ish¨ u ysñlï weúßKs] All Rights Reserved] 1 AL/2024/01-S-I

fuu m%Yak m;%fha iïmQ¾K whs;sh iqismj a ka Wiia wOHdmk ^fm!oa& iud.u i;= jk w;r fuu m%Yak m;%fha wka;¾.; lsisjla
bf,lafg%dakslj" hdka;%slj fyda Pdhd msgm;a lsÍu yd .nvd lr ;eîu imqrd ;ykï fõ' tfia l<fyd;a Bg úreoaOj wm iud.fï
kS;s wxYh u`.ska kS;suh mshjr .kq ,nhs

2024
2024
2024
04

meh 02
02 hours

ie<lsh hq;=hs.
 fuu m%Yak m;%h msgq 12 lska iukaú; jk w;r m%Yak 50 lska iukaú; fõ.
 ish¨ u m%Yakj,g W;a;r imhkak.
 W;a;r m;%fha kshñ; ia:dkfha Tfí úNd. wxlh ,shkak.
 W;a;r m;%fha msgqmi § we;s wfkla Wmfoia o ie,ls,su;a j lshjkak .
 1 isg 50 f;la jQ tla tla m%Yakh i`oyd (1), (2), (3), (4), (5) hk ms<s;=re j,ska ksjerÈ fyda b;du;a
.e<fmk fyda ms<s;=r f;dardf.k, th, W;a;r m;%fha ±lafjk mßÈ l;srhla (x) fhdod olajkak.
.Kl hka;% Ndú;hg bv fokq fkd ,efí.
(g = 10 N kg-1)

1. mdrfõoH;dfõ tall SI uQ,sl tallj,ska ,shkq ,nkafka"

(1) kgmA−1s −3 (2) kgm3 A−2 s −3 (3) A2 s 4 kg −1m−3
(4) As3kg −1m −3 (5) kgm4 A−2 s −3

2. my; rEm igyfka ±lafjk bial=remamq wdudkfha

mdGdxlh l=ulao@ l=vdu ñkqu 0.01mm fõ'

(1) 2.48cm
(2) 0.248mm
(3) 0.0248cm
(4) 2.48mm
(5) 24.8mm

3. lsishï m%ldY ixfõ§ mDIaGhla u;g wdf,dalh m;s; jQ úg uqla; jk m%ldY bf,lafg%dakj, Wmßu
fõ.h (V) m;s; wdf,dalfha ixLHd;h (f) iu`. úp,kh jkqfha"

(1) (2) (3) (4) (5)

ish¨ u ysñlï weúßKs] All Rights Reserved] 2 AL/2024/01-S

4. ,laIHdldr wdfrdamK folla w;r n,h (F) iy tu wdfrdamK fol w;r ÿr (D) w;r weÈ m%ia;drh
my; i`oyka tajdhska l=ula fõo@

(1) (2) (3) (4) (5)

5. ;S¾hla ;rx. yd wkajdhdu ;rx. iïnkaOfhka isÿ lr we;s my; m%ldYhkaf.ka ksjerÈ fkdjkafka"
(1) ish¿u ;S¾hla ;rx. yd wkajdhdu ;rx. új¾;khg ,la l, yel'
(2) ;s¾hla ;rx. yd wkajdhdu ;rx. hk ish,af,ysu kq.eiqï we;s l, yel'
(3) ish¿u ;S¾hla ;rx. yd wkajdhdu ;rx.hka ys kq.eiqï Y%jKh l< yel'
(4) ;S¾hhla ;rx. yd wkajdhdu ;rx. ish,a,u ksfrdaOkhg ,la l< yel'
(5) ;s¾hhla ;rx. yd wkajdhdu ;rx. hk ish,a, wêia:dmkh úh yel'

6. ffoYsl yd wÈY ms<sn`o my; j.ka;s i,lkak'

(A) ÈYdjla ;sfí kï tu rdYsh wksjd¾hfhkau ffoYslhls'
(B) ffoYsl rdYs ffoYsl wdl,k ;%sfldaK kshuh ms,smÈhs'
(C) ffoYsl 2la .=Ks;fhka iEuúgu ffoYslhla ,efí'
fïjdhska wi;H jkafka"
(1) C muKs (2) A yd C muKs (3) B yd C muKs
(4) A yd B muKs (5) ish,a,u i;H fõ

7. iqug mDIAGhla u; jQ ialkaOh 0.09Kg jk jia;=jla

th ÿkq ksh;h 4.5Nm-1 jQ ÿkq folla wdOdrfhka ;sriaj
r`ojd ;sria osYdj Tiafia l=vd n,hla ÿka úg jia;=j
foda,kh jk ixLHd;h jkqfha,
52
(1) 42 Hz (2) 52 Hz (3) Hz
4
5 4
Hz (5) Hz
(4)  

8. rEmfha olajd we;s wdk; ;,fha mDIaGh u; d >klñka hqla;j

ÿiai%dú;d ix.=Klh  jk f;,a j¾.hla wdf,am lr we;' ;,h u;
;nd ,S l=Üáh uqod y, úg ,nd .kakd wdka; m%fõ.h V0 kï 
iu`. V0 úp,kh jkq we;af;a"

(1) (2) (3) (4) (5)

ish¨ u ysñlï weúßKs] All Rights Reserved] 3 AL/2024/01-S

9. i¾jiu A, B, C wxY= ;=kla 3ms-1, 4ms-1, 5ms-1 fõ.j,ska mQ¾K m%;Hdia: f,i .efghs' .egqfuka
wk;=rej wxY+ka i;= kj fõ. jkafka"

(1) 0ms-1, 1ms-1, 7ms-1 (2) 2ms-1, 5ms-1, 5ms-1 (3) 3ms-1, 4ms-1, 3ms-1
(4) 3ms-1, 3ms-1, 3ms-1 (5) 2ms-1, 4ms-1, 6ms-1

10. lDIaK jia;= foll Wmßu ;Sj%;djhg wkqrEm ;rx. wdhdu ms<sfj,ska 1nm yd 1 m fõ' tu jia;=
u`.ska tall j¾.M,hla yryd Yla;s úfudapkh lrk iS>%;d w;r wkqmd;h jkafka"

(1) 103 (2) 104 (3) 106

(4) 108 (5) 1012

11. isriaj by<g m%lafIamkh lrk ,o jia;=jl pd,l Yla;h

s (E) jia;=j .uka l, ÿr (S) iu`.
fjkiajk wdldrh olajk m%ia;drh f;darkak'

(1) (2) (3)

(4) (5)

12. rEmfha olajd we;af;a iqug ieye,a¨ lmamshla jgd ieye,a¨ wú;kH ;ka;= u`.ska
ialkaO iïnkaO lr we;s wdldrhhs' tys§ ÿkq ;rdÈfha ialkaOh 2kg kï moaO;sfha
;ajrKh jkafka"
(1) 0.9 ms-2 (2) 1.2 ms-2
(3) 1 ms-2 (4) 0.5 ms-2
(5) 1.5 ms-2

13. /<s;s gexls mÍlaIKhl§ fhdod.;a /<s;s gexlsfha ùÿrefõ isg wdf,dal m%Njhg ÿr 0.5m fõ' ùÿrefõ
isg lv;srhg ÿr 1.5m fõ' lv;srfha Èia jQ wkqhd; wdf,dalu;a f¾Ld folla w;r ÿr 3cm úh' fuu
c, ;rx.fha ixLHd;h 100Hz nj fidhd .eKqks kï tys m%fõ.h jkq we;af;a"
(1) 75ms-1 (2) 100ms-1 (3) 120ms-1
(4) 0.8ms-1 (5) 0.75ms-1

14. iudk uOHkH >k;aj j,ska hqla; jk A yd B kï .%yf,dal 02l wrhka mss,sfj,ska R yd 4R fõ'
tla tla .%yf,dalfha mDIaGhg b;d wdikakfhka PA yd PB kï pkaøsld folla .%yf,dal jgd
jD;a;dldr llaIj, .uka lrñka mj;S' PA ys fõ.h V kï PB ys fõ.h jkafka"
V V
(1) (2) (3) V
4 2
(4) 2V (5) 4V
ish¨ u ysñlï weúßKs] All Rights Reserved] 4 AL/2024/01-S-I

15. my; i`oyka m%ldYk w;ßka idjoH jkqfha"

(a) jia;=jla u; l%shd lrk n,j, iïm%hqla;h Y+kH úg tu jia;=j iEu úgu ksYap,j
mj;shs'
(b) úYajfha fld;ekl jQjo jia;=jl nr ksh; fõ'
(c) jia;=jla u; l%shd lrk n,j, iïm%hqla;fha ÈYdjg iEu úgu jia;=j p,s; fõ'
(1) a yd b (2) b yd c (3) a yd c
(4) a, b, c (5) by; lsisjla fkdfõ'

16. ixLHd;h 384 Hz jk iriq,la Bg b;d wdikak ixLHd;hlska hq;a fojk iriq,la iu. tlg kdo
l< úg ;;amrhg kq.eiqï 3 la weiqks' fojk iriqf,a tla oe;a;l lïì fmdgj,a lsysmhla mg,ejQ
úg ;;amrhg wefik kq.eiqï m%udKh wvq jknj fmkqks' fojk iriqf,a ixLHd;h jkafka"

(1) 381 Hz (2) 382 Hz (3) 383 Hz

(4) 386 Hz (5) 387 Hz

17. f,day j¾. ;=kl ld¾h Y%s;  x   y   z jk w;r tajd u;g ;Sj%;djh I x fjk fjku I y , I z jk
úoHq;a pqïNl ;rx. m;s; lrhs' I x  I y  I z f,i ;sj%;dj úp,kh fõ kï kej;=ï úNjh (Î) yd
m;s; wdf,dal ixLHd;h (f) w;r wÈkq ,nk m%ia;dr ksjerÈj ±lafjkafka"

(1) (2) (3) (4) (5)

18. ia:djr ;rx. iïnkaOfhka lr we;s my; i`oyka m%ldYk n,kak'

(a) m%;súreoaO ÈYdjg .uka .kakd i¾jiu ;rx. folla wêia:dmkfhka fïjd we;s fõ'
(b) wkqkdo k<hla ;=< ia:djr wkajdhdu ;rx. we;s fõ'
(c) újD; wkqkdo k<hla i`oyd fofl<jr i`oydu wdka; fYdaOk fhdohs'
ñka i;H jkafka,
(1) a muKs' (2) a yd c muKs' (3) b yd c muKs'
(4) a yd b muKs' (5) a, b, c ish,a,u

19. tal flakaøhSh ikakdhl f.da,hlg yd f.da,Sh lfnd,lg

ms<sfj,ska − 2Q yd + 6Q wdfrdamK ,nd § we;' flakaøfha isg
uksk ÿr r iu`. ;ekska ;ek úoHq;a fCIa;% ;Sj%;djh (E) fjkia
jk m%ia;drfha o< yevh jkafka"

(1) (2)

(3) (4) (5)

ish¨ u ysñlï weúßKs] All Rights Reserved] 5 AL/2024/01-S-I

20. l=vd f,day f.da,hla Wl= f;,a iys; Wi irdjla ;=<g fiñka w; yßkq ,efí' my; § we;s m%ldY
i,ld n,kak'
(A) f.da,fhys nr Wvql=re f;rmqu yd ÿiai%dù n,fha tl;=jg jeä ksid f.da,h uq,ska
;ajrKh fõ'
(B) iaj,am ld,hlg miq f.da,fha nr Wvql=re f;rmqu iy ÿiai%dù n,h u`.ska yßhgu
ix;=,kh lrhs'
(C) f.da,fha wdka; m%fõ.h tys wrfha j¾.fhys yd f;,aj, ÿiai%dù ix.=Klfhys
.=Ks;hg wkqf,dau jYfhka iudkqmd;sl fõ'
by; i`oyka m%ldY w;=ßka i;H jkafka"
(1) A muKs' (2) A iy B muKs' (3) A iy C muKs'
(4) B iy C muKs' (5) A, B iy C ish,a,

21. jdfka f.da,hla tys úIalïNhla Tiafia hk wlaIhla jgd N%uKh fõ' jdfkaj, f¾Çh m%idrK
ix.=Klh 110−5 0C −1 kï WIaK;ajh 1000 C ka by< .sh úg f.da,fha N%uK wjiaÓ;s >Q¾Kfha
m%;sY; jeä ùu jkqfha"

(1) 0.1% (2) 0.2% (3) 0.3%

(4) 0.5% (5) 0.002%

22. øjhla ;=< jQ jia;=jl iu;=,s;;djh ms<sn`o lr we;s my; m%ldY i,lkak'
(A) jia;=jla øjhla ;=, iu;=,s;j mej;Sug kï tys .=re;aj flakaøh W;ama,djl;d
flakaøhg jvd my,ska mej;sh hq;=h'
(B) jia;=jl .=re;aj flakaøh W;ama,djl;d flakaøhg by,ska mj;S kï lsisfia;a tu
jia;=j iu;=,s; fkdfõ'
(C) jia;=jl iu;=,s;;djfha iajNdjh tys .=re;aj flakaøfha msysàu u; r`od mj;S'
by; m%ldY w;ßka ksjerÈ fkdjkafka"
(1) A (2) C (3) A, B
(4) B, C (5) A, B yd C ish,a,u

23. m1 , m2 yd m3 ialkaO ;=kl msysàï rEmfha ±lafõ'

m1 = 3kg, m2 = 4kg yd m3 = 8kg fõ' moaO;sfha .=re;aj yv
flakaøfha (centre of gravity) LKavdxl ( x1 , y1 ) o" m2 ys w.h
jeä l< úg moaO;sfha .=re;aj flakaøfha LKavdxl
(coordinates) ( x, y ) o kï"

(1) x  x1 y  y1
(2) x  x1 y  y1
(3) x  x1 y  y1
x
(4) x  x1 y  y1
(5) x = x1 y = y1

24. 3F yd 8F Odß;%l folla iudka;r.;j iïnkaO lr ta yryd V úNjhla mj;ajdf.k we;' fuu
Odß;%l foflys wka;¾.; jk Yla;s w;r wkqmd;h jkafka"
9 1 3
(1) (2) (3)
64 1 8
64
(4) (5) by; tajd lsisjla fkdfõ'
9
 ish¨ u ysñlï weúßKs] All Rights Reserved] 6 AL/2024/01-S-I

25. rEmfha ±lafjk mßm:fha P yd Q w;r iul m%;sfrdaOh

l=ula fõo@
(1) 1 (2) 2
(3) 3 (4) 4
(5) 5

26. P lïìh idod we;s øjHfha hxudmdxlh Q lïìh idod we;s øjHfha tu w.hg jvd jeäh' lïì
folu tlu wd;;shlg ,la l< úg P lïìfha ú;;sh Q lïìfha tu w.hg jvd jeä nj fidhd
.kakd ,§' my; i`oyka m%ldY i,ld n,kak'
(A) P lïìfha úIalïNh Q g jvd wvqjj
q fyd;a muKla by; isÿùu isÿ úh yel'
(B) P lïìh i`oyd uq,a È. úIalïNhg ork wkqmd;h Q ys tu w.hg jvd jeä jqjfyd;a
muKla my; isÿùu isÿ úh yel'
(C) P lïìfha È. Q lïìfha È.g jvd wvq jqjfyd;a by; isÿ ùu lsis úfgl isÿúh
fkdyel'
by; m%ldYj,ska"
(1) A muKla i;H fõ' (2) B muKla i;H fõ' (3) C muKla i;H fõ'
(4) A iy B muKla i;H fõ' (5) B iy C muKla i;H fõ'

1 2
27. rEmfha fmkajd we;s fjda,aàh;d mdGdxl V2 = V0 yd V1 = V0 fõ' túg R1, R2 m%;sfrdaOj, w.hka
5 5
jkafka"
V0
(1) 2R, 2R R
(2) R, 2R R V1
2R R2 V2
(3) 2R, R
(4) R, R
(5) R/2, R

28. rEmfha ±lafjk mßÈ gexlshl m;=f,a  È.e;s ;sria isyska k<hla
we;' h Wil c, uÜgu mj;ajd f.k hdu i`oyd gexlshl c,h
iemhshs hq;= iS>%;djh Q fõ' iudk yrialv j¾.M,fhka hq;a 
È.e;s ;j;a isyska k,hla fY%aK.
s ;j iïnkaO lsÍfuka miq c,
uÜgu Wi 2h ksh; w.hl mj;ajd .kafka kï fuúg gexlsfhka
c,h bj;a jk is>%;dj jkafka" c,h ÿiai%dù ;r,hla f,i
yeisfrkafka hehs Wml,amkh lrkak'
Q
(1) (2) 4Q
4
(3) 2Q (4) Q
Q
(5)
2
ish¨ u ysñlï weúßKs] All Rights Reserved] 7 AL/2024/01-S-I

29. Wi 5m jQ isria fldä .ila úYd, msyskqï ;gdlhl

tla fl<jrl iú fldg we;' rEmfha ±lafjk mßÈ
iQ¾hdf,dalh ;sri iu`. 450 l fldaKhla idoñka
fldä .i u; m;kh jk úg§ ;gdlfhys m;=, u;
iEfok fldä .fiys Pdhdfjys È.
(1) 6m g jvd jeäh'
(2) 6m fõ'
(3) 6m g jvd wvq jk w;r 5m g jvd jeäh'
(4) 5m fõ'
(5) 5m g jvd wvq fõ'

30. kdNsh ÿr 10cm jQ ir, wkaùCIhla fhdodf.k YsIHfhl= óg¾ rE,l jQ b,lalï ksÍCIKh lrhs'
wkaùCIh u.ska ,nd.; yels Wmßu úYd,kh hgf;a óg¾ rE, ksÍCIKh l, úg óg¾ rEf,a 23cm
yd 24cm i,l=Kq 02 w;r ÿr 37mm nj fidhd.kakd ,§' YsIHhdf.a úIo oDIAáfha wju ÿr jkqfha"
(1) 25cm (2) 26cm (3) 27cm
(4) 28cm (5) 30cm

31. ixLHd;h 1320Hz jQ k,djla y`vjñka m%Njhla (source)ksYap, ksÍlaIlfhl= foig 10 ms −1

fõ.fhka .uka lrhs' ksÍlaIlhd fj;g tk ;rx.fha ;rx. wdhduh(wave length) lSho@
(jd;fha èjks m%fõ.h 340 ms −1 )

(1) 30cm (2) 25cm (3) 28cm

(4) 27cm (5) 26cm

32. f¾Çh m%idrK;d ix.=Klh  jk f,day nÿkl h Wilg c,h mqrjd we;s w;r n`ÿfka m;=f,a l=vd

isÿrlska c,h bj;aj hk iS>%;djh Q1 fõ' miqj n`ÿfka c,h bj;a lr n`ÿfka WIaK;ajh 
m%udKhlska jeä lr kej;;a c,h óg fmr Wi olajd mqrjkq ,nhs' fuúg mßud .e,Sfï iS>%;djh
Q2 fõ' wjia:d fofla§u n`ÿfka c, uÜgu my< hk fõ.h fkd.sksh yels ;rï l=vd kï wjia:d
fofla§ isÿrej,ska mßudj bj;a hdfï iS>%;djh Q1/Q2 .Kkh lrkak'

(1) (1 + 2 ) / h (2) 1 /(1 +  ) (3) 1 /(1 + 2 )

(4) (1 + 2) (5) (1 + 2) /(1 + )

33. f¾Çh m%idrK;djhka 1 ,  2 ,  3 ,  4 f,day má 4 la rEmfha mßÈ mdiaid we;' tys

WIaK;ajh wvq l, úg S wl=rl yevh .kS'

(1) 1   2 iy  3   4
(2)  2  1 iy  4   3
(3) 1   2 iy  4   3
(4)  2  1 iy  3   4
(5) 1 =  2 iy  3 =  4
ish¨ u ysñlï weúßKs] All Rights Reserved] 8 AL/2024/01-S-I

34. ABC iumdo ms%iauhls' wdf,dal lsrK .uka ud¾.h fuys ±lafõ' ùÿre
j, j¾;kdxlh

3
(1)
2
(2) 3
(3) 2
2
(4)
3
(5) 2 3

35. f¾Çh m%idrK;djh  jk f,daNhlska ;ekQ" wNHka;r mßudj 2V jk

n`ÿkla ;=< mßudj V jk yd f¾Çh m%idrK;djh  jk f,day l=Üáhla
;nd we;' n`ÿfka b;sß wjldYh øjhlska mqrjd we;' ´kEu WIaK;ajhl §
n÷fka lg olajd u øjh msÍ mej;Sug øjfha mßud m%idrK;djh úh hq;af;a"

(1) 3(2 −  )
(2) 3( +  )
(3) a−
(4) 2 − 
(5)  + 2

36. rEmfha wdldrhg ld¾hlaIu;djh η jk úÿ,s n,anhla ialkaOh

m yd úYsIag ;dm Odß;djh C jk øjhla wvx.= n`ÿkl .s,ajd we;'
n,anhg v úNj wka;rhla iemhQ úg I ksh; Odrdjla .,d hhs'
c,fha WIaK;ajh  0C m%udKhlska by, kexùug .; jk ld,h
jkafka"

mc  100  mc  + 100 

(1) (2)
vI 100 −  
  vI 100 −  

100mc mc
(3) (4)
vI 100vI

mc 100 −  
(5)
vI  100 

37. 220V úNj wka;rhla hgf;a 200W ;dmk o`.rhla yd 100W úÿ,s n,anhla tajdfha Wmßu
laIu;djfhka l%shd lrúh yelsh' tajdfha m%;sfrdaO ms<sfj,ska R1 yd R2 fõ' R1 yd R2 w;r
iïnkaOh úh yelafla"
(1) R1 = R2 (2) R2 = 2R1 (3) R1 = 2R2
(4) R1 = 3R2 (5) 3R1 = R2
ish¨ u ysñlï weúßKs] All Rights Reserved] 9 AL/2024/01-S-I

38. d mr;rhla we;s iudka;r ;yvq Odß;%lhl ;yvq

fol w;rg mdr úoHq;a ksh;h k1 yd k2 jk øjH
folla iudkj rEmfha mßÈ fhdod we;' fuu
ieleiafï iul Odß;dj úh yelafla"

A 0 (k1 + k 2 ) (k1 + k 2 )
(1) (2) A 0
d 2d

A 0 1 1 A 0 k1k 2 A 0 k1k 2
(3)  +  (4) (5)
d  1
k k 2 d k1 + k 2 2d k1 + k 2

39. iúê Ivdi%hl Ys¾I myl +q(C) ne.ska jQ ,laISh wdfrdamK myla ;nkq ,efí' Ivdi%fha mdohl È.
a kï" tys flakaøfha ;enQ -q(C) wdfrdamKhla u; fhfok iïm%hqla; úoHq;a n,h jkafka"
2 2 2
1 q 2 q 1 q
(1)   (2)   (3)  
 0  a   0  a  2 0  a 
2 2
4 q 1 q
(4)   (5)  
 0  a  4 0  a 

40. rEmfha oelafjk >k fla;=fõ Wi h o" wdOdrlfha wrh r o fõ' fla;=j
fmr,Sug fmr fkd,siaihs kï iu;=,s;;dj fkdìf`ok mßÈ wdk;
;,h we, l< yels Wmßu fldaKh" ^G .=re;aj flakaøhhs'&

(1) tan −1 (h / r ) (2) tan −1 (r / h)

(3) tan −1 (h / 3r ) (4) tan −1 (h / 4r )

(5) tan −1 (4r / h)

41. rEmfha fmkajd we;s Odß;%l moaO;sfha AB yryd 1200V

úNj wka;rhka fh¥ úg CD yryd 450V úNj wka;rhla
we;súh' ál fõ,djlska CD yryd úNj wka;rh 600V olajd
jeäúh' l=uk Odß;%lh $ Odß;%l ¨yqj;a ù we;ao@

(1) 1μF
(2) 2μF
(3) 3μF
(4) 4μF
(5) ish¨u Odß;%l
ish¨ u ysñlï weúßKs] All Rights Reserved] 10 AL/2024/01-S-I

42. A, B yd C hkq jdfkaj,ska idod we;s lïì 3 ls' A lïìfha È. l o yrialv j¾.M,h A o fõ' B
lïìfha È. 2l o yrialv j¾.M,h A o fõ' C lïìfha È. l jk w;r yrialv j¾.M,h 2A fõ'
tla tla lïìj, ú;;s (e) n, (F) ksjerÈj olajd we;af;a

(1) (2) (3)

(4) (5)

43. ;srig 450 l fldaKhlska wdk; r`: ;,hla u; 10kg l P

ialkaOhla we;s jia;=jla iSudldÍ iu;=,s; wjia:dfõ ;nd ;nd
we;af;a P fl<jrg .eg .eiQ ieye,a¨ ;sria ;ka;=jla wdOdrfhks'
;ka;=fõ wd;;sh 25N kï" jia;=j yd ;,h w;r iaÓ;sl >¾IK
ix.=Klh"

(1) 0.5
(2) 0.4
(3) 0.6
(4) 0.45
(5) 0.25

44. kdNsh ÿr 20cm jk W;a;, ldphl isg 30cm ÿrlska m%Odk wlaIh
u; l=vd lDñfhl= jid we;' lDñhd tljru rEmfha wdldrhg
 = 600 jk fia 20cms-1 m%fõ.fhka by,g b.s,Shdug mgka .kshs'

lDñhd by,g kslau hdu wrUk fudfydf;a isg ;;amr 1la olajd
ld,h ;=< lDñhdf.a m%;sìïnfha uOHkH iïm%hql;
a m%fõ.h
jkafka"

(1) 20 𝑐𝑚𝑠 −1 (2) 10 √3 𝑐𝑚𝑠 −1 (3) 20 √5 𝑐 𝑚𝑠 −1

−1
(4) 10 √7 𝑐𝑚𝑠 −1 (5) 50 cms
ish¨ u ysñlï weúßKs] All Rights Reserved] 11 AL/2024/01-S-I

45. YsIHfhla yg mÍlaIKhla i`oyd 1000C yqud,h 200g la wjYH úh' ta i`oyd Tyq 250C ys c,h 150g
iy 00C ys whsia 50g la ;dm mßjrKh l< le,ß ógrhlg oud .s,a¨ï ;dmlhla fhdod r;a lsÍu
wdrïN lf<Ah' 270V úNj iemhqug ;dmlh iïnkaO l< úg c,h keàug ñka;a;= 20 la .; úh'
.s,a¨ï ;dmlh yryd .uka l< Odrdj fldmuK o@ (c,fha úYsIaG ;dm Odß;djh = 4000JK-
1
Kg-1 , c,fha ú,hkfha .=ma; ;dm Odß;djh = 2 x105 JKg-1, c,fha jdIamSlrKfha .=ma; ;dm
Odß;djh = 3 x 106 JKg-1)

(1) 1A (2) 2A (3) 3A

(4) 4A (5) 5A

46. tlsfkflys >klu t ne.ska jk tlsfklg fjkia

j¾;kdxl iys; ia:r 03la tlafldg ixhqla; ùÿre l=Üáhla
idod we;' jd;fha isg l=Üáh fj;g ,ïnlj we;=¿jk
wdf,dal lsrKhla A, B, C ia:r ;=k yryd .uka lrhs' B,
C ia:rj, we;sjk ;rx. jl% ixLHdfõ tl;=j fuka
fo.=Khl ;rx. jl% ixLHdjla A ia:rh ;=, we;súh'
B yd C ia:rj, j¾;kdxl ms,sfj,ska 1.5 yd 2 la fõ kï
A ia:rfha j¾;kdxlh jkafka"
(1) 1.2 (2) 2.4 (3) 3.5
(4) 7 (5) 8

47. tlsfklg ,ïnlj r`: ì;a;s folla we;s uq,a,lg  0 fldaKSl

m%fõ.h N%uKh lrk ,o is,skavrhla ;nd ksYap, ùug bv yÍ' r`:
s avrh w;r .;sl >¾IK ix.=Klh  fõ kï is,skavrh
ì;a;s yd is,k
ksYap, ùug fmr lerflk jg .Kk jkafka, is,skavrh W;a;drK
p,s;hla fkdolajk nj Wml,amkh lrkak'
02 R(1 +  2 ) 02 R(1 −  2 )
(2)
8 (1 +  )g 8 (1 +  )g
(1)

02 R(1 −  ) 02 R( 2 + 1)

8 (1 +  2 )g
(3) (4)
8 (1 −  )g
𝜔02 𝑅
(5)
8𝜋(1+𝜇)𝜇𝑔

48. ;srig 300, 600 wdk; ;, folla u; iqug w nr f.da,hla ;nd we;af;a f.da, mDIAGh wdk; ;,
folu iam¾Y lrk mßosh' tajd u.ska we;s lrk m%;sl%shd n, fudkjdo @
√3 𝑤 𝑤
(1) w, w (2) , w (3) , √3𝑤
2 3 2

√3 𝑊 √3
(4) w, (5) w, √3𝑤
2 2 2
ish¨ u ysñlï weúßKs] All Rights Reserved] 12 AL/2024/01-S-I

49. rEmfha ±lafjk mßÈ mdrfõoH;djh  0 jk udOHhl wrh R jk

jD;a;hl +Q ,laISh wdfrdamK 8 la ;nd we;' jD;a;fha ;,hg
,ïnlj tys flakaøh jk O ,laIHh yryd hk f¾Ldj u; O ys isg
r ÿrlska jQ ,laIhla u; lafIa;% ;Sj%;djh jkafka

Qr 2Qr
(1) (2)
 0 ( R + r )
2 2 3/ 2
 0 ( R 2 + r 2 )

2Qr Qr
(3) (4)
 0 ( R 2 + r 2 ) 3 / 2  0 ( R 2 + r 2 )1/ 2

2Qr
(5)
 0 ( R 2 + r 2 )1/ 2

50. wdfrdamKh +Q jk taldldr f,i wdfrdams; wrh R jQ mßjdrl >k f.da,hl

flakaøfha isg d ,ïn ÿrlska rEmfha wdldrhg b;d isyska isÿrla f.da,h yryd
ks¾udKh fldg we;' tu újrfha fl<jf¾ isg ksoyia lrk ialkaOh m jQ
l=vd –q wdfrdamKhla ,lajk ir, wkqj¾;Sh p,s;fha wdj¾: ld,h jkafka"

8 0R 3m  0R 3 m
(1) 2 (2) 4
qQ R 2 + d 2 qQ

 0R 3 Qq 3 0 R 3 m
(3)  (4) 2 (5) 8
Qmq 4 0 R 3 m Qq
ish¨ u ysñlï weúßKs] All Rights Reserved] 0 AL/2024/01-S-II

7 >laudkam:l l%irhg ka ,
ujjllóudK

04

20

jHqy.; rpkd - (A fldgi)

ish¨ u ysñlï weúßKs] All Rights Reserved] 1 AL/2024/01-S-II

jHqy.; rpkd - (A) fldgi)

1. ÿkakla hkq ndysßka fhdok Ndrhka fya;f

= jka ie,lsh hq;= ú;;shla ,nd .kakd m%;Hdia: jia;=jls'
ÿkakla ks¾udKh lsÍu i`oyd wvq hxudmdxlhla iys; jdfka f,dayh Ndú;d lrk w;r" ÿkakl
uQ,slu ,laIKh ÿkq ksh;h fõ' my; olajd we;af;a ÿkakl ÿkq ksh;h mÍlaId lsÍu i`oyd orkakd
jQ W;aidyhls'

ÿkak

C B

(1) rEmh

(a) (i) by; wegjqfuys A,B,C fldgia kï lrkak'

A- ………………………………………………………………………
B- ………………………………………………………………………
C- ………………………………………………………………………
(ii) YsIHfhla úiska ;=,d ;eáh u; Ndrhka ;nñka ÿkak olajk ú;;sh mÍlaId lsÍug
n,dfmdfrd;a;= fõ kï" ;=,d ;eáfhys ialkaOh M0 o" ta u; ;nk ;rdos mäfha
ialkaOh M o f,i .ksñka ÿkafka ú;;sh X ÿkq ksh;h k iy M, M0 w;r
iïnkaO;djhla f.dv k.kak'
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
(iii) M iy X w;r m%ia;drhla we`oSug n,dfmdfrd;a;= fõ kï ta i`oyd iqÿiq .Ks;uh
iólrKhla f.dvk.kak'
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
ish¨ u ysñlï weúßKs] All Rights Reserved] 2 AL/2024/01-S-II

(iv) ;=,d ;eáh u; ;nk ialkaOh iy thg wkqrEm X(cm) ys w.h my; j.=fõ olajd
we;'
;=,d mäh u; we;s ialkaOh (g) ÿkafka ú;;sh (cm)
50 1
100 2
150 3
200 4.2
250 5
300 5.8

my; olajd we;s lvodisfhys M g tosß X m%ia;dr.; lrkak'

(v) m%ia;drfha wkql%uKh fiùug Tn fhdod .kakd ,laIH fol meyeos,sj m%ia;drh
u; ,l=Kq lr m%ia;drfha wkql%uKh .Kkh lrkak'
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
(vi) m%ia;drfha wkql%uKh weiqßka ÿkq ksh;h (kgs-2) tall weiqßka .Kkh lrkak'
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
ish¨ u ysñlï weúßKs] All Rights Reserved] 3 AL/2024/01-S-II

(vii) m%ia;drh weiqßka ;rdos mä r`ojkfha ialkaOh g j,ska .Kkh lrkak'

…………………………………………………………………………………………..
…………………………………………………………………………………………...
(viii) by; mÍlaIKh i`oyd ;rdos mä r`ojkhg Ndrhka tla lrñka mdGdxl .ekSfïoS
Tn úiska ms<smeosh hq;= w;HjYH mshjr folla olajkak'
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
(b) (i) fy,slaih
S ÿkakg l=vd ialkaOhla iïnkaO lr thg l=vd foda,khla ,nd ÿka úg
tu p,s;h ir, wkqj¾;Sh nj fmkajkak' foda,k ld,hg .Ks;uh m%ldYhla
,nd .kak'
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
(ii) by; ÿkakg iïnkaO lr we;s ialkaOh 20g kï" π = 3 f,i f.k foda,k
ld,h i`oyd w.hla ,nd .kak'
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..
…………………………………………………………………………………………..

2. úoHd.drfhaoS pd,aiaf.a fojk kshuh i;H nj fmkaùug;a ksh; mßudfõoS jdhqjl mSvk
m%idrK;d ix.=Klh fiùug;a my; wiïmQ¾K wegjqu Ndú;d lrhs'

flá ma,diaála ngh

A C

c,h

úh<s wp, jdhq ialkaOh

jg wä ma,dial=j (500cm3)

(1) rEmh
ish¨ u ysñlï weúßKs] All Rights Reserved] 4 AL/2024/01-S-II

(a) (i) by; rEmfha my; fldgia kï lrkak'

A-…………………………………………………………………………………
B-…………………………………………………………………………………
C-…………………………………………………………………………………
(ii) by; mÍlaIKh isÿ lsÍu i`oyd fhdod .kakd wegjqfï w;HjYH fldgila
ksrEmKh lr fkdue;'tu fldgi ksjerosj we`o olajkak'
(iii) tu fhdod .kakd fldgfika n,dfmdfrd;a;= jk wNsm%dhka folla kï lrkak'
……………………………………………………………………………………….
……………………………………………………………………………………….
……………………………………………………………………………………….
(iv) mÍlaIKh isÿ lr ,nd .;a mdGdxl hq.,a lsysmhla my; j.=fõ oelafõ'
(1) tajd weiqßka mÍlaIKhg wod< m%ia;drh ks¾udKh lrkak'

θ0C mSvkh Pa
50 1× 105
100 1.1× 105
150 1.15× 105
200 1.3× 105
250 1.45× 105
300 1.5× 105
ish¨ u ysñlï weúßKs] All Rights Reserved] 5 AL/2024/01-S-II

(2) Tn ,nd .kakd o;a; weiqßka jdhqjl ksh; mßudfõ mSvk m%idrK;d
ix.=Klh .Kkh lrkak'
…………………………………………………………………………….…
…………………………………………………………………………….…
…………………………………………………………………………….…
………………………………… ……………………………………………
(3) by; (a) (iv) (2) fldgfia Tng ,enqKq w.h i;H w.hg jvd fjkia
ùug fya;=jla i`oyka lrkak'
…………………………………………………………………………….…
……………………………………………………………………….………
(b) (i) lsishï WIaK;ajhlg wod, mdGdxlhla ,nd .ekSu i`oyd by; wegjqu Ndú;d
lrk wdldrh ,shd olajkak'
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
(ii) fuu mÍlaIKfhaoS c, îlrh Rcqj f;mdj u; ;nkjd fjkqjg lïì oe,la u;
;eîug fya;=j ,shd olajkak'
………………………………………………………………………………………
………………………………………………………………………………………
(iii) fuysoS c, îlrh r;a lrjd .ekSu i`oyd nkaika odylh r;a lrkjd fjkqjg
úoHq;a W`ÿka ;eáhla Ndú;d l< yelso hkak fya;= iys;j ,shd olajkak'
………………………………………………………………………………………
………………………………………………………………………………………

3. m%ia;dßl l%uhla Ndú;d lrñka ixLHd;h okakd iriq,a lÜg,hla yd wkqkdo k<hla Ndú;fhka
jd;fha èjks m%fõ.h (v) yd k<fha wdka; fodaIh (e) fiùu i`oyd fhdod.kakd mÍlaIKd;aul
wegjqula my; rEmfha oelafõ'

A B C D E

(1) wegjqu
ish¨ u ysñlï weúßKs] All Rights Reserved] 6 AL/2024/01-S-II

(a) (i) by; WmlrK wegjqu wiïmQ¾K fõ' th iïmQ¾K lrk wdldrh rEm igyk u;
we`o olajkak'
(ii) YsIHfhl= mÍlaIKh wdrïN lsÍfïoS Ndú;d lrk ish¨ iriq,a i`oyd uQ,l
s wkqkdo
os.g wod,j mÍlaIKh isÿ l< yels o hkak mÍlaId lr .; hq;= fõ' fuh
mÍlaIKd;aulj isÿ lrk wdldrh úia;r lrkak'
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
(iii) mÍlaIKfha uq,au wkqkdo os. ,nd .ekSu i`oyd Tn úiska f;dard .kq ,nkafka
l=uk iriq,o hkak i`oyka lr tu wkqkdo os. ,nd .kakd wdldrh
meyeos,sj i`oyka lrkak'
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
(iv) fuu mÍlaIKfhaoS wkqkdo k,h c,h ;=< .s,aùfï wjYH;djh l=ula o hkak
i`oyka lrkak'
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..

(b) (i) iriq,lg wod<j k<h ;=< f.dvef.k uQ,l s ;dkhg wod< ;rx. rgdj by;
rEmfhau we`o olajd th wkajdhdu o ;S¾hla o hkak;a" m%.uk o ia:djr o hkak;a
i`oyka lrkak'
………………………………………………………………………………………..
………………………………………………………………………………………..
(ii) ixLHd;h f iriq,la Ndú;d lrk úg uQ,sl ;dkhg wkqrEmj k<fha os. l o úg
ixLHd;h f i`oyd m%ldYkh l, e yd v weiqßka ,shd olajkak'
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
(iii) m%ia;dßl l%uhla Ndú;fhka v yd e .Kkh lsÍug by; m%ldYkh iajdhla; yd
mrdhla; úp,Hhka meyeos,sj olajñka ilia lrkak'
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
ish¨ u ysñlï weúßKs] All Rights Reserved] 7 AL/2024/01-S-II

(c) (i) úoHd.drfhaoS YsIHfhl= úiska os. l jk fl<jrla ixjD; wkqkdo k<hla Ndú;d
lr tys újD; fl<jr wi, úp,H ixLHd; m%Njhla ;nd k<h wkqkdo lrjhs'
2𝑙
fuu k<fha újD; fl<jf¾ isg ÿrlska l=vd isÿrla mj;skf
a ka kï" k<h ;=<
3
we;s úh yels uQ,sl iy m<uq wkqkdo wjia:d we`o olajkak'

(ii) by; os.u iys; fofl<jr újD; k<fha uOH ,laIHfha l=vd isÿrla mej;sh fyd;a
ta ;=< we;s úh yels uQ,sl iy m<uq Wmß;dk wjia:d we`o olajkak'

4. úoHd.drfhaoS fya.ka fmdhsfi,a iólrKh Ndú;fhka ;sriaj we;s flaYsl k<hla ;=<ska .,d hk
ødjKhl ,laIK wOHhkh lr ødjKfha ÿiai%dù ix.=Klh fiùug n,dfmdfrd;a;= fõ' YsIHhka
ta i`oyd 20cm la os. flaYsl k<hla f.k th msßis`ÿ lr .kS'
(a) (i) úoHd.drfhaoS flaYsl k<hla ksjerosj msßis`ÿ lr .kafka flfia o@
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
bka miq flaYsl k<h wdOdrlhlg iú lr tys tla fl<jrl ksh; mSvk øj uÜgï
WmlrKhla iú lr my; wegjqu idod .kS'

(1) rEmh
(ii) A yd B fldgia kï lrkak'
A- ……………………………………………………………………………………
B- ……………………………………………………………………………………
ish¨ u ysñlï weúßKs] All Rights Reserved] 8 AL/2024/01-S-II

(iii) ksh; mSvk øj uÜgï WmlrKh yd B fldgfia mÍlaIKh i`oyd isÿ lrk ld¾hh
Nd¾hh l=ula o@
……...…………………………………………………………………………………
……...…………………………………………………………………………………
……...…………………………………………………………………………………
(iv) fhdod .;a flaYsl k<h ;sriaj mj;skf
a ka oehs ;yjqre lr .kafka flfia oehs
fláfhka meyeos,s lrkak'
……...…………………………………………………………………………………
……...…………………………………………………………………………………
……...…………………………………………………………………………………
(v) fuu mÍlaIKfhaoS ñkqï ird j, jeä øj mßudjla tl;= ùu i`oyd .; jk ld,h
uekSu isÿ l< hq;=h' tu.ska n,dfmdfrd;a;= jkafka l=ula o@
……...…………………………………………………………………………………
……...…………………………………………………………………………………
……...…………………………………………………………………………………
(vi) øjhl ÿiai%dú;d ix.=Klh ks¾Kh lsÍug tu mÍlaIKh fhdod .ekSfï wjdishla
,shd olajkak'
……...…………………………………………………………………………………
……...…………………………………………………………………………………
……...…………………………………………………………………………………
(b) fuysoS lsishï t ld,hloS îlrhg tl;= jk øj mßudj V kï" V/t yd h w;r YsIHhska
úiska w`osk ,o m%ia;drhla my; oelafõ'
V/t

h
hx
(i) x = hx j,ska miqj m%ia;drfha yevh fjkia ùug fya;=j l=ula o@
……...…………………………………………………………………………………
……...…………………………………………………………………………………
……...…………………………………………………………………………………
(ii) fuu øjfha ÿiai%dú;d ix.=Klhg jvd jeä ÿiai%dú;d ix.=Klhla iys; øjhla
fhdod f.k by; mÍlaIKh isÿ l< fyd;a w`oskq ,nk m%ia;drfha
oelsh hq;= o< yevh fuu m%ia;drfha we`o X f,i kï lrkak'
(c) flaYsl k<fhys wNHka;r wrh uek .ekSu i`oyd úoHd.drfhys riosh Ndú;hg bv ,nd
fkdfoa' tneúka mÍlaIKfhka wk;=rej flaYsl k<fha ia:dk ;=klska lmd fjka lr
p, wkaùlaIh Ndú;fhka wNHka;r úIalïNh uekSug n,dfmdfrd;a;= fõ'
ish¨ u ysñlï weúßKs] All Rights Reserved] 9 AL/2024/01-S-II

(i) fuu p, wkaùlaIh ksmojd we;af;a w¾O ñ,s óg¾ fldgia 49 la jʹksh¾ fldgia
50 lg fnoSfuks' fuys l=vd ñkqu .Kkh lrkak'
……...………………………………………………………….………………………
……...…………………………………………………………………………………
……...…………………………………………………………..……………………

(ii) fï i`oyd fhdod .kakd tlsfklg ,ïNl úIAlïNhka folla ,nd .ekSfïoS my;
wdldrhg ksrEmKh fõ' tu.ska tu úIalïN fol i`oyd m%ldYk ,nd .kak'

1 wjia:dj 2 wjia:dj
;sria mdGdxlh x1 x2
isria mdGdxlh y1 y2

………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
(iii) tfia ,nd .;a úIAlïN yhlg wod< w.hka my; oelafõ' tu.ska fuu flaYsl
k<fha uOHkH úIalïN .Kkh lrkak'
1.03mm, 1.05mm, 2.56mm, 0.97mm, 0.95mm, 1mm
………………………………………………………………………………………..
………………………………………………………………………………………..
………………………………………………………………………………………..
ish¨ u ysñlï weúßKs] All Rights Reserved] 10 AL/2024/01-S-II

fuu m%Yak m;%fha iïmQ¾K whs;sh iqismajka Wiia wOHdmk ^fm!oa& iud.u i;= jk w;r fuu m%Yak m;%fha
wka;¾.; lsisjla bf,lafg%dakslj" hdka;%slj fyda Pdhd msgm;a lsÍu yd .nvd lr ;eîu imqrd ;ykï fõ'
tfia l<fyd;a Bg úreoaOj wm iud.fï kS;s wxYh u`.ska kS;suh mshjr .kq ,nhs

2024
2024
2024
2024
04
03

meh
meh úkdä
úkdä
0202 1515
2
02 02 Hour
Hour 15 15 Minutes
Minutes
3
B fldgi – rpkd
m%Yak 04 muKla ms<s;=re imhkak'
[ g = 10Nkg-1 ]
5. (a) l%slÜ l%Svdj hkq fN!;sl úoHd lreKq rdYshla
wka;¾.; ukrï l%Svdjls' fuu .eg¨fõoS wm úiska A ω
wOHhkh lrkq ,nkafka l%slÜ l%Svdfõ mj;sk fuu
fN!;sl fhoSï lsysmhla iïnkaOfhks' my; olajd r
we;af;a mkaÿ hjkafkl= osj ú;a fmdf<djg
v O
idfmalaIj ;sriaj v m%fõ.fhka ms;slrejd foig
mkaÿjla fhduq lrk wdldrh jk w;r tysoS mkaÿjg
rEmfha olajd we;s wdldrhg ;sriaj v m%fõ.hla iy B
mkaÿfõ N%uKh i`oyd ω fldaKsl m%fõ.hla ,nd
oS mkaÿj bosßhg úis lrkq ,nhs'

(i) mkaÿfõ flakaøh O o A yd B hkq ms<sfj,ska flakaøfha isg isriaj by<ska iy

my<ska msysá ,laIH folla fõ' mkaÿj by; olajd we;s wdldrhg fhduq l< úgoS
A yd B ,laIH j, mkaÿfõ flakaøhg idfmalaIj iam¾YSh m%fõ.h osYdj;a iu.
,shd olajkak
(ii) mkaÿj f¾Çh m%fõ.h fya;=fjka fmdf<djg idfmalI a j A yd B wjg we;s wxY=
j, m%fõ.fha osYdj iu`. ,shd olajkak
(iii) mkaÿfõ f¾Çh m%fõ.h yd N%uKh i,lñka A yd B wjg jd; wxY= j,
fmdf<djg idfmalaIj m%fõ.hka ms<sfj,ska (v – rω) yd (v + rω) nj fmkajkak'
(iv) A yd B ,laIH j,g n'kQ,s uQ,O¾uh fhoSfuka mkaÿfõ isÿ jk N%uKh
fya;=fjka mkaÿj fomi we;s jk mSvk wka;rh i`oyd m%ldYkhla P = 2r v
u.ska ,efnk nj fmkajkak' fuys r, ρ iy ω hkq ms<sfj,ska mkaÿfõ wrh"
jd;fha >k;ajh yd mkaÿ hjkakd úiska mkaÿjg ,nd fok fldaKsl m%fõ.h nj
i,lkak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 11 AL/2024/01-S-II

(v) by; rEmh Tnf.a ms<s;=re m;%hg msgm;a lr mkaÿj u; n,h l%shd lrk wdldrh
tu rEm igyfka olajkak'
(vi) fuu mSvk wka;rh ksid yg .kakd n,h mkaÿfõ wrh iys; jD;a;dldr ;eáhla
u; n,mdk n,hg iudk nj Wml,amkh lrñka mkaÿj u; my<g l%shd lrk
3 v
iM, ;ajrKh a = g + u.ska ,efnk nj fmkajkak' fuys d hkq mkaÿj
2d
idod we;s øjHfha uOHl >k;ajh fõ'
(vii) l%Svlhd mkaÿj msßkuk ia:dkh fj; ÿj ú;a mkaÿj Tyqg idfmalaIj 20 ms-1
m%fõ.fhka ;sriaj msßkukq ,nhs' tysoS mkaÿj l%Svlhdf.a w;ska .s,sfyk
ia:dkhg fmdf<dj uÜgfï isg we;s Wi 2.16 m jk w;r" mkaÿjg l%Svlhd
úiska ,nd fok fldKsl m%fõ.h 80 rad s-1 fõ' fuu mkaÿj fmdf<dj yd .eàug
.; jk ld,h .Kkh lr tu ld,h ;=<oS mkaÿj bosßg .uka l< ÿr .Kkh
lrkak' fuu fldgi i`oyd jd;fha >k;ajh 1.2 kgm-3 o" mkaÿj idod we;s
øjHfha uOHkH >k;ajh 1800 kgm-3 o f,i .kak'
(viii) fï osk j, ngysr bkaoSh fldfoõ ¥m;a yd wefußldfõ i;aldrl;ajfhka f,dal
l=i,dk ;r`.dj,shla meje;afjk w;r fuu ;r`.dj,shg t,a, jk m%Odk
fodaIdfrdamKh jkafka ukao.dó ;K ;Sre Ndú;d lr ;r`. ixúOdkh lr
;sîuhs' wefußldfõ jd;fha >k;ajh 1.4kgm-3 kï" fuu mkaÿj fmdf<dj yd
.eàug .; jk ld,h .Kkh lr tu ld,h ;=< mkaÿj .uka l, ;sria ÿr
.Kkh lrkak'
(ix) by; o;a; wkqj wefußldfõ ;K ;Sre j, ukao.dñ;ajhg fya;= meyeos,s
lrkak'
(b) fujr f,dal l=i,dkh i`oyd wefußld tlai;a ckmoh úiska ksõfhdalays Nassau County
kï kj l%Svdx.Khla ks¾udKh lrk ,oS' wfkl=;a lS%vdx.K j,g idfmalaIj fuys
úfYaI;ajh jkafka tys ;K ;Sre f,i idïm%odhsl ;K ;Sre fjkqjg dropping pitch ;K
;Sre Ndú;d lsÍuhs' dropping pitch ;K ;Sre j, úfYaI;ajh jkafka tu ;K ;Sre ms<sfh,
lrkafka idïm%%odhsl f,i l%Svd msáh ;=< fkdj l%Svdx.kfhka msg; msysá úfYAI ;DK
ksIAmdokh lrk wdh;k (turf farm) ;=<oSh' Nassau County l%Svdx.kfha ;K ;Sre
´iafÜ%,h
s dfõ Adelaide ysoS ks¾udKh lr 2023 foieïn¾ udifhaoS weußldjg wdkhkh
lrk ,oaols'
idudkHfhka dropping pitch ;K ;Sre fuá%la fgdka 20 la muK ialkaOhla mj;S'
dropping pitch ;K ;Sre l%Svd msáfha mssg; kshñ; ia:dkhg f.k hdug my; oelafjk
wdldrfha ieleiaula iys; fodUlr Ndú;d lrhs' A, B yd C frdao j, wrhka ms<sfj,ska
40 cm, 20cm yd 50 cm fõ'

C B

(1) rEmh
ish¨ u ysñlï weúßKs] All Rights Reserved] 12 AL/2024/01-S-II

(i) ;r`.fhka wk;=rej kej;;a ;K ;Srej turf farm fj; f.k hdug fodUlrhla
u.ska ;K ;Srej 2m Wila A cj frdaoh u.ska 100s la ;=< Tijhs' ;K ;Sre fuysoS
taldldr m%fõ.fhka Tijhs kï" tu m%fõ.h .Kkh lrkak'
(ii) C oe;s frdaofha fldaKl
s m%fõ.h fidhkak'
(iii) B j, iam¾YSh m%fõ.h .Kkh lrkak'
(iv) B frdaoh fkd,siaik mßos A iu. máhlska iïnkaO lr we;' A j, fldaKsl
m%fõ.h .Kkh lrkak'
(v) ;K ;Srejla 2m la tiùfïoS cj frdaofha fldaKsl úia:dmkh .Kkh lrkak'
(vi) ;K ;Sre tiùfï wjia:dj i`oyd fodUlrfha laIu;dj .Kkh lrkak'

6. (a) (1) rEmfha mßos wdf,dal lsrKhla j¾;k wxlh n1 jQ .yk udOHhlska jd;hg ks¾.;
fkdjkafka kï Bg by<ska fjk;a j¾;k wxlh n2 jQ udOHhla fhÿj o wdf,dal
lsrKh tu udOH Tiafia .uka lr kej;;a jd;hg ks¾.; fkdjk nj oS we;s ixfla;
weiqßka fmkajkak'
a

r
a n2
r

n1 θ
n1 θ θ

(1) rEmh (2) rEmh

(b) rEmfha olajd we;af;a j¾;kxlh 1.46 la jk

øjHhlska idod we;s ùÿre l=Üáhls' fuys AB 1.46
uqyqK;g we`È wNs,ïNh iu`.  fldaKhla
;kñka wdf,dal lsrKhla m;s; fõ'
(i)  = 0 wjia:dfõ yer wfkl=;a lsisÿ 
w.hla i`oyd lsrKh AB uqyqK;ska jd;hg ks¾.; úh fkdyels nj fmkajkak'
(ii) AB uqyqK;g by< wjldYh j¾;kdxlh 1.29 jk øjHhlska mqrjd we;afkï
by; wdf,dal lsrKh AB uqyqKf;a§ mQ¾K wNHka;r mrdj¾;khg ,la ùu
i`oyd  fldaKfha Wmßu w.h .Kkh lrkak'
(iii)  = 300 jk wjia:dj i`oyd by; wdf,dal lsrKfha .uka ud¾.h fldaK
iys;j we`o olajkak'

(c) by; ùÿre l=Üáh my; rEmfha olajd we;s

wdldrhg j¾;kdxlh 1.35 jk udOHhl .s,ajd 1.35
we;akï fuu wdf,dal lsrKh AB uqyqKf;a§
mQ¾K wNHka;r mrdj¾;khg ,la ùu i`oyd 
i`oyd Wmßu w.h .Kkh lrkak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 13 AL/2024/01-S-II

7. úYd,j bÈ lrk ,o .nvd ixlS¾Khl we;=<; >kldldr i¾jiu fmÜá r`ojd ;eîu i`oyd
;Ügqjla bÈ lsÍug ie,iqï lr we;' my; rEmfha olajd we;s wdldrhg fuu ;Ügqfjys me;a;l
È. 20m ne.ska fõ' rEmfha olajd we;s wdldrhg jfÜ iú lr we;s jdfka lKq u`.ska ;Ügqfjys
Ndrh iy ta u; ;nk NdKavj, Ndrh ord .kS' ieleiafuys uq`M Ndrh ord .ekSu i`oyd my;
rEmfha olajd we;s wdldrhg lKq 16 la Ndú;d lrhs' ;Ügqfjys tall j¾.M,hl ialkaOh
480kgm-2 jk w;r ta u; ;nk >kldldr fmÜáhl ialkaOh 3840kg fõ' fï wdldrfha >kl
100 la taldldrj fuu m%foaYfha jHdma; lsÍug ie,iqï lr we;'
20m

20m

(a) (i) ;Ügqfjys iy ;Ügqj u; wka;¾.; iïmQ¾K NdKavj, ialkaOh 5.76 x 105 kg
nj fmkajkak'
(ii) tla lKqjlg ,efnk Ndrh .Kkh
lrkak' F/A
(b) fuu lKq ilia lsÍu i`oyd jdfka o`vq Ndú;d
lsÍug wfmalaId lrk w;r fuys olajd we;af;a 8
jdfkaj, úl%shdjg tÈß m%;Hdn, m%i;a drh fõ' 4 x10
(i) jdfka j, hxudmdxlh .Kkh lrkak'
8
(ii) fuu l=`Mkla ks¾udKh lsÍug 3 x10
n,dfmdfrd;a;= jkafka yriallv
2
j¾.M,h 20cm jQ iup;=ri%dldr
yrialvlska hqla;j tys Wi 4m jk
mßÈh' ta wkqj tla l=`Mklg ,efnk
m%;Hdn,h tys iSudldÍ m%;Hdn,fha
l=uk m%;sY;hlao hkak .Kkh
e / l0
1.5 x10-3 4 x10-3
lrkak'
(iii) fuys§ Ndú;d lrk jdfka oKafâ Wi 4m kï oKav ,lajk iïmSvkh .Kkh
lrkak'
(c) fuu bÈlsÍfï§ úhou wvq lr .ekSu i`oyd .nvdj wh;a iud.u u`.ska fjk;a
l%ufõohla we;ao hkak ms,sn`oj jr,;a bxðfkare uy;df.ka úuiSula isÿ lrkq ,nhs' ta
wkqj Tyq úiska m%ldY lrkq ,nkafka .nvdfõ lKqj, Wi wvq lsÍu u`.ska fuh isÿ
lr.; yels njhs'
(i) lKqjl Wi 3m jk wdldrhg ks¾udKh lsÍug ie,iqï lrkafka kï by;
wjia:dfõ lKqfõ mßudjg iudk mßudjlska ks¾udKh l<yels iup;=ri%dldr
yrialvla we;s lKqfjys yrialv lafIa;%M,h .Kkh lrkak'
(ii) ta wkqj by; lKqj úiska ,nd.;a m%;Hdn,hu ,nd .kakd wdldrhg fuu
lKqjg
±ßh yels Wmßu Ndrh .Kkh lrkak'
(iii) .nvdj wh;a iud.u bxðfkare uy;df.a fuu fhdackdjg tl`. jk w;r ta
wkqj 3m Wi lKq Ndú;d lsÍug ;SrKh lrhs' ta wkqj (a) (ii) ys Ndrh ±Íug
yels jk mßÈ f;dard.; hq;= jdfka l=`Mfkys yrialv lafIa;%M,h .Kkh
lrkak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 14 AL/2024/01-S-II

(d) jr,;a bxðfkare uy;d úiska fuu

F
bÈlsÍfï§ ,nd § we;s ;j;a
m%Odk;u o;a;hla jkafka fuu
l=`MKl w;a;sjdrug wod< o;a; fõ'
ta wkqj l=`MK u; fhfok n,h iy 3m 3Ft
l=`MfKa Ndrh ord.; yels wdldrhg 3Ft
w;a;sjdru ks¾udKh l< hq;=h' h
fï wkqj me;a;l È. wä 3la (90cm FS
h
la) jk iup;=ri%dldr yrialvlska Fb
3Ft
hq;a fldkal%SÜ l=`MKq f,i
w;a;sjdrï bÈ lsÍug ie,iqï flf¾' w;a;sjdru u; fhfok n,h;a m%Odk jYfhka
fldgia follg fjkalr ±laúh yelsh' tajd kï w;a;sjdru u; isriaj by<g
fmdf<dfjka we;s lrk Fb n,h iy tys me;s mDIaGh u; we;sjk Fs n,h fõ'
(i) l=`MK idod we;s jdfkaj, >k;ajh 7500kgm-3 kï l=`MfKa Ndrh" l=`MK u;
by<ska fhfok n,hg ork wkqmd;h .Kkh lrkak' ^fuu w.h 1% g jvd wvq
ùfï§ .eg¨ úi§fï§ th fkdi,ld yßk nj i,lkak')
(ii) w;a;sjdru u; by<g m;=f,a tall j¾.M,hla u; n,h 4  10 5 Nm −2 kï m;=<
u; isriaj by<g we;s jk n,h .Kkh lrkak'
(iii) w;a;sjdrfï m;=f,ka isriaj by<g we;sjk n,h tys Ndrh ord .ekSug
m%udKj;a fkdjk nj bxðfkare uy;dg fmkS hhs' ta wkqj wjYH lrk w;sßla;
n,h Fs kï iam¾YSh n,fhka ,nd .ekSug Tyq ie,iqï lrhs' tall
lafIa;%M,hla u; iam¾YSh n,h 8 10 3 Nm −2 kï by; wjYH lrk w;sßla; n,h
ord .ekSu i`oyd w;a;j
s dru fldmuK .eUqrlg (h) bÈl< hq;=o hkak .Kkh
lrkak'

8. my; rEmfha olajd we;af;a ndysr wrh 20cm o wNHka;r

wrh 10cm jQo f.da,dldr f,day lfnd,ls' fuu f,day O
-10μC
lfnd, ;=< +5μC wdfrdamKhla ia:dms; fldg tys msg; +5μC
f.da,Sh lfnd,g -10μC wdfrdamKhla ,ndfok ,§'
1
= 9  109 Nm2C − 2
4 0
(a) (i) rEmh Tnf.a ms,s;=re m;%hg msgm;a fldg f.k lfnd, ;=, fm%arKfhka
wdfrdamK jHdma; ùfuka wk;=rej lfndf,a ndysr yd wNHka;r mDIaGj, fm%aß;
wdfrdamK rEmfha ,l=Kq fldg fmkajkak'
(ii) f.da,fha flakaøfha isg ms<sfj,ska 5cm, 15cm, 25cm ÿrj,aj,ska msysá A, B, C
hk ,laIHj, ^rEmfha olajd ke;'& úoHq;a lafIa;% ;Sj%;d .Kkh lrkak'
(iii) A, B, C hk ,laIHj, úNjhka .Kkh lrkak'
(iv) lfndf,a flakaøfha isg ÿr;a iu. úNjh úp,kh jk wdldrh m%ia;dr .;
lrkak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 15 AL/2024/01-S-II

(b) by; (a) fldgfia § f.da,dldr lfnd,g msg;ska -20μC

ndysr wrh 40cm jQ o wNHka;r wrh 30 cm jQ o
f.da,dldr lfnd,la my; rEmfha wdldrhg ;nkq
-10μC
,nhs' lfnd¨ folu tal flakaøShj ;nd we;' oeka
+5μC wfrdamKh moaO;sfha flakaøfha ia:dms; fldg
O
ndysr lfnd,g -20μC wdfrdamKhla o we;=,;
+5μC
lfnd,g -10μC wdfrdamKhla o ,ndfohs'
(i) by; moaO;sh Tnf.a ms,s;=re m;%hg msgm;a
fldg f.k fm%ArKfhka wdfrdamK
jHdma;ùu i,ld tla tla f.da,dldr
lfnd¨j, ndysr yd wNHka;r mDIaGj,
mj;sk wdfrdamKhka tu rEm igyfka ksrEmKh lrkak'
(ii) moaO;sh flakaøfha isg 5 cm yd 40 cm ÿr j,ska msysá D yd E ,laIHj, úoHq;a
lafIa;% ;Sj%;d .Kkh lrkak'
(iii) lfndf,a flakaøfha isg mj;sk ÿr;a iu. úoHq;a lafIa;% ;Sj%;djh úp,kh jk
wdldrh m%i; a dßlj ksrEmKh lrkak' m%ia;drh ;=, x wlaIh u; x = 10cm,
x = 20cm, x = 30cm, x = 40cm hk f¾Ld ,l=Kq lrkak'

9. (A) fldgig fyda (B) fldgig muKla ms<s;=re imhkak'

(A) fldgi

wm tosfkod cSú;fhaoS Ndú;d lrkq ,nk úoHq;a WmlrK wêl Odrd .e,Su ;=<ska ms,siaiS hdu
j<lajd .ekSug úoHq;a ú,dhl Ndú;d lrkq ,nhs' úoHq;a ú,dhlhla hkq hï lsis ld,hla ;=<oS hï
lsis ks¾foaY;
s Odrdjlg jvd ta ;=<ska .uka lsÍug fkdyels jk mßos ilid we;s úfYaIs; jQ
lïìhls' tu l=vd ld,h ;=<oS ks¾foaY;
s Odrdjg jvd jeä Odrdjla ú,dhlh ;=<ska .uka l<
fyd;a tu ú,dhlh tys øjdxlh lrd <`.d ù ms<siaiS hhs' (øj fõ') lsishï mßm:hla i`oyd
ú,dhlhla f;dard .ekSfïoS tu mßm:h i`oyd iqÿiq m%udKkhkaf.ka hq;a ú,dhlhla f;dard .;
hq;=h' (π = 3)
(a) (i) m%;sfrdaOh R jk lïìhla ;=<ska I Odrdjla t ld,hla ;=< .,d hdfïoS
lïìfha W;ai¾ckh jk ;dm Yla;sh i`oyd m%ldYkhla ,shkak'
(ii) ú,dhlhla i`oyd f;dard .kq ,nk tla;rd lïìhla idod we;s øjHfha
m%;sfrdaOl;d ix.=Klh 1.6 ×10-7Ωm o" lïìfha wrh 2 mm o" lïìfha os.
18.75 cm o kï tu ú,dhl lïìfha m%;sfrdaOh .Kkh lrkak'
(iii) fuu lïìh ;=<ska 9A Odrdjla .,d hk úg lïìfha ;dmh W;ai¾ckh jk
YS>%;dj .Kkh lrkak' fuysoS lïìfha isÿ jk WIAK;aj jeä ùu fya;=fjka
lïìfha uOHl m%;sfrdaOh by; .Kkh l< m%;sfrdaOh fuka isõ .=Khla jk
nj i,lkak'
(iv) tu wjia:dfõoS fuu lïìfha W;ai¾ckh jk ish¨u ;dmh Ndysr mßirhg
ydks jkafka kï fuu lïìfha mDIAGfha WIAK;ajh .Kkh lrkak' fuu
lïìh idod we;s øjHfha mDIAÀl úfudapl;d ix.=Klh 15 Wm-2 K-1 jk w;r
mßir WIAK;ajh 260C fõ'
ish¨ u ysñlï weúßKs] All Rights Reserved] 16 AL/2024/01-S-II

(b) (i) idudkHfhka iïu; ú,dhlhl Wmßu Odrd m%udKkh jkafka tu ú,dhlh
ms,siaiS hdug" tu ú,dhlh ;=<ska 1ms l ld,hla ;=, .uka l< hq;= ksh;
Odrdjhs' fuu mßm:h ;=<ska 9A Odrdjla .uka lrñka ;sfnk wjia:djloS
tljr 1ms ld,hla ;=< by; Wmßu Odrdj .uka lrùug ie,eiajQfha kï
fuu ld,fhaoS lïìfha ckkh jk ;dmh mßirh yd yqjudre fkdjk nj
i,lñka fuu ú,dhlh i`oyd ks¾foaYs; Odrdj .Kkh lrkak' fuu
ú,dhlh lïìfha ialkaOh 1.5 mg jk w;r tys ú,hkfha úYsIag .=ma; ;dmh
2 ×105 Jkg-1 fõ' th idod we;s øjHfha úYsIag ;dm Odß;djh 400 Jkg-1 0C-1
jk w;r tys øjdxlh 10500 C jk w;r fuysoS isÿ jk WIAK;aj jeä ùu
fya;=fjka ú,dhlfha m%;f
s rdaOh by; (a)(ii) ys .Kkh l< m%;sfrdaOh fuka
100 .=Khla jk nj i,lkak'
(ii) fuu ú,dhlfha hï lsis mßm:hlg iïnkaO lr we;s wdldrh my; rEmfha
oelafõ' fuu mßm:h ;=<ska 9A Odrdjla .,d hkafka kï mßm:fha iul
m%;sfrdaOh .Kkh lr fuu mßm:fha isÿ jk ¨yqj;a ùula fya;=fjka iul
m%;sfrdaOh 2Ω olajd wvq jkafka kï by; (b) (i) ys .Kkh lsÍu Ndú;fhka
1ms ;=<oS by; ú,dhlh ms,siaiS hkafka o hk j. ks¾Kh lrkak'

ú,dhlh

240 V R

(iii) oeka fuu mßm:h xy w.% yryd iïmQ¾Kfhkau ¨yqj;a jqKs kï 1ms ;=<oS
ú,dhlh ms,siaiS hkafka o hk j. ks¾Kh lrkak' (m%;sfrdaOh (a)(iii) ys
.Kkh l< w.h f,i i,lkak')
(iv) fuu ú,dhlh ;=<ska 1200A l Odrdjla 2μs l ld,hla ;=< .uka lf<a kï"
ú,dhlh ms,i
s aiS fkdhk nj fmkajd thg fya;=j úia;r lrkak'

(B) fldgi
ue.akSishï mrudKqj kHIaáh jgd ilia jQ Yla;s uÜgï ;=kls iuka ú; fõ' tys m<uq Yla;s
uÜgu hkq kHIaáhg wdikaku Yla;s uÜgu jk w;r th ;=< bf,lafg%dak folla o f;jk
Yla;s uÜgu hkq wE;skau msysá Yla;s uÜguo fõ' tu Yla;s uÜgfïo bf,lafg%dak folla
wka;¾.; fõ' ue.akSishï mrudKqjl lsishï Yla;s uÜgul mj;sk bf,lafg%dakhl X - lsrK
f*dafgdakhla .egqKq úg tu f*dafgdakfha Yla;sh wjfYdaIKh lrf.k bf,lafg%dakh bj;aj
hhs' fuu bf,lafg%dakh bj;aùfï l%shdj,sh m%ldY úoHq;a l%shdj,shla jk w;r bf,lafg%dakhla
bj;a lsÍug wjYH wju Yla;sh m%ldY úoHq;a iólrKfha i`oyka ld¾h Y%s;h f,i .; yel' X
lsrK f*dafgdakfha ixLHd;h foay,Sh ixLHd;hg iudk jQ úg lsisÿ pd,l Yla;shla fkd§
bf,lafg%dakh hka;ï .e,úh yel'
ma,dkala ksh;h = 6.6  10−34 Js o wdf,dalfha m%fõ.h = 3  108 ms −1 fõ'
ish¨ u ysñlï weúßKs] All Rights Reserved] 17 AL/2024/01-S-II

0
(a) ;rx. wdhduh 3.3 A jk X lsrK f*dafgdakhlg Mg mrudKqfõ m<uq Yla;s uÜgfï
we;s bf,lafg%dakhla hka;ñka bj;a l< yels kï Mg mrudKqfõ m<uq Yla;s uÜgfï
we;s bf,lafg%dakhla bj;a lsÍug wjYH wju Yla;sh (1 ) .Kkh lrkak'
(b) (i) by; ;rx. wdhduh iys; fjk;a X lsrK f*dafgdakhla Mg mrudKqfõ f;jk
Yla;s uÜgfï we;s bf,lafg%dakhla yd .eà f*dafgdakh i;= uq`M Yla;sh
bf,lafg%dakhg m%odkh l< úg bf,lafg%dakh 1.5 10 −16 J pd,l Yla;shla iys;j
bj;a fõ' Mg mrudKqjl f;jk Yla;s uÜgfï we;s bf,lafg%dakhla bj;a ùug
wjYH wju Yla;h s (2 ) .Kkh lrkak'
(ii) Mg mrudKqjl f;jk Yla;s uÜgfï bf,lafg%dakhla bj;a lsÍu i`oyd m;k X
lsrKj, foay,Sh ;rx. wdhduh .Kkh lrkak'
(c) m<uq Yla;s uÜgfuka bf,lafg%dakhla bj;a jQ miq tys ys±ila we;s jk w;r fuu ys±i
msrùug f;jk Yla;s uÜgfï we;s bf,lafg%dakhla m<uq Yla;s uÜgug jefÜ' fuu
ixl%uKfha§ 1 yd  2 w;r jQ Yla;s fjkig iudk Yla;shla we;s f*dafgdakhlao iEfoa'
fuu f*dafgdakfha ;rx. wdhduh ks¾Kh lrkak'
(d) f*dafgdakhl Yla;sh (E) yd tys .uH;dj (p) w;r iïnkaOh E = pc iQ;%fhka ,nd fohs' c
hkq wdf,dalfha m%fõ.hhs'
(i) by; (a) ys i`oyka m;k X lsrK f*dafgdakfha .uH;dj ks¾Kh lrkak'
(ii) by; (a) wjia:dfõ§ bf,lafg%dakh lsisÿ .uH;djla fkdue;sj hka;ñka bj;a fõ
kï Mg mrudKqj jdx.= jk m%fõ.h .Kkh lrkak' Mg mrudKqjl ialkaOh
3.6  10−26 kg nj i,lkak'
(iii) jdx.= jk Mg mrudKqfõ pd,l Yla;h
s .Kkh lrkak'
(iv) tkhska fuu pd,l Yla;sh m;kh jk X lsrK f*dafgdakfha Yla;sh yd
iei§fïÈ fkd.sKsh yels nj fmkajkak'

10. (A) fldgig fyda (B) fldgig muKla ms<s;=re imhkak'

(A) fldgi
wêl ysu m;kh fï Èk j, W;=re weußldkq rgj, fnfyúka w;a olsk mdßißl .eg`Mjls '
óg¾ 1la muK Wig ;ekqKq ysu ;Ügq fya;=fjka ffoksl jev lghq;= fnfyúka wvmK ù we;s
w;r idudkH jdhqf.da,Sh mdßißl WIaK;ajh -100C muK w.hl mj;S' fujeks mdßißl ;;aj
hgf;a i;aj úfYaI j, meje;au ;¾ckhg ,la fõ' tfy;a úYd, fmdl=Kq wdYs%;j c,c Ôùkaf.a
meje;au wdrlaId ùug fya;=j c,h i;= yhsv%cka nkaOk j, ieleiau ksid we;s jk wkshï
m%idrK .=Khhs' úf,ys u;=msg c,h whsia f,i mej;sh o >k;ajh by<u wjia:dfõ mj;sk
c,h my< ú,am;=f,ys /f|a' tneúka tys WIaK;ajh by< neúka c,c Ôùkag ish meje;au ;yjqre
lr .ekSug yelsù ;sfí'
(a) (i) úYd, fmdl=Kq wjg c,c ÔúSka wdrlaIdùug fya;= ù we;af;a c,h i;= l=uk
.=Kdx.ho@
(ii) by; wdldrfha .=Khla c,hg ysñùug c,fhys we;s iqúfYAIS nkaOk úfYaIh
l=ulao@
(iii) by< whsia ia;rhla iEÿkq úYd, fmdl=Kla mfil olajd
;sfí' by; A, B, C ia:dk j, mej;sh hq;= WIaK;aj
my; olajd we;s w.hkaf.ka
ljrlao@ (00C, -100C, -40C, 20C)
(iv) t ld,hl§ whsia m ialkaOhla iEÿks kï tu whsia m
ialkaOh iE§ug wjYH ;dm m%udKh Q i|yd m%ldYkhla
,shd olajkak' ^c,h 00C mj;sk nj Wml,amkh lrkak& wu;r ixfla;h
yªkajkak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 18 AL/2024/01-S-II

(v) oekg we;s whsia ;Ügqj taldlro, tys >klu 2m o kï tys tall j¾.M,hlg
whsia tl;= ùfï iS>%;djh kghr-1m-2 tallfhka .Kkh lrkak' ^whsia ;Ügqfõ
w¨;ska tlajQ fldgi .Kkfha§ fkdi,ld yßkak&
whsia j, ú'.=';d' = 3×105Jkg-1, whsia j, ;dm ikakdhl;dj = 1.5Wm-1K-1
(vi) whsia ;Ügqfõ >klu jeä ùfï iS>%;dj cmhr-1 tallhka .Kkh lrkak'
whsia j, >k;ajh = 900kgm-3
(b) iS; R;= we;s ùu;a iuÕu fuu l<dmfha mj;sk m%Odku .eg`Mj jkafka ñksia
mßfNdackh i|yd mj;sk c,ho fï wdldrhg
ñ§ug m;aùuhs. ta wkqj mßfNdackh i|yd c,h
,nd .ekSfï w¾nqohla we;sfõ. Bg ms<shula f,i
iS; R;=j wdrïNù ál Èkla .; jk úg§
iajhxl%Shj whsia c,h njg m;a l< yels
moaO;shla my; olajd we;.

fuys§ úYd,j bÈ lrk ,o gexls j, m;=f,ys

yqud,h /f.k hk úYd, iarms,dldr ;U k, rEmfha olajd we;s wdldrhg iú lr
we;. ;dmlhla iy ;dmk fmdïmhla uÕska tu ;U k, yryd yqud,h heùfuka
ksrka;rfhka wNHka;r c,hg ;dmh imhd whsia iE§u j<ld øjuh ;;ajfha c,h
mj;ajd .kS.
ta wkqj fuys § 1000C mj;sk yqud,h ;U k, yryd hjk w;r tys§ yqud,h uÕska
iEfok c,h kej; kej;;a yqud,h njg m;a lr ;U k, yryd heùfuka th pl%Sh
l%shdj,shla njg m;a lrhs. gexlsh ;=< we;s c,h ish,a, 00C g <Õd jQ úg iajhxl%Shj
yqud, ;dmk l%ufõoh l%shd;aul jk w;r tuÕska mehl§ 50kg c,h ialkaOhla 300C
fj; /f.k hhs.
(i) mehl§ c,h r;a ùug ,nd .;a ;dmh fldmuKo@
^c,fha úYsIag ;dm Odß;dj = 4200Jkg-1K-1&
(ii) yqud,h 2.5kg la θ0C la olajd >kSNjkh fõ. yqud, ialkaOh m;ajk θ0C
WIaK;ajfha w.h .Kkh lrkak'
(c,fha jdIamSlrKfha úYsIag .=ma; ;dmh = 2.26«106Jkg-1)
(iii) fuu l%shdj,sfha yqud,h ksmoùu i|yd ãi,a odylhla Ndú;d l< yelsh . ta
wkqj by; pl%Sh l%shdj,sh, c,fha wdrïNl WIaK;ajh θ0C w.fha mj;sk mßÈ
isÿ lrkafka kï mehlg fuu
l%shdj,shg jehjk Lksc f;,a
ialkaOh .Kkh lrkak'
(LKsc f;,a 1kg oykh
lsÍfuka ,efnk laIu;djh
12kWh jk w;r by; oyk l%shdj,sfha ld¾hlaIu;dj 80% ls')
(iv) w;ajer§ulska yqud,h f.k hk AB k<fha mßjrKh .e,ù hhs' A isg B
olajd tall mßudjlska ydks jk ;dm Yla;sh A isg .Kkh l< ÿr yd úp,kh
jk whqre olajkak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 19 AL/2024/01-S-II

(B) fldgi
(a) iQ¾hhd ms<sn`o wOHhkh lsÍug n,dfmdfrd;a;= jk YsIH lKavdhula úiska
iQ¾hhdf.a wrh 7 × 108 m nj;a iQ¾hhdf.a isg mDÓú llaIhg mj;sk uOHl ÿr
1.5 × 1011 m nj;a fidhd .kakd ,oS' YsIH lKavdhu fuysoS m%:ufhka iQ¾hh ksh;h
iïnkaOfhka wjOdkh fhduq lsÍug ;SrKh lrhs'
(iafg*dka fnda,aÜiaudk ksh;h = 5.67 x10-8 W m2 K-4 )
(i) iQ¾hh ksh;fhys w¾: oelaùu ,shd olajkak'
(ii) iQ¾hh ksh;hg .e,fmk ia:dkhl ;nk ,o 4m2 l lafIa;%M,hla iys; c,
;gdlhl c,h 20kg wka;¾.; lr uoaoyfkaoS tys WIaK;aj jeä ùu ms<sn`oj
YsIHhska lKavdhu úiska wOHhkh lrk ,oS' c,fha úYsIaG ;dm Odß;dj
4000Jkg-1K-1 f,i .ksñka 200s l ld,hla ;=<oS c,fha WIAK;ajh 50C lska jeä
jQfha kï c,h u.ska iQ¾hh úlsrKh wjfYdaIKh lr .;a YS>; % djh .Kkh
lrkak'
(iii) c,h u.ska wjfYdaIKh lr.kq ,nkafka mDÒú mDIaGh u;g m;s; jk iQ¾hh
úlsrK ;Sj%;djfhka 40% la kï mDÒú mDIAGh u;g ,;s; jk iQ¾hh úlsrK
;Sj%;dj .Kkh lrkak'
(iv) mDÒú jdhqf.da,hg we;=¨ jk úlsrKfhka 20% la jdhqf.da,h u.ska wjfYdaIKh
lr .kafka hehs ie,l+ úgoS mDÒú llaIh wdikakfha iQ¾hh úlsrK ;Sj%;djh
.Kkh lrkak'
(v) mDÓúh wi, iQ¾hh úlsrK ;Sj%;djh Ndú;d lrñka iQ¾hh mDIaGfha WIAK;ajh
wdikak m<uq oYuia:dkhg .Kkh lrkak'
(vi) YsIH lKavdhu úiska .Kkh lrk ,o iQ¾hhdf.a WIAK;ajh hehs i,lñka
mDÒúh;a iQ¾hhd;a w;r msysá isl=re .%yhdf.a msysgqug iQ¾hhdf.a isg mj;sk ÿr
1× 1011 m f,i i,lñka isl=re .%yhd wdikakfha iQ¾hh úlsrK ;Sj%;dj .Kkh
lrkak'
(a) (i) my; olajd we;af;a -2 -1
iQ¾hhdg i¾jiu fjk;a I (Wm nm )
;drldjl ;rx. wdhduhg tosß
úfudapl n, m%ia;drh fõ'
fuys Wmßu úfudapl n,fhka
uqod yefrk úlsrKfha ;rx.
wdhduh 400nm la kï" wod,
;drldfõ mDIAGfha WIAK;ajh
.Kkh lrkak' iQ¾hhd u.ska λ
by; WIAK;ajfhaoS Wmßu 400nm (nm)
úfudapl n,fhka uqod yefrk úlsrKfha ;rx. wdhduh 480nm f,i i,lkak'
(ii) by; ;drldfõ isg mDÒúhg mj;sk ÿr 2×1014m kï ;drldj fya;=fjka mDÓúh
wdikakfha úlsrK ;Sj%;dj .Kkh lrkak'