Vyoma Grama Sachivalayam Online

Exams

https://www.vyoma.net/exams/ap-grama-sachivalayam/

B…{«§ýl{糧ólÔŒæ ÝëÐ]l*hMýS, BǦMýS çÜÆó‡Ó 2018&19

1. B…{«§ýl{糧ólÔŒæ ç³…rÌS Ýë…{§ýl™èl G…™èl?1) 1.24 2) 1.253) 1.26 4) 1.27

2. Møyìl VýS$yýlÏ E™èlµ†¢ÌZ §ólÔèæ…ÌZ B…{«§ýl{糧ólÔŒæG¯ø² Ýë¦ ]l…ÌZ E…¨?1) 1 2) 23) 3 4) 4

3. 2018 & ----19 çÜÐ]lÇ…_ ]l A… èl¯éÌS {ç³M>Æý‡…Æ>çÙ‰ Ý÷…™èl ç³ ]l$² Æ>ºyìl MýS*Æý‡$µÌZA™èlÅ« MýS Ðésê MýSÍW ]l A…Ôèæ… H¨?1) AÐ]l$ÃMýSç³# ç³ ]l$² 2) hGïÜt 3) Æ>çÙ‰ GOMð ÞgŒæ çÜ$…MýS…4) Ýët…ç³#Ë$, Çhõ܉çÙ ŒlË$

4. Æ>çÙ‰…ÌZ Ððl¬™èl¢… Ð]lÅÐ]lÝëĶæ$ Ö™øçÙ~íܦ†Ð]l$…yýlÌêË$ G°² E¯é²Æ‡$$1) 5 2) 6 3) 7 4) 8

5. B…{«§ýl{糧ólÔŒæ ´ëÇ{Ô>Ñ$MýS E™èlµ†¢ çÜ*_ÌñæMìSP… èlyé°MìS H çÜ…Ð]l™èlÞÆ>°² B«§éÆý‡çÜ…Ð]l™èlÞÆý‡…V> ç³ÇVýS×ìæçÜ$¢¯é²Æý‡$1) 2010&11 2) 2011&123) 2017&18 4) 2014&15

6. 2018&19 Ð]l$«§ýlÅ B…{«§ýl{糧ólÔŒæ ´ëÇ{Ô>Ñ$MýSE™èlµ†¢ çÜ*_ G…™èlV> ]lÐðl*O§ðl…¨?1) 125.6 2) 133.783) 123.78 4) 123.5

7. B…{«§ýl{糧ólÔŒæ Æ>çÙ‰…ÌZ° Ððl¬™èl¢… Æ>çÙ‰ Ýë¦Æ‡$${糿¶æ$™èlÓ Æý‡…VýS çÜ…çܦË$ G°²? 1) 36 2) 37 3) 38 4) 39

8. »Ÿyólzç³ÍÏ Æ>fVø´ëÌSÆ>Ð]l# Ð]l…Ôè櫧éÆý‡ {´ëgñæMŠStH hÌêÏÌZ° 9 Ð]l$…yýlÌêÌSMýS$ ðl…¨ ]l 225{V>Ð]l*ÌSMýS$ {ç³Äñæ*f¯]l… ^ólMýS*Æý‡$çÜ$¢…¨?1) }M>MýS$âýæ… 2) ÑfĶæ$ ]lVýSÆý‡…3) ÑÔ>Qç³rt×æ… 4) ™èl*Æý‡$µ Vø§éÐ]lÇ

9. B…{«§ýl{糧ólÔŒæ çÜÒ$MýS–™èl ÝëVýS$±sìæ Ð]lÅÐ]l-ÝëĶæ$ ç³ÇÐ]lÆý‡¢ ]l {´ëgñæMŠStMýS$ çÜ…º…« …_çÜOÆð‡ ]lÑ HÑ? G. D {´ëgñæMŠSt ÌS„ýSÅ…, VýS$…r*Æý‡$ Ñ$ ]là

Ñ$VýS™é 12 hÌêÏÌZÏ G…í³MýS ólíÜ ]l 1000_ ]l² ±sìæ´ëÆý‡$§ýlÌS ðlÆý‡$Ð]l#ÌS MìS…§ýl2,26, 556 GMýSÆ>ÌS BĶæ$MýSr$t ]l$íܦÈMýSÇ… èlyýl…

¼. D {´ëgñæMŠSt AÐ]l$Ë$ M>ÌS… 2018 & 19]l$…_ 2023 & 24 Ð]lÆý‡MýS$

íÜ. D {´ëgñæMýS$tMýS$ BǦMýS çÜàĶæ$… A… -çÜ$¢…¨ {ç³ç³… èl »êÅ…MŠS (1120 Mør$Ï)

yìl. D {´ëgñæMýS$t B…{«§ýl{糧ólÔŒæ {糿¶æ$™èlÓ Ðésê480 Mør$Ï1) Oò³Ð]l±² çÜOÆð‡ ]lÐól 2) G, ¼ Ð]l*{™èlÐól$3) ¼, íÜ Ð]l*{™èlÐól$ 4) G, yìl Ð]l*{™èlÐól$

10. 2019 Ð]l*Ça ¯ésìæMìS Æ>çÙ‰…ÌZ E ]l² Ððl¬™èl¢…Ð]lÅÐ]lÝëĶæ$ ѧýl$Å™Œæ MýS ðlMýSÛ ]l$Ï G°²?1) 18.07 ÌS„ýSË$ 2) 17.07 ÌS„ýSË$3) 19.07 ÌS„ýSË$ 4) 20.07 ÌS„ýSË$

11. 2019 òÜò³t…ºÆŠæÌZ Ñyýl$§ýlÌS ólíÜ ]l Ô>…í³ÌŒæÇhõ܉çÙ Œl íÜçÜt… º$Ìñæsìæ Œl {ç³M>Æý‡… 2017çÜ…Ð]l™èlÞÆ>°MìS, B…{«§ýl{糧ólÔŒæ Æ>Ú‰ë°MìSçÜ…º…« …_ ]l BÆøVýSÅ çÜ*`ÌZÏ çÜOÆð‡ ]lÑ?1) f¯]l¯]lÆó‡r$&16.22) Ð]l$Æý‡×æÆó‡r$& 7.23) ÕÔ¶æ$Ð]l$Æý‡×êÌS Æó‡r$& 32

4) Oò³Ð]l±² çÜOÆð‡ ]lÐól12. Æ>çÙ‰…ÌZ {ç³çÜ*† Ð]l$Æý‡×êË °çÙµ†¢ G…™èl?

1) 74 2) 76 3) 72 4) 7113. A…§ýlÇMîS ÝëÆý‡Ó{†MýS BÆøVýSÅ Ð]lç܆ MýS͵…-

^éÌS ól ÌS„ýSÅ…™ø B…{«§ýl{糧ólÔŒæ {糿¶æ$™èlÓ…§éÇ{§ýlÅÆó‡QMýS$ GVýS$Ð]l¯]l E ]l² MýS$r$…»êÌSMýS${ç³ÐólÔèæò³sìæt ]l BÆøVýSÅ Æý‡„ýS A ól ç³£ýlMýS… {ç³Äñæ*-f¯éË$ ´÷…§ýlyé°MìS {糆 ÌS¼®§éÆý‡$yýl$Hyé¨MìS G…™èl {ï³Ñ$Ķæ$… ðlÍÏ…^éÍ?1) 1000 2) 12003) 1500 4) 2400

14. Æ>çÙ‰…ÌZ 2018&19 çÜ…Ð]l™èlÞÆ>°MìS °MýSÆý‡ÝëVýS$ ±sìæ Ð]lç܆ E ]l² ¿¶æ*Ñ$ G…™èl?1) 28.06 ÌS„ýSÌS òßæM>tÆý‡$Ï 2) 38.6 ÌS„ýSÌS òßæM>tÆý‡$Ï3) 37.60 ÌS„ýSÌS òßæM>tÆý‡$Ï4) 36.45 ÌS„ýSÌS òßæM>tÆý‡$Ï

15. MìS…¨ ÐésìæÌZ çÜOÆð‡ ]l §é°² VýS$Ç¢… èl…yìl.1) B…{«§ýl{糧ólÔŒæ A„ýSÆ>çÜÅ™èl 67.35 Ô>™èl… 2) B…{«§ýl{糧ólÔŒæ Í…VýS °çÙµ†¢ 9773) B…{«§ýl{糧ólÔŒæ f ]lÝë…{§ýl™èl 304 4) Oò³Ð]l±² çÜOÆð‡ ]lÐól

16. Æ>çÙ‰…ÌZ° ¿¶æ*MýSÐ]l$™éÌS ÑÐ]lÆ>ÌSMýS$çÜ…º…« …_ MìS…¨ ÐésìæÌZ çÜOÆð‡ ]l ÐéM>ÅË$-(2015&16 VýS×æ ]l {ç³M>Æý‡…) HÑ? 1) Æ>çÙ‰…ÌZ° Ððl¬™èl¢… MýSÐ]l$™éÌS çÜ…QÅ

85.24 ÌS„ýSË$2) Æ>çÙ‰…ÌZ° Ððl¬™èl¢… ¿¶æ*MýSÐ]l$™éÌS

ÑïÜ¢Æý‡~… 80.04 ÌS„ýSÌS òßæM>tÆý‡$Ï 3) B…{«§ýl{糧ólÔŒæ çÜVýSr$ ¿¶æ*MýSÐ]l$™èl ÑïÜ¢Æý‡~…

0.94 òßæM>tÆý‡$Ï4) Oò³Ð]l±² çÜOÆð‡ ]lÐól

17. 2018&19ÌZ Æ>çÙ‰…ÌZ Ð]l$à™éÃV>…«©gê¡Ä¶æ$ {V>Ò$×æ E´ë« àÒ$ ç³£ýlMýS…ç³°¡Æý‡$MýS$ çÜ…º…« …_ (2019 Ð]l*Ça 31¯ésìæMìS) D MìS…¨ ÐésìæÌZ çÜOÆð‡…¨?1) JMøP MýS$r$…»ê°MìS çÜVýSr$ ]l 58.15

ÆøkÌS E´ë« MýS͵…^éÆý‡$2) Ð]lÅMìS¢VýS™èl ç³°¨¯éË$ MýS͵…^èlyýl…ÌZ

§ólÔèæ…ÌZ ¯éË$Vø Ýë¦ ]l…ÌZ E…¨. 3) çÜM>ÌS…ÌZ Ðól™èl¯éË$ ^ðlÍÏ… èlyýl…ÌZ,

100 ÆøkÌS ]l$ ç³NÇ¢ ólĶæ$yýl…ÌZ B…{«§ýl-{糧ólÔŒæ §ólÔèæ…ÌZ A{VýSÝë¦ ]l…ÌZ E…¨

4) Oò³Ð]l±² çÜOÆð‡ ]lÐól18. çÜÓĶæ$… çÜàĶæ$MýS º–…§éÌS çÜ¿¶æ$ÅÌZÏ

BÆøVýSÅ…Oò³ AÐ]lV>çßæ¯]l MýS͵… ól…§ýl$MýS$ BÆø-VýSÅÔ>Q™ø MýSÍíÜ Ð]l$íßæâê BÆøVýSÅ çÜÑ$-™èl$ÌS ]l$ Æ>çÙ‰ {糿¶æ$™èlÓ… HÆ>µr$ ólíÜ…¨.AƇ$$™ól 2019 Ð]l*Ça 31 ¯ésìæMìS Æ>çÙ‰…ÌZHÆ>µr$ ólíÜ ]l Ððl¬™èl¢… Ð]l$íßæâê BÆøVýSÅçÜÑ$™èl$Ë çÜ…QÅ? 1) 10,800 2) 10,9003) 10,700 4) 10,500

19. B…{«§ýl{糧ólÔŒæÌZ Ððl¬™èl¢… ÝëVýS$ ÑïÜ¢Æý‡~…ÌZ H±sìæ Ð]l ]lÆý‡$ÌS Ðésê GMýS$PÐ]l E…¨?1) M>Ë$Ð]lË$ 2) ðlÆý‡$Ð]l#Ë$ 3) »êÐ]l#Ë$ 4) Ð]lÆý‡Ûç³# ±Æý‡$

20. B…{«§ýl{糧ólÔŒæÌZ A™èlÅ« MýS…V> ™ðlËÏÆó‡çÙ¯ŒlM>Æý‡$zË$ H hÌêÏÌZ E¯é²Æ‡$$?1) ™èl*Æý‡$µVø§éÐ]lÇ 2) A ]l…™èlç³#Æý‡…3) ç³ÕaÐ]l$Vø§éÐ]lÇ 4) VýS$…r*Æý‡$

21. B…{«§ýl{糧ólÔŒæÌZ {ç³çÜ$¢™èl ArÒ ÑïÜ¢Æý‡~…?1) 37007 èl. MìS. Ò$. 2) 36067 èl. MìS. Ò$.3) 37707 èl. MìS. Ò$. 4) 38707 èl. MìS. Ò$.

22. Æ>çÙ‰…ÌZ {ç³gê ç³…í³×îæ Ð]lÅÐ]lçܦ MìS…§ýl JMøPM>Æý‡$z §éÓÆ> çÜÆý‡çœÆ> ólõÜ ¼Ä¶æ*Å°MìSçÜ…º…« …_ MìS…¨ ÐésìæÌZ çÜOÆð‡…¨ H¨?1) ™ðlÌSÏÆó‡çÙ Œl M>Æý‡$z & 5 MìS.{V>

2) A…™øŧýlĶæ$ A ]l² Äñæ*f ]l M>Æý‡$z & 35 MìS.{V>.3) A ]l²ç³NÆý‡~ M>Æý‡$z & 10 MìS.{V>.4) Oò³Ð]l±² çÜOÆð‡ ]lÐól

23. Æ>çÙ‰…ÌZ 2017 &18 çÜ…Ð]l™èlÞÆý‡…ÌZ E™èlµ†¢AƇ$$ ]l Ððl¬™èl¢… BàÆý‡ «§é¯éÅË$ 167.2ÌS„ýSÌS r ]l$²Ë$ M>V>, 2018&19ÌZ ]lÐðl*-O§ðl ]l BàÆý‡«§é¯éÅÌS E™èlµ†¢ G…™èl?1) 149.2 ÌS„ýSÌS r ]l$²Ë$2) 143.8 ÌS„ýSÌS r ]l$²Ë$3) 151.1 ÌS„ýSÌS r ]l$²Ë$4) 160.0 ÌS„ýSÌS r ]l$²Ë$

24. MìS…¨ ÐésìæÌZ OÐðlGÝëÞÆŠæ OÆð‡™èl$ ¿ýæÆøÝëç³£ýlM>°MìS çÜ…º…« …_ çÜOÆð‡ ]lÑ HÑ?1) D ç³£ýlMýS… MìS…§ýl Æ>çÙ‰ÐéÅç³¢…V> E ]l² {糆

OÆð‡™èl$ MýS$r$…»ê°MìS ò³r$tºyìl ÝëĶæ$…MìS…§ýl 12,500 BǦMýS çÜàĶæ$… A…¨Ýë¢Æý‡$

2) C…§ýl$ÌZ MóS…{§ýl {糿¶æ$™èlÓ… {糿¶æ$™èlÓÐésê 6000 M>V>, Æ>çÙ‰ {糿¶æ$™èlÓ Ðésê6500

3) MúË$OÆð‡™èl$ÌS ÑçÙĶæ$…ÌZ Æ>çÙ‰ ÐéÅç³¢…V>{糆 MúË$ OÆð‡™èl$MýS$ ç³NÇ¢V> Æý‡*.12500]l$ Æ>çÙ‰ {糿¶æ$™èlÓÐól$ CçÜ$¢…¨

4) Oò³Ð]l±² çÜOÆð‡ ]lÐól25. 2018&19ÌZ MúË$OÆð‡™èl$ÌSMýS$ gêÈ ólíܯ]l

Ððl¬™èl¢… ÝëVýS$ §ýl–ÒMýSÆý‡×æ ç³{™éË$ G°²?1) 5,81,635 2) 6,81,6353) 7,81,635 4) 8,81,635

26. B…{«§ýl{糧ólÔŒæÌZ Ððl¬™èl¢… Ð]l$™èlÞÅM>Æý‡ çÜçßæ-M>Æý‡ çÜ…çœ*Ë$ G°² E¯é²Æ‡$$?1) 2112 2) 22123) 2312 4) 2412

27. B…{«§ýl{糧ólÔŒæ ArÒ AÀÐ]l– ® çÜ…çܦ GMýSPyýlE…¨?1) VýS$…r*Æý‡$ 2) {ç³M>Ôèæ… 3) MýSyýlç³ 4) ðlË*ÏÆý‡$

28. ç³r$t E™èlµ†¢ÌZ ¿êÆý‡™èl§ólÔèæ…ÌZ B…{«§ýl-{糧ólÔŒæ G¯ø² Ýë¦ ]l…ÌZ E…¨?1) 1 2) 2 3) 3 4) 4

29. ðlO ðl² & »ñæ…VýSâ¶æ*Æý‡$ C…yýl{íÜtĶæ$ÌŒæ M>ÇyéÆŠæ§éÓÆ> Æ>çÙ‰… ]l$…_ G…í³MýS ólíÜ ]l Ð]lÊyýl$´÷sñæ°ÛĶæ$ÌŒæ C…yýl{íÜtĶæ$ÌŒæ ¯øyŠæÌSÌZ Ìôæ°¨? 1) ðlË*ÏÆý‡$ hÌêÏÌZ° MýS–çÙ~ç³r²…2) _™èl*¢Æý‡$ hÌêÏÌZ° MýSÍMìSÇ3) A ]l…™èlç³#Æý‡… hÌêÏÌZ° íßæ…§ýl*ç³#Æý‡… 4) _™èl*¢Æý‡$ hÌêÏÌZ° HÆó‡µyýl$

30. OÐðlgêVŠæ& ðlO ðl² C…yýl{íÜtĶæ$ÌŒæ M>ÇyéÆŠæ §éÓÆ>B…{«§ýl{糧ólÔŒæÌZ AÀÐ]l– ® M> ]l$¯]l² ¯éË$VýS$¯øyŠæÌSÌZ Ìôæ°§ól¨?1) ÑÔ>Qç³r²… ¯øyŠæ2) ÑfĶæ$Ðéyýl ¯øyŠæ 3) §ö ]lMö…yýl ¯øyŠæ4) HÆó‡µyýl$ & }M>âýæçßæíÜ¢ ¯øyŠæ

31. 2001&2011 Ð]l$«§ýlÅ B…{«§ýl{糧ólÔŒæ f¯é¿êÐ]l– ® Æó‡r$ G…™èl?1) 7.21% 2) 8.21%

3) 9.21% 4) 10.21% 32. MìS…¨ ÐésìæÌZ Æ>çÙ‰ VýS×ê…M>ÌSMýS$ çÜ…º…«-

¨…_ çÜOÆð‡ ]lÑ HÑ?1) {ç³çÜ*† Ð]l$Æý‡×êÌS °çÙµ†¢ 742) ç³#Æý‡$çÙ$ÌS çÜVýSr$ BĶæ¬@{ç³Ð]l*×æ…

68.4 çÜ…Ð]l™èlÞÆ>Ë$3) ï܈ÌS çÜVýSr$ BĶæ¬@{ç³Ð]l*×æ… 72.1 çÜ….4) Oò³Ð]l±² çÜOÆð‡ ]lÐól

33. MìS…¨ÐésìæÌZ Æ>çÙ‰ VýS×ê…M>ÌSMýS$ çÜ…º…-« …_ çÜOÆð‡ ]lÑ HÑ?1) I§ólâýæÏÌZç³# »êÌSÅ Ð]l$Æý‡×êÌSÆó‡r$& 372) VýSÆý‡Â °Æø§ýlMýS ÐéÅí³¢ Æó‡r$& 66.73) çÜ…™é ]l ÝëçœÌSÅ Æó‡r$& 1.74) Oò³Ð]l±² çÜOÆð‡ ]lÐól

34. Æ>çÙ‰…ÌZ° B…{«§ýl{糧ólÔŒæ OÐðl§ýlÅÑ«§é ]l ç³ÇçÙ™ŒæMìS…§ýl E ]l² Ððl¬™èl¢… BçÜ$ç³{™èl$ÌS ÑÐ]lÆ>ÌSMýS$çÜ…º…« …_ çÜOÆð‡ ]lÑ HÑ?1) hÌêÏ Bçܵ{™èl$Ë$& 13 2) HÇĶæ* Bçܵ{™èl$Ë$& 283) MýSÐ]lÊÅ°sîæ BÆøVýSÅ MóS…{§éË$& 195 4) Oò³Ð]l±² çÜOÆð‡ ]lÐól

35. 2018&19 Ð]l¬…§ýlçÜ$¢ A… èl¯éÌS {ç³M>Æý‡…,íܦÆý‡ «§ýlÆý‡ÌZÏ ÑÑ«§ýl Æý‡…V>ÌS Ð]l– ®Æó‡rÏMýS$çÜ…º…« …_ çÜOÆð‡ ]lÑ HÑ?1) Ð]lÅÐ]lÝëĶæ$ Æý‡…VýS…& 10.78% 2) ´ëÇ{Ô>Ñ$MýS Æý‡…VýS…& 10.24%3) õÜÐé Æý‡…VýS…&11.09%4) Oò³Ð]l±² çÜOÆð‡ ]lÐól

36. 2017&18 çÜ…Ð]l™èlÞÆ>°MìS Æ>Ú‰ë°MìS Ýët…ç³#Ë$& Çhõ܉çÙ Œl §éÓÆ> çÜÐ]l$MýS*Ç ]l B§éĶæ$…?1) 4271 Mør$Ï 2) 3476 Mør$Ï3) 5428 Mør$Ï 4) 5460 Mør$Ï

37. 2018&19 Ð]l¬…§ýlçÜ$¢ A… èl¯éÌS {ç³M>Æý‡…Æ>çÙ‰… Ððl¬™èl¢… Aç³#µ G…™èl?1) 1,94,862 Mør$Ï 2) 2,23,706 Mør$Ï3) 2,58,928 Mør$Ï 4) H©M>§ýl$

38. MìS…¨ ÐésìæÌZ çÜOÆð‡ ]l Ðésì ° VýS$Ç¢… èl…yìl.1) A™èlÅ« MýS…V> ™ðlËÏ Æó‡çÙ Œl M>Æý‡$zË$ MýSÍW ]l

hÌê& ™èl*Æý‡$µ Vø§éÐ]lÇ2) A™èlÅ« MýS…V> A ]l²ç³NÆý‡~ Æó‡çÙ Œl M>Æý‡$zË$

MýSÍW ]l hÌêÏ & ™èl*Æý‡$µVø§éÐ]lÇ3) A™èlÅ«¨MýS…V> A…™øŧýlĶæ$ A¯]l²Äñæ*f ]l

Æó‡çÙ Œl M>Æý‡$zË$ MýSÍW¯]l hÌêÏ&A¯]l…™èlç³#Æý‡…4) Oò³Ð]l±² çÜOÆð‡ ]lÐól

39. B…{«§ýl{糧ólÔŒæÌZ A™èlÅ« MýS…V>, A™èlÅÌSµ…V>©ç³… MýS ðlMýSÛ ]l$Ï MýSÍW ]l hÌêÏË$ Ð]lÆý‡$çÜV>..?1) A ]l…™èlç³#Æý‡…&MýSyýlç³2) ™èl*Æý‡$µVø§éÐ]lÇ, ÑfĶæ$ ]lVýSÆý‡…3) ™èl*Æý‡$µVø§éÐ]lÇ, MýSyýlç³4) A¯]l…™èlç³#Æý‡…, ÑfĶæ$ ]lVýSÆý‡…

40. B…{«§ýl{糧ólÔŒæÌZ A™èlÅ« MýS ÑïÜ¢Æý‡~…ÌZ ÑçÜ¢-Ç…_ E ]l² AyýlÐ]l#Ë$ HÑ?1) _rtyýlÐ]l#Ë$ 2) Kò³ Œl ¸ëÆð‡‹Üt3) çÜÓÌSµ Ýë…{§ýl™èl AyýlÐ]l#Ë$4) A† Ýë…{§ýl™èl AyýlÐ]l#Ë$

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36. From the four words, identify theone which can be substituted forthe sentences in question.A person who can speak severallanguagesa) Philologist b) Etymologistc) Polyglot d) Linguist

37. Fill in the blanks with suitablewords.The Titanic ___ the Atlantic whenit _______ an ice berg.a) has been crossing, struckb) was crossing, struckc) had been crossing, struckd) is crossing, struck

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67. MìS…¨ÐésìæÌZ çÜÇM>° f™èl H¨? a) MýS… èl$& M>ç³ÆŠæ, sìæ Œlb) C™èl¢yìl& M>ç³ÆŠæ, h…MŠS c) °{MøÐŒl$& IÆý‡ Œl, {MøÑ$Ķæ$…, °MðSÌŒæ d) fÆý‡Ã Œl íÜÌSÓÆŠæ& íÜÌSÓÆŠæ, fÆó‡Ã°Ä¶æ$…

68. Ð]l$ÌôæÇĶæ* ÐéÅ« H AÐ]lĶæ$Ð]l…Oò³ {糿êÐ]l…èl*ç³#™èl$…¨?

a) ï³Ïçßæ… b) õ³VýS$ c) M>ÌôæĶæ$… d) Fí³Ç†™èl$¢Ë$

69. C ]l$ÞÍ Œl ]l$ E™èlµ†¢ ólõÜ MýS×êË$? a) BÌê¹ b) ½sêc) V>Ð]l* d) Oò³Ð]l±²

70. Ð]l ]lçܵ†™ø M>MýS$…yé, ]l* ðl™ø Ð]l…r^ólçÜ$MøÐéÌS° ^éÌêÐ]l$…¨ yéMýStÆý‡$ÏçÜ*_Ýë¢Æý‡$. G…§ýl$MýS$? a) ¯]l*¯ðlÌZ çÜ…™èl–ç³¢ MöÐ]l#ÓË$…sêƇ$$b) MöÐ]l#ÓÌZ AçÜ…™èl–ç³¢ MöÐ]l#ÓË$…sêƇ$$c) ]l* ðl™ø çÜ$Ë$Ð]l#V> Ð]l…r ólÄñæ¬ èl$a d) ]l* ðl ^éÌê ^úMýS

71. ÑrÑ$ Œl&G A« MýS…V> §ól°ÌZ E…r$…¨? a) Bí³ÌŒæ b) AÆý‡sìæ c) ¯éÇ…f d) VýS$yýl$z

72. C§ýlªÆý‡$ Ô>çÜÐól™èl¢ÌS õ³Æý‡Ï ]l$ MýSÍí³ ¯éÐ]l$MýSÆý‡×æ…ólíÜ ]l A×æ$Ð]l# »ZçÜ Œl (BOSON). ÒÇÌZJMýSÆý‡$ I ŒæïÜt Œæ Æð‡…yø ¿êÆý‡¡Ä¶æ$ Ô>ç܈Ðól™èl¢?a) çÜ™ólÅ…{§ýl¯é£Šl »Z‹Üb) ÌZMóS…{§ýl¯é£Šl »Z‹Ü c) ÔèæÆý‡™Œæ èl…{§ýl »Z‹Üd) fVýS©ÔŒæ èl…{§ýl »Z‹Ü

73. ¿êÆý‡¡Ä¶æ$ çÜ…™èl†MìS ðl…¨ ]l ç³Ë$Ð]l#Æý‡$¯ø»ñæÌŒæ ºçßæ$Ð]l$† {VýSïßæ™èlË$¯é²Æý‡$. AƇ¬™ól MìS…¨ ÐéÇÌZ GÐ]lÆý‡$ ¯ø»ñæÌŒæºçßæ$Ð]l$† {VýSïßæ™èl M>§ýl$?a) çÜ${ºçßæÃ×æÅ… èl…{§ýlÔóæQÆŠæ b) çßæÆý‡VøÑ…§Šæ Q$Æ>¯éc) }°ÐéçÜ Æ>Ð]l* ]l$f Œl d) Ððl…MýSrÆ>Ð]l$ Œæ Æ>Ð]l$MýS–çÙ~ Œl

74. çÜÓ§ólÖ Ýë…MóS†MýS ç³Çgêq ]l…™ø ™èlĶæ*Æý‡$ólíÜ ]l Ððl¬§ýlsìæ A×æ$ ÇĶæ*MýStÆŠæ õ³Æý‡$?

a) Aç³ÞÆý‡ b) Ðól$¯]lMýSc) M>Ñ$° d) Æøíßæ×îæ

75. "OòÜÃÍ…VŠæ º$§é®" A ól MøyŠæ õ³Æý‡$™ø Ððl¬§ýlsìæA×æ$ ç³È„ýS Æ>fÝë¦ ŒæÌZ fÇW ]l çÜ…Ð]l™èlÞÆý‡…? a) 1968 b) 1974c) 1982 d) 1995

76. MìS…¨ÐésìæÌZ Æý‡${§ýlç³#Æý‡$çÙ§ýl™èl$¢yýl$ ÐólíÜ ]l Ô>çܯ]l…? a) VýS$Æý‡gêÌS Ô>çÜ ]l…b) fVýSYĶæ$Åõ³r Ô>çܯ]l…c) ÑfĶæ$ç³#Ç Ô>çÜ ]l… d) } ç³Æý‡Ó™èl Ô>çÜ ]l…

77. H {´ë…™èl…ÌZ° Ô>çÜ ]l… èl{MýSÐ]lÇ¢ ÑÑ«§ýlÐ]lÆ>YÌSMýS$, çÜ…çܦÌSMýS$ C_a ]l ºçßæ$âýæ§é¯éÌS¯]l$ õ³ÆöP…¨?a) M>Æó‡Ï b) ÒÆ>ç³#Æý‡… c) Æ>Ð]l$WÇ d) AË*ÏÆý‡$

78. VøÐ]lÆý‡® é°MìS ðl…¨ ]l JMýS ól™èl M>ÇÃMýS$ÌS{Ôóæ×ìæÌZ EçÙÐ]l§ýl™èl$¢yýl$ 2,000 M>Æý‡Û糯éË$fÐ]l$ ólíÜ ]lr$tV> H Ô>çÜ ]l… õ³ÆöP…¨? a) Ýù´ëÆý‡ Ô>çܯ]l… b) ¯éíÜMŠS Ô>çÜ ]l… c) MýSO ðlÇ Ô>çܯ]l… d) {糆Úët ]l Ô>çÜ ]l…

79. MìS…¨ ÐésìæÌZ H {VýS…£ýl… ïÜÌS Æý‡ èl ]lË$ MýSÍWE…¨?a) º–çß晌æ MýS£ýl b) M>Ð]l$ çÜ*{™èl c) V>£é çÜç³¢Ôèæ† d) ÎÌêÐ]l†

80. "Äñæ*VýSÝëÆý‡' A ól {VýS…£é°² Æý‡_…_…§ðlÐ]lÆý‡$? a) ¯éV>Æý‡$j ]l$yýl$ b) «§ýl ]l´ëË$yýl$ c) Mö…yýl MýS$…yé^éÆý‡Åd) Ð]lçÜ$¢ ´ëË$yýl$

81. Ñç³µÆý‡Ï Ô>çܯ鰲 Ñyýl$§ýlÌS ólíÜ ]l ™èl*Æý‡$µ^éâ¶æ$MýSÅ Æ>k GÐ]lÆý‡$?a) MýS$ºj ÑçÙ$~ Ð]lÆý‡® ]l$yýl$ b) «§ýl¯]l$…fĶæ¬yýl$c) fĶæ$íÜ…çßæ Ð]lÌSÏ¿¶æ$yýl$ d) ÔèæMìS¢ Ð]lÆý‡Ã

82. MìS…¨ Æ>kÌZÏ "{†ç³#Æý‡ Ð]l$Æý‡¢Å Ð]l$õßæÔèæÓÆý‡'A ]l² ¼Æý‡$§ýl$ ]l$ «§ýlÇ…_ ]l ÐéÆð‡Ð]lÆý‡$? a) Ððl¬§ýlsìæ ÑçÙ$~ Ð]lÆý‡® ]l$yýl$ b) Ððl¬§ýlsìæ ÑfĶæ*¨™èl$Åyýl$c) Ð]lÊyø ÑçÙ$~ Ð]lÆý‡® ]l$yýl$ d) VýS$×æVýS ÑfĶæ*¨™èl$Åyýl$

83. ™èl*Æý‡$µ ^éâ¶æ$MýS$ÅÌS M>ÌS…ÌZ ´÷rÏ ðlÆý‡$Ð]l#§ól°MìS {ç³íÜ ® ðl…¨ ]l MóS…{§ýl…? a) »o§ýl® Ð]l$™èl… b) Ogñæ ]l Ð]l$™èl… c) OÔðæÐ]l Ð]l$™èl… d) OÐðlçÙ~Ð]l Ð]l$™èl…

84. Æ>fÆ>f ]lÆó‡…{§ýl$°™ø ¯]l…§ýl…ç³Nyìl {V>Ð]l*-°² §é ]l…V> ïÜÓMýSÇ…_ ]l Ð]lÅMìS¢ GÐ]lÆý‡$?a) ¯]l ]l²Ä¶æ$Å ¿ýær$t b) ¯éÆ>Ķæ$×æ ¿ýær$t c) h ]l Ð]lÌSÏ¿¶æ$yýl$ d) ´ëÐ]l#Ë*Ç Ð]l$ÌSÏ ]l

85. M>MýS¡Ä¶æ¬ÌS VýS$Ç…_ ™öÍ {ç³Ýë¢Ð]l ]l HÔ>çÜ ]l…ÌZ E…¨? a) Ð]l*VýSË$Ï Ô>çܯ]l… b) ºÄ¶æ*ÅÆý‡… Ô>çÜ ]l… c) ´ùÌSÐ]lÆý‡… Ô>çÜ ]l… d) í³ÌSÏÌSÐ]l${Ç Ô>çܯ]l…

86. MìS…¨ÐésìæÌZ ¿êÆý‡™èl çÜ…_™èl °« ]l$…_¡çÜ$Mø° Ð]lÅĶæ$… H¨?a) ¿êÆý‡™èl {糿¶æ$™èlÓ… »ê«§ýlÅ™èl Ð]líßæ… ól

º¬×æ ^éÆý‡$tb) çÜ${ï³…MøÆŠ‡t ¯éÅĶæ$Ð]lÊÆý‡$¢ÌSMýS$ ^ðlÍÏ…^é-

ÍÞ ]l i™éË$, ¿ýæ™éÅË$, ò³ ]lÛ ]l$Ï

c) Æ>Ú‰ëÌS OòßæMøÆý‡$t ¯éÅĶæ$Ð]lÊÆý‡$¢ÌSMýS$^ðlÍÏ…^éÍÞ¯]l ò³¯]lÛ ]l$Ï

d) Æ>Ú‰ëÌS VýSÐ]lÆý‡²Æý‡ÏMýS$ ^ðlÍÏ…^éÍÞ¯]l ò³¯]lÛ ]l$Ï87. BÇ®MýS ¼Ë$ÏMýS$ çÜ…º…« …_ MìS…¨ ÐéM>ÅÌZÏ

çÜÇM>°¨ H¨?a) JMýS ¼Ë$Ï BǦMýS ¼ÌêÏ, M>§é! A ]l²

ÑçÙĶæ$…ÌZ ÌZMŠS çÜ¿ýæ ïܵMýSÆŠæ °Æý‡~Ķæ$Ðól$™èl$¨ °Æý‡~Ķæ$…

b) JMýS ¼Ë$Ï BǦMýS ¼Ë$ÏV> ïܵMýSÆŠæ °Æý‡~Ƈ$$…-_ ]l ™èlÆ>Ó™èl B A…Ô>°² MøÆý‡$tË$,´ëÆý‡ÏÐðl$…sŒæ E¿ýæĶæ$ çÜ¿ýæË$, Æ>çى糆™øçÜà GÐ]lÆý‡$ {ç³Õ²… èlyé°MìS ÒÌôæϧýl$

c) BǦMýS ¼Ë$Ï MóSÐ]lÌS… ÌZMŠS çÜ¿ýæÌZ ól {ç³ÐólÔèæò³sêtÍ

d) BǦMýS ¼Ë$Ï ]l$ ´ëÆý‡ÏÐðl$…sŒæ ç³# ]l:ç³Ç-ÖÌS¯]lMýS$ Æ>çى糆 ç³…ç³Ð]l^èl$a.

88. ´ëÆý‡ÏÐðl$…sŒæ çÜ¿¶æ$ÅÌS ÑÔóæÚ뫨M>Æ>ÌSMýS$çÜ…º…« …_ çÜÇM>°¨ H¨?a) AÆð‡‹ÜtË ]l$…_ õÜÓ èleb) Ýë„ìSV> àfÆý‡$ M>Ð]lyýl… ]l$…_ õÜÓ èlac) ¿êÐ]l{ç³MýSr ]l õÜÓ èled) çÜ¿¶æ$ÅÌS Ð]lÅMìS¢VýS™èl õÜÓ^èla Ð]l*{™èlÐól$

õ³ÆöP¯é²Æý‡$. Ððl¬™èl¢… çÜ¿ýæMýS$ GÌê…sìæõÜÓ èla Ìôæ§ýl$

89. BÇtMýSÌŒæ 17, 18 MýS͵… ól çÜÐ]l* ]l™èlÓ…?a) ÝëÐ]l*hMýS çÜÐ]l*¯]l™èlÓ…b) BǦMýS çÜÐ]l*¯]l™èlÓ…c) Æ>fMîSĶæ$ çÜÐ]l*¯]l™èlÓ…d) Ð]l$™èl çÜÐ]l*¯]l™èlÓ…

90. MìS…¨Ðé°ÌZ H¨ ¿êÆý‡™èl Æ>gêÅ…VýS…{ç³M>Æý‡… {´ë£ýlÑ$MýS çßæMýS$P, Ð]l* ]lÐ]l çßæMýS$PA° MýS*yé ™ðlË$ç³#™èl$…¨?a) çÜÐ]l*^éÆý‡ çßæMýS$P b) ѧéÅ çßæMýS$P c) èl°´ùÄôæ$ çßæMýS$P d) VýS–çßæ çßæMýS$P

91. ¿êÆý‡™èl§ólÔèæ…ÌZ fÇVóS A°² ÑÐéàÌSÇhõ܉çÙ¯Œl ( ]lÐðl*§ýl$) ™èlç³µ°çÜÇV> fÆý‡´ë-ÌS° çÜ${ï³…MøÆŠ‡t H MóSçÜ$ÌZ B§ólÕ…_…¨ a) yé°Ä¶æ$ÌŒæ ËVs ¿êÆý‡™èl {糿¶æ$™èlÓ…b) AÔZMŠS MýS$Ð]l*ÆŠæ Vs ¿êÆý‡™èl {糿¶æ$™èlÓ… c) ïÜÐ]l* Vs AÕÓ Œl MýS$Ð]l*ÆŠæ d) Ô>Æý‡§ýl Vs «§ýlÆý‡… ´ëÌŒæ

92. MìS…¨ ÐésìæÌZ ÌZMŠSçÜ¿ýæÌZ JMýSsìæ MýS…sôæA« MýS…V> çÜ¿¶æ$ÅË$ E ]l² Æ>{çÙt…?a) Ðól$çœ*ÌSĶæ$ b) ¯éV>Ìê…yŠæ c) íÜMìSP… d) Ñ$gZÆ>…

93. ¿êÆý‡™èl§ólÔèæ…ÌZ G°² Æ>Ú‰ëÌZÏ §ýlÓ…§ýlÓçÜ¿ýæË$ E¯é²Æ‡$$? a) 5 b) 6 c) 7 d) 4

94. 73Ð]l Æ>gêÅ…VýS çÜÐ]lÆý‡×æ èlrt… §éÓÆ>]l*™èl¯]l çç³…^éĶæ$¡Æ>gŒæ Ð]lÅÐ]lçܦ Gç³µsìæ]l$…_ AÐ]l$ÌZÏMìS Ð]l_a…¨?

a) 1992 H{í³ÌŒæ 24b) 1993 H{í³ÌŒæ 24c) 1992 þ Œæ 1d) 1993 þ Œæ 1

çÜÐ]l*«§é¯éË$

34) b 35) c 36) c 37) b 38) d 39) a 40) b 41) a 42) a 43) c44) a 45) c 46) b 47) b 48) d 49) d 50) c 51) d 52) b 53) d 54) b 55) c 56) c 57) c 58) c 59) d 60) b 61) c 62) a 63) d 64) c 65) c 66) c 67) c 68) c69) b 70) b 71) d 72) a 73) c74) a 75) b 76) a 77) c 78) b79) c 80) a 81) d 82) d 83) b84) c 85) c 86) d 87) d 88) d89) a 90) b 91) c 92) a 93) b94) b

Hï³ {V>Ð]l$/ÐéÆý‡$z çÜ_ÐéËĶæ$… (MóSrWÈ&1) Ððl*yýlÌŒæ õ³ç³ÆŠæNo. of Questions: 150 Max. Marks: 150 Time: 150 min

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H Á‹Ö–ö˛ô˲fiΔÊˇÖÃZ f∞√Ö^ÈΔÊˇ$? G) 1863 º) 1867 Ì‹) 1861 yÏ˛) 1866

2. – ˛*ÑʸVʸ$ÖyÊ˛Ö —‘Û˝”‘Ë˝”Δ ÊˇƒÊ˝$≈ yÏ˛{X GMʸPyÊ˛ Á≥N«¢^Û˛‘ÈΔÊˇ$?G) A–ö˛$ÃÍÁ≥#ΔÊˇÖ º) ªÒ˝ÖVʸ‚Ê˝îΔÊ $ Ì‹) —‘ÈQÁ≥r≤Ö yÏ˛) ÜΔÊˇ$Á≥Ü

3. G∞≤ ƒÊ˝$*∞–ö˛«fisÓ˝À$ – ˛*ÑʸVʸ$ÖyÊ˛Ö —‘Û˝”‘Ë˝”Δ ÊˇƒÊ˝$≈Mʸ$ yëMʸtΔÛˇså˝ Á≥sÍtÕ_a V˙ΔÊˇ—Ö^ÈΔˇ$$?G) AΔˇ$$ßÊ˛$ º) ØÈÀ$Vʸ$ Ì‹) ôˆ—$√® yÏ˛) G∞—$®

4. øÍΔÊˇô˲ {Á≥øÊ˝$ô˲”Ö –˛*ÑʸVʸ$ÖyÊ˛Ö —‘Û˝”‘Ë˝”ΔÊˇƒÊ˝$≈Ø˲$ HºΔÊˇ$ßÊ˛$ô¯ V˙ΔÊˇ—Ö_Ö®? G) øÍΔÊˇô˲ ΔÊˇô˲≤ º) Á≥ßÊ˛√{÷ Ì‹) Á≥ßÊ˛√ —øÊ˝*ÁŸ◊ä˝ yÏ˛) Mʸ‚Í {Á≥Á≥NΔÊˇ~

5. øÍΔ Êˇô˲ {Á≥øÊ˝$ô˲”Ö – ˛*ÑʸVʸ$ÖyÊ˛Ö —‘Û˝”‘Ë˝”Δ ÊˇƒÊ˝$≈Á‹À‡Ú≥O Ø˙M> ∞Δ>√◊Í∞≤ GMʸPyÊ˛ Ø˛ÀMˆÕµÖ®?

G) —‘ÈQÁ≥r≤Ö º) ÜΔÊˇ$Á≥Ü Ì‹) MʸyÊ˛Á≥ yÏ˛) ªÒ˝ÖVʸ‚Ê˝îΔÊˇ$

{¥ÎMÓ¸tã‹ sÒ˝ã‹t & 2ô˛À$Vʸ$ øÍÁŸÃZ {V>Ö§Mʸ –Èßë∞Mϸ Á‹”Ì‹¶ ^˛Ì≥µ –ö˛≈–ö˛‡«Mʸ–Èßë∞Mϸ ØÈÖ® Á≥ÕMϸØ˲ øÍ⁄˘ßÊ˛≈–ö˛$M>Δ Êˇ$yÊ˛$ WyÊ˛$Vʸ$Δ>–ö˛$–ö˛$*«¢ Á≥Öô˲$À$. Δ>g͛ζØÈÃZœ, f“$ÖßëΔÊˇ$À MˆÀ$–ö˛#ÃZœ EÖyÛ˛ øÍÁŸØ˲$ {Á≥fÀ ØÈÀ$MʸÃZœMϸ °Á‹$Mʸ$Δ>–ÈÀ∞WyÊ˛$Vʸ$ B‘Ë˝ƒÊ˝$Ö. ‘ÈÔ‹àƒÊ˝$– $OØ˲ B´ßÊ˛$∞Mʸô˲ BƒÊ˝$Ø˲Mϸ BΔÊˇ–ö˛{¥Î◊˝Ö. Á‹Ö{Á≥ßëƒÊ˝$ —ßÊ˛≈ MʸÖsÙ˝ B´ßÊ˛$∞Mʸ —ßÊ˛≈ÃZ —‘ÈÀßÊ˛ñÌŸt, {Á≥Á≥Ö^˲gÍqØË Ö —‘Û˝ÁŸ–ö˛$∞ Vʸ$«¢Ö^ÈΔÊˇ$. W«fØ˲$À$EÖyÛ˛ {V>–ö˛*ÃZœ∞ ¥ÎuÊˇ‘ÈÀÃZœ Á≥∞^Û˛‘ÈΔÊˇ$. Á‹–ö˛ΔÊˇÀ —ßë≈¿–ö˛ñ®ÆMϸ MʸñÌŸ ^Û˛‘ÈΔÊˇ$. Ar$ øÍ⁄˘ßÊ˛≈–ö˛$Ö M¯Á‹–Û˛$ M>Mʸ$ÖyëW«fØ˲$À A¿–ö˛ñ®ÆMϸ Mʸ*yë —‘Û˝ÁŸÖV> MʸñÌŸ ^Û˛‘ÈΔÊˇ$. WyÊ˛$Vʸ$Δ>–ö˛$–ö˛$*«¢ Á≥Öô˲$À$ EßÊ˛≈–ö˛*∞≤ Mʸ— ›Î{–ö˛*så˝ —‘Ë˝”ØÈ£Ê˛Á‹ô˲≈ØÈΔ>ƒÊ˝$◊˝ Mʸ*yë Á‹–ö˛$«¶Ö^ÈΔÊˇ$. –ÈVʸ–ö˛$ ‘ÈÁ‹Ø˲$yÊ˛$Ø˲Ø˲≤ƒÊ˝$ô¯ WyÊ˛$Vʸ$Ø˲$ –ÈΔÊˇ$ ¥˘ÃÍaΔÊˇ$. ô˛À$Vʸ$ –È≈–ö˛‡«MʸøÍ⁄ΖÈßë∞Mϸ {÷M>ΔÊˇÖ ^˲$sÏ˝tÖ® WyÊ˛$Vʸ$ Δ>–ö˛$–ö˛$*«¢Á≥Öô˲$ÃÙ˝. {V>Ö§Mʸ øÍ⁄ΖÈßÊ˛$ÀMʸ$ –ö˛≈ÜΔÛˇMʸÖV> 1910ÃZ JMʸMˆô˲¢ EßÊ˛≈–ö˛*∞≤ Ø˲yÏ˛Ì≥ ô˛À$Vʸ$ øÍÁŸMʸ$ WyÊ˛$Vʸ$ i–ö˛Ö¥˘‘ÈΔÊˇ$. –ö˛$ØË˛Ö –ö˛*sÍœyÛ˛ –ÈyÊ˛$Mʸ øÍıŸ Δ>ƒÊ˝*À∞ BƒÊ˝$Ø˲AØÈ≤ΔÊˇ$. JMʸ Ø˲*ô˲Ø˲ øÍ⁄Î –Èßë∞Mϸ ØÈÖ® Á≥ÕMϸ GÖßÊ˛Δ¯Á≥ÖyÏ˛ô˲$À A–ö˛–ö˛*ØÈÀMʸ$, DÁ‹yÏ˛ÖÁ≥#ÀMʸ$ Vʸ$ΔÊˇƒÊ˝*≈ΔÊˇ$. G∞≤BrÖM>À$ GßÊ˛$ΔˇOØÈ ôÈØ˲$ {Á≥–Û˛‘Ë˝Ú≥rtßÊ˛À_Ø˲ Ø˲*ô˲Ø˲øÍ⁄Î –Èßë∞≤ –È≈Ì≥¢ÃZMϸ ô˛^Û˛aÖßÊ˛$Mʸ$ BƒÊ˝$Ø˲ EßÊ˛≈—$Ö^ÈΔÊˇ$. 1913ÃZ –ö˛≈–ö˛‡«Mʸ øÍÁŸÃZ ªZ´ßÊ˛Ø˲ fΔÊˇV>À∞ AÁ≥µsÏ˝–ö˛${ßëÁ‹$ Vʸ–ö˛ΔÊˇ≤ΔäˇMʸ$ WyÊ˛$Vʸ$ JMʸ —ØË˛Ü Á≥{ôÈ∞≤ Á‹–ö˛$«µÖ^ÈΔÊˇ$. –˛$$ô˲¢Ö i—ôÈØÛ˛≤ EßÊ˛≈–ö˛$ÖV> øÍ—Ö_Ø˲ ∞ΔÊˇÖô˲ΔÊˇ

©Ñ>- ô˲ô˲µΔÊˇ$À$ WyÊ˛$Vʸ$–È«ÃÍ AΔÊˇ$ßÊ˛$V> EÖsÍΔÊˇ$. “«ı‹–ö˛Ø˲$ Vʸ$«¢Ö_Ø˲ –ö˛${ßëã‹ {Á≥øÊ˝$ô˲”Ö 1913ÃZ "Δ>–ö˛# ∫Áfl˝ßÊ˛*™Δäˇ' ºΔÊˇ$ßÊ˛$ô¯ Á‹ØÈ√∞Ö_Ö®. ô˛À$Vʸ$ –ö˛^˲ØÈ∞≤ {¥Î`Ø˲{Á≥∫Ö´ßëÀ Ø˲$Ö_ —yÏ˛Ì≥Ö_ ô˛À$Vʸ$ øÍÁŸÃZ∞ ›˚ÖßÊ˛Δ>≈∞≤›Î–ö˛*Ø˲$≈ÀMʸ$ AÖ®Ö_Ø˲ B◊Ï˝–ö˛$$ô˲≈Ö WyÊ˛$Vʸ$ Ì≥yÊ˛$Vʸ$.^˛‚Ê˝ÂÌ≥‚Ê˝œ –Û˛ÖMʸr ‘ÈÌ‹à AØ˲≤r$œ øÍ⁄Î ı‹–ö˛ÃZ WyÊ˛$Vʸ$ –È«Mϸ–ÈΔÛˇ ›ÎsÏ˝.

{Á≥‘Ë˝≤À$1. WyÊ˛$Vʸ$ Δ>–ö˛$–ö˛$*«¢ Á≥Öô˲$À$ EßÊ˛≈–ö˛*∞≤ G–ö˛ΔÊˇ$

Á‹–ö˛$«¶Ö^ÈΔÊ $? G) ÜÀMä¸ º) ßÛ˛–ö˛#ÀÁ≥Õœ MʸñÁŸ~‘ÈÌ‹à Ì‹) {÷{÷ yÏ˛) —‘Ë˝”ØÈ£Ê˛ Á‹ô˲≈ØÈΔ>ƒÊ˝$◊˝

2. –ÈVʸ–ö˛$ ‘ÈÁ‹Ø˲$yÊ˛$ Ø˲Ø˲≤ƒÊ˝$ô¯ WyÊ˛$Vʸ$ Δ>–ö˛$–ö˛$*«¢Á≥Öô˲$À$Ø˲$ ¥˘ÕaØ˲–ÈΔÊˇ$ G–ö˛ΔÊˇ$?G) ∫Á‹–ö˛Δ>k A¥ÎµΔ>–ö˛# º) —‘Ë˝”ØÈ£Ê˛ Á‹ô˲≈ØÈΔ>ƒÊ˝$◊˝ Ì‹) EØ˲≤–ö ÀÑÓ¸√ ØÈΔ>ƒÊ˝$◊˝ yÏ˛) AyÊ˛— ªÍÌ≥Δ>k

3. WyÊ˛$Vʸ$ H Á‹Ö–ö˛ô˲fiΔÊˇÖÃZ Mˆô˲¢ EßÊ˛≈–ö˛*∞≤ Ø˲yÏ˛Ì≥ô˛À$Vʸ$ øÍÁŸMʸ$ i–ö˛Ö ¥˘‘ÈΔÊˇ$? G) 1910 º) 1912 Ì‹) 1916 yÏ˛) 1908

4. –ö˛≈–ö˛‡«Mʸ øÍÁŸÃZ ªZ´ßÊ˛Ø˲ fΔÊˇV>À∞ –ö˛${ßëã‹Vʸ–ö˛ΔÊˇ≤ΔäˇMʸ$ H Á‹Ö–ö˛ô˲fiΔÊˇÖÃZ WyÊ˛$Vʸ$ —ØË˛Ü Á≥{ô˲ÖÁ‹–ö˛$«µÖ^ÈΔÊ $? G) 1911 º) 1910 Ì‹) 1913 yÏ˛) 1916

5. "øÍ⁄Î ı‹–ö˛ÃZ WyÊ˛$Vʸ$ –È«Mϸ –ÈΔ Ûˇ ›ÎsÏ˝'AØ˲≤߲–ö˛ΔÊ $? G) MʸÖßÊ˛$Mʸ*« “ΔÛˇ‘Ë˝ÕÖVÊ¸Ö º) ªÒ˝f–ÈyÊ˛ V¯¥ÎÀΔˇyÏ˛zÌ‹) د« Ø˲ΔÊˇÌ‹ÖÁfl˝ ‘ÈÌ‹à yÏ˛) ^˛‚Ê˝œÌ≥‚Ê Â –Û˛ÖMʸr ‘ÈÌ‹à

{¥ÎMÓ¸tã‹ sÒ˝ã‹t & 3Á≥Δ>≈–ö˛Δ Êˇ◊˝Ö ô˲Ø˲ÃZ AÖô˲Δ>¬Vʸ– ˛$OØ˲ i–ö˛#À∞≤ÖsÏ˝Ú≥ OØ˲BΔ¯Vʸ≈ —ÁŸƒÊ˝$ÖÃZ Mʸ_aô˲–˛$OØ˲ {Á≥øÍ–È∞≤ ^˲*Ì≥Á‹$¢Ö®.BΔ¯Vʸ≈MʸΔÊˇÖV> {¥Î◊˝$À±≤ i—Ö^ÈÀÖsÙ˝ BΔ¯Vʸ≈MʸΔÊˇ–˛$OØ˲Á≥Δ>≈–ö˛Δ Êˇ◊˝Ö A–ö˛ Á‹Δ ÊˇÖ. ©∞ØÛ˛ CÃÍ ^ ˛ Á≥µ–ö˛^˲$a.Á≥Δ>≈–ö˛ΔÊˇ◊˝ÖÃZ∞ {¥Î◊˝$À±≤ BΔ¯Vʸ≈ÖV> EÖsÙ˝ Á≥Δ>≈–ö˛ΔÊˇ◊˝ÖBΔ¯Vʸ≈ÖV> EÖr$Ö®. øÊ˝*—$ MʸÀ$ÌŸôË˛Ö M>–ö˛yë∞Mϸ ØÛ˛ÀÚ≥OÁ≥yÊ˛–Û˛Ì‹Ø˲ —Áú$rØÈ∞Mϸ “À$ ÃÙ˝∞ ¥˘Õ–ö˛$Δäˇ Á≥ßëΔ>¶ÃÙ˝ØË ∞^˛Á≥µ–ö˛^˲$a. AÖsÙ˝ CsÓ˝–ö˛À –ö˛$ØË˛Ö A´®MʸÖV> EÁ≥ƒÒ˝*WÖ^Û˛¥Î≈MϸÖVä¸ Á‹Ö^˲$À$, Mʸ–ö˛ΔÊˇ$œ –˛$$ßÊ˛ÃÒ˝OØ˲ ¥˘Õ•Øå˛ ¥˜Õ{¥ÎÌ≥ŒØå˛ Á≥ßëΔ>¶À$. C— —Áú$rØÈ∞Mϸ A–ö˛M>‘Ë˝ÖÃÙ˝∞ΔÛˇyÏ˛ƒÒ˝* ßë«√Mʸ Á≥ßëΔ>¶À$. Cr$–ö˛ÖsÏ˝ –ö˛≈Δ>¶ÀØ˲$ {Á≥ôÛ˛≈MʸÖV>Ô‹À$ –Û˛Ì‹Ø˲ ÑÛ¸–ö˛$MʸΔÊˇ–˛$OØ˲ Á‹Ö^˲$ÃZœ øÊ˝{ßÊ˛Á≥ΔÊˇ_ –ÈsÏ˝Mϸ–ö˛*{ô˲–Û˛$ ∞ΔÛˇÆ’Ö_Ø˲ Á‹¶ÃÍÃZœ EÖ^ÈÕ. “ÃÒ˝OôÛ˛ –ÈsÏ˝∞Á≥#Ø˲«”∞ƒÒ˝*VÊ¸Ö M¯Á‹Ö »Ú‹OMϸÕÖVä¸ ^Û˛ƒÊ˝*Õ. Mˆ∞≤{Á≥–ö˛*ßÊ˛MʸΔÊˇ–˛$OØ˲ –ÈƒÊ˝$$–ö˛#À$ V>ÕÃZ MʸÀ–ö˛yÊ˛Ö –ö˛Àœ V>ÕMʸÀ$ÌŸô˲ –ö˛$–ö˛#ô˲$Ö®. Mˆ∞≤ Á≥ßëΔ>¶À$ V>ÕÃZ MʸÕı‹¢ GÀ»j–ö˛ÖsÏ˝ gÍyë≈À$ MʸÀ$Vʸ$ ôÈΔˇ$$. GΔˇ$$Δäˇ MʸÖyÏ˛ÁŸØ˲ΔÊ œÃZEÁ≥ƒÒ˝*WÖ^Û˛ Ô‹GãúÔ‹À$ V>ÕÃZMϸ ^Û˛«ôÛ˛ –ÈsÏ˝–ö˛Àœ KgZØå˛

¥˜ΔÊˇÃZ ΔÊˇÖ{´ßëÀ$ HΔÊˇµyÊ˛ôÈΔˇ$$. AyÊ˛–ö˛#ÀØ˲$ Ø˲«Mϸ–Û˛ƒÊ˝$yÊ˛Ö–ö˛Àœ Áfl˝«ô˲ VʸñÁfl˝ {Á≥øÍ–ö˛Ö GMʸ$P–ö˛–ö˛#ôË $Ö®. ±sÏ˝ÃZ ‡∞M>ΔÊˇMʸ–˛$OØ˲ ΔÊˇ›Î ƒÊ˝$ØÈÀ$ MʸÀ–ö˛yÊ˛Ö –ö˛Àœ yÓ˛yÓ˛sÓ˝ –ö˛ÖsÏ˝ Mˆ∞≤{Mϸ—$ Á‹Ö‡ΔÊˇMʸ ΔÊˇ›ÎƒÊ˝$ØÈÀ$ MʸÀÌ‹Ø˲ ±sÏ˝∞ {ôÈVʸyÊ˛Ö –ö˛ÀœM>≈Ø˲fiΔäˇ –È≈´® ›˘MÛ¸ {Á≥–ö˛*ßÊ˛–ö˛$$Ö®. AÖßÊ˛$–ö˛Àœ –ö˛$Ø˲ÖEÁ≥ƒÒ˝*WÖ^Û˛ ±sÏ˝∞ ‘Ë˝ì®Æ ^Û˛Ì‹Ø˲ ô˲ΔÊˇ–Èô˲ –ö˛*{ô˲–Û˛$EÁ≥ƒÒ˝*WÖ^ÈÕ. Á≥Δ>≈ –ö˛ΔÊˇ◊˝ÖÃZMϸ Mˆ∞≤ ΔÊˇM>ÃÒ˝OØ˲ Á‹*Ñʸ√i–ö˛#À$ {Á≥–Û˛’Ö_Ø˲Á≥#yÊ˛$ –È≈´® M>ΔÊˇM>ÃÒ˝OØ˲ B {Mϸ–ö˛$$À$i–ö˛#À ‘Ë˝»Δ>ÃZœMϸ ^Û˛« {Á≥–ö˛*ßÊ˛MÊ¸Δ Êˇ– ˛$OØ˲ –È≈ ´ßÊ˛$ÀØ˲$MʸÕY›Î¢Δˇ$$. “sÏ˝ –ö˛Àœ MʸÀΔ>, M>–˛$ΔÊˇ$œ –ö˛ÖsÏ˝ –È≈´ßÊ˛$À$›˘Mʸ$ôÈΔˇ$$. AÖßÊ˛$–ö˛Àœ ±ΔÊˇ$, V>Õ, ØÛ˛À, i–ö˛#À$ MʸÀ$ÌŸô˲ÖM>Mʸ$Öyë ô˲WØ˲ gÍ{Vʸô˲¢À$ °Á‹$M¯–ÈÕ. Á≥Δ>≈–ö˛ΔÊˇ◊˝ Á≥«ΔÊˇÑʸ◊˝M¯Á‹Ö {Á≥Ü JMʸPΔÊˇ* MʸñÌŸ ^Û˛ƒÊ˝*Õ.

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1. The first party from the north-easternregion declared as a national party bythe Election Commission of India is: (a) National People's Party (b) National North East People's Party (c) United North East Party (d) North-East Democratic Alliance

2. The Archaeological Survey of India hasdeclared Chaukhandi Stupa as a 'pro-tected area of national importance'.Chaukhandi Stupa is one of the impor-tant ancient Buddhist site located in: (a) Bihar (b) Madhya Pradesh (c) Uttar Pradesh (d) Andhra Pradesh

3. India and Portugal will cooperate in thesetting up of a national maritime her-itage museum at Lothal in: (a) Rajasthan (b) Madhya Pradesh (c) Uttar Pradesh (d) Gujarat

4. The Ministry of Home Affairs hasamended the Foreigners (Tribunals)Order, .............., and has empowered dis-trict magistrates in all States and UnionTerritories to set up tribunals to decidewhether a person staying illegally inIndia is a foreigner or not. (a) 1954 (b) 1964 (c) 1974 (d) 1980

5. The annual 'Mela Kheer Bhawani', themost important festival of: (a) Bihar (b) Jammu & Kashmir (c) Goa (d) Kerala

6. Which of the following countries is thefirst country visited by the Indian PrimeMinister Narendra Modi after takingoffice for a second term on 30 May? (a) Maldives (b) Sri Lanka (c) Bhutan (d) Nepal

7. On June 7, RBI had issued revisedguidelines for resolution of stressedassets. Under the new framework, it is amandatory requirement for lenders toenter into an Inter-Creditor Agreement(ICA) during the review of the borroweraccount within ................. days from dateof first default to any lender. (a) 60 (b) 30 (c) 90 (d) 120

8. The International Centre for Automotive Technology (ICAT) awardedIndia's first type approval certificate fortwo-wheelers complying with BS-VInorms to ................ (a) Bajaj Auto Ltd (b) Mahindra Two Wheelers Ltd (c) Hero Motocorp's Splendor iSmart (d) Suzuki Motorcycle India Pvt Ltd

9. Yuvraj Singh played his ODI debutmatch against which of the followingcountries?

(a) South Africa (b) England (c) Pakistan (d) Kenya

10. Noted actor, dramatist and Jnanpithawardee Girish Karnad passed away inBengaluru. He was conferred the PadmaShri in: (a) 1974 (b) 1980 (c) 1984 (d) 1990

11. The 45th summit of the G7 group ofcountries will take place in: (a) France (b) India (c) China (d) Italy

12. Who has been appointed the Leader ofthe House for the Rajya Sabha?

(a) Arun Jaitley (b) Thawar Chand Gehlot (c) Piyush Goyal (d) Narendra Modi

13. Who has been re-appointed as PrincipalSecretary to Prime Minister NarendraModi?

(a) Nripendra Misra (b) Kalaram Mishra (c) Vikram Singh (d) Vinod Sharma

14. The first village in India to have zerowooden stoves and almost no use forLPG cylinders is: (a) Velagalagudem (b) Rewa (c) Bancha (d) Pulivendala

15. Amasebailu in Kundapura Taluk ofUdupi district has become .............. firstsolar-powered Gram Panchayat. (a) Kerala (b) Tamil Nadu (c) Karnataka (d) Andhra Pradesh

16. Prime Minister Narendra Modi embarked on a two-day visit to Bishkek in................ for the Shanghai CooperationOrganisation (SCO) summit. (a) Kyrgyzstan (b) Russia (c) China (d) Turkmenistan

G7 Summit will be held in..?Current Affairs

Key & Explanations

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1. a The Election Commission of Indiadeclared the National People's Party ledby Meghalaya Chief Minister Conrad K.Sangma as a national party. This madethe NPP, formed by his father and for-mer Lok Sabha Speaker Purno A.Sangma in 2013, the first from thenorth-eastern region to earn the tag.

2. c Notification issued by Union Ministryof Culture, the Archaeological Surveyof India (ASI) has declared ChaukhandiStupa as a 'protected area of nationalimportance'. Chaukhandi Stupa is one ofthe important ancient Buddhist sitelocated in Sarnath, Uttar Pradesh (UP).

3. d India and Portugal will cooperate in thesetting up of a national maritime her-itage museum at Lothal in Gujarat.

4. b With Assam's National Register ofCitizens as the backdrop, the Ministryof Home Affairs (MHA) has laid outspecific guidelines to detect, detain anddeport foreign nationals staying illegal-ly across the country. The MHA hasamended the Foreigners (Tribunals)Order, 1964, and has empowered dis-trict magistrates in all States and UnionTerritories to set up tribunals to decidewhether a person staying illegally inIndia is a foreigner or not. Earlier, thepowers to constitute tribunals were vest-ed only with the Centre.

5. b The annual 'Mela Kheer Bhawani', themost important festival of Kashmiripandits, associated with Hindu GoddessRagnya Devi was celebrated with reli-gious fervor and gaiety at Tulmulla areaof central Kashmir's Ganderbal districtand Kupwara with thousands of Pandithdevotees participated in the function.

6. a Prime Minister Narendra Modi is inMale on a day long visit, his first visitabroad after taking office for a secondterm on 30 May, underlining NewDelhi's "neighbourhood first" foreignpolicy focus that has continued from hisfirst term in office.

7. b The Sashakt Committee has recom-mended that the existing Inter-CreditorAgreement (ICA) to incorporate therevised voting threshold and otherchanges for decision making stipulatedby the Reserve Bank of India. In a state-ment it said that this will enable expedi-tious implementation of the new frame-work on stressed assets. On June 7, RBIhad issued revised guidelines for resolu-tion of stressed assets. Under the newframework, it is a mandatory require-ment for lenders to enter into an Inter-Creditor Agreement (ICA) during thereview of the borrower account within30 days from date of first default to anylender.

8. c The International Centre for Automotive Technology (ICAT) has released

the first BS-VI certification for a two-wheeler --Hero MotoCorp's SplendoriSmart model --in the country, the test-ing and certification agency said. Thecompany stated that it is now eligible tostart production of the certified modelcompliant with the fuel emission normscoming into force from April 2020.

9. d India's swashbuckling all-rounder Yuvraj Singh announced his decision toretire from all forms of cricket. In near-ly two decades at the highest level, sincehis ODI debut against Kenya in 2000,Yuvraj featured in 40 Tests, 304 ODIsand 58 T20Is, while also playing a piv-otal role in India's two big triumphs -the2007 World T20 and the 2011 WorldCup.

10. a Noted actor, dramatist and Jnanpithawardee Girish Karnad passed away inBengaluru. He was conferred the PadmaShri in 1974 for his contributions to the-atre. In 1992, the Government of Indiahonoured him with the Padma Bhushan

11. a Prime Minister Narendra Modi hasaccepted an invitation from FrenchPresident Emmanuel Macron to attendthe outreach session of the G7 Summitin Biarritz as a special invitee, said asenior official. The 45th summit of theG7 group of countries will take placefrom August 24 to August 26 in Biarritz,France.

12. b Union Minister for Social Justice andEmpowerment Thawar Chand Gehlothas been appointed the Leader of theHouse for the Rajya Sabha. Meanwhile,Union Minister for Railways andCommerce Piyush Goyal will takecharge as the Deputy Leader for theUpper House of the Indian Parliament.

13. a Nripendra Misra has been re-appointedas Principal Secretary to Prime MinisterNarendra Modi. PK Mishra has alsobeen re-appointed as Additional Principal Secretary to Mr Modi.

14. c Bancha in Betul district, MadhyaPradesh is the first village in India tohave zero wooden stoves and almost no use for LPG cylinders with all its 75houses relying on solar-powered stovesto meet their cooking needs, claimssocial activist Mohan Nagar.

15. c Amasebailu in Kundapura Taluk ofUdupi district has become Karnataka'sfirst solar-powered Gram Panchayat.

16. b Prime Minister Narendra Modi embarked on a two-day visit to Bishkek inKyrgyzstan on June 13 for the ShanghaiCooperation Organisation (SCO) summit.

These model questions areprepared by the subject experts of

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GENERALAWARENESS

12 ôV’≤<äsêu≤<é X¯óÁø£yês¡+ 23.8.2019

1) Write the complex number (2-3i)(3+4i) in the form A+iB

Sol: (2-3i)(3+4i) =2(3)+2(4i)-3i(3)-3i(4i) = 6+8i-9i+12 [i2 = -1] = 18-i

2) Express (1-i)3 (1+i) in the form a+ibSol: (1-i)3 (1+i)=(1-i)2 [(1-i)(1+i)]=(1+i2 -2i)(12 -i2) =(1-1-2i)(1+1)i2 = -1] = (-2i)(2)= -4i = 0+i(-4)

3) Write the conjugate of (3+4i)(2-3i)Sol: (3+4i)(2-3i)=3(2)-3(3i)+4i(2)-4i(3i)=6-9i+8i+12 [ i 2 =-1] = 18-i

The conjugate of 18-I is 18+i4) Write the conjugate of (2+5i)(-4 +6i)

Sol: (2+5i)(-4+6i)=2(-4)+2(6i)+5i(-4)+5i(6i) = -8+12i-20i-30 [ i 2 =-1]= -38-8iThe conjugate of -38-8i is -38+8i

Mr. K. KumarSenior Faculty

Hyderabadph:9492956214

MATHS

CompetitiveExams Special

[∵

2

2 2

2 2

2 2

2 2

2 2 2 2

:

( )( ) ( )( )( )

( ) 2abi

2

Sol

a ib a ib a ib a iba ib a ib a ib a b

a ba b

a b aba b a b

− − − −= =+ + − +

− −=+

− − = + + +

5) Write the complex number in the form A+iB

2

2 2

2 2

2 2

2 2

2 2 2 2

2 2

2 2

2 2

:

( )( ) ( )( )( )

( ) 2abi

2

. .

2.

Sol

a ib a ib a ib a iba ib a ib a ib a b

a ba b

a b abi

a b a b

a bR P

a bab

I Pa b

− − + += =+ − + +

− +=+

− − = + + + −∴ =+

=+

6) Find the real and imaginary parts of the complex number

:1 7 24 7 24

7 24 (7 24 )(7 24 ) 49 5767 24 7 24

625 625 625

Sol

i ii i i

i i

− −= =+ + − +

−= = −

7) Find the multiplicative inverse of 7+24i

8) Find the multiplicative inverse of

5 3:

The multiplicative inverse of 5+3i is

1 5 3i 5+3i5 95+3i ( 5+3i )( 5 3i )

5+3i 5 3i14 14 14

i

Sol

+

−= =+−

= = −

( )

2 2 2 2

:7 24 7,b 24

7 24

49 576 625 25

:

2 2

25 7 25 77 24

2 2

32 2816 9

2 2

(4 3 )

Sol

let i a bi a

r a b

Formula

r a r aa ib i

i i

i

i

+ = + ⇒ = =

∴ = + = +

= + = =

+ −+ = ± + + −∴ + = ± +

= ± + = ± +

= ± +

9) Find the square root of 7+24i

( )

2 2 2 2

:512 5,b 12

( 5) 12

25 144

169 13:

2 2

13 5 13 55 12

2 2

8 182 2

4 9 (2 3i)

Sol

let i a bi a

r a b

Formula

r a r aa ib i

i i

i

i

= + ⇒ = − =

∴ = + = − +

= +

= =

+ −+ = ± + − +∴ − + = ± +

= ± +

= ± + = ± +

10) Find the square root of -5+12i

2 2 2 2

2

11) 7 21

: 7 21

7, 21

( 7) ( 21)

7 21 28 4 7 2 7

21tan tan

7

23 tan

32

( 7, 21)3

7 21(cos sin )

22 7 cos

3

Write Z i inthe polar

form

Sol let i x iy

x y

r x y

yx

lies inQ

The polar farmof i is

r i

i

θ θ

π

πθ

θ θπ

= − +

− + = +

⇒ = − =

∴ = − + = − +

+ = = × =

= ⇒ = −

= − =

⇒ = −

− ++

= +

∵

2sin

3π

2 2 2 2

12) 1 3 mod

: 1 3 1, 3

(1) ( 3)

1 3 4 2

3tan tan 3 tan

1 3

Express i in the ulus

amplitude form

Sol let i x iy x y

r x y

yx

πθ θ

+

+ = + ⇒ = =

∴ = + = +

= + = =

= ⇒ = = =

1(1, 3)3

mod 1 3

(cos sin ) 2 cos sin3 3

lies inQ

the amp form of i is

r i i

πθ

π πθ θ

⇒ =

∴ +

+ = +

∵

[ ]

2 2 2 2

3

: 1 , 1, 1

(1) ( 1)

1 1 2

1, tan tan 1

113

tan4

3( 1, 1)

4mod (cos sin )

3 32 cos sin

4 4

Sol let i x iy x y

r x y

yNow

x

lies inQ

the amp form is r i

i

θ θ

π

πθ

θ θ

π π

− − = + ⇒ = − = −

∴ = + = + −

= + =−= ⇒ = =

− =

⇒ = − −

∴ +

= +

∵

13) Express -1-i in the modulus – Amplitude form

[ ]

2 2 2 2

4

: 1 , 1, 1

(1) ( 1)

1 1 2

1, tan tan 1

1

tan4

(1, 1)4

mod (cos sin )

2 cos sin4 4

2 cos sin4 4

Sol let i x iy x y

r x y

yNow

x

lies inQ

The amp form is r i

i

i

θ θ

π

πθ

θ θ

π π

π π

− = + ⇒ = = −

∴ = + = + −

= + =−= ⇒ = = −

= − −⇒ = −

∴ +

− − = + − = −

∵

14) Express 1-i in the modulus –amplitude form.

1

2

15) 1 1, 2 , rg

:

( 1) ,2

zIf Z Z i find A

z

Sol We know that

Arg Arg iππ

= − =

− = =

11 2

2

1 2

1 2

1

1

2 1

2 2

16. , / 5, / 3

then find Arg ( ) ( )

:5

5

(3

zArg Argz Argz

z

If Arg Z Arg Z are

Z Arg Z

Sol Giventhat Arg Z

Arg Z

Also Arg Z Arg Z

π ππ

π π

π

π

π

−

−

∴ = = −

= = =

+

=

⇒ = −

= ∴ 2

1 2

1 2

1 2 1 2

2 2 2

2

) Arg( )

5 3 25 3 3 5 15 15

17. 1,

( )

: ( 1)

( 1)2

( ) ( ) ( )

2 218. ( ) , ( )

Sol : ( )( ) ( ) x iy

Z

If Z Z i then find the

Arg Z Z

Sol Weknow Arg and

Arg

Arg Z Z Arg Z Arg Z

If a ib x iv find x v

a ib x iy

a ib a ib

π π π π π π π

ππ

π ππ

+

−= − + = − = =

= − = −

− =

− = −

∴ = +

= =

+ = + +

+ = +⇒ + + = +

2 2 2 2

2 2 2 2 2 2

2 2 2 2 2

.

,

( )

a ib a ib x iy

a b a b

x y a b x y

Squaringonboth sides we get

a b x y

⇒ + + = +

⇒ + +

⇒ + ⇒ + = +

+ = +

B|æø£ ù|J\ô|’ MT n_ÛÁbÕj·÷\qT, dü\Vü‰\qTe÷≈£î ‘Ó*j·TCÒj·T+&ç.

dipika.navatelangana21@gmail.com

to be continued

Express 1-i in the modulus amplitude form

13ôV’≤<äsêu≤<é X¯óÁø£yês¡+ 23.8.2019

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18. uÛ≤s¡‘· Á|üuÛÑT‘·«+ ªø£s¡Te⁄ |”&ç‘· ÁbÕ+‘ê\ n_Ûe�~Δ |ü<∏äø£+µqT m|ü&ÉT Á|üy˚X¯ ô|{Ϻ+~? 1) 1949 2) 1954 3) 1973 4) 1976

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