Maths NCERT

1. v/;k; & 6 eSa rsjk xq.ku[kaM] xq.kt rw esjk
iz’u 1- fuEu iz’uksa ds mRrj fy[kks &
¼1½ os [kkus ftu ij pwgk dwnk &
mRrj & 2 ] 4 ] 6 ] 8 ] 10 ] 12 ] 14 ] 16 ] 18 ] 20 ] 22 ] 24 ] 26] 28
¼2½ os [kkus ftu ij fcYyh dwnh &
mRrj & 3] 6] 9] 12] 15] 18] 21] 24] 27]
¼3½ os [kkus ftu ij fcYyh vkSj pwgk nksuksa dwns &
mRrj & 6] 12] 18] 24
iz’u 2- irk djks & vxj fcYyh 5 ls 'kq: djds ,d ckj esa ikap [kkus dwnrh gS vkSj
pwgk 8 ls 'kq: djds ,d ckj esa pkj [kkus dwnrk gS rks D;k pwgk cp ik,xk
mRrj & fcYyh dwnsxh & 5] 10] 15] 20] 25] 30
pwgk dwnsxk & 8 ] 12] 16] 20] 24] 28
ugha pwgk dks fcYyh idM ysxh 20 ij
iz’u 3- rqeus dkSu lh la[;kvksa dks E;kÅ¡ ls cnyk
mRrj & geus 3] 6] 9] 12] 15] 18] 21] 24] 27] 30
bu la[;kvksa dks 3 ds xq.kt dgrs gSaA
iz’u 4- la[;k 4 vkSj 5 dks dksbZ Hkh 10 xq.kt fy[kks
mRrj & 4 ds xq.kt & 4] 8] 12] 16] 20] 24] 28] 32] 36] 40
5 ds xq.kt & 5] 10] 15] 20] 25] 30] 35] 40] 45] 50
iz'u 5- lk>k xq.kt fdls dgrs gSa 3 vkSj 5 ds lk>k xq.kt fy[kks
mRrj & 3 ds xq.kt & 3] 6] 9] 12] 15] 18] 21] 24] 27] 30
5 ds xq.kt & 5] 10] 15] 20] 25] 30] 35] 40] 45] 50
Lkk>k xq.kt & 15] 30
;fn dksbZ la[;k ¼xq.kt½ nksuksa la[;kvksa ds xq.ktksa esaa gks rks mls lk>k xq.kt
dgrs gSaA
iz'u 6- 2 vkSj 7 ds lk>k xq.kt fy[kks
mRrj & 2 ds xq.kt & 2] 4] 6] 8] 10] 12] 14] 16] 18] 20
7 ds xq.kt & 7] 14] 21] 28] 35] 42] 49] 56] 63] 70
Lkk>k xq.kt & 14 gSA

2. iz'u 7- 4] 6 vkSj 5 ds xq.kt dks xksyksa esa j[kdj fuEu iz’uksa ds mRrj fy[kks &
¼1½ 5 vkSj 6 ds dkSu ls lk>k xq.kt rqeus gjs
Hkkx esa fy[ks gSa
mRrj & 30
¼2½ 4 vkSj 6 ds dkSu ls lk>k xq.kt rqeus
ukjaxh Hkkx esa fy[ks gSa
mRrj & 12] 24] 36
¼3½ dkSu ls jax okys Hkkx esa rqeus 4] 6 vkSj 5
ds lk>k xq.kt fy[ks gSa
mRrj & chp okys lQsn Hkkx esaA
¼4½ 4] 6 vkS 5 dk lcls NksVk lk>k xq.kt dkSu lk gS
mRrj & 60
iz’u 8- fuEu iz’uksa ds mRrj fyf[k;s &
¼1½ bldh yackbZ fdruh gS
mRrj & bldh yackbZ 20 oxZ bdkbZ gSA
¼2½ 20 [kkuksa ls vyx rjg ls cuh ,d vk;r dks jaxks A
mRrj &
¼3½ rqeus tks vk;r jaxh mldh yackbZ vkSj pkaSMkbZ fdruh gS
mRrj & bl vk;r dh yackbZ 5 rFkk pkSaMkbZ 4 oxZ bdkbZ gSA
¼4½ rqe 20 [kkuksa dh vk;r dks fdrus rjhds ls jax ldrs gks bu lddks fxzM esa
jaxks vkSj jaxs gq, gj vk;r dh yackbZ vkSj pkSaMkbZ dks fy[kksA
12, 36
60
12, 36

3. iz’u 9- pkVZ Hkjks &
pwfM;ksa dh la[;k vyx vyx lewg tks ge cuk ldrs gSa
18 1, 2, 3, 6, 9, 18
24 1, 2, 3, 4, 6, 8, 12, 24
5 1, 5
9 1, 3, 9
7 1, 7
2 1, 2
10 1, 2, 5, 10
1 1
20 1, 2, 4, 5, 10, 20
13 1, 13
21 1, 3, 7, 21

4. iz’u 10- xq.ku[k.M gSa &
x 1 2 3 4 5 6 7 8 9 10 11 12
1 1 2 3 4 5 6 7 8 9 10 11 12
2 2 4 6 8 10 12 14 16 18 20 22 24
3 3 6 9 12 15 18 21 24 27 30 33 36
4 4 8 12 16 20 24 28 32 36 40 44 48
5 5 10 15 20 25 30 35 40 45 50 55 60
6 6 12 18 24 30 36 42 48 54 60 66 72
7 7 14 21 28 35 42 49 56 63 70 77 84
8 8 16 24 32 40 48 56 64 72 80 88 96
9 9 18 27 36 45 54 63 72 81 90 99 108
10 10 20 30 40 50 60 70 80 90 100 110 120
11 11 22 33 44 55 66 77 88 99 110 121 132
12 12 24 36 48 60 72 84 96 108 120 132 144
¼1½ 10 ds xq.ku[k.M dkSu ls gSa D;k rqe bls pkVZ ls dj ldrs gks
mRrj & 1] 2 ] 3 ] 4 ] 5 ] 6 ] 7 ] 8 ] 9 ] 10
¼2½ 36 ds xq.ku[kaM dkSu ls gSa
mRrj & 1] 2] 3 ] 4 ] 6 ] 9 ] 12] 18 ] 36
¼3½ bl xq.kk ds pkVZ ls 36 ds lHkh xq.ku[k.M <wa<ksA
mRrj & bldh yackbZ 20 oxZ bdkbZ gSA
¼4½ ,slh lcls cMh la[;k dkSUk lh gS ftlds xq.ku[k.M ge bl pkVZ ls ekywe dj
ldrs gkas
mRrj & 144
¼5½ mlls cMh la[;kvksa ds fy;s rqe D;k dj ldrs gks
mRrj & pkVZ dks vkSj vkxs c<kdj
12, 36
12, 36

5. iz’u 11- lk>k xq.ku[k.M fdls dgrs gSa 25 o 35 ds lk>k xq.ku[k.M dhft;s
mRrj & ftl la[;k dk Hkkx nksuksa l[;kavksa esa pyk tkrk gS vFkkZr tks xq.ku[k.M nksuksa
la[;k ds gksa mls lk>k xq.ku[k.M dgrs gSaA
25 35
iz’u 12- 40 o 60 ds lk>k xq.ku[k.M dhft;s
mRrj &
40 60
iz’u 13- xq.ku[k.M isM+
D;k rqe 24 dk xq.ku[k.M isM fdrus rjhdksa ls cuks ldrs gks muesa ls rhu
dks uhps cukvks &
nwljh la[;kvksa ds fy, Hkh xq.ku[k.M isM cukus dh dksf’k’k djks
1 , 1,
5, 5 5, 7,
25 35
1 ,2, 4,
5, 8, 10
, 20, 40
1, 2, 3, 4
5, 6, 10,
12, 15,
30, 60
1, 2,
4, 5,
10
3 3
9 2
3
18
3 2
6 3
3
18
2 2
4 3
24
4 3
12 2
24
4 3
6 2
12 2
24
3 2

6. iz’u 14- ikdZ dk jkLrk &
¼1½ vuq ds ?kj esa ,d ikdZ gS ml ikdZ ds chp esa ,d jkLrk gS mUgksusas jkLrs dks 2
QhV] 3 QhV vkSj 5 QhV dh Vkbyksa ls Vkby djus dk QSlyk fd;k
feL=h us igyh iafDr dks 2 QhV dh Vkby ls nwljh iafDr dks 3 QhV dh Vkby
ls vkSj rhljh iafDr dks 5 QhV dh Vkby ls Vkby fd;kA feL=h us fdlh Hkh
Vkby dks ugha dkVkA jkLrs dh yackbZ de ls de fdruh gS
mRrj & jkLrs dh yackbZ 30 QhV gksxhA D;ksafd 2x3x5 = 30
¼2½ eukst us ,d u;k ?kj cuk;k gSA og Q’kZ ij Vkby fcNkuk pkgrk gSA dejs dk
vkdkj 9 QhV X 12 QhV gSA cktkj esa rhu rjQ dh pkSdksj Vkbysa gSa
1QqVX1QqV] 2 QqV X 2 QqV vkSj 3 QqV X 3 QqVA mls dkSu ls vkdkj dh
Vkby [kjhnuh pkfg, rkfd og fcuk dkVs mUgsa fcNk lds
mRrj & pawfd dejs dk vkdkj ¾ 9 QhV X 12 QhV ¾ 108 oxZ QhV
vr% Vkby dk iwjk djus ds fy, Vkby dk
108 » 1 ¼1 QqV X 1 QqV½ ¾ 108 Vkby pkfg, gksaxh
108 » 4 ¼2 QqV X 2 QqV½ ¾ 27 Vkby pkfg, gksaxh
108 » 9 ¼3 QqV X 3 QqV½ ¾ 12 Vkby pkfg, gksaxh
¼3½ jkuh] ulhek vkSj xhrk ,d nwljs ds ikl jgrh gSa muds ?kj ls lMd dh nwjh
90 QqV gS mUgksaus ?j ls lMd rd Vkby djus dk QSlyk fy;kA mu lcus
vyx&vyx fMtkbu vkSj yackbZ dh Vkbysa [kjhnhaA jkuh us lcls NksVh VkbZy
[kjhnh] xhrk us chp ds vkdkj dh Vkby [kjhnh vkSj ulhek us lcls yach
Vkby [kjhnhA vxj os fcuk fdlh Vkby dks dkVs jkLrs dks Vkby dj ldrh gSa
rks rhuksa us fdl vkdkj dh Vkby [kjhnha rhu vyx vyx rjhds crkvksA
le>kvks fd rqEgsa ;g mRrj dSls feyrk gS
mRrj & pawfd jkLrs dh nwjh ¾ 90 QhV
vr% jkLrs dk iwjk djus ds fy, Vkby dk mi;ksx gksxk
jkuh 90 » 1 ¼1 QqV X 1 QqV½ ¾ 90 Vkby pkfg, gksaxh
ulhek 90 » 9 ¼3 QqV X 3 QqV½ ¾ 10 Vkby pkfg, gksaxh
xhrk 90 » 15 ¼3 QqV X 5 QqV½ ¾ 6 Vkby pkfg, gksaxh