Section – 4 Mr. A.K.
Abdul Haleem
Name:................................... juk;-11 NDT in Maths [ merit ]
Tel : 0754255545
epfo;jfT
01. ngl;b xd;wpy; 3 rptg;G> 4 nts;is epw khgps;fs; cs;sd.
(i) rpg;wh]; xU khgpis vOkhwhf vLf;Fk; kutupg;glk; fPNo jug;gl;Ls;sJ mij
G+uzg;gLj;Jf.
rptg;G
(ii) khgpis ngl;bapDs; kPz;Lk; ,l;L fky; kPz;Lk; xU khgpis vLf;fpd;whd;
,tu;fSf;fhd kutupg;glj;ij tpupTgLj;Jf.
(iii) rpg;wh]; nts;isiaAk;> fky; rptg;G epw khgpisAk; ngWtjw;fhd epfo;jfitf;
fhz;f.
(iv) ,UtUk; xNu epwKilajhf ,Ug;gjw;fhd epfo;jfit nea;aupapy; Fwpj;Jf;
fhl;Lf.
W4
W3
W2
W1
R3
R2
R1
R1 R2 R3 W1 W2 W3 W4
Grade-11 Section – 4 Probability Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~1~
02. rptg;G> ePy epwq;fis cila ,U ehd;Kfpj; jhaf;fl;ilfspd; Kfq;fspy; 1 , 2 , 3 ,4
vd ,yf;fkplg;gl;Ls;sd. mit xNu Neuj;jpy; cUl;lg;;gLfpd;wd. mtw;wpd; NgWfs; Gs;sp
tiugpy; fhl;lg;gl;ls;sJ.
4 × × × ×
3 × × × ×
rptg;G
2 × × × ×
1 × × × ×
1 2 3 4
ePyk;
(i) ,U jhaf;fl;ilfspd; NgWfSk; Kjd;ik vz;zhf ,Uf;Fk; NgWfspd;
epfo;jfit fhz;f.
(ii) ,U jhaf;fl;ilfspdJk; $l;Lj;njhif 5 ,Yk; $Ljyhf ,Ug;gjw;fhd
epfo;r;rpia fl;lkpl;Lf; fhl;Lf.
(iii) tpdh (ii) ,w;fhd epfo;jfT ahJ?
03. (a) gapw;rp xd;wpy; fye;Jnfhz;ltu;fis 25 tajpYk; $ba Mz; 25 tajpYk; Fiwe;j
Mz; 25 tajpYk; $ba ngz; 25 tajpYk; Fiwe;j ngz; vd tFf;fg;gl;L fPNo jug;gl;l
kutpg;glk; jahupf;fg;glLs;sJ.
8 25 tajpYk; $batu;
13
13 Mz;
20
𝐵 25 tajpYk; Fiwe;jtu;
b3 25 tajpYk; $batu;
7
𝐴 ngz;
4 25 tajpYk; Fiwe;jtu;
7
(i) A , B vd;gtw;iwf; fzpf;f.
Grade-11 Section – 4 Probability Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~2~
(ii) gpd;tUk; epfo;r;rpfspd; epfo;jfTfis fzpf;f.
(i) njupT nra;ag;gl;l xUtu; ngz;zhf ,Uj;jy;.
(ii) njupT nra;ag;gl;l xUtu; 25 tajpYk; Fiwe;j Mzhf ,Uj;jy;.
(iii) 25 tapYk; Fiwe;j ngz;zhf ,Uj;jy;.
1 1
(b) A , B vd;gd rhuh epfo;r;rpfs; MFk;. 𝑃(𝐴) = , 𝑃(𝐵) = vdpd; 𝑃(𝐴 ∩ 𝐵) I fhz;f.
2 3
04. 1 – 4 tiu ,yf;fkplg;gl;l Nfhlhj ehd;Kfp jhaf;fl;il xd;Wk;> 1 – 6 tiu
,yf;fkplg;gl;l Nfhlhj rJuKfp jhaf;fl;il xd;Wk; xUkpj;J cUl;lg;Lfpd;wd.
(i) ,U jhaf;fl;ilfspYk; fpilf;Fk; khjpupntspia jug;gl;Ls;s nea;aupapy; “ X”
vd milahskpl;lf; fhl;Lf.
1 2 3 4 5 6
(ii) ,U jhaf;fl;ilfspYk; fpilf;Fk; NgWfs; rkNgWfis nfhz;bUf;Fk;
epfo;r;rpia fl;lkpl;L “ A ” vdf; Fwpf;f. 𝑃(𝐴) I fhz;f.
(iii) ,U jhaf;fl;ilfspYk; fpilf;Fk; NgWfspd; $l;Lj;njhif 6 ,Yk; $Ljyhf
,Uf;Fk; epfo;r;rpia fl;lkpl;L “ B ” vdf; Fwpf;f.
(iv) ,U jhaf;fl;ilfspYk; fpilf;Fk; NgWfs; ,ul;il vz;fshf ,Ug;gjw;fhd
NgWfis tl;lq;fshy; fl;lkpl;L mjw;fhd epfo;jfitf; fhz;f.
(v) A Ak; B Ak; jk;Ks; GwePq;Fk; epfo;r;rpfsh? mt;thwhapd; 𝑃(𝐴 ∩ 𝐵) I fhz;f.
Grade-11 Section – 4 Probability Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~3~
05. xU igapDs; rkkhd 2 rptg;G epw khgps;fSk;> 3 ePy epw khgps;fSk; cs;sd.
(i) rpahk; igapypUe;J vOkhwhf xU khgpis ntspNa vLf;fpd;whd; kutupg;glk; fPNo
jug;gl;Ls;sJ mij G+uzg;gLj;Jf.
rpahk; njupT
rptg;G
(ii) rpahk; vLj;j khgps; kPz;Lk; igapDs; ,lg;gLfpwJ. mg;igapypUe;J mg;uj; xU
khgpis ntspNa vLf;fpd;whd; mUtupdJk; vLg;Gfis fhl;l jug;gl;l
kutupg;glj;ij tpupTgLj;Jf.
(iii) ,UtUk; NtWgl;l khgpis vLg;gjw;fhd epfo;jfitf; fhz;f.
(iv) rptg;G epw khgps;fis R ,dhYk;> ePy epw khgps;fis B ,dhYk; Fwpj;J
rpahk;> mg;uj; MfpNahuJ khgps; njupit mUfpy; cs;s nea;aupapy;
Fwpf;fg;gl;Ls;sd. ,UtUk; NtWgl;l khgpis vLf;Fk; NgWfis
fl;lkpl;Lf;fhl;b mjd; epfo;jfitf; fhz;f.
B3
B2
B1
R2
R1
R1 R2 B1 B2 B3
(v) fl;lkpl;Llg;gl;Ls;s epfo;r;rpfspd; NgWfis tpgupf;f.
Grade-11 Section – 4 Probability Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~4~
06. xU G+e;Njhl;lj;jpy; fhzg;gl;l Nuh[h kunkhd;wpy; 4 rptg;G epw G+f;fSk;> 3 nts;is epw
G+f;fSk; G+j;Jf; fhzg;gl;ld. A , B vDk; ,uz;L tz;zhj;Jg; G+r;rpfs; ,g;G+f;fspy; Njid
mUe;jp te;jd. ,U tz;zhj;Jg; G+r;rpfSk; xNu g+tpy; ed;whf Njid mUe;j KbAk;.
(i) ,U tz;zhj;Jg; G+r;rpfSk; Njid mUe;Jk; re;ju;g;gq;fis fhl;Lk; khjpup
ntspia jug;gl;l nea;aupapy; “ X ” ,l;L tifFwpf;f.
W3
W2
W1
R4
R3
R2
R1
R1 R2 R3 R4 W1 W2 W3
(ii) ,U tz;zhj;Jg; G+r;rpfSk; xNu G+tpy; Njid mUe;jf;$ba Kiapy; nea;aupapy;
fl;lkpl;Lf;fhl;b mjd; epfo;jfitf; fhz;f.
(iii) ,U tz;zhj;Jg; G+r;rpfSk; Njid mUe;jf;$ba re;ju;gg ; q;fis fhl;l
tiuag;gl;l G+uzkw;w kutupg;glk; fPNo jug;gl;Ls;sJ. fpisfspy; cupa
epfo;jfTfis ,l;L kutupg;glj;ij G+uzg;gLj;Jf.
R;
R;
R;
(iv) ,U tz;zhj;Jg;G+r;rpfSk; ahjhapDk; xU rptg;G epw G+tpy; Njd; mUe;Jtjw;fhd
epfo;jfitf; fhz;f.
Grade-11 Section – 4 Probability Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~5~
07. nfhOk;gpypUe;J tpkhd epiyak; nry;y mjpNtfg;ghijiaAk; nghJg;Nghf;Ftuj;J
ghijiaAk; njupT nra;a KbAk;. thfdq;fspy; jdpahu; thfdj;ijAk;
nghJg;Nghf;Ftuj;J NritiaNah ngwKbAk;.
xUtu; tpkhd epiyak; nry;y nghJg;Nghf;Ftuj;J Nritia gad;gLj;Jtjw;fhd
7 3
epfo;jfT mjpNtfg;ghijia njupT nra;tjw;fhd epfo;jfT vdpd; kutupg;glj;ij
10 10
G+uzg;gLj;Jf.
(i)
……….. nghJg;Nghf;F
3
10 mjpNt
……….. …………………
7 ….
nghJg;Nghf;F
10
……….. ………..
…………………
….
(ii) jdpahu; Ng&e;j xd;wpy; mjpNtfg;ghij topNa nry;tjw;fhd epfo;jfT ahJ?
(iii) nghJg;Nghf;Ftuj;J Nritia gad;gLj;Jtjw;fhd epfo;jfT ahJ?
08. A , B , C Mfpad xNu ghijapy; gazk; nra;Ak; %tifg; Ng&e;Jfs; MFk;. ,k;%tifg;
Ng&e;Jfspy; VNjDnkhd;wpy; gazpg;gjw;fhd tha;g;G rkkhdjhFk;.
A B C
(i) gazp xUtu; nry;tjw;Fk;> jpUk;gp tUtjw;Fkhd Ng&e;J tiffis fhl;Lk;
midj;J NgWfisAk; jug;gl;l nea;aupapy; fhl;Lf.
(ii) nry;Yk;NghJk;> jpUk;gp tUk;NghJk; xNu tif my;yhj Ng&e;J tiffspy;
gazpg;gjw;fhd epfo;jfT ahJ?
Grade-11 Section – 4 Probability Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~6~
09. ngl;b xd;wpy; 3 ePy epw iff;Fl;ilfSk;> 2 rptg;G epw iff;Fl;ilfSk;> fhzg;gLfpd;wd.
xUtu; mjpypUe;J xU iff;Fl;ilia ntspNa vLj;J epwk; Fwpj;J gpd; cs;Ns ,lhky;>
NtW iff;Fl;ilia vLj;J epwk; Fwpf;fpd;whu;.
R2
R1
B3
B2
B1
B1 B2 B3 R1 R2
(i) epfo;r;rpfSf;fhd khjpup ntspia jug;gl;l nea;aupapy; ,Ue;J Fwpj;Jf; fhl;Lf.
( B – ePy epwk; > R – rptg;G epwk; )
(ii) vLf;fg;l;l ,uz;L iff;Fl;ilfSk; xNu epwkhdjhf ,Ug;gjw;fhd epfo;jfT ahJ?
(iii) Kjyhtjhf vLf;fg;gLk; iff;Fl;il ePy epwkhfTk;> ,uz;lhtjhf
vLf;fg;gLk; iff;Fl;il rptg;G epwkhfTk; ,Ug;gjw;fhd epfo;jfT ahJ?
10. xU ngl;bapy; gUkdpy; xj;j 3 rptg;G epw nghj;jhd;fSk;>; 1 ePy epw nghj;jhDk; cs;sd.
ngl;bapypUe;J ,U nghj;jhd;fs; gpujpitg;gpd;wp xd;wd; gpd; xd;whf vOkhwhf
vLf;fg;gLfpd;wd.
(i) 2Mk; nghj;jhd;
R3
R2
R1
B1
1Mk; nghj;jhd;
B1 R1 R2 R3
(ii) ,uz;L nghj;jhd;fSk;; ntt;NtW epwkhf ,Ug;gjw;fhd epfo;jfitf; fhz;f?
Grade-11 Section – 4 Probability Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~7~
(iii) Kjyhtjhf vLf;fg;;gl;l nghj;jhid ngl;bapy; ,l;L kPz;Lk; xU nghj;jhd;
ntspapy; vLf;fg;gLk; NghJ NkNy (ii) ,y; Fwpg;gpl;l epfo;r;rpf;fhd
epfo;jfitf; fhz;f?
11. ghlrhiy xd;wpy; f.ngh.j (c.j) guPl;irapy; Njhw;wpa khztd; xUtd; rpj;jpailtjw;fhd
3
epfo;jfT ck;> guPl;irapy; rpj;jpaile;j khztd; xUtDf;F gy;fiof;fof mDkjp
5
1
fpilg;gjw;fhd epfo;jfT ck; MFk;.
5
(i) khztd; f.ngh.j (c.j) guPl;irapy; rpj;jpailtjw;fhd epfo;jfitf; fhz;f?
(ii) guPl;irapy; rpj;jpailjy;> rpj;jpailahik vd;gtw;iw fhl;Lk; kutupg;glk; xd;W
tiuf.
(iii) rpj;jpaile;j khztDf;F gy;fiof;fof mDkjp fpilj;jy;> fpilf;fhjpUj;jy;
vd;gtw;iwf; fhl;Lk; fpisfis Nkw;gb kutupg;glj;jpy; Fwpj;J tpupTgLj;Jf.
(iv) cau;ju guPl;irapy; Njhw;wpa xUtDf;F gy;fiof;fof mDkjp fpilg;gjw;fhd
epfo;jfT ahJ?
(v) mg;ghlrhiyapypUe;J 150 khztu;fs; cau;ju guPl;irf;F Njhw;wpdhu;fs; vdpd;>
gy;fiof;fof mDkjp fpilf;f njupthFk; khztu;fspd; vz;zpf;ifiaf;
fhz;f.
12. NghQ;rp tiffspd; khjpupapypUe;J njupT nra;ag;gl;l NghQ;rp tpij xd;W Kisg;gjwfhd
3
epfo;jfT MFk;.
4
(i) elg;gl;l NghQ;rp tpijnahd;W Kisj;jy;> Kisf;fhik Mfpa epfo;r;rpfisf;
fhl;Lk; kutupg;glj;ij tiuf.
7
(ii) Kisj;j gpd; cUthd jhtuk; fha;g;gjw;fhd epfo;jfT MFk;. vdpd; Kisj;j
8
jhtuk; fha;j;jy;> fha;f;fhik Mfpa epfo;r;rpfisf; fhl;Lk; tifapy; NkNy (i) ,y;
tiue;j kutupg;glj;ij tpupTgLj;Jf.
(iii) kutupg;glj;ijg; gad;gLj;jp elg;gl;l NghQ;rp tpijapypUe;J fha;f;Fk; jhtuj;ijg;
ngWk; epfo;jfitf; fhz;f.
Grade-11 Section – 4 Probability Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~8~
13. (a) xU ngl;bapy; 3 nts;is epw 2 fWg;G epw xNu khjpupahd khgps;fs; cs;sd. mtw;wpypUe;J
vOkhwhf xU khgps; vLf;fg;gl;L epwk; Fwpf;fg;gl;L mg;igapDs; ,lhky; ,d;ndhU khgps;
vLf;fg;gLfpd;wJ.
(i) khjpup ntspia jug;gl;l nea;aupapy; tifFwpf;f.
B2
B1
W3
W2
W1
W1 W2 W3 B1 B2
(ii) ,U KiwAk; xNu epwk; fpilg;gjw;fhd epfo;r;rpia nea;aupapy; Fwpj;Jf; fhl;Lf.
(b) vLf;fg;gl;l khgps;fs; mg;igapDs; ,lg;gl;L 1 njhlf;fk; 5 tiu vz;zplg;gl;L
xd;wd; gpd; xd;whf gpujp itg;gpd;wp ,U khgps;fs; vLf;fg;gLfpd;wJ. vLf;fg;gl;l vz;
Kf;Nfhz vz;zh? ,y;iyah? vd Fwpf;fg;gLfpd;wJ.
2
A;
5
A1
A1
A1
(i) kutupg;glj;ij g+uzg;gLj;Jf.
(ii) ,UKiw vLf;fg;gl;ljpy; xU Kiw kl;Lk; Kf;Nfhz vz; fpilg;gjw;fhd epfo;jfT
ahJ?
Grade-11 Section – 4 Probability Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~9~
14. njhow;rq;fnkhd;wpd; jiytu;. nrayhsu; njupTf;fhf epWtdnkhd;wpypUe;J 9 Mz;fSk;>
4 ngz;fSk; Nghlbapl;ldu;. xU gjtpf;fhf xUtu; kl;LNk njupT nra;ag;gLtu;. jiytu;
gjtpf;fhd kutupg;glk; jug;gl;Ls;sJ. G+uzg;gLj;Jf.
jiytu; njupT
(i) Mz;
4
13 ngz;
(ii) nrayhsu; njupTf;fhf tpupthf;fg;gl;l kutupg;glj;jpy; ,ilntspfis epug;Gf.
nrayhsu; njupT
……….. Mz; Mz; ngz; …………………
….
Mz;
………..
……….. ngz; Mz; ngz; …………………
….
……….. Mz;
3 ………………… …………………
10 …. ….
ngz;
……….. ngz; ………………… …………………
…. ….
(iii) gpd;tUtdtw;wpd; epfo;jfTfisf; fhz;f.
(i) njupT nra;ag;gl;l ,UtUk; ngz;fs;.
(ii) jiytu;; MzhfTk; nrayhsu; ngz;zhfTk; ,Ug;gjw;fhd epfo;jfT
(iii) xUtNuDk; MzhfTk; ,Ug;gjw;fhd epfo;jfT
Grade-11 Section – 4 Probability Mr. A.K. Abdul Haleem Maths Sonic AK
fzpjf; flypy; ePe;j vk;NkhL ,izAq;fs; ~ 10 ~
