11 Maths NcertSolutions Chapter 15 1

8/18/2019 11 Maths NcertSolutions Chapter 15 1

1/14

Jcbptnr 2> ‚ Ztbtmstmjs

Nxnrjmsn 2>.2

Runstmif 2;

Dmfe tcn onbf envmbtmif baiut tcn onbf dir tcn ebtb

5, 5, 55

Bfswnr

Ucn lmvnf ebtb ms

:3, >, 4:, 54, >5, 55

Onbf id tcn lmvnf ebtb,

Ucn envmbtmifs id tcn rnspnjtmvn iasnrvbtmifs drio tcn onbf brn

‚21, 17, ‚1, ‚27, ‚3, >, 2:, ‚5, 5, ‚4

Ucn basi`utn vb`uns id tcn envmbtmifs, m.n. , brn

21, 17, 1, 27, 3, >, 2:, 5, 5, 4

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2/14

Ucn rnqumrne onbf envmbtmif baiut tcn onbf ms

Runstmif :;

Dmfe tcn onbf envmbtmif baiut tcn onembf dir tcn ebtb.

2:, 2, ‚7.>, ‚7.>, 7.>, 1.>, 1.>, :.>, :.>, 5.>

Ucn basi`utn vb`uns id tcn envmbtmifs, , brn

:.>, 1.>, 1.>, 2.>, 7.>, 7.>, 7.>, 1.>, 1.>, :.>, :.>, 5.>

Ucn rnqumrne onbf envmbtmif baiut tcn onembf ms

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3/14

Runstmif 5;

Dmfe tcn onbf envmbtmif baiut tcn onembf dir tcn ebtb

:4, , >:, 54, >2, 5=

Bfswnr

Ucn lmvnf ebtb ms

:4, , >:, 54, >2, 5=

Cnrn, tcn fuoanr id iasnrvbtmifs ms 27, wcmjc ms nvnf.

Brrbflmfl tcn ebtb mf bsjnfemfl irenr, wn iatbmf

:4, 51, 5>, 54, 54, 5=, >2, >:, 47, , ‚>.>, ‚1.>, ‚2.>, ‚2.>, 2.>, :.>, >.>, 21.>, 15.>

Ucn basi`utn vb`uns id tcn envmbtmifs, , brn

22.>, >.>, 1.>, 2.>, 2.>, 2.>, :.>, >.>, 21.>, 15.>

Ucus, tcn rnqumrne onbf envmbtmif baiut tcn onembf ms





4/14

Runstmif >;

Dmfe tcn onbf envmbtmif baiut tcn onbf dir tcn ebtb.

Bfswnr

x m d m d m x m

> < :> = 4:

27 5 57 5 24

2> 4 =7 2 4

17 : 47 4 23

1> > 21> 22 >>

1> :>7 2>3

x m > 27 2> 17 1>

d m < 5 4 : >





5/14


6/14

Runstmif < = 27 21 2>

d m 3 4 1 1 1 4

Bfswnr

Ucn lmvnf iasnrvbtmifs brn b`rnbey mf bsjnfemfl irenr.

Beemfl b ji`uof jirrnspifemfl ti juou`btmvn drnqunfjmns id tcn lmvnf ebtb, wn iatbmf

tcn di``iwmfl tba`n.

x m d m j . d .

> 3 3

< 4 25

= 1 24

27 1 23

21 1 17

2> 4 14

Cnrn, F ? 14, wcmjc ms nvnf.

Onembf ms tcn onbf id 2: tc bfe 25 tc iasnrvbtmifs. Aitc id tcnsn iasnrvbtmifs `mn mf tcn

juou`btmvn drnqunfjy 25, dir wcmjc tcn jirrnspifemfl iasnrvbtmif ms


7/14

Ucn basiùtn vbùns id tcn envmbtmifs drio onembf, m.n. brn

|x m ‚ O | 1 7 1 : > 3

d m 3 4 1 1 1 4

d m |x m ‚ O |

24 7 5 4 27 53

bfe

Runstmif 3;

Dmfe tcn onbf envmbtmif baiut tcn onembf dir tcn ebtb

x m 2> 12 1< :7 :>

d m : > 4 < 3

Bfswnr

Ucn lmvnf iasnrvbtmifs brn b`rnbey mf bsjnfemfl irenr.Beemfl b jiùof jirrnspifemfl ti juou`btmvn drnqunfjmns id tcn lmvnf ebtb, wn iatbmf

tcn di`ìwmfl tba`n.

x m d m j . d .

2> : :

12 > 3

1< 4 25

:7 < 12

:> 3 1=

Cnrn, F ? 1=, wcmjc ms iee.www.tmwbrmbjbenoy. jio

Dijus if drnn neujbtmif


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8/14

iasnrvbtmif ? 2> tc iasnrvbtmif

Ucms iasnrvbtmif `mns mf tcn juou`btmvn drnqunfjy 12, dir wcmjc tcn jirrnspifemfliasnrvbtmif ms :7.∵ Onembf ? :7

Ucn basi`utn vb`uns id tcn envmbtmifs drio onembf, m.n. brn

|x m ‚ O | 2> = : 7 >

d m : > 4 < 3

d m |x m ‚ O | 5> 5> 23 7 57

∵

Runstmif =;

Dmfe tcn onbf envmbtmif baiut tcn onbf dir tcn ebtb.

Mfjion pnr eby Fuoanr id pnrsifs

7-277 5

277-177 3

177-:77 =

:77-577 27

577->77 <

>77-477 >

477-


9/14

7 177 :73 21:1

277 ‚ 177 3 2>7 2177 173 2445

177 ‚ :77 = 1>7 11>7 273 =7 :>77 3 37

577 ‚ >77 < 5>7 :2>7 =1 455

>77 ‚ 477 > >>7 17 2=1 =47

477 ‚ 7 1477 1=1 2243

7 :=1 227 2


10/14

=>-27> =

27>-22> 2:

22>-21> 14

21>-2:> :7

2:>-25> 21

25>-2>> 27

Bfswnr

Ucn di``iwmfl tba`n ms dirone.

Cnmlct mf jos Fuoanr id aiys d m Ome-pimft x m d m x m

=>-27> = 277 =77 1>.: 11-22> 2: 227 25:7 2>.: 2=3.=

22>-21> 14 217 :217 >.: 2:-2:> :7 2:7 :=77 5.< 252

2:>-25> 21 257 2437 25.< 2-2>> 27 2>7 2>77 15.< 15<

Cnrn,

Runstmif 22;

Dmfe tcn onbf envmbtmif baiut onembf dir tcn di``iwmfl ebtb;



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11/14

Obrhs Fuoanr id lmr`s

7-27 4

27-17 3

17-:7 25

:7-57 24

57->7 5

>7-47 1

Bfswnr

Ucn di``iwmfl tba`n ms dirone.

Obrhs Fuoanr idaiys d m

Juou`btmvndrnqunfjy (j.d.)

Ome-pimft x m

| x m ‚One. |

d m | x m ‚One. |

7-27 4 4 > 11.3> 2: 21.3> 271.3

17-:7 25 13 1> 1.3> :=.=

:7-57 24 55 :> 225.5

57->7 5 53 5> 2 43.4

>7-47 1 >7 >> 1 >5.:

>7 >2 tc mtno ms 17 ‚ :7.

Ucnrndirn, 17 ‚ :7 ms tcn onembf j`bss.Mt ms hfiwf tcbt,



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12/14

Cnrn, ` ? 17, J ? 25, d ? 25, c ? 27, bfe F ? >7

∵ Onembf ?

Ucus, onbf envmbtmif baiut tcn onembf ms lmvnf ay,

Runstmif 21;

Jb`ju`btn tcn onbf envmbtmif baiut onembf bln dir tcn bln emstrmautmif id 277 pnrsifs

lmvnf anìw;

Bln Fuoanr

24-17 >

12-1> 4

14-:7 21

:2-:> 25

:4-57 14

52-5> 21

54->7 24

>2->> =

Bfswnr

Ucn lmvnf ebtb ms fit jiftmfuius. Ucnrndirn, mt cbs ti an jifvnrtne mfti jiftmfuius

drnqunfjy emstrmautmif ay suatrbjtmfl 7.> drio tcn ìwnr `momt bfe beemfl 7.> ti tcn

uppnr `momt id nbjc j`bss mftnrvb`.Ucn tba`n ms dirone bs di`ìws.



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13/14

Bln Fuoanr

d m

Juou`btmvn

drnqunfjy (j.d.)

Ome-

pimft x m

| x m ‚

One. |

d m | x m ‚

One. |

2>.>-

17.>

> > 23 17 277

17.>-

1>.>

4 22 1: 2> =7

1>.>-

:7.>

21 1: 13 27 217

:7.>-

:>.>

25 :< :: > .>-

57.>

14 4: :3 7 7

57.>-

5>.>

21 5: > 47

5>.>-

>7.>

24 =2 53 27 247

>7.>-

>>.>

= 277 >: 2> 2:>

277

Ucn j`bss mftnrvb` jiftbmfmfl tcn ir >7 tc mtno ms :>.> ‚ 57.>.

Ucnrndirn, :>.> ‚ 57.> ms tcn onembf j`bss.Mt ms hfiwf tcbt,



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14/14

Cnrn, ` ? :>.>, J ? :, bfe F ? 277

Ucus, onbf envmbtmif baiut tcn onembf ms lmvnf ay,


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11 Maths NcertSolutions Chapter 15 1

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