arithmetic,

(α+в+¢)²= α²+в²+¢²+2(αв+в¢+¢α)
1. (α+в)²= α²+2αв+в²
2. (α+в)²= (α-в)²+4αв b
3. (α-в)²= α²-2αв+в²
4. (α-в)²= f(α+в)²-4αв
5. α² + в²= (α+в)² - 2αв.
6. α² + в²= (α-в)² + 2αв.
7. α²-в² =(α + в)(α - в)
8. 2(α² + в²) = (α+ в)² + (α - в)²
9. 4αв = (α + в)² -(α-в)²
10. αв ={(α+в)/2}²-{(α-в)/2}²
11. (α + в + ¢)² = α² + в² + ¢² + 2(αв + в¢ + ¢α)
12. (α + в)³ = α³ + 3α²в + 3αв² + в³
13. (α + в)³ = α³ + в³ + 3αв(α + в)
14. (α-в)³=α³-3α²в+3αв²-в³
15. α³ + в³ = (α + в) (α² -αв + в²)
16. α³ + в³ = (α+ в)³ -3αв(α+ в)
17. α³ -в³ = (α -в) (α² + αв + в²)
18. α³ -в³ = (α-в)³ + 3αв(α-в)
ѕιη0° =0
ѕιη30° = 1/2
ѕιη45° = 1/√2
ѕιη60° = √3/2
ѕιη90° = 1
¢σѕ ιѕ σρρσѕιтє σƒ ѕιη
тαη0° = 0
тαη30° = 1/√3
тαη45° = 1
тαη60° = √3
тαη90° = ∞
¢σт ιѕ σρρσѕιтє σƒ тαη
ѕє¢0° = 1
ѕє¢30° = 2/√3
ѕє¢45° = √2
ѕє¢60° = 2
ѕє¢90° = ∞
¢σѕє¢ ιѕ σρρσѕιтє σƒ ѕє¢
2ѕιηα¢σѕв=ѕιη(α+в)+ѕιη(α-в)
2¢σѕαѕιηв=ѕιη(α+в)-ѕιη(α-в)
2¢σѕα¢σѕв=¢σѕ(α+в)+¢σѕ(α-в)
2ѕιηαѕιηв=¢σѕ(α-в)-¢σѕ(α+в)
ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв.
» ¢σѕ(α+в)=¢σѕα ¢σѕв - ѕιηα ѕιηв.
» ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв.
» ¢σѕ(α-в)=¢σѕα¢σѕв+ѕιηαѕιηв.
» тαη(α+в)= (тαηα + тαηв)/ (1−тαηαтαηв)
» тαη(α−в)= (тαηα − тαηв) / (1+ тαηαтαηв)
» ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв)
» ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα)
» ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв.
» ¢σѕ(α+в)=¢σѕα ¢σѕв +ѕιηα ѕιηв.
» ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв.
» ¢σѕ(α-в)=¢σѕα¢σѕв+ѕιηαѕιηв.
» тαη(α+в)= (тαηα + тαηв)/ (1−тαηαтαηв)
» тαη(α−в)= (тαηα − тαηв) / (1+ тαηαтαηв)
» ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв)
» ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα)
α/ѕιηα = в/ѕιηв = ¢/ѕιη¢ = 2я
» α = в ¢σѕ¢ + ¢ ¢σѕв
» в = α ¢σѕ¢ + ¢ ¢σѕα
» ¢ = α ¢σѕв + в ¢σѕα
» ¢σѕα = (в² + ¢²− α²) / 2в¢
» ¢σѕв = (¢² + α²− в²) / 2¢α
» ¢σѕ¢ = (α² + в²− ¢²) / 2¢α
» Δ = αв¢/4я
» ѕιηΘ = 0 тнєη,Θ = ηΠ
» ѕιηΘ = 1 тнєη,Θ = (4η + 1)Π/2
» ѕιηΘ =−1 тнєη,Θ = (4η− 1)Π/2
» ѕιηΘ = ѕιηα тнєη,Θ = ηΠ (−1)^ηα

1. ѕιη2α = 2ѕιηα¢σѕα
2. ¢σѕ2α = ¢σѕ²α − ѕιη²α
3. ¢σѕ2α = 2¢σѕ²α − 1
4. ¢σѕ2α = 1 − ѕιη²α
5. 2ѕιη²α = 1 − ¢σѕ2α
6. 1 + ѕιη2α = (ѕιηα + ¢σѕα)²
7. 1 − ѕιη2α = (ѕιηα − ¢σѕα)²
8. тαη2α = 2тαηα / (1 − тαη²α)
9. ѕιη2α = 2тαηα / (1 + тαη²α)
10. ¢σѕ2α = (1 − тαη²α) / (1 + тαη²α)
11. 4ѕιη³α = 3ѕιηα − ѕιη3α
12. 4¢σѕ³α = 3¢σѕα + ¢σѕ3α
🍄🍄🍄🍄🍄
» ѕιη²Θ+¢σѕ²Θ=1
» ѕє¢²Θ-тαη²Θ=1
» ¢σѕє¢²Θ-¢σт²Θ=1
» ѕιηΘ=1/¢σѕє¢Θ
» ¢σѕє¢Θ=1/ѕιηΘ
» ¢σѕΘ=1/ѕє¢Θ
» ѕє¢Θ=1/¢σѕΘ
» тαηΘ=1/¢σтΘ
» ¢σтΘ=1/тαηΘ
» тαηΘ=ѕιηΘ/¢σѕΘ

Daily GK Update 25th and 26th June 2017

1. International Day Against Drug Abuse and Illicit Trafficking: 26 June

i. By resolution 42/112 of 7 December 1987, the General Assembly decided to observe 26 June as the International Day against Drug Abuse and Illicit.
ii. The theme for 2017 is- "Listen First - Listening to children and youth is the first step to help them grow healthy and safe."

Important Takeaways from Above-

• Antonio Guterres is the ninth United Nations Secretary-General.
• UN Headquarters in New York, The USA.

2. India, Portugal sign 11 MoUs across various fields

i. India and Portugal have signed eleven MOUs for cooperation in areas including double taxation avoidance, science and technology, trade and investment, nanotechnology, space research, administrative reforms and culture.
ii. 11 MoU's were exchanged in the meeting and there was the announcement of the launch of a joint science fund for which both India and Portugal will contribute Euros two million each. 5 of the MoU's were in the area of science and technology.

Important Takeaways from the above News:

• Lisbon is Capital city of Portugal.
• The currency of Portugal is Euro.
• Antonio Guterres is Secretary-General of the United Nations and former Prime Minister of Portugal.
• Marcelo Rebelo de Sousa is present president of Portugal.
• Antonia Costa is present Prime Minister of Portugal.

3. Manushi Chhillar from Haryana wins the title of Miss India 2017

i. The 54th Femina Miss India World 2017 winner is Manushi Chhillar from Haryana, while the first runner-up is Sana Dua from Jammu and Kashmir and the second runner-up is Priyanka Kumari from Bihar.

ii. The event was held at Yash Raj Studios in Mumbai. This is the first time the participants wore an Indian dress at the finale designed by Manish Malhotra. The show was hosted by Karan Johar and Riteish Deshmukh. Besides,

Important Takeaways from News-

• Reita Faria was the first Miss India ever to win any international beauty pageant.
• Miss World 2016 was Stephanie Del Valle.

4. Doon girl Bhumika Sharma wins Miss World title in bodybuilding championship

i. Bhumika Sharma, another Indian has become Miss World in bodybuilding championship.

ii. Dehradun’s girl gained maximum points in three categories – individual posing, body posing and fall in that eventually bagged her the Miss World title and the gold medal at the world championship in Venice, Italy. The championship drew 50 competitors from different countries.

5. Aadhaar not valid for travel to Nepal, Bhutan: Home ministry

i. Aadhaar is not a valid identification document for Indians traveling to Nepal and Bhutan, according to the Union home ministry. Indians can travel to Nepal and Bhutan- both countries for which they don't need visas - if they possess a valid national passport or election ID card issued by the Election Commission.

ii. Moreover, to ease travel, persons over 65 and below 15 years can show documents with photographs to confirm their age and identity. These include PAN card, driving licence, Central Government Health Service (CGHS) card and ration card but not Aadhaar. The move is aimed at ensuring hassle-free movement of Indians going abroad. 

Important Takeaways from Above News-

• Nepal shares borders with 5 Indian states- Sikkim, West Bengal, Bihar, Uttar Pradesh and Uttarakhand. 
• Bhutan shares borders with 4 Indian States- Sikkim, Assam, Arunachal Pradesh and West Bengal.

6. IDFC Bank elevates Sunil Kakar as MD and CEO for 3 Years

i. IDFC Ltd announced the elevation of its CFO Sunil Kakar as the Managing Director and Chief Executive Officer of the company with effect from July 16 for three years.
ii. Mr. Kakar has also been appointed as additional director. Both the appointments are subject to shareholders' approval at the annual general meeting (AGM).

iii. Besides, the company announced that the Board has approved the resignation of veteran banker Vikram Limaye from the post of MD and CEO who is set to join leading stock exchange NSE as its new Managing Director and CEO. 

Important Takeaways from Above News-

• Vikram Limaye is a member of a panel appointed by the Supreme Court to administer the Board of Control for Cricket in India (BCCI). 
• Headquarter of IDFC Bank is in Mumbai.

7. Team India create world record for most 300-plus scores in ODIs

i. India became the team to score the most 300-plus totals in One Day International (ODI) Cricket. India did so when they scored a total of 310 for the loss of five wickets in the second ODI against West Indies.

ii. It was the 96th time that India crossed the 300-run mark, surpassing Australia’s 95.

iii. The other teams posted 300+ scores in ODIs as follows: Australia 95, South Africa 77, Pakistan 68, Sri Lanka 62, England 57 and New Zealand 51.

Important Takeaways from Above News-

• The International Cricket Council is the international governing body of cricket.
• Chairperson of ICC is Mr. Shashank Manohar.
• ICC Headquarters in Dubai, United Arab Emirates.

8. Ankush claims gold, Devendro gets silver at Mongolia boxing tournament

i. The fast-rising Ankush Dahiya (60kg) clinched a gold while the experienced L Devendro Singh (52kg) settled for a silver medal on the final day of the Ulaanbaatar Cup boxing tournament in Mongolia.

ii. The 19-year-old Ankush, who is a former Asian youth silver-medalist, defeated Korean Man Choe Chol in a split verdict, while Devendro lost to Indonesia's Aldoms Suguro, again a split decision. India thus signed off with a gold, a silver and three bronze medals from the tournament.

Important Takeaways from Above News-

• Ulaanbaatar is the Capital of Mongolia. 
• Its currency is Mongolian togrog.

9. Anish Bhanwala set a junior world record at World Championship

i. Haryana's Anish Bhanwala gave a robust start for the Indian challenge by clinching the 25-metre standard pistol gold with a world junior record in the Junior World Shooting Championship in Suhl, Germany.
ii. The 14-year-old Anish shot 579 to win the gold seven points ahead of Florian Peter of Germany. In the process, Anish also bettered the junior world record of 574 set by Denis Koulakov of Russia in Lahti, Finland, in 2002.

10. Kidambi Srikanth wins Australia Open Super Series

i. In Badminton, ace Indian shuttler Kidambi Srikanth has lifted the Australian Open Superseries trophy in Sydney. In the summit clash, 11th world ranked Srikanth stunned former world number one and Rio Olympics Gold medalist Chen Long of China in straight games, 22-20, 21-16.
ii.  It was Srikanth's first victory over the Chinese in 6 matches.

iii. The trophy is Srikanth's second this season and fourth overall. He had won the Indonesian Open last week.

11. Naidu launches book titled ‘The Emergency-Indian Democracy’s Darkest Hour'

i. Venkaiah Naidu has launched the book which titled 'The Emergency - Indian Democracy’s Darkest Hour'.

ii. A book is written by Surya Prakash who is a chairman of Prasar Bharati.
iii. The book was launched at a conference to mark the anniversary of the Emergency and to honor all those who fought for the restoration of democracy in the country in the mid-1970s.

Important Takeaways From Above News-

• 25 June marks the anniversary of Indian Emergency.

*అర్థమేటిక్ (క్యాలెండర్)*

*అర్థమేటిక్ (క్యాలెండర్)*
➖➖➖➖➖➖➖➖
*ఏదైనా సాదారణ సంవత్సరంలో మొత్తం 365 రోజులు ఉండును.
52 వారాలు+1రోజు అదనపు రోజు
*ఏదైనా ఒక లీపు సంవత్సరంలో 366 రోజులు ఉండును.
52 వారాలు+2 అదనపు రోజులు
*యివ్వబడిన సంవత్సరం లీపు సంవత్సరం కావలెనన్న ఆ సంవత్సరంలోని చివరి 2 సంఖ్యలు 4 చె భాగించబడవలెను.కాని శతాబ్ధంతో మొదలయ్యే సంఖ్య వచ్చిన 400 చే భాగించబడవలెను .
ఉదా: 1856, 1992,200,1600
*ఒక నెలలో 28/29/30/31 రోజులు ఉండును
*క్యాలెండర్ లోని మొదటి తేది జనవరి1 ఒకటవ శతాబ్ధం సోమవారం తో ప్రారంభం అయ్యింది.
*B.C అనగా(క్రీ.పూర్వం ).
*A.D అనగా (క్రీ.శకం)
*28 రోజులు కలిగిన నెలలో 4 వారాలు 0 అదనపు రోజులు ఉండును.
*29 రోజులు కలిగిన నెలలో 4 వారాలు 1 అదనపు రోజులు ఉండును.
*30రోజులు కలిగిన నెలలో 4 వారాలు 2 అదనపు రోజులు ఉండును.
*31 రోజులు కలిగిన నెలలో 4 వారాలు 3 అదనపు రోజులు ఉండును.
అదనపు రోజులు: ఇచ్చిన రోజులని 7 చే భాగించినపుడు వచు శేషమే అదనపు రోజులు.
ఉదా: 45 రోజులకు 3 అదనపు రోజులు ఉండును
odd days(అదనపు రోజులు) :0,1,2,3,4,5,6 వరకు ఉండును
వారాలకు కోడులు:
ఆదివారం - 0
సోమవారం - 1
మంగళవారం - 2
బుదవారం - 3
గురువారం - 4
శుక్రవారం - 5
శనివారం - 6
తరువాత అంటే ± రాయాలి
క్రితం అంటే - రాయాలి
నెలలకు కోడులు :
జనవరి- 0
ఫిబ్రవరి - 3
మార్చి- 3
ఏప్రియల్ - 6
మే - 1
జూన్ - 4
జులై - 6
ఆగష్టు - 2
సెప్టెంబర్ - 5
అక్టొబర్ - 0
నవంబర్ - 3
డిసెంబర్ - 5
శతాబ్ధపు కొడ్స్ :
1500 నుండి 1599 వరకు -0
1600 నుండి 1699 వరకు -6
1700 నుండి 1799 వరకు -4
1800 నుండి 1899 వరకు -2
1900 నుండి 1999 వరకు -0
2000 నుండి 2099 వరకు -6
2100 నుండి 2199 వరకు -4...

Q. 07-03-2017 నాడు ఏమి వారం?

A. సూత్రం :తేది+సం.పు చివరి రెండు అంకెలు +నెల కోడ్+శతాబ్ధం కోడ్+(సం.పు చివరి రెండు అంకెలు4 చెస్తే వచ్చు బాగఫలం)7చేయగా వచ్చు శేషమే జవాబు
07+17+3+6+4(174లభ.ఫ)7 = 377 ల యొక్క శేషం = 2
2 అంటే మంగళవారం

Q. 10-05-1990 నాడు ఏమి వారం?

A. 10+90+1+0+227 ల యొక్క శేషం =4
4 అంటే గురువారం

Q. నేడు సోమవారము అయినా 32 రోజుల తరువాత ఏ వారం వచ్చును?

A. నేడు ---> సోమవారము (1)
32 ----> 327 అదనపు రోజులు 4 = 4+1=5
5 అనగా శుక్రవారం

Q.నేడు మంగళవారం అయినా 57 రోజుల తరువాత ఏ వారం వాచ్చును?

A. నేడు ---> మంగళ(2)
57 --->577 అదనపు రోజులు 1 = 1+2= 3
3 అనగా బుధవారము

Q. నేడు శనివారము అయినా 73 రోజుల క్రితం ఏ వారం అగును?

A. నేడు ---> శనివారము = 6
73 --->737 అదనపు రోజులు 3 = 3-6= 3(క్రితం అంటే - చెయ్యాలి)
3 అనగా బుధవారము

Q. నేడు శుక్రవారము అయినా 89 రోజుల క్రితం ఏ వారం అగును?

A. నేడు --->శుక్రవారము=5
89 --->897 అదనపు రోజులు 5 = 5-5= 0
0 అనగా ఆదివారము

Q. ఏప్రియల్ 3,2012 సోమవారము అయినచో అదే సంవత్సరంలో ఆగష్టు 1 ఏ వారము అగును?

A. సోమవారము = 1
ఏప్రి--27
మే --31
జూన్ --30
జులై --31
ఆగష్టు --1 మొత్తం కూడగా 120 రోజులు
1207 అదనపు రోజులు = 1 రోజు
1+1 =2 అనగా మంగళవారము

Q. డిసెంబర్ 5,2012 నాడు శనివారము అయినా సెప్టెంబర్15,2012 న ఏమి వారము?

A. శనివారము = 6
సెప్టెంబర్ ---15
అక్టొబర్ ----31
నవంబర్ ---30
డిసెంబర్ ---5 మొత్తం 817 = 4-6= 2 మంగళవారము

Q. 2096 వ సంవత్సరము తరువాత వచ్చు లీపు సంవత్సరము ఏది?

A. లీపు సంవత్సరము వచ్చేవరకు 4 ను కుడుతూపోవాలి
2096+4 = 2100 ఇది శతాబ్దిక సంవత్సరము కావున 400 చే బాగించబడాలి కావున ఇది లీపు సంవత్సరము కాదు
2100+4 =2104 ఇది లీపు సంవత్సరం

Q. 2196 తరువాత వచ్చు లీపు సంవత్సరము ఏది?

A. 2196+4 = 2200 లీపు సంవత్సరం కాదు
2200+4 = 2204 లీపు సంవత్సరము

Q. 1996 తరువాత వచ్చు లీపు సంవత్సరము ఏది?

A.1996+4 = 2000 లీపు సంవత్సరం

Q. జనవరి 20,2016 గురువారము అయినచో జనువరి 20,2017 ఏవారము అగును?

A. గురువారము = 4
2016 లీపు సంవత్సరము కావున 2 అదనపు రోజులు వుంటాయి
2+4 = 6 అంటే శనివారము అగును

Q. ఆగష్టు 15,2004 బుధవారం అయినచో ఆగష్టు 15,2009 ఏవారము అగును?

A. బుధవారం = 3
ఆగష్టు 15,2004
ఆగష్టు 15,2009
మొత్తం 6 అదనపు (2008 లీపు సం..)రోజులు + 3 = 97 = 2 అంటే మంగళవారము

Q. ఒక సంవత్సరంలో ఏప్రియల్ నెలను పోలిన నెల ఏది ?

A. అప్రియల్ - 2 అదనపు రోజులు
మే - 3 అదనపు రోజులు
జూన్ - 2 అదనపు రోజులు
మొత్తం 7 అదనపు రోజులు కావున జులై నెల ఏప్రియల్ నెలను పోలి వుంటుంది

Q. ఒక సంవత్సరంలోమార్చ్ నెలను పోలిన నెల ఏది ?

A. మర్చ్ - 3
ఏప్రియల్ --2
మే --3
జూన్ -- 2
జులై --3
అగష్టు --3
సెప్టెంబరు -2
అక్టోబరు - 3
మొత్తం అదనపు రోజులు 21
217 కావున నవంబరు నెల మార్చ్ నెలను పోలి వుంటుంది.

Q.2005 ను పోలిన సంవత్సరము?

A. 2005-1
2006-1
2007-1
2008-2
2009-1
2010-1 మొత్తం 7 అదనపు రోజులు కావున 2011 సంవత్సరము 2005 ను పోలిన సంవత్సరము

Q.1987 ను పోలిన సంవత్సరము 1987 తర్వాత ఏప్పుడు వచ్చును?

A. 1987-1
1988-2
1989-1
1990-1
1991-1
1992-2
1993-1
1994-1
1995-1
1996-2
1997-1
మొత్తం 14 అదనపు రోజులు కావున 1998 సం.1987సం.ను పోలివుండును.
            🍃🌷🤗🌷🍃

General Knowledge

🏹 కరెంట్ఎఫైర్స్🏆

1. గాంబియా యొక్క కొత్త అధ్యక్షుడిగా ప్రమాణస్వీకారం చేసింది ఎవరు ?--------------అధమ బార్రౌ.

2. ఔషధ మరియు భారతదేశం యొక్క సుగంధ మొక్కల ఇంటర్నేషనల్ సింపోసియం ఏ  నగరంలో జరుగుతుంది?----------------------న్యూ ఢిల్లీ .

3. "ది స్టోరీ అఫ్ ఎస్కేప్ " అనే పుస్తక రచయిత ఎవరు ?---------------------సుర్జీత్ సింగ్ బార్నాల .

4. భారతదేశం యొక్క 2017 రిపబ్లిక్ డే ముఖ్య అతిథి ఎవరు ?-------------మొహమ్మద్ బిన్ జాయెద్ అల్ నహ్యాన్.

5. ఏ జట్టు 2017 ప్రో రెజ్లింగ్ లీగ్ గెలుచుకుంది ?-------------------పంజాబ్ రాయల్స్ .

6. ప్రపంచ బ్యాంకు త్రిపుర పవర్ అభివృద్ధి ప్రాజెక్టుకు ఎంత మొత్తం మంజూరు చేసింది ?--------------------1376 కోట్లు.

7. నేషనల్ ఓటర్స్ డే ని ఎప్పుడు జరుపుకుంటారు ?---------------జనవరి 25.

8. 2017 కంబైన్డ్ కమాండర్స్ 'కాన్ఫరెన్స్  భారతదేశం లో ఏ రాష్ట్రము లో  జరుపబడుతోంది?----------------------ఉత్తరాఖండ్.

9. "60 ఇండియన్ పోయెట్స్" అనే  పుస్తక రచయిత ఎవరు ?--------------జీత్ తయిల్.

10. యుద్ధనౌకల లో  ఏ బోర్డు ఎటిఎం కలిగి భారతదేశం యొక్క మొట్టమొదటి యుద్ధనౌక మారింది?--------------------ఐన్ఎస్ విక్రమాదిత్య.

General Knowledge Important Bits,

🌺🍇🍇🌺

*1) పరిమాణం మాత్రమే ఉండి దిశపై ఆధారపడని భౌతక రాశులను ఏమని అంటారు?*

*జ: ఆదిశ రాశులు*

*2) పాద రసం సాంద్రత ఎంత?*

*జ: 13.6 గ్రా / సెం.మీ.*

*3) మనిషి శరీరంలో ఉష్ణోగ్రతలను కొలవడానికి ఉపయోగించే థర్మామీటర్ ను ఏమంటారు ?*

*జ: క్లినికల్ థర్మామీటర్*

*3) ఏదైనా భౌతిక రాశిని పూర్తిగా వర్ణించడానికి దిశ పరిమాణం రెండూ అవసరమైతే దానిని ఏమని అంటారు?*

*జ: సదిశరాశి*

*4) వస్తువు స్దానంలో నిర్ణీత దిశలో వచ్చే మార్పును ఏమంటారు ?*

*జ: స్దానభ్రంశం*

*5) పైకి విసిరిన వస్తువు కిందకి పడేటప్పుడు అది పొందే త్వరణాన్ని ఏమని అంటారు?*

*జ: గురుత్వరణం*

*6) నిట్ట నిలువుగా విసిరిన రాయి గరిష్ట ఎత్తుకు చేరుకున్నప్పుడు దాని వేగం ఎంత ఉంటుంది ?*

*జ: శూన్యం*

*7) వస్తువు గరిష్ట ఎత్తుని చేరడానికి పట్టే కాలాన్ని ఏమని అంటారు?*

*జ: ఆరోహణ కాలం*

*8) స్వేచ్చా పతన వస్తువు భూమిని చేరడానికి పట్టే కాలాన్ని ఏమంటారు?*

*జ: అవరోహణ కాలం*

*9) తడి టవల్ ను దులిపితే అందులో నుంచి నీటి బిందువులు బయటకు వస్తాయి. అందుకు కారణమేంటి ?*

*జ: జడత్వం*

*10) బనానా ఆయిల్ దేని నుంచి తయారు చేస్తారు ?*

*జ: పెట్రోలియం*

*11) బ్యాటరీలో శక్తి ఏ రూపంలో ఉంటుంది ?*

*జ: రసాయన శక్తి*

*12) థర్మామీటర్ ను మొదట రూపొందించింది ఎవరు ?*

*జ: గెలీలియో గెలిలీ*

Eid MUBARAK

General Knowledge

☔గోదావరి నది - Godavari river⛱

- గోదావరి నది జన్మస్థానం-- నాసిక్.

- గోదావరి నది తెలంగాణలో ప్రవేశించు స్థలం-- బాసర.

- దేశంలోని పెద్ద నదులలో గోదావరి నది స్థానం-- రెండవది (దక్షిణ భారతదేశంలో పెద్దది).

- గోదావరి అంటే అర్థం-- అఖండ జలరాశి.

- గోదావరి జల వివాదాల ట్రిబ్యునల్ ఏ సంవత్సరంలో ఏర్పాటైంది-- 1969.

- పుష్కరాలు జరుపుకొనే గోదావరి నది యొక్క ఉపనది-- ప్రాణహిత నది.

- నిజామాబాదు జిల్లాలో గోదావరి నదిపై ఉన్న ప్రాజెక్టు-- శ్రీరాంసాగర్ ప్రాజెక్టు.

- గోదావరి నది తెలంగాణ మరియు ఆంధ్రప్రదేశ్‌లో ప్రవహించు దూరం-- 770 కిలోమీటర్లు.

- పశ్చిమ గోదావరి జిల్లాలో గోదావరి నదిపై నిర్మించనున్న ప్రాజెక్టు-- పోలవరం ప్రాజెక్టు.

- గోదావరి నది ముఖద్వారంగా పిలువబడు నగరం-- రాజమండ్రి.

New Pattern English

Directions (1-10): In each of the following questions, a paragraph with a blank is given. From the five choices given below, select the sentence which can go into the blank to make the paragraph logically coherent.

Q1. Srinagar is the capital of Kashmir. There are very beautiful scenes all round. The Dal Lake is one among them. [__________] We can hire one of them and voyage along the length and breadth of the lake or live in it for a week or so.

(a) There are several guides to take us round.
(b)There we can see a number of house boats waiting to be hired by the tourists.
(c)It is difficult to count them.
(d)It was dark inside and bright outside.
(e) There are several tourists looking around the place.


Q2.Polio-affected children are found everywhere in India. Recently the Government has started Polio-eradication Scheme. [__________] Unless we take care to co-operate the purpose cannot be fulfilled.

(a) We must help children to take the proper vaccine.
(b) We must take the children to get vaccinated.
(c) Children must remain without any movement.
(d) We must make children exercise.
(e) We need experts to undertake such projects.


Q3. Many film-stars have recently migrated to the area of television. [__________] As the viewers increase their popularity also increases. T.V serials appear to be more paying than the feature films.

(a) Television gives a better chance of action.
(b) There they have a greater number of viewers.
(c) Television is a house hold affair.
(d) If we do not like a TV program we can turn it off. 
(e) Television is useful in many ways.


Q4. Man is trying to find out modern means of producing electric power. The solar panel is one of them. [__________] This electricity can light lamps, turn fans or work small household appliances.

(a) It is very cheap and affordable.
(b) We ourselves can make one such device.
(c) It converts sunlight into electricity.
(d) It is easy to work and beautiful to look at.
(e) Electricity is a good substitute for sunlight.


Q5. Air-pollution is one of the gravest problems faced by city-dwellers. Foul gas liberated from heaps of waste matter is one source of pollution. [__________] Recently the Government has made arrangements to measure it. If it is above the allowable limit the vehicles are prohibited from plying along the public roads.

(a) Another source is the smoke emitted by vehicles.
(b) Foul water in the channels is another. 
(c) The smell from toddy shops pollutes the air.
(d) Open drainage pollutes the air.
(e) People suffer due to smoke emitted by vehicles.


Q6. Corruption has become rampant in India. Corrupt officials and politicians are ruling over the hapless common man. [__________] People must join together and force them to take necessary legal action.

(a) Politicians with integrity simply withdraw from the scene.
(b) Such officials are welcomed by the general public.
(c) Even police authorities are reluctant to face them.
(d) They do it with the connivance of topmost authorities.
(e) Corruption is the breeding ground for all evils.


Q7. Feature films have a very great influence upon the common people. They have no hesitation in regarding actors as gods. [__________] They must utilize this love and regards to serve the people, not to exploit them.

(a) Gods are expected to protect the devotees.
(b) Though they are gods they are human enough to err.
(c) Gods never walk on earth or collect money.
(d) Some people are ready even to die for them.
(e) Actors are viewed as gods.


Q8. Most of us fall victim to some sort of disease or the other. We can avoid diseases by leading a hygienic life. It is better to bear in mind a simple truth. [__________] The consciousness of this truth will lead us to happiness.

(a) It is impossible to have constant health.
(b) Hygienic life is less costly than medical treatment.
(c) Man is mortal and likely to die at any moment.
(d) Happiness is always evasive.
(e) Health needs good care as we may fall victim to some sort of disease.


Q9. A doctor has succeeded in raising a variety of monkeys similar to human beings. They clean their teeth with brushes and mop their face with towels. [__________] In that case these animals may be called monkey – man and we may be called man – monkeys. 

(a) Perhaps they may learn and use human language.
(b) Sometimes they may die after a few days.
(c) The method adopted by the doctor is wonderful.
(d) We can expect a lot of change in the case of other animals also.
(e) Monkeys are good subjects unlike human beings.


Q10. It is wonderful how a word can acquire diagonally opposite meaning. Gandhiji called the socially downcast people by the name Harijans. [__________] But now the Harijans themselves feel that it is a word of insult.

(a) Gandhiji was a social reformer.
(b) Gandhiji had many Harijan friends.
(c) Gandhiji expected to bring them respect by calling them the children of God.
(d) Harijans have risen to such a high position that they feel their brand name ‘Harijan’ to be degrading.
(e) Only Harijans are children of God.

Directions (11-15): Each of the following questions has a paragraph from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way.


Q11. Lower winter temperatures were common in Europe during the second half of the 17th century, famously allowing frost fairs to be held on the frozen Thames in London before riverine developments increased the flow rate. These cold winters coincided with the Maunder minimum in solar activity when the Sun remained virtually free of sunspots for almost 50 years. However, establishing that this was not just a chance occurrence requires that the relationship continue to hold over a long interval, such that cold European winters become less frequent when solar activity is high and then more common again when solar activity falls. Various indicators show that during the recent minimum of the 11 year sunspot cycle, the Sun has been quieter than at any time in the previous 90 years.

(a) This means that solar activity during the current sunspot minimum has fallen to levels unknown since the start of the 20th century.
(b) This yields an opportunity for a better test of the relationship between solar activity and cold European winters.
(c) This proves that cold winters occur more commonly in the UK during low solar activity.
(d) This regional and seasonal effect relating to European winters may have a global effect.
(e) None of the above


Q12. Debt is more common in families with disabled children: the parents were unable to keep up with any local property taxes, water, and telephone bills, and were not likely to be able to afford basic items such as a family holiday once a year,a bicycle, or even two pairs of shoes. A disabled baby needs more nappies. Families’ ability to work grows difficult, and finding childcare is a real burden. Households with disabled childrenwill depend more on social security benefits and are faced with the additional financial costs associated with caring for a disabled child.

(a) There is a strong link between child disability and poverty.
(b) The highest prevalence of childhood disability is found in the poorest families.
(c) It is an adverse and serious social gradient that families with disabled face.
(d) But thanks to science, these children live longer and medicines keep them alive.
(e) None of the above


Q13. What a super film experience Green Zone is! From the firecracker opening to the sucker-punch climax, the film is a non-stop adrenalin rush. The hand-held camera and natural light make you feel as if you are seeing the action from the front, as if you have access to footage shot from a sniper’s sights. Whether it is a Bourne-in-Baghdad kind of relentless action thriller or a strong statement against the U.S. war in Iraq, (incidentally, it is both) Green Zone succeeds as a pure cinema, delivering thrills, spills and chills in breathless succession hardly giving anyone time to breathe.

(a) This is a movie that takes you on a thrilling, provocative, exhilarating ride.
(b) There is really nothing more you could ask for from a movie.
(c) Green Zone effectively knits several strands together to make a cohesive whole.
(d) The plot is taut and truthful.
(e) None of the above


Q14. Talented youth can ill-afford to resign to their fate just because they can’t properly communicate in English. They should confront the challenges which should, in fact, bring out their best. A little confidence and hard work are all that is needed for them to climb up the career ladder. For that they need to develop communication skills in English, shape up their personalities and acquire the much-needed knowledge.

(a) Knowledge and communication skills are the key ingredients that make up the recipe for success.
(b) Students have to act as leaders in the college itself.
(c) Success will automatically follow.
(d) Speaking and writing in English are important, thinking in English is twice as important.
(e) None of the above


Q15. Philosophy of music has been dominated by the view that the best music is autonomous and formally complex. As recently as 1990, philosophy of popular music consisted of variations on a single theme. Philosophers defended the twin assumptions that popular music is essentially different from “serious” or art music, and that the former is aesthetically inferior to the latter.

(a) As a result, music could not be regarded as art if it lacked genius and autonomy.
(b) As a result, popular music competes with and replaces local and regional folk traditions.
(c) As a result, most philosophers concentrated on identifying the aesthetic deficiencies inherent in popular music.
(d) As a result, philosophers have investigated popular music by identifying and critiquing key concepts that shape our response to this music.
(e) None of the above

Solutions

S1. Ans.(b) 

Sol. There we can see a number of house boats waiting to be hired by the tourists. This sentence is the continuation of the idea expressed in the first sentence. 

S2. Ans.(b) 

Sol. We must take the children to get vaccinated.

S3. Ans.(b) 

Sol. There they have a greater number of viewers. The next sentence also talks about the viewers. 

S4. Ans.(c) 

Sol. It converts sunlight into electricity. 

S5. Ans.(a) 

Sol. Another source is the smoke emitted by vehicles. In previous sentence, first source is talked about.

S6. Ans.(c) 

Sol. Even police authorities are reluctant to face them.

S7. Ans.(d) 

Sol. Some people are ready even to die for them. 

S8. Ans.(b) 

Sol. Hygienic life is less costly than medical treatment.

S9. Ans.(a) 

Sol. Perhaps they may learn and use human language.

S10. Ans.(c) 

Sol.  Gandhiji expected to bring them respect by calling them the children of God.

S11. Ans.(b)

Sol. “...establishing that this was not just a chance occurrence requires that the relationship continue to hold over a long interval...” is the crux of the paragraph. Hence the sun being “quiet” is an opportunity to find this correlation. Options (C) and (D) can be very easily eliminated as not related to the purpose of the paragraph. Option (A) is true, is an inference not related to the purpose of the paragraph.

S12. Ans.(c)

Sol. This statement is a very low level inference that logically closes the paragraph. The paragraph is not sufficient to establish the link as in option (A). Option (B) goes farther away from the paragraph. Option (D) is unrelated to the purpose of the paragraph.

S13. Ans.(b)

Sol. All options may appear correct. The scoring option, however, has to close the paragraph, andnot merely continue it. Option (A) will be repetitive. Options (C) and (D) will continue the paragraph.

S14. Ans.(c)

Sol. The purpose of the paragraph is in the first sentence - “can ill-afford to resign to their fate.” Option (A) is already clearly stated-it just states the same thing in different words. Option (B) takes off on a tangent and brings in leadership; option (D) also does not close the paragraph. Option (C) just does that-the paragraph has no loose ends.

S15. Ans.(c)

Sol. The purpose of the paragraph is: Philosophers consider popular and serious music different. The former lacks complexity and autonomy, the later is variations on a single them-and that popular music is inferior. “As a result” will discuss its direct consequences and close the paragraph. Hence option (C) scores. Option (A) is stated. Option (B) is irrelevant in “replace” and “folk music”. Option (D) is irrelevant in “our response.”

New Pattern English

Directions (1-15): Four sentences are given with a blank in each. Five words are also given. The blank in each sentence can be filled by one or more words. Similarly, each word given in the choices can go into any number of sentences. Identify the number of sentences each word can go into and mark as your answer the maximum number of sentences any word can go into. 

Q1. A. The millionaire has __________ Rs. 10,00,000 for this priceless artifact.

B. In a/an __________ to rescue the child who was caught in fire, she sustained burns.

C. I went to the railway station to __________ goodbye to my friend.

D. I was asked to __________ a price by the auctioneer.

(a) quoted

(b) attempt

(c) bid

(d) say

(e) spend

Q2. A. He __________ many spine-chilling anecdotes to us.

B. The law extends to several __________ groups.

C. This person is not __________ to me in any way, he is a trickster.

D. The two groups are __________ to each other.

(a) allied

(b) connected

(c) related

(d) recounted

(e) narrated

Q3. A. Can you please __________ the bell?

B. The words spoken by him still __________ in my ears.

C. Mahatma Gandhi was the __________ leader of the Non-Cooperation movement.

D. I shall give you a __________ after reaching home.

(a) sound

(b) ring

(c) chief

(d) call

(e) sell

Q4. A. Many students still __________ around the college, even after the classes are over.

B. Every citizen of India should __________ his head in shame at the brutal killings in the name of religion.

C. There is ample space in the wardrobe for you to __________ your clothes.

D. “__________ the perpetrators of the crime!” shouted the angry mob.

(a) execute

(b) loiter

(c) hang

(d) bend

(e) store

Q5. A. This book pertaining to fine arts is beyond a __________ man’s comprehension.

B. I helped mother to __________ the table for breakfast.

C. In her hour of distress she had to __________ her hopes on her relatives to help her.

D. He requested me to __________ some money.

(a) pin

(b) lay

(c) lend

(d) ordinary

(e) common

Q6. A. My friends tried to cheer me up, as I was in a depressed __________ of mind.

B. All the senior leaders of the party have assembled together to __________ a new election strategy.

C. He wanted to change the __________ of his spectacles.

D. Can you please __________ this picture for me?

(a) build

(b) bend

(c) frame

(d) state

(e) draw

Q7. A. Despite being hardworking he could never __________ success in his career.

B. He is such a spoilsport that he cannot __________ a joke against himself.

C. This toothpaste has the __________ of mint.

D. The __________ of mango is relished by the young and old alike.

(a) taste

(b) flavour

(c) enjoy

(d) experience

(e) small

Q8. A. Akbar was known for his benevolence, people were happy during his __________.

B. Cleopatra has an ambition to __________ the world as a queen of beauty.

C. Better to __________ in hell than to serve in heaven.

D. One should not allow indolence to __________ over oneself.

(a) reign

(b) dominate

(c) rule

(d) tenure

(e) overpower

Q9. A. I do not __________ him as a brilliant performer.

B. The __________ of interest offered by Nationalized banks is very low.

C. At any __________ I shall see that you get over the crisis.

D. He rose from the __________ of a soldier to that of a commissioned officer.

(a) rank

(b) cost

(c) rate

(d) value

(e) see

Q10. A. The __________ accused in the murder, was sentenced to death.

B. __________ time soap operas on the television charge exorbitant rates from advertisers.

C. Abolition of illiteracy should be the __________ concern of every state government.

D. The office of the Vice-chancellor is in the __________ building of the University.

(a) mainly

(b) prime

(c) primitive

(d) chief

(e) only

Q11. A. The little boy was pampered by his grandparents, who catered to his every __________.

B. “Your __________ is my command”, said the genie to the prince.

C. I __________ you could understand me better.

D. Being an easygoing person, she behaves according to her own __________ and fancy.

(a) whim

(b) demand

(c) wish

(d) hope

(e) need

Q12. A. I could finish my work __________ ahead of time.

B. He is __________ off when compared to his other siblings.

C. By his attitude, I could make out that he does not mean __________.

D. She is __________ dressed when compared to other women in the gathering.

(a) much

(b) better

(c) well

(d) good

(e) harm

Q13. A. For many years India was __________ in a tricky situation, whether to go in for a nuclear weapon or not.

B. The marathon innings of the batsman came to an end when he was finally __________ by the same bowler who troubled him the most.

C. The notorious burglar was finally __________ by the cops.

D. I was __________ unaware when my photograph was clicked.

(a) held

(b) seized

(c) apprehended

(d) caught

(e) trapped

Q14. A. The management took no __________ of the problems pertaining to the workers.

B. The class teacher was called to __________ for the dismal performance of the students in the examination.

C. Many young cricket fans __________ Tendulkar as a hero.

D. The principal promised the students that he would __________ their demands.

(a) consider

(b) explain

(c) accurate 

(d) estimate 

(e) notice

Q15. A. The jail authorities have decided to __________ some of the prisoners, who possessed a clean record, as a gesture of good will.

B. He decided to __________ himself of all responsibilities by handing over charge to his successor.

C. Since he is a spendthrift he is very __________ in spending money.

D. Government aided schools are now offering to teach computer course to students __________ of charge.

(a) devoid

(b) release

(c) lavish

(d) free

(e) parole

SOLUTIONS

S1. Ans.(c)
Sol. ‘bid ‘fits in all the above sentences correctly.

S2. Ans.(c)
Sol. ‘related ‘ fits in all the above sentences correctly.

S3. Ans.(b)
Sol. ‘ring ‘fits in all the above sentences correctly.

S4. Ans.(c)
Sol. ‘hang ‘fits in all the above sentences correctly.

S5. Ans.(b)
Sol. ‘lay ‘fits in all the above sentences correctly.

S6. Ans.(c)
Sol. frame -fits in all the above sentences correctly.

S7. Ans.(a)
Sol. taste -fits in three sentences correctly.

S8. Ans.(c)
Sol. ‘rule ‘fits in all the above sentences correctly.

S9. Ans.(c)
Sol. ‘rate ‘ fits in all the above sentences correctly.

S10. Ans.(b)
Sol. fits in all the above sentences correctly.

S11. Ans.(c)
Sol. ‘WISH’ fits in all the above sentences correctly. 

S12. Ans.(c)
Sol. ‘well ‘fits in all the above sentences correctly.

S13. Ans.(d)
Sol. caught -fits in all the above sentences correctly.

S14. Ans.(a)
Sol. ‘consider ‘ fits in all the above sentences correctly.

S15. Ans.(d)
Sol. ‘free ‘fits in all the above sentences correctly.