Education 21 09 2017

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"CÖyÏ˛ƒÊ˝*; {Á≥ƒÊ˝*«sÓ˝ã‹ ÁúΔäˇ ßÊ˛ ÁúN≈^Ë˛Δäˇ' ΔÊˇ^Ë˛Δˇ$$ôË˛? 1. ô˛ÀÖV>◊˝ Δ>{ÁŸt {Á≥´ßëØË˛ Á‹–ö˛*^ÈΔÊˇ MÊ¸—$ÁŸØË˛ΔäˇV> G–ö˛ΔÊˇ$ ∞ƒÊ˝$—$ôË˛$ÀƒÊ˝*≈ΔÊˇ$? G) ∫${Δ> –˛ÖMÊ¸sÙ˝‘Ë˝Ö º) Δ>gÍ Á‹ßëΔ>Ö Ì‹) ∫$ßë™ –ö˛$$ΔÊˇ„ yÏ˛) –ö˛{Δˇ –˛ÖMÊ¸sÙ˝‘Ë˝”ΔÊˇ$œ 2. ¥ÎMä¸ÃZ øÍΔÊˇôË˛ ØË˛*ôË˛ØË˛ Δ>ƒÊ˝$ªÍ«V> G–ö˛ΔÊˇ$ ∞ƒÊ˝$—$ôË˛$ÀƒÊ˝*≈ΔÊˇ$? G) V˙ôË˛–í˛$ ∫ÖªÍ–ÈÃÙ˝ º) ©¥Î –˛$Áfl˝ôÈ Ì‹) «^Ë˛Δäˇz Δ>Áfl˝ìÃå˝–ö˛ΔÊˇ√ yÏ˛) Afƒå˝$ º›Î«ƒÊ˝* 3. CsÓ˝–ö˛À –ö˛$ΔÊˇ◊Ï˝Ö_ØË˛ {Á≥Á≥Ö^Ë˛ÖÃZØÛ˛ AÜ –ö˛ñßÊ˛Æ –ö˛$Ìfl˝‚Ê˝ –ö˛ƒÒ˝$ÃÒ˝så˝ {ªõØ¨˛(117) H ßÛ˛‘Ë˝Á‹$¶Δ>À$? G) f¥ÎØ¨˛ º) f–˛$OM> Ì‹) A–˛$«M> yÏ˛) M¸ØË˛yë 4. ô˛À$VÊ¸$ Ì‹∞–ö˛* ΔÊˇÖV>∞MÏ¸ ^Û˛Ì‹ØË˛ —’ÁŸt MÊ¸ñÌŸMÏ¸V>ØË˛$ "AMÏ¸PØÛ˛∞ ØÈVÛ¸‘Ë˝”ΔÊˇΔ>–ö˛# gÍ°ƒÊ˝$ A–ÈΔÊˇ$z'MÏ¸ D Hyë® G–ö˛ΔÊˇ$ GÖÌ≥MÊ¸ƒÊ˝*≈ΔÊˇ$? G) M¸OM>À Á‹ôË˛≈ØÈΔ>ƒÊ˝$◊˝ º) f–ö˛$$ØË˛ Ì‹) M¯ßÊ˛ÖyÊ˛Δ>—$ΔˇyÏ˛z yÏ˛) Gã‹.Gã‹.Δ>f–ö˛ò„ 5. {Á≥Á≥Ö^Ë˛ KgZØ¨˛ ®Ø¯ôË˛fi–ö˛Ö? G) Ú‹Ú≥tÖ∫ΔÊˇ$ 8 º) Ú‹Ú≥tÖ∫ΔÊˇ$ 14 Ì‹) Ú‹Ú≥tÖ∫ΔÊˇ$ 16 yÏ˛) Ú‹Ú≥tÖ∫ΔÊˇ$ 18 6. G–ö˛« fƒÊ˝$ÖÜ∞ Á≥#ΔÊˇÁ‹P«Ö^Ë˛$Mˆ∞ Ú‹Ú≥tÖ∫ΔÊˇ$ 15ØË˛ gÍ°ƒÊ˝$ CÖf±ΔÊˇœ ®Ø¯ôË˛fi–ö˛ÖV> ∞ΔÊˇ”Ìfl˝›Î¢ΔÊˇ$? G) M¸.GÃå˝.Δ>–ö˛# º) –˛*ÑÊ¸VÊ¸$ÖyÊ˛Ö —‘Û˝”‘Ë˝”ΔÊˇƒÊ˝$≈ Ì‹) BΔÛˇ™’Δäˇ V¯{ß˛gå˝ yÏ˛) –ö˛$Ø¯√Áfl˝Ø¨˛‘Ë˝ΔÊˇ√ 7. ƒÊ˝$$Δ¯Ì≥ƒÊ˝$Ø¨˛ ßÛ˛‘Ë˝Ö ›˘œ–ÈMä¸ «Á≥ºœMä¸MÊ¸$ ØË˛*ôË˛ØË˛ øÍΔÊˇôË˛ Δ>ƒÊ˝$ªÍ«? G) –ö˛$Ø¨˛{Ô≥ô¨˛ –ˆ{Áfl˝ º) ØË˛–ö˛©ã≥ Á‹*« Ì‹) gÒ˝O©ã≥ Á‹Δ>PΔäˇ yÏ˛) Áfl˝ΔÊˇ¤MÊ¸$–ö˛*Δäˇ gÒ˝OØ¨˛ 8. {ºrØ¨˛ÃZ∞ Áfloã‹ Bãú M>–ö˛$Ø¨˛fi ØË˛$Ö_ "V¯œ∫Ãå˝ y˛O–ö˛«fisÓ˝ A–ÈΔÊˇ$z&2017' ¥˜Ö®ØË˛ øÍΔÊˇ °ƒÊ˝$$yÊ˛$? G) —.ØÈΔ>ƒÊ˝$◊˝–ö˛$*«¢ º) Á‹ÃÍ√Ø¨˛RÍØ¨˛ Ì‹) Á‹$∞ôÈ ØÈΔ>ƒÊ˝$◊ä˝ yÏ˛) ^ÈÖ© {Á≥›Îßä˛ øÊ˝så˝ 9. MÊ¸ÀaΔäˇ, Áfl˝ì≈–ö˛*∞sÏ˝ã‹, ØÛ˛^Ë˛$ΔÊˇÃå˝ Ú‹OØ˛fiã‹ÃZ AÖ®Ö^Û˛ {Á≥Ü⁄ÎxôË˛√MÊ¸ ∫ÃÍjØ¨˛ [Ú≥Ogå˝&2017 ¥˜Ö®ØË˛ øÍΔÊˇôË˛ Á‹ÖôË˛Ü –ö˛≈MÏ¸¢? G) Δ¯›ÎÕØ¨˛ Ìfl˝WYØ¨˛fi º) ı‹rΔäˇ {ªõØ¨˛ Ì‹) ºØÈ AVÊ¸Δ>”Ãå˝ yÏ˛) «^Ë˛Δäˇz gÒ˝OØ¨˛ 10. 2017 Ú‹Ú≥tÖ∫ΔÊˇ$ 11&12 –ö˛ΔÊˇMÊ¸$ øÍΔÊˇô¨˛ÃZ Á≥ΔÊˇ≈sÏ˝Ö_ØË˛ ªÒ˝ÃÍΔÊˇã‹ A´ßÊ˛≈ÑÊ¸$yÊ˛$? G) ƒÊ˝$*ÕƒÒ˝* ô˛O–˛$$ÚŸÖM¯ º) GyÛ˛Δäˇz ÌúÀã≥fi Ì‹) AÃÒ˝V>jÖyÊ˛Δäˇ À$≈MÊ¸ÚŸÖM¯ yÏ˛) y¯«ã‹ À*≈£ëMÊ¸Δäˇz 11. 2017 Ú‹Ú≥tÖ∫ΔÊˇ$ 13&14 –ö˛ΔÊˇMÊ¸$ øÍΔÊˇô¨˛ÃZ Á≥ΔÊˇ≈sÏ˝Ö_ØË˛ f¥ÎØ¨˛ {Á≥´ßë∞? G) ÌŸÖgZ AªÒ˝ º) ƒÒ˝*ÌŸƒÊ˝*MÏ¸ CÌŸgÍ–È Ì‹) ƒÒ˝$ÌŸΔ¯ –˛*© yÏ˛) ƒÊ˝$$MÏ¸ƒÒ˝* Áfl˝sZƒÊ˝*–ö˛* 12. ƒÒ˝$–˛$Ø¨˛ÃZ∞ C›Îœ—$Mä¸ ı‹tså˝ E{VÊ¸–ÈßÊ˛$À ^˛ΔÊˇ ØË˛$Ö_ CsÓ˝–ö˛À —yÊ˛$ßÊ˛ÃÒ˝OØË˛ [M¸OÁ‹¢–ö˛ –ö˛$ôË˛ªZ´ßÊ˛MÊ¸$yÊ˛$ ∏ÎßÊ˛Δäˇ EΔÊˇn*ØÈÕØ¨˛ H ßÛ˛‘È∞MÏ¸ ^˛Ö®ØË˛–ÈyÊ˛$? G) ØÛ˛¥ÎÃå˝ º) ØÈΔÛˇ” Ì‹) BÁúÉ∞›Î¶Ø¨˛ yÏ˛) CÖyÏ˛ƒÊ˝* 13. –ö˛$ƒÊ˝$ØÈ√Δäˇ AÖôË˛ΔÊˇ$≈ßÊ˛ÆÖ M>ΔÊˇ◊˝ÖV> ∫ÖV>œßÛ˛‘¨˝MÊ¸$ –ö˛ÀÁ‹–ö˛_aØË˛ Δ¯Ìfl˝ÖV>≈ –ö˛$$Ì‹œÖÀ Á‹‡ƒÊ˝$Ö M¯Á‹Ö øÍΔÊˇô¨˛ ^Û˛Á≥sÏ˝tØË˛ M>ΔÊˇ≈{MÊ¸–ö˛$Ö? G) BÁ≥Á≥ΔÛˇÁŸØ¨˛ Á‹Ø¨˛ΔˇOgå˝ º) BÁ≥ΔÛˇÁŸØ¨˛ CØ¨˛›Î∞ƒÊ˝$ô¨˛ Ì‹) BÁ≥ΔÛˇÁŸØ¨˛ CØ¨˛Ìú∞sÏ˝–í˛ fÌ‹tã‹ yÏ˛) BÁ≥ΔÛˇÁŸØ¨˛ GÖyÊ˛*≈«ÖVä¸ {ÔúyÊ˛Ö 14. "gÍ°ƒÊ˝$ Ìfl˝Ö© øÍ⁄Î ®Ø¯ôË˛fi–ö˛Ö(Ú‹Ú≥tÖ∫ΔÊˇ$ 14) Á‹ÖßÊ˛ΔÊˇ¬ÖV> Ìfl˝Ö© {Ì≥ƒÊ˝$$À M¯Á‹Ö Δ>{ÁŸtÁ≥Ü Δ>–í˛$ØÈ£ä˛ M¯—Ößä˛ B—ÁŸP«Ö_ØË˛ –˛$$ªÒ˝OÃå˝ ƒÊ˝*ã≥? G) ÕÃÍ º) ôË˛ßëÁ‹$¶ Ì‹) Á‹ÖMÊ¸r –˛*^Ë˛Ø¨˛ yÏ˛) Ìfl˝Ö© ı‹–È 15. øÍΔÊˇôË˛ –ö˛*i {MÏ¸M¸rΔäˇ Á‹_Ø¨˛ {¥ÎΔÊˇÖ¿Ö_ØË˛ "—$ÁŸØ¨˛ 24' {¥ÎgÒ˝MÊ¸$t {Á≥´ßëØË˛ ÀÑÊ¸≈Ö? G) 2024 ØÈsÏ˝MÏ¸ {MÓ¸yë ΔÊˇÖVÊ¸ A¿–ö˛ñ®Æ º) 24 H‚Ê˝œÃZÁ≥# –È«MÏ¸ E_ôË˛ÖV> {MÏ¸M¸så˝ÃZ ’ÑÊ¸◊˝ Ì‹) Δ>ªZƒÙ˝$ 24 Ø˛ÀÃZœ –ö˛$$ÖªÒ˝O –ö˛$$«MÏ¸–ÈyÊ˛À A¿–ö˛ñ®Æ yÏ˛) 24 VÊ¸ÖrÀ ı‹Á≥# –ö˛$$«MÏ¸–ÈyÊ˛À {Á≥fÀMÊ¸$ —ßÊ˛$≈ô¨˛ ›˚MÊ¸ΔÊˇ≈Ö 16. Δ¯k–È» M>ΔÊˇ≈{MÊ¸–ö˛*À ∞ΔÊˇ”Áfl˝◊˝ÃZ Ìfl˝Ö©

—∞ƒÒ˝*V>∞MÏ¸ V>ØË˛$ 2016&17 31. H –ö˛Á‹$¢–ö˛#ÀÚ≥O Á≥ßÛ˛‚Ê˝ìœV> Á‹Ö–ö˛ôË˛fiΔ>∞MÏ¸ "Δ>f≈ øÍ⁄Î MÓ¸«¢ MˆØË˛›ÎVÊ¸$ôË˛$ØË˛≤ GVÊ¸$–ö˛$ôË˛$À ∞ıŸ´ßë∞≤ Á≥#ΔÊˇ›ÎPΔÊˇÖ' ¥˜Ö®ØË˛ ªÍ≈ÖMä¸? CsÓ˝–ö˛À MÛ¸Ö{ßÊ˛Ö ôˆÀWÖ_Ö®? G) Á≥ÖgÍªå˝ ØÛ˛ÁŸØË˛Ãå˝ ªÍ≈ÖMä¸ G) ^Ë˛MÊ¸PΔÊˇ º) –ö˛*ÖÁ‹Ö º) —fƒÊ˝$ ªÍ≈ÖMä¸ Ì‹) ßÛ˛ØÈ ªÍ≈ÖMä¸ Ì‹) Á≥Á≥#µ´ßëØÈ≈À$ yÏ˛) ºƒÊ˝$≈Ö yÏ˛) ªÍ≈ÖMä¸ Bãú ∫Δ¯yë 32. øÍΔÊˇôË˛ ƒÒ˝*VÊ¸ ∞Á≥#◊˝$yÊ˛$ ºÁŸ$~ ^Ë˛ΔÊˇ◊ä˝ 17. Á‹–ö˛$${ßëÀ Á≥«ΔÊˇÑÊ¸◊˝ÃZ øÍVÊ¸ÖV> Úú*ãŸÚ≥O CsÓ˝–ö˛À ¥˘Á‹tÃå˝ ›ÎtÖÁ≥#ØË˛$ IMÊ¸≈Δ>f≈ Á‹—$Ü {Á≥ôÛ˛≈MÊ¸ Gã‹.–ö˛$Ìfl˝¥ÎÃå˝ΔˇyÏ˛z —yÊ˛$ßÊ˛À ^Û˛Ì‹ØË˛ ßÛ˛‘Ë˝Ö? Δ>ƒÊ˝$ªÍ«V> CsÓ˝–ö˛À G–ö˛ΔÊˇ$ G) ^˛OØÈ º) fΔÊˇ√± Ì‹) IΔ>œÖyä˛ yÏ˛) f¥ÎØ¨˛ Ô‹∞ƒÊ˝$Δäˇ ∏Î≈MÊ¸Œt 33. yÏ˛hrÃå˝ ^˛ÕœÖÁ≥#À M¯Á‹Ö CsÓ˝–ö˛À ∞ƒÊ˝$—$ôË˛$ÀƒÊ˝*≈ΔÊˇ$? G) –˛*gÒ˝Ø¨˛fi ÕM¸Prãút VÊ¸*VÊ¸$Ãå˝ Á‹ÖÁ‹¶ ΔÊˇ*¥˜Ö®Ö_ØË˛ ƒÊ˝*ã≥? º) ‘ÈØÛ˛ MÊ¸Áfl˝ÖªÍ MÊ¸$sÙ˝›Î G) _{Ãå˝ º) ôÛ˛gå˝ Ì‹) ¡–í˛$ yÏ˛) Ω –˛$OIã‹ Ì‹) Ô≥rΔäˇ £ë–ö˛$fiØ¨˛ yÏ˛) ∞MÏ¸P Áfl˝Õ 34. 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Ì‹»ã‹ sÒ˝OsÏ˝Ãå˝ØË˛$ ›˜ÖôË˛Ö G) ›˜œ–Û˛MÏ¸ƒÊ˝* º) ªÒ˝ÃÍΔÊˇã‹ Ì‹) f¥ÎØ¨˛ yÏ˛) DhÁ≥#t ^Û˛Á‹$MˆÖ®? 21. 2017 Ú‹Ú≥tÖ∫ΔÊˇ$ 13ØË˛ ∫ƒÒ˝* sÒ˝M>≤Àh G) CÖÜƒÊ˝*Ø¨˛ ΔÊˇ^Ë˛Ø¯Mä¸(£ëƒå˝$ÃÍÖyä˛) ΔÊˇÖVÊ¸ÖÃZ AÖôË˛Δ>j°ƒÊ˝$ {Á≥ƒÒ˝*VÊ¸‘ÈÀ HΔ>µr$MÊ¸$ º) Œ kΔÊˇ$ƒå˝$(^˛OØÈ) øÍΔÊˇô¨˛ô¯ {Á≥ôÛ˛≈MÊ¸ JÁ≥µßÊ˛Ö MÊ¸$ßÊ˛$ΔÊˇ$aMˆØË˛≤ ßÛ˛‘Ë˝Ö? Ì‹) Ø¯gZ—$ JMÊ¸$Áfl˝ΔÊˇ(f¥ÎØ¨˛) G) DhÁ≥#t º) {∏ÎØ¨˛fi Ì‹) f¥ÎØ¨˛ yÏ˛) A–˛$«M> MÊ¸Δ¯ÕØÈ –ö˛*«Ø¨˛(Ú‹µΔˇ$$Ø¨˛) 22. 2017 Ú‹Ú≥tÖ∫ΔÊˇ$ 15ØË˛ "Á‹”^Ë˛eôÈ Ìfl˝ ı‹–ö˛' 37. yÏsÏ˛˝)20ÃZ 100 Ì‹MÊ¸fiΔÊˇ$œ ›Î´®Ö_ØË˛ ôˆÕ {MÏ¸M¸rΔäˇ? M>ΔÊˇ≈{MÊ¸–ö˛*∞≤ Δ>{ÁŸtÁ≥Ü GMÊ¸PyÏ˛ ØË˛$Ö_ G) yÊ˛$Ú≥œÌ‹ã‹(ßÊ˛ÑÏ¸◊Í{ÌúM>) {¥ÎΔÊˇÖ¿Ö^ÈΔÊˇ$? º) Áfl˝«™Mä¸ ¥ÎÖyÊ˛≈ (CÖyÏ˛ƒÊ˝*) G) M>ØË˛*µΔäˇ(EôË˛¢ΔÊˇ{Á≥ßÛ˛‘¨˝) º) MÊ¸‚Í≈◊ä˝(–ö˛$‡Δ>{ÁŸt) Ì‹) {MÏ¸ã‹VÛ¸Ãå˝(–˛Ì‹tÖyÓ˛ã‹) yÏ˛) yÏ˛M>Mä¸(ßÊ˛ÑÏ¸◊Í{ÌúM>) Ì‹) EØÈ(VÊ¸$fΔ>ô¨˛) yÏ˛) EyÏ˛Ì≥(MÊ¸Δ>~rMÊ¸) ªÍ≈yÏ˛√ÖrØ¨˛ {MÓ¸yëM>«◊Ï˝ Ì≥.—.Ì‹Ö´ßÊ˛$ 23. Á‹Δ>™Δäˇ Á‹Δ¯–ö˛Δäˇ yë≈ÖØË˛$ {Á≥´ßë∞ –˛*© gÍÜMÏ¸ 38. 2017ÃZ V¸Õ_ØË˛ sÒ˝OsÏ˝‚Ê˝œÃZ ÃÙ˝∞®? AÖMÏ¸ôË˛Ö ^Û˛Ì‹ØË˛ Δ¯k? 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VÊ¸$ΔÊˇ$–ÈΔÊˇÖ 21 Ú‹Ú≥tÖ∫ΔÊˇ$ 2017

Eß¯≈V>À$ —$∞Ô‹â Bãú Ì‹—Ãå˝ H—ƒÙ˝$ÁŸØ¨˛ —$∞Ô‹â Bãú Ì‹—Ãå˝ H—ƒÙ˝$ÁŸØ¨˛ B´ßÊ˛”ΔÊˇ≈ÖÃZ∞ ∫*≈Δ¯ Bãú Ì‹—Ãå˝ H—ƒÙ˝$ÁŸØ¨˛ Ú‹MÊ¸*≈«sÓ˝ & MÏ¸Ö® ¥˘Á‹$tÀ øÊ˝»¢MÏ¸ ßÊ˛ΔÊˇRÍÁ‹$¢À$ M¯ΔÊˇ$ô¯Ö®. –˛$$ôË˛¢Ö RÍ‰À$: 121 yÏ˛Á≥N≈sÓ˝ H—ƒÙ˝$ÁŸØ¨˛ Ú‹MÊ¸*≈«sÓ˝ BÔúÁ‹Δäˇ RÍ‰À$: 73 AΔÊˇ·ôË˛: yÏ˛{X E°¢ΔÊˇ~ôË˛ô¯ ¥Îr$ ¥˘Œã‹/ Ú‹MÊ¸*≈«sÓ˝/ CÖsÒ˝ÕgÒ˝Ø¨˛fi —øÍV>ÃZœ –ö˛$*yÛ˛‚Ê˝œ AØË˛$øÊ˝–ö˛Ö EÖyëÕ. Ô‹∞ƒÊ˝$Δäˇ H—ƒÙ˝$ÁŸØ¨˛ Ú‹MÊ¸*≈«sÓ˝ AÌ‹Ú‹tÖså˝ RÍ‰À$: 32 AΔÊˇ·ôË˛: Ú‹Ö{rÃå˝ BΔäˇ√yä˛ ¥˘Œã‹ ∏˘Δˇfiã‹/ ı‹tså˝ ¥˘Œã‹ BΔÊˇYØ˛OgÙ˝ÁŸØ¨˛fi / ƒÊ˝$*∞ƒÊ˝$Ø¨˛ sÒ˝«r» ¥˘Œã‹ BΔÊˇYØ˛OgÙ˝ÁŸØ¨˛fiÃZ BÔúÁ‹Δäˇfi MÛ¸yÊ˛ΔäˇÃZ Á≥∞^Û˛Ì‹ EÖyëÕ. ›Îtãú M>Δäˇ [y˛O–ö˛Δäˇ RÍ‰À$: 16({VÛ¸yä˛ 1 MÛ¸yÊ˛ΔäˇÃZ 8, {VÛ¸yä˛ 2 MÛ¸yÊ˛ΔäˇÃZ 8) AΔÊˇ·ôË˛: Úfl˝“/ ÃÒ˝Oså˝ –˛*sÍΔäˇ –˛Ìfl˝MÏ¸Ãå˝ ÃÒ˝OÚ‹Ø¨˛fi + Ú≥{sZÃå˝/ yÓ˛hÃå˝ CÖhØ¨˛ –ö˛«PÖVä¸ÃZ AØË˛$øÊ˝–ö˛Ö EÖyëÕ. ßÊ˛ΔÊˇRÍÁ‹$¢ ^Û˛ΔÛˇÖßÊ˛$MÊ¸$ BQΔÊˇ$ ôÛ˛©:ØË˛–ö˛Ö∫ΔÊˇ$ 15 –˛ªå˝Ú‹Oså˝: www.bcasindia.nic.in

Ì‹ÖVÊ¸ΔÛˇ◊Ï˝ M>À»ã‹

ô˛ÀÖV>◊˝ MˆôË˛¢VÊ¸*y˛ÖÃZ∞ Ì‹ÖVÊ¸ΔÛˇ◊Ï˝ M>À»ã‹ MÊ¸ÖÚ≥± Õ—$sÒ˝yä˛ & –Û˛$ØÛ˛gå˝–˛$Öså˝ [sÒ˝O± ¥˘Á‹$tÀ øÊ˝»¢MÏ¸ ßÊ˛ΔÊˇRÍÁ‹$¢À$ M¯ΔÊˇ$ô¯Ö®. RÍ‰À$: 12 AΔÊˇ·ôË˛: Ô‹H/ IÌ‹yÊ˛∫$œ≈H/ Ì‹GÖH Á≥N«¢^Û˛Ì‹ EÖyëÕ –ö˛ƒÊ˝$Á‹$: BVÊ¸Á‹$t 1 ØÈsÏ˝MÏ¸ 18 ØË˛$Ö_ 30 H‚Ê˝œ –ö˛$´ßÊ˛≈ EÖyëÕ. BØ¨˛ÃÒ˝OØ¨˛ ßÊ˛ΔÊˇRÍÁ‹$¢MÊ¸$ BQΔÊˇ$ ôÛ˛©: AM¯t∫ΔÊˇ$ 5 –˛ªå˝Ú‹Oså˝: www.scclmines.com

GÖBΔäˇÌ≥GÃå˝ JGØ¨˛hÌ‹ B´ßÊ˛”ΔÊˇ≈ÖÃZ∞ –ö˛$ÖVÊ¸‚Ê˝îΔÊˇ$ «ÚúOØË˛» AÖyä˛ Ú≥{sZ M¸—$MÊ¸Ãå˝fi Õ—$sÒ˝yä˛(GÖBΔäˇÌ≥GÃå˝)& {V>yÊ˛$≈ ƒÙ˝$så˝ {¥˜ÚúÁŸØË˛Ãå˝ ¥˘Á‹$tÀ øÊ˝»¢MÏ¸ ßÊ˛ΔÊˇRÍÁ‹$¢À$ M¯ΔÊˇ$ô¯Ö®. –˛$$ôË˛¢Ö RÍ‰À$: 74 —øÍV>À–È» RÍ‰À$: M¸—$MÊ¸Ãå˝ 23, –˛$M>∞MÊ¸Ãå˝ 36, GÀMÏ¸âMÊ¸Ãå˝ 2, GÀM>â∞Mä¸fi á MÊ¸–ö˛$*≈∞MÛ¸ÁŸØ¨˛ 5, Ì‹—Ãå˝ 8 AøÊ˝≈ΔÊˇ$¶À$ Δ>ƒÊ˝*ÕfiØË˛ VÛ¸så˝ 2017 ı≥Á≥Δäˇ M¯yä˛: M¸—$MÊ¸Ãå˝&Ì‹Úfl˝^¨˛, –˛$M>∞MÊ¸Ãå˝&GÖC, GÀMÏ¸âMÊ¸Ãå˝ & CC, GÀM>â∞Mä¸fi á MÊ¸–ö˛$*≈∞MÛ¸ÁŸØ¨˛ & CÌ‹, Ì‹—Ãå˝ & Ì‹C AΔÊˇ·ôË˛: ºC/ ºsÒ˝Mä¸(M¸—$MÊ¸Ãå˝ CÖf±«ÖVä¸/ M¸—$MÊ¸Ãå˝ sÒ˝M>≤Ài/ Ú≥{sZ M¸—$MÊ¸Ãå˝ CÖf±«ÖVä¸/ Ú≥{sZ M¸—$ MÊ¸Ãå˝ sÒ˝M>≤Ài/ –˛$M>∞MÊ¸Ãå˝ CÖf±«ÖVä¸/ GÀMÏ¸âMÊ¸Ãå˝/ GÀMÏ¸âMÊ¸Ãå˝ á GÀM>â∞Mä¸fi/ GÀM>â∞Mä¸fi á MÊ¸–ö˛$*≈∞MÛ¸ ÁŸØ¨˛/ GÀM>â∞Mä¸fi CÖf±«ÖVä¸/ GÀM>â∞Mä¸fi á sÒ˝Õ MÊ¸–ö˛$*≈∞MÛ¸ÁŸØ¨˛fi / Ì‹—Ãå˝) E°¢ΔÊˇ$~ÃÒ˝O EÖyëÕ. ºC ({¥˜yÊ˛ÑÊ¸Ø¨˛/ Bsü–˛$$ªÒ˝OÃå˝/ –˛$MÊ¸{sÍ∞Mä¸fi/ MÊ¸Ø¨˛Á‹âÑÊ¸Ø¨˛ CÖf±«ÖVä¸) AøÊ˝≈ΔÊˇ$¶À$ ßÊ˛ΔÊˇRÍÁ‹$¢MÊ¸$ AØË˛ΔÊˇ$¤À$. GÖÌ≥MÊ¸: VÛ¸så˝ 2017 ›˘PΔÊˇ$ B´ßëΔÊˇÖV>ØÛ˛ AøÊ˝≈ΔÊˇ$¶À GÖÌ≥MÊ¸ EÖr$Ö®. 2016 AÖôË˛MÊ¸$–ö˛$$ÖßÊ˛$ ØÈsÏ˝ ›˘PΔÊˇœØË˛$ Á≥«VÊ¸◊˝ØË˛ÃZMÏ¸ °Á‹$M¯ΔÊˇ$. BØ¨˛ÃÒ˝OØ¨˛ ßÊ˛ΔÊˇRÍÁ‹$¢MÊ¸$ BQΔÊˇ$ ôÛ˛©: AM¯t∫ΔÊˇ$ 19 –˛ªå˝Ú‹Oså˝: www.mrpl.co.in

AyÏ˛√ÁŸØå˛ﬁ

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W hat is the total number of female students.. QUANTITATIVE APTITUDE B. Krishna Kishore Senior Faculty Dimensions Coaching Centre, Guntur.

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for Post Graduate Studies and DE (CPGS&DE), National Institute of Rural Development and Panchayati Raj, Rajendranagar, Hyderabad- 500030 –˛ªå˝Ú‹Oså˝: www.nird.org.in/pgdrdm.aspx

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BÖ{´ßÊ˛{Á≥ßÛ˛‘¨˝, ôÈyÛ˛Á≥ÕœVÊ¸*y˛ÖÃZ∞ ØÛ˛ÁŸØË˛Ãå˝ CØ¨˛Ì‹tr*≈så˝ Bãú sÒ˝M>≤Ài(∞så˝)& ØÈØ¨˛ sÓ˝_ÖVä¸ ¥˜hÁŸØ¨˛fi á ∏Î≈MÊ¸Œt ¥˜hÁŸØ¨˛fi øÊ˝»¢M¯Á‹Ö {Á≥MÊ¸rØË˛ —yÊ˛$ßÊ˛À ^Û˛Ì‹Ö®. AΔÊˇ·ôË˛: ÁúÁ‹$t M>œã‹ –ö˛*ΔÊˇ$PÀô¯ yÏ˛{X / Ì≥Úfl˝^¨˛yÏ˛ Á≥N«¢^Û˛Ì‹ EÖyëÕ ßÊ˛ΔÊˇRÍÁ‹$¢ ^Û˛ΔÛˇÖßÊ˛$MÊ¸$ BQΔÊˇ$ ôÛ˛©: AM¯t∫ΔÊˇ$ 20 ßÊ˛ΔÊˇRÍÁ‹$¢ ‡ΔÊˇ$z M>Ô≥ ^Û˛ΔÛˇÖßÊ˛$MÊ¸$ BQΔÊˇ$ ôÛ˛©: AM¯t∫ΔÊˇ$ 30 –˛ªå˝Ú‹Oså˝: www.nitw.ac.in

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Final Counselling for admission into Diploma courses at PJTSAU

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Dr. B.R. Ambedkar Open University B.Ed. 2017 Exam Hall Tickets

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Andhra University: B.Sc. IV Sem. May 2017 Exam Results

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IBPS RRB OFFICE ASSISTANT MODEL PAPER Marks: 80

°¯]l²sìæ "Ñ§ýlÅ' ™èlÆý‡$ÐéÆ‡¬.. 43. A batsman makes a score of 58 runs in the 15th innings and thus increases his average by 3 runs. What is the average after 15th innings? a) 12 b) 14 c) 16 d) 18 e) None of these 44. How many integers greater than 5000 can be formed with the digit 7, 6, 5, 4 and 3 using each digit at most once? a) 72 b) 144 c) 84 d) 192 e) None of these 45. Two balls are selected from a box containing 2 blue and 7 red balls. What is the probability that at least one ball is blue? 2 a) 9

7 b) 9

5 c) 12

d)

Sales 17% July

12% er Novemb 8% tober Oc 25% September

22% August

The respective ratio between the number of mobile phones sold of company A and Company B during six months. Month July August September October November December

48.

7 12

e) None of these Directions (Q. No. 46-50): Study the following pie-chart and table carefully and answer the questions given below. Percentagewise Distribution of the Number of Mobile Phones Sold by a Shopkeeper During Six Months Total number of mobile phones sold = 45,000

16% December

47.

Ratio 8:7 4:5 3:2 7:5 7:8 7:9

46. What is the respective ratio between the number of mobile phones sold of company B during July and those sold during December of the same company?

49.

50.

Time: 45 Minutes

a) 119 : 145 b) 116 : 135 c) 119 : 135 d) 119 : 130 e) None of these If 35% of the mobile phones sold by company A during November were sold at a discount, how many mobile phones of company A during that month were sold without a discount? a) 882 b) 1635 c) 1638 d) 885 e) None of these If the shopkeeper earned a profit of Rs. 433/- on each mobile phone sold of company B during October, what was his total profit earned on the mobile phones of that company during the same month? a) Rs. 6, 49,900/b) Rs. 6, 45,900/c) Rs, 6,49, 400/d) Rs. 6,49,500/e) None of these The number of mobile phones sold of company A during July is approximately what percent of the number of mobile phones sold of company A during December? a) 110 b) 140 c) 150 d) 105 e) 130 What is the total number of mobile phones sold of company B during August and September together? a) 10,000 b) 15,000 c) 10,500 d) 9,500 e) None of these

Directions (Q.No. 51-55): What should come in place of the questions mark (?) in the following questions? 51. 20.2 × 64 × 81.3 × 40.2 = 8? a) 2.7 b) 2.5 c) 3.7 d) 3.2 e) None of these 52. 83% of 6242 × 12% of 225 = ? a) 146286.42 b) 134263.18 c) 139883.22 d) 1562218.23 e) None of these 1 8

6 7 121 a) 8 140 177 d) 7 140

3 5

53. 1 +1 + 3 = ? b) 6

163 280

c) 9

197 280

e) None of these

54. ? ÷ 25 ÷ 12 = 248.76 a) 74628 b) 497.52 c) 62452 d) 870.66 e) None of these 55. (73)3 = ? a) 365127 b) 298627 c) 305867 d) 389017 e) None of these

Direction (Q. No. 56-60) : In the following questions two equations numbered I and II are given. You have to solve both equations and Given answer If: a) x > y b) x ≥ y c) x < y d) x ≤ y e) x = y or the relationship cannot be established 56. I. x2 − 7x + 10 = 0 II. y2 + 11y + 10 = 0 57. I. x2 + 28x + 192 = 0 II. y2 + 16y + 48 = 0 58. I. 2x − 3y = − 3.5 II. 3x + 2y = − 6.5 59. I. x2 + 8x + 15 = 0 II. y2 + 11y + 30 = 0 60. I. x = 3136 II. y2 = 3136 Directions (Q.No. 61-65) : Study the following graph and table carefully and answer the questions given below. Time Taken to Travel (in hours) by Six Vehicles on Two different Days. 20 Time (in hours)

Questions: 80

15

18

16 16

15 12

11

12

16

19

second? a) 15.3 b) 12.8 c) 11.5 d) 13.8 e) None of these 64. The distance travelled by vehicle F on day 2 was approximately what percent of the distance Students Anushka Archit Arpan Garvita Gunit Pranita

65.

66.

67.

14 12

10 5 0 A

B

C D Vehicles Day 1

E

F

Day 2

Distance Covered (in Kilometers) by Six Vehicles on Each Day Vehicle A B C D E F

Day 1 832 516 693 552 935 703

Day 2 864 774 810 765 546 636

61. Which of the following vehicles travelled at the same speed on both the days? a) Vehicle A b) Vehicle C c) Vehicle F d) Vehicle B e) None of these 62. What was the difference between the speed of vehicle A on day 1 and the speed of vehicle C on the same day? a) 7 km/hr b) 12 km/hr c) 11 km/hr d) 8 km/hr e) None of these 63. What was the speed of vehicle C on day 2 in terms of meters per

68.

69.

70.

Direction (Q. No. 71-75) : Study the table carefully to answer the questions that follow. Percentage of Marks Obtained by Different Students in Different Subjects of MBA.

Strategic Brand Compensation Management Management Management (150) (100) (150) 66 75 88 82 76 84 76 66 78 90 88 96 64 70 68 48 56 50

travelled by it on day 1? a) 80 b) 65 c) 85 d) 95 e) 90 What is the respective ratio between the speeds of vehicle D and vehicle E on day 2? a) 15 : 13 b) 17 : 13 c) 13 : 11 d) 17 : 14 e) None of these The cost of 5 pens and 8 pencils is Rs. 31. What would be the cost of 15 pens and 24 pencils? a) Rs. 93 b) Rs. 99 c) Rs. 96 d) Cannot be determined e) None of these The difference between a twodigit number and the number obtained by interchanging the position of its digits is 36. What is the difference between the two digits of that number? a) 3 b) 4 c) 9 d) Cannot be determined e) None of these With an average speed of 40 km/h, a train reaches its destination in time. If it goes with an average speed of 35 km/h, it is late by 15 minutes. The length of the total journey is: a) 40 km b) 70 km c) 30 km d) 80 km e) None of these 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish in 10 days. In how many days will 10 women finish it? a) 20 days b) 30 days c) 40 days d) 50 days e) None of these A invests Rs. 64,000 in a business. After few months B joined him with Rs. 48,000. At the end of year, the total profit was divided between them in the ratio 2:1. After how many months did B join? a) 7 b) 8 c) 4 d) 6 e) None of these

Consumer Service Training & Behaviour Marketing Development (125) (75) (50) 56 56 90 96 92 88 88 72 70 76 84 86 72 68 74 64 64 58

71. How many marks did Anushka get in all the subjects together? a) 369 b) 463 c) 558 d) 496 e) None of these 72. Who has scored the highest total marks in all the subjects together? a) Archit b) Gunit c) Pranita d) Garvita e) None of these 73. Marks obtained by Garvita in Brand Management are what percent of marks obtained by Archit in the same Subject? (rounded off to two digits after decimal) a) 86.36 b) 101.71 c) 115.79 d) 133.33 e) None of these 74. How many students have scored the highest marks in more than one subject? a) Three b) Two c) One d) None e) None of these 75. What are the average marks obtained by all students together in Compensation Management? a) 116 b) 120 c)123 d) 131 e) None of these Directions (Q. No. 76-80): In each of these questions a number series is given. In each series only one number is wrong. Find out the wrong number. 76. 850 843 829 808 788 745 703 a) 843 b) 829 c) 808 d) 788 e) 745 77. 6 7 9 13 26 37 69 a) 7 b) 26 c) 69 d) 37 e) 9 78. 7 18 40 106 183 282 403 a) 18 b) 282 c) 40 d) 106 e) 183 79. 4 3 9 34 96 219 435 a) 4 b) 9 c) 34 d) 435 e) 219 80. 157.5 45 15 6 3 2 1 a) 1 b) 2 c) 6 d) 157.5 e) 45

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2) 3

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OÐðlG‹ÜBÆŠæ hÌêÏ l VýS$Æý‡$ÐéÆý‡… l òÜò³t…ºÆŠæ l 21 l 2017

14 Ñ§ýlÅ

IBPS RRB OFFICE ASSISTANT MODEL PAPER Key & Solutions 43) c; Let average for 14 innings be x. Then, 14 x + 58 =x+3 15

14x + 58 = 15x + 45 ⇒ x = 13 ∴ New average = (x + 3) = 13 + 3 = 16 runs. 44) d; 4 digit number 3× 4P3 = 3×4×3×2 = 72 5 digit number 5!= 5 × 4 × 3 × 2 × 1 =120 Total = 72 + 120=192 45) c; No. of blue balls = 2 No. of red balls = 7 Total no. of balls = 9 Required probability P = (one ball is blue) P = 1−

7C 2 5 = 9C 2 12

(46-50) Total No.of Total No.of Total No.of Mobiles Sold Mobiles Sold Mobiles Sold of Company A of CompanyB Jul

7650

4080

3570

Aug

9900

4400

5500

Sep

11250

6750

4500

Oct

3600

2100

1500

Nov

5400

2520

2880

Dec

7200

3150

4050

46) c; Number of mobiles sold of company B in July = 3570 Number of mobiles sold of company B in December = 4050 Required ratio = 3570 : 4050 = 119 : 135 47) c; Total mobiles sold by company A during November = 2520 Total mobiles sold by this company at discount = 35% of 2520 = 882 Total mobiles sold by company A without discount = 2520 − 882 = 1638 48) d; Mobile phones sold of company B during October = 1500 Total profit earned on the mobile phones = Rs. (433 × 1500) = Rs. 6,49,500 49) e; Number of mobile phones sold of company A during July = 4080 Number of mobile phones sold by company A during December = 3150 Required percentage =

4080 × 100 = 129.5 ≈ 130 % 3150

50) a; Mobile phones sold of company B during August = 5500 Mobile phones sold of company B during September = 4500 Total number of mobile phones

= 5500 + 4500 = 10,000 (51-55) 51) e; (2)0.2×(2)6×(2)3.9×(2)0.4 = (23)? (2)10.5 = (2)3×? 10.5 = 3 × ? ?=3.5  83 × 6242   12 × 225   ×  100    100 

52) c; 

= 5180.86×27 = 139883.22

9 13 18 315 + 520 +1008 53) b; + + = 8 7 5 280 1843 163 = =6 280 280 ? 54) a; 25 × 12 = 248.76

⇒ ? = 248.76 × 300 = 74628 55) d; (73)3 = 389017 (56-60) 56) a; From Statement (I) x2 − 7x + 10 = 0 x2 − 5x −2x + 10 = 0 (x − 2)(x − 5) = 0 ∴x = 2 or 5 From statement (II) y2 + 11y + 10 = 0 y2 + 10y + y + 10 = 0 (y + 1) (y + 10) = 0 ∴ y = −1 or −10 So, x > y 57) d; x2 + 28x + 192 = 0 x2 + 16x + 12x+192= 0 (x + 16) (x+12) = 0 x= − 16, −12 From statement (II) y2+12y+4y+48 = 0 (y + 12)(y + 4) = 0 y= − 12, − 4 So, x ≤ y 58) c; 2x − 3y = − 3.5 ….(i) 3x + 2y = − 6.5 …..(ii) Equation (i) × 2 + (ii) × 3 Substract (ii) from (i) ∴ We get x = − 2.038 ⇒ x in Equation….(i) we get y = − 0.192 So, from above it is clear that x<y 59) b; From statement (I) x2 + 8x + 15 = 0 x2 + 5x + 3x + 15 = 0 (x + 3) (x +5) = 0 ∴ x = −3 or −5 From statement (II) y2 + 11y + 30 = 0 y2 + 6y + 5y + 30 = 0 (y + 5) (y + 6) = 0 ∴ y = −5 or −6 From statement (I) and (II), we have x = y or x > y Hence x ≥ y 60) b; From Statement (I) x = 3136 = 56

From Statement (II) y2 = 3136 ∴ y = ± 56

(61-65) Vehicle A B C D E F

Day 1 Distance in km 832 516 693 552 935 703

Time in hr 16 12 11 12 16 19

Speed in km/hr 52 43 63 46 58.4 37

61) d; Vehicle B 62) c; Speed of vehicle A on day 1 = 52 km/hr Speed of vehicle C on day 1 = 63 km/hr Difference = 63 − 52 = 11 km/hr 63) e; Speed of vehicle on day 2 = 45 km/hr 5  ⇒  45 ×  m / sec = 12.5 m / sec 18  

64) e; Percentage = Dis tan ce travelled by vehicle F on day2 × 100 Dis tan ce travelled by vehicle F on day1 =

636 × 100 ≈ 90% 703

65) b; Speed of vehicle D on day 2 = 51 km/hr Speed of vehicle E on day 2 = 39 km/hr Required ratio = =

51 17 = or 17 :13 39 13

66) a; Cost of 5 pens + 8 pencils = Rs. 31 On multiplying by 3 15 pens + 24 pencils = 3 × 31 = Rs. 93 67) b; Let the ten's digit be x and unit's digit be y Then, (10x+y) − (10y+x) = 36 ⇒ 9(x − y) = 36 ⇒x−y=4 68) b;

Pr oduct of speed D= Difference of speed ×Time difference

=

40 × 35 15 × 5 60

= 70 km

69) c; Method I. Considering one day's work 1 ……….(1) 8 1 3m + 7w = 10 …….(2)

4m + 6w =

(1) × 3 − (2) × 4 gives 3 4 1 or,10w = 8 10 40

18w−28w = −

∴10 women can do the work in 40 days 70) c; Suppose, B joined after x months Then B's money was invested for (12−x) months ∴ According to question

Time in hr 16 18 18 15 14 12

Day 2 Distance in km 864 774 810 765 546 636

Speed in km/hr 54 43 45 51 39 53

16 2 = ⇒16 = 24 – 2 x 12 − x 1

2x = 24 − 16 = 8 ⇒ x = 4 Hence, B joined after 4 months. (71-75) 71) b; Marks scored by Anushka

66 75 88 + 100 × + 150 × + 100 100 100 56 56 90 125 × + 75 × + 50 × 100 1 00 100

Clearly, Garvita scored the highest total marks in all the subjects together. 73) c; Required percentage =

74) b; Two students i.e. Garvita strategic management brand management & compensation management and Archit consumer behaviour and service marketing. 75) a; Required average Marks =

(88 + 84 + 78 + 96 + 68 + 50 )× 150

150 ×

= 99 + 75 + 132 + 70 + 42 + 45 = 463 72) d; Marks scored by Archit 82 76 + 100 × + 150 × 100 100 84 96 92 88 + 125 × + 75 × + 50× 100 100 100 100 = 150 ×

= 123 + 76 + 126 + 120 + 69 + 44 = 558 Marks scored by Arpan = 150 ×

76 66 78 + 100 × + 150 × 100 1 00 100

+125 ×

88 72 70 + 75 × + 50× 100 100 100

= 114 + 66 + 117 + 110 + 54 + 35 = 496 Marks scored by Garvita 90 88 + 100 × + 150 × 100 100 96 76 84 86 + 125 × + 75 × + 50× 100 100 100 100 = 150 ×

= 135 + 88 + 144 + 95 + 63 + 43 = 568 Marks scored by Gunit 64 70 + 100 × + 150 × 100 100 68 72 68 74 + 125 × + 75 × + 50× 100 100 100 100 = 150 ×

= 96 + 70 + 102 + 90 + 51 + 37 = 446 Marks scored by Pranita 48 56 + 100 × + 150 × 100 100 50 64 64 58 + 125 × + 75 × + 50× 100 100 100 100 = 150 ×

= 72 + 56 + 75 + 80 + 48 + 29 = 360

88 × 100 = 115.79 % 76

=

100 × 6 464 × 150 = 116 600

(76-80) 76) d; The pattern of the number series is: 850 − 1 × 7 = 843 843 − 2 × 7 = 829 829 − 3 × 7 = 808 808 − 4 × 7 = 780 ≠ 788 780 − 5 × 7 = 745 745 − 6 × 7 = 703 77) b; 6 + 20 = 6 + 1 = 7; 7 + 21= 7 + 2 = 9; 9 + 22 = 13; 13 + 23 = 21; 21 + 24 = 37; 37 + 25 = 69 ∴ The 26 should be 21 78) c; The pattern of the number series is 7 + 1 × 11 = 7 + 11 = 18 18 + 3 × 11 = 18 + 33 = 51 ≠ 40 51 + 5 × 11 = 51 + 55 = 106 106 + 7 × 11 = 106 + 77 = 183 183 + 9 × 11 = 183 + 99 = 282 282 + 11 × 11 = 282 + 121 =403 79) d; Difference is: 13 − 2, 23 − 2, 33 − 2, 43 −2, 53 − 2, 63 − 2 Then, 219 + 214 = 433 80) a; 157.5 45 15 6 = 45; = 15; = 6; = 3; 3.5 3 2.5 2

∴The last number should be 2 Prepared by: N. Vinaykumar Reddy, IACE, Hyderabad.

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 21,  2017-  

ntbhadradri.com

Parametric eqs of the circle is .. CIRCLE Important formulae to remember �� The equation of the circle in the centre form is �� where centre is (a, b), radius r. �� The equation of the circle in the general form is �� + 2gx + 2fy + c=0 then

Centre C= (�g, �f), radius �� x�� If S� �� + 2gx + 2fy + c = 0 then �� + 2g�� + 2f�� + c �� + g�� + f�� + c ��

�� The equation of tangent at (�� ) on the circle S =0 is �� =0 �� The equation of the tangent at (r�� , r�� ) on �� is x�� + y�� = r ��

�� The equation of the tangent with slope m to the circle �� + 2gx + 2fy + c=0

is y + f = m(x + g) � r�� l��

�

SOLVED QUESTIONS 1. Find the centre and radius of the

circle �� Sol.��

��

�

��

� �

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� � 2. If � � � � 4x + 6y + c = 0 represents �� a circle with radius 6, find the value of c. Sol: ��

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�� 3. �� ax + by � 12 = 0 has centre (2, 3) then find a, b and radius�� Sol.��

��

�

��

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�� 4. Find the values of a, b if �� 5x + 2y � 3 = 0 represents a circle. Also find the radius and centre. Sol.�� (i) ��

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� � � � � � ��

� �

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MATHS - 2B 5. Find the parametric equation of the circle �� +�� =4 Sol:�� 6. Find the Parametric equations of the circle �� 6x + 4y � 12 = 0

�� Sol:��

�� 7. Find the value of k if the length of the �� tangent from (2, 5) to�� 5x + 4y �k = 0 Sol.�� 8. Find the equation of the polar of (2, 3) w.r.to the circle �� 6x + 8y � 96 �� = 0. Sol.��

9. Show that the points (�6, 1), (2, 3) are conjugate w.r.to the circle�� 2x �� 2y �� = 0 Sol.��

��

10. Find the value of k if the points (4, 2), (k,�3) are conjugate w.r.to the circle �� 5x � 8y �� = 0.�� Sol.��

��

�� 11. Find the equation of the circle, which passes through (2,�3), (�4, 5) and whose centre lies on the line 4x + 3y + 1 = 0. Sol.��

��

�

��

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� ��

� � ��

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�� 12.Show that the line 5x+12y �4 =0 �� touches the circle�� 6x � 4y �� = 0. Sol: ��

�

��

� ��

�� 13. Find the pole of the line x + y+ 2 = 0

B. LAXMINARAYANA M.Sc., B.Ed., Senior Math Faculty 9849386253

w. r. t. the circle �� 4x � 6y �� = 0. Sol: ��

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�� PRA ACTICE QUESTIO Q ONS�� 1�� 2�� 3�� 4. �� 5�� 6�� 7. �� 8�� 9. �� 10. ��

�� 11 1. �� 12 2. �� 13 3. ��

08

 21,  2017-  

ntbhadradri.com

ntnews.com

TN Speaker disqualifies 18 MLAs Constitution of India, through 52nd amendment act in 1952 September disqualified the 18 AIADMK MLAs �The disqualification effectively reduces the state supporting T T V Dinakaran, the nephew of jailed Assembly to 216 seats with 116 AIADMK MLAs, party leader V K Sasikala. In response, leaders in the including the Speaker. It also brings the total number Dinakaran faction said they would approach the of AIADMK seats lying vacant to 19, following the court against the decision, which has come as a big death of J Jayalalithaa in December last year. The boost for the united ruling group led by Chief Opposition has a strength of 98, including 89 MLAs Minister E Palaniswami and Deputy Chief Minister of DMK, eight of Congress and one of the IUML O Panneerselvam. Anti Defection Law was added to

� TamilNadu, the state’s Speaker P Dhanapal on 18th

Height of the Sardar Sarovar Dam is ? Current Affairs 1) India's first Centre forAnimal Law has been established at the city-based NALSAR University of Law . In which city it is ? a. Hyderabad b. Pune c. Ranchi d. New delhi 2) The International Day for the Preservation of the Ozone Layer is observed globally on ……………? a. September 15 b. September 16 c. September 17 d. September 20 3) The first recipient of the lifetime achievement award instituted by the Badminton Association of India (BAI) is.? a. Prakash padukone b. Chetan anand c. Pullela gopichand d. Aparna popat 4) The International Day of Democracy is observed every year on ………..? a. September 12 b. September 15 c. September 16 d. September 17 5) The first-ever National Ayurveda Youth Festival (NAYF) was started in which city? a. Jaipur b. Kanpur c. Belpur d. Jaitser 6) India’s rank in the 2017 Global Human Capital Index (GHCI) is ..? a. 102 b. 105 c. 103 d. 110 7) The first Indian State to approve e-vehicle policy is …………..? a. Karnataka b. Andhra Pradesh c. Arunachal Pradesh d. Kerala 8) In which city, India’s first advanced Homoeopathy Virology lab has come up? a. Chennai b. Kolkata c. Dispur d. Bhubhaneshwar 9) From which city, President Ram Nath Kovind has launched a nationwide campaign ‘Swacchata Hi Seva? a. Jaipur b. Kochi c. Kanpur d. Rajpur 10) The Indo-Sri Lanka Hindi conference was organized at Kelaniya University. In which city it is?

Raghunath Pavan Kumar Kautilya careers, Hyderabad

For All Competitive exams a. Colombo b. New Delhi c. Jaipur d. Raipur 11) Name the city that hosts the 2028 Summer Olympics? a. Washington b. Paris c. Moscow d. Los angeles 12) The 12th edition of the India-Japan annual summit-2017 was held in which state? a. Gujarath b. Madhya Pradesh c. Manipur d. Sikkim 13) The 5th edition of the ‘Coastal Shipping and Inland Water Transportation Business Summit 2017’ will be held at Hotel Crown Plaza. In which city it is? a. Kottayam b. Kochi c. Indore d. Bhopal 14) The National Hindi Day (NHD) is celebrated every year on ……? a. September 12 b. September 13

Sardar Sarovar Dam dedicated to the nation � Indian Prime Minister Narendra Modi on 17th September dedicated to the nation the Sardar Sarovar Dam, almost 56 years after its foundation stone was laid.The foundation stone of the dam was laid on April 5, 1961 by the country’s first Prime Minister, Jawaharlal Nehru. It took 56 years to finally complete its construction due to court cases and protests by the affected villagers. � The delay in the completion of the dam was due to numerous reasons. Medha Patkar-led Narmada Bachao Andolan took the government to the Supreme Court over environmental and rehabilitation issues, and obtained a stay in 1996. The court allowed resumption

of work in October 2000. � The height of the dam was recently raised to 138.68 metres, which will allow maximum ‘usable storage’ of 4.73 million acre feet of water and will greatly benefit the participating States of Gujarat, Rajasthan, Madhya Pradesh and Maharashtra. � It said that the project has helped transport the waters of the Narmada river to the water-deficient areas of Gujarat through an elaborate canal and pipeline network. The project has been described as one of the biggest human endeavours for water transport. Up to a billion units of hydropower are also expected to be generated annually.

c. September 14 d. September 15 15) Name the state that is hosting the 2017 Border Security Force (BSF) sports? a. Uttar Pradesh b. Gujarath c. Punjab d. Jammu & Kashmir 16) The new president of the Society of Indian Automobile Manufacturers (SIAM) for 2017-18 is ………..? a. Abhay Firodia b. Ajay mehtha c. Manohar chawla d. Madhukar Sharma 17) Which of the following ports has won the 2017 Container Terminal of the Year Award? a. Viakhapatnam port b. Haldia port c. Jawahar lal Nehru port d. Kolkata port 18) Who among the following has been appointed as the first special envoy for the oceans by the United Nations? a. Peter Thomson b. James Thomson c. David Mathew d. Jimmy carter 19) The Food Safety and Standards Authority of India (FSSAI) has launched a nationwide online platform to bring in transparency in food safety inspection and sampling. Identify among the following? a. FoSFoRIS b. FoSCoRIS c. FoSBoRIS d. FoSMoRIS 20) The BWF World Senior Badminton Championship has started at Rajiv Gandhi Indoor Stadium . in which state it is? a. Karnataka b. Andhra pradesh c. Kerala d. Odisha 21) Minister Ravi Shankar Prasad, , has launched a nation-wide hackathon #OpenGovDataHack on recently. He is which union minister? a. Union Minister for Electronics & Information Technology

b. Union minister for coal mines c. Union minister for science and technology d. Union minister for child and women empowerment 22) Dr Harsh Vardhan, the Union Minister of Environment, Forest and Climate Change, has launched which campaign at conference on “Sustainable Landscapes & Forest Ecosystems: Theory to Practice” in New Delhi recently? a. Wood is nice b. Wood is good c. Wood is mood d. Wood is best 23) The joint bilateral air force exercise “Shaheen VI” has started between which country and Pakistan? a. China b. Japan c. North korea d. India 24) Who among the following has won gold in the 8th Modern Pentathlon National Championship – 2017. ? a. P S Payal b. P S Kayal c. P Madhuri d. S Sanjana 25) Name the city that has topped the 2017 Global Financial Centres Index (GFCI)? a. Paris b. London c. Los angeles d. Washington 26) Which institute researchers have developed a low-cost method for treating Osteoarthritis (OA)? a. IIT Roorkee b. IIT Madras c. IIT Pune d. IIT Ranchi 27) Who among the following has won the 2017 Men’s singles US Open Tennis tournament? a. Rafael nadal b. Novok Djkovic c. Stan wawrinka d. Kevin Anderson 28) Who among the following has won the 2017 women’s singles US Open Tennis tournament? a. Madison keys b. Angelique kerber c. Sloane Stephens d. Serena Williams 29) The World Suicide Prevention Day (WSPD) is observed every year on..? a. September 11 b. September 14 c. September 10 d. September 9 30) Among the following, which country’s team has won the 2017 U-16 South Asian Basketball (SABA) Championship? a. India b. Bangladesh c. China d. Japan

ANSWERS 1.a 7.a 13.b 19.b 25.b

2.b 8.b 14.c 20.c 26.a

3.a 9.c 15.d 21.a 27.a

4.b 10.a 16.a 22.b 28.c

5.a 11.d 17.c 23.a 29.c

6.c 12.a 18.a 24.b 30.a

6

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Ð-û¦-è[ª While solving number series questions, first try to identify the numbers in the series (they may be squares, cubes, prime number etc.,). Then find the difference between the numbers. If unable to get any clue then see the relation between the numbers with multiplication division etc.

Quantitative Aptitude Directions (Q.1-5): What will come in place of the question mark (?) in the following number series ? 1. 958 833 733 658 608 (?) 1) 577 2) 583 3) 567 4) 573 5) None of these 2. 11 10 18 51 200 (?) 1) 885 2) 1025 3) 865 4) 995 5) None of these 3. 25 48 94 186 370 (?) 1) 738 2) 744 3) 746 4) 724 5) None of these 4. 14 24 43 71 108 (?) 1) 194 2) 154 3) 145 4) 155 5) None of these 5. 144 173 140 169 136 (?) 1) 157 2) 148 3) 164 4) 132 5) None of these Directions (Q. 6-9): The following question is accompanied by three statements A, B and C. You have to determine which statement (s) is/ are necessary/ sufficient to answer the question. 6. What is the speed of the train? I. The train crosses 300 meters long platform in 21 seconds. II. The train crosses another stationary train 1 of equal length in 2 ⎯ seconds. 19 III. The train crosses a signal pole in 3 4 ⎯ seconds. 9 1) Only I and II 2) Only II and either I or III 3) Only I and either II or III 4) Only III and either I or II 5) None of these 7. A boat takes 4 hours to go upstream from x to y and back downstream from y to x on a river.

Pattern of the number series is.. Writer : - Dr. G.S. Giridhar Director, RACE Institute What is the speed of the boat on still water? (A) The distance between x and y is 6 km. (B) The boat takes 2 hours less to go downstream than to go upstream. (C) The speed of the current is 2 kmph. 1) Only A and B are sufficient 2) Only A and C are sufficient 3) Any two of the three are sufficient 4) B alone is sufficient 5) All even together are not sufficient 8. In how many days can a work be completed by X, Y and Z together? (A) Ratio of the work efficiencies of X, Y and Z is 3 : 2 : 1. (B) Z works for 5 days and leaves the job and the remaining work is done by X and Y together in 5 days. (C) 60% of the work is done by X alone in 6 days. 1) Any two of them 2) Only A and C together 3) Only B 4) Either B alone or A and C together 5) None of these 9. In how many days can 10 women finish a work? I. 10 men can complete the work in 6 days. II. 10 men and 10 women together can

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ë«S©’: áTb-èπÿu-öÀ¢˛ võ„®·F ë«S Ö†o N¶μ«-í¬©’: ¢Á’é¬-E-éπ™¸, ÈéN’-éπ™¸, á©-éZ-Àéπ™¸, á©-é¬Z-Eé˙q Åçú˛ éπ´‚u-E-Íé-≠æØ˛q, ÉØ˛-Ææ’Z-¢Á’ç-õ‰-≠æØ˛, ÆœN™¸. ✪ áç°œéπ: Ææç•ç-Cμûª N¶μ«-í∫ç™ Ííö¸ 2017/ 2018™ ≤ƒCμç-*† ≤Ú\®˝, Éçô®Ω÷yu ÇüμΔ-®Ωçí¬. ✪ °æ‹Jh N´-®√-©†’ Ííö¸ °∂æL-û√©’ ¢Á©’-´úÕ† °æC-®ÓV™x ¢Á¶¸-ÂÆj-ö¸™ §Òçü¿’-°æ-®Ω’-≤ƒh®Ω’. ✪ ¢Á¶¸-ÂÆjö¸: www.npcilcareers.co.in ✪

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Â£j«ü¿-®√-¶«-ü˛-™E áç§ƒx-®‚Æˇ ÊÆdö¸ É†÷q-È®Ø˛q é¬®Ìp-Í®≠æØ˛ (Ñá-Æˇ-âÆ‘) ¢Á’úÕ-éπ™¸ é¬™‰ñ ¸ é¬çvö«èπ◊d v§ƒA-°æ-C-éπ† éÀçC §ÚÆæ’d© ¶μºKhéÀ ¢√é˙ ÉØ˛ Éçô®Ω÷yu E®Ωy-£œ«ç-îª†’çC. ✪ ë«S©’: ô÷uô®Ω’x – 11 (ÅØ√-ôO’ – 1, °∂œ>-ßª÷-©@ – 2, §ƒü∑Δ-©@ – 2, ¢Á’ivéÓ-•-ßª÷-©@ – 2, §∂ÚÈ®-Eqé˙ ¢Á’úÕ-ÆœØ˛ – 1, éπ-´‚u-E-öÃ ¢Á’úÕ-ÆœØ˛ – 3). ✪ Æ‘E-ßª’®˝ È®Æœ-úÁçô’x – 15 (ï†-®Ω™ ¸ ¢Á’úÕ-Æ œØ˛ – 2, úÁ®Ωtö«-©@ – 1, öÃH/ îÁÆˇd – 1, °‘úÕ-ßª÷-vöÀé˙q – 2, ï†®Ω™¸ Ææ®ΩbK – 3, Ç®Ón-Â°-úÕé˙q – 1, Å¶¸-ÂÆZ-öÀé˙q Åçú˛ Èíj†-é¬-©@ – 1, ÅØÁ-Æ‘h-≠œßª÷ – 2, Í®úÕßÁ÷ úøßª÷-í∫oÆœÆˇ – 2). ✪ WE-ßª’®˝ È®Æœ-úÁçô’x – 26 (ï†-®Ω™ ¸ ¢Á’úÕ-Æ œØ˛ – 3, úÁ®Ωt-ö«-©@ – 1, öÃH/ îÁÆˇd – 1, °‘úÕ-ßª÷-vöÀé˙q – 4, ÂÆjéÀ-ßª÷vöÀ – 1, ï†-®Ω™¸ Ææ®ΩbK – 3, Ç®Ón-Â°-úÕé˙q – 3, Ç°æh-™«t-©@ – 2, Ñá-Ø˛öÃ – 2, ãH-@¢Áj – 3, ÅØÁ-Æ‘h≠œßª÷ – 3). ✪ ü¿®Ω-ë«Ææ’h: 25 ÂÆÂ°dç-•®Ω’ †’ç* ÇØ˛-™„jØ˛ ü¿®Ω-ë«-Ææ’h©’ Åçü¿’-¶«-ô’™ Öçö«®·. ✪ áç°œéπ: Éçô®Ω÷yu ÇüμΔ-®Ωçí¬. ✪ *´J ûËC: 16 ÅéÓd-•®Ω’ ¢Á¶¸-ÂÆjö¸: www.esicmchyd.ac.in

†÷uéÀx-ßª’®˝ °æ´®˝ é¬®Ìp-Í®-≠æØ˛ Ç°∂ˇ ÉçúÕßª÷ LN’-õ„ú˛ Ííö¸ 2017– 18 üΔy®√ áTb-èπÿu-öÀ¢˛ võ„®·F §ÚÆæ’d-©†’ ¶μºKh îËßª’-†’çC.

13

éπ%≥ƒg ßª‚E-´-JqöÃ

´’*M-°æ-ôoç-™E éπ%≥ƒg ßª‚E-´-JqöÃ v§ÒÂ°∂-Ææ®˝ §ÚÆæ’d© ¶μºKhéÀ ü¿®Ω-ë«-Ææ’h©’ éÓ®Ω’-ûÓçC. ✪ ë«S©’: ÉçTx≠ˇ – 1, ï®Ωo-Lïç Åçú˛ ´÷Æˇ éπ´‚uE-Íé-≠æØ˛ – 1, ÅÂ°kxú˛ ´÷uü∑¿-¢Á’-öÀé˙q – 1, •ßÁ÷-ÂÆj-ØÁqÆˇ Åçú˛ •ßÁ÷-õ„-é¬o-©@ – 1, ÈéN’Æ‘Z – 1, °∂œ>é˙q – 1. ✪ ë«S Ö†o v°æüË-¨»©’: ´’*-M-°æôoç, †÷>-Oúø’. ✪ ü¿®Ω-ë«Ææ’h: ¢Á¶¸-ÂÆjö¸ †’ç* úˆØ˛-™ ú˛ îËÆæ’-éÓ-´îª’a. ✪ ü¿®Ω-ë«Ææ’h ®Ω’Ææ’´·: ®Ω÷.2000. ✪ *´J ûËC: 16 ÅéÓd-•®Ω’ ✪ ¢Á¶¸-ÂÆjö¸: www.krishnauniversity.ac.in

´·ç•®·-™E ´’ñ¸-í¬¢˛ ú≈é˙ ≠œ°ˇ-G-©f®˝q LN’-õ„ú˛ Ííö¸ – 2018 ≤Ú\®Ω’ ÇüμΔ-®Ωçí¬ áTb-èπÿu-öÀ¢˛ võ„®·F §ÚÆæ’d© ¶μºKhéÀ ü¿®Ω-ë«-Ææ’h©’ éÓ®Ω’-ûÓçC. ✪ N¶μ«-í¬©’: ¢Á’é¬-E-éπ™ ¸, á©-éÀZ-éπ™ ¸. ✪ áç°œéπ: Ííö¸ – 2018 ≤Ú\®Ω’ ÇüμΔ-®Ωçí¬. ✪ ü¿®Ω-ë«Ææ’h: 8 ï†-´J 2018 †’ç* ÇØ˛-™„jØ˛ ü¿®Ω-ë«Ææ’h©’ Åçü¿’-¶«-ô’™ Öçö«®·. ✪ *´J ûËC: 7 °∂œv•-´J 2018 ¢Á¶¸-ÂÆjö¸: www.mazdock.com

3 complete the work in 3 ⎯ days. 7 III. If 10 men work for 3 days and thereafter 10 women replace them, the remaining work is completed in 4 days. 1) Only I and II 2) Any two of the three 3) Only I and III 4) Only II and III 5) None of these

Key with Explanations 1-2; The pattern of the number series is: 958 − 833 = 125; 833 − 733 = 100 733 − 658 = 75; 658 − 608 = 50 ∴ ? = 608 − 25 = 583 2-4; The pattern of the number series is: 11 × 1 − 1 = 10; 10 × 2 − 2 = 18 18 × 3 − 3 = 51; 51 × 4 − 4 = 200 200 × 5 − 5 = 995 3-1; The pattern of the number series is: 25 × 2 − 2 = 50 − 2 = 48 48 × 2 − 2 = 96 − 2 = 94 94 × 2 − 2 = 188 − 2 = 186 186 × 2 − 2 = 372 − 2 = 370 370 × 2 − 2 = 740 − 2 = 738 4-2; The pattern of the number series is: 14 + 10 = 24 24 + 19 (= 10 + 9) = 43 43 + 28 (= 19 + 9) = 71 71 + 37 (= 28 + 9) = 108 108 + 46 (= 37 + 9) = 154 5-5; The pattern of the number series is :

144 + 29 = 173; 173 − 33 = 140 140 + 29 = 169; 169 − 33 = 136 136 + 29 = 165 6-3; 7-3; From (A) and (C) let speed of boat in still water be x. 6 6 ⎯⎯⎯ + ⎯⎯⎯ = 4 2+x x−2 ⇒ 6(x − 2) + 6(x + 20) = 4 × (x2 − 4) x = −1, 4 (Negative value) From (A) and (B) let time taken to go upstream be y hour, (y − 2) + y = 4 implies y = 3 hours. 6 6 ⎯ + ⎯ 1 2 Speed in still water = ⎯⎯⎯⎯⎯⎯ = 4 kmph 2 From (B) and (C), 3+1 Speed in still water = 2 × ⎯⎯⎯ = 4 kmph 3−1 8-4; From statements (A) and (C), X alone can do the work in 5 6 × ⎯ days = 10 days 3 3 Y alone can do the work in 10 × ⎯ days 2 = 15 days Z alone can do the work in 30 days. Hence, all three together can do the work in 5 days. From statement (B) alone, Z works for 5 days and the remaining work is done by X and Y together. Hence, all three together can do the work in 5 days. Hence B alone or A and C together is sufficient. 9-2

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¶„çí∫∞¡⁄-®Ω’-™E ¶μ«®Ωû˝ á©-é¬Z-Eé˙q LN’-õ„ú˛ é¬çvö«èπ◊d v§ƒA-°æ-C-éπ† éÀçC §ÚÆæ’d© ¶μºKhéÀ ü¿®Ω-ë«-Ææ’h©’ éÓ®Ω’ûÓçC. ✪ ë«S©’: Æ‘E-ßª’®˝ ÅÆœ-ÂÆdçö¸ Éç>-F®˝ – 6 ✪ Å®Ω|ûª: á©-é¬Z-Eé˙q/ á©-éÀZ-éπ™ ¸ Åçú˛ á©-é¬Z-E-é˙q™ úÕ§Òx´÷ ÖBh-®Ω’g™„j Öçú≈L. ñ‰Æ‘ã ™‰üΔ ûªûªq-´÷† ≤ƒn®·™ 15 à∞¡Ÿx °æE-îË-Æœ† Å†’-¶μº´ç Å´-Ææ®Ωç. ✪ ´ßª’Ææ’: 1 ÂÆÂ°dç-•®Ω’ 2017 Ø√öÀéÀ 50 à∞¡xèπ◊ N’çîªèπÿ-úøü¿’. áÆ‘q/ áÆ‘d Å¶μºu-®Ω’n-©èπ◊ Å®·-üË∞¡Ÿx, ãHÆ‘ Å¶μºu-®Ω’n-©èπ◊ ´‚úË∞¡Ÿx ´ßÁ÷-°æ-J-N’-A™ N’†-£æ…-®·ç°æ¤ Öçô’çC. ✪ -áç°œéπ: ®√-ûª°æ-Kéπ~, -Éç-ô®Ω÷yu -Ç-üμΔ®Ωçí¬. ✪ -*-´-J -ûË-C: 12 -ÅéÓd-•®Ω’ ✪ ¢Á¶¸-ÂÆjö¸: www.bel-india.com

✪ ✪

îËÆœ-† -ü¿®Ω-ë«Ææ’h-©-†’ EKgûª í∫úø’-´¤-™í¬ éÓÇ-Jf-ØË-ô®˝ (ÅúÕt-≠æØ˛q), ÂÆçô®˝ °∂æ®˝ §ÚÆˇd ví¬úø’u-ßË’ö¸ ÆædúŒÆˇ Åçú˛ úŒÑ, ØË≠æ-†™¸ ÉØ˛-Æœd-ô÷uö¸ Ç°∂ˇ ®Ω÷®Ω™¸ úÁ´©-°ˇ-¢Á’çö¸ Åçú˛ °æçî√-ßª’-B-®√ñ¸, ®√ñ‰ç-vü¿-†-í∫®˝, Â£j«ü¿-®√-¶«ü˛ – 500 030 ÅØË *®Ω’-Ø√-´÷èπ◊ °æç§ƒL. ü¿®Ω-ë«Ææ’h ®Ω’Ææ’´·: ®Ω÷.400. (áÆ‘q/ áÆ‘d/ °‘úø-•÷xuúŒ Å¶μºu-®Ω’n-©èπ◊ ®Ω÷.200). *´J ûËC: 10 †´ç-•®Ω’ ✪ ¢Á¶¸-ÂÆjö¸: www.nird.org.in

ßª‚Æ‘-Ñ-ÑúŒ – 2018

ÉçúÕßª’Ø˛ ÉØ˛-Æœd-ô÷uö¸ Ç°∂ˇ õ„é¬o-©@ ¶«ç¶‰ Åçúø-®˝-ví¬úø’u-ßË’ö¸ é¬´’Ø˛ áçvôØ˛q áí¬b¢˛’ °∂æ®˝ úÕñ„jØ˛ (ßª‚Æ‘Ñ-ÑúŒ) E®Ωy-£æ«-ùèπ◊ ØÓöÀ-°∂œ-Íé-≠æØ˛ Núø’-ü¿© îËÆœçC. DE üΔy®√ ââöÃ ¶«ç¶‰, ââöÃ í∫’´-£æ«öÀ, ââ-â-öÃ-úŒáç ï•™¸-°æ‹-®˝-©™ H. úÕñ„jØ˛ éÓ®Ω’q™ v°æ¢Ë¨¡ç éπLp-≤ƒh®Ω’. éÓ®Ω’q ´u´Cμ: Ø√©’-Íí∞¡Ÿx. ✪ Å®Ω|ûª: 2017™ Éçô®˝ ÖBh-®Ω’g-™„j-†-¢√®Ω’ ™‰üΔ 2018™ °æ‹Jh îËÊÆ-¢√®Ω’ ü¿®Ω-ë«Ææ’h îËÆæ’-éÓ-´îª’a. ✪ ¢Á¶¸-ÂÆjö¸: www.uceed.iitb.ac.in

áØ˛-â-Ç-®˝úŒ

Â£j«ü¿®√-¶«-ü˛-™E ñ«Bßª’ ví¬O’-ù«-Gμ-´%Cl¥, °æçî√-ßª’-B®√ñ¸ ÆæçÆæn 2018 NüΔuÆæç´-ûªq-®√-EéÀ ®Ω÷®Ω™¸ úÁ´-©-°ˇ¢Á’çö¸ ¢Ë’ØË-ñ ¸-¢Á’ç-ö¸™ §ÚÆˇd-ví¬-úø’u-ßË’ö¸ úÕ§Òx´÷ éÓ®Ω’q™ v°æ¢Ë-¨»-EéÀ ü¿®Ω-ë«-Ææ’h©’ éÓ®Ω’-ûÓçC. ✪ Å®Ω|ûª: àüÁjØ√ úÕvU ÖBh-®Ω’g™„j Öçú≈L. úÕvU *´J Ææç´-ûªq®Ωç îªü¿’-´¤-ûª’†o NüΔu-®Ω’n©’ èπÿú≈ ü¿®Ω-ë«Ææ’h îËÆæ’-éÓ-´îª’a. ✪ éÓ®Ω’q ´u´Cμ: àú≈C (ï†-´J – úÕÂÆç-•®Ω’) ✪ áç°œéπ: v°æ¢Ë¨¡ °æKéπ~ ÇüμΔ-®Ωçí¬. ✪ v°æ¢Ë¨¡ °æKéπ~: 19 †´ç-•®Ω’ ✪ ü¿®Ω-ë«Ææ’h: Å¶μºu-®Ω’n©’ ÇØ˛-™„jØ˛™  ü¿®Ω-ë«Ææ’h îËßÁ·îª’a ™‰üΔ ¢Á¶¸-ÂÆjö¸ †’ç* úˆØ˛-™ú˛ îËÆæ’éÓ-´-îª’a. °æ‹Jh

Æ‘Ñ-ÑúŒ – 2018

ââöÃ ¶«ç¶‰ ââ-á-ÆˇÆ‘ ¶„çí∫-∞¡⁄®Ω’, ââöÃ ¶«ç¶‰, ââöÃ CMx, ââöÃ í∫’´-£æ«öÀ, ââöÃ Â£j«ü¿-®√-¶«ü˛, ââöÃ é¬†÷p®˝, ââ-â-öÃ-úŒáç ï•-™ ¸-°æ‹-®˝™  áç.úÕ-ñ„jØ˛/ °‘Â£«î˝úŒ ÉØ˛ úÕñ„jØ˛ éÓ®Ω’q™ v°æ¢Ë-¨»-EéÀ E®Ωy-£œ«çîË é¬´’Ø˛ áçvôØ˛q áí¬b¢˛’ °∂æ®˝ úÕñ„jØ˛ (Æ‘Ñ-ÑúŒ) éÓÆæç ü¿®Ωë«Ææ’h©’ éÓ®Ω’-ûÓçC. ✪ -ü¿®Ω-ë«Ææ’h: 9 ÅéÓd-•®Ω’ †’ç* 10 -†-´ç-•®Ω’ -´®Ωèπ◊ ÇØ˛™„jØ˛-™ ü¿®Ω-ë«Ææ’h-©’ -Åç--ü¿’-¶«-ô’-™ -Öç-ö«®·. ✪ °æKéπ~ ûËD (ßª‚Æ‘-Ñ-ÑúŒ/ Æ‘Ñ-ÑúŒ): 20 ï†-´J 2018 ¢Á¶¸-ÂÆjö¸: www.ceed.iitb.ac.in

12

Þœªô¢ªî¦ô¢Ù 21 -šúšídÙñô¢ª 2017

Ð-û¦-è[ª vAéÓ-ù-N’A ÅØËC vUé˙ °æüΔ-™„j† Trigonon (Åçõ‰ vA¶μº’ïç) Metron (Åçõ‰ éÌ©-ûª) †’ç* ´*açC. vA¶μº’-ïç-™E éÓù«©’, ¶μº’ñ«-©èπ◊ Ææç•ç-Cμç* Åüμ¿u-ßª’†ç îËÊÆ í∫ùÀ-ûª-¨»ÆæYç ÅE Å®Ωnç. Ñ ¨»≤ƒYEo áûª’h-©†’, ü¿÷®√-©†’ éÌ©´ú≈-EéÀ, ÆæçUûª ¢√®·-üΔu© ûªßª÷-KéÀ, Ææ´·-vü¿ç-™E Å©© áûª’h-©†’ éπ†’éÓ\-´ú≈-EéÀ áèπ◊\-´í¬ Ö°æ-ßÁ÷-T-≤ƒh®Ω’. ÅEo ¨»≤ƒY™x ´·êuçí¬ ¶μ˜Aéπ ¨»ÆæYç, Éçï-F-Jç-í˚-©™ vAéÓ-ù-N’-AéÀ áØÓo Å†’-´-®Ωh-Ø√©’ ÖØ√o®·.

í∫-ùÀ-ûªç -vAéÓ-ù-N’-A ★ a, b

a ⎯ b

A c b

-v°æ:

sec2 A = 1 + tan2 A tan2 A = sec2 A − 1

θ

C

®Ω-îª®·-ûª

©ç•-éÓù vA¶μº’-ïç™ Ç®Ω’ E≠æp-ûª’h-©†’ à®Ωp-®Ω-îª-´îª’a. b a b c c a ÅN: ⎯, ⎯, ⎯, ⎯, ⎯, ⎯ . c c a b a b Ñ Ç®Ω’ E≠æp-ûª’h©†’ éÓùç 'θ— éÀ 'vAéÓ-ù-N’-Bßª’ E≠æp-ûª’h©’— Åçö«®Ω’. b áü¿’-öÀ- ¶μº’-ïç sin B = ⎯ = ⎯⎯⎯⎯⎯ c éπ®Ωgç ÇÆæ †o ¶μº’ïç a cos B = ⎯ = ⎯⎯⎯⎯⎯ c éπ®Ωgç b áü¿ ’ -öÀ- ¶μº’ïç tan B = ⎯ = ⎯⎯⎯⎯⎯ a ÇÆæ-†o- ¶μº’ïç a ÇÆæ†o ¶μº’ïç cot B = ⎯ = ⎯⎯⎯⎯⎯ b áü¿’-öÀ- ¶μº’ïç c éπ®Ωgç sec B = ⎯ = ⎯⎯⎯⎯⎯ a ÇÆæ-†o- ¶μº’ïç éπ®Ωgç c cosec B = ⎯ = ⎯⎯⎯⎯⎯ b áü¿’-öÀ- ¶μº’ïç

sin θ =

-v°æ:

†’

cos θ

©™

⎯⎯⎯⎯

Å®·ûË

sin C

(∠B = 90°)

C

≤ƒ-üμ¿-†: ΔABC ™

B

⎯⎯ ∴ x = √ 144 = 12 12 ∴ sin C = ⎯ 13

-v°æ: cos2 θ + cos θ ≤ƒ-üμ¿-†: é¬ü¿’.

Åçõ‰

B

A

q

x

A

´·êu Ææ÷vû√©’

ÅE ®Ω´’u ÅçC.

LHS sin2 θ + cos2 θ 1 ⎯⎯⎯⎯⎯ = ⎯⎯ = sec θ RHS cos θ cos θ (... sin2 θ + cos2 θ = 1) tan θ + cot θ = 2 tan2 θ + cot2 θ = ?

-v°æ: Å®·ûË ≤ƒ-üμ¿-†: (tan θ + cot θ)2 = tan2θ + cot2 θ + 2 tan θ × cot θ (2)2 = tan2 θ + cot2 θ + 2(1) (... tan θ × cot θ = 1)

-v°æ: cot2 θ − cos2 θ = cos2θ × cot2 θ ÅE îª÷°æçúÕ. cos2 θ ≤ƒ-üμ¿-†: LHS cot2 θ − cos2 θ = ⎯⎯ − cos2 θ 2 sin θ

1 1 − sin2 θ = cos2 θ ⎯⎯ − 1 = cos2 θ ⎯⎯ 2 sin θ sin2 θ

[

sin C

éπ†’-éÓ\-´îª’a. = 1 Å†úøç ÆæÈ®jç-üËØ√?

(a + b) (a − b) = a2 − b2 ∴ cosec2 θ − cot2 θ = 1

∴ tan2 θ + cot2 θ = 4 − 2 = 2

13

5

132 = x2 + 52 2 ∴ x = 169 − 25 = 144

.

2. sec2 A − tan2 A = 1

sin θ

p

sin2 θ ⎯⎯ + cos θ = sec θ cos θ

-v°æ: (cosec θ + cot θ) (cosec θ − cot θ) = 1 Å-†-úøç ÆæÈ®jç-üË-Ø√? ≤ƒ-üμ¿-†: ÆæÈ®jç-üË-.

⎯⎯⎯

√ p2 + q2

- O’®Ω’ àéÃ-¶μº-N-≤ƒh®√?≤ƒ-üμ¿-†: àéÃ-¶μº-Nç-îª†’.

√ cos2 θ − 1

5 sin A = ⎯ 13

1 sin2 A + cos2 A = 1

-v°æ:

Å®·ûË

N©’-´©’ áçûª?

C

p2 + q2

q cos A = ⎯⎯⎯ ⎯⎯⎯ √ p2 + q2

1 sin θ − ⎯ = 0 θ=? 2 1 sinθ = ⎯ 2 1 ° sin 30 = ⎯ ⇒ θ = 30° 2

√

-v°æ: cos2θ = 1 − sin2 θ †’ç* ´uéπh-°æ-®Ω-îªçúÕ. ≤ƒ-üμ¿-†: sin2 θ = cos2 θ − 1

sin A, cos A

p

cosec2 A = 1 + cot2 A cot2 A = cosec2 A − 1

-v°æ: ≤ƒ-üμ¿-†:

Å®·ûË

≤ƒ-üμ¿-†: ∴sin A = ⎯⎯⎯ ⎯⎯⎯

3. cosec2 A − cot2A = 1

B

a

p tan A = ⎯ q

]

[

]

cos2 θ = cos2 θ . ⎯⎯ = cos2 θ.cot2 θ RHS sin2 θ

1 1 ★ cosec θ = ⎯⎯⎯ (or) sin θ = ⎯⎯⎯⎯ sin θ cosec θ ∴ sin θ × cosec θ = 1 1 1 ★ sec θ = ⎯⎯⎯ (or) cos θ = ⎯⎯⎯ cos θ sec θ ∴ cos θ × sec θ = 1 1 1 ★ cot θ = ⎯⎯⎯ (or) tan θ = ⎯⎯⎯ tan θ cot θ ∴ tan θ × cot θ = 1 sin θ ★ tan θ = ⎯⎯⎯ cos θ cos θ ★ cot θ = ⎯⎯⎯ sin θ ★ sin (90 − θ) = cos θ ★ cos (90 − θ) = sin θ ★ tan (90 − θ) = cot θ ★ cot (90 − θ) = tan θ ★ sec (90 − θ) = cosec θ ★ cosec (90 − θ) = sec θ

®Ω-îª®·-ûª

-ñ«-B-ßª÷-üΔ-ßª÷-Eo í∫-ùÀç-îË ÆæçÆæn -à-C? 4)

9. 2017

1.

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