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MÛ¸-Ü-Mʸ-ÖV> AØÛ˛Mʸ –ö˛*ΔÊˇ$µÀ$ –ö˛Á‹$¢ØÈ≤Δˇ$$. MʸÖÚ≥-±À$ B AØ˲$-–ö˛-ΔÊˇ¢-ØÈÀØ˲$ ô˲–ö˛$ –È≈¥ÎΔÊˇ —Á‹¢-ΔÊˇ-◊˝Mʸ$ EÁ≥ƒÒ˝*-WÖ-^˲$-Mʸ$Ö-r$-ØÈ≤Δˇ$$. ÁúÕ-ô˲ÖV> IsÓ˝ ΔÊˇÖVʸÖÃZ Gد≤ Mˆô˲¢ ô˲ΔÊˇ‡ E߯≈-V>À$ AÖßÊ˛$-ªÍ-r$ÃZMϸ –ö˛Á‹$¢-ØÈ≤Δˇ$$. D Hyë® Mʸ*yë “sÏ˝Mϸ Aô˲≈Öô˲ {¥Î´ßëØ˲≈Ö À¿Ö^Û˛ A–ö˛-M>‘Ë˝Ö EÖ®. –˛$ÔŸØå˛ ÃÒ˝«≤ÖVä¸ {sÒ˝OØ˲Δäˇ / -Ú‹OÖ-sÏ˝ã‹t, B«t-Ôú-ÌŸ-ƒÊ˝$Ãå˝ CÖsÒ˝-Õ-gÒ˝Øå˛fi y˛–ö˛-À-Á≥Δäˇ, CÖyÊ˛{Ì‹t-ƒÊ˝$Ãå˝ CÖr-Δˇ≤så˝ Bãú §ÖVä¸fi (IKsÓ˝) CÖf-±Δäˇ, ªÍœMä¸ ^˛Δˇ$$Øå˛ y˛–ö˛-À-Á≥Δäˇ / CÖf-±Δäˇ, Δ¯ªZ-sÏ˝Mä¸fi CÖf-±Δäˇ Ar$–ö˛ÖsÏ˝ –ÈsÏ˝ÃZ –ö˛$$Q≈-–˛$O-Ø˲—. Á‹“$Á≥ øÊ˝—-ÁŸ≈-ô¨˛-ÃZ D E߯≈-V>-ÀMʸ$ A´®Mʸ yÏ˛–ö˛*Öyä˛ EÖr$Ö®. –È≈¥ÎΔÊˇ ∞ΔÊˇ”-Áfl˝◊˝Ø˲$ yÏ˛h-rÃå˝ ¥Îœœså˝-∏Î-–í˛$ÃZ ∞ΔÊˇ”-Ìfl˝Ö-^˲-yë-∞Mϸ MʸÖÚ≥-±À$ BÁ‹Mϸ¢ {Á≥ßÊ˛-«ÿ-Á‹$¢-ØÈ≤Δˇ$$. ßëÖô¯ CÖr-Δˇ≤så˝ Bãú §ÖVä¸fi, B«t-ÔúÌŸ-ƒÊ˝$Ãå˝ CÖsÒ˝-Õ-gÒ˝Øå˛fi, –˛$ÔŸØå˛ ÃÒ˝«≤ÖVä¸, BsZ-–Û˛$-ÁŸØå˛, yÏ˛h-rÃå˝ –ö˛*ΔˇP-sÏ˝ÖVä¸ –ö˛ÖsÏ˝ ›ÎÖMÛ¸-ÜMʸ B—-ÁŸP-ΔÊˇ-◊˝-ÀØ˲$ –È≈¥Î-ΔÊˇ-Á≥-ΔÊˇÖV> AØ˲”-Δˇ$$Ö-^˲$-M¯-–ö˛-yë-∞Mϸ MʸÖÚ≥-±À$ {¥Î´ßëØ˲≈Ö CÁ‹$¢-ØÈ≤Δˇ$$. ÁúÕ-ô˲ÖV> Á‹Ö∫Ö-´®ô˲ —øÍ-V>ÃZœ Á≥#ÁŸP-À-–˛$OØ˲ A–ö˛-M>-‘ÈÀ$ AÖßÊ˛$-ªÍ-r$-ÃZMϸ –ö˛Á‹$¢-ØÈ≤Δˇ$$. ● AΔˇ$$ôÛ˛ D E߯≈-V>-ÀØ˲$ AÖßÊ˛$-M¯-–È-ÀÖsÙ˝ –ö˛*{ôË˛Ö Mˆ∞≤ Ì‹PÃå˝fi EÖyëÕ. AÃÍY-«-£Ê˛–í˛$fi Δ>ƒÊ˝$rÖ, Áfl˝îßÊ˛*ã≥ –ö˛ÖsÏ˝ yÛ˛sÍ-ªÙ˝ã‹ K«-ƒÒ˝$Ö-sÒ˝yä˛ Ì‹Á‹t-–í˛$fiÚ≥O Á≥∞ ^Û˛ı‹ Ø˛OÁ≥#◊˝≈Ö ô˲Á≥µ-∞-Á‹«. Eßë-Áfl˝-ΔÊˇ-◊˝Mʸ$ Hß˛OØÈ JMʸ AÌ≥œ-MÛ¸-ÁŸ-Øå˛Ø˲$ °Á‹$-Mʸ$ÖsÙ˝ AÖßÊ˛$ÃZ —∞-ƒÒ˝*-Vʸ-ßëΔÊˇ$À A–ö˛-Á‹-Δ>-ÀMʸ$ A-Ø˲$-Vʸ$-◊˝ÖV> «Mʸ-–˛$Ö-yÛ˛-ÁŸØå˛fi ^Û˛ƒÊ˝$rÖ, BÁ≥¤Øå˛fi C–ö˛”rÖ –˛$ÔŸØå˛ ßë”Δ> fΔÊˇ$-Vʸ$ô˲$Ö®. AΔˇ$$ôÛ˛ Ar$-–ö˛ÖsÏ˝ AÌ≥œ-MÛ¸-ÁŸ-Øå˛Ø˲$ A¿-–ö˛ñ®Æ ^Û˛ƒÊ˝$-yë-∞Mϸ ∞Á≥#-◊˝$À$ M>–ÈÕ. Ar$-–ö˛ÖsÏ˝ ∞Á≥#-◊˝$ÀMʸ$ yÛ˛sÍØ˲$ A–ö˛-V>-Áfl˝Ø˲ ^Û˛Á‹$-M¯-–ö˛rÖ, —‘Û˝œ-ÌŸÖ^˲rÖ, –˛$ÔŸØå˛ ÃÒ˝«≤ÖVä¸, B«t-Ôú-ÌŸ-ƒÊ˝$Ãå˝ CÖsÒ˝-Õ-gÒ˝-Øå˛fiÚ≥O Á≥∞ ^Û˛ƒÊ˝$rÖ –ö˛ÖsÏ˝ ›ÎÖMÛ¸-ÜMʸ Ø˛OÁ≥#-◊Í≈À$ A–ö˛-Á‹-ΔÊˇ–ö˛$-–ö˛#-ôÈΔˇ$$.

IsÓ˝ Ø˲$Ö_ BsZ-–˛*-sÏ˝–í˛fi 2019ÃZ gÍªå˝ –ö˛*ΔˇPså˝, «{Mʸ*-så˝-–˛$Öså˝ {sÒ˝Öyä˛fi B‘È-fØ˲-MʸÖV> EÖsÍ-ƒÊ˝$∞ Á≥À$ Á‹ΔÛˇ”À$, CÖyÊ˛{Ô‹t –ö˛Δ>YÀ$ AÖ^˲ØÈ –Û˛Á‹$¢-ØÈ≤Δˇ$$. D Mˆô˲¢ Hyë-®ÃZ sÍã≥&10 ΔÊˇÖV>ÃZœ ßëßëÁ≥# Á≥® ÀÑʸÀ –ö˛ΔÊˇMʸ* Mˆô˲¢V> MˆÀ$-–ö˛#À$ À¿Ö^Û˛ A–ö˛-M>‘Ë˝Ö EÖßÊ˛∞ ∞Á≥#-◊˝$À$ ı≥ΔˆPÖ-r$-ØÈ≤ΔÊˇ$.

IsÓ˝, IsÓ˝-D-Gã‹, CÖf-±-«ÖVä¸, BsZ-–˛*-sÏ˝–í˛, {sÍ–˛Ãå˝ AÖyä˛ ‡Ì‹µ-sÍ-ÕsÓ˝, ∏ÎΔ>√ AÖyä˛ Úfl˝Ãå˝¢-MÛ¸Δäˇ, ΩÔ≥K, MÛ¸Ô≥K, ÚúOØÈ-∞¤-ƒÊ˝$Ãå˝ Á‹»”-Ú‹ã‹, ªÍ≈ÖMϸÖVä¸, CØ˲*fi-ΔˇØå˛fi, –ö˛*Ø˲$≈-∏Î≈Mʸa-«ÖVä¸ ΔÊˇÖV>À$ sÍã≥ «{Mʸ*-r-ΔäˇfiV> ∞Õ^Û˛ “À$Ö®.

IsÓ˝ÃZ 5 ÀÑʸÀ$ ßÛ˛÷ CØ˲π-ΔÛˇ√-ÁŸØå˛ sÒ˝M>≤-Ài (IsÓ˝) Á‹»”-Á‹$À ΔÊˇÖVʸÖ, ›ÎtΔÊˇtã≥À$ –ö˛^Û˛a Hyë® ÀÑʸÀ Á‹ÖQ≈ÃZ ∞ƒÊ˝*-–ö˛$-M>À$ ^Û˛Á≥-rt-Ø˲$-ØÈ≤Δˇ$$. IsÓ˝ ®VʸYfÖ Cدπ-Ì‹ã‹ –ö˛*i Ô‹Gã-ú–¯, –ö˛$◊Ï˝-¥ÎÃå˝ V¯œ∫Ãå˝ GyÊ˛$≈-MÛ¸-ÁŸØå˛ Á‹»”-Ú‹ã‹ ^˛OΔÊˇ√Øå˛ sÏ˝.—.-–˛*Áfl˝-Øå˛-ßëã‹ ¥Îƒå˝$ A¿-{¥Î-ƒÊ˝$ÖÃZ 2019ÃZ ßëßëÁ≥# 5

{ÚúÁŸ-ΔäˇfiMʸ$.. D ΔÊˇÖV>À$ Mˆô˲¢ Á‹Ö–ö˛-ô˲fi-ΔÊˇÖÃZ ôÈgÍ {V>yÊ˛$≈-ƒÙ˝$-rœMʸ$ –ö˛*Ø˲$≈-∏Î≈-Mʸa-«ÖVä¸, BsZ-–˛*-sÏ˝–í˛, ∏ÎΔ>√, Úfl˝Ãå˝¢MÛ¸Δäˇ, ‡Ì‹µ-sÍ-ÕsÓ˝, ΩÔ≥K, MÛ¸Ô≥K ΔÊˇÖV>À$ –ö˛$$Q≈–˛$OØ˲ E¥Î´® –Û˛®-Mʸ-À$V> ∞À-–ö˛-Ø˲$-ØÈ≤Δˇ$$.

–˛$$ô˲¢Ö ∞ƒÊ˝*-–ö˛$-M>ÃZœ 25 Ø˲$Ö_ 30 ‘ÈôË˛Ö –Û˛$ΔÊˇMʸ$ ôÈgÍ {V>yÊ˛$≈-ƒÙ˝$-rœMʸ$ À¿-›Î¢-ƒÊ˝$∞ ∞Á≥#◊˝$À A¿-{¥ÎƒÊ˝$Ö. MʸÖÚ≥-±À$ Ø˲*ô˲Ø˲ ›ÎÖMÛ¸-ÜMʸ-ô˲À$ —∞-ƒÒ˝*-WÁ‹*¢ M>ΔÊˇ≈-Mʸ-ÃÍ-¥ÎÀ$ ∞ΔÊˇ”-Ìfl˝Ö^˲yÊ˛Ö {¥ÎΔÊˇÖ-¿Ö-^ÈΔˇ$$. ÃÙ˝sÒ˝ã‹t sÒ˝M>≤-À-iÀÚ≥O Á≥r$tØ˲≤–È«Mϸ Ú≥ßÊ˛™-Ô≥r –Û˛Á‹$¢-ØÈ≤Δˇ$$.

ÀÑʸÀ –ö˛$Ö® E߯≈-Vʸ$-ÀØ˲$ IsÓ˝ Á‹»”-Á‹$À ΔÊˇÖVʸÖ, ›ÎtΔÊˇtã≥À$ «{Mʸ*så˝ ^Û˛Á‹$-Mʸ$ØÛ˛ A–ö˛-M>‘Ë˝Ö EÖ®. AßÛ˛ Á‹–ö˛$ƒÊ˝$ÖÃZ {ÚúÁŸ-ΔÊˇœMʸ$ yÏ˛–ö˛*Öyä˛ Ú≥ΔÊˇ$-Vʸ$-ô¯Ö®. –Û˛ô˲-ØÈÀ Á≥ΔÊˇÖV> ^˲*ı‹¢ {ÚúÁŸ-ΔäˇfiMʸ$ 20 ‘ÈôË˛Ö –Û˛$ΔÊˇ A´®Mʸ –Û˛ô˲ØË˛Ö À¿Ö^Û˛ A–ö˛-M>-‘ÈÀ$ EØÈ≤Δˇ$$. sÓ˝Ô‹-Gã‹ Ø˲*≈Hgå˝ yÏ˛h-rÃå˝ Ì‹PÃå˝fiÃZ (AØ˲-Õ-sÏ˝Mä¸fi, MʸÖsÒ˝Öså˝ –ö˛*ΔˇP-sÏ˝ÖVä¸ –ö˛ÖsÏ˝) Ø˛OÁ≥#◊˝≈Ö EØ˲≤ {ÚúÁŸ-ΔäˇfiMʸ$ Hyë®Mϸ ΔÊˇ*.6.5 ÀÑʸÀ –Û˛ô˲-ØÈ∞≤ BÁúΔäˇ ^Û˛Á‹$¢Ö®.

Ø˲*ô˲Ø˲ —´ßë-ØÈÀ$ IsÓ˝ Á‹ÖÁ‹¶À$ AÖßÊ˛-«MÓ¸ A–ö˛-M>‘Ë˝Ö MʸյÖ^Û˛ EßÛ˛™‘Ë˝Öô¯ ∞ƒÊ˝*-–ö˛$Mʸ {Á≥{Mϸ-ƒÊ˝$ÃZ Gد≤ –ö˛*ΔÊˇ$µÀ$ Mʸ*yë ^Û˛Á‹$¢-ØÈ≤Δˇ$$. M>≈ÖÁ≥ã‹ ı≥œã‹-–˛$Öså˝fi AØÛ˛— Á≥rt-◊Í-ÃZœ∞ Mˆ∞≤ {Á≥–ö˛$$Q M>ÃÙ˝-i-ÀMʸ$ –ö˛*{ô˲–Û˛$ Á≥«-—$ô˲Ö. —$VʸôÈ M>ÃÙ˝-iÀ$, {V>“$◊˝ {¥ÎÖôÈÃZœ∞ Mʸ‚Í-‘È-À-ÀØ˲$ H–¯ Mˆ∞≤ {¥Î´ßë-Ø˲≈Ö ÃÙ˝∞ MʸÖÚ≥-±À$ –ö˛*{ô˲–Û˛$ ı≥œã‹-–˛$Öså˝ {y˛O–í˛ M¯Á‹Ö Á‹ÖßÊ˛-«ÿ-Á‹$¢Ö-sÍΔˇ$$. ©Öô¯ BƒÊ˝* M>ÃÙ˝-i-ÃZœ∞ —ßë≈-ΔÊˇ$¶-ÀMʸ$ ô˲–ö˛$ {Á≥Ü-øÊ˝Ø˲$ ∞ΔÊˇ*-Ì≥Ö-^˲$-Mʸ$ØÛ˛ A–ö˛-M>‘Ë˝Ö ßÊ˛MʸPyÊ˛Ö ÃÙ˝ßÊ˛$. D AÖ‘È∞≤ ßÊ˛ñÌŸtÃZ Ú≥r$t-Mˆ∞ sÓ˝Ô‹-Gã‹ "ØÛ˛ÁŸ-Ø˲Ãå˝ M>”ÕÁúƒÊ˝$-Δäˇ sÒ˝ã‹t' AØÛ˛ {Á≥{Mϸ-ƒÊ˝$Ø˲$ {Á≥–Û˛-‘Ë˝-Ú≥-sÏ˝tÖ®. Cr$-–ö˛ÖsÏ˝ Mˆô˲¢ —´ßë-ØÈ-ÀØ˲$ Mʸ*yë E߯≈-V>-ΔÊˇ$¶À$ Vʸ–ö˛$-∞Á‹*¢ EÖyëÕ. AÖßÊ˛$Mʸ$ AØ˲$-Vʸ$-◊˝ÖV> ô˲–ö˛$∞ ôÈ–ö˛$$ Ì‹ßÊ˛ÆÖ ^Û˛Á‹$-M¯-–ÈÕ.

›ÎtΔÊˇtã-≥-ÀÃZ 2 ÀÑʸÀ$ {Á≥Á‹$¢ôË˛Ö ›ÎtΔÊˇtã-≥À Áfl˝–È Ø˲yÊ˛$-›˘¢Ö®. ›ÎtΔÊˇtã-≥..- ƒÊ˝$*-ô¨˛ Á‹«P-Ãå˝fiÃZ ÃÙ˝sÒ˝ã‹t ∫gå˝. GyÊ˛$≈-MÛ¸-ÁŸØå˛, {sÍ–˛-ÕÖVä¸, ºh-Ø˛ã‹ CÃÍ A∞≤ ΔÊˇÖV>ÃZœ ›ÎtΔÊˇtã≥ {¥ÎgÒ˝-Mä¸tÀ$ —Á‹¢-«-Á‹$¢-ØÈ≤Δˇ$$.

JMʸ IyÏ˛ƒÊ˝* i—-ôÈØÛ˛≤ –ö˛*ΔÛˇa-Á‹$¢Ö-ßÊ˛-ØÛ˛® ›ÎtΔÊˇtã≥fi —ÁŸƒÊ˝$ÖÃZ ∞f-–ö˛$-–ö˛#-ô˲$Ö®. «{Mʸ*-så˝-–˛$Ö-så˝ÃZ ›ÎtΔÊˇtã-≥À$ ô˲–ö˛$ Á‹ôÈ¢ ^Èr$-ô˲$-ØÈ≤Δˇ$$. ßÛ˛÷ ›ÎtΔÊˇtã≥ Á‹ÖÁ‹¶À$ –ö˛^Û˛a Hyë® Á‹$–ö˛*ΔÊˇ$ 2,00,000 –ö˛$Ö® E߯≈-Vʸ$-ÀØ˲$ °Á‹$-Mʸ$ØÛ˛ A–ö˛-M>‘Ë˝Ö EÖ®. {Á≥Á‹$¢ôË˛Ö ßÛ˛÷ ›ÎtΔÊˇtã-≥ÃZœ 6,00,000 –ö˛$Ö® E߯≈-Vʸ$-À$-ØÈ≤ΔÊˇ$. VʸôÛ˛-yë® Mˆô˲¢V> 1,50,000 –ö˛$Ö® E߯≈-Vʸ$-ÀØ˲$ «{Mʸ*så˝ ^Û˛Á‹$-Mʸ$-ØÈ≤Δˇ$$. ● ›ÎtΔÊˇtã-≥À$ ô˲–ö˛$ Á≥«-´®∞ —Á‹¢-«Ö-^˲$-Mʸ$Ö-r$-ØÈ≤Δˇ$$. Ú≥ßÊ˛™ MʸÖÚ≥-±-À$V> GßÊ˛-Vʸ-yë-∞Mϸ {Á≥ƒÊ˝$-ôÈ≤À$ ›ÎW-Á‹$¢ØÈ≤Δˇ$$. —ßÛ˛÷ ªÍ≈ÖMʸ$À$, Á‹ÖÁ‹¶À Á‹Áfl˝-M>-ΔÊˇÖô¯ Ú≥ßÊ˛™ Gô˲$¢Ø˲ ∞´ßÊ˛$-ÀØ˲$ Á‹“$-Mʸ-«-Á‹$¢-ØÈ≤Δˇ$$. {Á≥Á‹$¢ôË˛Ö ßÛ˛÷ƒÊ˝$ÖV> 39,000 Ú≥O_-À$Mʸ$ ›ÎtΔÊˇtã≥fi EØÈ≤Δˇ$$. {Á≥° Á‹Ö–ö˛-ô˲fiΔÊˇÖ Mˆô˲¢V> 5,000 HΔÊˇµ-yÊ˛$-ô˲$-ØÈ≤Δˇ$$. ^˲ßÊ˛$–ö˛#, –ö˛ƒÊ˝$-Á‹$ô¯ ∞—$ô˲¢Ö ÃÙ˝Mʸ$Öyë M>Ì‹Öô˲ sÒ˝Mϸ≤-MʸÃå˝

ØÈÃÒ˝yä˛j, –Û˛$ØÛ˛-gÒ˝-–˛$Öså˝ Ì‹PÃå˝fi EÖsÙ˝ ^ÈÀ$ ›ÎtΔÊˇtã≥ ®‘Ë˝V> –ö˛yÏ˛-–ö˛-yÏ˛V> AyÊ˛$-Vʸ$À$ –Û˛ƒÊ˝$-–ö˛^˲$a. ô˲ßÊ˛-Ø˲$-Vʸ$◊˝ÖV> ›ÎtΔÊˇtã-≥À$ MÛ¸–ö˛ÀÖ CÖf-±Δäˇ, sÒ˝Mϸ≤-MʸÃå˝ ªÍ≈{V˙Öyä˛ EØ˲≤ –È«ØÛ˛ M>Mʸ$Öyë ›Î´ßë-ΔÊˇ◊˝ {V>yÊ˛$≈ƒÙ˝$-rœØ˲$ Mʸ*yë ∞ƒÊ˝$-—$Ö-^˲$-Mʸ$Ö-r$-ØÈ≤Δˇ$$. CßÛ˛ JΔÊˇ–ö˛yÏ˛ D Hyë® Mʸ*yë MˆØ˲-›Î-Vʸ$-ô˲$Ö®.

16 ÀÑʸÀ E߯≈-V>À$ Aô˲≈-´®Mʸ –ö˛$Ö®Mϸ E¥Î´® Mʸյ-›˘¢Ø˲≤ ΔÊˇÖV>ÃZœ ªÍ≈ÖMϸÖVä¸, ÚúOØÈØå˛fi, CØ˲*fi-ΔˇØå˛fi —øÍ-V>À$ –ö˛$$ÖßÊ˛Ö-fÃZ EÖsÍΔˇ$$.

AÖôÛ˛-M>-Mʸ$Öyë ^ÈÃÍ –ö˛$Ö® Á‹ßÊ˛ΔÊˇ$ ΔÊˇÖV>ÃZœ Ì‹¶ΔÊˇ-Á≥-yÊ˛-sÍ∞Mϸ BÁ‹Mϸ¢ ^˲*Ì≥-Á‹$¢Ö-sÍΔÊˇ$. BƒÊ˝* ΔÊˇÖV>ÃZœ –Û˛ÃÍ® A–ö˛-M>-‘ÈÀ$ ›Î”VʸôË˛Ö Á≥À$-Mʸ$-ô˲$Ö-sÍΔˇ$$. MÛ¸–ö˛ÀÖ –ö˛$Ø˲ ßÛ˛‘Ë˝Ö-ÃZ-ØÛ˛-M>-Mʸ$Öyë —ßÛ˛-‘ÈÃZœ Mʸ*yë ^˲MʸP∞ A–ö˛-M>-‘ÈÀ$ EÖsÍΔˇ$$.

——´ßÊ˛ Á‹ΔÛˇ”À AÖ^˲ØÈ {Á≥M>ΔÊˇÖ —Á‹¢ñô˲-–˛$OØ˲ E¥Î´® A–ö˛-M>-‘È-ÀMʸ$ Fô˲-—$Á‹$¢Ø˲≤ ªÍ≈ÖMϸÖVä¸, ÚúOØÈ-∞¤-ƒÊ˝$Ãå˝ Á‹»”Ú‹ã‹, CØ˲*fi-ΔˇØå˛fi ΔÊˇÖVÊ¸Ö 2022 ØÈsÏ˝Mϸ 16 ÀÑʸÀ E߯≈-V>À MʸÀµØ˲ ®‘Ë˝V> –ö˛$$ÖßÊ˛$Mʸ$ –˛‚Ê˝ì-ô¯Ö®. ªÍ≈ÖMϸÖVä¸, ÚúOØÈ-∞¤-ƒÊ˝$Ãå˝ Á‹»”-Ú‹ã‹, ØÈØå˛ ªÍ≈ÖMϸÖVä¸ ÚúOØÈØå˛fi M>Δˆµ-ΔÛˇ-ÁŸØå˛fi —øÍVʸÖ-ÃZØÛ˛ 7.8 ÀÑʸÀ E߯≈-V>À$ HΔÊˇµ-yÊ˛Ø˲$-ØÈ≤Δˇ$$. “sÏ˝Mϸ ô¯yÊ˛$V> {Á≥øÊ˝$ô˲”, {Ú≥O–Û˛r$ CØ˲*fi-ΔˇØå˛fi MʸÖÚ≥-±À$ 70 –Û˛À E߯≈-V>À$ Á‹ñÌŸtÖ-^˲-Ø˲$-ØÈ≤Δˇ$$. ›ÎtMä¸ {ªZMϸÖVä¸ Á‹ÖÁ‹¶À$ –ö˛$Δ¯ 20 –Û˛À$, –ö˛$*≈^˲$-–ö˛Ãå˝ ÁúÖyÊ˛œÃZ ÀÑʸ E߯≈-V>À$ øÊ˝»¢ ^Û˛ƒÊ˝$-Ø˲$-ØÈ≤ΔÊˇ$. ∞ƒÊ˝*-–ö˛$M>À Á≥ΔÊˇÖV> –˛$$ô˲¢Ö ∞ƒÊ˝*-–ö˛$-M>ÃZœ Á‹$–ö˛*ΔÊˇ$ 73 ‘ÈôË˛Ö {Á≥øÊ˝$ô˲” ΔÊˇÖVʸ ªÍ≈ÖMʸ$-ÃZœØÛ˛ fΔÊˇ-Vʸ-Ø˲$-ØÈ≤Δˇ$$. ªÍ≈ÖMϸÖVä¸ ΔÊˇÖVʸÖ-ÃZØÛ˛ 2019ÃZ ßëßëÁ≥# ΔˇÖyÊ˛$ ÀÑʸÀ E߯≈-V>À$ À¿Ö-^˲-Ø˲$-Ø˲≤r$œ AÖ^˲ØÈ. {Ú≥O–Û˛r$ ªÍ≈ÖMʸ$ÃÙ˝ M>Mʸ$Öyë.. gÍ°ƒÊ˝$ ªÍ≈ÖMʸ$À$ Mʸ*yë Mˆô˲¢ Á‹Ö–ö˛-ô˲fi-ΔÊˇÖÃZ ∞ƒÊ˝*-–ö˛$M>À$ ^Û˛Á≥-sÙ˝tÖ-ßÊ˛$Mʸ$ Ì‹ßÊ˛¶-–ö˛$-–ö˛#-ô˲$-ØÈ≤Δˇ$$. “sÏ˝ÃZ 40 ‘ÈôË˛Ö –Û˛$ΔÊˇMʸ$ Ú‹µÁŸ-ÃÒ˝Ogå˝z {¥˜ÚúOÃå˝fi (yÛ˛sÍ AØ˲-Õã‹t, ºVä¸ yÛ˛sÍ –Û˛$ØÛ˛-gå˝-–˛$Öså˝ ô˲®-ô˲-ΔÊˇ)-ÃZØÛ˛ Mˆô˲¢ MˆÀ$-–ö˛#À$ EÖyÛ˛ A–ö˛M>‘Ë˝Ö EÖ®. ● {Á≥øÊ˝$ô˲” ΔÊˇÖVʸ ªÍ≈ÖMʸ$À$ HsÍ IΩ-Ô≥-Gã‹ ßë”Δ> Mʸœ«MʸÃå˝, {¥˜ªÙ˝-ÁŸØ˲» BÔú-Á‹Δäˇ, Ú‹µÁŸ-Õã‹t BÔú-Á‹Δäˇ MÛ¸yÊ˛-ΔäˇÃZ ∞ƒÊ˝$-–ö˛*-M>-ÀØ˲$ ^Û˛Á≥-yÊ˛$-ô˲$Ö-sÍΔˇ$$. IΩ-Ô≥-Gã‹ –˛ªå˝Ú‹Oså˝ ßë”Δ> Á‹Ö∫Ö-´®ô˲ Á‹–ö˛*-^È-Δ>∞≤ ¥˜Ö߈^˲$a.

–˛$ΔÊˇ$-V¸OØ˲ ı‹–ö˛À$ AÖ®Ö^Û˛ {Mʸ–ö˛$ÖÃZ CØ˲*fi-ΔˇØå˛fi MʸÖÚ≥-±À$ –Û˛$ØÛ˛-gå˝-–˛$Öså˝ {sÒ˝O±, AÌ‹-Ú‹tÖså˝, –ö˛$Œt-sÍÌ‹PÖVä¸ ›Îtãú, ô˲®-ô˲ΔÊˇ E߯≈V>À M¯Á‹Ö دsÏ˝-Ìú-MÛ¸-ÁŸØ˲$œ —yÊ˛$-ßÊ˛À ^Û˛ı‹ A–ö˛-M>‘Ë˝Ö EÖ®. ÚúOØÈØå˛fi ΔÊˇÖVʸÖÃZ ›ÎtMä¸ –ö˛*ΔˇPså˝fi, «ã‹P –Û˛$ØÛ˛-gå˝-–˛$Öså˝, M>≈Ì≥-rÃå˝ –ö˛*ΔˇPså˝, ›ÎtMä¸ GMÛ¸fieÖgå˝, CØ˛”ã-‹t-–˛$Öså˝, ÁúÖyä˛ –Û˛$ØÛ˛-gå˝–˛$Öså˝ ô˲®-ô˲ΔÊˇ —øÍ-V>ÃZœ Á≥#ÁŸP-À-–˛$OØ˲ A–ö˛-M>-‘ÈÀ$

EÖsÍΔˇ$$. D A–ö˛-M>-‘È-ÀØ˲$ AÖßÊ˛$-M¯-–È-ÀÖsÙ˝ Á‹Ö∫Ö-´®ô˲ —øÍ-VʸÖÃZ GÖΩ-H / -–ö˛*-Á‹tΔäˇfi yÏ˛{X ^Û˛ƒÊ˝*Õ. AÖôÛ˛-M>-Mʸ$Öyë GØå˛-Gã-‹D –ö˛ÖsÏ˝ Á‹ÖÁ‹¶À$ BÁúΔäˇ ^Û˛ı‹ M¯ΔÊˇ$fiÀ$ ^Û˛ƒÊ˝$yÊ˛Ö AßÊ˛-Ø˲Á≥# {Á≥ƒÒ˝*-fØ˲ÖV> EÖr$Ö®.

Á‹$-Ì‹¶-ΔÊˇ-–˛$OØ˲ M¸»Δäˇ ÀÑʸ≈Ö-V> {Á≥øÊ˝$ô˲”Ö ΔÊˇÖVʸ Á‹ÖÁ‹¶À$ (Ô≥Gã-‹-ƒÊ˝$*À$) BMʸ-ΔÊˇ¤-◊Ó˝-ƒÊ˝$–˛$OØ˲ iô˲Ö, {Ú≥O–Û˛så˝ ΔÊˇÖVʸÖô¯ ¥˘ÕaôÛ˛ Á‹$Ì‹¶-ΔÊˇ-–˛$OØ˲ M¸»ΔäˇMʸ$ ‡“$-∞-›Î¢Δˇ$$ AØ˲-yÊ˛ÖÃZ Gr$-–ö˛ÖsÏ˝ Á‹ÖßÛ˛Áfl˝Ö ÃÙ˝ßÊ˛$. Ô≥Gã-‹-ƒÊ˝$*-ÀØ˲$ —$±ΔÊˇô˲≤ (ΩD-GÖ-GÃå˝, ΩGã-‹-G-Øå˛GÃå˝, KG-Øå˛-iÔ‹ —ßÛ˛‘å˝ –ö˛ÖsÏ˝ Á‹ÖÁ‹¶À$), –ö˛$‡ΔÊˇô˲≤ (GØå˛-sÓ˝-

“sÏ˝MÛ¸ yÏ˛–ö˛*Öyä˛

Ô≥Ô‹, M¯Ãå˝ CÖyÏ˛ƒÊ˝*, V¸Δˇ$$Ãå˝, ΩÚfl˝-^å˛-D-GÃå˝, KG-Øå˛-iÔ‹ –ö˛ÖsÏ˝ Á‹ÖÁ‹¶À$), Ø˲–ö˛ΔÊˇô˲≤ (Á≥–ö˛-Δäˇ-{Wyä˛, Úfl˝^å˛-Ô≥-Ô‹-GÃå˝, –˛OgÍVä¸ Ô‹tÃå˝, ΩÔ≥-Ô‹-GÃå˝ –ö˛ÖsÏ˝ Á‹ÖÁ‹¶À$) AØÛ˛ MÛ¸r-W-»-À$V> —øÊ˝-hÖ-^ÈΔÊˇ$. –È≈¥ÎΔÊˇ ∞ΔÊˇ”-Áfl˝◊˝, —Á‹¢-ΔÊˇ◊˝ –ö˛ÖsÏ˝ M>ΔÊˇ-◊ÍÀô¯ Ô≥Gã-‹-ƒÊ˝$*À$ HsÍ –Û˛À Á‹ÖQ≈ÃZ E߯≈-Vʸ$-ÀØ˲$ ∞ƒÊ˝$-—$Ö-^˲$-Mʸ$Ö-r$-ØÈ≤Δˇ$$. A{Ú≥Ö-sÓ˝ã-‹-ÌŸã≥, –Û˛$ØÛ˛-gå˝-–˛$Öså˝ {sÒ˝O±, M¸—$ã‹t, GWj-Mʸ*≈-sÏ˝–í˛, AÌ‹-Ú‹tÖså˝ –Û˛$ØÛ˛-fΔäˇ, l∞-ƒÊ˝$Δäˇ AÌ‹-Ú‹tÖså˝, –ö˛$Œt-sÍ-Ì‹PÖVä¸ ›Îtãú ô˲®-ô˲ΔÊˇ E߯≈-V>-ÀØ˲$ HsÍ ô˲Á≥µ-Mʸ$Öyë øÊ˝»¢ ^Û˛›Î¢Δˇ$$. D JΔÊˇ-–ö˛yÏ˛ D Á‹Ö–ö˛ô˲fiΔÊˇÖ Mʸ*yë MˆØ˲-›ÎVÛ¸ A–ö˛-M>‘Ë˝Ö EÖ®. VÛ¸så˝, ƒÊ˝$*i-Ô‹ &Ø˛så˝ Á≥»-ÑʸÃZœ ›Î´®Ö-_Ø˲ ›˘PΔäˇ B´ßë-ΔÊˇÖV> –Û˛$ØÛ˛-gå˝-–˛$Öså˝ {sÒ˝O± ô˲ΔÊˇ‡ E߯≈-V>-ÀØ˲$ øÊ˝»¢ ^Û˛›Î¢Δˇ$$. M>∫sÏ˝t BƒÊ˝* Á≥»-Ñʸ-ÀMʸ$ Ì‹ßÊ˛ÆÖ M>–ÈÕ. —$VʸôÈ E߯≈-V>-ÀMʸ$ BƒÊ˝* Á‹ÖÁ‹¶À$ ØÛ˛ΔÊˇ$V> دsÏ˝-Ìú-MÛ¸-ÁŸ-Ø˲œØ˲$ gÍ» ^Û˛›Î¢Δˇ$$. gÍªå˝ ÕÌ‹tÖVä¸ –˛ªå˝-Ú‹Oså˝fi, G֥Μ-Δˇ$$-–˛$Öså˝ Ø˲*≈ã‹ ßë”Δ> –ÈsÏ˝ —–ö˛-Δ>-ÀØ˲$ ô˛À$-Á‹$-M¯-–ö˛^˲$a.

–Û˛ô˲-ØÈÀ$ B‘È-f-Ø˲-Mʸ–Û˛$ Mˆô˲¢ Á‹Ö–ö˛-ô˲fi-ΔÊˇÖÃZ –Û˛ô˲-ØÈÀ Á≥ΔÊˇÖV> B‘È-f-Ø˲Mʸ Á≥«-Ì‹¶ô˲$ÃÙ˝ Mʸ∞-Ì≥-Á‹$¢-ØÈ≤Δˇ$$. ôÈgÍ sÒ˝Mϸ≤-MʸÃå˝ {V>yÊ˛$≈-ƒÙ˝$-rœMʸ$ Á‹Vʸr$Ø˲ ΔÊˇ*. ØÈÀ$Vʸ$ ÀÑʸÀ –È«¤Mʸ –Û˛ô˲ØË˛Ö À¿Ö-^˲–ö˛^˲$a.

IsÓ˝ ΔÊˇÖVʸÖÃZ MˆÀ$–ö˛# ›Î´´®ı‹¢.. AØ˲-Õ-sÏ˝Mä¸fi {¥˜ÚúO-Ãå˝fiÃZ Á‹Vʸ-r$Ø˲ ΔÊˇ*.HyÊ˛$ ÀÑʸÀ –È«¤Mʸ –Û˛ô˲ØË˛Ö RÍƒÊ˝$Ö. fØ˲-ΔÊˇÃå˝ {V>yÊ˛$≈-ƒÙ˝$-rœMʸ$ ΔÊˇ*. –ö˛$*yÊ˛$ ÀÑʸÀ Á‹Vʸr$ –Û˛ô˲ØË˛Ö À¿Ö^˲-Ø˲$Ö®. –Û˛$ØÛ˛-gå˝-–˛$Öså˝ {¥˜Úú-ÁŸ-Ø˲Ãå˝fi ΔÊˇ*.5 ÀÑʸÀ –ö˛ΔÊˇMʸ$ Á‹Vʸr$ –È«¤Mʸ –Û˛ô˲ØË˛Ö AÖßÊ˛$-Mʸ$ØÛ˛ “À$Ö®. IsÓ˝I, yÏ˛¥˜œ–ö˛* —ßë≈-ΔÊˇ$¶-À$ MʸÖÚ≥-±-∞ -∫-sÏ˝t ΔÊˇ*.1.5 ÀÑʸÀ Ø˲$Ö_ ΔÊˇ*. 2.5 ÀÑʸÀ –ö˛ΔÊˇMʸ$ –Û˛ô˲ØË˛Ö ¥˜Ö߈-^˲$a.

r*«-fÖ.. -‡-Ì‹µ-sÍ-ÕsÓ˝ Á‹»”ã‹ ΔÊˇÖVʸÖÃZ r*«fÖ, ‡Ì‹µ-sÍ-ÕsÓ˝ ΔÊˇÖV>-∞® MÓ¸ÀMʸ ¥Î{ô˲. D Á≥«-{‘Ë˝–ö˛$ 2020 ØÈsÏ˝Mϸ 9 ºÕ-ƒÊ˝$-ب˛ A–˛$-«-Mʸ-ب˛ yëÀ-ΔÊˇœMʸ$, 2028 ØÈsÏ˝Mϸ 30.5 —$Õ-ƒÊ˝$-ب˛ A–˛$-«-Mʸ-ب˛ yëÀΔÊˇœMʸ$ ^Û˛ΔÊˇ$-Mʸ$Ö-r$-ßÊ˛∞ JMʸ AÖ^˲ØÈ. AÖsÙ˝ AÖôÛ˛›Î¶Δˇ$$ÃZ E߯≈-V>À MʸÀµØ˲ Mʸ*yë fΔÊˇ$-Vʸ$-ô˲$Ö®. D {Mʸ–ö˛$ÖÃZ {ÁúÖså˝ BÔúã‹, ªÍ≈Mä¸ BÔúã‹, Mϸ^˛Øå˛ –Û˛$ØÛ˛-gå˝-–˛$Öså˝, Áfloã‹ MÓ¸Ì≥ÖVä¸ –Û˛$ØÛ˛-gå˝-–˛$Öså˝, ÚúOœså˝ Mϸ^˛Øå˛fi / BØå˛-ªZΔäˇz ÚúOœså˝ Á‹»”Ú‹ã‹, MʸÁ‹t-–ö˛$Δäˇ «ÃÙ˝-ÁŸØå˛ GWjMʸ*≈-sÏ˝–í˛ –ö˛ÖsÏ˝ E߯≈-V>-ÀØ˲$ ¥˜Ö߈^˲$a. Á‹Ö∫Ö-´®ô˲ M¯ΔÊˇ$fi-ÀØ˲$ ^Û˛ƒÊ˝$yÊ˛Ö ßë”Δ> D E߯≈-V>-ÀØ˲$ AÖßÊ˛$-M¯-–ö˛^˲$a.

M>∫sÏ˝t E߯≈-V>-ΔÊˇ$¶À$ Cr$-–ö˛ÖsÏ˝ Ø˛OÁ≥#-◊Í≈À$ ØÛ˛ΔÊˇ$a-M¯–ö˛yÊ˛Ö ô˲Á≥µ-∞-Á‹«. GÖßÊ˛$-MʸÖsÙ˝ ªÍ≈ÖMʸ$À$, IsÓ˝ ı‹–ö˛À$, GyÊ˛$≈-MÛ¸-ÁŸØå˛, {sÍ–˛Ãå˝ AÖyä˛ ‡Ì‹µ-sÍ-ÕsÓ˝, Úfl˝Ãå˝¢-MÛ¸Δäˇ, «ƒÊ˝*-ÕsÓ˝, Á‹*Á≥Δäˇ –ö˛*ΔˇPså˝, D&M>-–ö˛$Δäˇfi, sÒ˝ÕMʸÖ, ÚúOØÈ-∞¤-ƒÊ˝$Ãå˝ Á‹»”-Ú‹ã‹, –ö˛*≈Ø˲$-∏Î≈-Mʸa-«ÖVä¸, Ω–ö˛*, Úfl˝^å˛-BΔäˇ, –ö˛*ΔˇP-sÏ˝ÖVä¸ –ö˛ÖsÏ˝ ΔÊˇÖV>-ÃZœ∞ Á‹ÖÁ‹¶-À-ô¯¥Îr$ –˛$O{M¯-›Îãút, Vʸ*Vʸ$Ãå˝, gÒ˝Øå˛-¥Î≈Mä¸t, sÓ˝Ô‹-Gã‹, IΩGÖ, —{¥˘, y˛Ãå˝ –ö˛ÖsÏ˝ IsÓ˝ Á‹ÖÁ‹¶À$ Cr$-–ö˛ÖsÏ˝ ∞Á≥◊˝$-ÀØ˲$ ∞ƒÊ˝$-—$Ö-^˲$-M¯-–ö˛-yë-∞Mϸ {¥Î´ßëØ˲≈Ö CÁ‹$¢-ØÈ≤Δˇ$$.

B«tÔú-ÌŸ-ƒÊ˝$Ãå˝ CÖsÒ˝-Õ-gÒ˝Øå˛fi, yÏ˛gÒ˝OØå˛, AØ˲-Õ-sÏ˝Mä¸fi, »Ú‹Δäˇa AÖyä˛ y˛–ö˛-Àã-≥-–˛$Öså˝, –˛$ÔŸØå˛ ÃÒ˝«≤ÖVä¸ –ö˛ÖsÏ˝ Ø˲*≈Hgå˝ Ì‹PÃå˝fiÃZ Ø˛OÁ≥#-◊Í≈-ÀMʸ$ {Á≥Á‹$¢ôË˛Ö –ö˛$Ö_ yÏ˛–ö˛*Öyä˛ EÖ®. IsÓ˝ Á‹ÖÁ‹¶À$ Cr$-–ö˛ÖsÏ˝ –È«Mϸ Ú≥ßÊ˛™-Ô≥r –Û˛Á‹$¢MÛ¸Ö{ßÊ˛ {Á≥øÊ˝$ô˲” —øÍØÈ≤Δˇ$$. –˛$$ô˲¢Ö BÁú-ΔÊˇœÃZ “sÏ˝ –ÈsÍØÛ˛ 50 V>ÃZœ M¸»Δäˇ {¥ÎΔÊˇÖ-¿Ö-^˲-yë-∞Mϸ ‘ÈôË˛Ö Ú≥OV> EÖr$Ö-ßÊ˛∞ ^˲MʸP∞ A–ö˛-M>‘Ë˝Ö Mʸյ-›˘¢Ö® ƒÊ˝$*∞-ƒÊ˝$Øå˛ Á≥ºœMä¸ AÖ^˲ØÈ. Á‹»”ã‹ Mʸ—$-ÁŸØå˛ (ƒÊ˝$*Ô≥-GÔ‹fi). IH-Gã‹, IÔ≥-Gã‹, IGã-ú-Gã‹, IB-Δäˇ-Gã‹, CÖf-±Δäˇ, yëMʸtΔäˇ, AÌ‹-Ú‹tÖså˝ Mʸ–ö˛*Ö-y˛Öså˝ –ö˛ÖsÏ˝ MˆÀ$-–ö˛#-À-ô¯¥Îr$, MÛ¸Ö{ßÊ˛ B«¶Mʸ –ö˛$Ö{Üô˲” ‘ÈQ, {Ü—´ßÊ˛ ßÊ˛‚Í-ÀMʸ$ M>–ö˛-ÕfiØ˲ –Û˛ÃÍ® A´®-M>-ΔÊˇ$À ∞ƒÊ˝*-–ö˛$Mʸ {Á≥{Mϸ-ƒÊ˝$Ø˲$ ƒÊ˝$*Ô≥-GÔ‹fi Á≥ΔÊˇ≈-–Û˛-Ñϸ-Á‹$¢Ö®. D Á‹ÖÁ‹¶ E߯≈-Vʸ$À «{Mʸ*-så˝-–˛$Öså˝ M¯Á‹Ö M>≈ÃÒ˝Ö-yÊ˛Δäˇ —´ßë-ØÈ∞≤ AØ˲$-Á‹-«-Á‹$¢Ö®. AÖßÊ˛$ÃZ ı≥ΔˆPØ˲≤ —´ßÊ˛Ö-V>ØÛ˛ دsÏ˝-Ìú-MÛ¸-ÁŸØ˲$œ —yÊ˛$-ßÊ˛-À-–ö˛#-ôÈΔˇ$$. Ø˲*ô˲Ø˲ Á‹Ö–ö˛-ô˲fi-ΔÊˇÖÃZ ƒÊ˝$*Ô≥-GÔ‹fi Ø˲$Ö_ ôˆÕ دsÏ˝-Ìú-MÛ¸-ÁŸØå˛ fØ˲-–ö˛« 9Ø˲ (GØå˛-yÓ˛-H&-G-Øå˛H) –˛À$-–ö˛-yÊ˛$-ô˲$Ö®. ô˲ΔÊˇ-–Èô˲ Ìú{∫-–ö˛-«ÃZ Ì‹—Ãå˝fi, Ar$Ú≥O ID-Gã‹ /- IGã-‹-Gã‹, DGã-‹D ô˲®-ô˲ΔÊˇ دsÏ˝-Ìú-MÛ¸-ÁŸØ˲$œ —yÊ˛$-ßÊ˛-À-–ö˛#-ôÈΔˇ$$. —–ö˛-Δ>ÀØ˲$ ƒÊ˝$*Ô≥-GÔ‹fi –˛ªå˝-Ú‹Oså˝

{Á≥øÊ˝$ô˲” E߯≈-V>À$ –ö˛ƒÊ˝*..- Á≥-ºœMä¸ Á‹»”ã‹ Mʸ—$-ÁŸØå˛

(http://www.upsc. gov.in/)

Ø˲$Ö_ ¥˜Ö߈^˲$a. MÛ¸Ö{ßÊ˛ {Á≥øÊ˝$-ô˲”ÖÃZ∞ ——´ßÊ˛ —øÍ-V>-ÃZœ∞ {Vʸ*ã≥&º, {Vʸ*ã≥&Ì‹, l∞-ƒÊ˝$Δäˇ CÖf-±Δäˇ, Ú‹tد-{V>-ÁúΔäˇ, Ú‹OÖsÏ˝-ÌúMä¸ AÌ‹Ú‹tÖså˝, hƒÊ˝*-À-hã‹t MÛ¸yÊ˛Δäˇ E߯≈-V>-À-ô¯-¥Îr$ ›ÎƒÊ˝$$´ßÊ˛ ¥˘Œã‹ ßÊ˛‚Í-ÃZœ∞ ——´ßÊ˛ R͉À øÊ˝»¢Mϸ D Hyë® ›Îtãú Ú‹ÃÒ˝-ÑʸØå˛ Mʸ—$-ÁŸØå˛ (http://ssc.nic.in/) øÍ» Gô˲$¢Ø˲ دsÏ˝-Ìú-MÛ¸-ÁŸØ˲$œ —yÊ˛$-ßÊ˛-À–ö˛#-ôÈΔˇ$$. BÖ{´ßÊ˛-{Á≥-ßÛ˛-‘å˝ÃZ {Vʸ*ã≥&1, {Vʸ*ã≥&2 دsÏ˝-Ìú-MÛ¸-ÁŸØ˲$œ D Mˆô˲¢ Á‹Ö–ö˛-ô˲fi-ΔÊˇÖÃZ Δ>–ö˛^˲$a. AßÛ˛-—-´ßÊ˛ÖV> {Vʸ*ã≥&3, ∏ÎΔˇã‹t ΔÛˇÖgå˝ BÔú-Á‹Δäˇ, ‡«t-Mʸ-ÀaΔäˇ BÔú-Á‹Δäˇ, BΔäˇ-sÓ˝K, HDD E߯≈-V>ÀMʸ$ D Hyëô˲®ô˲ΔÊˇ ®ÃZ Δ>ô˲ Á≥»-ÑʸÀ$ ∞ΔÊˇ”-Ìfl˝ÖAÖ‘ÈÀ$ MÓ¸ÀMʸÖ. A–Û˛ ^˲-Ø˲$-ØÈ≤ΔÊˇ$.

–È«Mϸ E߯≈Vʸ A–ö˛-M>-‘È- ÀØ˲$ ô˛_aÚ≥yÊ˛ôÈΔˇ$$. “sÏ˝∞ ßÊ˛ñÌŸtÃZ EÖ^˲$-MˆØÛ˛ “$Mʸ$ Á‹«-¥˘ƒÙ˝$ MˆÀ$-–ö˛#Ø˲$ GÖ^˲$-M¯-–ÈÕ. B –ö˛ñÜ¢Mϸ M>–È-ÕfiØ˲ Mʸ±Á‹ AΔÊˇ·ô˲-Àô¯ ¥Îr$.. {Á≥ôÛ˛≈Mʸ Ø˛OÁ≥#-◊Í≈À$, {Á≥Ü-øÊ˝Ø˲$ Mʸ*yë BÁ‹Mϸ¢ –ö˛$$Q≈Ö ›Î´®Ö-^Û˛Ö-ßÊ˛$Mʸ$ MʸñÌŸ ^Û˛ƒÊ˝*Õ. ©∞ –ö˛Àœ “$Mʸ$ ô˲WØ˲ ^ÈÃÍ –ö˛$Ö® ^˲ßÊ˛$–ö˛# Á≥NΔÊˇ¢-ƒÊ˝*≈Mʸ E߯≈Vʸ A–ö˛-M>-‘ÈÀ$ AØ˲$-øÊ˝–ö˛Ö ÃÙ˝Mʸ$ØÈ≤ Á‹ÖÁ‹¶ E߯≈VÊ¸Ö C^Û˛aÖ-ßÊ˛$Mʸ$ –˛$$Vʸ$Y Δ>Mʸ$ÖsÙ˝ Á‹–ö˛$-ƒÊ˝*∞≤ –ö˛ñ£ë ^Û˛Á‹*¢ EÖsÍΔÊˇ$. C® ^˲*Á≥#-ô˲$Ö®.

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M>Ë ^èl{MýS… WÆý‡$-MýS$P¯]l †Ç-W…¨.

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çܵÆý‡®Ä¶æ* Ð]lÆý‡®™ól ѧýlÅ

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1-1-2019

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çÜÓ§ólÖ ç³Ç-gêq-¯]l…™ø AÀ-Ð]l–¨® ^ólíܯ]l VýSVýS-¯]l™èlË… ¯]l$…_ VýSVýS-¯]l-™èl-Ë…-ÌZ° Ë„>Å-˯]l$ ból¨…^èl-VýSË "A-ç܈' „ìSç³-×ìæ° òÜò³t…-º-ÆŠ‡ÌZ ç³È-„ìS…-^éÆý‡$. ©°² çÜ$RZ-ÄŒæ$-&-30 Ķ欧ýl® ÑÐ]l*¯]l… ¯]l$…_ {ç³Äñæ*-W…-^éÆý‡$. ➠ AMøt-º-ÆŠ‡ÌZ ÑÔ>-Q-ç³-r²…ÌZ ¿êÆý‡™Œl, f´ë-¯ŒlË ¯úM>-§ýl-âêË$ ç܅Ķæ¬-MýS¢…V> hÐðl$-MŠSÞ-&-2-0-18 õ³Çr ç܅Ķæ¬MýS¢ ѯéÅ-ÝëË$ °Æý‡Ó-íßæ…-^éƇ¬. ➠ ¯]lÐ]l…-º-ÆŠ‡ÌZ ´ùÆŠ‡t-»ôæÏ-ÆŠ‡ÌZ íÜ…»ñæMŠSÞ õ³Çr ¿êÆý‡™Œl, íÜ…VýS-ç³NÆŠ‡ ¯úM>-§ýl-âêË$ ç܅Ķæ¬MýS¢ ѯéÅ-ÝëË$ °Æý‡Ó-íßæ…-^éƇ¬. ➠ IMýSÅ-Æ>fÅ çÜÑ$† Ðé™é-Ð]l-Æý‡×æ Ð]l*Æý‡$µË çܧýlçÜ$Þ (M>-‹³-&-2-4) yìlòÜ…-º-ÆŠ‡ÌZ ´ùË…-yŠl-ÌZ° MýSsZ-Ñ^Œl ¯]lVýS-Æý‡…ÌZ fÇ-W…¨. ➠ ¿êÆý‡™Œl A™èlÅ…™èl ºÆý‡$-OÐðl¯]l iÔ>-sŒæ-&-11 Eç³-{VýSà°² yìlòÜ…-ºÆŠ‡ 5¯]l {òœ…^Œl VýSĶæ*-¯é-ÌZ° MúÆý‡$ ¯]l$…_ {ç³Äñæ*-W…-_…¨. ©° ºÆý‡$Ð]l# 5,854 MìSÌZË$. ➠ AW²-&V Q…yé…-™èlÆý‡ „ìSç³-×ìæ° Jyìl-Ô>-ÌZ° Aº$ªÌŒæ MýSÌê… ©Ñ ¯]l$…_ yìlòÜ…-ºÆŠ‡ 10¯]l ÑfĶæ$-Ð]l…-™èl…V> ç³È-„ìS…-^éÆý‡$. C¨ 5 ÐólË MìS.Ò$. §ýl*Æý‡…-ÌZ° Ë„>Å-˯]l$ ból¨…-^èl-VýSË ©Æý‡ƒ-{Ôóæ×ìæ „ìSç³×ìæ. ➠

OòܯŒlÞ A…yŠl sñæM>²-Ëi A™èlÅ…™èl ÐólVýS-Ð]l…-™èl-OÐðl$¯]l çÜ*ç³ÆŠ‡ MýS…ç³NÅ-rÆŠ‡ "{ç³-™èl*Å-‹Ù-'¯]l$ MóS…{§ýl Ô>ç܈, Ýë…MóS-†MýS Ð]l$…{† çßæÆý‡Û-Ð]l-Æý‡®¯Œæ f¯]l-Ð]l-ÇÌZ {´ëÆý‡…-À…-^éÆý‡$. ©°² ç³#×ñæ-ÌZ° C…yìl-Ķæ$¯Œl C¯Œl-íÜt-r*ÅsŒæ B‹œ {sêí³MýSÌŒæ Ððl${sê-Ëi (I-I-sîæ-G…-)ÌZ HÆ>µr$ ^ólÔ>Æý‡$. ➠ ¿êÆý‡™èl A…™èl-Ç„ýS ç³Ç-ÔZ-«§ýl¯]l çÜ…çܦ (C-{Ýù).. f¯]l-Ð]lÇ 12¯]l ï³G-‹Ü-G-ÌŒæ-Ò-&-ïÜ-40 §éÓÆ> 31 Eç³{VýS-à-˯]l$ Ñf-Ķæ$-Ð]l…-™èl…V> {ç³Äñæ*-W…-_…¨. ➠ Eç³-Ç-™èlË… ¯]l$…_ Eç³-Ç-™èl-Ë…-Oò³MìS {ç³Äñæ*-W…^ól ç³–¥Ó-&2 „ìSç³-×ìæ° íœ{º-Ð]lÇ 7¯]l ç³È-„ìS…-^éÆý‡$.

C¨ 350 MìS.Ò$. ç³Ç-«¨-ÌZ° Ë„>Å-˯]l$ ból¨…-^èl-VýS˧ýl$. ➠ AÐðl$-ÇM> A…™èl-Ç„ýS çÜ…çܦ "õܵ‹Ü GMŠSÞ'.. ¸ëËP¯Œl-&9 G‹œsîæ(»êÏMŠæ 5) Æ>MðS-sŒæ¯]l$ Ðól$ 11¯]l {ç³Äñæ*W…-_…¨. C¨ º…VýS-º…-«§ýl$-&1 A¯ól º…V>Ï-§ólÔŒæ Eç³-{VýS-à°² A…™èl-Ç-„ýS…-ÌZMìS ç³…í³…¨. ➠ òÜ•µ‹Ü-gñæsŒæ MýS…ò³± ¿êÆý‡-™ŒlÌZ ™öÍ-Ýë-ÇV> BVýSçÜ$t 27¯]l iÐ]l C…«§ýl-¯]l…™ø GWÆó‡ ÑÐ]l*-¯é°² {´ëÆý‡…-À…-_…¨. C¨ yðl{à-yýl*¯Œl ¯]l$…_ ÉìlÎÏMìS

2-0-18

Mö™èl¢ Ð]l¬QÅ-Ð]l$…-{™èl$Ë$

AÐé-Æý‡$zË$

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Mathematics

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{ç³Ä¶æ*-×ìæ…-_…¨. f{sZ´ë Ððl¬MýSPË ¯]l$…_ iÐ]l C…«§ýl-¯é°² ™èlĶæ*Æý‡$ ^ólÔ>Æý‡$. ➠ G°-Ñ$¨ Úë…Oòœ$ çÜçßæ-M>Æý‡ çÜ…çܦ (G-‹Ü-ïÜ-Ðø) §ólÔ>Ë$ Æý‡ÚëÅÌZ BVýS-çÜ$tÌZ "ï³‹Ü Ñ$çÙ-¯Œl' õ³Çr ç܅Ķæ¬MýS¢ OòÜ°MýS ѯéÅ-ÝëË$ °Æý‡Ó-íßæ…-^éƇ¬. ➠ "íÜÏ-¯ðlMŠSÞ 20-1-8' õ³Çr }Ë…-MýS-ÌZ° {sìæMø-Ð]l$ÎÌZ òÜò³t…-º-ÆŠ‡ÌZ ¿êÆý‡™Œl, }Ë…MýS ¯úM>-§ýl-âêË ç܅Ķæ¬MýS¢ ѯéÅ-ÝëË$ fÇ-V>Ƈ¬. ➠ ¼ÐŒl$Þ-sñæMŠS §ólÔ>Ë$ ™öÍ-Ýë-ÇV> òÜò³t…-º-ÆŠ‡ÌZ ç³#×ñæÌZ "OÐðl$-Ìñæ-MŠSÞ-&-2-0-1-8' õ³Çr ç܅Ķæ¬MýS¢ OòÜ°MýS ѯéÅ-ÝëË$ °Æý‡Ó-íßæ…-^éƇ¬. ➠ ¿êÆý‡™Œl, AÐðl$-Ç-M>Ë$ òÜò³t…-º-ÆŠ‡ÌZ "Ķ欧Šæ® A¿êÅ-‹Ü' õ³Æý‡$™ø E™èl¢-Æ>-Q…-yŠl-ÌZ° ^úº-†Ä¶æ*ÌZ ç܅Ķæ¬MýS¢ OòÜ°MýS ѯéÅ-ÝëË$ °Æý‡Ó-íßæ…^éƇ¬.

Ô>…†: yðl°‹Ü Ð]l¬MðSÓVðS (yðl-Ððl*-{MýS-sìæMŠS Çç³-¼ÏMŠS B‹œ M>…Vø), ¯]l¨Ä¶æ* Ð]l¬Æ>§Šæ (C-Æ>-MŠS). ➠ Ð]l*ůŒl º$MýSÆŠ‡ {ò³•gŒæ: ĶæÊMóS Æý‡^èl-Ƈ¬{† A¯é² ºÆŠ‡²ÞMýS$ AMøt-º-ÆŠ‡ÌZ 'Ñ$-ÌŒæP-Ð]l*Å-¯Œl" A¯ól B…VýSÏ ¯]lÐ]l-ËMýS$ V>¯]l$ ËÀ…-_…¨. ➠ íÜÄñæ*ÌŒæ Ô>…† ºçßæ$-Ð]l$†: 20-1-8MìS V>¯]l$ ¿êÆý‡™èl {糫§é° ¯]lÆó‡…{§ýl Ððl*©MìS §ýl„ìS×æ MöÇĶæ* D AÐé-Æý‡$z¯]l$ AMøt-º-ÆŠ‡ÌZ {ç³MýS-sìæ…-_…¨.

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61. ñ|ü⁄Œ dü‘ê´Á>∑Vü≤ dü+<äs¡“¤+˝À Á‹|ü⁄s¡H˚ì sêeTkÕ«$T (1920 »qe]) ªuÛ≤s¡‘·<˚XÊìï Á_{Ïwt kÕÁe÷»´|ü⁄ |ü⁄Hê<äT\H˚ ø£~*+∫ y˚dæq dü+‘·è|æÔ |üs¡#·˝Ò<äT. <˚X¯yê´|üÔ+>± á dü+düÿs¡D\ |ü≥¢ rÁe 48. ôd’eTHé ø£$TwüHé ‘·q ìy˚~ø£qT @ dü+e‘·‡s¡+˝À #Í<ä] ªMs¡>∑+<∏äeTT ‘Ó∫ÃHês¡eTT, Ms¡T˝…e«s√ ‘Ó\T|ü⁄&çµµ nH˚ düeT]Œ+∫+~ ` 1930 7. Nsê\`ù|sê\ ñ<ä´eTø±\+˝À <äTs¡TdüT>± Á|üe]Ô+∫, ñ<ä´eT+µ e´‹πsø£‘· |ü⁄≥Tºø=∫Ã+~. B+‘√ Á_{Ïwt Á|üuÛÑT‘·«+ düsYC≤Hé 49. ø±øÏHê&É u≤+ãT dü+|òüT≥q »]–q dü+e‘·‡s¡+` 1933 π>j·T+‘√ ‘ÓHê*˝À ñ|ü⁄Œ dü‘ê´Á>∑Vü‰\qT ÄVü‰«ì+#ês¡T. Ä+Á<ÛäT\ n_Ûe÷Hêìï nee÷q|ü]∫q eTÁ<ëdüT 25. |üs¡«‘·H˚ì Ms¡j·T´ #Í<ä] @sêŒ≥T #˚dæq dü«#·Ã¤+<ä ôd’eTHé n<Ûä´ø£å‘·q @&ÉT>∑Ts¡T düuÛÑT´\T>∑\ ˇø£ ø£$TwüHéqT 62. ªe÷ ø=B› ‘Ó\¢<=s¡‘·q+µ π>j·TeTT me] s¡#·q 50. ø±øÏHê&É u≤+ãT πødüT˝À Á|ü<Ûëq ì+~‘·T&ÉT mes¡T eTTK´eT+Á‹ ` sêC≤sêeTsêj·Tì+>±sY (»dæºdt bÕغ) <äfi≤ìøÏ @eTì ù|s¡T ` XÊ+‹ùdq 8`11`1927q ìj·T$T+∫+~. á dü+düÿs¡D\T |üì#˚ùd ` >∑]yÓTfi¯¢ dü‘·´Hêsêj·TD ` Á|ü‹yê<ä uÛÑj·T+ø£sê#ê] 8. Nsê\`ù|sê\ ñ<ä´eT+˝À <äT–Zsê\ @s¡Œs¡∫q 1000 26. ªÄ+Á<Ûä•yêJµ>± U≤´‹>±+∫qyês¡T mes¡T rs¡T‘ÓqTï\qT dü«j·T+bÕ\q neø±XÊ\T |ü]o*+∫, ˇø£ 63. ñ|ü⁄Œ dü‘ê´Á>∑Vü≤+ dü+<äs¡“¤+>± ñ|ü⁄ŒbÕ≥qT mes¡T eT+~ düuÛÑT´\T >∑\ ªsêeT<ä+&ÉTµ (XÊ+‹ùdq) Äj·Tq≈£î ` |üs¡«‘·H˚ì Ms¡j·T´ #Í<ä] ìy˚~ø£qT düeT]Œ+#ê*‡+~>± eTq <˚XÊìøÏ |ü+bÕs¡T. BìH˚ 51. ø±øÏHê&É u≤+ãT πødüT˝À ø±sê>±sêìøÏ yÓ[¢q s¡∫+#ês¡T ` >∑]ø£bÕ{Ï eT˝≤¢e<Ûëì u≤\ì+~‘·T&Óes¡T ` zs¡T>∑+{Ï sêeT#·+Á<äj·T´ ≈£î&çuÛÑT»yÓTÆ, Á|üeTTKbÕÁ‘· b˛wæ+∫+~.

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11. sêyéTq>∑sY Á>±e÷ìøÏ X¯+≈£îkÕú|üq »]|æq~ mes¡T y˚Ts¡≈£î $s¡$T+#ês¡T ` >±+BÛJ m+|æø£: |òæõø£˝Ÿ kÕº+&ÉsY¶/Á≥j·T˝Ÿ/|òæõø£˝Ÿ f…dtº Ä<Ûës¡+>±. ` >±+BÛJ 30. n\÷¢] kÕ–+∫q $|ü¢e+ ` s¡+bÕ $|ü¢e+ ôd+Á≥˝Ÿ ]»sY« b˛©dt bò˛sY‡ (d”ÄsY|”m|òt) Áø°&Ü <äs¡U≤düTÔ $<Ûëq+: Ä|òt˝…’Hé. <äs¡U≤düTÔ\qT yÓuŸôd’{Ÿ qT+∫ 12. sêyéTq>∑sY (‘ê{≤≈£î >∑T&çôd\ eTVü‰q>∑s¡+)˝À 31. n\÷¢] ‘·*¢<ä+Á&ÉT\T |ü•ÃeT>√<ëe] õ˝≤¢˝Àì ns¡Ω‘·: b˛düTºqT ã{Ϻ dü+ã+~Û‘· $uÛ≤>±˝À¢ ;á/;f…ø˘, ø√{≤˝À 359 ø±ìùdºãT˝Ÿ, ôV≤&é ø±ìùdºãT˝Ÿ b˛düTº\ uÛÑØÔøÏ &ÍHé˝À&é #˚düTø√yê*.

Nsê\`ù|sê\ Á|ü»\T mìï HÓ\\bÕ≥T yÓ÷>∑\T¢ yêdüÔe⁄´\T. (4`7`1897q »qq+) u≤´∫\sY‡ &çÁ^ ñrÔs¡í‘·. <äs¡U≤düTÔ\T ø√s¡T‘√+~. <äs¡U≤düTÔ |ò”E: s¡÷.100. ìedæ+#ês¡T ` 11 HÓ\\T 32. »qe] 1922 qT+∫ y˚T 1924 es¡≈£L ø=qkÕ–q ej·TdüT: »qe] 15, 2019 Hê{ÏøÏ 35 @fi¯ó¢ b˛düTº\ $esê\T... <äs¡U≤düTÔ≈£î ∫e]‘˚B: »qe] 13, 2019.

13. <äT–Zsê\ Nsê\`ù|sê\ ñ<ä´eT Ks¡TÃ\ ì$T‘·Ô+ s¡+bÕ $|ü¢yêìøÏ Hêj·Tø£‘·«+ eVæ≤+∫+~ mes¡T $T+#·≈£L&É<äT. ]»πs«wüHé nuÛÑ´s¡Tú\≈£î dü&É*+|ü⁄ ñ+≥T+~. yÓuŸôd’{Ÿ: https://crpf.gov.in m≈£ÿ&É »s¡T>∑T‘·Tqï Ä+Á<ÛäeTVü‰düuÛÑ Á|ü‹ì<ÛäT\qT ` n\÷¢] d”‘êsêeTsêE ø±ìùdºãT˝Ÿ/ »qs¡˝Ÿ &É÷´{°: 339 (Ç+<äT˝À |ü⁄s¡Twüß\≈£î m+|æø£: sê‘· |üØø£å, Ç+≥s¡÷«´ Ä<Ûës¡+>±.

295, eTVæ≤fi¯\≈£î 44 b˛düTº\THêïsTT). ø£*ùd+<äT≈£î yÓfi¯¢>± n‘·ìì ìs¡“¤+~+#ês¡T ` 1921 33. ø£èwüí<˚$ ù|≥≈£î düMT|ü+˝À ñqï ‘ê+&Éeq~ ˇ&ÉT¶q <äs¡U≤düTÔ |ò”E: s¡÷.100. sê‘· |üØø£å‘˚B: e÷]à 10, 2019. ns¡Ω‘·: yÓTÁ{Ï≈£î´˝ÒwüHé ñrÔs¡í‘·‘√ bÕ≥T dü+ã+~Û‘· Áø°&É˝À ôdô|º+ãsY˝À ãs¡+|ü⁄s¡+˝À »s¡T>∑T‘·Tqï Ä+Á<ÛäeTVü‰düuÛÑ n\÷¢] HÓ\ø=\TŒ≈£îqï ÄÁX¯eT+ ù|s¡T ` sêeT $»j·Tq>∑s¡+ u…+>∑fi¯Ss¡T Á|ü<Ûëq πø+Á<ä+>± ø±s¡´ø£˝≤bÕ\T |üØøå± πø+Á<ë\T: nVü≤à<ëu≤<é, u…+>∑fi¯Ss¡T, uÛÀbÕ˝Ÿ, Á|ü‹uÛÑ, ì]›wüº XÊØs¡ø£, yÓ’<ä´ Á|üe÷D≤\T+&Ü*.

14. <äT–Zsê\ J$‘·#·]Á‘· sêdæ+~ mes¡T ` >∑$Tà&Ó<ä\ 34. n\÷¢]øÏ düVü‰j·T|ü&çq düVü≤#·s¡T\T mes¡T ` y˚–sêE ìs¡«Væ≤k˛Ôqï uÛ≤s¡‘· n+‘·]ø£å |ü]XÀ<Ûäq dü+düú (ÇÁk˛) 18 #·+&û>∑&Ûé, #ÓHÓ’ï, >∑TyêVü≤{Ï, ôV’≤<äsêu≤<é, ø√˝Ÿø£‘ê, \ø√ï, ôV≤&é ø±ìùdºãT˝Ÿ/ »qs¡˝Ÿ &É÷´{°: 20 (Ç+<äT˝À |ü⁄s¡Twüß\≈£î yÓ+ø£≥ düTu≤“sêe⁄ dü‘·´Hêsêj·TDsêE, >±+eT\T¢<=s¡, >±+>∑+≥+<=s¡ ôd’+{Ïdtº/ Ç+»˙sY b˛düTº\≈£î <äs¡U≤düTÔ\T ø√s¡T‘√+~. eTT+u…’, q÷´&Ûç©¢, ‹s¡Teq+‘·|ü⁄s¡+.

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35. ªn–ZsêEµ>± Á|üdæ~Δ¬øøÏÿq~ mes¡T ` y˚–sêE m\ÁøϺø£˝Ÿ-6, ]Á|òæõπswüHé n+&é msTTsY ø£+&çwüì+>¥-2, |üP]Ô $esê\T : yÓuŸôd’{Ÿ˝À |ü]o*+#=#·TÃ. ì]›wüº XÊØs¡ø£, yÓ’<ä´ Á|üe÷D≤\T+&Ü*. b˛©düT\ <äTs¡Tôd’q Á|ües¡Ôq‘√ ñÁ~≈£îÔ˝…’q Á|ü»\T dü‘·´Hêsêj·TDsêE Ä]ÿf…ø£ÃsY-1). yÓuŸôd’{Ÿ: www.isro.gov.in ej·TdüT: »qe] 13, 2019 Hê{ÏøÏ 18-23 @fi¯¢ eT<Ûä´

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16 ÷ªÙÞœüŒî¦ô¢Ù 1 áì÷J 2019 - email: help@eenadupratibha.net

KALIA.. for farmers!

GST Rates Slashed On 22nd December 2018, the 31st meeting of GST Council at New Delhi took following decisions relating to changes in GST rates.

GST rates reduced from 28% to 18% include Pulleys, transmission shafts and cranks, gear boxes, Monitors and TVs of up to screen size of 32 inches, Re-traded or used pneumatic tyres of rubber, Power banks of lithium ion batteries, Digital cameras and video camera recorders and Video game consoles etc.

With this, only 28 goods are left in the highest 28% GST rate slab. Now, the 28% slab is restricted to only luxury and sin goods, apart from auto parts and cement - tax rates on which could not be cut due to high revenue implication.

Writer Amara Veeraswamy Subject Expert

New Chairman of CBIC

“Strategy for New India@75” NITI Aayog unveiled a strategy document called the “Strategy for New India@75” suggesting reforms to make India a 4-trillion dollar economy by 2022-23.

The document’s main idea is to go for such reforms in the economy that will keep India growing at 8% annually that could be quicken to 9-10% by 2022-23.

The document suggests increasing the share of taxes in the national income from current 17% to 22%. The report calls for the

GST rate on cinema tickets above Rs. 100 shall be reduced from 28% to 18% and on cinema tickets up to Rs. 100 reduced from 18% to 12%.

Vegetables, (uncooked or cooked by steaming or boiling in water), frozen, branded and put in a unit container and Vegetable provisionally preserved (for example by sulphur dioxide gas, in brine, in sulphur water or in other preservative solutions) are totally exempted from GST. These items earlier taxed at 5%.

The chairman of Railways Board Ashok Lohani has been named the Vice Chancellor of the University.

First Railway University

Hockey World Cup 2018

National Rail and Transportation Institute (NRTI), is India’s first Railway university focused on transport-related education, multidisciplinary research and training dedicated to the nation by Union Minister of Railways and Coal Piyush Goyal and Gujarat Chief Minister Vijay Rupani on 15 December 2018.

Located in Vadodara, Gujarat offering two courses, Bachelor of Science in Transportation Technology and a Bachelor of Business Administration in Transport Management.

On 16th December 2018, Belgium Hockey team won their first ever World cup title.

Belgium defeated the Netherlands 3–2 in the final on a penalty shoot-out after a 0–0 draw.

Australia stood third and India got sixth place.

Arthur Van Doren, the Belgian Hockey player, was awarded as the Best Player and Spain won the Fair Play award. Young player of the tournament won by Thijs van Dam of Netherland. Blake Govers of Australia and Alexander Hendrickx of Belgium are the top goal scorers, who scored 7 goals each.

Model Questions 1. The recent decision of GST council made that Music Books attract how much GST rate?

1) 28% 2) 18% 3) 12% 4) 5% 5) Nil 2. GST council reduced the GST rate on Parts and accessories for the carriages for disabled persons from 28% to………

1) 18% 2) 5% 3) 0% 4) 12% 5) 8% 3. The Services supplied by banks to Basic Saving Bank Deposit (BSBD) and account holders under Pradhan Mantri Jan Dhan Yojana (PMJDY) attract how much GST rate as per the decision of GST council recently?

1) 28% 2) 18% 3) 12% 4) 5% 5) totally exempted from GST 4. On 18th December 2018, Naveen Patnaik, CM of Odisha announced financial aid of

support for cultivation, livelihood support for landless households, financial assistance to vulnerable agriculture households and landless labourers, life insurance cover and exemption of interest for crop loans of up to Rs 50,000.

Under the KALIA scheme, all small and marginal farmers numbering around 3 million will be covered. An assistance of Rs 10,000 will be provided per family for Kharif and Rabi seasons. The scheme also promises Rs.2 Lakh life insurance cover.

5.

6.

7.

8.

Rs.10 Crore for the establishment of Odiya Cultural Centre in………

1) Hyderabad 2) Bangalore 3) Chennai 4) Guwahati 5) Surat What is the official mascot for the Odisha Men’s Hockey World Cup is.....

1) Winkey 2) Rohoey 3) Olly 4) Phoneyh 5) Wi Wi Which software launched by Indian Railways to keep track of punctuality of trains and freight and passenger earnings from anywhere in India?

1) Rwire 2) Rpole 3) eDrishti 4) epromote 5) eskill Which state launched Saura Jalnidhi scheme to encourage use of solar energy in irrigation by farmers?

1) UP 2) Maharashtra 3) Odisha 4) Tamilnadu 5) MP NITI Aayog document “Strategy for New

inclusion of fuel and electricity within the ambit of GST. All of the 250,000 gram panchayats should be digitally connected by 2019 through the Bharat Net programme. The government services should be delivered digitally to all the gram panchayats by 202223. The document also says that Bharatmala Pariyojana and roads-construction in the north-eastern region should be completed and Power for All and a pucca house for every family have to be ensured. FDI limits should be liberalised also

Senior IRS officer Pranab Kumar Das appointed as Chairman of the Central Board of Indirect Taxes and Customs (CBIC), the apex policy-making body for indirect taxes.

The Appointments Committee of the Cabinet on 17 December 2018 appointed P.K.Das replacing S.Ramesh as the head of CBIC. CBIC deals with the tasks of formulation of policy concerning levy and collection of Customs & Central Excise duties and Service Tax, prevention of smuggling and administration of matters relating to Customs, Central Excise, Service tax etc.

New CM for Rajasthan Ashok Gehlot took oath as the Rajasthan chief minister on 17 December 2018 , while state party chief Sachin Pilot became deputy chief minister in a ceremony held at Albert Hall in Jaipur.

Governor Kalyan Singh administered oath of office. Congress president Rahul Gandhi, former Prime Minister Manmohan Singh, outgoing chief minister Vasundhara Raje also attended the event.

Bhupesh Baghel

KALIA scheme for Farmers Odisha CM Naveen Patnaik announced Rs.10,800 crore scheme for farmers on 21 December 2018. It is the Krushak Assistance for Livelihoods & Income Augmentation (KALIA), which benefits both farmers and share croppers. Lord Jagannath in Odisha is also called Kalia.

The scheme has 5 components- financial

India@75” said that the Investment rate should be boosted from 29% of GDP in FY18 to ………….by FY23.

1) 42% 2) 34% 3) 46% 4) 36% 5) 50% 9. 15 women entrepreneurs were given awards at the recently concluded Women Transforming India Awards 2018 in New Delhi. Theme of the WTI Awards 2018 is……

1) Women and Entrepreneurship 2) Women and Empowerment 3) Women and Rise of them 4) Women for Entrepreneurship for all 5) Women and Care 10. NITI Aayog inked agreement with ………. to deploy artificial intelligence (AI) technologies to address challenges in agriculture and healthcare 1) Infosys 2) TCS 3) Tech Mahindra 4) Microsoft India 5) Amazon India

Bhupesh Baghel took oath of office as third Chief Minister of Chhattisgarh at Balbir Singh Juneja Indoor Stadium in Raipur.

The two senior leaders in the fray for the CM post, T S Singhdeo and Tamradwaj Sahu also inducted as cabinet ministers.

Congress President Rahul Gandhi and former Prime Minister Manmohan Singh were present among the guests attended the ceremony. New Chief Minister Bhupesh Baghel announced to waive off farm loans to the tune of Rs 6,100 crore for the benefit of more than 16 lakh farmers.

11. Service-specific exercise AVIAINDRA between Indian Air Force (IAF) and Russian Federation Aerospace Force (RFAF), held ………

1) Vishakapatnam, Andhra Pradesh 2) Pune, Maharastra 3) Kochi, Kerala 4) Jodhpur in Rajasthan 5) Agra, Uttar Pradesh 12. Union Ministry of Tourism inaugurated India’s first tribal circuit project connecting 13 tourism sites in………….. under Swadesh Darshan Scheme.

1) Chhattisgarh 2) Jharkhand 3) Arunachal Pradesh 4) Manipur 5) Mizoram

Key 1-5 7-3

2-2 8-4

3-5 9-1

4-5 10-4

5-3 11-4

6-3 12-1

17 ÷ªÙÞœÎCî¦ô¢ üŒî¦ô¢ÙÙ 1ÎÞœáì÷J help@eenadupratibha.net ú£ªd 12,2019 2018- - email: email: help@eenadupratibha.net

PRESENT TENSE The Simple Present Tense

õª óμ³ÚÛ\ Þ¥ ÑÙç˶ î¦æ¨ Ú¨ öË¶ë¯ ìª

Mode of the verb: I / We / You / They subjects verb plain form He /She / It subjects verb plain form ‘s’ ‘es’

Þ¥ ÑÙç˶ î¦æ¨ êŸô¦yêŸ ìª ô¦óŸ«L. õª êŸô¦yêŸ óμ³ÚÛ\ à¶Ja ô¦óŸ«L.

Uses of the Simple Present Tense: (a) To

describe

êμLóŸªâ˶óŸªè¯EÚ¨z

your

I have known his address!

Examples: H I have worked for this company last year.

(Wrong) H I worked for this company last year.

(Correct)

sÍõî¦åxìª

habits

(b) To talk about an action that happened in the past where the time is not mentioned.

sí£E áJTì ú£÷ªóŸ«Eo ví£þ§hNÙàŸÚÛªÙè¯, ÖÚÛ í£E áJTÙë]E êμLóŸªâ˶óŸªæ°EÚ¨ Ñí£óμ«TÙàŸ÷àŸªa.z

H I always brush my teeth before 7 am daily.

H I meet my best friend every Sunday. (b) To describe factual information - things that are true.

Examples:

H Red meat is a good source of iron.

H She has completed her homework.

sú£ê¦uEo êμLóŸªâ˶óŸªè¯EÚ¨z

H I have had three different offices at ABC.

H Walking in the mornings gives you good health.

Note: If the time is mentioned, the simple past tense is used. simple past tense

sí£E

áJTì

ú£÷ªóŸ«Eo ìª

(c) To describe things that are true for a long time.

ví£þ§hNÙ#ìåxô³ê¶ Ñí£óμ«TÙà¦L.z

H He works in this office.

(c) To talk about experiences without indicating time.

sDô¢+Ú¥õÙÞ¥ î¦ú£h÷ÙÞ¥ Ñìo Nù£óŸ«Eo êμõí£è¯EÚ¨z

sú£÷ªóŸ«Eo ví£þ§hNÙàŸÚÛªÙè¯ ÍìªòÅ¡î¦õ ÞœªJÙ# êμLóŸªâ˶óŸªæ°EÚ¨ Ñí£óμ«TÙàŸ÷àŸªa.z

H He lives in this street. (d) We can make present simple questions with do (do before I/ we/ you/ they and does before he/ she/ it). (Simple present tense interrogative sentence I / we / you / they do, he / she / it does ) H Do you like your job?

H Do they come here regularly?

H Does he go to temple on Sundays?

H Does your teacher give you excessive homework?

ìª ô¦óŸªè¯EÚ¨

õÚÛª ÷³Ùë]ª ìª Ñí£óμ«TÙà¦L.

÷³Ùë]ª

ö˺

õÚÛª

(e) We make negative sentences with don’t (I/ we/ you/ they don’t) or doesn’t (he/ she/ it doesn’t). (Simple present tense negative sentence I / we / you / they do, he / she / it does )

ìª ô¦óŸªè¯EÚ¨

êŸô¦yêŸ Ñí£óμ«TÙà¦L.

õ êŸô¦yêŸ

õ ìª

H I don’t like sweets.

H She doesn’t work hard.

H He doesn't come to office by bus.

The Present Continuous Tense

êŸô¦yêŸ êŸô¦yêŸ

ìª

Mode of the Verb: I am + verb (ing) , We / You / They are + verb (ing) , He / She / It is + verb (ing)

êŸô¦yêŸ

ìª ìª ô¦óŸ«L.

çËμæÀ ÚÛîª æ©ÎôÂæ© ví£ê¶uÚÛÙ

Examples: H I am studying for my last exam.

H She is living in the quarters at the moment. (c) The present continuous can also be used to talk about a current trend. (Present Continuous Tense

ìª ví£ú£ªhêŸ ð¼ÚÛè[õìª êμLóŸªâ˶óŸªè¯EÚ¨ Ñí£óμ«TÙàŸ÷àŸªa.z

Examples:

H Work absenteeism rates are increasing.

Navuluri Peraiah Subject Expert

Uses of the Present Continuous Tense: (a) To describe something happening at the time of speaking.

s÷ªìÙ ÷«æ°xè[ªêŸ« Ñìo ú£÷ªóŸ«EÚ¨ áô¢ªÞœªêŸªìo í£ìªõìª êμõí£è¯EÚ¨ Present Continuous Tense Ñí£óμ«TÙà¦L.z

Examples: H I am reading this email.

H Look! She is sleeping at her desk!

H They are working in the fields now.

(d) The present continuous tense can be used to talk about a future action using the verb ‘going to’. (Present Continuous Tense ‘going to’ future actions

êμõí£÷àŸªaz

Examples: H He is going to buy a new car. (Indicates future action) H I am going to meet my childhood friend next week. (Indicates future action) (e) Some verbs are not normally used in the present continuous tense or in any other continuous tense. These verbs are not actions. ( verb present continuous tense continuous tense verb )

Ú•Eo õìª öË¶ë¯ Ô ÏêŸô¢ î¦è[ÚÛ«è[ë]ª. Ð

ö˺ öËºì« õª í£ìªõìª ú£«#ÙàŸ÷±.

Examples: hate, like, love, prefer, want, wish, appear, feel, hear, see, seem, smell, sound, taste, agree, deny, disagree, mean, promise, satisfy, surprise, believe, imagine, know, mean, realise, recognise, remember, understand. (f) We can make present continuous questions with am/ is/ are (I/ we/ you/ they) + verb + ing (Subject am / is/ are interrogative sentences

Ñí£óμ«TÙ# ô¦óŸª÷àŸªa.z

ÚÛª ÷³Ùë]ª

Examples:

H We do not have to be doing the action as we are speaking.

H Are you writing anything?

H I need to go back to work. I'm writing a report on absenteeism.

(b) We use the present continuous tense when describing actions that are temporary.

ö˺ ìª

E Ñí£óμ«TÙ#

H Rithwik is making a kite at present.

H I'm doing two courses at night school this year.

Examples:

present continuous

H People are thinking more about how work will affect their families now.

Writer

ö˺

sê¦ê¦\LÚÛîμªiì í£ìªõìª tense ö˺ àμí£p÷àŸªa.z

ìª ìª

English negative sentence

ìª ô¦óŸª÷àŸªa.

Examples: H I'm not sleeping! I’m taking rest.

H She isn't sitting at her desk. She's standing by the computer.

The Present Perfect Tense Mode of Verb: The present perfect tense is made with ‘has/ have + the past participle’. (I / We / You / They subjects have + the past participle He / She / It subjects has + the past participle

õª

Þ¥ ÑÙç˶ î¦æ¨ êŸô¦yêŸ ìª ô¦óŸ«L. õª Þ¥ ÑÙç˶ î¦æ¨ êŸô¦yêŸ ìª ô¦óŸ«L.z J Negative sentence ö˺ have / has êŸô¦yêŸ not ìª Ñí£óμ«TÙà¦L. Interrogative sentenceö˺ have / has ìª subject ÚÛª ÷³Ùë]ª ÑÙà¦L. Examples: H I have worked in this office since 2005.

H She has not passed the exam yet.

H He has watched the movie several times.

H We have just completed our work.

Uses of the Present Perfect Tense: (a) To talk about an action that began in the past and continued to the present.

H I have worked for this company for the last six years.

H I have sent a lot of emails in the last few minutes.

H How long have you worked here?

Note: It is used with words like ‘since, this

week/ year/ month, over the last few weeks, for the last six months’ etc. and today. These

H I have worked for three other companies but this company is the best!

The present perfect simple is used in questions with ever. It is used with never and yet.

H Have you ever slept at work?

H No, I've never slept at work. (d) To talk about something that has happened using the adverbs ‘just, already, several times, yet, just now, recently, before, this week, this morning, this month’ etc.

Examples: H My sister has just come home.

H She has resigned to her job just now.

H I have met him recently.

H She has not passed her examination yet.

H We have watched that movie several times.

H I have seen him before somewhere.

The Present Perfect Continuous Tense Mode of the Verb: have been + verb (ing) after the subjects‚ ‘I / We / You / They and has been + verb (ing) after the subjects, He / She / It.

Use of the Present Perfect Tense: (a) To express an action that started in the past and still it has not been finished.

sÞœêŸÙö˺ vð§ô¢ÙòÅ¡îμªi ÷«æ°xè[ªÚÛªû¶ ú£÷ªóŸ«EÚ¨ í£²Jh Ú¥ÚÛªÙè¯ ÏÙÚ¥ áô¢ªÞœªêŸªìo í£EE àμí£pæ°EÚ¨ î¦è•àŸªa.z

Examples: H She has been waiting for me for two hours.

H They have been living in this town for ten years.

H She has been writing letters since morning.

H It has been raining since yesterday.

Note: hate, hear, know, forget, remember, verb present perunderstand, want fect continuous tense Present perfect tense

îμ³ë]öËμjì

õìª ö˺ Ñí£óμ«TÙàŸô¦ë]ª. ö˺ Ñí£óμ«TÙà¦L.

Examples:

H I have worked here since 2000.

H I have been knowing his address for a long time. (Wrong)

H Is she working long hours at the moment?

H I have interviewed four applicants this morning.

H Is your boss making you work long hours during the New Year Sales?

H I have known his address for a long time.

(Correct)

H I have worked with her for two years.

(g) We make negative sentences with (I/ we/ you/ they) am/ is/ are + not + verb + ing. (Is / am/ are not

week, last year, yesterday, five minutes ago, in 1998 etc. These words describe a finished time.

We use the past simple with these words.

words describe an unfinished time.

H Are they preparing for examinations?

õ êŸô¦yêŸ

ìª Ñí£óμ«TÙ#

Note: It is never used with time words like last

Note: Present Perfect Continuous Tense ö˺ ú£÷ªóŸ«Eo ú£«#ÙàŸæ°EÚ¨ since ÷ªJóŸ³ for ìª Ñí£óμ«Tþ§hô¢ª. Exact time or point of time ìª êμõí£è¯EÚ¨ since ìª, period of time or amount of time ìª ú£«#ÙàŸæ°EÚ¨ for ìª Ñí£óμ«TÙà¦L.

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1) MýS£éç³NÆý‡×æ ç³È„ýSË$ 2) Üí †¦ ³ç È„ýS 3) 糧ýl çÜ…çÜÆý‡Y ç³È„ýS 4) ÐéMýSÅç³NÆý‡×æ ç³È„ýS {糄óSç³MýS ç³È„ýSËMýS$ çÜ…º…«¨…_ MìS…¨ ÐésìæÌZ çÜÇM>°¨?

1) Ð]lÅMìS¢ A…™èlÆý‡Y™èl ¿êÐé˯]l$, BÌZ^èl¯]l˯]l$ ÐðlÍMìS ¡Ä¶æ$Ð]l^èl$a 2) M>Ëç³ÇÑ$† Ìôæ§ýl$ M>± M>Ìê°² ç³ÇVýS×æÌZMìS ¡çÜ$MýS$…sê…

3) E©ªç³¯]l AçܵçÙt…V>, AÆý‡¦Æý‡íßæ™èl…V> E…r$…¨ 4) ^ól™èl¯]l A…Ô>˯]l$ Ð]l*{™èlÐól$ ™ðlË$çÜ$MøVýSË… Ð]lÊÇ¢Ð]l$™èlÓ A…^èl¯é ç³È„ýSÌZÏ Ñ$MìSPÍ ™èlÆý‡^èl$V> Eç³Äñæ*W…^ól¨?

1) °Æ>®Æý‡×æ Ð]l*ç³° 2) Ð]lÊÇ¢Ð]l$™èlÓ ÔZ«¨MýS 3) {ç³Ô>²Ð]lã 4) ÔZ«§ýl¯é çÜ*_MýS ѧéÅÆý‡$¦Ë$ Ý뫧éÆý‡×æ…V> ç³È„ýSMýS$ Ð]l¬…§ýl$ gêqç³MýS… E…^èl$MøÐ]lyýl…ÌZ çÜÐ]l$çÜÅË VýS$Ç…_ íœÆ>ŧýl$ ^ólçÜ$¢…sêÆý‡$. ©°MìS M>Æý‡×æ…?

1) çÜ…çœ$Æý‡Û×æ 2) ÐéÅMýS$Ë™èl 3) HM>{VýS™èl ÌZí³…^èlyýl…

4) BçÜMìS¢ ÌZí³…^èlyýl…

MìS…¨ ÐésìæÌZ Ð]lÊÇ¢Ð]l$™èlÓ Ë„ýS×æ… M>°¨ H¨?

1) Ð]lÊÇ¢Ð]l$™éÓ°² MýSÍW E…yýlr…ÌZ OÐðlĶæ$MìS¢MýS ¿ôæ§éË$ E¯é²Æ‡2) Ð]lÊÇ¢Ð]l$™èlÓ… iÐ]l#Ë…§ýlÇMìS ^ðl…¨…¨

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3) Ð]lÊÇ¢Ð]l$™èlÓ… Ð]lÅMìS¢ Ô>ÈÆý‡MýS, Ð]l*¯]líÜMýS, E§ólÓVýS, Ýë…íœ$MýS, O¯ðl†MýS Ððl¬§ýlOÌñæ¯]l A°² A…Ô>ËMýS$ ^ðl…¨…¨ 4) Ð]lÊÇ¢Ð]l$™èlÓ… VýSÐ]l$Å °Æó‡ªÔ¶æMýSOÐðl$…¨ H Æý‡MýSOÐðl$¯]l VýS–çßæ Ðé™éÐ]lÆý‡×æ…ÌZ ò³ÇW¯]l í³ËÏË$ ¿¶æ{§ýl™é ¿êÐ]l¯]l, ÝëÓÐ]lË…º¯]l {ç³Ð]lÆý‡¢¯]l Ìê…sìæ Ë„ýS×êË$ MýSÍW E…sêÆý‡$?

1) ÌŸ…W E…yól ™èlÍϧýl…{yýl$Ë$ 2) ™éÇPMýS & Ô>ï܈Ķæ$ §ýl–MýSµ£ýl…

3) A† V>Æ>¿¶æ… 4) †Æý‡çÜPÆý‡×æ çÜ$Æó‡ÔŒæ ™èlÆý‡VýS† VýS¨ÌZ¯ól M>MýS$…yé ç³ÇçÜÆ>ÌZÏ MýS*yé ÝùÐ]l$Ç™èl¯]l…V>, Ð]l$…§ýlº$¨® E¯]l²ÐéyìlV> {ç³Ð]lÇ¢çÜ$¢¯é²yýl$. D Ë„ýS×ê°MìS M>Æý‡×æ…?

1) O£ðlÆ>MìSÞ¯Œæ ¡{Ð]lÐ]l$Ð]lyýl…

2) O£ðlÆ>MìSÞ¯Œæ ÌZí³…^èlyýl…

3) G{yìl¯]lͯŒæ A«¨MýSÐ]l$Ð]lyýl…

4) G{yìl¯]lͯŒæ ÌZí³…^èlyýl… {MðSsìæ°fÐŒl$MýS$ M>Æý‡×æ…?

1) Ķæ$Ð]lÓ¯]l §ýlÔ¶æÌZ O£ðlÆ>MìSÞ¯Œæ ÌZí³…^èlyýl…

2) Ķæ$Ð]lÓ¯]l §ýlÔ¶æÌZ O£ðlÆ>MìSÞ¯Œæ A«¨MýSÐ]l$Ð]lyýl…

3) Ð]lÄñæ*f¯]l §ýlÔ¶æÌZ O£ðlÆ>MìSÞ¯Œæ ÌZí³…^èlyýl…

4) Ð]lÄñæ*f¯]l §ýlÔ¶æÌZ O£ðlÆ>MìSÞ¯Œæ A«¨MýSÐ]l$Ð]lyýl… °º…«§ýl¯]l çÜíßæ™èl, °º…«§ýl¯]l Æý‡íßæ™èl {糆 ^èlÆý‡ÅË$ §ól° B«©¯]l…ÌZ fÆý‡$VýS$™éƇ¬?

1) MóS…{©Ä¶æ$ ¯éyîl Ð]lÅÐ]lçܦ 2) {ç³™èlÅ„ýS ¯éyîl Ð]lÅÐ]lçܦ 3) çÜÓĶæ$… ^ø¨™èl ¯éyîl Ð]lÅÐ]lçܦ 4) ç³Ç«©Ä¶æ$ ¯éyîl Ð]lÅÐ]lçܦ MìS…¨ ÐésìæÌZ Ð]lÊÇ¢Ð]l$™éÓ°² {糿êÑ™èl… ^ólõÜ Ýë…íœ$MýS, Ýë…çÜP–†MýS M>Æý‡M>ËMýS$ çÜ…º…«¨…^èl°¨ H¨?

1) ÝëÐ]l*hMýS °Ä¶æ$Ð]l$ °º…«§ýl¯]lË$ 2) Ð]lÅMìS¢ ò³ÇVóS çÜÐ]l*f…ÌZ Eç³Äñæ*W…^ól ¿êçÙ 3) ™èlÍϧýl…{yýl$Ë, E´ë«§éÅĶæ¬Ë OÐðlQÆý‡$Ë$ 4) ¯éyîl Ð]lÅÐ]lçܦ ç³°¡Æý‡$ MìS…¨ ÐésìæÌZ Ð]lÊÇ¢Ð]l$™èlÓ Ë„ýS×æ… M>°¨ H¨?

1) íܦÆý‡…V> E…r$…¨ 2) A¨Ó¡Ä¶æ$OÐðl$…¨, °Æý‡…™èlÆý‡OÐðl$…¨ 3) gêq¯é™èlÃMýS, ¿êÐ]lÐólÔ¶æ, Ð]l*¯]líÜMýS ^èl˯é™èlÃMýS A…Ô>˯]l$ MýSÍW E…r$…¨ 4) ´÷…¨OMðS…¨, °Æý‡…™èlÆý‡OÐðl$…¨ Ð]l*¯]lÐ]l Ð]lÊÇ¢Ð]l$™éÓ°MìS çÜ…º…«¨…_ MìS…¨ ÐésìæÌZ çÜOÆð‡…¨?

1) A¯]l$Ð]l…ÕMýS™èl MýS…sôæ ç³ÇçÜÆ>Ë {糿êÐ]l…

A«¨MýS… 2) ç³ÇçÜÆ>Ë MýS…sôæ A¯]l$Ð]l…ÕMýS™èl {糿êÐ]l…

A«¨MýS… 3) A¯]l$Ð]l…ÕMýS™èl, ç³ÇçÜÆ>Ë {糿êÐ]l… çÜÐ]l*¯]l…

4) A¯]l$Ð]l…ÕMýS™èl, ç³ÇçÜÆ>Ë™ø çÜ…º…«§ýl… ÌôæMýS$…yé Ķæ*§ýl–_eMýS…V> Ð]lÅMýS¢Ð]l$Ð]l#™èl$…¨ MýS$Ð]l*ÆŠæ A¯ól E´ë«§éÅĶæ¬yýl$ AËçÜr M>Æý‡×æ…V> Ñ{Ô>…† ¡çÜ$MøÐé˯]l$MýS$…r$¯é²yýl$. M>± 10Ð]l ™èlÆý‡VýS† ç³È„ýSË$ §ýlVýSYÆý‡ç³yýlr… Ð]lËÏ ´ëuý‡Ô>ËMýS$ àfÆý‡$ M>Ðé˯]l$MýS$…r$¯é²yýl$. A™èlyýl$ G§ýl$ÆöP…r$¯]l² çÜÐ]l$çÜ-Å?

1) Eç³VýSÐ]l$ & Eç³VýSÐ]l$ 2) Eç³VýSÐ]l$ & ç³ÇàÆý‡ 3) ³ç ÇàÆý‡ & ³ç ÇàÆý‡ 4) ¨Ó Eç³VýSÐ]l$ & ³ç ÇàÆý‡ {¸ëƇ¬yŠæ õ³ÆöP¯]l² H Ð]l$¯ø OÌñæ…WMýS ÑM>çÜ §ýlÔ¶æÌZ ™èl§é¡ÃMýSÆý‡×æ…, A…™èlÈÏMýSÆý‡×æ… A¯ól Ë„ýS×êË$ {´ëÆý‡…¿¶æÐ]l$Ð]l#™éƇ¬?

1) Ð]l˜üMýS §ýlÔ¶æ 2) Bçܯ]l §ýlÔ¶æ 3) ÕÔ¶æ² §ýlÔ¶æ 4) VýS$ç³¢ §ýlÔ¶æ Ð]lÅMìS¢ÌZ çÜ…çœ$Æý‡Û×æ Gç³#µyýl$ HÆý‡µyýl$™èl$…¨?

1) E§ólÓV>ËMýS$ °{íÙPĶæ*™èlÃMýS…V> E¯]l²ç³#µyýl$ 2) ™èl¯]l Ë„>ÅË™ø Æ>iç³yýlÌôæMýS ´ùƇ¬¯]lç³#µyýl$

32.

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38.

3) MýS–™éÅ°² ^ólĶæ$yé°MìS çÜÇ´ùÄôæ$ ÝëÐ]l$Æý‡¦Å… Ìôæ¯]lç³#µyýl$ 4) iÑ™èl…ÌZ A¿¶æ{§ýl™èl¯]l$ ¿êÑ…_¯]lç³#µyýl$ Ð]l*¯]líÜMýS A¯éÆøVýSÅ… E¯]l² ѧéÅǦ Ë„ýS×ê°MìS ^ðl…§ýl°¨?

1) BÔ>iÐ]l¯é°² MýSÍW E…yýlr…

2) Ð]lÊÇ¢Ð]l$™èlÓ çÜ…«§é¯]l ÌZç³…

3) ÝëÐ]l*hMýS Aç³Çç³MýSÓ™èl 4) ¿êÐø{§ólMýS AçÜÐ]l$™èl$ËÅ™èl ÐéÅMýS$Ë™èl, MýS$…uý‡¯éË ¯]l$…_ Aà°² Æý‡„ìS…^èl$MøÐ]lyé°MìS Eç³Äñæ*W…^ól Ð]lNÅà°² HÐ]l$…sêÆý‡$?

1) A¯]l$VýS$×æÅ™èl 2) Ð]l*¯]líÜMýS BÆøVýSÅ…

3) õßæ™èl$MîSMýSÆý‡×æ 4) Æý‡„ýSMýS™èl…{™èl… çÜÆý‡$ª»êr$ ÝëÐ]l*¯]lÅ çÜ…¿êÐ]lÅ™èl {MýSÐ]l$… {ç³M>Æý‡… {糆 100 Ð]l$…¨ÌZ: 1) 33.3% Ý뫧éÆý‡×æ çÜÆý‡$ª»êr$, 33.3% A«¨MýS çÜÆý‡$ª»êr$, 33.3% ™èlMýS$PÐ]l çÜÆý‡$ª»êr$ MýSÍW E…sêÆý‡$ 2) 60% Ý뫧éÆý‡×æ çÜÆý‡$ª»êr$, 20% A«¨MýS çÜÆý‡$ª»êr$, 20% ™èlMýS$PÐ]l çÜÆý‡$ª»êr$ MýSÍW E…sêÆý‡$ 3) 68% Ý뫧éÆý‡×æ çÜÆý‡$ª»êr$, 16% A«¨MýS çÜÆý‡$ª»êr$, 16% ™èlMýS$PÐ]l çÜÆý‡$ª»êr$ MýSÍW E…sêÆý‡$ 4) 50% Ý뫧éÆý‡×æ çÜÆý‡$ª»êr$, 25% A«¨MýS çÜÆý‡$ª»êr$, 25% ™èlMýS$PÐ]l çÜÆý‡$ª»êr$ MýSÍW E…sêÆý‡$ JMýS çÜ…çœ$r¯]lMýS$, JMýS Ð]l*Æý‡$µ¯]lMýS$, JMýS çÜÐéË$MýS$ Ð]lÅMìS¢ Ô>ÈÆý‡MýS…V>, Ð]l*¯]líÜMýS…V> çܵ…¨…^èlyýl…?

1) çÜ…çœ$Æý‡Û×æ 2) MýS$…uý‡¯]l…

3) ÐéÅMýS$Ë™èl 4) J†¢yìl Æý‡„ýSMýS™èl…{™éËMýS$ çÜ…º…«¨…_ çÜOÆð‡…¨?

G) G‹ÜI E§øÅVýS… Ý뫨…^èlÌôæMýS´ùƇ¬¯]l ¯]lÆó‡ÔŒæ Èf°…VŠæ° »Z«¨çÜ*¢ A¯ólMýS Ð]l$…¨° G‹ÜIË$V> ¡Ça¨§ýlªyýl… ¼) Æð‡Ððl¯]l*ÅÌZ E§øÅVýS… ^ólçÜ$¢¯]l² }°Ðé‹Ü ç³°¿êÆý‡… ™èlr$tMøÌôæMýS _¯]l² í³ËÏÐéyìlÌê HyýlÐ]lyýl… Üí ) ѧéÅÆý‡$¦Ë…§ýlÇ Ð]l¬…§ýl$ {糫§é¯ø´ëĶæ¬yìl™ø °…¨…^èlºyìl¯]l MýS$Ð]l*ÆŠæ B »ê«§éMýSÆý‡ ÑçÙĶæ*°² Ð]l$Ç_´ùÐ]lyýl…

1) {糄óSç³×æ… & ÑÝë¦ç³¯]l… & ³ç ÇàÆý‡…

2) ÑÝë¦ç³¯]l… & {糄óSç³×æ… & §ýlÐ]l$¯]l…

3) ç³ÇàÆý‡… & {糆VýSÐ]l$¯]l… & §ýlÐ]l$¯]l…

4) {糄óSç³×æ… & {糆VýSÐ]l$¯]l… & §ýlÐ]l$¯]l…

E´ë«§éÅĶæ¬yýl$ §ýl…yìl…_¯]l ™èlÆ>Ó™èl ѧéÅǦ° í³Í_ ±Ð]l# »ê«§ýlç³yýl$™èl$¯é²Ðé A…sôæ ÌZç³Ë »ê«§lý V> E¯]l² Oò³MìS Ìôæ§ýl$ A° ™ðlËç³yýl… H Æý‡„ýSMýS ™èl…{™èl…?

1) {糄óSç³×æ…

2) §ýlÐ]l$¯]l…

3) Eç³çÜ…çßæÆý‡×æ 4) {糆^èlÆ>Å °ÇÆ E´ë«§éÅĶæ$ º¨ÎÌZ ´ëÌŸY¯]l² Ððl…MýSr¯éÆ>Ķæ$×æ C…sìæMìS §ýl*Æý‡OÐðl$¯é CçÙtOÐðl$¯]l B…VýSÏ Ð]l*«§ýlÅÐ]l$ ´ëuý‡Ô>ËMýS$ ÐðlâêÏÌê Ìôæ§é C…sìæMìS §ýlVýSYÆý‡ E¯]l² CçÙt… Ìôæ° ™ðlË$VýS$ Ð]l*«§ýlÅÐ]l$ ´ëuý‡Ô>ËMýS$ ÐðlâêÏÌê °Æý‡~Ƈ¬…^èl$MøÌôæ° ç³Çíܦ†. D çÜ…çœ$Æý‡Û×æ?

1) Eç³VýSÐ]l$&Eç³VýSÐ]l$ çÜ…çœ$Æý‡Û×æ 2) ç³ÇàÆý‡ & ç³ÇàÆý‡ çÜ…çœ$Æý‡Û×æ 3) Eç³VýSÐ]l$ & ç³ÇàÆý‡ çÜ…çœ$Æý‡Û×æ 4) ¨Ó Eç³VýSÐ]l$ & ç³ÇàÆý‡ çÜ…çœ$Æý‡×Û æ

çÜÐ]l*«§é¯éË$ 1) 4 6) 2 11) 2 16) 2 21) 2 26) 4 31) 2 36) 3

2) 4 7) 4 12) 2 17) 4 22) 2 27) 1 32) 1 37) 4

3) 1 8) 4 13) 4 18) 4 23) 2 28) 1 33) 4 38) 4

4) 2 9) 4 14) 3 19) 3 24) 1 29) 2 34) 3

5) 4 10) 4 15) 1 20) 2 25) 3 30) 4 35) 4

ѧýlÅ

A¯]l…™èlç³#Æý‡… l Ð]l$…VýSâ¶æÐéÆý‡… l f¯]lÐ]lÇ l 1 l 2019

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16

ÑÑ«§ýl ç³ÇÐ]l*×êÌZÏ Æ>íܯ]l ½iĶæ$ çÜÐ]l*ÝëÌôæ ºçßæ$糧ýl$Ë$ ºçßæ$糨 Ô¶æ*¯éÅËMýS$ gêÅÑ$¡Ä¶æ$ AÆ>¦Ë$

Ķæ*Æý‡ÏVýSyýlz Ð]l¯]l…Æ>k çÜ*PÌŒæ AíÜòÜt…sŒæ, {糿¶æ$™èlÓ E¯]l²™èl ´ëuý‡Ô>Ë ºçßæ$糧ýl$Ë$

❖ ❖ ❖

❖

❖

❖

❖

❖

y −1

^èlÆý‡Æ>Õ x ÌZ E¯]l² ºçßæ$糨 p(x)ÌZ x VýSÇçÙt çœ*™é…M>°² ºçßæ$糨 ç³ÇÐ]l*×æ… A…sêÆý‡$. ç³ÇÐ]l*×æ… '0' V> E¯]l² ºçßæ$糨° íÜÆý‡¦ ºçßæ$糨 A…sêÆý‡$. E§é: −5, 73

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ç³ÇÐ]l*×æ… '1' E¯]l² ºçßæ$糨° Æó‡TĶæ$ ºçßæ$糨 A…sêÆý‡$. E§é: 3x + 5, y − 1 ç³ÇÐ]l*×æ… '2' V> E¯]l² ºçßæ$糨° Ð]lÆý‡Y ºçßæ$糨 A…sêÆý‡$. E§é: ax + bx + c, a ≠ 0, x2 – 5x + 7 ç³ÇÐ]l*×æ… 3V> E¯]l² ºçßæ$糨° çœ$¯]l ºçßæ$糨 A…sêÆý‡$.

E§é: ax + bx + cx + d, a ≠ 0, 3

❖

❖

❖

2

5x3 − 4x2 + 7x + 3 ºçßæ$糨 p(x)ÌZ x º§ýl$Ë$ k ¯]l$ Æ>õÜ¢ Ð]l^óla ÑË$Ð]l p(k)¯]l$ ºçßæ$糨 ÑË$Ð]l A…sêÆý‡$. p(x) = x2 + 4x – 5 ºçßæ$糨 ÑË$Ð]l x = 2 Ð]l§ýlª p(2) = 22 + 4 × 2 – 5 = 7 p(k)=0 AƇ¬™ól k¯]l$ p(x) ºçßæ$糨 Ô¶æ*¯]lÅ… A…sêÆý‡$. p(x) = x2 – 5x + 6 AƇ¬™ól p(2) = 22–5×2 + 6 = 0 A…§ýl$Ð]lËÏ C_a¯]l p (x) ºçßæ$糨 Ô¶æ*¯]lÅ… '2' Æó‡TĶæ$ ºçßæ$糨 ax + b MýS$ JMóS JMýS Ô¶æ*¯]lÅ… E…r$…¨. Ð]lÆý‡Y ºçßæ$糨 ax2 + bx + cMýS$ VýSÇçÙt…V> Æð‡…yýl$

2

Ô¶æ*¯éÅË Ëº®…

f(x) = 3–2x–x2

ºçßæ$糨 Æó‡Rê _{™é°² XíÜ, Ô¶æ*¯éÅ˯]l$ MýS¯]l$MøP…yìl. çœÍ™é˯]l$ çÜÐ]l$Ǧ…^èl…yìl. y=3–2x–x2 A¯ól¨ JMýS Ð]lÆý‡Y ºçßæ$糨 A¯]l$Mø…yìl. ©°MìS VýSÇçÙt…V> Æð‡…yýl$ Ô¶æ*¯éÅË$…sêƇ¬. ÑÑ«§lý x ÑË$Ð]lËMýS$ y ÑË$Ð]lË$ MìS…¨ Ñ«§ýl…V> E…sêƇ¬. {V>‹œÌZ (–4, –5), (–3, 0), (–2, 3), (–1, 4), (0, 3), (1, 0), (2, –5), (3, –12), (4, –21) ¼…§ýl$Ð]l#˯]l$ VýS$Ç¢…_, Òsìæ° çÜÆý‡â¶æ Ð]l{MýS…™ø MýSÍí³™ól y=3–2x–x2 ºçßæ$糨 Æó‡Rê_{™èl… HÆý‡µyýl$™èl$…¨. x

-4

-3

-2

-1

■

■

1.

f.

2.

f.

3.

f.

4.

f.

MýS¯]l$MøP…yìl

p(a) = a2 – 2a + 1 p(1)=12 – 2 × 1 + 1 = 0 p(–1) = (–1)2 –2 × (–1) + 1 = 4 ∴ p(1) + p (–1) = 0 + 4 = 4 3x −1 p(x) = 4x2+ ¼, –1Ë$ Ô¶æ*¯éÅË$ AÐ]l#™éÄñæ*, M>§ø p(x) = 4x2 + 3x –1

(x, y)

0

1

2

3

K≠0 ⇒ K{x2 –14x+41}, K≠0

4

4 −3 + 4 1 −( −1) = − x VSý$×æMSý… = −1 + = = = 2 3 3 3 3 x VSý$×æMSý…

{V>‹œ ¯]l$…_ y=3–2x–x2 Æó‡Rê_{™èl… ç³Æ>Ð]lËĶæ$…

BM>Æý‡…ÌZ E…r$…¨. X-A„>°² (1, 0), (&3, 0) ¼…§ýl$Ð]l#Ë Ð]l§ýlª Q…yìlçÜ$¢…¨. Òsìæ X- °Æý‡*ç³M>Ë$ ÑË$Ð]l 1,&3Ë$ Ð]lÆý‡Yºçßæ$糨 f(x)= 3–2x–x2 Ô¶æ*¯éÅË$ AÐ]l#™éƇ¬. çÜÇ^èl*yýlr…: f(x) = 3–2x–x2 f(1) = 3 – 2 (1)–12 = 0

2

VýSÇçÙt…V> Ð]lÊyýl$ Ô¶æ*¯éÅË$…sêƇ¬. ºçßæ$糨 Ô¶æ*¯éÅË MøçÜ… p(x) = 0 A¯]l$Mø…yìl.

x3– 4x = 0 ⇒ x(x2– 4) = 0 ⇒ x(x–2)(x+2) = 0 x = 0, x – 2 = 0, x + 2 = 0, x=0, x = 2, x = – 2 ∴ x3–4x ºçßæ$糨 Ô¶æ*¯éÅË$ 0, –2, 2

α, βË$ Ô¶æ*¯éÅË$V> VýSË Ð]lÆý‡Y ºçßæ$糨 K {x2 – (α+β) x +αβ}, K ≠ 0 α, β, γË$ Ô¶æ*¯éÅË$V> VýSË œ ç $¯]l ºçßæ$糨 K {x3 – (α+β+γ)x2 +(αβ+βγ+γα) x– α β γ} K≠0 7+2√2, 7–2√2 Ô¶æ*¯éÅË$V> VýSË Ð]lÆý‡Y ºçßæ$糨°

Ô¶æ*¯éÅË Ððl¬™èl¢…

1 3 1 1  1 p   =4   +3   − 1 = + − 1 = 0 4 4  4  4  4

p(–1) = 4(–1)2 +3 (–1) –1 = 4–3–1= 0 1 P   = 0 , p(–1) = 0 M>ºsìæt  4 ¼, –1Ë$ p(x) MýS$ Ô¶æ*¯éÅË$ x3 – 4x ºçßæ$糨 Ô¶æ*¯éÅ˯]l$ MýS¯]l$MøP…yìl. p(x) = x3– 4x A¯ól¨ çœ$¯]l ºçßæ$糨. ©°MìS

& íܦƇý ³ç §ýl…/ x3 VýS$×æMýS…

3x2−x−4 = (3x − 4)(x+1) = 0 3x − 4 = 0 Ìôæ§é x + 1= 0 4 4 2 1, − x= Ìô æ §é Ô¶ æ *¯éÅË$ x = −1 ∴3x −x−4 3 3

f(–3) = 3–2(–3)– (–3)2 = 0 f(1) = 0, f(–3)=0. M>ºsìæt 1, &3Ë$ f(x) = 3 – 2x–x2 Ð]lÆý‡Yºçßæ$糨 Ô¶æ*¯éÅË$.

ºçßæ$糨MìS çÜÇ^èl*yýl…yìl.

Ô¶æ*¯éÅË Ëº®…

3.

 4  −4 = (−1)   = = 3 3  

JMýS Ð]lÆý‡Y ºçßæ$糨 Ô¶æ*¯éÅË Ððl¬™èl¢…, ˺®… Ð]lÆý‡$çÜV> 1 1 − , AƇ¬™ól B Ð]lÆý‡Y ºçßæ$糨° MýS¯]l$Vö¯]l…yìl.

4 4 α = −¼, β = ¼ α+β=−¼+¼=0 −1 αβ = (− ¼)(¼) = 16

α, βË$ Ô¶æ*¯éÅË$V> E¯]l² k{x2 − (α + β)x + αβ)

ax+b, a≠0 A¯ól

Ð]lÆý‡Y ºçßæ$糨

Æó‡TĶæ$ ºçßæ$糨 Ô¶æ*¯]lÅ −b ÑË$Ð]l α A¯]l$Mö…sôæ α = a

1 1   ⇒  x 2 − 0 x −  = k  x2 −  16  16   

ºçßæ$糨 Ô¶æ*¯éÅË$ α, β AƇ¬™ól Ô¶æ*¯éÅË Ððl¬™èl…¢ = −b α +β= = & x VýS$×æMýS…/ x2 VýS$×æMýS…

16 x 2 − 1 k 2 = k  = {16 x − 1}  16  16

ii. ax2+bx+c, a≠0 Ð]lÆý‡Y

a

Ô¶æ*¯éÅË Ëº®…

= αβ =

c = íܦÆý‡ç³§ýl…/x2 VýS$×æMýS… a

iii. ax3+bx2+cx+d, a≠0 çœ$¯]l ºçßæ$糨 Ô¶æ*¯éÅË$ α, β, γ AƇ¬™ól Ô¶æ*¯éÅË Ððl¬™èl¢… −b = α+β+ γ= = &x2 VýS$×æMýS…/ x3 VýS$×æMýS… a

Æð‡…yólíÜ Ô¶æ*¯éÅË Ë»ê®Ë Ððl¬™èl¢… = c αβ + βγ + γα = = x VýS$×æMýS…/ x3 VýS$×æMýS… a

Üí¦Æ‡ý ³ç §lý…

2 x VýS$×æMýS…

f. Ð]lÆý‡Y ºçßæ$糨 Ô¶æ*¯éÅË$ Ð]lÆý‡$çÜV> α, β A¯]l$MýS$…sôæ

ºçßæ$糨 VýS$×æM>ËMýS$, Ô¶æ*¯éÅËMýS$ Ð]l$«§ýlÅ çÜ…º…«§ýl… i.

−1 5 1 −1 − 5 − 2 + 8 =0 − − +2= 4 4 2 4 p(1) =2(1)3 – 5(1)2 +1+2= 0 p(2) =2(2)3 – 5(2)2 + 2+2 =0  −1  p   = 0 , p(1) =0, p(2)=0  2 −1 M>ºsìæt p(x) MýS$ 2 ,1, 2 Ë$ Ô¶æ*¯éÅË$. −1 α= , β=1, γ=2 A¯]l$Mö…sôæ 2 −1 5 −b α +β+ γ = + 1+ 2 = = 2 2 a αβ+βγ+γα=  −1   −1  1 c =   (1) + (1)(2 ) + (2 )  = =  2   2  2 a  −1 

−2

−d

αβγ =  2  (1)(2 ) = −1= 2 = a  

ºçßæ$糧ýl$Ë ¿êVýSàÆý‡ °Ä¶æ$Ð]l$… p(x), g(x) A¯ólÑ Æð‡…yýl$ ºçßæ$糧ýl$Ë$. g(x)≠0 AƇ¬¯]lç³#µyýl$ p(x)=g(x)×q(x)+r(x) AƇ¬¯]lr$Ï Ð]l$Ç Æð‡…yýl$ ºçßæ$糧ýl$Ë$ q (x), r(x) ´÷…§ö^èl$a.

C…§ýl$ÌZ r(x)=0 Ìôæ§é r(x) ç³ÇÐ]l*×æ… <g(x) ç³ÇÐ]l*×æ….

D çœÍ™é°² ºçßæ$糧ýl$Ë ¿êVýSàÆý‡ °Ä¶æ$Ð]l$… A…sêÆý‡$.

0 3 4 3 0 -5 -12 -21 1. x4–6x3–26x2+138x–35 A¯ól ºçßæ$糨MìS Æð‡…yýl$ Ô¶æ*¯éÅË$ 2±√3 AƇ¬™ól Ñ$Wͯ]l Æð‡…yýl$ Ô¶æ*¯éÅ˯]l$ (-4, -5) (-3,0) (-2, 3) (-1, 4) (0, 3) (1, 0) (2, -5) (3, -12) (4,-21) MýS¯]l$Vö¯]l…yìl.

2. 3x2 − x − 4 A¯ól Ð]lÆý‡Y ºçßæ$糨 Ô¶æ*¯éÅ˯]l$ MýS¯]l$Vö°, f. 2+√3, 2–√3Ë$ C_a¯]l ºçßæ$糨MìS Æð‡…yýl$ Ô¶æ*¯éÅË$, M>ºsìæt Ô¶æ*¯éÅËMýS$, ºçßæ$糨 VýS$×æM>ËMýS$ çÜ…º…«§é°² çÜÇ {x–(2+√3)}{x-(2–√3)} ^èl*yýl…yìl. = {(x–2) –√3} {(x–2)+√3} 3x2 − x − 4 ⇒ 3x2 − 4x + 3x −4 = (x–2)2–(√3)2 = x2–4x+1 JMýS M>Æý‡×ê…MýS….

C_a¯]l ºçßæ$糨° x2–4x+1™ø ¿êWõÜ¢ = x(3x − 4) + 1(3x − 4) = (3x−4)(x+1) 3x2 − x − 4 Ð]lÆý‡Y ºçßæ$糨 Ô¶æ*¯éÅË$ MýS¯]l$Vö¯éË…sôæ x 2 − 4 x + 1) x 4 − 6 x3 − 26 x 2 + 138 x − 35( 2 3x −x−4 = 0 M>ÐéÍ.

2

p(x) = 2x5– 5x4 + 3x2 + 4x –7 AƇ¬™ól i) p(x) ç³ÇÐ]l*×æ…, ii) x4 VýS$×æMýS…, iii) íܦÆý‡ 糧é˯]l$ MýS¯]l$MøP…yìl p(x) = 2x5 – 5x4 + 3x2 + 4x–7 i) p(x) ç³ÇÐ]l*×æ… = 5 ii) x4 VýS$×æMýS… = –5 iii) íܦÆý‡ç³§ýl… = –7 p(a) = a2– 2a +1AƇ¬™ól p(1)+ p(–1)

−d = a

MýS¯]l$Vö¯]l…yìl. f. α, βË$ Ô¶æ*¯éÅË$V> E¯]l² Ð]lÆý‡Y ºçßæ$糨 K{x2–(α+β)x+αβ}, K≠0 7+2√2, 7–2√2 Ô¶æ*¯éÅË$V> VýSË Ð]lÆý‡Y ºçßæ$糨 K{x2–(7+2√2+7–2√2)x+(7+2√2)(7−2√2)},

Ð]l*¨Ç {ç³Ô¶æ²Ë$ 1.

αβγ =

y=3-2x -x2 -5

Ô¶æ*¯éÅË$ E…sêƇ¬. çœ$¯]l ºçßæ$糨 ax + bx + cx + dMýS$ VýSÇçÙt…V> Ð]lÊyýl$ Ô¶æ*¯éÅË$ E…sêƇ¬.

3

Ð]l*Å£ýlÐðl$sìæMŠæÞ

¼…§ýl$Ð]l#Ë Ð]l§ýlª Q…yìlçÜ$¢…¨. y = ax + bx + cx+d, a≠0 çœ$¯]l ºçßæ$糨 Æó‡Rê_{™èl… xA„ýS…¯]l$ VýSÇçÙt…V> Ð]lÊyýl$ ¼…§ýl$Ð]l#Ë Ð]l§ýlª Q…yìlçÜ$¢…¨.

çÜÐ]l$çÜÅË$

2

❖

y=ax+b, a≠0 Æó‡TĶæ$ ºçßæ$糨 Æó‡Rê_{™èl… JMýS çÜÆý‡â¶æÆó‡Q. C¨ x-A„ýS…¯]l$ JMóS JMýS ¼…§ýl$Ð]l# Ð]l§ýlª Q…yìlçÜ$¢…¨. y = ax2 + bx + c, a≠0 Ð]lÆý‡Y ºçßæ$糨 Æó‡Rê_{™èl… JMýS ç³Æ>Ð]lËĶæ$…. C¨ x-A„ýS…¯]l$ VýSÇçÙt…V> Æð‡…yýl$ 3

2

=

AÐ]l#™éƇ¬.

^èlÆý‡Æ>Ô¶æ$˯]l$, Mö°² íܦÆý‡Æ>Ô¶æ$Ë™ø VýS$×ìæ…^èlV> Ð]l^óla VýS$×æM>˯]l$ Æý‡$×ôæ™èlÆý‡ «§ýl¯]lç³NÆý‡~ çÜ…QÅË çœ*™éËMýS$ òßæ_a…_ ÑÑ«§ýl ç³ÇÐ]l*×êÌZÏ Æ>íܯ]l ½iĶæ$ çÜÐ]l*ÝëÌôæ ºçßæ$糧ýl$Ë$.

–5, 3x+7, x2−5x+7 Ððl¬§ýlOÌñæ¯]lÑ ºçßæ$糧ýl$Ë$.

1 1 , , 3 x3 Ððl¬§ýlOÌñæ¯]lÑ ºçßæ$糧ýl$Ë$ M>Ð]l#.

2 x

3

 −1   −1   −1   −1  p   = 2   − 5  +   + 2  2   2   2  2

p(x) A¯ól¨ HO§ðl¯é ºçßæ$糨 A¯]l$Mø…yìl. y = p(x) A¯ól ({V>‹œ) x- A„ýS…¯]l$ G°² ¼…§ýl$Ð]l#Ë Ð]l§ýlª Q…yìlçÜ$¢…§ø p(x) ºçßæ$糨MìS A°² Ô¶æ*¯éÅË$…sêƇ¬. x-A„ýS…¯]l$ Q…yìl…^ól ¼…§ýl$Ð]l#Ë x-°Æý‡*ç³M>Ìôæ p(x) ºçßæ$糨 Ô¶æ*¯éÅË$ ❖

❖

b= –5, c=1, d=2 AÐ]l#™éƇ¬. p(x) = 2x3–5x2+x+2

4.

=k1{16x2 − 1} k1 ÐéçÜ¢Ð]l çÜ…QÅ çœ$¯]l ºçßæ$糨 p(x)= 2x3–5x2+x+2

Ô¶æ*¯éÅË$

1 − , 1, 2 2

AÐ]l#™éĶæ$° ^èl*ç³…yìl.

ºçßæ$糨 VýS$×æM>ËMýS$, Ô¶æ*¯éÅËMýS$ Ð]l$«§ýlÅ E¯]l² çÜ…º…«§é°² çÜÇ^èl*yýl…yìl. f. C_a¯]l œç $¯]l ºçßæ$糨 p(x) =2x3–5x2+x+2¯]l$ ax3+bx2+ cx+d™ø ´ùÍõÜ¢ a = 2,

x4 − 4 x3 + x2 (−) ( +) ( −)

− 2 x3 − 27 x 2 + 138 x − 2 x3 + 8 x2 − 2 x (+) (−) (+) −35 x2 + 140 x − 35 −35 x2 + 140 x − 35 (+) (−) (+) 0

ºçßæ$糧ýl$Ë ¿êVýSàÆý‡… °Ä¶æ$Ð]l$… {ç³M>Æý‡…

x4–6x3–26x2+138x–35 = (x2–4x+1) (x2–2x–35)

C_a¯]l ºçßæ$糨 Ñ$Wͯ]l Æð‡…yýl$ Ô¶æ*¯éÅ˯]l$ x2–2x–35 ¯]l$…_ ´÷…§ö^èl$a. ºçßæ$糨 Ô¶æ*¯éÅË MøçÜ… x2–2x–35=0 A¯]l$Mø…yìl.

x2–7x+5x–35=0 (x–7)(x+5) =0 x–7=0, x+5 =0 x=7, x= –5 ∴C_a¯]l ºçßæ$糨 Ñ$Wͯ]l

Æð‡…yýl$ Ô¶æ*¯éÅË$ –5, 7