Math
MwYZ
Lecture-01
Av‡jvP¨
welqÑmsL¨vi
aviYv (AsK, †gŠwjK I mn †gŠwjK
msL¨v,g~j` I Ag~j`,c~Y©msL¨v)
eM©g~j, fMœvsk, M.mv.¸ I j mv ¸|
cvwUMwYZ
we¯ÍvwiZ
Av‡jvPbvt-
msL¨vi aviYv (AsK, †gŠwjK I mn†gŠwjK
msL¨v, g~j` I Ag~j`, c~Y©msL¨v) BZ¨vw` wel‡q wkÿK gnv`q K¬v‡k we¯ÍvwiZfv‡e
we‡kl Av‡jvPbv Ki‡ebt-
eM©g~j
eM©g~jt-
‡Kvb msL¨v‡K HB msL¨v Øviv ¸b Ki‡j †h ¸bdj cvIqv hvq Zv‡K HB
msL¨vi eM© ejv nq| Ges H msL¨vwU‡K ¸YdjwUi eM©g~j ejv nq|
c~Y©eM©tчh
msL¨vi eM©g~j †Kvb c~Y©msL¨v ev fMœs‡ki mgvb Zv‡K c~Y©eM© ejv nq| †hgb-
4,16,81, 1/16, 16/25, 0.09 BZ¨vw`|
D‡jøL¨ †h, `yB cÖwµqvq eM©g~j wbY©q Kiv
hvqt- 1.fvM cÖwµqvq
2.
Drcv`K cÖwµqvq
1. 0.1 Gi eM©g~j KZ? DËit-0.3162
2. (0.003) 2
= KZ?? DËit-0.000009
3. †Kvb msL¨vi eM©g~‡ji mv‡_ 10 †hvM
Ki‡j †hvMdj 4- Gi eM© n‡e? DËit-36
4. 6558 Gi mv‡_ †Kvb ÿz`ªËg msL¨v †hvM
Ki‡j †hvMdj GKwU c~Y©eM© msL¨v n‡e| DËit-3
5. 20740 Rb ˆmb¨‡K eM©vKv‡i mvRv‡Z wM‡q
4 Rb AwZwi³ nq| cÖwZ mvwi‡Z ˆmb¨ msL¨v KZ? DËit-144
6. 87080 Rb ˆmb¨ †_‡K KZRb ˆmb¨ miv‡j
ˆmb¨`j‡K eM©vKv‡i mvRv‡bv hv‡e? DËit-424
7. GKwU ¯‹z‡j Qv·`I wWªj Kivi mgq
8,10,12 mvwi‡Z mvRv‡bv hvq Avevi eM©vKv‡iI mvRv‡bv hvq| H ¯‹z‡j Kgc‡ÿ KZRb QvÎ
Av‡Q?? DËit-3600
8. ‡Kv‡bv ‡kÖwY‡Z hZRb wkÿv_x© cÖ‡Z¨‡K
ZZUvKv K‡i cÖ`vb Ki‡j †gvU 6561 UvKv nq| QvÎ msL¨v KZ??? DËit-30
9. GKwU msL¨vi 3¸‡bi mv‡_ 2¸b †hvM Ki‡j
90 nq| msL¨vwU KZ? DËit-18
10. 0.0009 Gi eM©g~j = KZ? DËit-0.03
fMœvsk
ØfMœvs‡ki
j.mv.¸ =je ¸‡jvi j.mv.¸/ ni ¸‡jvi M.mv.¸
ØfMœvs‡ki
M.mv.¸ = je ¸‡jvi M.mv.¸/ ni ¸‡jvi j.mv.¸
1. 1/4, 3/16, 9/20 Gi mvaviY ¸wYZK
wb‡Pi †KvbwU? DËit-9/4
2. 5/7=KZ? DËit-7
3. †Kvb msL¨vi 2/7Ask 64-Gi mgvb? DËit-224
4.125 †K 2.5 Øviv fvM Ki‡j fvMdj
KZ? DËit-1.25
5. 0.001´0.01= KZ? DËit-0.00001
6. 108Gi 4/9 Ask= KZ?? DËit-48
7. †KvbwU me‡P‡q †QvU-2/11, 3/11, 2/13,
4/15 DËit-2/13
8. 4wU 1 UvKvi †bvU I 8 wU 2 UvKvi †bvU
GK‡Î 8wU 5 UvKvi †bv‡Ui KZ Ask? DËit-1/2
9.GKwU fMœv‡ki je I n‡ii mgywó 5 Ges
AšÍidj 1| fMœvskwU KZ? DËit-3/2
10.GKwU cÖK…Z fMœvs‡ki ni I j‡ei AšÍi 2,
ni I je Dfq †_‡K 3 we‡qvM Ki‡j †h fMœvsk cvIqv hvq Zvi m‡½ KZ †hvM Ki‡j †hvMdj
1 nq, fMœvskwU KZ? DËit-9/11
GQvov K¬vk 5g,6ô †kÖwYi eB †_‡K co‡Z
n‡e|
M.mv.¸ Ges j.mv.¸
1| ‡Kvb e„nËg msL¨v Øviv 105, 1001 Ges 2436 wbt‡k‡l wefvR¨?
K. 3 ÖL. 7 M. 11 N. 21
mgvavb: wb‡Y©q e„nËg msL¨v n‡e 105, 1001 Ges 2436 Gi M.mv.¸|
105 = 3 ´ 5 ´ 7
1001 = 7 ´ 11 ´ 13
2436 = 2 ´ 2 ´ 3 ´ 7 ´ 29
\ wb‡Y©q
e„nËg msL¨v = 7
2| 30wU Avg Ges 36wU wjPz m‡e©v”P KZRb evj‡Ki g‡a¨ mgvbfv‡e
fvM Kiv †h‡Z cv‡i?
K. 3 Rb L. 5 Rb ÖM. 6 Rb N.
9 Rb
mgvavb: wb‡Y©q evj‡Ki msL¨v n‡e 30 I 36 Gi M.mv.¸|
\ wb‡Y©q
evjK msL¨v 6 Rb|
3| ‡Kvb e„nËg msL¨v w`‡q 102 I 186 †K fvM Ki‡j cÖ‡Z¨Kevi 6
Aewkó _vK‡e?
ÖK. 12 L. 15 M. 16 N. 22
mgvavb: 102-6 = 96, 186-6=180
wb‡Y©q e„nËg msL¨v n‡e 96 I 180 Gi M.mv.¸|
\ wb‡Y©q
e„nËg msL¨v = 12|
4| cÖ_g I wØZxq msL¨vi ¸Ydj 42 Ges wØZxq I Z…Zxq msL¨vi ¸Ydj
49| wØZxq msL¨vwU KZ?
K. 5 L. 6 ÖM. 7 N. 8
mgvavb: 42 I 49 Gi M.mv.¸ n‡e wb‡Y©q wØZxq msL¨v|
\ wb‡Y©q
wØZxq msL¨v = 7
5| K GKwU †gŠwjK msL¨v Ges K, L Øviv wefvR¨ bq| K Ges L Gi
j.mv.¸ KZ?
K. 1 L. 1K ÖM. KL N. 1L
6| ‡Kvb ÿz`ªZg msL¨v 12, 15, 20 Ges 27 Øviv wbt‡k‡l wefvR¨?
K. 360 L. 480 M. 520 Ö N. 540
mgvavb: 
\ wb‡Y©q
ÿz`ªZg msL¨v = 2 ´ 2 ´ 3 ´ 5 ´ 9 = 540|
7| 4, 6, 10 I 18 Rb wkïi g‡a¨ Kgc‡ÿ KZ¸‡jv Kgjv m¤ú~Y©fv‡e
eÈb Kiv hvq?
K. 16 L. 60 M. 240 ÖN. 180
mgvavb: 4, 6, 10 I 18 Gi j.mv.¸ n‡e wb‡Y©q Kgjvi msL¨v|
\ 4, 6, 10
I 18 Gi j.mv.¸ = 2 ´ 3 ´ 2 ´ 5 ´ 3 = 180|
8| †Kvb †mbvevwnbx‡Z hw` Av‡iv 11 Rb ˆmb¨ wb‡qvM Kiv †hZ Z‡e
Zv‡`i‡K 20, 30, 40, 50, 60 mvwi‡Z `uvo Kiv‡bv †hZ| H †mbvevwnbx‡Z KZRb ˆmb¨
wQj?
K. 59 Rb L. 79 Rb ÖM. 589 Rb N. 619
mgvavb: 
20, 30, 40, 50 I 60 Gi j.mv.¸ = 2 ´ 2 ´ 3 ´ 5 ´ 2 ´ 5 = 600|
\ wb‡Y©q
‰mb¨ msL¨v = (600-11) = 589 Rb|
9| cuvPwU NÈv GK‡Î †e‡R h_vµ‡g 3, 5, 7, 8 I 10 †m‡KÛ AšÍi
AšÍi evR‡Z jvMj| KZÿY c‡i NÈv¸‡jv cybivq GK‡Î evR‡e?
K. 10 wgwbU L. 90 †m‡KÛ
ÖM. 14
wgwbU N. 240 †m‡KÛ
mgvavb: 
3, 5, 7, 8 Ges 10 Gi j.mv.¸ = 2 ´ 5 ´ 3 ´ 7 ´ 4 = 840
NÈv¸‡jv cybivq GK‡Î evR‡e = 840 †m. = 
wgwbU = 14 wgwbU ci|
wgwbU = 14 wgwbU ci|
10| GKwU †Nvovi Mvwoi PvKvi cwiwa 3 wgUvi, wcQ‡bi PvKvi
cwiwa 4 wgUvi| MvwowU KZ c_ †M‡j mvg‡bi PvKv wcQ‡bi PvKvi †P‡q 100 evi †ewk
Nyi‡e?
K. 1 wK.wg. ÖL. 1.2
wK.wg.
M. 1.6 wK.wg. N. 1.8 wK.wg.
mgvavb: mvg‡bi PvKv wcQ‡bi PvKvi †P‡q 1 evi †ewk Nyi‡j
AwZµvšÍ `~iZ¡ n‡e 3 I 4 Gi j.mv.¸ Gi mgvb|
3 I 4 Gi j.mv.¸ = 12
1 evi †ewk Nyi‡j AwZµvšÍ `~iZ¡ 12 wgUvi
100 Ó
Ó Ó
Ó Ó (12 ´ 100) wgUvi ev 1200 wgUvi ev 1.2 wK.wg.
11| `yBwU msL¨vi M.mv.¸ I j.mv.¸- Gi ¸Ydj msL¨v `yBwUiÑ
K. ‡hvMd‡ji mgvb ÖL. ¸Yd‡ji mgvb
M. we‡qvMd‡ji
mgvb N. fvMd‡ji mgvb
12| `yBwU msL¨vi ¸Ydj 4235 Ges Zv‡`i j.mv.¸ 385| msL¨v
`yBwUi M.mv.¸ KZ?
K. 17 L. 15 ÖM. 11 N. 13
mgvavb: j.mv.¸ ´ M.mv.¸ = msL¨v `ywUi ¸Ydj
385 ´ M.mv.¸ =
4235
M.mv.¸ = 
= 11
= 11
13| `ywU msL¨vi M.mv.¸ 16 Ges j.mv.¸ 192| GKwU msL¨v 48 n‡j
Aci msL¨vwU KZ?
K. 60 L. 62 ÖM. 64 N.
80
mgvavb: msL¨v؇qi ¸Ydj = j.mv.¸ ´ M.mv.¸ =
16´192
\ Aci msL¨vwU = 
= 64
= 64
14| `yBwU msL¨vi AbycvZ 15 : 11| Zv‡`i M.mv.¸ 13 n‡j,
msL¨vØq wbY©q Kiæb|
ÖK. 195 Ges
143 L. 190 Ges 143
M. 195 Ges 145 N. †KvbwU bq
mgvavb: wb‡Y©q msL¨vØq = (15 ´ 13) Ges (11 ´ 13) = 195
Ges 143|
15| `yBwU msL¨vi AbycvZ 5 : 7 Ges Zv‡`i M.mv.¸ 6 n‡j, msL¨v
`yBwUi j.mv.¸ KZ?
ÖK.
210 L. 180 M. 150 N.
120
mgvavb : †h‡nZz msa¨v؇qi AbycvZ 5 : 7 Ges M.mv.¸ 6
j.mv.¸ = AbycvZ؇qi ¸Ydj ´ M.mv.¸ = 5 ´ 7 ´ 6 = 210
Abykxjbt-
1. `ywU msL¨vi M mv ¸ 11 Ges jmv¸ 7700| GKwU msL¨v 275 n‡j AciwU KZ?
DËi-308
2. `ywU msL¨vi ¸bdj 1536, msL¨v`ywUi jmv¸ 96 n‡j Mmv¸ KZ? DËi-16
3.2wU Now h_vµ‡g 10 I 25 wgwbU AšÍi ev‡R| GKevi GK‡Î evRvi ci Avevi
KLb GK‡Î evR‡e ? DËi-50wgwbU
4. ‡Kvb ÿz`ªËg msL¨v‡K 3,4I 5 Øviv fvM Ki‡j wbt‡k‡l wefvR¨? DËi-60
5. 999999 Gi mv‡_ †Kvb ÿy`ªËg msL¨v †hvM Ki‡j †hvMdj 2,3,4,5,I 6 Øviv
wbt‡k‡l wefvR¨ n‡e ? DËi-21
6. `ywU msL¨vi AbycvZ 5t6 , Zv‡`I M mv ¸ 4 n‡j , msL¨v `ywUi j mv My
KZ? DËi-120
7. `ywU msL¨vi Mmv¸ , we‡qvMdj, jmv¸ h_vµ‡g 12, 60, Ges 2448| msL¨v
`ywU KZ? DËi-188,204
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