous civilian aircraft of India is?
-Saras

70.)Who was the first human to walk in space?
-Alexei Leonov-Russia

71.)First Indian to be appointed as the Governor of the Reserve Bank of India (RBI) was?
-C.D. Deshmukh in 1943

72.Which Mauryan ruler defeated Alexander's general Seleucus Nicator and received the territories of
Kabul and Balochistan?
-Chandragupta Maurya in 305 BC

73.)Who was also known as the 'Saint of the Gutters'?
-Mother Teresa

74.)Oldest mountain range in India is?
-Aravali range

75.)The capital of USA, Washington D. C. is located on the banks of which river?
-Potomac

76.)Highest mountain peak of North America is?
-Mount McKinley

77.)Which hormone is also known as Emergency hormone?
-Adrenaline

78.)Which Indian freedom fighter gave the slogan 'Dilli Chalo'?
-Subhas Chandra Bose
79.)Who is the only President of India to be elected unopposed?
-Neelam Sanjiva Reddy

80.How many bones are there in the adult human skeleton?
-206 bones

81.Who propounded the 'Theory of Relativity'?
-Albert Einstein

82.)In 15th century, which Italian traveller visited the Vijayanagar empire?
-Nicolo de Conti

83.)Minimum age limit to become the Governor of a state in India?
-35 years

84.)Which Sikh guru developed the Gurumukhi script?
-Guru Angad

85.)Which place recently becomes the 9th Indian reserve in UNESCO world network list?
-Great Nicobar Biosphere Island reserve

86.)Who conducted the first human heart transplant operation in the world?
-Dr. Christian Bernard

87.)First China War was fought between whichcountries?
-China and Britain

88.) World Red Cross is celebrated on?
-May 8

89.)Film and TV Institute of India is located at which place?
-Pune

90.)Which layer of the atmosphere restricts the Ultra-violet radiation?
-Ozone layer

91.)Full form of DRDO is?
-Defence Research and Development Organisation

92.)Who was the first Indian Chief of Army Staff of the Indian Army?
-Gen. K.M. Cariappa

93.)What is the full form of GATT?
-General Agreement on Tariffs and Trade

94.The melting point of fuse wire should be high or low?
-Low

95.Largest Gurudwara in India is?
-Golden Temple in Amritsar

96.)Headquarter of United Nation Organisation (UNO) is in which country?
-USA (at New York)

97.)The instrument which is used for seeing objects at the surface of water from a submarine under water is called?
-Periscope

98.)G-15 is an economic grouping of?
-Third World Nations

99.Excessive secretion from the pituitary gland in the children results in?
-Increased height

100.)Who is the only person to have won two Nobel prizes individually?
-Dr. Linus Pauling

Important Vocabulary for SSC CGL-2018

Important Vocabulary for SSC CGL-2018

 Hello Readers, Today we are uploading 15 Most important Vocab's for SSC CGL-2018.
These Vocab's are found from Previous year paper's and from other exams held in 2018, these are most important because these vocab's are asked in many exams again and again.So there are a lot of chances that SSC can ask these vocab's in CGL-2018.


1.) FLORID:- चमकीला (reddish)

2.)PERSPICUITY:- स्पष्टता (clearness of style or exposition)

3.)VERITY:- हक़ीक़त (a true principle or belief, especially one of fundamental importance.)

4.)FERVENT:- उत्सुक (having or displaying a passionate intensity.)

5.)MEANDERING:- घुमावदार (twisty)

6.)LUXURIANT:- आनंदपूर्ण ( rich and profuse in growth; lush)

7.)CANTANKEROUS:- चिड़चिड़ा (bad-tempered, argumentative, and uncooperative.)

8.)ONUS:- दायित्व (something that is one's duty or responsibility.)

9.)DERISION:- जिस पर हंसी हो (contemptuous ridicule or mockery.)

10.) TRITE:- घिसा-पिटा ( lacking originality or freshness; dull on account of overuse.)

11.) DOLOROUS :-दुःखी (feeling or expressing great sorrow or distress.)

12.)EMBARK:- शुरुआत करना (begin, commence, undertake, set about, enter on, go into, take up)

13.) EXTEMPORE:- बिना तैयारी के (impromptu, spontaneous, unscripted)

14.)GROTESQUE:- भद्दा (malformed, deformed, misproportioned, distorted, mangled, mutilated)

15.)JEOPARDY:- ख़तरा (danger, peril)

IIT Jam Mathmatics Notes

To Download the PDF please click on the Download Link given below:

Padma Awards -2018

Hello friends, today we are going to share the list of Padma Award winners in 2018. Its not too much important but there is only 85 names and there are chances that examiner can ask a question from this topic.So it will be good if you take a look on this list.

 Total  85 Padma Awards
 The list comprises 3 Padma Vibhusan
 9 Padma Bhusan And
73 Padam Shri Awards

Simple and Compound Interest Tricks - 1

Simple and Compound Interest Tricks - 1

 

After reading this series (Part-1 and Part-2), you will be able to solve all the questions that are asked by SSC from this topic.

(1) The basic concept of CI and SI
Let's say you have Rs. 30000 and you keep this money in three different banks for 2 years(Rs. 10000 each). The three banks have different policy :
a) Bank A keeps your money at simple interest and offers you 5% interest
b) Bank B keeps your money at compound interest and offers you 5% interest. The interest is compounded annually.
Bank C keeps your money at compound interest and offers you 5% interest. The interest is compounded half-yearly.
After 2 years, which bank will give you most interest?
Let us calculate
Case (A)
Simple interest is calculated simply as (P*R*T)/100
Here P= 10000, r = 5% and T = 2 years
T = 2 years. Let's divide this period in two equal intervals of 1 year each
Hence SI received for the period 0 to 1 = 10000*5*1/100 = Rs. 500
SI received for the period 1 to 2 = 10000*5*1/100 = Rs. 500
So after 2 years, you will get Rs. 10000 + 500 + 500 = Rs. 11000
Note : Simple Interest is proportional. The interest received is same each year. So in the above example where SI was Rs. 500 for 1 years, that will mean the SI for 3 years is Rs. 1500, the SI for 5 years is Rs. 2500 and so on.

Case (B)
Compounded annually means whatever interest you will earn on first year, that interest will be added to the principal to calculate the interest for 2nd year. Let us see how
We know the CI formula is, Amount = P(1 + r/100)^t   (where Amount = P + CI)
CI received for the period 0 to 1 = Amount - Principal = 10000(1 + 5/100)^1 - 10000= Rs. 500
Now the amount received after 1 year will act as the Principal for calculating the Amount for next year
For calculating the amount for second year, you won't take P as 10000, but as Rs. 10500. So unlike SI where the interest was same each year, in CI the interest increases every year (because the principal increases every year)
CI received for the period 1 to 2 = Amount - Principal = 10500(1 + 5/100)^1 - 10500 = Rs. 525
Total interest received after two years = Rs. 500 + Rs. 525 = Rs. 1025
Total amount received after two years = Rs. 11025
Note :  In Case (b), to calculate the amount received after 2 years, I had divided the calculation into 2 intervals. It was done just for the sake of explanation. You can calculate the amount received after 2 years directly by 10000(1 + 5/100)^2

Case (C)
Just like case (b), where Principal was getting updated every year, in case (c) we will update the Principal every 6 months (half-year)
Since I have given the explanation in case (b), so in this case I will directly apply the formula
Amount received after 2 years = 10000(1 + 2.5/100)^4 = Rs. 11038 approx.

So sum it up
Case A - amount received after two years= Rs. 11000
Case B - amount received after two years= Rs. 11025
Case C - amount received after two years= Rs. 11038

Case C is giving the maximum return and rightly so because in Case (C) principal is increasing every 6 months.

Important formulas for Compund Interest - 

(2) A sum of money becomes x times in T years. In how many years will it become y times?

The approach to solve such questions is different for SI and CI

For SI : Formula = [(y - 1)/(x - 1)] * T
Q. 1) A sum of money becomes three times in 5 years. In how many years will the same sum become 6 times at the same rate of simple interest?
Solution : [(6 - 1)/(3 - 1)] * 5 = 5/2 * 5 = 12.5 years
Answer : 12.5 years

For CI : Formula = (logy/logx) * T
Now dont worry, I wont be asking you to study logarithms :)
But just remember one property of logs and that is enough to solve the questions
log(x ^y) = y.log(x)
Hence log(8) = log(2³) = 3.log(2)
Q. 2) A sum of money kept at compound interest becomes three times in 3 years. In how many years will it be 9 times itself?
Solution : (log9/log3) * 3         ... (1)
log9 = log(3²) = 2.log(3)
Put this value in (1)
= 2.log(3)/log(3) * 3
= 2 * 3 = 6 years
Answer : 6 years

(3) Interest for a number of days

Q. 3)

Here P = 306.25
R = 15/4 %
T = Number of days/365
Number of days = Count  the days from March 3rd to July 27th but omit the first day, i.e., 3rd March
   = 28 days(March) + 30 days(April) + 31 days(May) + 30 days(June) + 27 days(July)
   = 146 days
We know SI = (P * r * t)/100

Answer : Rs. 4.59

(4) Annual Instalments
This is the most dreaded topic of CI-SI. Before giving you the direct formula, I would like to tell you what actually is the concept of annual instalments(if you only want the formula and not the explanation, you can skip this part. But I would like you to read it)
Suppose you want to purchase an iPhone and its price is Rs. 100000 but you dont have Rs. 1 lakh as of now. What would you do? You have two options - either you can sell your kidney (which most the iphone buyers do :D), or you can go for instalments. But if you want to buy the iPhone through this instalment route, the seller will incur a loss. How? Had you paid Rs. 1 lakh in one go, the seller would have kept that money in his savings account and earned some interest on it. But you will pay this Rs. 1 lakh in instalments and that means the seller will get his Rs. 1 lakh after several years. So the seller is incurring a loss. The seller will compensate for this loss and will charge interest from you.

Let the annual instalment be Rs. x. and you pay it for 4 years.

After 1 year you will pay Rs. x and the seller will immediately put this money in his savings account (or somewhere else) to earn interest. He will earn interest on this Rs. x at the rate of r% for 3 years (because the total duration is 4 years and 1 year has already passed)

Hence the amount which the seller will get from this Rs. x instalment = x(1 + r/100)^3

After 2nd year, you will again pay Rs. x and the seller will earn interest on this Rs. x for 2 years.

The amount which the seller will get from this Rs. x instalment = x(1 + r/100)^2

After 3rd year, you will again pay Rs. x and the seller will earn interest on this Rs. x for 1 year.

The amount which the seller will get from this Rs. x instalment = x(1 + r/100)^1

After 4th year, you will pay Rs. x and your debt would be paid in full (no interest on this Rs. x)

The amount which the seller will get from this Rs. x instalment = x

Now let's add all the above four amounts to get the total amount the seller would get from all the instalments =
x(1 + r/100)^3 + x(1 + r/100)^2 + x(1 + r/100)^1 + x     ... (1)

Now, had you paid Rs. 1 lakh in one go (without going for the instalment route), then the amount received by the seller after 4 years would have been = 100000(1+r/100)^4      ... (2)

Now (1) should be equal to (2) because only then the two routes (instalment route and direct payment route) will give the same return and seller would have no problem in giving you the iPhone in instalments.

100000(1+r/100)^4 = x(1 + r/100)^3 + x(1 + r/100)^2 + x(1 + r/100)^1 + x  
[Remember the above equation for solving questions of compound interest]

P + P*r*4/100 = (x + x*r*3/100) + (x + x*r*2/100) + (x + x*r*1/100) + x  
[Remember the above equation for solving questions of simple interest]

Although for Simple Interest, we have a direct formula-
The annual instalment value is given by-

Now coming to the questions. There are two types of questions and they are bit confusing. In one type, the Amount is given and in another type, Principal is given

Type 1(Amount is given):

Q. 4) What annual installment will discharge a debt of Rs.6450 due in 4 years at 5% simple interest?
When the language the question is like "what annual payment will discharge a debt of ...", it means the Amount is given in the question.
In this question, the Amount(A) is given, i.e., Rs. 6450. So we can apply the formula directly
Here A = 6450, r = 5%, t = 4 years
Solution : 100*6450/[100*4 + 5*4*3/4]
Answer : 1500

Type 2 (Principal is given) :

Q. 5) A sum of Rs. 6450 is borrowed at 5% simple interest and is paid back in 4 equal annual installments. What is amount of each installment?

Here the sum is given. Sum means Principal.
But our formula requires Amount(A)
So we will calculate Amount from this Principal
A = P + SI = 6450 + 6450*5*4/100 = Rs. 7740

Now put the values in the formula
A = 7740, r = 5%, t = 4
Annual instalment = 100*7740/(100*4 + 5*4*3/2)

Answer : Rs. 1800

Q. 6) 

"Sum borrowed" means Principal.
This question is of Compound Interest and hence we cant apply the direct formula. We will solve this question with the help of the equation we derived earlier.

P(1+r/100)^2 = x(1+r/100) + x

P(1 + 5/100)^2 = 17640(1 + 5/100) + 17640

Solve for P, you will get P = Rs.32800
Answer : (B)

Q. 7) What annual instalment will discharge a loan of Rs. 66000, due in 3 years at 10% Compound Interest?
Solution : Here again the question is of "Compound Interest" and hence we will solve it by equation :
Let each annual instalment be of Rs. x. Note that in this question, amount is given
Amount = x(1 + 10/100)^2 + x(1 + 10/100)^1 + x
66000 = x (1.21 + 1.1 + 1)
So x = Rs. 19939.58

Q. 8) What annual instalment will discharge a loan of Rs. 66000, due in 3 years at 10% Simple Interest?
I have just converted Q.7 into Simple Interest
Now we can either solve it by direct formula, or by equation
By Equation method :
66000 = (x + x*10*2/100) + (x + x*10*1/100) + x
66000 = x(3 + 0.2 + 0.1)
x = Rs. 20000
By Direct formula method :
A = 66000, t = 3, r = 10%
x = 100A/[100t + t(t-1)r/2]
x = 100*66000/[100*3 + 3*2*10/2]
x = 6600000/(300 + 30)
x = Rs. 20000
Don't forget to read Part - 2

•   Simple and Compound Interest Part-2

If you have any doubt Please Drop a comment...

Simple and Compound Interest Tricks - 2

Simple and Compound Interest Tricks - 2

 

Please Check Part-1 Before Reading Part-2

• Simple and Compound Interest Part- 1

In this post I will give some extremely important formulas that will save your time. Read this post carefully and note down all the formulas in a piece of paper for quick revision.

Q. 1) If a sum of money becomes 3 times itself in 20 years at simple interest. What is the rate of interest?
In such questions apply the direct formula-
Rate of interest = [100*(Multiple factor - 1)]/T
So R = 100*(3 - 1)/20
Answer : 10%
Note : With this formula you can find Rate if Time is given and Time if rate is given.

Q. 2) 

In such questions, just write this line :
1st part : 2nd part : 3rd part = 1/(100+T1 * r) : 1/(100+T2 * r) : 1/(100+T3 * r)
 = 1/(100+2 * 5) : 1/(100+3 * 5) : 1/(100+4*5)
 = 1/110 : 1/115 : 1/120
 = 23*24 : 22*24 : 23*22
Hence 1st part = (23*24)/ (23*24 + 22*24 + 23*22) * 2379
Answer : 828
Note : Surprisingly, such questions when asked mostly have this same data, i.e., R=5% and T1, T2, T3 = 2, 3, 4 years, respectively. Only the Principal is changed. So it would be wise if you can just mug this line :
1st part : 2nd part : 3rd part = 23*24 : 22*24 : 23*22
Based on the above line, you would be able to solve such questions in a jiffy. 
But note that it will only work if the question is on Simple Interest. Like the below question appeared in SSC CGL Tier 2-

Q. 4

Here the data is same. i.e., R=5% and T1, T2, T3 = 2, 3, 4 years, respectively. So we will write directly -
1st part : 2nd part : 3rd part = 23*24 : 22*24 : 23*22
A received = (23*24)/ (23*24 + 22*24 + 23*22) * 7930
Answer : Rs. 2760

Q. 5) If a certain sum of money P lent out for a certain time T amounts to P₁ at R₁% per annum and to P₂ at R₂% per annum, then

The above formula is for calculating the Time, if the question asks the rate, then just interchange the rate and time. Hence the formula will become

R = (P_{1 -} P_2)*100/P₂T_{1 -} P₁T₂

Apply the formula:
R = (650-600)*100/600*6 - 650*4
R = 5%

Alternative Method :

You can solve such questions quickly without mugging the above formula. How?

The sum amounts to Rs. 600 in 4 years and Rs. 650 in 6 years. This means the simple interest is Rs. 50 for 2 years (because the amount increased from Rs. 600 to Rs. 650 in 2 years)

So the SI for 4 years is Rs. 100 (we have seen earlier than SI is proportional. So if SI = 100 for 2 years, then SI = 150 for 3 years, SI = 250 for 5 years and so on)

Now SI = Rs. 100; P = 600-100 = Rs. 500; t = 4 years

R = 100*SI/(P*t) = 10000/2000

Answer: 5%

For CI, the formula is different

Difference between CI and SI

This topic is very important from examination point of view. Note the following things-

If t=1 year, then SI = CI

If t=2 years then difference between CI and SI can be given by two formulas-

 If t=3 years then difference between CI and SI can be given by two formulas-

In all the above formulas we have assumed that the interest is compounded annually

Let us solve some CGL questions

Q. 6

A = P(1+r/100)^t

Given, A=1.44P t = 2 years

1.44P = P(1 + r/100)^2

r = 20%

Answer : (D)

Q. 7

Here the interest is compounded half yearly, so the formulas we mugged earlier are of no use here. We will have to solve this question manually

SI = P*10*1.5/100 = 0.15P

CI = P(1 + 5/100)^3 - P = P(1.05^3 - 1)

Given CI - SI = 244

P(1.05^3 - 1) - 0.15P = 244
P = Rs. 32000

Answer : (C)

Q. 8

Time = 2 years

Hence apply the formula: Difference(D) = R*SI/200

CI - SI = R*SI/200

CI - SI = (12.5/200)*SI

510 = 1.0625*SI    [Since CI = Rs. 510]

SI = Rs. 480

Answer : (D)

       Q. 9

CI for 1st year = 10% of 1800 = Rs. 180

CI for 2nd years = 180 + 10% of 180 = Rs. 198

Total = 180+198 = Rs. 378

Hence time = 2 years

Or you can apply the formula

A = P(1+r/100)^t

Answer : (B)

Q. 10

2.5 = P*R*2/100 - P*r*2/100
2.5 = 10R - 10r
R - r = 0.25
Answer : (D)

       Q. 11

CI for 1st year = 5% of P = 0.05P

CI for 2nd year = 5% of P + 5% of (5% of P) = 0.05P + 0.0025P = 0.0525P

Total CI = 0.05P + 0.0525P = 0.1025P

Given, 0.1025P = 328

P = Rs. 3200

Answer : (C)

Note : You can solve this question by the formula A = P(1+r/100)^t as well

Q. 12

Note that in this question the CI for 2 years in not given, but the CI for the 2nd year is given.

CI for 2nd year = 10% of P + 10% of (10% of P) = 0.1P + 0.01P = 0.11P

Given, 0.11P = 132

P = Rs. 1200

Answer : (D)

Q. 13

Interest = Re. 1 per day = Rs. 365 for 1 year

SI = P*r*t/100

t=1, r=5%, SI = Rs. 365

So, P = 365*100/5 = Rs. 7300

Answer : (A)

Q. 14

We know 

Difference = P(r/100)^2(r/100 + 3)

P = Rs. 10000, r = 5%, t = 3 years

Hence D = Rs. 76.25

Answer : (C)

Q. 15

We know, R = [(y/x)^(1/T2 - T1) - 1]*100

 = [(1587/1200)^1/(3 - 1) - 1]*100

 = [(1587/1200)^1/2 - 1]*100

 = 3/20 * 100

 = 15%

Answer : (B)

So this is the end of CI and SI series. If you have any doubt in this topic, please drop a comment...