Page 1
¦)þöì†yœ ç þ™!îûöìîŸ
˜î› ö×!’
¢Á™)’Å þ™yàþÄ¢)!‰þ
!Ó°ÏÎ˚Óhfl$˛ ı 1. @˘Ã£Ó˚)ˆÏ˛ô ˛ô,!ÌÓ#
2. ô,!ÌÓ#Ó˚ Ü!ì˛¢õ)£
3. ô,!ÌÓ# ô,ˆ¤Ï ˛ ˆÑ˛yˆÏòy fl˛iyˆÏòÓ˚ xÓfl˛iyò !òí≈Î˚
4. ¶)˛!õÓ˚)˛ô ܇˛òÑ˛yÓ˚# ≤Ã!e´Î˚y Á ˛ô,!ÌÓ#Ó˚ !Ó!¶˛ß¨ ¶)˛!õÓ˚)˛ô
5. xyÓ£!ÓÑ˛yÓ˚
6. î%ˆÏÎ≈yÜ Á !Ó˛ôÎ≈Î˚
7. ¶˛yÓ˚ˆìÏ ˛Ó˚ ¢¡ôî
8. ô!ÿ˛õÓD
9. õyò!â˛e Á ˆfl˛Òú
õyò!â˛e S¶˛yÓ˚ˆìÏ ˛Ó˚ ¢¡ôî Á ˛ô!ÿ˛õÓDV
≤ÃÌõ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò Èı ˛ô)í≈õyò 40
xhs˛Ó≈ì≈˛# ≤Ãhfl$˛!ì˛Ñ˛yú#ò õ)úƒyÎ˚Ïò ı ˛ô)í≈õyò 10
!Ó°ÏÎ˚Óhfl$˛ ı 1. @˘Ã£Ó˚)ˆÏ˛ô ˛ô,!ÌÓ# õ)úƒyÎ˚ˆÏòÓ˚ õy¢ ı ~!≤Ãú
2. ô,!ÌÓ#Ó˚ Ü!ì˛¢õ)£
7. ¶˛yÓ˚ˆìÏ ˛Ó˚ ¢¡ôî
õyò!â˛e S¶˛yÓ˚ˆìÏ ˛Ó˚ ¢¡ôîV
!mì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò Èı ˛ô)í≈õyò 40
xhs˛Ó≈ì≈˛# ≤Ãhfl$˛!ì˛Ñ˛yú#ò õ)úƒyÎ˚Ïò ı ˛ô)í≈õyò 10
!Ó°ÏÎ˚Óhfl$˛ ı 3. ô,!ÌÓ# ô,ˆÏ¤˛ ˆÑ˛yˆÏòy fl˛iyˆÏòÓ˚ xÓfl˛iyò !òí≈Î˚ õ)úƒyÎ˚ˆÏòÓ˚ õy¢ ı xyÜfi›˛
4. ¶)˛!õÓ˚)˛ô ܇˛òÑ˛yÓ˚# ≤Ã!e´Î˚y Á ˛ô,!ÌÓ#Ó˚ !Ó!¶˛ß¨ ¶)˛!õÓ˚)˛ô
5. xyÓ£!ÓÑ˛yÓ˚
8. ô!ÿ˛õÓD SxÓfiÌyò Á ≤Ãüy¢!òÑ˛ !Ó¶˛yÜñ ≤ÃyÑ,˛!ì˛Ñ˛ ˛ô!Ó˚ˆÏÓüV
ì,˛ì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò Èı ˛ô)í≈õyò 90
xhs˛Ó≈ì≈˛# ≤Ãhfl$˛!ì˛Ñ˛yú#ò õ)úƒyÎ˚Ïò ı ˛ô)í≈õyò 10
!Ó°ÏÎ˚Óhfl$˛ ı 6. î%ˆÏÎ≈yÜ Á !Ó˛ôÎ≈Î˚ õ)úƒyÎ˚ˆÏòÓ˚ õy¢ ı !v˛ˆÏ¢¡∫Ó˚
8. ô!ÿ˛õÓD S≤Ãïyò ≤Ãïyò xÌ≈˜Ïò!ì˛Ñ˛ !Ñ˛Î˚yÑ˛úy˛ôV
9. õyò!â˛e Á ˆfl˛Òú
õyò!â˛e S˛ô!ÿ˛õÓDV
!Ó. o. ı ~Ó˚ ¢ˆÏAÜ ≤ÃÌõ ~ÓÇ !mì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ˆÏòÓ˚ !Ó°ÏÎ˚Óhfl$˛¢õ)£ xhs˛¶%≈˛=˛ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ S≤ÃÌõ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ˆÏòÓ˚ õyò!â˛ˆÏe
!â˛!£´ì˛Ñ˛Ó˚í Óƒ!ì˛ˆÏÓˆ˚ ÑÏ ˛V–
123
Page 2
¶)˛ˆÏÜyú Á ˛ô!Ó˚ˆÏÓü
òÓõ ˆ◊!íÓ˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ˆÏòÓ˚ ≤ß¿ Ñ˛y‡˛yˆÏõy Á ò¡∫Ó˚ !Óòƒy¢
≤ÃÌõ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò ˛ô)í≈õyò – 40
!Ó¶˛yÜ ÈÙÈ Ñ˛ !Ó¶˛yÜ ÈÙÈ Ö !Ó¶˛yÜ ÈÙÈ Ü !Ó¶˛yÜ ÈÙÈ á !Ó¶˛yÜ ÈÙÈ à !Ó¶˛yÜ ÈÙÈ â˛
Ó£%!ÓÑ˛“!¶˛!_Ñ˛ x!ì˛¢Ç!«˛Æ ¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ¢Ç!«˛Æ î#á≈ õyò!â˛e ˆõy›˛
!Ó°ÏÎ˚Óhfl$˛ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ ≤ß¿ ÓƒyÖƒyõ)úÑ˛ v˛z_Ó˚ïõ≈# ≤ß¿
v˛z_Ó˚ïõ≈# ≤ß¿
≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚
õyòÈ 1 õyò 1 õyò 2 õyò 3 õyò 5 õyò 1
≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú
1. @˘Ã£Ó˚)ˆÏ˛ô ˛ô,!ÌÓ# 1×2 =2 1×2 =2 2×1 =2 3×1 =3 9
2. ˛ô,!ÌÓ#Ó˚ Ü!ì˛¢õ)£ 1×2 =2 1×3 =3 2×1 =2 3×1 =3 10
5 × 1 = 5* ÈÙÙÙÈ
xyM˛È!úÑ˛ ¶)˛ˆÏÜyú +5
124
7. ¶˛yÓ˚ˆìÏ ˛Ó˚ ¢¡ôî 1×3 =3 1×3 =3 2×1 =2 3×1 =3 11
õyò!â˛e S¶˛yÓ˚ˆÏì˛Ó˚ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ 1×5 =5 05
¢¡ôîV
07 08 06 09 05 05 40
!ÓˆÏü°Ï o‹TÓƒ ≠
!Ó¶˛yÜ ÈÙÈ Ñ˛ ≠ Ó£%!ÓÑ˛“!¶˛!_Ñ˛ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ì˛Ìƒ Á ïyÓ˚íy!¶˛!_Ñ˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ !òÓ≈yâ˛ˆÏò â˛yÓ˚!›˛ Ñ˛ˆÏÓ˚ !ÓÑ˛“ !îˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙÈ Ö ≠È x!ì˛¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ~£z !Ó¶˛yˆÏÜÓ˚ ≤Èϟ¿Ó˚ ïÓ˚í ÙÈÈ ü)òƒfl˛iyò ˛ô)Ó˚íñ ÷k˛/x÷k˛ñ hfl˛Ω˛ ˆõúyˆÏòyñ ~Ñ˛!›˛ xÌÓy î%!›˛ üˆÏ∑Ó˚ v˛z_Ó˚–
!Ó¶˛yÜ ÈÙÈ Ü ≠ ¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ÚÑ˛#Û/ ÚˆÑ˛yÌyÎ˚Û ïÓ˚ˆÏòÓ˚ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙ á ≠ ¢Ç!«˛Æ ÓƒyÖƒyõ)úÑ˛ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ v˛z_ˆÏÓ˚Ó˚ ˆ«˛ˆÏe !ü«˛yÌ≈#ˆÏîÓ˚ !ì˛ò!›˛ Ñ˛ˆÏÓ˚ ì%˛úòy/˛ôyÌ≈Ñ˛ƒ/Î%!_´Ó˚ v˛zˆÏÕ‘Ö Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙÈ à ≠ î#á≈ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ~õò ≤ß¿ Ñ˛Ó˚y ÓyN˛ò#Î˚ ÎyˆÏì˛ ˆÓ˚Öy!â˛e ÓƒÓ£yˆÏÓ˚Ó˚ ¢%ˆÏÎyÜ ÌyÑ˛ˆÏÓ– xyM˛!úÑ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ÚÑ˛#¶˛yˆÏÓÛ/ ÚˆÑ˛òÛ ïÓ˚ˆÏòÓ˚ ≤ß¿ Ñ˛Ó˚y
ÓyN˛ò#Î˚–
!Ó¶˛yÜ ÈÙÈⲠ≠ õyò!â˛e ÈÙÙÙÈ ¶˛yÓ˚ˆÏì˛Ó˚ ≤Ãî_ ˆÓ˚Öyõyò!â˛ˆÏe ˆ¶˛ÔˆÏÜy!úÑ˛ !Ó°ÏÎ˚¢õ)ˆÏ£Ó˚ òyõ¢£ !â˛!£´ì˛Ñ˛Ó˚í ˛Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– î,!‹T£#ò !ü«˛yÌ≈#Ó˚ ãòƒ õyò!â˛ˆÏeÓ˚ ˛ô!Ó˚ÓˆÏì≈˛ 5!›˛ !ÓÑ˛“ ≤ß¿ !îˆÏì˛ £ˆÏÓ– ≤Ã!ì˛!›˛
≤Èϟ¿Ó˚ õyò £ˆÏÓ 1–
*≤ÃyÑ,˛!ì˛Ñ˛ Á xyM˛È!úÑ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ~Ñ˛!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ î%!›˛ ≤ß¿ Ñ˛Ó˚ˆìÏ ˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ ˆÎˆÏÑ˛yˆÏòy ~Ñ˛!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
Page 3
¶)˛ˆÏÜyú Á ˛ô!Ó˚ˆÏÓü
òÓõ ˆ◊!íÓ˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ˆÏòÓ˚ ≤ß¿ Ñ˛y‡˛yˆÏõy Á ò¡∫Ó˚ !Óòƒy¢
!mì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò ˛ô)í≈õyò – 40
!Ó¶˛yÜ ÈÙÈ Ñ˛ !Ó¶˛yÜ ÈÙÈ Ö !Ó¶˛yÜ ÈÙÈ Ü !Ó¶˛yÜ ÈÙÈ á !Ó¶˛yÜ ÈÙÈ à
Ó£%!ÓÑ˛“!¶˛!_Ñ˛ x!ì˛¢Ç!«˛Æ ¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ¢Ç!«˛Æ î#á≈
!Ó°ÏÎÓ˚ hfl˛$ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ ≤ß¿ ÓƒyÖƒyõ)úÑ˛ v˛z_Ó˚ïõ≈# ≤ß¿
v˛z_Ó˚ïõ≈# ≤ß¿ ˆõy›˛
≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚
õyò 1 õyò 1 õyò 2 õyò 3 õyò 5
≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú
3. ˛ô,!ÌÓ# ô,ˆÏ¤˛ ˆÑ˛yˆÏòy 1×2 =2 1×2 =2 2×1 =2 3×1 =3 09
fl˛iyˆÏòÓ˚ xÓfl˛iyò !òí≈Î˚
4. ¶)˛!õÓ˚˛) ô ܇˛òÑ˛yÓ˚# ≤Ã!e´Î˚y Á 1×2 =2 1×2 =2 2×1 =2 3×1 =3 09
˛ô,!ÌÓ#Ó˚ !Ó!¶˛ß¨ ¶)˛!õÓ˚)˛ô
5 × 1 = 5*
08 +5
5. ˛xyÓ£!ÓÑ˛yÓ˚ 1×1 =1 1×2 =2 2×1 =2 3×1 =3
125
xyM˛È!úÑ˛ ¶)˛ˆÏÜyú
8. ˛ô!ÿ˛õÓD SxÓfiÌyò 1×2 =2 1×2 =2 2×1 =2 3×1 =3 09
Á ≤Ãüy¢!òÑ˛ !Ó¶˛yÜñ
≤ÃyÑ,˛!ì˛Ñ˛ ˛ô!Ó˚ˆÏÓüV
07 08 08 12 05 40
!ÓˆÏü°Ï o‹TÓƒ ≠
!Ó¶˛yÜ ÈÙÈ Ñ˛ ≠È Ó£%!ÓÑ˛“!¶˛!_Ñ˛ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ì˛Ìƒ Á ïyÓ˚íy!¶˛!_Ñ˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ !òÓ≈yâ˛ˆÏò â˛yÓ˚!›˛ Ñ˛ˆÏÓ˚ !ÓÑ˛“ !îˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙÈ Ö ≠ x!ì˛¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ~£z !Ó¶˛yˆÏÜÓ˚ ≤Èϟ¿Ó˚ ïÓ˚í ÙÈ ü)òƒfl˛iyò ˛ô)Ó˚íñ ÷k˛/x÷k˛ñ hfl˛Ω˛ ˆõúyˆÏòyñ ~Ñ˛!›˛ xÌÓy î%!›˛ üˆÏ∑Ó˚ v˛z_Ó˚–
!Ó¶˛yÜ ÈÙÈ Ü ≠ ¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ÚÑ˛#Û/ ÚˆÑ˛yÌyÎ˚Û ïÓ˚ˆÏòÓ˚ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙ á ≠ ¢Ç!«˛Æ ÓƒyÖƒyõ)úÑ˛ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ v˛z_ˆÏÓ˚Ó˚ ˆ«˛ˆÏe !ü«˛yÌ≈#ˆÏîÓ˚ !ì˛ò!›˛ Ñ˛ˆÏÓ˚ ì%˛úòy/˛ôyÌ≈Ñ˛ƒ/Î%!_´Ó˚ v˛zˆÏÕ‘Ö Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙÈ à ≠ î#á≈ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ~õò ≤ß¿ Ñ˛Ó˚y ÓyN˛ò#Î˚ ÎyˆÏì˛ ˆÓ˚Öy!â˛e ÓƒÓ£yˆÏÓ˚Ó˚ ¢%ˆÏÎyÜ ÌyÑ˛ˆÏÓ– xyM˛!úÑ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ÚÑ˛#¶˛yˆÏÓÛ/ ÚˆÑ˛òÛ
ïÓ˚ˆÏòÓ˚ ≤ß¿ Ñ˛Ó˚y ÓyN˛ò#Î˚–
* ≤ÃyÑ,˛!ì˛Ñ˛ Á xyM˛È!úÑ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛ ~Ñ˛!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ !ì˛ò!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ ˆÎˆÏÑ˛yˆÏòy ~Ñ˛!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
Page 4
¶)˛ˆÏÜyú Á ˛ô!Ó˚ˆÏÓü
òÓõ ˆ◊!íÓ˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ˆÏòÓ˚ ≤ß¿ Ñ˛y‡˛yˆÏõy Á ò¡∫Ó˚ !Óòƒy¢
ì,˛ì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò ˛ô)í≈õyò – 90
!Ó¶˛yÜ ÈÙÈ Ñ˛ !Ó¶˛yÜ ÈÙÈ Ö !Ó¶˛yÜ ÈÙÈ Ü !Ó¶˛yÜ ÈÙÈ á !Ó¶˛yÜ ÈÙÈ à !Ó¶˛yÜ ÈÙÈ â˛
Ó£%!ÓÑ˛“!¶˛!_Ñ˛ x!ì˛¢Ç!«˛Æ ¢Ç!«˛Æ ¢Ç!«˛Æ ÓƒyÖƒyõ)úÑ˛ î#á≈ õyò!â˛e
!Ó°ÏÎÓ˚ hfl˛$ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ ˆõy›˛
≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚
õyò 1 õyò 1 õyò 2 õyò 3 õyò 5 õyò 1
≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú
1. @˘Ã£Ó˚)ˆÏ˛ô ˛ô,!ÌÓ#
2. ô,!ÌÓ#Ó˚ Ü!ì˛¢õ)£ 1×8 = 8 1 ×11 = 11 2×3 = 6 3 ×2 = 6 5×2 = 10 ÈÙÙÙÈ 41
3. ô,!ÌÓ# ô,ˆ¤Ï ˛ ˆÑ˛yˆÏòy fl˛iyˆÏòÓ˚ xÓfl˛iyò !òí≈Î˚
4. ¶)˛!õÓ˚˛) ô ܇˛òÑ˛yÓ˚# ≤Ã!e´Î˚y Á ˛ô,!ÌÓ#Ó˚ !Ó!¶˛ß¨
¶)˛!õÓ˚˛) ô
5. xyÓ£!ÓÑ˛yÓ˚
126
õyò%°Ï Á ˛ô!Ó˚ˆÏÓü 1×1 = 1 1×1 = 1 2×1 = 2 3×1 = 3 ÈÙÙÙÈ ÈÙÙÙÈ 07
6. î%ˆÏÎ≈yÜ Á !Ó˛ôÎ≈Î˚
xyM˛È!úÑ˛ ¶)˛ˆÏÜyú
7. ¶˛yÓ˚ˆìÏ ˛Ó˚ ¢¡ôî 1 ×5 = 5 1×10 = 10 2×2 = 4 3×1 = 3 5×2 = 10 ÈÙÙÙÈ 32
8. ô!ÿ˛õÓD
9. õyò!â˛e Á ˆfl˛Òú
õyò!â˛e S˛ô!ÿ˛õÓDV ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ 1×10 = 10 10
14 22 12 12 20 10 90
!ÓˆÏü°Ï o‹TÓƒ ≠ !Ó¶˛yÜ ÈÙÈ Ñ˛ ≠ ~£z !Ó¶˛yˆÏÜ ˆõy›˛ 14!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓñ ˆÑ˛yˆÏòy !ÓÑ˛“ ≤ß¿ ÌyÑ˛ˆÏÓ òy– l≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚Óhfl$˛ ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 8!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– xyM˛È!úÑ˛
¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚Óhfl$˛ ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 5!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–n
!Ó¶˛yÜ ÈÙÈ Ö ≠ ~£z !Ó¶˛yˆÏÜ ˆõy›˛ 25!›˛ ≤ß¿ ˆÌˆÏÑ˛ !ü«˛yÌ≈#ˆÏîÓ˚ 22!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– l≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚Óhfl$˛ ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛ 2!›˛ Ñ˛ˆÏÓ˚ ~ÓÇ xyM˛È!úÑ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚Óhfl$˛
ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛ 3!›˛ Ñ˛ˆÏÓ˚ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–n
!Ó¶˛yÜ ÈÙÈ Ü ≠ ≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyˆÏúÓ˚ 5!›˛ !Ó°ÏÎ˚Óhfl$˛ ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 6!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ 3!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– î%ˆÏÎ≈yÜ Á !Ó˛ôÎ≈Î˚ ˆÌˆÏÑ˛ 1!›˛ !ÓÑ˛“¢£ 2!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!ü«˛yÌ≈#ˆÏîÓ˚ 1!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– xyM˛È!úÑ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚Óhfl$˛ ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 4!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ 2!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙÈ á ≠ ≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ˆÎˆÏÑ˛yˆÏòy 4!›˛ !Ó°ÏÎ˚Óhfl$˛ ˆÌˆÏÑ˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 4!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ 2!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– î%ˆÏÎ≈yÜ Á !Ó˛ôÎ≈Î˚ ˆÌˆÏÑ˛ 1!›˛ !ÓÑ˛“¢£ 2!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!ü«˛yÌ≈#ˆÏîÓ˚ 1!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– xyM˛È!úÑ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚Óhfl$˛ ˆÌˆÏÑ˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 3!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ 1!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙÈ à ≠ ≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ˆÎ ˆÑ˛yˆÏòy 4!›˛ !Ó°ÏÎ˚Óhfl$˛ ˆÌˆÏÑ˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 4!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ 2!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– xyM˛È!úÑ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚Óhfl$˛ ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛
1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 4!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ 2!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
Page 5
ì,˛ì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ˆÏòÓ˚ ≤Èϟ¿Ó˚ ïÓ˚ò Á ò¡∫Ó˚ !Óòƒy¢
≤ÈŸÏ ¿Ó˚ ïÓ˚ò ≤Ã!ì˛!›˛ xÓüƒ Ñ˛Ó˚í#Î˚ ˆõy›˛ ò¡∫Ó˚ ˆõy›˛ ≤Èϟ¿Ó˚ ≤Èϟ¿Ó˚ ≤ÃÑ,˛!ì
!Ó¶˛yÜ
≤ÈŸÏ ¿Ó˚ õyò ≤ÈŸÏ ¿Ó˚ ¢ÇÖƒy ¢ÇÖƒy
Ó£%!ÓÑ˛“ !¶˛!_Ñ˛ ì˛Ìƒ Á ïyÓ˚íy!¶˛!_Ñ˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛
Ñ˛ 01 14 1 ' 14 = 14 14
v˛z_Ó˚ïõ≈# ≤ß¿ £ˆÏÓ Sâ˛yÓ˚!›˛ !ÓÑ˛“ ÌyÑ˛y ÓyN˛ò#Î˚V
(MCQ)
ü)òƒfiÌyò ˛ô)Óí˚ ñ ÷k˛/x÷k˛ñ hfl˛Ω˛
Ö
x!ì˛ ¢Ç!«˛Æ 01 22 1 ' 22 = 22 25 ˆõúyˆÏòyñ 1/2 üˆÏ∑Ó˚ v˛z_Ó˚
v˛z_Ó˚ïõ≈#˛ ≤ß¿
ÈÜ ¢Ç!«˛Æ 06 2 ' 6 = 12 12 ÚÑ˛#Û/ ÚˆÑ˛yÌyÎ˚Û ïÓ˚ˆÏòÓ˚ ≤ß¿
02
v˛z_Ó˚ïõ≈#˛ ≤ß¿
≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ v˛z_ˆÏÓ˚Ó˚ ˆ«˛ˆÏe
¢Ç!«˛Æ ÓƒyÖƒyõ)úÑ˛ 03 04 3 ' 4 = 12 09 !ü«˛yÌ≈#Ó˚y !ì˛ò!›˛ Ñ˛ˆÏÓ˚ ì%˛úòy/
á
v˛z_Ó˚ïõ≈#˛ ≤ß¿ ˛ôyÌ≈Ñ˛ƒ/Î%!_´Ó˚ v˛zˆÕÏ Ö‘ Ñ˛Ó˚ˆÓÏ
≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ~õò
04 5 ' 4 = 20 08 ≤ß¿ Ñ˛Ó˚y ÓyN˛ò#Î˚ ÎyˆÏì˛ ˆÓ˚Öy!â˛e
Èà î#á≈ v˛z_Ó˚ïõ≈#˛ ≤ß¿ 05 ÓƒÓ£yˆÏÓÓ˚ ˚ ¢%ˆÎÏ yÜ ÌyÑ˛ˆÏÓ–
xyM˛!úÑ˛ ¶) ˛ ˆÏ Ü yú ˆÌˆÏ Ñ ˛
ÚÑ˛#¶˛yˆÏÓÛ/ ÚˆÑ˛òÛ ïÓ˚ˆÏòÓ˚ ≤ß¿
Ñ˛Ó˚y ÓyN˛ò#Î˚–
˛ô!ÿ˛õÓˆÏDÓ˚ ≤Ãî_ ˆÓ˚Öyõyò!â˛ˆÏe
Ⲡõyò!â˛e * 01 10 1 × 10 = 10 10 ˆ¶˛ÔˆÏÜy!úÑ˛ !Ó°Ï΢˚ õ)ˆ£Ï Ó˚
òyõ¢£ !â˛!£´ì˛Ñ˛Ó˚í ˛
ˆõy›˛ " 60 ˆõy›˛ " 90 ˆõy›˛ " 78
* î,!‹T£#ò !ü«˛yÌ≈#Ó˚ ãòƒ õyò!â˛ˆÏeÓ˚ ˛ô!Ó˚ÓˆÏì≈˛ 10!›˛ !ÓÑ˛“ ≤ß¿ !îˆÏì˛ £ˆÏÓ– ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ õyò £ˆÏÓ 1–
127
Page 6
Geography and Environment
Class - IX
Syllabus
Theme : 1. Earth as a planet
2. Movements of the Earth
3. Determination of location of a place on the Earth’s surface
4. Geomorphic Processes and Landforms of the Earth
5. Weathering
6. Hazards and Disasters
7. Resources of India
8. West Bengal
9. Maps and Scale
Map (Resources of India and West Bengal)
First Summative Evaluation : 40 marks
Month of evaluation : April
Internal Formative Evaluation : 10 marks
Theme : 1. Earth as a planet
2. Movements of the Earth
7. Resources of India
Map (Resources of India)
Second Summative Evaluation : 40 marks
Month of evaluation : August
Internal Formative Evaluation : 10 marks
Theme : 3. Determination of location of a place on the Earth’s surface
4. Geomorphic Processes and Landforms of the Earth
5. Weathering
8. West Bengal (Location, Administrative Divisions, Physical Environment)
Third Summative Evaluation : 90 marks
Month of evaluation : December
Internal Formative Evaluation : 10 marks
Theme : 6. Hazards and Disasters
8. West Bengal (Major Economic Activities)
9. Maps and Scale
Map (West Bengal)
N.B. : Themes chosen for the first and second summative evaluations are also to be included in the third
summative evaluation (except map work of first summative evaluation).
128
Page 7
Geography and Environment
Question pattern and distribution of marks for Summative Evaluation – Class IX
First Summative Evaluation Full marks-40
Group - A Group - B Group - C Group - D Group - E Group - F
MCQ type Very short Short Short Long Map
answer answer type explanatory answer type
type question answer type question
Total
Theme question question
1 mark 1 mark 2 marks 5 marks 1 mark
3 marks
Physical Geography
1. Earth as a Planet 1×2 =2 1×2 =2 2×1 =2 3×1 =3 09
2. Movements of the Earth 1×2 =2 1×3 =3 2×1 =2 3×1 =3 10
Regional Geography 5 × 1 = 5* +5
129
7. Resources of India 1×3 =3 1×3 =3 2×1 =2 3×1 =3 11
Map (Resources of India) ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ 1×5 =5 05
07 08 06 09 05 05 40
N. B. :
Group-A : MCQ type – Information based and concept oriented questions to be set (four options to be provided).
Group-B : Very short answer type question – should consist of • fill in the blanks • true/ false • column matching • one or two word answer.
Group-C : Short answer type question – Consists of ‘what’/ ‘where’ type questions.
Group-D : Short explanatory answer type question – Compare/contrast/reasoning type of questions to be set (three points to be asked).
Group-E : Long answer type question – Preferably diagram-based questions from physical geography, ‘how’/ ‘why’ questions from Regional
Geography.
Group-F : Outline map of India to be provided and questions to be set to locate and label geographical features. Five alternative questions
should be provided for sightless candidates in lieu of map work. Each question carries 1 mark.
* Total 2 questions to be given, 1 each from Physical and Regional Geography. Any 1 to be answered.
Page 8
Geography and Environment
Question pattern and distribution of marks for Summative Evaluation – Class IX
Second Summative Evaluation Full marks-40
Group - A Group - B Group - C Group - D Group - E
MCQ type Very short Short Short Long
Theme answer answer type explanatory answer type Total
type question answer type question
question question
1 mark 1 mark 2 marks 3 marks 5 marks
Physical Geography
3. Determination of location of a 1×2 =2 1×2 =2 2×1 =2 3×1 =3 09
place on the Earth’s surface
4. Geomorphic Processes and 1×2 =2 1×2 =2 2×1 =2 3×1 =3 09
Landforms of the Earth 5 × 1 = 5*
5. Weathering
130
1×1 =1 1×2 =2 2×1 =2 3×1 =3 08 + 5
Regional Geography
8. West Bengal (Location, Admin- 1×2 =2 1×2 =2 3×1 =3 09
2×1 =2
istrative Divisions, Physical
Environment)
07 08 08 12 05 40
N. B. :
Group-A : MCQ type – Information based and concept oriented questions to be set (four options to be provided).
Group-B : Very short answer type question – should consist of • fill in the blanks • true/ false • column matching • one or two word answer.
Group-C : Short answer type question – Consists of ‘what’/ ‘where’ type questions.
Group-D : Short explanatory answer type question – Compare/contrast/reasoning type of questions to be set (three points to be asked).
Group-E : Long answer type question – Preferably diagram-based questions from Physical Geography, ‘how’/ ‘why’ questions from Regional
Geography.
* Total 3 questions to be given, at least 1 each from Physical and Regional Geography. Any 1 to be answered.
Page 9
Geography and Environment
Question pattern and distribution of marks for Summative Evaluation – Class IX
Third Summative Evaluation Full marks-90
Group - A Group - B Group - C
Group - D Group - E Group - F
MCQ type Very short Short Short Long answer Map
Theme
Total
answer answer type explanatory type
type answer type
question question
question question
1 mark 2 marks 3 marks 5 marks 1 mark
1 mark
Physical Geography
1. Earth as a Planet
2. Movements of the Earth
3. Determination of location of a place on ÈÙÙÙÈ
the Earth’s surface 1×8 = 8 1 ×11 = 11 2×3 = 6 3 ×2 = 6 5×2 = 10 41
4. Geomorphic Processes and Landforms
of the Earth
5. Weathering
131
Man and Environment
6. Hazards and Disasters 1 ×1 = 1 1×1 = 1 2 ×1 = 2 3 ×1 = 3 ÈÙÙÙÈ ÈÙÙÙÈ 07
Regional Geography (Including Maps
and Scale)
7. Resources of India 1 ×5 = 5 1×10 = 10 2×2 = 4 3 ×1 = 3 5×2 = 10 ÈÙÙÙÈ 32
8. West Bengal
9. Maps and Scale
Map (West Bengal) ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ 1×10 = 10 10
14 22 12 12 20 10 90
N. B. : Group - A : Total 14 questions to be given. [Total 8 questions to be given including at least 1 from each theme of Physical Geography. Total 5 questions
to be given including at least 1 from each theme of Regional Geography.] There will be no alternative in this group.
Group - B : Total 25 questions to be set, out of which 22 to be answered. [At least 2 questions and 3 questions from each theme of Physical Geography and
Regional Geography respectively to be given.]
Group - C : Total 6 questions to be given including at least 1 each from 5 themes of Physical Geography. Any 3 to be answered. 1 out of 2 alternatives from
Hazards and Disasters to be answered. Total 4 questions to be given including at least 1 from each theme of Regional Geography. Any 2 to be answered.
Group - D : Total 4 questions to be given including 1 each from any 4 selected themes of Physical Geography. Any 2 to be answered. 1 out of 2 alternatives from
Hazards and Disasters to be answered. Total 3 questions to be given including 1 from each theme of Regional Geography. Any 1 to be answered.
Group - E : Total 4 questions to be given including 1 each from any 4 selected themes of Physical Geography. Any 2 to be answered. Total 4 questions to be
given including at least 1 from each theme of Regional Geography. Any 2 to be answered.
Page 10
Distribution of marks and question pattern for Third Summative Evaluation
Type of Marks for Number of Total No. of Nature of question
Group question each ques- questions to marks questions
tion be attempted to be set
Information based and
A MCQ type 01 14 1 × 14 = 14 14 concept oriented ques-
tions to be set (four op-
tions to be provided)
• Fill in the blanks
Very short • True/ false
B answer type • Column matching
01 22 1 × 22 = 22 25
question • One or two word
answer
Short
C answer type 12 ‘What’/ ‘where’ type
02 06 2 × 6 = 12
question questions
Short Compare / contrast / rea-
D explanatory 03 04 3 × 4 = 12 09 soning type of questions
answer type to be set (three points to
question be asked)
Long • Preferably diagram-
E based questions from
answer type 05 04 5 × 4 = 20 08 Physical Geography,
question ‘how’/ ‘why’ ques-
tions from Regional
Geography
Outline map of West
10 Bengal to be provided
F Map work* 01 10 1 × 10 = 10 and questions to be set
to locate and label geo-
graphical features
Total = 60 Total = 90 Total = 78
*10 questions to be provided for sightless candidates in lieu of map work. Each question carries 1 mark.
132
Page 11
¦)þöì†yœ ç þ™!îûöìîŸ
”Ÿ› ö×!’
¢Á™)’Å þ™yàþÄ¢)!‰þ
!Ó°ÏÎ˚ ı 1. Ó!£ã≈yì˛ ≤Ã!Ñ˛Î˚y Á ì˛yˆÏîÓ˚ myÓ˚y ¢,T˛ ¶)˛!õÓ˚)˛ô
2. ÓyÎ˚õ% [˛ú
3. Óy!Ó˚õ[˛ú
4. Óã≈ƒ ÓƒÓfl˛iy˛ôòy
5. ¶˛yÓ˚ì˛
6. v˛z˛ô@˘Ã£ !â˛e Á ¶)˛ÈÙȘÓ!â˛eƒ¢)â˛Ñ˛ õyò!â˛e
õyò!â˛e S˛¶˛yÓ˚ì˛V
õ)úƒyÎ˚ˆÏòÓ˚ õy¢ ı ~!≤Ãú
≤ÃÌõ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò Èı ˛ô)í≈õyò 40
xhs˛Ó≈ì≈˛# ≤Ãhfl$˛!ì˛Ñ˛yú#ò õ)úƒyÎ˚Ïò ı ˛ô)í≈õyò 10
!Ó°ÏÎ˚˛ ı 1. Ó!£ã≈yì˛ ≤Ã!Ñ˛Î˚y Á ì˛yˆÏîÓ˚ myÓ˚y ¢,T˛ ¶)˛!õÓ˚)˛ô
5. ¶˛yÓ˚ì˛ÈÈÙÙÙÈ È¶)˛!õÑ˛yñ ¶˛yÓ˚ˆÏì˛Ó˚ ≤ÃyÑ,˛!ì˛Ñ˛ ˛ô!Ó˚ˆÏÓü
!mì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò Èı ˛ô)í≈õyò 40 õ)úƒyÎ˚ˆÏòÓ˚ õy¢ ı xyÜfi›˛
xhs˛Ó≈ì≈˛# ≤Ãhfl$˛!ì˛Ñ˛yú#ò õ)úƒyÎ˚Ïò ı ˛ô)í≈õyò 10
!Ó°ÏÎ˚ ı 2. ÓyÎ˚õ% [˛ú
3. Óy!Ó˚õ[˛ú
5. ¶˛yÓ˚Ïì˛ ÈÙÙÙÈ xÌ≈˜Ïò!ì˛Ñ ˛ô!Ó˚ˆÏÓü
ì,˛ì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò Èı ˛ô)í≈õyò 90 õ)úƒyÎ˚ˆÏòÓ˚ õy¢ ı !v˛ˆÏ¢¡∫Ó˚
xhs˛Ó≈ì≈˛# ≤Ãhfl$˛!ì˛Ñ˛yú#ò õ)úƒyÎ˚Ïò ı ˛ô)í≈õyò 10
!Ó°ÏÎ˚ ı 4. Óã≈ƒ ÓƒÓfl˛iy˛ôòy
6. v˛z˛ô@˘Ã£ !â˛e Á ¶)˛ÈÙȘÓ!â˛eƒ¢)â˛Ñ˛ õyò!â˛e
õyò!â˛e S¶˛yÓ˚ì˛V
!Ó.o ı ~Ó˚ ¢ˆÏAÜ ≤ÃÌõ ~ÓÇ !mì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ˆÏòÓ˚ !Ó°ÏÎ˚¢õ)£ xhs˛¶%≈˛=˛ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
133
Page 12
¶)˛ˆÏÜyú Á ˛ô!Ó˚ˆÏÓü
îüõ ˆ◊!íÓ˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ˆÏòÓ˚ ≤ß¿ Ñ˛y‡˛yˆÏõy Á ò¡∫Ó˚ !Óòƒy¢
≤ÃÌõ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò ˛ô)í≈õyò – 40
!Ó¶˛yÜ ÈÙÈ Ñ˛ !Ó¶˛yÜ ÈÙÈ Ö !Ó¶˛yÜ ÈÙÈ Ü !Ó¶˛yÜ ÈÙÈ á !Ó¶˛yÜ ÈÙÈ à
Ó£%!ÓÑ˛“!¶˛!_Ñ˛ x!ì˛¢Ç!«˛Æ ¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ¢Ç!«˛Æ î#á≈
v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ ≤ß¿ ÓƒyÖƒyõ)úÑ˛ v˛z_Ó˚ïõ≈# ≤ß¿
!Ó°ÏÎ˚ v˛z_Ó˚ïõ≈# ≤ß¿ ˆõy›˛
≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚
õyò 1 õyò 1 õyò 2 õyò 3 õyò 5
≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú
1. Ó!£ã≈yì˛ ≤Ã!Ñ˛Î˚y Á ì˛yˆÏîÓ˚ 1×4 = 4 1×4 = 4 2×2 = 4 3 ×1 = 3 5×1 = 5 20
myÓ˚y ¢,T˛ ¶)˛!õÓ˚)˛ô
xyM˛!úÑ˛ ¶)˛ˆÏÜyú
5. ¶˛yÓ˚ì˛ÈÙÙÙ¶)˛!õÑ˛yñÈ ¶˛yÓ˚ˆìÏ ˛Ó˚ 1×4 = 4 1×4 = 4 2×2 = 4 3 ×1 = 3 5×1 = 5 20
134
≤ÃyÑ,˛!ì˛Ñ˛ ˛ô!Ó˚ˆÏÓü
08 08 08 06 10 40
!ÓˆÏü°Ï oT˛Óƒ ı
!Ó¶˛yÜ ÈÙÈ Ñ˛ ≠ Ó£%!ÓÑ˛“!¶˛!_Ñ˛ v˛z_Ó˚ïõ≈# ≤ß¿ È ÙÙÙÈ ì˛Ìƒ Á ïyÓ˚íy!¶˛!_Ñ˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ !òÓ≈yâ˛ˆÏò â˛yÓ˚!›˛ Ñ˛ˆÏÓ˚ !ÓÑ˛“ !îˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙÈ Ö˛ ≠ x!ì˛¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ≤ß¿ È ÙÙÙÈ ~£z !Ó¶˛yˆÏÜÓ˚ ≤Èϟ¿Ó˚ ïÓ˚í ÈÙÈ Èü)òƒfl˛iyò ˛ô)Ó˚íñ ÷k˛/x÷k˛ñ hfl˛Ω˛ ˆõúyˆÏòyñ ~Ñ˛!›˛ xÌÓy î%!›˛ üˆÏ∑Ó˚ v˛z_Ó˚–
!Ó¶˛yÜ ÈÙÈ Ü ≠ ¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ÚÑ˛#Û/ ÚˆÑ˛yÌyÎ˚Û ïÓ˚ˆÏòÓ˚ ≤ß¿˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙ á ≠ ¢Ç!«˛Æ ÓƒyÖƒyõ)úÑ˛ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ v˛z_ˆÏÓ˚Ó˚ ˆ«˛ˆÏe !ü«˛yÌ≈#ˆÏîÓ˚ !ì˛ò!›˛ Ñ˛ˆÏÓ˚ ì%˛úòy/˛ôyÌ≈Ñ˛ƒ/Î%!_´Ó˚ v˛zˆÏÕ‘Ö Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙÈ à ≠ î#á≈ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ~õò ≤ß¿ Ñ˛Ó˚y ÓyN˛ò#Î˚ ÎyˆÏì˛ ˆÓ˚Öy!â˛e ÓƒÓ£yˆÏÓ˚Ó˚ ¢%ˆÏÎyÜ ÌyÑ˛ˆÏÓ– xyM˛!úÑ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ÚÑ˛#¶˛yˆÏÓÛ/ ÚˆÑ˛òÛ ïÓ˚ˆÏòÓ˚
≤ß¿ Ñ˛Ó˚y ÓyN˛ò#Î˚–
Page 13
¶)˛ˆÏÜyú Á ˛ô!Ó˚ˆÏÓü
îüõ ˆ◊!íÓ˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ˆÏòÓ˚ ≤ß¿ Ñ˛y‡˛yˆÏõy Á ò¡∫Ó˚ !Óòƒy¢
!mì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò ˛ô)í≈õyò – 40
!Ó¶˛yÜ ÈÙÈ Ñ˛ !Ó¶˛yÜ ÈÙÈ Ö !Ó¶˛yÜ ÈÙÈ Ü !Ó¶˛yÜ ÈÙÈ á !Ó¶˛yÜ ÈÙÈ à
Ó£%!ÓÑ˛“!¶˛!_Ñ˛ x!ì˛¢Ç!«˛Æ ¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ¢Ç!«˛Æ î#á≈
!Ó°ÏÎ˚ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ ≤ß¿ ÓƒyÖƒyõ)úÑ˛ v˛z_Ó˚ïõ≈# ≤ß¿
v˛z_Ó˚ïõ≈# ≤ß¿ ˆõy›˛
≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚ ≤Ã!ì˛!›˛ ≤ÈŸÏ ¿Ó˚
õyò 1 õyò 1 õyò 2 õyò 3 õyò 5
≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú
2. ÓyÎ˚õ% [˛ú 1×3=3 1×3=3 2×1=2 3×1=3 5 × 1= 5 16
3. Óy!Ó˚õ[˛ú 1×2=2 1×2=2 2×1=2 3×1=3 – 09
xyM˛!úÑ˛ ¶)˛ˆÏÜyú
135
5. ¶˛yÓ˚ì˛ÈÈÙÙÙÈÈxÌ≈˜òÏ !ì˛Ñ˛ ˛ô!Ó˚ˆÓÏ ü 1×3=3 1×3=3 2×2=4 È– 5 × 1= 5 15
08 08 08 06 10 40
!ÓˆÏü°Ï oT˛Óƒ ı
!Ó¶˛yÜ ÈÙÈ Ñ˛ ≠ Ó£%!ÓÑ˛“!¶˛!_Ñ˛ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ì˛Ìƒ Á ïyÓ˚íy!¶˛!_Ñ˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ !òÓ≈yâ˛ˆÏò â˛yÓ˚!›˛ Ñ˛ˆÏÓ˚ !ÓÑ˛“ !îˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙÈ Ö ≠È x!ì˛¢Ç!«˛Æ˛ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ~£z !Ó¶˛yˆÏÜÓ˚ ≤Èϟ¿Ó˚ ïÓ˚í ÈÙÙ ü)òƒfl˛iyò ˛ô)Ó˚íñ ÷k˛/x÷k˛ñ hfl˛Ω˛ ˆõúyˆÏòyñ ~Ñ˛!›˛ xÌÓy î%!›˛ üˆÏ∑Ó˚ v˛z_Ó˚–
!Ó¶˛yÜ ÈÙÈ Ü ≠ ¢Ç!«˛Æ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ÚÑ˛#Û/ ÚˆÑ˛yÌyÎ˚Û ïÓ˚ˆÏòÓ˚ ≤ß¿˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙ á ≠ ¢Ç!«˛Æ ÓƒyÖƒyõ)úÑ˛ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ v˛z_ˆÏÓ˚Ó˚ ˆ«˛ˆÏe !ü«˛yÌ≈#ˆÏîÓ˚ !ì˛ò!›˛ Ñ˛ˆÏÓ˚ ì%˛úòy/˛ôyÌ≈Ñ˛ƒ/Î%!_´Ó˚ v˛zˆÏÕ‘Ö Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!Ó¶˛yÜ ÈÙÈ à ≠ î#á≈ v˛z_Ó˚ïõ≈# ≤ß¿ ÈÙÙÙÈ ≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ~õò ≤ß¿ Ñ˛Ó˚y ÓyN˛ò#Î˚ ÎyˆÏì˛ ˆÓ˚Öy!â˛e ÓƒÓ£yˆÏÓ˚Ó˚ ¢%ˆÏÎyÜ ÌyÑ˛ˆÏÓ– xyM˛!úÑ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ÚÑ˛#¶˛yˆÏÓÛ/ ÚˆÑ˛òÛ ïÓ˚ˆÏòÓ˚
≤ß¿ Ñ˛Ó˚y ÓyN˛ò#Î˚–
Page 14
¶)˛ˆÏÜyú Á ˛ô!Ó˚ˆÏÓü
îüõ ˆ◊!íÓ˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ˆÏòÓ˚ ≤ß¿ Ñ˛y‡˛yˆÏõy Á ò¡∫Ó˚ !Óòƒy¢
˛ô)í≈õyò – 90
ì,˛ì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò/!òÓ≈yâ˛ò# ˛ôÓ˚#«˛y
!Ó¶˛yÜ ÈÙÈ Ñ˛ !Ó¶˛yÜ ÈÙÈ Ö !Ó¶˛yÜ ÈÙÈ Ü !Ó¶˛yÜ ÈÙÈ á !Ó¶˛yÜ ÈÙÈ à !Ó¶˛yÜ ÈÙÈ â˛
Ó£%!ÓÑ˛“!¶˛!_Ñ˛ x!ì˛¢Ç!«˛Æ ¢Ç!«˛Æ ¢Ç!«˛Æ ÓƒyÖƒyõ)úÑ˛ î#á≈ õyò!â˛e
!Ó°ÏÎ˚ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ v˛z_Ó˚ïõ≈# ≤ß¿ ˆõy›˛
≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚
õyò 1 õyò 1 õyò 2 õyò 3 õyò 5 õyò 1
≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú
1. Ó!£ã≈yì˛ ≤Ã!Ñ˛Î˚y Á ì˛yˆÏîÓ˚ myÓ˚y ¢,T˛ ¶)˛!õÓ˚)˛ô
2. ÓyÎ˚%õ[˛ú 1×6 = 6 1×9 = 9 2×2 = 4 3×1 = 3 5×2 = 10 ÈÙÙÙÈ 32
3. Óy!Ó˚õ[˛ú
˛ô!Ó˚ˆÏÓü ¶)˛ˆÏÜyú 08
4. Óã≈ƒ ÓƒÓfl˛iy˛ôòy 1×1 = 1 1×2 = 2 2×1 = 2 3×1 = 3 ÈÙÙÙÈ ÈÙÙÙÈ
xyM˛!úÑ˛ ¶)˛ˆÏÜyú
5. ¶˛yÓ˚ì˛ÈÙÙÙÈ ¶)˛!õÑ˛yñ ≤ÃyÑ,˛!ì˛Ñ˛ ˛ô!Ó˚ˆÏÓüñ 1×6 = 6 1×9 = 9 2×2 = 4 3×1 = 3 5×2 = 10 ÈÙÙÙÈ 32
136
xÌ≈˜Ïò!ì˛Ñ ˛ ô!Ó˚ˆÏÓü
v˛z˛ô@˘Ã£ !â˛e Á ¶)˛ÈÙȘÓ!â˛eƒ¢)â˛Ñ˛ õyò!â˛e 1×2 = 2 ÈÙÙÙÈ ÈÙÙÙÈ 08
1×1 = 1 2×1 = 2 3×1 = 3
6. v˛z˛ô@˘Ã£ !â˛e Á ¶)˛ÈÙȘÓ!â˛eƒ¢)â˛Ñ˛ õyò!â˛e
õyò!â˛e S¶˛yÓ˚ì˛V ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ 1×10 = 10 10
14 22 12 12 20 10 90
!ÓˆÏü°Ï oT˛Óƒ ı
!Ó¶˛yÜ ÈÙÈ Ñ˛ ı ~£z !Ó¶˛yˆÏÜ ˆõy›˛ 14!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓñ ˆÑ˛yˆÏòy !ÓÑ˛“ ≤ß¿ ÌyÑ˛ˆÏÓ òy– l≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚ ˆÌˆÏÑ˛ 2!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 6!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–n
!Ó¶˛yÜ ÈÙÈ Ö ı ~£z !Ó¶˛yˆÏÜ ˆõy›˛ 26!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ 22!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– l≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚ ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛ 3!›˛ Ñ˛ˆÏÓ˚ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–n
!Ó¶˛yÜ ÈÙÈ Ü ı ~£z !Ó¶˛yˆÏÜ ˆõy›˛ 12!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ 6!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– l≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚ ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 4!›˛ ~ÓÇ xyM˛!úÑ˛ ¶)˛ˆÏÜyú
ˆÌˆÏÑ˛ 4!›˛ Ñ˛ˆÏÓ˚ ¢Ó≈ˆÏõy›˛ 8!›˛ S4`4V ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ ≤ÃyÑ,˛!ì˛Ñ˛ Á xyM˛!úÑ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ 2!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 4!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– ˛ô!Ó˚ˆÏÓü ¶)˛ˆÏÜyú ~ÓÇ v˛z˛ô@˘Ã£!â˛e Á
¶)˛ÈÙȘÓ!â˛eƒ¢)â˛Ñ˛ õyò!â˛e ÈÙÙÙÈ ≤Ã!ì˛!›˛ ˆÌˆÏÑ˛ 2!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 4!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ ≤Ã!ì˛!›˛ xÇü ˆÌˆÏÑ˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 2!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–n
!Ó¶˛yÜ ÈÙÈ á ı ~£z !Ó¶˛yˆÏÜ ˆõy›˛ 8!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– l≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyúñ ˛ô!Ó˚ˆÏÓü ¶)˛ˆÏÜyúñ xyM˛!úÑ˛ ¶)˛ˆÏÜyú ~ÓÇ v˛z˛ô@˘Ã£!â˛e Á ¶)˛ÈÙȘÓ!â˛eƒ¢)â˛Ñ˛ õyò!â˛e ÈÙÙÙÈ ≤Ã!ì˛!›˛ ˆÌˆÏÑ˛ 1!›˛ !ÓÑ˛“¢£ 2!›˛
Ñ˛ˆÏÓ˚ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– !ü«˛yÌ≈#ˆÏîÓ˚ ≤Ã!ì˛!›˛ xÇü ˆÌˆÏÑ˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 4!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–n
!Ó¶˛yÜ ÈÙÈ à ı ~£z !Ó¶˛yˆÏÜ ˆõy›˛ 8!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ– l≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyˆÏúÓ˚ ≤Ã!ì˛!›˛ !Ó°ÏÎ˚ ˆÌˆÏÑ˛ Ñ˛õ˛ôˆÏ«˛ 1!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 4!›˛ ≤ß¿ ~ÓÇ xyM˛!úÑ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ˆõy›˛ 4!›˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–
!ü«˛yÌ≈#ˆÏîÓ˚ ≤ÃyÑ,˛!ì˛Ñ˛ Á xyM˛È!úÑ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ 2!›˛ Ñ˛ˆÏÓ˚ ˆõy›˛ 4!›˛ ≤Èϟ¿Ó˚ v˛z_Ó˚ Ñ˛Ó˚ˆÏì˛ £ˆÏÓ–n
Page 15
ì,˛ì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò/!òÓ≈yâ˛ò# ˛ôÓ˚#«˛yÓ˚ ≤Èϟ¿Ó˚ ïÓ˚ò Á ò¡∫Ó˚ !Óòƒy¢
!Ó¶˛yÜ ≤ÈŸÏ ¿Ó˚ ïÓ˚ò ≤Ã!ì˛!›˛ xÓüƒ Ñ˛Ó˚í#Î˚ ˆõy›˛ ò¡∫Ó˚ ˆõy›˛ ≤Èϟ¿Ó˚ ≤Èϟ¿Ó˚ ≤ÃÑ,˛!ì
≤ÈŸÏ ¿Ó˚ õyò ≤ÈŸÏ ¿Ó˚ ¢ÇÖƒy ¢ÇÖƒy
Ñ˛ Ó£%!ÓÑ˛“!¶˛!_Ñ˛ ì˛Ìƒ Á ïyÓ˚íy!¶˛!_Ñ˛ ≤ß¿ Ñ˛Ó˚ˆÏì˛
01 14 1 ' 14 = 14 14
v˛z_Ó˚ïõ≈# ≤ß¿ £ˆÏÓ Sâ˛yÓ˚!›˛ !ÓÑ˛“ ÌyÑ˛y ÓyN˛ò#Î˚V
(MCQ)
ü)òƒfiÌyò ˛ô)Óí˚ ñ ü%Âï/xü%Âïñ hfl˛Ω˛
Ö x!ì˛¢Ç!«˛Æ 01 22 1 ' 22 = 22 26
ˆõúyˆÏòyñ 1/2 üˆÏ∑Ó˚ v˛z_Ó˚
v˛z_Ó˚ïõ≈#˛ ≤ß¿
¢Ç!«˛Æ ÚÑ˛#Û/ ÚˆÑ˛yÌyÎ˚Û ïÓ˚ˆÏòÓ˚ ≤ß¿
ÈÜ 02 06 2 ' 6 = 12 12
v˛z_Ó˚ïõ≈#˛ ≤ß¿
≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ v˛z_ˆÏÓ˚Ó˚ ˆ«˛ˆÏe
á ¢Ç!«˛Æ ÓƒyÖƒyõ)úÑ˛ 03 04 3 ' 4 = 12 08 !ü«˛yÌ≈#Ó˚y !ì˛ò!›˛ Ñ˛ˆÏÓ˚ ì%˛úòy/
v˛z_Ó˚ïõ≈#˛ ≤ß¿ ˛ôyÌ≈Ñ˛ƒ/Î%!_´Ó˚ v˛zˆÕÏ Ö‘ Ñ˛Ó˚ˆÓÏ
≤ÃyÑ,˛!ì˛Ñ˛ ¶)˛ˆÏÜyú ˆÌˆÏÑ˛ ~õò
≤ß¿ Ñ˛Ó˚y ÓyN˛ò#Î˚ ÎyˆÏì˛ ˆÓ˚Öy!â˛e
Èà î#á≈ v˛z_Ó˚ïõ≈#˛ ≤ß¿ 05 04 5 ' 4 = 20 08 ÓƒÓ£yˆÏÓÓ˚ ˚ ¢%ˆÎÏ yÜ ÌyÑ˛ˆÏÓ–
xyM˛!úÑ˛ ¶) ˛ ˆÏ Ü yú ˆÌˆÏ Ñ ˛
ÚÑ˛#¶˛yˆÏÓÛ/ ÚˆÑ˛òÛ ïÓ˚ˆÏòÓ˚ ≤ß¿
Ñ˛Ó˚y ÓyN˛ò#Î˚–˚
¶˛yÓ˚ˆÏì˛Ó˚ ≤Ãî_ ˆÓ˚Öyõyò!â˛ˆÏe
Ⲡõyò!â˛e D 01 10 1 × 10 = 10 10 ˆ¶˛ÔˆÏ Ü y!úÑ˛ !Ó°Ï Î ˚ ¢ õ) ˆ Ï £ Ó˚
òyõ¢£ !â˛!£´ì˛Ñ˛Ó˚í˛
ˆõy›˛ " 60 ˆõy›˛ " 90 ˆõy›˛ " 78
D î,!T˛£#ò !ü«˛yÌ≈#Ó˚ ãòƒ õyò!â˛ˆÏeÓ˚ ˛ô!Ó˚ÓˆÏì≈˛ 10!›˛ !ÓÑ˛“ ≤ß¿ !îˆÏì˛ £ˆÏÓ– ≤Ã!ì˛!›˛ ≤Èϟ¿Ó˚ õyò £ˆÏÓ 1–
!Ó.o.ÈÙÈ ~£z ≤ß¿ Ñ˛y‡˛yˆÏõy õyïƒ!õÑ˛ ˛ôÓ˚#«˛yÓ˚ !òˆÏî≈üÑ˛–
137
Page 16
Geography and Environment
Class - X
Syllabus
Topic : 1. Exogenetic processes and resultant landforms
2. Atmosphere
3. Hydrosphere
4. Waste management
5. India
6. Satellite imagery and Topographical map
Map (India)
First Summative Evaluation : 40 marks Month of Evaluation : April
Internal Formative Evaluation : 10 marks
Topic : 1. Exogenetic processes and resultant landforms
5. India – Introduction, Physical environment
Second Summative Evaluation : 40 marks
Internal Formative Evaluation : 10 marks Month of Evaluation: August
Topic : 2. Atmosphere
3. Hydrosphere
5. India – Economic environment
Third Summative Evaluation : 90 marks
Month of Evaluation : December
Internal Formative Evaluation : 10 marks
Topic : 4. Waste management
6. Satellite imagery and Topographical map
Map (India)
N.B. : Topics chosen for the first and second summative evaluations are also to be included in the third
summative evaluation.
138
Page 17
Geography and Environment
Question pattern and distribution of marks for Summative Evaluation — class x
First Summative Evaluation Full marks-40
Group - A Group - B Group - C Group - DGroup - E
MCQ type Very short Short Short Long
answer answer type explanatory answer type
Topic answer type Total
type question question
question
question
1 mark 1 mark 2 marks 3 marks 5 marks
Physical Geography
1. Exogenetic processes
1×4 = 4 1×4 = 4 2×2 = 4 3×1 = 3 5×1 = 5 20
and resultant landforms
Regional Geography
5. India – Introduction, 1×4 = 4 1×4 = 4 2×2 = 4 3×1 = 3 5×1 = 5 20
139
Physical Environment
08 08 08 06 10 40
N. B. :
Group-A : MCQ type – Information based and concept oriented questions to be set (four options to be provided).
Group-B : Very short answer type – should consist of • fill in the blanks • true/ false • column matching • one or two word answer.
Group-C : Short answer type question – Consists of what’/ ‘where’ type questions.
Group-D : Short explanatory answer type question – Compare/contrast/reasoning type of questions to be set (three points to be asked).
Group-E : Long answer type question – Preferably diagram-based questions from Physical Geography, ‘how’/ ‘why’ questions from Regional
Geography.
Page 18
Geography and Environment
Question pattern and distribution of marks for Summative Evaluation — class x
Second Summative Evaluation Full marks-40
Group - A Group - B Group - C Group - D Group - E
MCQ type Very short Short Short Long
answer answer type explanatory answer type
Topic type Total
question answer type question
question
question
1 mark 1 mark 2 marks 3 marks 5 marks
Physical Geography
2. Atmosphere 1×3=3 1×3=3 2×1=2 3×1=3 5×1=5 16
3. Hydrosphere 1×2=2 1×2=2 2×1=2 3×1=3 – 09
Regional Geography
140
5. India – Economic 1×3=3 1×3=3 2×2=4 – 5×1=5 15
Environment
08 08 08 06 10 40
N. B. :
Group-A : MCQ type – Information based and concept oriented questions to be set (four options to be provided).
Group-B : Very short answer type – should consist of • fill in the blanks • true/ false • column matching • one or two word answer.
Group-C : Short answer type question – Consists of ‘what’/ ‘where’ type questions.
Group-D : Short explanatory answer type question – Compare/contrast/reasoning type of questions to be set (three points to be asked).
Group-E : Long answer type question – Preferably diagram-based questions from Physical Geography, ‘how’/ ‘why’ questions from Regional
Geography.
Page 19
Geography and Environment
Question pattern and distribution of marks for Summative Evaluation — class x
Full marks-90
Third Summative Evaluation / Selection Test
Group - A Group - B Group - C Group - D Group - E Group - F
Short Short Long Map
MCQ type Very short
answer answer type explanatory
Topic answer type Total
type question answer type
question question
question
1 mark 1 mark 2 marks 3 marks 5 marks 1 mark
Physical Geography
1. Exogenetic processes and resultant landforms ÈÙÙÙÈ
1×6 = 6 1×9 = 9 2×2 = 4 3×1 = 3 5×2 = 10 32
2. Atmosphere
3. Hydrosphere
Environmental Geography ÈÙÙÙÈ ÈÙÙÙÈ 08
1×1 = 1 1×2 = 2 2×1 = 2 3×1 = 3
4. Waste management
Regional Geography
141
5. India–Introduction, Physical environment, 1×6 = 6 1×9 = 9 2×2 = 4 3×1 = 3 5×2 = 10 ÈÙÙÙÈ 32
Economic environment
Satellite imagery and Topographical map
6. Satellite imagery and Topographical map 1×1 = 1 1×2 = 2 2×1 = 2 3×1 = 3 ÈÙÙÙÈ ÈÙÙÙÈ 08
Map (India) ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ ÈÙÙÙÈ 10
1×10 = 10
14 22 12 12 20 10 90
N. B. : Group-A : Total 14 questions to be given. [Total 6 questions to be given including 2 questions from each topic of Physical Geography.] There will be no
alternative in this group.
Group-B : Total 26 questions to be set, out of which 22 to be answered. [At least 3 questions from each topic of Physical Geography to be given.]
Group-C : Total 12 questions to be given in this group, out of which 6 to be answered. [Total 4 questions at least 1 from each topic of Physical Geography
and 4 questions from Regional Geography to be given. 2 questions each from Physical Geography and Regional Geography to be answered.
4 questions, 2 each from Environmental Geography and Satellite imagery and Topographical map to be given. 1 question each from Environmental
Geography and Satellite imagery and Topographical map to be answered.]
Group-D : Total 8 questions to be given in this group. [1 out of 2 alternatives from each of Physical Geography, Environmental Geograpghy, Regional
Geography, Satellite imagery and Topographical map to be answered.]
Group-E : Total 8 questions to be given in this group. [4 questions to be given at least 1 from each topic of Physical Geography and 4 questions to be given
from Regional Geography. Total 4 questions including 2 questions each from Physical Geography and Regional Geography to be answered.]
Page 20
Distribution of marks and question pattern for Third Summative Evaluation/Selection Test
Type of Marks for Number of Total No. of Nature of question
Group
question each ques- questions to marks questions
tion be attempted to be set
Information based and
A MCQ type 01 14 concept oriented ques-
1 × 14 = 14 14
tions to be set (four op-
tions to be provided)
• Fill in the blanks
Very short • True/ false
B answer type • Column matching
01 22 1 × 22 = 22 26
question • One or two word
answer
Short ‘What’/ ‘where’ type
C answer type 02 06 2 × 6 = 12 12 questions
question
Short Compare / contrast / rea-
D soning type of questions
explanatory 03 04 3 × 4 = 12 08 to be set (three points to
answer type
question be asked)
• Preferably diagram-
Long based questions from
E 05 04 5 × 4 = 20 08
answer type Physical Geography,
question ‘how’/ ‘why’ ques-
tions from Regional
Geography
Outline map of India to
be provided and ques-
F *Map work 01 10 1 × 10 = 10 10 tions to be set to locate
and label geographical
features
Total = 60 Total = 90 Total = 78
* 10 questions to be provided for sightless candidates in lieu of map work. Each question carries 1 mark.
N. B.- This question pattern is indicative of Madhyamik Examination.
142
Page 21
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ì,˛ì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò Èı ˛ô)í≈õyò 90
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xhs˛Ó≈ì≈˛# ≤Ãhfl$˛!ì˛Ñ˛yú#ò õ)úƒyÎ˚Ïò ı ˛ô)í≈õyò 10
First Summative Evaluation : 40 marks Month of Evaluation : April
Internal Formative Evaluation : 10 marks
Second Summative Evaluation : 40 marks
Month of Evaluation : August
Internal Formative Evaluation : 10 marks
Third Summative Evaluation : 90 marks
Month of Evaluation : December
Internal Formative Evaluation : 10 marks
ì,˛ì˛#Î˚ ˛ôÎ≈yÎ˚Ñ˛!õÑ˛ õ)úƒyÎ˚ò È!v˛ˆÏ¢¡∫ˆÏÓ˚Ó˚ ≤ÃÌõ ¢ÆyˆÏ£Ó˚ xyˆÏÜ ˆòÁÎ˚y ÎyˆÏÓ òy–
Third Summative Evaluation is not to be held before first week of December.
143