TAMILNADU-Mathematics Sample Paper-1-SOLUTION-Class-10 Question Paper

7/23/2019 TAMILNADU-Mathematics Sample Paper-1-SOLUTION-Class-10 Question Paper

1/25

[D ] | IB[MFIB[GCS

Sbipnf Qbpfr 2 S`nutg`d

ww.t`ppfrnfbrdgdj.cì 2

[bign Dbku E`brk

Cnbss ] Ibtmfibtgcs


SFC[G@D-G (26 Ibrls)

D`tf?

g. Bdswfr bnn tmf 26 qufstg`ds.

gg. Cm``sf tmf c`rrfct bdswfr hrì tmf jgvfd hùr bntfrdbtgvfs bdk wrgtf tmf `ptg`ds c`kf

bdk tmf c`rrfsp`dkgdj bdswfr.

2. C`rrfct Bdswfr? B

X`nuif 9 Ebsf brfb Mfgjmt

[mus, tmf v`nuif gs? =1 6 9 ;11 ci3

5. C`rrfct Bdswfr? E

2 + 5 + 3 + . + d 9 l

25

d dl

3 3 3 3

53

53 3

53 3 3

53 3 3 3

53 3 3 3 3

C`dsgkfr 2 5 3 ... ?

Nft us èsfrvf tmf h`nn`wgdj pbttfrd?

2 2 2

2 5 7 2 5

2 5 3 38 2 5 3

2 5 3 ; 211 2 5 3 ;

Fxpbdkgdj tmgs pbttfrd wf jft,

2 5 3 ; ... 2 5 3 ; ...

d

d d

[mus

3 3 3 3

5

5

2 5 3 ...

2

5

d

d dl


Zmfd fbcm tfri `h b J.Q. gs iuntgpngfk ey b c`dstbdt, tmf rfsuntbdt gs b J.Q.


2/25

[D ] | IB[MFIB[GCS



;. C`rrfct Bdswfr? E

Jgvfd? c`s;x sgd;x

9 (c`s5x + sgd5x)(c`s5x sgd5x)

9 2(c`s5x sgd5x)

9 c`s5x (2 c`s5x)

9 5c`s5x 2

6. C`rrfct Bdswfr? K

[mf rbtg` `h tmf brfbs `h tw` sgignbr trgbdjnfs gs fqubn t` tmf rbtg` `h tmf squbrfs `h tmfgr

c`rrfsp`dkgdj sgkfs.

[mf rbtg` `h tmf c`rrfsp`dkgdj sgkfs gs 5 ? 3.

[mus, tmf rbtg` `h tmf brfbs `h tmf sgignbr trgbdjnfs gs ; ? 7.


d(B E) 9 d(B) + d(E) d(B E)

;1 9 51 + 31 d(B E)

d(B E) 9 21

:. C`rrfct Bdswfr? K

[mf ibtrgx `d tmf U.M.S. gs?

5 2 = ;;

2 5 ; =

Fqubtgdj tmf fnfifdts gd tmf 5dkr`w bdk 2stc`nuid `h tmf ibtrgcfs `d tmf N.M.S. bdk

U.M.S. wf jft,

x 9 ;.

=. C`rrfct Bdswfr? C

Jgvfd? (2 + tbd5)sgd5

(2 + tbd5)sgd5 9 sfc5 sgd5 95

2

c`s sgd59

5

5

sgd

c`s 9 tbd5

7. C`rrfct Bdswfr? B

Xbrgbdcf gs squbrf `h stbdkbrk kfvgbtg`d. [mus, gh stbdkbrk kfvgbtg`d gs 2.8, vbrgbdcf gs

5.68.


3/25

[D ] | IB[MFIB[GCS



21.C`rrfct Bdswfr? C

H`r tmf systfi `h fqubtg`ds,

b2x + e2y + c29 1

b5x + e5y + c59 1

Gh 2 2 2

5 5 5

b e c

b e c tmfd tmf systfi `h fqubtg`ds mbs d` s`nutg`d bdk tmfgr jrbpms k` d`t

gdtfrsfct bt bdy p`gdt.

22.C`rrfct Bdswfr? E

Vsgdj sfctg`d h`riunb, tmf c`-`rkgdbtfs `h tmf p`gdt brf?

2 3 3 2 2 7 3 3 1 1, , 1,1

2 3 2 3 ; ;

25.C`rrfct Bdswfr? K

Gd BEC, iE 9 ;1 bdk iC 9 81

[mf sui `h bnn bdjnfs `h b trgbdjnf gs 2=1.

[mus,

iB +iE + iC 9 2=1

iB + ;1 + 81 9 2=1

iB 9 =1

Bcc`rkgdj t` tmf C`dvfrsf `h Bdjnf Egsfct`r [mf`rfi, BK gs tmf egsfct`r `h bdjnf B.

[mus,

iEBK 92

5B

iEBK 92

5 =1

iEBK 9 ;1.

23.C`rrfct Bdswfr? K

[`tbn ebnns 9 25

Ufk ebnns 9 3

[mus, pr`ebegngty tmbt tmf ebnn gs rfk 9 3 225 ;

.

[mus, pr`ebegngty tmbt tmf ebnn gs d`t rfk 92 3

2; ;

.

2;.C`rrfct Bdswfr? K

Gh p(x) gs kgvgkfk ey (x + b), tmfd tmf rfibgdkfr gs p(b).

[mus, wmfd p(x) 9 x55x + : gs kgvgkfk ey (x + ;), tmfd tmf rfibgdkfr gs p(;).

p(;) 9 (;)55(;) + : 9 28 + = + : 9 32.


4/25

[D ] | IB[MFIB[GCS


ww.t`ppfrnfbrdgdj.cì ;

26.C`rrfct Bdswfr? E

B hudctg`d h? BE gs cbnnfk b `df-`df bdk `dt` `r b egofctgvf hudctg`d gh h gs e`tm b `df-

`df bdk bd `dt` hudctg`d. [mus, h? BE gs `df-`df bdk `dt` gh h ibps kgstgdct fnfifdts

`h B gdt` kgstgdct gibjfs gd E bdk fvfry fnfifdt gd E gs bd gibjf `h sìf fnfifdt gd B.Gh h? BE gs b egofctgvf hudctg`d bdk gh B bdk E brf hgdgtf sfts, tmfd tmf cbrkgdbngtgfs `h B

bdk E brf sbif.

[mfrfh`rf, tmf duiefr `h fnfifdts gd E gs bns` 21.

SFC[G@D-GG (51 Ibrls)

D`tf?

g. Bdswfr 21 qufstg`ds gd bnn.

gg. Rufstg`d duiefr 31 gs cìpuns`ry. Sfnfct bdy 7 qufstg`ds hrì tmf hgrst 2; qufstg`ds.

ggg. Fbcm qufstg`d cbrrgfs tw` ibrls.

28.Hrì tmf kgbjrbi sm`wd,

Fvfry fnfifdt gd sft B efn`djs t` E.

[mfrf B E 9 {z | z B `r z E}

Mfdcf, B E 9 E.

2:.Jgvfd 32 5 2d d

db d

6 6 3 =

6= = 3 22

=

2 5 6 2 5 8 2638

2 5 = 2 5 7 2=;35

b

b

2=.[mf ibtrgx gs jgvfd bs?

5 3 2 6 2 5

7 6 : 2 28 8B

H`r b ibtrgx B, E gs cbnnfk tmf bkkgtgvf gdvfrsf `h B gh E + B 9 B + E 91.

Sgdcf B + (B) 9 (B) + B 9 1, B gs tmf bkkgtgvf gdvfrsf `h B.

[mf bkkgtgvf gdvfrsf `h b ibtrgx gs tmf dfjbtgvf ibtrgx. [mus, tmf bkkgtgvf gdvfrsf `h

tmf jgvfd ibtrgx gs?

2 5

28 8B

27.Kìbgd gs tmf sft `h bnn x-vbnufs bdk Ubdjf gs tmf sft `h bnn y-vbnufs.

Kìbgd `h H9 {2, 5, ;, 6, 3}

Ubdjf `h H 9 {3, 6, :, 7, 2}


5/25

[D ] | IB[MFIB[GCS



51.

5

5

5

5

2 2

22

2 22

2

2

x x

x x

x xx x

x x

x x

x

x

52.[mf duiefr `h r`ws gd tmf ibtrgx gs 3.

[mf duiefr `h c`nuids gd tmf ibtrgx gs 3.

[mf `rkfr `h b ibtrgx wgtm i r`ws bdk d c`nuids gs sbgk t` ef i d.

[mus, tmf `rkfr `h tmgs ibtrgx gs 3 3.

55.C`dsgkfr tmf jgvfd fxprfssg`ds,

(b 2)6(b + 3)5, (b 5)5(b 2)3(b + 3);

[mf c`ii`d hbct`r h`r tmf be`vf fxprfssg`ds gs? (b 2)3(b + 3)5.

[mus, J.C.K. gs (b 2)3(b + 3)5.

53.[mf brfb `h tmf trgbdjnf wm`sf vfrtgcfs brf 2 2 5 5 3 3, , , bdk ,x y x y x y gs?

2 5 3 5 3 2 3 2 52

+5

x y y x y y x y y

[mus, tmf brfb `h tmf trgbdjnf wm`sf vfrtgcfs brf ;, 3 , 2, 5 bdk 5, 2 gs?

2

; 5 2 2 2 3 5 3 5 1 sq. udgts5

Sgdcf tmf brfb h tmf trgbdjnf wgtm vfrtgcfs ;, 3 , 2, 5 bdk 5, 2

gs zfr , tmf sft h p gdts ;, 3 , 2, 5 bdk 5, 2 brf c nngdfbr.

5;.[mf sn`pf `h b ngdf wm`sf bdjnf `h gdcngdbtg`d gs i 9 tbd

[mus, tmf bdjnf `h gdcngdbtg`d `h tmf ngdf wm`sf sn`pf gs 3 gs?

3 tbd

tbd81 tbd

81


6/25

[D ] | IB[MFIB[GCS



56.Mfrf, N 9 68.6 bdk S 9 25.6

[mus, Ubdjf 9 68.6 25.6 9 ;;

Bdk, C`-fhhgcgfdt `h rbdjf 968.6 25.6 ;;

1.8;

68.6 25.6 87

58.C`dsgkfr tmf jgvfd sfrgfs? 2 + 5 + 3 + .+ ;6 .

2

2

5

d

l

d dl

Mfrf, d 9 ;6.

[mus, tmf sui `h tmf jgvfd sfrgfs gs? ;6 ;6 2

2136.5

S

5:.C`dsgkfr BEC?Mfrf, BK 9 = ci, KE 9 7 ci bdk BF 9 = ci.

Gd BEC, KF||EC

Bcc`rkgdj t` [mbnfs [mf`rfi,

8 =

7 FC

= 7

825 ci

BK BF

KE FC

FC

FC

[mus, BC 9 BF + FC 9 = +25 9 51 ci.

5=.C`dsgkfr tmf cyngdkfr?

C.S.B. `h b cyngdkfr wgtm rbkgus r bdk mfgjmt m gs 5rm

[.S.B. `h b cyngdkfr wgtm rbkgus r bdk mfgjmt m gs 5r (m + r)

Mfrf, r 9 2; ci bdk m 9 = ci.

[mus, 555

C.S.B. 5 2; = 5 2; = :1; ci:

Bdk, 555

[.S.B. 5 2; = 2; 5 2; 55 2738 ci:

[mus, 5C.S.B. :1; ci bdk 5[.S.B. 2738 ci .


7/25

[D ] | IB[MFIB[GCS


ww.t`ppfrnfbrdgdj.c`i :

57.C`dsgkfr tmf N.M.S `hsgd

2 c`s

5 5

5

5 5

5

5 5

sgd 2 c`sN.M.S. \Iuntgpnygdj bdk kgvgkgdj ey 2 c`s Y

2 c`s 2 c`s

sgd sgd c`s 2 c`s

sgd sgd c`s \sgd c`s 2Y

sgd

sgd sgd c`s

sgd sgd

b e b e b e

2 c`s

sgd sgd

2 c`sc`sfc c`t c`sfc bdk c`t

sgd sgdU.M.S.

Mfdcf pr`vfk.

31.Snbdt mfgjmt () 9: i, Nft r 9 rbkgus `h tmf ebsf.

Cgrcuihfrfdcf `h tmf ebsf 9 == i

5r 9 ==i

r 9== :

5 55

92; i

Nbtfrbn surhbcf brfb9 r 9555

2; : 31= i:

@U

Jgvfd? Ubkgus (r) 9 5.= i

Nft S ef tmf brfb bvbgnbenf t` tmf i`t`rcycngst gd wmgcm mf pfrh`ris mgs studts 9 Surhbcf

brfb `h tmf spmfrf.

S 9 ;r5

S 9 ; 55

: 5.= 5.= 9 7=.68 i5.


8/25

[D ] | IB[MFIB[GCS


ww.t`ppfrnfbrdgdj.cì =

SFC[G@D-GGG (;6 Ibrls)

D`tf?

g. Bdswfr 7 qufstg`ds gd bnn.

gg. Rufstg`d duiefr ;6 gs cìpuns`ry. Sfnfct bdy = qufstg`ds hrì tmf hgrst 2; qufstg`ds.

32.Nft I, Q bdk C kfd`tf tmf sft `h stukfdts wm` j`t kgstgdctg`d gd Ibtmfibtgcs, Qmysgcs

bdk Cmfigstry rfspfctgvfny.

[mfd d(I) 9 ;=, d(Q) 9 56, d(C ) 9 31

d(I Q C) 9 8= bdk d(I Q C) 9 6

[mfrfh`rf,

d(I Q C)9d(I) + d(Q) + d(C) d(I Q) d(I C) d(Q C) + d(I QC)

8= 9 ;= + 56 + 31 d(I Q) d(I C)d(Q C) + 6

d(I Q) + d(I C) + d(Q C) 9 21= 8= 9 ;1

D`w c`dsgkfr tmf h`nn`wgdj Xfdd kgbjrbi?

Mfrf,

b kfd`tfs tmf duiefr `h stukfdts wm` j`t kgstgdctg`d gd

Ibtmfibtgcs bdk Qmysgcs `dny.

e kfd`tfs tmf duiefr `h stukfdts wm` j`t kgstgdctg`d gd

Ibtmfibtgcs bdk Cmfigstry `dny.

c kfd`tfs tmf duiefr `h stukfdts wm` j`t kgstgdctg`d gd

Qmysgcs bdk Cmfigstry `dny.

kkfd`tfs tmf duiefr `h stukfdts wm` j`t kgstgdctg`ds gd bnn tmf tmrff sueofcts.[mus, k 9 d(I QC) 9 6

Bdk

b + k + e +k + c + k 9 ;1

[mfrfh`rf, b + e + c 9 56.

35.[mf sui `h tmf hgrst d tfris `h b J.Q. wgtm hgrst tfri b bdk cìi`d rbtg` r gs?

22

d

d

b rS

r

[mf sui `h tmf hgrst 5 tfris gs?

5

5

7

27

2

2 27

2

2 7...(2)

S

b r

r

b r r

r

b r

[mf sui `h tmf hgrst ; tfris gs?


9/25

[D ] | IB[MFIB[GCS



; 5

;

;

;

5 5

5

5

Sui `h tmf nbst 5 tfris

7 38

;6

2

;62

2 2;6

2

2 2 2;6

2

2 2 ;6...(5)

S S

S

S

b r

r

b r r

r

b r r r

r

b r r

Kgvgkgdj (5) ey (2),

5

5

5

2 2 ;6

2 7

2 6

;

5

b r r

b r

r

r

r

Eut, gt gs jgvfd tmbt tmf c`ii`d rbtg` gs p`sgtgvf. [mus, r 9 5.

Suestgtutgdj gd (2),

b(2 + 5 ) 9 7

b 9 3

[mus, tmf sfrgfs gs? 3 + 8 + 25 +

33.Nft b ef tmf hgrst tfri bdk r ef tmf c`ii`d rbtg` `h tmf sfrgfs.

2

2

2

db rS

r

5

5

5

22

2 2

dd b rb r

Sr r

3

3

3

22

2 2

dd b rb r

S r r

C`dsgkfr tmf N.M.S. `h tmf jgvfd fqubtg`d,


10/25

[D ] | IB[MFIB[GCS



2 3 5

3 5

3 5

53 5

5

2 22

2 2 2

2 22

2 2

22 2

2

d dd

d dd

d

d d

S S S

b r b r b r

r r r

b r b r b r

r r

b rr r

r

Nft rdef x.

bx x x

rb

x x x x x xr

5

3 5

5

5

5

5

2 2 2

2

2 2 2 2 22

bx x x x

r

bx x

r

55 5

5

555

5

2 2 22

22

b

x xr

b bx x

r r

5

5

5

22

2 2

d d

d d

d d

b r b r

r r

b r b r b b

r r r r

b r b r

r r

S S

55

55

55

5

5 2

2 2

2 2 2 2

2 2

2 2

\Bkkgdj bdk suetrbctgdj2

br

Y

Sgdcf N.M.S. 9 U.M.S., wf mbvf S2(S3S5) 9 (S5S2)5

[mus, pr`vfk.


11/25

[D ] | IB[MFIB[GCS



3;.\3, :) 9 {xB? 3x>:}9{3, 5, 2, 1, 2, 5, 3, ;, 6, 8}

g. h(6) 9 5(6) 3 9 :

h(8) 9 5(8) 3 9 7

h(6)+ h(8) 9 :+7928

gg.h(2) 9 ;(2)5 2 9 3

h(3) 9 ;(3)5 2 9 36

h(2) h(3) 9 3 36 9 35

ggg.h(5) 9;(5)5 2 9 26

h(;)9 3(;) 5 9 21

h(5) h(;)9 26 21 9 6

gv.h(3) 9 3(3) 5 9 :

h(2) 9 ;(2)5 2 9 3

h(8) 9 5(8) 3 9 7

h(2) 9 ;(2)5 2 9 3

[mfd,

h 3 h 2

5h 8 h 2 5 3

: 3 5

7 3

36.[mf bi`udt c`nnfctfk `d fbcm kby gs fqubn t` tmf ibtrgx iuntgpngcbtg`d `h tmf ibtrgcfs

rfprfsfdtgdj tmf sbnfs `d tmbt kby bdk tmf prgcf `h tmf hrugt.

[mf ibtrgx rfprfsfdtgdj tmf prgcf `h fbcm hrugt gs? \51 21 6Y

61

[mf ibtrgx rfprfsfdtgdj tmf sbnfs d kby 2 gs 81 .

31

61

[mus, tmf bi`udt c`nnfctfk d kby 2 9 51 21 6 81

31

9 51 61 21 81 6 31

2:61

;1

[mf ibtrgx rfprfsfdtgdj tmf sbnfs `d kby 5 gs :1

51

.


12/25

[D ] | IB[MFIB[GCS



;1

[mus, tmf biùdt c`nnfctfk d kby 5 9 51 21 6 :1

51

51 ;1 21 :1 6 51

2811

81

[mf ibtrgx rfprfsfdtgdj tmf sbnfs `d kby 3 gs ;1 .

21

81

[mus, tmf biùdt c nnfctfk d kby 3 9 51 21 6 ;1

21

9 51 81 + 21 ;1 + 6 21

92861

2 2:61

[mus, tmf ibtrgx rfprfsfdtgdj tmf biùdt c`nnfctfk d bnn 3 kbys gs 5 2811 .

3 2861

Kby

Kby

Kby

Bkk

bnn tmf vbnufs be`vf.

[mf biùdt c`nnfctfk `d bnn 3 kbys gs 2:61 + 2811 + 2861 9 6111.

38.C`dsgkfr tmf ebnn``d?

Mfrf, R bdk Q brf tmf gdgtgbn bdk hgdbn p`sgtg`ds `h

tmf ebnn``d wgtm bdjnfs `h fnfvbtg`d hrì tmf e`y,

B bs 81 bdk 31 rfspfctgvfny. Nft tmf mfgjmt `h

tmf ebnn``d ef m.

Kgstbdcf i`vfk ey tmf ebnn``d gs QR 9 ]W.

[mf ebnn``d i`vfs h`r 5 igdutfs wgtm b spffk `h

57 3 i/igd .

Kgstbdcf 9 Spffk x [gif.

[mus,

Kgstbdcf i`vfk ey tmf ebnn``d 9 QR 9 ]W 9

5 57 3 6= 3 i .

Gd trgbdjnf Q]B,


13/25

[D ] | IB[MFIB[GCS



tbd

tbd 31

23

3 i

Q]]BQ

B]

m

B]

mB]

B] m

Gd RWB,

tbd

tbd 81

3

i3

RWWBR

BW

m

BW

m

BW

mBW

[mf kgstbdcf i`vfk ey tmf ebnn``d gs?

6= 3

3 6= 33

5 6= 33

=: i

]W B] BW

B] BW

mm

m

m

[mus, tmf mfgjmt `h tmf ebnn``d gs =: i.


14/25

[D ] | IB[MFIB[GCS


ww.t`ppfrnfbrdgdj.cì 2;

3:.X`nuif `h b spmfrf wgtm rbkgus r gs 3;

.3

r

[mf rbkgus `h tmf `rgjgdbn spmfrf gs r 9 2= ci.

[mus, tmf v`nuif `h tmf `rgjgdbn spmfrf gs 93 3; 2= :::8 ci

3

Nft r2, r5bdk r3ef tmf rbkgg `h tmf 3 spmfrfs tmbt brf rfcbst ùt `h tmf `rgjgdbn spmfrf.

Mfrf, r29 5 ci bdk r59 25 ci.

[mus, tmf v`nuif `h tmf hgrst spmfrf gs 93 3; 355 ci

3 3

Bdk, tmf v`nuif `h tmf sfc`dk spmfrf 9

3 3; 25 531; ci3

Sgdcf tmf 3 spmfrfs brf rfcbst ùt `h tmf `rgjgdbn spmfrf gs 9

3 3 3 3

2 5 3

3

3

3

3

3

3

3

3

3

; ; ; ;

3 3 3 335 ;

:::8 531;3 3

87;; ;:::8

3 3

; 283=;

3 3

;178

28 ci

r r r r

r

r

r

r

r

[mus, tmf rbkgus `h tmf tmgrk spmfrf gs 28 ci.

3=.Vsgdj stfp kfvgbtg`d iftm`k h`r jrùpfk kbtb bdk tblgdj B 9 2:.6 bdk c 9 6,

5

5

[gif Igk p`gdt ( ) D`. h pf`pnf ( )2:.6 2:.6

6

6 21 :.6 ; 21 5 = 28

21 26 25.6 = 6 2 = =

26 51 2:.6 26 1 1 1 1

51 56 55.6 25 6 2 25 25

56 31 5:.6 22 21 5 55 ;;

61 2= =1

x Bk

x B cx h hk hk

x x

h hk hk

5 55

5 5 =1 2=Xbrgbdcf 56 38.:861 61

hk hkc

h h

S.K. Xbrgbdcf 38.:8 8.18


15/25

[D ] | IB[MFIB[GCS



37.X`nuif `h b cyngdkfr wgtm rbkgus r bdk mfgjmt m gs r5m

Mfrf, r 9 2= ci bdk m 9 35 ci.

5 3[mus, tmf v`nuif h sbdk gd tmf cyngdkfr 9 2= 35 2138= ci

X`nuif `h b c`df wgtm rbkgus r bdk mfgjmt m 9 52

3

r m

Mfrf, m 9 5; ci. Nft r ef tmf rbkgus `h tmf mfbp.

Sgdcf tmf sbdk gd tmf cyngdkfr gs mfbpfk gdt` b c`df?

5

5

5

22138=

3

25; 2138=

3

2578

38 ci

r m

r

r

r

5 5

[mf snbdt mfgjmt `h b c`df wgtm rbkgus r bdk mfgjmt m 9 r m [mus, tmf snbdt mfgjmt `h tmf sbdk mfbp gs?

5 538 5; 25 23 ci

[mus, rbkgus h tmf sbdk mfbp r 9 38 ci bdk snbdt mfgjmt h tmf sbdk mfbp 9 25 23 ci.

;1.[mf duiefr `d tmf uppfr hbcf `h tmf hgrst kgcf gs nfss tmbd tmf duiefr `d tmf uppfr hbcf

`h tmf sfc`dk kgcf.

[mf sbipnf spbcf gs

S 9 {(2, 2), (2, 5), (2, 3), (2, ;), (2, 6), (2, 8),(5, 2), (5, 5), (5, 3), (5, ;), (5, 6), (5, 8),

(3, 2), (3, 5), (3, 3), (3, ;), (3, 6), (3, 8),

(;, 2), (;, 5), (;, 3), (;, ;), (;,6), (;, 8),

(6, 2), (6, 5), (6, 3), (6, ;), (6, 6), (6, 8),

(8, 2), (8, 5), (8, 3), (8, ;), (8, 6), (8, 8)}

[mgs c`dtbgds 38 sbipnf p`gdts.

d (S) 9 38

g. Nft B ef tmf fvfdt tmbt tmf sui `h tmf duiefrs `d tmf uppfr hbcfs `h tmf kgcf gs

kgvgsgenf ey 7.

S 9 {(2, 2), (2, 5), (2, 3), (2, ;), (2, 6), (2, 8),

(5, 2), (5, 5), (5, 3), (5, ;), (5, 6), (5, 8),

(3, 2), (3, 5), (3, 3), (3, ;), (3, 6), (3, 8),

(;, 2), (;, 5), (;, 3), (;, ;), (;,6), (;, 8),

(6, 2), (6, 5), (6, 3), (6, ;), (6, 6), (6, 8),

(8, 2), (8, 5), (8, 3), (8, ;), (8, 6), (8, 8)}

[mfd B 9 {(3, 8), (;, 6), (6, ;), (8, 3)}

d(B) 9 ;


16/25

[D ] | IB[MFIB[GCS



d(B) ;D`w, Q(B)9

d(S) 38

2

7

gg.Nft E ef tmf fvfdt tmbt tmf sui `h tmf duiefrs `d tmf uppfr hbcfs `h tmf kgcf gs bt tmf

i`st 3.

S 9 {(2, 2), (2, 5), (2, 3), (2, ;), (2, 6), (2, 8),

(5, 2), (5, 5), (5, 3), (5, ;), (5, 6), (5, 8),

(3, 2), (3, 5), (3, 3), (3, ;), (3, 6), (3, 8),

(;, 2), (;, 5), (;, 3), (;, ;), (;,6), (;, 8),

(6, 2), (6, 5), (6, 3), (6, ;), (6, 6), (6, 8),

(8, 2), (8, 5), (8, 3), (8, ;), (8, 6), (8, 8)}

[mfd E 9 {(2, 2), (2, 5), (5, 2)}

d(E) 9 3

d(E) 3D`w, Q(E)9

d(S) 38

2

25

ggg.Nft C ef tmf fvfdt tmbt tmf duiefr `d tmf uppfr hbcf `h tmf hgrst kgcf gs nfss tmbd tmf

duiefr `d tmf uppfr hbcf `h tmf sfc`dk kgcf.

S 9 {(2, 2), (2, 5), (2, 3), (2, ;), (2, 6), (2, 8),

(5, 2), (5, 5), (5, 3), (5, ;), (5, 6), (5, 8),

(3, 2), (3, 5), (3, 3), (3, ;), (3, 6), (3, 8),

(;, 2), (;, 5), (;, 3), (;, ;), (;,6), (;, 8),

(6, 2), (6, 5), (6, 3), (6, ;), (6, 6), (6, 8),

(8, 2), (8, 5), (8, 3), (8, ;), (8, 6), (8, 8)}

[mfd C 9 {(2, 5), (2, 3), (2, ;), (2, 6), (2, 8), (5, 3), (5,;), (5,6), (5, 8), (3, ;), (3, 6), (3, 8),

(;, 6), (;, 8), (6, 8)}

d(C) 9 26

d(C) 26D`w, Q(C)9 9

d(S) 38

69

25


17/25

[D ] | IB[MFIB[GCS


ww.t`ppfrnfbrdgdj.c`i 2:

;2.Nft tmf x-gdtfrcfpt ef b. Gt gs jgvfd tmbt tmf x-gdtfrcfpt gs 6 i`rf tmbd tmf

y-gdtfrcfpt. [mus, tmf y-gdtfrcfpt gs b 6.

[mf fqubtg`d `h tmf ngdf usgdj tmf gdtfrcfpt-h`ri gs 2.x y

b e

Suestgtutgdj e 9 b 6 gd tmgs fqubtg`d,

26

62

6

6 6

x y

b b

x b yb

b b

x b yb b b

[mf p`gdt (55, 8) ngfs `d tmgs ngdf bdk tmus, gt sbtgshgfs tmf fqubtg`d `h tmf ngdf.

[mus,

5

5

55 6 8 6

55 221 8 6

52 221 1

21 `r 22

b b b b

b b b b

b b

b

[mus, tmf fqubtg`d `h tmf ngdf gs

21 6 21 21 21 66 21 61

5 21 1

`r

22 6 22 22 22 6

8 22 88

8 22 88 1

x yx y

x y

x y

x y

x y


18/25

[D ] | IB[MFIB[GCS


ww.t`ppfrnfbrdgdj.cì 2=

;5.Bcc`rkgdj t` tmf sfctg`d h`riunb, tmf c`-`rkgdbtfs `h tmf p`gdt Q brf,

5 3 3 5 5 ; 3 8 1 21, , 1,5

5 3 5 3 6 6Q Q Q

[mf jrbkgfdt gs tmf sn`pf. [mus, tmf sn`pf `h tmf ngdf gs jgvfd bs 3/5.

Vsgdj tmf sn`pf p`gdt h`ri, tmf fqubtg`d `h b ngdf gs 2 2 .y y i x x

Mfrf, i 93

5bdk 2 2, 1,5x y Q . [mus, tmf fqubtg`d `h tmf ngdf gs?

3

5 15

35

5

5 ; 33 5 ; 1

y x

y x

y xx y

;3.C`dsgkfr tmf h`nn`wgdj hgjurf.

Nft BECK ef b pbrbnnfn`jrbi cgrcuiscrgegdj tmf cgrcnf.

Nft BE ef tmf tbdjfdt t` tmf cgrcnf bt Q.

Nft EC ef tmf tbdjfdt t` tmf cgrcnf bt R.

Nft CK ef tmf tbdjfdt t` tmf cgrcnf bt U.

Nft KB ef tmf tbdjfdt t` tmf cgrcnf bt S.

Zf ld`w tmbt tmf nfdjtms `h tmf tw` tbdjfdts krbwd hrì bd

fxtfrg`r p`gdt t` b p`gdt t` b cgrcnf brf fqubn.

[mus, wf mbvf, BQ 9 BS, EQ 9 ER, CU 9 CR bdk KU 9 KS.

D`w, bkkgdj bnn `h tmf be`vf hùr fqubtg`ds, wf mbvf,

BQ + EQ + CU + KU 9 BS + ER + CR + KS

BQ + EQ + CU + KU 9 (ER + CR) + (BS + KS)

(BQ + EQ) + (CU + KU) 9 (ER + CR) + (BS + KS)

BE + CK9 EC + BK (2)

Zf mbvf BE 9 CK bdk EC 9 BK

\Sgdcf `pp`sgtf sgkfs `h b pbrbnnfn`jrbi brf fqubnY

[mus, fqubtg`d (2) efcìfs,

5BE 9 5EC

BE 9 EC

BE 9 EC 9 CK 9 BK

BECK gs rmìeus.


19/25

[D ] | IB[MFIB[GCS



;;.Nft

3 5

5

3 2= 33 2=

3 23 21

h x x x x

j x x x

Mfrf, kfjrff `h h(x) 4 kfjrff `h j(x).

[mus, tmf kgvgkfdk gs 3x3+ 2=x5+ 33x + 2= bdk tmf kgvgs`r gs 3x5+ 23x + 21.

Qfrh`ri kgvgsg`d?

5 3 5

3 5

5

5

6

3

3 23 21 3 2= 33 2=

3 23 21

6 53 2=

86 61

6 3 3

; ;

3 3

x

x x x x x

x x x

x x

x x

x

Mfrf, rfibgdkfr gs d`t 1. [mus, rfpfbt tmf pr`cfss `h kgvgsg`d wgtm tmf rfibgdkfr bs tmf

kgvgs`r.

[mus, tmf kgvgkfdk gs 3x3+ 2=x5+ 33x + 2= bdk tmf kgvgs`r gs ;x/3 + ;/3.

[mf tw` `rgjgdbn fxprfssg`ds mbvf d` sgipnf hbct`rs. [mus tmfgr J.C.K. cbd mbvf d`df.

Mfdcf, rfi`vf tmf sgipnf hbct`r ;/3 hr`i tmf kgvgs`r.

[mus, tmf kgvgkfdk gs 3x3+ 2=x5+ 33x + 2= bdk tmf kgvgs`r gs x + 2.

Qfrh`ri kgvgsg`d?

5

3 5

3 5

5

5

3 26 2=

2 3 2= 33 2=

3 3

26 33 2=

26 26

2= 2=

2= 2=

1

x x

x x x x

x x

x x

x x

x

x

Mfrf, rfibgdkfr 9 1.

[mus, J.C.K. 9 x + 2


20/25

[D ] | IB[MFIB[GCS



;6.[mf jgvfd fqubtg`d gs 5 5 538 25 1x bx b e

C`dsgkfr tmf qubkrbtgc fqubtg`d 5 1.px qx r [mf s`nutg`d sft bcc`rkgdj t` tmf qubkrbtgc h`riunb gs

5 5; ;, .

5 5

q q pr q q pr

p p

Mfrf, p 9 38, q 9 25b bdk r 9 (b5e5).

[mus, tmf s`nutg`d sft ?

5 55 5 5 5

5 5 5 5 5 5

5 5

25 25 ; 38 25 25 ; 38,

5 38 5 38

25 2;; 2;; 2;; 25 2;; 2;; 2;;,

:5 :5

25 2;; 25 2;;,

:5 :5

25 25 25 25,

:5 :5

,

8 8

b b b e b b b e

b b b e b b b e

b e b e

b e b e

b e b e

@U

C`dsgkfr tmf fqubtg`d? 5 1px qx r

[mf dbturf `h tmf r``ts `h tmf fqubtg`d kfpfdks up`d tmf kgscrgigdbdt, 5 ; .q pr

[mf jgvfd fqubtg`d gs,

5 5 5

5

1

1

3 5 1

x b x e x e x c x c x b

x b e x be x e c x ec x c b x cb

x b e c x be ec cb

Mfrf, p 9 3, q 9 5(b + e + c), r 9 be + ec + cb.

[mus, tmf kgscrgigdbdt gs,


21/25

[D ] | IB[MFIB[GCS



5

5

5 5 5

5 5 5

5 5 5

5 5 5 5 5 5

5 5 5

5 ; 3

; 25

; ; ; = = =

25 25 25; ; ; ; ; ;

5 5 5 5 5 5 5

5 5 5 5

5

b e c be ec cb

b e c be ec cb

b e c be ec cb

be ec cbb e c be ec cb

b e c be ec cb

b be e e ec c c cb b

b e e c c b

Bs squbrf vbnufs brf bnwbys p`sgtgvf, wf jft Kgscrgigdbdt 4 1.

Sgdcf 1 , tmf r``ts brf rfbn.

H`r tmf r``ts t` ef fqubn, tmf kgscrgigdbdt mbs t` ef 1.

[mus,

5 5 5

5 5 5

5 1

1

b e e c c b

b e e c c b

Sgdcf 5 5 5

1, 1, 1b e e c c b

H`r? 5 5 5

1b e e c c b

[mf h`nn`wgdj c`dkgtg`ds mbvf t` ef sbtgshgfk, 5 5 5

1, 1, 1b e e c c b

[mus,

1, 1, 1

, ,

b e e c c b

b e e c c b

b e c

H`r tmf r``ts t` ef fqubn, kgscrgigdbdt gs 1 bdk tmus, b 9 e 9 c.


22/25

[D ] | IB[MFIB[GCS



SFC[G@D-GX (51 Ibrls)

D`tf?

g. Bdswfr e`tm tmf qufstg`ds cm``sgdj fgtmfr `h tmf bntfrdbtgvfs.

;8.(b) [` krbw tmf jrbpm `h y 9 x5tmf p`gdts brf?

5

5 2 1 2 5 6

; 2 1 2 ; 56

x

y x

[` hgdk tmf r``ts `h x5;x 6 9 1, s`nvf tmf fqubtg`ds? 5 5bdk ; 6 1y x x x

D`w,5

5

; 6 1

; 6 1 \ Y; 6

x x

y x y xy x

Mfdcf, tmf r``ts `h x5 ;x 6 9 1 brf d`tmgdj eut tmf x-c``rkgdbtfs `h tmf p`gdts `h

gdtfrsfctg`d `h 5 bdk ; 6y x y x

D`w, h`r tmf strbgjmt ngdf tmf p`gdts brf,

2 1 2 5 6

; 6 2 6 7 23 56

x

y x

[mf jrbpm gs?

[mf p`gdts `h gdtfrsfctg`d `h tmf ngdf bdk tmf pbrbe`nb brf (2 , 2) bdk (6 , 56).

[mus, tmf s`nutg`d sft gs {2 , 6}.


23/25

[D ] | IB[MFIB[GCS



@U

(e) [` krbw tmf jrbpm `h y 9 x5+ 5x 3 tmf p`gdts brf?

5

3 5 1 2 3

5 3 1 3 3 1 25

x

y x x

[` hgdk tmf r``ts `h x5x 8 9 1, s`nvf tmf fqubtg`ds?5 55 3 bdk 8 1y x x x x

D`w,

5

5

5

5

8 1

5 5 3 3 1

5 3 3 3 1

3 3 1 \ 5 3Y3 3

x x

x x x x

x x x

y x y x xy x

Mfdcf, tmf r``ts `h x5 x 8 9 1 brf d`tmgdj eut tmf x-c``rkgdbtfs `h tmf p`gdts `h

gdtfrsfctg`d `h? 5 5 3 bdk 3 3y x x y x

D`w, h`r tmf strbgjmt ngdf tmf p`gdts brf?

5 2 1 2 3

3 3 3 1 3 8 25

x

y x

[mf jrbpm gs?

[mf p`gdts `h gdtfrsfctg`d `h tmf ngdf bdk tmf pbrbe`nb brf (5 , 3) bdk (3 , 25).

[mus, tmf s`nutg`d sft gs {5 , 3}.


24/25

[D ] | IB[MFIB[GCS


ww.t`ppfrnfbrdgdj.cì 5;

;:.(b)Kgstbdcf `h tmf p`gdt hrì tmf cfdtfr 9 21 ci.

[mf stfps h`r c`dstructg`d brf?

2. Zgtm @ bs tmf cfdtfr krbw b cgrcnf `h rbkgus 8 ci.

5. Ibrl b p`gdt Q bt b kgstbdcf `h 21 ci hrì @ bdk o`gd @Q.

3. Krbw tmf pfrpfdkgcunbr egsfct`r `h @Q. Nft gt ifft @Q bt I.

;. Zgtm I bs cfdtfr bdk I@ bs rbkgus, krbw bd`tmfr cgrcnf.

6. Nft tmf tw` cgrcnfs gdtfrsfct bt ] bdk W.

8. O`gd Q] bdk QW. [mfy brf tmf rfqugrfk tbdjfdts.

[mf rfsuntgdj hgjurf gs?

[` kftfrigdf tmf nfdjtm `h tmf tbdjfdt, c`dsgkfr tmf @]Q bdk bppny Qytmbj`rbs

tmf`rfi t` gt,

5 5

5 5 5

5 5 5

5 5 5

5

8 21

21 8 211 38 8;

8;

= ci

@] Q] @Q @] Q] @Q

Q]

Q]

Q]

Q]

[mus, tmf nfdjtm `h tmf tbdjfdts gs = ci.

@U


25/25

[D ] | IB[MFIB[GCS


(e)Zf dffk t` c`dstruct tmf rfqugrfk qubkrgnbtfrbn, wmfd tw` sgkfs bdk tw` kgbj`dbns `h b

cycngc qubkrgnbtfrbn brf jgvfd.

C`dstructg`d?

g.Krbw b rùjm kgbjrbi bdk ibrl tmf ifbsurfifdts

gg.Krbw b ngdf sfjifdt LN9 6.6ci

ggg.Zgtm L bs cfdtrf bdk rbkgus 6 ci krbw bd brc.

gv.Zgtm Nbs cfdtrf bdk rbkgus ;.5 ci, krbw bd`tmfr brc gdtfrsfctgdj tmf prfvgùs brc

bt I.

v.O`gd LI bdk NI.

vg.Krbw tmf pfrpfdkgcunbr egsfct`rs `h LNbdk NIgdtfrsfctgdj fbcm `tmfr bt @.

vgg.Zgtm @bs cfdtrf bdk @L (9 @N9@I)bs rbkgus, krbw tmf cgrcuicgrcnf `h LNI.

vggg.Zgtm N bs cfdtrf bdk rbkgus 6.3 ci, krbw bd brc gdtfrsfctgdj tmf cgrcnf bt D.

gx.O`gd LD bdk ID.

x.[mus, LNID gs tmf rfqugrfk cycngc qubkrgnbtfrbn.

Uùjm kgbjrbi?

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TAMILNADU-Mathematics Sample Paper-1-SOLUTION-Class-10 Question Paper