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
06

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. ksõgkaf.a fojk kshuh wkqj jia;=jla u; ndysr wix;=,s; n,hla l%shd lsÍfï§ F = kma u`.ska ,nd
foa' F N j,skao m kg yd a ms-2 kao uksk úg k = 1fõ' m ys w.h g u`.ska o a ys w.h cms-2 kao
wdfoaY l<fyd;a F ys w.h N j,ska u ,eîu i`oyd k ys w.h úh hq;af;a
(1) 103 (2) 10-3 (3) 10-5
5
(4) 10 (5) 1

2. my; oelafjk tajd w;ßka taldx. fodaIhla fkdjkafka

(1) wiïmd; fodaIh (2) wyUq fodaIh
(3) m%idrKh ùu ksid isÿjk fodaI (4) wdka; fodaIh
(5) uQ,dxl fodaIh

sin (ab −  ) hk iólrKfha f, x, t yd  u.ska ms,sfj,ska ;ajrKh" úia:dmkh" ld,h yd

ax
3. f =
t
ld,drïNl fldaKh ^f¾ähkaj,ska ñkQ& ksrEmKh lrhs kï a yd b ys udk ms,sfj,ska,
(1) L, L (2) LT-1, L-1T
-1
(3) T ,T (4) L2T-1, LT-1
(5) a yd b hk folgu udk fkdue;'

2
4. z kï tla;rd fN!;sl rdYshla z = ax hk iólrKfhka ks¾Kh lrkq ,nhs' fuys a, b, x uekSfï
b
m%;sY; fodaI ms<sfj,ska 1%, 9%, 4% fõ' z rdYsh uekSfï iuia; m%;sY; fodaIh jkafka"

^1& 13.5% ^2& 9% ^3& 6%

^4& 8% ^5& 12%
ish¨ u ysñlï weúßKs] All Rights Reserved] 2 AL/2024/01-S-I

5. q eÿ f;areï mj;sk úg jdhqjla ;=< èjks m%fõ.h V = RT f,i oelaúh yelsh'
ixfla;j,g iqmr
M
my; m%ldY i,ld n,kak'
(A) fuys  w.h tal mrudKql jdhqjlg yd oaú mrudKql jdhqjlg tlu fõ'
(B) M hkq jdhqfjys uOHkH ialkaOhhs'
(C) tlu jdhqfjys ksh; WIaK;ajhl § èjks m%fõ.h ksh; nj fuu iólrKh fmkajd
fohs'
by; m%ldY w;ßka wi;H m%ldY jkafka,
(1) A muKs (2) C muKs (3) B muKs
(4) A yd B muKs (5) A yd C muKs

6. 270F § jdhqjla ;=< èjks m%fõ.h V fõ' fuu jdhqj ;=< èjks m%fõ.h 3V jk WIaK;ajh jkafka
(1) 24270C (2) 2427K (3) 24320C
0
(4) 2482K (5) 2159 C

7. He jdhqfõ yd O2 jdhqfjys tlu WIaK;ajfha § èjks m%fõ. w;r wkqmd;h jkafka (He – 4, O – 16,
γHe – 1.5, γo2 – 1)

(1) 2:1 (2) 1:2 (3) 2 2 :1

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

8. taldldr L È. lUhla ;sria(horizontal) iqug fïihla u; fl,ska lr ;nd we;' tys tla fl<jrlg
F n,hla fhdod wÈk úg tu fl<jf¾ isg lUfha È. X ÿßka msysá ,laIHhl wd;;sh(tension) my;
i`oyka ljr m%ldYhlska ksjerÈj olajhso@
FL FX F (L − X )
(1) (2) (3)
X L L
L−X  L+ X 
(4) F  (5) F 
L+ X  L−X 

9. P yd Q n, foll iïm%hqla;h R fõ' Q n,fha w.h fo.=K l< úg túg iïm%hqla; n,h P g
,ïnl fõ' R ys w.h iudk jkafka,
P2 − Q2 P+Q (3) Q
(1) (2)
2 PQ P−Q
P
(4) (5) Q2
Q

10. i¾jiu ngk<d folla 270 C WIaK;ajfha§ 300Hz uQ,sl ixLHd;hlska hq;a ia:djr ;rx. ksmojhs'
tl ngk,djla ;=< we;s jd;fha WIaK;ajh 310 C la olajd by< .sh úg ;;amrhl§ wefik kq.eiqï
ixLHdj jkafka,
(1) 1 (2) 2 (3) 3
(4) 4 (5) 5

11. nia kej;=ïm<l isg niar:hla ksYap,;djfha isg bÈßhg ksh; 2ms-2 l ;ajrKhlska hkq ÿgq
ñksfila th miqmi ¨yqne`o thg hï;ñka f.dvfjhs' Tyqf.a taldldr fõ.h 20ms-1 o wdrïNfha §
Tyq yd niar:h w;r ÿr 100m o kï Tyqg niar:hg f.dvùug .;jQld,h jkafka"
(1) 5s (2) 10s (3) 15s
(4) 20s (5) 2s
ish¨ u ysñlï weúßKs] All Rights Reserved] 3 AL/2024/01-S-I

12. ol=Kq ÈYdjg .uka lrk c, ;rx.hl laIKsl

msysgqula by; ±lafõ' ;rx.h .uka fkdlrk úg
c, uÜgu lv bfrka ±lafjk w;r th iu
.eUqßka øj mDIaGh u; msysá ,laIH 2 la A yd B
fõ' A ys lïmk l,dj 300 0 kï B ys lïmk
l,dj jkqfha"
(1) 300 (2) 600 (3) 3300
(4) 2700 (5) 3000

13. A yd B i¾jiu f.da, 02la tlu pd,l Yla;shla iys;j tlu ;sria ;,hl isg B f.da,h N%uKh
jk wdldrhg;a A f.da,h N%uKh fkdjk wdldrhg;a tlu fudfydf;a isriaj by<g m%lafIamKh
lrhs' jd; m%;sfrdaOh fkdi,ld y< úg my; m%ldYj,ska wi;H jkafka"
(A) A yd B tlu Wilg by, k.shs'
(B) Wmßu Wfia § fofokdf.au pd,l Yla;sh Y=kH fõ'
(C) B Wmßu Wig t<UqKq fudfydf;a § B g idfmaCIj A ys m%fõ.h Y=kH fõ'
(1) A muKs
(2) B muKs
(3) A yd B muKs
(4) B yd C muKs
(5) A, B, C ish,a,u wi;H fõ'

14. hï fyhlska mDÓúh tljr yels,Sug mgka .;fyd;a"

(A) mDÓú mDIaGh u; .=re;ajdl¾IK lafIa;% ;Sj%;djh jeäfõ'
(B) mDÓúfha ojil ld,h wvqfjhs'
(C) mDÓú mDIaGh u; § úfhda. m%fõ.h jeäfjhs'
by; m%ldY j,ska i;H jkafka"
(1) A muKs (2) A yd B muKs (3) A yd C muKs
(4) B yd C muKs (5) A, B, C hk ish,a,u

15. my; olajd we;af;a fldaKsl p,s;fha fhfok wxY=jl ld,h iu`.
fldaKsl m%fõ.h úp,kh jk wdldrhhs' fï i`oyd ksjerÈj olajd
we;s ld,hg tÈß fldaKsl úia:dmk m%ia;drh jkafka"

(1) (2)

(3) (4) (5)

16. Yío foll èjks ;Sj%;d uÜgï ms<sfj,ska 72dB yd 66dB fõ' tu èjks ;Sj%;d w;r wkqmd;h jkqfha"
(1) 12/11 (2) 100.6 (3) 106
(4) 1011 (5) 1012
ish¨ u ysñlï weúßKs] All Rights Reserved] 4 AL/2024/01-S-I

17. f¾Çh m%idrK;djh  jk øjHlska ;ekQ >K jia;=jla WIaK;ajh ldur WIaK;ajfha isg 610C
olajd by< kxjhs' fuúg tu >K jia;=fõ
j¾.M,fha Nd.sl jeäùu jkafka"
mßudfõ Nd.sl jeäùu ^ldur WIaK;ajh 310C&  = 2  10 −3 K −1

112 118 2
(1) (2) (3)
118 112 3
3
(4) (5) 1
2
18. rEmfha § we;s fjda,aàh;d Ndcl mßm:fha V/V0 wkqmd;h iudk jkafka,

(1) 3 (2) 1/2

(3) 1/8 (4) 1/3
(5) 6

19. tla;rd ia:dkhl § isÿ jQ N+ñ lïmdjla u.ska ;S¾hla ;rx.hla ^S- ;rx.hla& iy wkajdhdu ;rx.hla
^P ;rx.hla& cks; lrhs' ;rx. 2 lu mDÓúh yryd .uka lrk w;r mDÓúh u; tla;rd ,CIHhlg
S ;rx. <`.dùug t ld,hlg fmr P ;rx. <`.d fjhs' N+ lïmdj isÿjQ ia:dkfha isg ksl=;a jQ
;rx.j, m%fõ. ms,sfj,ska 4kms-1 yd 8kms-1 kï o wkdjrlh yd wmsflakaøh w;r ÿr 3600km o
kï t ld,h jkqfha,
(1) ñks;a;= 10 (2) ñks;a;= 5 (3) ñks;a;= 7.5
(4) ñks;a;= 15 (5) ñks;a;= 20

20. my; i`oyka m%ldY w;ßka iaÓ;s úoHq;a n,f¾Ld iïnkaOj i;H jkafka"
(A) n, f¾Ld iEuúgu ikakdhl mDIaGhlg ,ïNl úh hq;=h'
(B) wdfrdamKhlska ksl=;ajk n, f¾Ld ixLHdj tu wdfrdamKfha úYd,;ajhg
iudkqmd;sl fõ'
(C) n, f¾Ld ixjD; mqvq ks¾udKh lrhs'
(1) A muKs (2) B muKs (3) A yd B muKs
(4) A yd C muKs (5) A, B, C hk ish,a,u

21. rEmfha olajd we;af;a ABC iuoaúmdo m%siaufha AC uqyqK;g ,ïnlj m;kh
jk lsrKhla j¾;kfhka miq AB uqyqK; u; m;kh jQ úg AB mDIaGh Èf.a
.uka lrhs'
(A) lsrKh m%siauh ;=<ska wju wm.ukhla iys;j j¾;kh fõ'
(B) m%siauh idod we;s øjHfha wjê fldaKh 450 ls'
(C) m%siauh idod we;s øjHfha j¾;kdxlh 1.41 ls'
ñka i;H jkafka"
(1) A yd B (2) A yd C (3) B yd C
(4) B muKs (5) A, B, C ish,a,u

22. ;srig θ fldaKhlska wdk;j m%lafIamkh l< wxY=jl Wmßu Wfia § tys m%fõ.h 10ms-1 ls' wxY=j
fmdf<dj uÜgfï isg 80 m Wmßu Wilg .uka lrhs kï wxY=fõ m%lafIamK fldaKh jkafka"
1
(1) 450 (2) tan −1 (2) (3) tan −1  
4
1
(4) tan −1   (5) tan −1 (4)
2
ish¨ u ysñlï weúßKs] All Rights Reserved] 5 AL/2024/01-S-I

23. wj,ïn nÜgka 6la ieye,a¨ wú;kH ;ka;=jlg isriaj t,a,d

we;s wdldrh my; ±lafõ' m<uq wj,ïn nÜgd uola weo w; yßkq
,nhs' túg wfkla wj,ïn nÜgkaf.a p,s;hka iïnkaOj lr
we;s my; m%ldY w;=ßka ksjerÈ jkafka"
(A) ish`M wj,ïn nÜgka A f.a ixLHd;fhka lD;
lïmkfha fhfoa'
(B) wj,ïn nÜgka ish,a, tlu øjHfhka idod
we;akï D wj,ïn nÜgd wkqkdohlg ,la fõ'
(C) C yd E wj,ïn nÜgka ys lD; lïmk
úia:drfhka iudk fjhs'
(D) A wj,ïn nÜgdf.a È. lïmkh jk w;r;=r wvq lsÍfuka F wj,ïn nÜgd
wkqkdohlg ,la l< yelsh'
(1) A muKla i;H fõ' (2) A, B muKla i;H fõ'
(3) A, D muKla i;H fõ' (4) C yd D i;H fõ'
(5) A, B, C i;H fõ'

24. m%ldY fldaIfhys lef;davh i`oyd A, B, C f,day ;=kla

fhdod .ksñka úNj wka;rh iu`. m%ldY Odrdj w;r tlu
ixLHd;h yd ;Sj%;djh i`oyd VI ,dlaIKsl ks¾udKh l<
úg§ ,efnk VI ,dlaIKslh my; mßÈ fõ' ta wkqj fuu
f,day 3 i`oyd m;s; f*dafgdakfha ixLHd;h(f) iu`.
kej;=ï úNj(Vs) m%ia;drh ksjerÈj olajd we;af;a"

(1) (2) (3)

(4) (5)

25. by; mßm:fha A yd B ,laIH w;r úNj

wka;rh jkqfha"
(1) 12V
(2) 16V
(3) 8V
(4) 18V
(5) 14V
26. lïìhla idod we;s f,dayfha m%;sfrdaOfha WIaK;aj ix.=Klh 1.25 × 10−3 𝐾 −1 fõ' 300K § tys
m%;sfrdaOh 1 ls' tys m%;sfrdaOh 2 jkafka ljr WIaK;ajhl§o@
(1) 1154K (2) 1400K (3) 1127K
(4) 1100K (5) 600K
ish¨ u ysñlï weúßKs] All Rights Reserved] 6 AL/2024/01-S-I

27. rEmfha fmkajd we;s mßm:fha .e,ajfkda ógrfhys

fkdief,k W;al%uKhla we;' B iy D ;U lïìhlska hd
l, úg fï W;al%uKfha fjkila fkdfõ' my; i`oyka
m%ldY i,ld n,kak'
(A) .e,ajfkdaógrfhys m%;sfrdaOh 40 ls'
(B) .e,ajfkdaógrh ;=<ska .,k Odrdj fldaIh
;=<ska .,k Odrdfjka 1/3 ls'
(C) B yd D hd lr we;s ;U lïìh bj;a lr
th fjkqjg ksfl%daï lïìhla fhÿjfyd;a
.e,ajfkdaógrh ;=<ska hk Odrdj wvq jkq
we;'
fuu m%ldY ;=<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 yd C muKla i;H fõ'

28. fuu mßm:fhys 12 m%;sfrdaOfhka ;dmhla

fkdbmsojkafka R ys l=uk w.hla i`oydo@
(1) 0
(2) 2
(3) 5
(4) 10
(5) 15

29. ÿiai%dù fkdjk, wiïmSvH, ñY% fkdjk >k;ajh d iy 2d jQ

;r, taldldr A yrialvlska hq;a Ndckhl oud th ;sria
;,hl ksYap,j ;nd we;' tla tla øj lf`oys Wi H/2 la jk
w;r Wi L yd yrialv j¾.M,h A/5 la jk is,skavrhla
>k;ajh jeä øjh ;=, L/4 l Wila mj;sk f,i rEmfha
oelafjk wdldrhg mdfõ' is,skavrfha >k;ajh jkafka,
3d
(1)
4
4d
(2)
3
5d
(3)
4
(4) 3d
3d
(5)
4
30.

a yd b rEmj, fmkajd we;af;a ;dm ikakdhl;dj K yd 2K jk øjH follska ;kd we;s i¾jiu
udk iys; o~q folla tlu WIaK;aj wka;rhlg ,lalr we;s wdldr folls'
WIaK;aj j,g újD; mDIaG yer wfkla ish¨ mDIaG mßjrKh lr we;akï yd (a) wjia:dfõ§
WIaK;ajh jeä fl<jf¾ isg wvq fl<jr olajd 30J l ;dm m%udKhla .,dhdug 270s ld,hla .;fõ
kï" (b) wjia:dfõ§ tu ;dm m%udKhu .,dhdug .;jk ld,h jkafka"
(1) 15s (2) 30s (3) 1min
(4) 2min (5) 4min
ish¨ u ysñlï weúßKs] All Rights Reserved] 7 AL/2024/01-S-I

31. jia;=jl wdfrdamKh 2C lska by< kexjQ úg tys .nvd ù we;s iaÓ;s úoHq;a úNj Yla;sh 21% lska
jeä fõ' jia;=fjys ;snQ wdrïNl wdfrdamKh jkafka"
(1) 10C (2) 20C (3) 30C
(4) 40C (5) 25C

32. ieye,a¨ ÿkq ;rdÈhlg iqug lmams fhdodf.k úúO Ndrhka fhdod we;s úúO wdldr my; oelafjhs'
ÿkq ;rdÈ ish,a, ieye,a¨ jk w;r tla tla ÿkq ;rdÈh olajkq ,nk mdGdxlh ksjerÈj olajk
ms,s;=r jkafka"

(A) (B) (C) (D)

(1) 200 100 100 160
(2) 200 50 50 500
(3) 100 50 100 320
(4) 100 100 50 600
(5) 100 20 100 500
33. rEmfha oelafjk wdldrhg wrh r yd 2r jk frdao folla
ieye,a¨ fkdksñ máhla u.ska my; wdldrhg lrljkq
,efí' tajd iudk N%uK pd,l Yla;s iys;j N%uKh fõ 2r r
kï"
úYd, frdaofha wjiaÓ;s >Q¾Kh $ l=vd frdaofha wjiaÓ;s
>Q¾Kh" hk wkqmd;h iudk jkafka"
(1) 4 (2) 2 (3) 1/2
(4) 1/4 (5) 1/16
34. by; wdlrhg Okdfrdams; ikakdhl f.da,hl isg hï
ÿrlska WodiSk ikakdhl jia;=jla ;nd w.%hla N+.;
lrkq ,efí' f.da, flakaøfha isg olajd we;s f¾Ldj
Tiafia úoHq;a úNjh úp,kh jkqfha"

(1) (2) (3)

(4) (5)
ish¨ u ysñlï weúßKs] All Rights Reserved] 8 AL/2024/01-S-I

35.

iQ¾h mDIaGfha WIaK;ajh wdikak jYfhka 6000 K ls' iQ¾hhd ysi uqÿfka we;s úg fmd<jg m;s;
jk úlsrK ;Sj%;djh(intensity of radiations) 1.4𝑘𝑊𝑚−2 la muK fõ' iQ¾h mDIaGfha WIaK;ajh
5000K olajd wvq jQ úg fuu w.h wdikak jYfhka jkafka"
(1) 1.2k Wm −2 (2) 1k Wm −2 (3) 0.9 kWm −2
(4) 0.7 kWm−2 (5) 0.4 kWm−2

36. l=vd >K f.da,hla ÿi%dù ;r,hla wvx.= n÷kla ;=<g iSrefjka w;yÍ' fuúg m%fõ.h yd úia:dmkh
w;r m%i:
a drh ;o mdáka ±lafõ' fuu n÷ku .=re;ajc ;ajrKh by< m%foaYhlg f.k f.dia by;
mßÈu l%shdj,sh isÿ lrkq ,efí' fuys§ ,efnk m%ia;drh l=ula úh yelso@

(1) (2) (3)

(4) (5)

37. laú,a k<hla ;=< 20cm È. riÈh l|la isrlr k<fha újD; fl<jr by<g isák fia ilia l< úg
jdhq lf|a È. 10cm fõ' fuu WIaK;ajh hgf;a jdhqf.da,Sh mSvkh 75cmHg fõ' k<h isrig 600
wdk;j újD; fl<jr by<g fhduqjk fia we;s úg isrù we;s jd; lf|a È. jkafka"
(1) 10cm (2) 10.32cm (3) 11.17cm
(4) 12.24cm (5) 20cm

38. rEmfha ±lafjk mßm:fha fldaIfha wNHka;r m%;sfrdaOh

fkdi,ld yeßh yels ;rï l=vdfõ' I1 / I 2 ys w.h l=ula
fõo@
(1) 1/3
(2) 4/3
(3) 2
(4) 3/2
(5) 3
ish¨ u ysñlï weúßKs] All Rights Reserved] 9 AL/2024/01-S-I

39. rEmfha fmkajd we;s m%;sfrdaOl cd,fha iukaú; ù

we;af;a tla tla ys R w.hla we;s fY%aKs.; n m%;sfrdaOl
ixLHdjlg iïnkaO lrk ,o iudka;r.; f,i
iïnkaO lr we;s ta yd iudk n m%;sfrdaOl ixLHdjlsks'
n úYd, kï XY w;r iul m%;sfrdaOh wdikak jYfhka"
R
(1) R (2)
n
(3) Rn (4) nR
1
(5)
nR

40. m%;sfrdaOh R1 yd R2 jQ úÿ,s myka foll V úNj wka;rhla hgf;a laIu;d mßfNdack P1 yd P2 fõ'
fuu myka tlsfklg iudka;r .;j iïnkaO lr ixhqla;h yryd V úNj wka;rh fh¥ úg
ixhqla;h u`.ska laIu;d mßfNdackh jkqfha"
P1 P2 (2) P1 + P2 2 P1 P2
(1) (3)
P1 + P2 P1 + P2

2 P1 P2 P1 P2 ( P1 + P2 ) 2
(4) (5)
( P1 + P2 ) 2 2( P1 + P2 )

41. kdNsh ÿr 37.5 cm jk W;a;, ldphla my;

wdldrhg x yd y kï iudk len,s 02lg lmd
tlsfklg 10cm ÿrla wE;ska ;nd we;' x isg 75cm
ÿrlska ;nk ,o bámkaoul m%;ì s ïnh ;srhla u;
,nd.ekSug kï ;srh ia:dmkh l, hq;af;a x isg
fldmuK ÿrlskao@ ^x, y ;srh yd bá mkaou tlu
ir, f¾Ldjl msysgk nj i,lkak&
(1) 37.5cm (2) 65cm
(3) 75cm (4) 85cm
(5) 95cm

42. iqug ;,hla u; ;nd we;s m ialkaO folla rEmfha wdldrhg ÿkq ksh;h k jk ÿkaklska tlsfkl
iïnkaO lr we;af;a ÿkafka ú;;shla fkdue;s f,ihs' tu ialkaO folgu fomiska rEmfha wdldrhg
fjk;a m ialkaO folla v m%fõ.fhka meñK tlu fj,dfõ ÿkakg iïnkaO ialkaO iu. mQ¾K
m%;Hia;j .efÜ' .egqfuka miqj ÿkafka we;sjk Wmßu iïmSvkh jkqfha,

mv 2 2mv 2 3mv 2
(1) (2) (3)
k k k

3mv 2 5mv 2
(4) (5)
2k k
ish¨ u ysñlï weúßKs] All Rights Reserved] 10 AL/2024/01-S-I

43. ksh; jd; m%;sfrdaOhla iys;j u m%fõ.h by<g m%lf

a IaK;h lrk ,o ialkaOh m jQ f.da,hla
lsishï ld,hlg wk;=rej h,ska m%lf
a IamK ,laIHhgu m;s; fjhs kï tys ld,hg tÈß m%fõ. yd
;ajrKhka úp,kh ksjerÈj olajkafka,

(1) (2) (3)

(4) (5)

44. my; olajd we;af;a >k f,day f.da,hla jgd ;nd we;s f.da,dldr f,day
lfnd,ls' uOHfha ;nd we;s f,day f.da,hg +Q wdfrdamKhla ,nd §
we;' l=vd f.da,fha flakøa fha isg ÿr iu`. úoHq;a lafIa;% ;Sj%;dj;a
iaÓ;s úoHq;a úNjh;a úp,kh jk wdldrh olajd we;af;a"

(1) (2)
ish¨ u ysñlï weúßKs] All Rights Reserved] 11 AL/2024/01-S-I

(3) (4) (5)

A/2 A A/2
45. iudka;r ;yvq jd; Odß;%lhl Odß;dj C 0 fõ' Odß;%lfha ;yvq
w;rg rEmfha ±lafjk wdldrhg mdr úoHq;a ksh; k1 , k 2 yd k 3 jk
øjH len,s ±uQ úg tys kj Odß;dj jkqfha" k2
 k k3   k + k3 k1 
(1) C0  1 +  (2) C0  2 +  k1
 k1 + k 2 k1 + k3   k 2 k3 k 2 + k3 
k k k   kk  k3
(3) C0  1 + 2 3  (4) C0  1 2 + k1 
 2 k 2 + k3   k1 + k 2 
 kk 1
(5) C0  1 2 +  B
k +
 1 2k k1

46. W;a;, ldphla u.ska ;srhla u; ;kkq ,nk §ma; jia;=jl m%;sìïnfha È. 1.2cm ls. fuu ldph;a
;srh;a w;r wj;, ldphla ;enQ úg meyeÈ,s m%;sìïnhla ,nd .ekSug ;srh 52cm la msgm q ig p,kh
lsÍug isÿ úh. fuu m%;sìïnfha È. 3.6cm la úh. wj;, ldpfha kdNsh ÿr fidhkak.
(1) 78cm (2) 52cm (3) 39cm
(4) 26cm (5) .eg¨ úi§u i`oyd § we;s o;a; m%udKj;a fkdfõ'

47. rEmfha olajd we;af;a wkka; ÿrlska

msysgqjd we;s wmßñ; f,i úYd,
wdfrdams; ikakdhl ;yvq folls'
;yvqj, mDIaGj, we;s j¾.M,
wdfrdamK >k;aj olajd we;' fuu
;yvq tlsfklg wdikak l< úg D
uqyqKf;a wdfrdams; >k;ajh jkafka"
(1) +(𝜎1 + 𝜎2 )
(2) +(𝜎1 − 𝜎2 )
(3) −(𝜎1 − 𝜎2 )
(4) −(𝜎1 + 𝜎2 )
(5) 0
48. my; olajd we;af;a l=vd yd úYd, l=yr ikakdhl
f,day f.da, folla ikakdhl lïìhla fhdodf.k
iïnkaO lr we;s wdldrhhs' fuu l=vd yd úYd,
f.da,dldr Odß;d ms<sfj,ska C1 yd C2 jk w;r lïìh
iïnkaO lsÍug fmr l=vd f.da,hg +Q wdfrdamKhla
,nd § we;' my; m%ldY i,ld n,kak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 12 AL/2024/01-S-I

(A) A rEmfha wdldrhg f.da, iïnkaO l<fyd;a l=vd f.da,h i;= iuia; wdfrdamKh úYd,
f.da,h olajd .uka lrkq we;'
(B) B rEmfha wdldrhg f.da, iïnkaO l< úg l=vd f.da,h i;= wdfrdamKfhka fldgila úYd,
f.da,h fj; .,d hk w;r fuu .,d hk wdfrdamK m%udKh f.da,j, Odß;d u; r`od mj;S'
(C) A wjia:dfõ§ f.da, fol w;r isÿjk wdfrdamK yqjudre ùu f.da,j, Odß;dj,ska iajdh;a;
fõ'
(D) A wjia:dfõ§ úYd, f.da,h ,nd .kakd wjika úNjh B wjia:dfõ§ moaO;sh ,nd .kakd
fmdÿ úNjhg jvd jeäh'
by; m%ldYj,ska i;H jkqfha,
(1) B muKs' (2) A iy B muKs'
(3) A, B yd D muKs' (4) A, B yd C muKs'
(5) ish,a,u

49. rEmfha ±lafjk mßÈ wrh R o ialkaOh M o jQ .%yf,dajl mDIaGfha isg

;srig  fldaKhla wdk;j wxY+jla m%lf
a IamKh lrhs' fuu wjia:dj i`oyd
úfhda. m%fõ.h jkqfha"

2GM 2GM
(1) (2)
R Cos  R Sin 

2GM  1 1  2GM
(3)  +  (4)
R  Cos Sin  R ( Sin  + Cos )

(5) by; lsisjla fkdfõ'

50. my; oelafjkqfha fldaI moaO;shls' tla tla fldaIfha úoHq;a

.dul n,h E ne.ska jk w;r ta ta fldaIfhka msg;g ,nd.;
yels Wmßu wdfrdamK m%udK wod< fldaIh wi,ska i`oyka fjhs'
tu fldaI moaO;sfhka ,nd.; yels Wmßu uq¨ Yla;sh jkqfha"
(1) 44 EQ (2) 36 EQ
(3) 28 EQ (4) 16 EQ (5) 12 EQ
ish¨ u ysñlï weúßKs] All Rights Reserved] 0 AL/2024/01-S-II

7 >laudkam:l l%irhg ka ,
ujjllóudK

06

20

jHqy.; rpkd - (A fldgi)

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

jHqy.; rpkd - (A) fldgi)

1. rEm igyfka fmkajd we;af;a úoHd.drfhaoS YsIHfhl= úiska ks¾udKh lrk ,o ir, ;=,d
wdlD;shls' fuys ABC hkq .=re;aj flakaøh C ,laIHfha isysgd we;s 30 cm la os. oKavla
jk w;r" DE hkq taldldr yrialvlska hqla; rn¾ ;ka;=jls' AB oKAfâ B fl<jrg
ialkaOh fkd.sKsh yels ;rï l=vd o¾Ylhla iú lr we;s w;r" tu o¾Ylh mm j,ska
l%udxlKh lr we;s S mßudKhg iam¾YShj by< my< .uka lsÍfï yelshdjla we;' P hkq
AB oKav u; C isg B olajd /f.k hd yels ieye,a¨ ;=,d r`ojkhls' P ;=,d ;eá r`ojkhg
Ndrhla fhdod fkdue;s úgoS DE rn¾ flkao fkdweoS mj;sk w;r S mßudKh 0 iu.
o¾Ylh iumd; ù we;'

(a) ;=,d ;eá r`ojkh 15cm i,l=fKys ;nd 100g l Ndrhla tu ;=,d ;eá r`ojkh u;
;enqj úgoS o¾Ylh 5mm l lshùula fmkakqï lrhs'
(i) fuúg iurEmS ;%sfldaK i,lñka rn¾ flkafoys ú;;sh .Kkh lrkak'
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(ii) rn¾ flkao u; f.dvkef.k n,h ksjqgka j,ska .Kkh lrkak'
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(iii) fuu Ndrh iys; ;=,d ;eáh 20cm i,l=K olajd /f.k .sh úg rn¾ flkao
;=< f.dvkef.k kj n,h .Kkh lrkak'
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ish¨ u ysñlï weúßKs] All Rights Reserved] 2 AL/2024/01-S-II

(b) (i) S mßudKfha mrdih 0 -10mm o" ;=,d ;eáh i¾mKh l< yels iSudjka
10cm ;a 25cm ;a w;ro muK kï" fuu ;=,d ;eáh Ndú; fldg ueksh yels
Wmßu Ndrh .Kkh lrkak'
…………………………………………………………………………………
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(ii) fuu Wmßu Ndrh uksk wjia:dfõoS rn¾ ;ka;=fjys ú;;sh;a th ;=<
f.dvkef.k n,h;a .Kkh lrkak'
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(c) (i) fuu rn¾ ;ka;=fjys lsishï wjia:djl f.dvkef.k m%;Hdn,h iy úl%shdj
.Kkh lsÍug YsIHhd n,dfmdfrd;a;= fjhs' fï i`oyd Tyq úiska rn¾
;ka;=jg wod<j ,nd .; hq;= ñkqï fudkjd o hkak i`oyka lr tu ñkqï
,nd .ekSu i`oyd úoHd.drfha Tn Ndú;d lrk ñkqï WmlrKh ksjerosj
.shd olajkak'
…………………………………………………………………………………
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(ii) rn¾ ;ka;=fjys yrialv lafIa;%M,h 5mm2 la o" tys wdrïNl os. 20cm la o
kï" by; (a)(i) wjia:dfõoS rn¾ ;ka;=j ;=< f.dvkef.k m%;Hdn,h;a
úl%shdj;a .Kkh lr ta weiqßka rn¾ ;ka;= wod< ld,h ;=< iudkqmd;sl
iSudj ;=< yeisfrkafka hehs Wml,amkh lr rn¾ j, hxudmdxlh .Kkh
lrkak'
…………………………………………………………………………………
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(d) m<uq rn¾ flkaog i¾jiu jQ fojk rn¾ flkaola m<uq rn¾ flkao iu.
iudka;r.;j iïnkaO l< fyd;a 100g l Ndrh i`oyd S mßudKh u; 5mm l
lshùula ,nd .ekSu i`oyd P ;=,d ;eáh ;eìh hq;= ia:dkh l=ula o hkak .Kkh
lrkak'
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ish¨ u ysñlï weúßKs] All Rights Reserved] 3 AL/2024/01-S-II

2. ksh; mSvkhla iys; wp, jdhq ialkaOhla WIaK;ajh

iu`. mßudj úp,kh wOHhkh lsÍu i`oyd taldldr
isyska ùÿre k<hla u`.ska ieliQ wegjqula rEmfha
±lafõ'

B
(a) (i) A yd B i`oyd fhdod we;s øj fudkjdo@ A
A - ……………………………… l
B - ……………………………… X

(ii) B øjh we;s ia:dkhg A øjh Ndú;d l<fyd;a we;s úh yels mÍlaIKd;aul
fodaI ljf¾o@
…………………………………………………………………………………
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(iii) by; mÍlaIK wegjqfï A øjh i`oyd weks,Ska fhdod .ekSug isiqfjla
wfmalaId lrhs' túg ñkqï .; yels mrdih iSudjk wdldrfha fodaI we;s jk
nj Tyqf.a fN!;sl úoHd .=rejrhd mjik ,§' .=rejrhdf.a m%ldYh iu`. Tn
tl`. jkafkao@ ms<s;=rg fya;= olajkak'
…………………………………………………………………………………
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(b) (i) mÍlaIKh i`oyd w;HdjYH jk jeo.;a wdhs;a;u folla wegjqfï olajd ke;'
th by; rEmfha iqÿiq ia:dkfha we`o kï lrkak'
(ii) k<fha my<g L È. keuqKq k< fldgila tla lr we;af;a l=ula i`oydo@
…………………………………………………………………………………
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ish¨ u ysñlï weúßKs] All Rights Reserved] 4 AL/2024/01-S-II

(iii) θ0C WIAK;ajfhaoS X i<l=Kg by<ska jdhq lf`oa os. l o" X i<l=Kg my<ska
k<fha keuqï os. L o hehs .ksñka pd,aiaf.a m<uq kshuh Ndú;fhka 0C
WIaK;ajh yd X i<l=Kg by<ska jdhq lf`oa os. (l) w;r m%ia;drh we`oSug
iqÿiq iólrKhla ,shd olajkak' 00C oS X i<l=Kg by<ska jdhq lf`oa
os. = l0 fõ'

…………………………………………………………………………………
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(iv) X i,l=Kg my<ska we;s jdhq lf`oa os. 10 cm la kï" by; m%ia;drfha
wka;#lKavh 0.2m la f,i f.k 00C oS X i,l=Kg by<ska jdhq lf`oa os. l0
.Kkh lrkak'
…………………………………………………………………………………
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(v) m%ia;drfha wkql%uKh 1.5 x 10-3 m 0C-1 kï" ksh; mSvkfha mßud m%idrK;d

ix.=Klh (γp) .Kkh lrkak'

…………………………………………………………………………………
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(c) by; mÍlaIKfhaoS lssih
s ï WIAK;ajhlg wod< jdhq lf`oa ksjeros os. mÍlaId lrk
wdldrh bosßm;a lrkak'
…………………………………………………………………………………………..
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3. (a) my; oelafjkafka èjksudkhl kï lrk ,o rEm igykls'

wp, fia;=j

iqug lmamsh

jd ljq`:
Ndrh
ish¨ u ysñlï weúßKs] All Rights Reserved] 5 AL/2024/01-S-II

(i) èjksudk lïìfha okakd ixLHd;hlska iqir lr .; yels wdldr ;=k ,shd
olajkak'
………………………………………………………………………………….
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(ii) iriq,la lïmkh lr èjksudk fmÜáh u; ;enQ úg iajNdúl lïmkh yd
lD; lïmkh jk wx. ljqrekao hkak olajkak'
………………………………………………………………………………….
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. …………………………………………………………….…………………….
(iii) èjksudk lïìh iriq,la Ndú;fhka uQ,l
s ;dkfhka wkqkdo lr .kakd
wdldrh ,shd olajkak'
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(iv) lïìh wkqkdo wjia:dfõoS lvodis wdfrdaylh bj;aj hk úg lïìh u.ska
lvodis wdfrdaylh u; we;s lrkq ,nk m%;sl%shdj fldmuKo@
…………………………………………………………………………………..
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(v) tla;rd wjia:djloS èjksudk lïìh 250Hz l ixLHd;hlska lïmkh jk
úgoS lvodis wdfrdaylh bj;aj hhs kï" lïìfha lïmk úia;drh .Kkh
lrkak' (π2=10)
…………………………………………………………………………………..
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1
(b) my; oelafjkafka l  iïnkaO;dj mÍlaIKd;aulj ks.ukh lsÍug isiqka msßila
f
,nd .;a mÍlaIKd;aul o;a; j.=jls' (uQ,sl wkqkdo wjia:dj i`oyd ,nd .;a w.hka
nj i,lkak')

1
(10−3 s ) 2.0 3.0 4.0 6.6 8.4
f

l (cm) 10 15 20 33 42
ish¨ u ysñlï weúßKs] All Rights Reserved] 6 AL/2024/01-S-II

(i) my; m%ia;drh iïmQ¾K lrkak'

(ii) m%ia;drfha wkql%uKh .Kkh lr ta weiqßka weos ;ka;=fõ ;S¾hla ;rx.

m%fõ.h .Kkh lrkak'

…………………………………………………………………………………
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(iii) fuu mÍlaIKfhaoS Ndrh i`oyd fldmuK ialkaOhla Ndú;d lrhs o@

…………………………………………………………………………………
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(iv) fuu mÍlaIKh i`oyd Ndú;d lrk iriq,a lÜg,fha ixLHd; mrdih
.Kkh lrkak'

…………………………………………………………………………………
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(v) YsIHhd úiska ;j;a wvq ixLHd;hl iriq,a folla i`oyd wkqkdo os. ,nd
.ekSug W;aidy l< o ta i`oyd ;ka;= os. m%udKj;a fkdjk nj fmkS hhs' ta
i`oyd fhosh hq;= Wml%uh ,shd olajkak'

…………………………………………………………………………………
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ish¨ u ysñlï weúßKs] All Rights Reserved] 7 AL/2024/01-S-II

(c) èjksudkh Ndú;d lr tys wd;;sh we;s lsÍu i`oyd t,a,d we;s Ndrfha >k;ajh
fiúh yel' fï i`oyd t,a,d we;s ;rdos mä bj;a lr ùÿre f.da,hla iïnkaO lr
m%:ufhka iriq,la Ndú;fhka wkqkdo lr uQ,sl wkqkdo os. ,nd .;a úgoS th
60cm la nj ksÍlaIKh lrk ,oS' miqj f.da,h iïmQ¾Kfhkau c,h ;=< .s,ajd
kej; by; iriq,g wod< wkqkdo os. ,nd .;a úg th 50cm la úh' c,fha >k;ajh
1000 kgm-3 f,i .ksñka ùÿre f.da,fhys >k;ajh .Kkh lrkak'
………………………………………………………………………………………….
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4. (a) ´ï kshuh ,shd olajkak'

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(b) (i) m%;sfrdaOl;d ix.=Klh ρ jk ikakdhl øjHlska idok ,o os. l yd yrialv
j¾.M,h A jQ lïìhl m%;sfrdaOh i`oyd m%ldYkhla ,shd olajkak'
………………………………………………………………………………………
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(ii) ρ = 1.5 ×10-6 Ωm jk øjHlska iE¥ taldldr yrialvla iys; 5 cm la os. lïìhl
yrialv wrh 5 mm la kï tys m%;sfrdaOh (R1) .Kkh lrkak' (π = 3)
[

………………………………………………………………………………………
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(iii) by; lïìhg iudk os.la iys; tfy;a by; lïìfha yrialv wrh fuka
fo.=Khl wrhla we;s lïìh m%;sfrdaOh (R2) .Kkh lrkak'

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ish¨ u ysñlï weúßKs] All Rights Reserved] 8 AL/2024/01-S-II

(iv)
R1 R2
A B
C
by; R1 yd R2 m%;sfrdaOl fol my; rEmfha mßos iïnkaO lr A yd B w.%
w;rg 9V l ir, Odrd úNjhla ,nd ÿkafka kï VCB .Kkh lrkak'
……………………………………………………….…………………………………
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(v)
R1

R1 R2
A B
C
bka miq R2 m%;sfrdaOhg iudka;rj ;r;a R1 m%;sfrdaOhla iïnkaO lf,a kï"
VCB ys oeka w.h .Kkh lrkak'
…………………………………………………………………………………………
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3Ω N
(c) (i) M O

12Ω 6Ω

120V P
V

8Ω 6Ω 24Ω

2Ω
Q
S R

by; rEmfha olajd we;s m%;sfrdaOl moaO;sfha M yd S w;rg 120V l ir, Odrd
úNjhla imhd we;' tys VPQ .Kkh lrkak'
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ish¨ u ysñlï weúßKs] All Rights Reserved] 9 AL/2024/01-S-II

(ii) by; mßm:fha PQ w;rg 5μFl Odß;%lhla

iïnkaO lrhs kï" ta ;=< .nvd jk
wdfrdamKh yd Yla;sh .Kkh lrkak' 6Ω
…………………………………………… P
……………………………………………
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24 Ω
……………………………………………
……………………………………………
Q
……………………………………………
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

03
06

meh 02 úkdä 15
2
02 Hour 15 Minutes
3
B fldgi – rpkd
m%Yak 04 muKla ms<s;=re imhkak'
[ g = 10Nkg-1 ]

5. l``ÿlr m%foaYhl jx.=jla ks¾udKh lr we;af;a wrh 400m jk wdldrhgh' ud¾.h ;sriaj
ks¾udKh lr we;s w;r ud¾.h yd r:hl gh¾ w;r f.dvkef.k >¾IK ix.=Klh 0.4 la
fõ' 15000kg ialkaOhla iys; Ôma r:hla iDcq ud¾.h Tiafia 180kmh-1 m%fõ.fhka meñK
tu fõ.fhkau jx.=j miq lrf.k hdug woyia lrhs'
(a) (i) Ôma r:fha ßhÿreg wdrlaId iys;j jx.=j miqlrf.k hdug fkdyels
nj fmkajkak'
(ii) Tyqg wdrlaIdldÍj jx.=j miqlrf.k hdug kï jx.=jg mej;sh hq;= wju
wrh .Kkh lrkak'
(iii) fuu r:h 108kmh-1 l m%fõ.fhka jx.=fõ .uka lrk úg § r:fha bÈß
mqjrej u; ;nd we;s iqj`o ú,jqka fnda;,hla yd r:fha mqjrej w;r >¾IK
ix.=Klh 0.2 la kï jx.=j ;=, .uka lrk úg § wod, iqj`o ú,jqka
fnda;,fhys p,s;h r:h ;=, isák ßheÿre ksÍCIKh lrk wdldrh ,shd
olajkak'
(b) Ôma r:h úiska by; jx.=j miq lrf.k hdfï oS mj;sk fõ.h wêl ùu fya;=fjka
r:h ud¾.fhka bj;g mek m%md;hla fj; fmr,S m%md;fha we;s c,dYhla ;=<g
we;=¨ fõ' miqj r:h by,g .ekSu i`oyd fuu rEmfha olajd we;s wdldrfha
fodUlrhla Ndú;d lrhs' r:fha ialkaOh 15000kg jk w;r" ndysr mßudj 11.96m3
fõ' r:fha ghr j, mßudj 0.04m3 fõ' (c,fha >k;ajh 1000 kgm-3)
(i) cSma r:h c,dYh ;=< .s,S m;=f,a Wvql=re f,i ;ekam;a fõ kï" r:fha frdaohla
u; c,dYfha m;=, u.ska we;s lrk wNs,ïN m%;sl%shdj .Kkh lrkak'
(ii) miqj r:h by<g .ekSu i`oyd fodUlrhla Ndú;d lrk w;r" r:h by<g
.ekSfïoS c,h ;=<oS fodUlrfha ;ka;= j, mej;sh hq;= wju wd;;sh .Kkh
lrkak'
(iii) r:h c,h ;=<oS 2ms-2 ;ajrKhlska by<g .ekSug kï" fodUlrfha ;ka;=
j, mej;sh hq;= wju wd;;sh .Kkh lrkak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 11 AL/2024/01-S-II

(c) fodUlrh A ys § iqugj új¾;kh fldg we;s w;r B ys § iqugj wdOdrlfhys

iam¾Yj we;' fodUlrfha .=re;aj flakaøh G ys msysgd we;s w;r lmamsh iys;
fodUlrfha ialkaOh 2000kg fõ' fodUlrfha fl,jr wrh 20cm la jk wjiaÓ;s
>Q¾Kh 50kgm2 jk r¨ lmamshla iïnkaO fldg we;s w;r tu lmamsh jgd .uka
lrk ieye,a¨ wú;kH ;ka;=jl fl,jrg fldlalla .eg .id we;'
my; .Kkh lsÍï i`oyd ldrh c,dYfha c, mDIAGfhka by<g .;a miq wjia:dj
i,lkak'

A G

2m B
3m
6.8m

(1) rEmh

(i) iu;=,s;j mj;sk fodUlrh u; A yd B ys § we;s jk m%;sl%shd .Kkh lrkak'

(ii) fodUlrfha lmamshg iïnkaO fudagrhla u.ska lmamsh my,g .uka lrjd
Ôma r:h fldlafla wuqKd .ekSu yryd Ôma r:h by,g Tijk wjia:djla
rEmfha ±lafõ' Ôma r:fha ialkaOh 15000kg f,i f.k kej;;a A yd B
wdOdrlhkays m%;sl%shd .Kkh lrkak' (cSma r:h taldldr m%fõ.fhka by<g
Tijñka mj;sk wjia:djla i,lkak')
(iii) 3000kW fudagrhla Ndú;fhka lmamsh N%uKh lr Ôma r:h 10ms-1 ksh;
m%fõ.fhka by,g Tijkafka kï fudagrh u.ska lmamsh u; fhdok
jHdj¾;h .Kkh lrkak'
(iv) by; wjia:dfõ § lmamsh u; n,mdk >¾IK jHdj¾;h .Kkh lrkak'

(d) fodUlrh u.ska fudag¾ r:h tiùfï § tu fudag¾ r:h 2ms-2 l ksh; ;ajrKfhka
by,g tiùug n,dfmdfrd;a;= jkafka kï ;jÿrg;a mj;sk >¾IK jHdj¾;h by;
(b) (iv) ys >¾IK jHdj¾;fha u mj;skafka kï fudagrh u.ska fhÈh hq;= jHdj¾;h
.Kkh lr Ôma r:fha m%fõ.h 10ms-1 la jk úg fudagrfha laIu;djh .Kkh
lrkak'

6. ñksia weig jia;=jla ksÍlaIKh ùug wod, jia;=j u`.ska oDIaÀ ú;dkh u; ;kk
m%;sìïnfha m%udKh b;d jeo.;a fõ' hï jia;=jla mqoa.,fhl=g o¾Ykh ùug kï tu`.ska
oDIaÀ ú;dkh u; ;efkk m%;sìïnfha m%udKh 8 m fyda Bg jvd úYd, úh hq;=h' oDIaÀ
ú;dkh u; ;efkk m%;sìïnhla l=vd ùu flfrys fya;= idOl folla n,mEï t,a, lrhs'
tkï jia;=fõ m%udKh l=vd ùu;a" ñksia wefia isg jia;=jg mj;sk ÿr úYd, ùu;a hk
lreKq fõ' ta wkqj ,`. msysá jia;+kays úYd,s; m%;sìïn ksÍlaIKh i`oyd wkaùlaIh;a" ÿr
msysá jia;=j, úYd,s; m%;sìïn ksÍlaIKhg ÿf¾laIh;a Ndú;d lrhs'
ish¨ u ysñlï weúßKs] All Rights Reserved] 12 AL/2024/01-S-II

(1) rEmh

(a) (i) (1) rEmfhys olajd we;s rEm igyk Wmfhda.S lr .ksñka h Wi jia;=jla
i`oyd oDIaÀú;dkh u; ;efkk m%;sìïnfha úYd,kh i`oyd m%ldYkhla
,shd olajkak'
(ii) úYo oDIaÀfha wju ÿr jk 25cm la bÈßfhka 6.25 m Wi jia;=jla ia:dms;
lrkafkao wlaIs ldpfha isg oDIaÀú;dkhg ÿr 2cm o kï oDIaÀ ú;dkh u;
;efkk m%;sìïnfha úYd,;ajh i`oyd jákdlula ,nd .kak'
(iii) fuu fmfkk m%;sìïnfha m%udKh hka;ñka fmkSug mej;sh hq;=
m%;sìïnfha m%udKh fuka mia .=Khla olajd /f.k hdug wkaùlaIhla
Ndú;d lrkafka kï tu`.ska fldmuK úYd,khla mshú weig fmfkk
m%;sìïnhg ,nd Èh hq;o= @
(iv) by; (a)(iii) ys úYd,kh ,nd .ekSu i`oyd idudkH iSreudrefõ mj;sk
wkaùlaIhla ilia lsÍug n,dfmdfrd;a;= jkafka kï ta i`oyd iqÿiq lsrK
igykla we`o olajkak'
(b) klaI;% ÿf¾laIhla Ndú;d lr wE; msysá .%yjia;=jla ksÍlaIKh lrk w;r
ksÍlaIlhd úiska wjika m%;sìïnh úIo oDIaÀfha wju ÿfrys ;kd .kS' wjfk;a
ldpfhys kdNs ÿr f0 o Wmfk;a ldpfhys kdNs ÿr fe o úYo oDIaÀfha wju ÿr D o
f,i .kak'
(i) wjika m%;ì
s ïnh úYo oDIaÀfha wju ÿfrys ;ekSu fmkaùug iqÿiq lsrK
igykla ks¾udKh lrkak' tys wkka;fha isg meñfKk lsrKh wlaIsj,h
yryd .uka lrk wdldrh we`o olajkak'
(ii) b)(i) lsrK igyk Wmfhda.S lr.ksñka fuu wjia:dfõ ,nd.; yels

úYd,kh idudkH iSreudre wjia:dfõ ,nd .; yels úYd,kh fuka  e +1

f
D 

.=Khla nj fmkajkak'
(iii) ÿf¾laIfha wjika m%;sìïnh úYo oDIaÀfha wju ÿfrys ;efkk wjia:dfõ§
fldaKsl úYd,kh ÿf¾laIh idudkH iSre udre wjia:dfõ mj;sk úg
fldaKsl úYd,kh fuka 1.8 .=Khla kï úYo oDIaÀfha wju ÿr 25cm jk
úg§ Wmfk;a ldpfha kdNs ÿr;a ÿf¾laIfha idudkH iSreudre wjia:dfõ
úYd,kh 8 la kï wjfkf;a kdNs ÿr;a .Kkh lrkak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 13 AL/2024/01-S-II

(c) klaI;% ÿf¾laIh Ndú;fha§ mj;sk m%Odk;u .eg¨jla jkafka wjidkfha ;efkk
m%;sìïnh hál=re ùuhs' tneúka fmdf<dj u; msysá jia;+ka ksÍlaIkhg hEfï§ fuh
.eg¨jla fõ' tneúka fuhg ms<shula f,i my; olajd we;s wdldrhg Wmfk;a ldph
wj;, ldphlska m%;sIaGdmkh lrk ,§' ta wkqj wjika m%;sìïnh Wvql=rej ±l.;
yelsh' fuys§ isÿ lrkq ,nkafka wkka;fha isg meñfkkafka hehs i,lk lsrK
W;a;, ldphla jk kdNsÿr f0 jk ldph u;g m;s; ù tys m%;sìïnh tu ldpfha kdNsh
;,fhys ;ekSug i,iajk w;r miqj fuu m%;sìïnh kdNsh ÿr fe jk wj;, ldphlg
jia;=jla fõ' tu`.ska wj;, ldphg bÈßfhka úYo oDIaÀfha wju ÿßka m%;sìïnh
;efka' fï i`oyd wkka;fha isg meñfKk lsrK fol i,lñka úYo oDIaÀfha wju
ÿßka ;efkk m%;sìïnh i`oyd lsrK igykla ks¾udKh lrkak'

(2) rEmh

7. (a) (i) ÿiai%dú;d ix.=Klh w¾: olajkak'

(ii) k<hla ;=<ska .,d hk ÿiai%dù ;r,hlg wod<j fmdhsfi,a iólrKh ,shd
olajd tys mo ish,a, y`ÿkajkak'
(b) ÿiai%dù ;r,hla k<hla ;=<ska m%jdy ùfïoS tu m%jdyh wkdl+, jk mßos tu
;r,fha wxY= j,g ,nd .; yels Wmßu m%fõ.hla mj;S' fuu m%fõ.h tu
k<fha udk yd ;r,fha iajNdjh u; r`od mj;S' fuu m%fõ.h tu k<h ;=< wod<
;r,fha wjê m%fõ.h (Critical velocity – VC ) f,i y`ÿkajkq ,nhs' hï lsis
m%jdyhl mj;sk ;r, wxY= fuu wjê m%fõ.h blaujd .uka l< fyd;a tu m%jdyh
m<uqj wkdl+, wkjr; ;;a;ajfhka ñoS wkjr; fkdjk ;aa;j a hlg .uka
lrhs' fuu m%fõ.h ;j ÿrg;a jeä jqj fyd;a fuh wdl+, m%jdyhla njg m;a fõ'
fuu wjê m%fõ.h (VC) ;r,fha ÿiaid% ú;d ix.=Klh (η) ;r,fha >k;ajh (ρ)
k<fha wNHka;r wrh (r) u; r`od mj;sk nj fidhd f.k we;'
udk rys; ksh;h RN f,i f.k VC i`oyd m%ldYkhla udk úYaf,aIKfhka f.dv
k.kak'
(c) lsishï m%jdyhl wdl+, wkdl+, Ndjh ;SrKh lsÍu i`oyd frfkda,âa wxlh (RN)
2rV
Ndú;d lrkq ,nhs' RN = u.ska fokq ,nk w;r fuys V hkq lsishï k<hla

;=<ska m%jdy jk m%jdyhl uOHl m%fõ.h fõ' fuu frfkda,aâ wxlh 2000 g jvd
l=vd jkafka kï tu m%jdyh wkdl+, wkjr; m%jdyhla f,i y`ÿkajkq ,nk w;r
fuu frfkda,aâ wxlh 2000 - 3000 ;a w;r mj;skf a ka kï th wkjr; fkdjk
(unsteady) m%jdyhla f,i y`ÿkajhs' frfkda,aâ wxlh 3000 g jeä kï th
uq`:ukskau wdl+, m%jdyhla f,i ms<s.kq ,nk w;r fuu wjia:dfõoS m%jdyh ;=<
ksrka;rfhka osh iq<s jeks jHdl+, ;;ajhka we;s fõ'
(π = 3, c,fha >k;ajh 1000 kgm-3 " c,fha ÿiai%dú;d ix.=Klh 1 × 10-3 Pa s )
ish¨ u ysñlï weúßKs] All Rights Reserved] 14 AL/2024/01-S-II

(i) wrh 5cm jQ k<hla ;=<ska ñks;a;=jg ,Sg¾ 3.6 l mßud YS>;
% djhlska m%jdy jk
c, m%jdyhla i,lkak' fuu m%jdyfha c,fha uOHl m%fõ.h .Kkh lrkak'
(ii) by; m%jdyh i`oyd frfkda,aâ wxlh .Kkh lr m%jdyh wdl+, o wkdl+, fõo
hkak ks¾Kh lrkak'
(iii) by; m%jdy YS>%;dj ñks;a;=jg ,Sg¾ 14.4 olajd jeä jqKs kï oeka m%jdyh
i`oyd frfkda,aâ wxlh .Kkh lr m%jdyfha wdl+, / wkdl+, Ndjh ks¾Kh
lrkak'
(iv) m%jdyh ñks;a;=jg ,Sg¾ 3.6 YS>;
% djhlska m%jdy jk úg m%jdyh yryd mj;sk
mSvk wkql%uKh .Kkh lrkak'
(v) m%jdyh ñks;a;=jg ,Sg¾ 3.6 YS>%;djfhka m%jdy jk úg tu m%jdyfha c,
wxY=jla i`oyd mej;sh yels Wmßu m%fõ.h (wjê m%fõ.h – VC) .Kkh
lrkak'

(d) >k;ajh 2000kgm-3 jk øjHhlska idod we;s wrh 1cm jk f.da,hla >k;ajh
1100 kgm-3 jk øjhl øj mDIAGfha isg 20m by<ska ksYAp,;djfha isg w;yßkq
,nhs'
(i) f.da,h øj mDIAGfha .efgk m%fõ.h fidhkak'
(ii) øjh øj mDIAGh iu. .eàu;a iu. f.da,fha m%fõ.h 50% la olajd wvq fjhs'
fuu øjfha ÿiai%dú;d ix.=Klh 1x10-2Pa s kï" øjhg iïmQ¾Kfhkau we;=,a jQ
ieKska f.da,fha ;ajrKh fldmuKo@ (f.da,h øjhg we;=¨ jk fudfydf;a
mgka iafgdla iólrKh ms<smosk nj i,lkak')
(iii) f.da,h øjh ;=<oS w;a lr .kakd wdka; m%fõ.h fldmuK o@
(iv) f.da,h w; yßk fudfydf;a isg wdka; m%fõ.h ,nd .kakd fudfyd; olajd
f.da,fha m%fõ. ld, m%ia;drfha o< igykla w`oskak'

8. (a) (i) mDÓúfha ialkaOh M yd wrh R kï mDÒú mDIAGh u; .=re;ajdl¾IK lafIa;%

;Sj%;dj (g0) i`oyd m%ldYkhla ,shkak'
(ii) mDÓúh taldldr >k f.da,hla hehs i,ld >k;ajh  f,i f.k mDÓú mDIaGh
u; lafIA;% ;Sj%;dj i`oyd m%ldYkhla ,shkak'
(iii) mDÓú mDIaGfha .=re;ajdl¾IK úNjh i`oyd m%ldYkhla G, M yd R weiqfrka
,shkak'
(iv) mDÓú mDIaGh u; isg m ialkaOhla h Wila by<g Tijk úg (R>>>h kï)
l< hq;= ld¾hh mgh nj fmkajkak'
(v) tfiau m ialkaOhla mDÓú mDIaGfha isg mDÓúfha wrhg iudk Wila by<g
tiùfïoS l< hq;= ld¾hh i`oyd m%ldYkhla ,shd olajkak'
(vi) mDÓúhg 36000 km ÿßka .uka lrk 1200 kg W,aldjla mDÓúh foig .uka
wrUhs' fuysoS W,aldj mDÓú flakaøhg 9000 km ÿrlg meñKSfïoS W,aldj u;
lrk ld¾hh .Kkh lrkak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 15 AL/2024/01-S-II

A
(b) ialkaOh M yd wrh R jk mDÓúfha flakaø yryd .uka lrk
wdldrhg úIalïNh Tiafia l,ams;uh isÿrla úo A ia:dkfha isg
ksYap,j m ialkaOhla uqod yÍ' (π = 3)
(i) ialkaOh u; n,mdk .=re;ajdl¾IK n,h mokï lr
.ksñka ialkaOh isÿr ;=< isÿ lrk p,kh ir, wkqj¾;Sh
B
nj fmkajd B ia:dkh fj; <`.d jk úg ialkaOfha m%fõ.h
.Kkh lrkak'
(ii) ialkaOfha foda,k ld,dj¾;h i`oyd m%ldYkhla ,shkak'
(iii) M = 6 x1024kg o R = 6400 km o kï" by; ialkaOfha foda,k ld,dj¾;h
 20 
.Kkh lrkak' G =  10−11 m3kg −1s − 2 
 3 
 20 
 M = 6  10 kg, G =
24
 10−11 m3kg −1s − 2 
 3 

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

(A) fldgi

(a)

by; olajd we;af;a V úNjhlg iïnkaO l< Odß;%l ;yvq folls'

(i) Odß;%l ;yvq fol muKla msgm;a lr f.k úoHq;a n, f¾Ld jHdma;sh we`o
olajkak'
(ii) Odß;%lfha wdfrdamKh Q o" Odß;%l ;yvqfõ j¾.M,h A o iy Odß;%l w;r
udOHfha mdrfõoH;dj  0 o kï ;yvq fol w;r úoHq;a lafIa;% ;Sj%;dj i`oyd
m%ldYkhla ,nd .kak'
(iii) Odß;%l ;yvq fol w;r mr;rh d o Odß;%lfha Odß;dj C o kï
A
C = 0 nj fmkajkak'
d
(iv) fuu Odß;%lfha .nvd jk Yla;sh E i`oyd m%ldYkhla C iy V weiqßka
,shd olajkak'
(b) (i) j¾.M,h 2m2 la jQ Odß;%l ;yvq folla tlsfkl 6μm l mr;rhlska ;nd
(
we;akï tu Odß;%lfha Odß;dj .Kkh lrkak'  0 = 9  10 Fm
−12 −1
)
(ii) tu Odß;%lhg 150V l úNjhla ,nd ÿkafka kï Odß;%lfha .nvd jk
wdfrdamK m%udKh;a Odß;%lfha .nvd jk Yla;sh;a .Kkh lrkak'
(iii) bka miq fuu wdfrdamKh jQ Odß;%lh úNjfhka bj;a lr Odß;dj 5μF jQ
wkdfrdaams; Odß;%lhl w.% folg iïnkaO lrhs kï" Odß;%l fofla w.%
w;r kj úNjh;a m<uq Odß;%lfha oeka .nvd ù we;s Yla;sh;a .Kkh
lrkak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 16 AL/2024/01-S-II

(c) by; (b) (i) fldgfia .Kkh l< Odß;djg iudk Odß;djla we;s l=vd Odß;%lhla
600V l úNjhla hgf;a wdfrdamKh lr my; rEmfha mßos 20Ω m%;sfrdaOhla yd
iïnkaO lrhs'
(i) fuu Odß;%lfha .nvd ù we;s wdfrdamKh úi¾ckh
ùug 0.15 ms la jeh jQfha kï m%;sfrdaOh yryd .,d
.sh uOHl Odrdj .Kkh lrkak'
(ii) fuu m%;sfrdaOh yryd .,d .sh Odrdj ksid m%;sfrdaOh
;=< W;ai¾ckh jQ ;dm Yla;sh Odß;%lfha .nvd ù ;snQ
uq`: Yla;fs hka fldmuK m%;sY;hla o hkak .Kkh
lrkak'
(iii) YsIHfhla by; i`oyka Odß;%lhla iy m%;sfrdaOlhla
iys; moaO;s úYd, m%udKhla tlsfklg iudka;r.;j
iïnkaO lr mßm:h ixjD; yd újD; lsÍu i`oyd thg iaúphla iïnkaO
lsÍfuka mßm:hla idod th l=vd c, n`ÿklg iïnkaO lr 200ml jeks l=vd c,
m%udKhla r;a lr .; yels cx.u c, ;dmlhla ks¾udKh lsÍug n,dfmdfrd;a;=
fõ' fuu ;dmlh l%shd lrùu i`oyd m<uqj fuu
Odß;%l moaO;sh by; i`oyka úNjfhkau wdfrdamKh
lr miqj Ndú;d lsÍug wjYH jQ úg tys iaúph 20Ω
ixjD; lsÍfuka wod< m%;sfrdaO yryd Odrdjla .uka
lrjd m%;f s rdaO ;=<ska W;ai¾ckh jk ;dm Yla;hs
u.ska c,h r;a lr .kq ,nhs' fuu cx.u c, 20Ω
;dmlh Ndú;fhka c,h 200 ml l WIAK;ajh 200C
lska jeä lr .ekSug kï" by; Ndú;d l< Odß;%l 20Ω
wju jYfhka fldmuK m%udKhla iudka;r.;j
iïnkaO l< hq;= o hkak .Kkh lrkak'
(fuysoS ish¨ wdfrdamK 0.15ms ld,hla ;=<oS
m%;sfrdaO yryd .uka lrk nj;a c, n`ÿfka ;dm Odß;djh 240JK-1)
(c,fha >k;ajh 1000kgm-3 " c,fha úYsIga ;dm Odß;dj 4200Jkg-1 K-1)
(B) fldgi
V0
(a) (i) my; rEmfha ±lafjk úNj Ndclfha ys w.h
V
.Kkh lrkak'

(ii) m%odk úNjh 240V jQ úg ,efnk m%;sodk úNjh

.Kkh lrkak'
(iii) 5V jQ m%;sodk úNjhla ,nd .ekSug m%odkh l<
hq;= úNjh .Kkh lrkak'

(b) uq`M m%;sfrdaOh R0 jQ yd È. L jQ taldldr lïìhla fhdod .ksñka RL

Ndr m%;sfrdaOhlg úp,H fjda,aàh;djla ,nd oSug ieliQ moaO;shla
my; oelafõ.
(1) rEmfha mßÈ AB lïì fomiska V0 cj iemhqulg iïnkaO lr
we;'
(i) lïìfha A ,laIHh yd W i¾mlh w;r ÿr x jk úg AB
w.% w;r iul m%;sfrdaOh i`oyd m%ldYkhla jHq;amkak
lrkak'
(ii) AB w.% w;r ;sìh yels Wmßu yd wju m%;sfrdaOh R0 yd
R0 RL
nj fmkajkak'
R0 + RL
(iii) RL = 22.5kΩ o R0 = 5kΩ o kï W i¾mlh AB lïìh uOHfha we;s úg Odrdfõ
isÿ ù we;s úp,kh wju Odrdfõ m%;sY;hla f,i fokak'
ish¨ u ysñlï weúßKs] All Rights Reserved] 17 AL/2024/01-S-II

(c) my; olajd we;s úoHq;a mßm:fhys 30V, 10V yd 5V fldaI ;=kla iïnkaO lr we;s
w;r tu fldaIhkaf.a m%;fs rdaO ms<sfj,ska 2 Ω, 2 Ω yd 1 Ω fõ'
30V/ 2 Ω 6Ω
A B

8Ω 4Ω

8Ω 10V/2 Ω
F C

5Ω
4Ω 5V/1Ω
E D

(i) tla tla fldaIh yryd .,k Odrdjka .Kkh lrkak'

(ii) 10V fldaIfha w.% w;r úNj wka;rh .Kkh lrkak'
(iii) E ,laIHh N+.; l<fyd;a VC yd VD .Kkh lrkak'
(iv) my; rEmfha olajd we;s mßÈ C yd D w;r we;s m%;sfrdaOh .,jd bj;a fldg
5F Odß;%lhla iïnkaO l<fyd;a tys .nvd jk wdfrdamKfha úoHq;a Yla;sh
.Kkh lrkak'

30V/ 2 Ω 6Ω
A B

8Ω 4Ω
8Ω 10V/ 2 Ω
F C

4Ω 5V/ 1Ω
E D

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

(A) fldgi
uqyqÿ m;=f,a ieÕj we;s u;aiH úfYaI yd Ydl úfYaI yªkd.ekSugo tys we;s N+ úIu;d
wOHhkh lsÍu i|yd o id.r úoHd{fhda úYd, f,i lsñÿï .fõIK j, ksr; fõ. óg
wu;r fldr,amr wdoS wjg we;s iqkaor mßirh keröugo" úfkdaoh Wfoid o" ixpdrlhka
lsñÿï pdßld j, ksr; fõ.

lsñ§ug yelshdj we;s ´kEu wfhl=g fujka lsñÿï .fõIK j, ksr; ùug yelshdj we;ehs
fmkqko fuys i;H ;;ajh óg yd;amiskau fjkiah. Bg n,mdk ndOl fndfyduhla mj;sk
w;r tajd ch.ekSfuka f;drj lsñ§u w;sYh wka;rdodhl lghq;a;ls . n, mj;akd m%uqL;u
.eg`Mj kï lsñÿïlreg c,h ;=<§ Yajikhg wjYH jd;h /f.k hduhs. óg ms<shula f,i
Tlaiscka jdhqj wêl mSvkhla hgf;a gexls j, nyd lsñÿïlref.a msgg iúlr lsñ§fï§
/f.k hk ,§.
ish¨ u ysñlï weúßKs] All Rights Reserved] 18 AL/2024/01-S-II

wfkla m%Odk;u .eg`Mj kï uqyqÿ m;af,a mj;akd WIaK;aj md;khhs . fuhg fya;=j jkafka
c,fha ;dm ikakdhl;dj jd;fha fuka oi.=Khla muK ùuhs . fï ksid lsñÿïlref.a
YÍrfhka wêl iS.%;djfhka ;dmh msgfõ. óg ms<shula f,i lsñÿï we`÷ï ks¾udKh lsÍfï§ Bg
;dm ikakdhl;dj b;d wvq øjH Ndú;d lrk ,§. idudkHfhka 1000m .eUqrl§ uqyqÿ c,fha
WIaK;ajh tys u;=msg WIaK;ajhg jvd 80C lska wvqfõ. by; i|yka l< .eg`M Bg iß,k
WmlrK uÕska j<lajd .; yels jqj;a tfia uÕyrjd .; fkdyels .eg`Mo rdYshla mj;S . fïjd
u.yeÍu lsñÿïlre i;= rdcldßhls. fï ksid uqyqÿ m;af,a lsñ§ug fmr fuu .eg`M yd tajd
uÕyßk wdldrh ms<sn| oekqj;a ùu w;sYh jeo.;a lghq;a;ls . lsñ§ug fmr ta ms<sn|j ukd
mqyqKqjla ,nd .ekSu wksjd¾h jkafka fï ksidh.

fï wdldrfha m%Odk;u .eg`Mjla f,i isref¾ we;s khsg%cka m%idrKh ùu ye£kaúh yel. fuh
Decompression Sickness f,i ye`oskafõ. uqyqÿ m;af,a we;s wêl mSvkh ;=<§ khsg%cka jdhqj
isref¾ mgl ;=<g .uka lrhs. md,khlska hq;=j kej; uqyqÿ uÜgug meñKSfï§ fuu jdhqj
kej; fmky`M yryd YÍrfhka msgfõ. tfy;a CIKslj by<g meñKsh fyd;a mSvkfha CIKsl
wvq ùu ksid mgl ;=<u fïjd nqnq`M njg m;aù mgl j,g ydks muqKqjhs . iß,k fõ.hlska
by<g meñKSu lsñÿïlre i;= lghq;a;ls.
(a) (i) fndhs,a kshuh m%ldY lr tys .Ks;uh iólrKh ,shd olajkak.
(ii) Tlaiscka jdhqj gexls j,g msrùfï§ wêl mSvkhla Ndú;d lsÍug fya;= myokak.
(iii) uqyqÿ m;=< olajd lsñ§fï§ mek k.sk .eg`M 2la i|yka lrkak.
(b) mqoa.,fhl= tla wdYajdihl§ jd;h 500cm3 muK YÍrhg ,nd.kS. lsñÿïlrefjl=
fuu jd;h ;uka i;= gexls j,ska ,nd.kS. m%dYajdi jd;h Tyq c,hg uqod yÍ.
lsñÿïlreg jd;h jdhqf.da,h
S mSvkfhkau wdYajdi lsÍug hdk;%Khla ilid we;.
(i) mqoa.,fhl= ñks;a;=jlg wdYajdi 12 la isÿ lrhs kï mehl ld,hl§ Tyq
wdYajdi lrk uq`M jd; mßudj fldmuKo@
(ii) lsñÿïlrefjl=g .eUqre c,fha meh 3la muK isàug wjYH jk w;r Tyq i;=
gexls j, uq`M mßudj 10dm3 fõ. gexlsh ;=< jd;h .nvd l< hq;= mSvkh
jkafka l=ulao@ (jdhqf.da,Sh mSvkh } 1«105Pa)
(c) (i) tla;rd Èkl uqyqÿ uÜgfï WIaK;ajh 250C muK fõ. Bg 1000m my<ska c,fha
WIaK;ajh .Kkh lrkak.
(ii) iu, YÍr wNHka;rh yd ndysr w;r ;dm ikakdhlhla f,i ls%shd lrhs . tys ;dm
ikakdhl;dj o< jYfhka 0.5Wm-1K-1 jk w;r iM, j¾.M,h 2m2 muK fõ.
lsñÿïlrefjl= 1000m .eUqrlg lsñÿKq úg ndysr mßjdrl fkdue;s kï Tyqf.a
YÍrfhka ;dmh ydks jk iS.%;djh .Kkh lrkak. ^ñksidf.a wNHka;r YÍr
WIaK;ajh } 370C, ifuys >klu } 5mm&
(iii) fuu w.h YÍrhg ys;lr fkdjk ksid lsñÿï we`ÿfuka fuu w.h wvq flf¾.
fuu we`÷fï j¾.M,h 2m2 jk w;r >klu 1cm muK fõ. we`÷u me<£fuka
miq ;dmh ydksùfï iS.%;djh 1KW olajd wvq úh. we`÷ï idod we;s øjHfha ;dm
ikakdhl;dj fidhkak.
ish¨ u ysñlï weúßKs] All Rights Reserved] 19 AL/2024/01-S-II

(d) (i) lsñÿïlrefjl= .eUqre c,fha isg tlajru by<g .uka l<fyd;a th Tyqg
ydkshla jkafka wehs@
(ii) 3«105Pa jeks mSvkhl§ fujka khsg%cka nqnq<l mßudj 0.1mm3 muK fõ.
khsg%cka bj;a fkdjqkfyd;a fïjd mgl ;=<u m%idrKh fõ. lsñÿïlrefjl=
uqyqÿ uÜgfï isg h ÿrla my<ska isáh§ Tyq u; 3«105Pa mSvkhla l%shd lrhs.
nqnqf,a mßudj 0.2mm3 lsÍug Tyq CIKfhka fldmuK ÿrla by<g wd hq;=o@
c,fha >k;ajh 1100kgm-3 fõ'
(iii) kshsg%cka nqnq<l mßudj 0.6mm3s-1 iS.%;djfhka jeä ùu ydksodhl fõ. by;
(b) (ii) ys lsñÿïlrejdg by<g .uka l< yels Wmßu m%fõ.h fidhkak.

(B) fldgi

(a) (i) úfudapkh jk m%ldY bf,lafg%dakj, Wmßu pd,l Yla;sh (Kmax) yd m%ldY
ixfõ§ øjHfha ld¾h Y%s;h ( ) iïnkaO flfrk whskaiaghskaf.a m%ldY
úoHq;a iólrKh ,shd olajkak'
(ii) m%ldY ixfõ§ øjHfha foay,sh lrk wdhduh (0 ) u`.ska  i`oyd m%ldYkhla
,nd .kak'
(b) my; wjia:djka j,g wod,j m%ldY fldaIfha V-I ,dlaIKslhla m%ia;dr .; lrkak'
(i) m;s; wdf,dalfha ixLHd;h ksh; úg úúO wdf,dal ;Sj%;djka i`oyd
(ii) m;s; wdf,dalfha ;Sj%;djh ksh; úg úúO ixLHd;hka i`oyd
(iii) by; tla tla wjia:djkays§ ixLHd;h yd ;Sj%;djhkays úp,khka wiudk;d
m%ia;drh wi, ,shd olajkak'
(c) iQ¾h Yla;sh ridhksl Yla;sh njg m;a lsßfï yelshdj Ydlj,g mj;S'
iQ¾hdf,dalfha wdf,dal Yla;sh wjfYdaIKh lsÍu i`oyd Ydl yß;m%o kï j¾Kl
Ndú;d lrhs' idudkHfhka yß;m%o wkqjla iQ¾hdf,dalfha r;= yd ks,a wdf,dalfha
;rx. wdhdu wjfYdaIkh lr .kS' tu ;rx. wdhdu ms<sfj,ska 660nm yd 420nm fõ'
yß;m%o wkq tu ;rx. wdhduj,g wkqrEm f*dafgdak wjfYdaIKh lrñka ielnqKq
(excited) wjia:djg m;a fõ' wKq W;af;ackh ùug wjYH wju Yla;sh wKqfõ
ieljqï Yla;sh (𝜑) f,i ye`Èkafõ' by; a(ii) 𝜑 i`oyd ,nd.;a m%ldYh u`.ska fuu
ielUqï Yla;sh .Kkh l< yel' (bf,lafg%dakhl wdfrdamKh = 1.6 x10 -19 C)
(i) r;= yd ks,a wdf,dalhg wkqrEmj isÿjk ielöï j,g j,g wod, yß;m%o
wKqfõ ielUqï Yla;Ska 𝜑1 yd 𝜑2 m<uq oYuia:dk folg .Kkh lrkak'
( hc = 1290eVnm )
(ii) Èjd ld,fha§ Y%S ,xldfõ mDÓú mDIaGfha tall j¾.M,hla u; m;kh jk
iQ¾h úlsrK ;Sj%;djfha uOHkH w.h 1400Wm-2 fõ' fuu m;s;
iS>%;djfhka 0.1% la muKla ks,a wdf,dalhg wkqrEm f*dafgdakj, Yla;shg
wh;a fõ' Ydlhl m;%hla u; mj;sk yß;m%o wkqj, iM, mDIaÀl j¾.M,h
3cm3 fõ kï ks,a wdf,dalhg wod, jk laIu;djh .Kkh lrkak'
(iii) by; (ii) fldgfiys Yla;s iS>; % djh wkqrEm f*dafgdak iS>%;djh .Kkh
lrkak'
(iv) yß;m%o wkq u; m;s; jk f*dafgdak 5 × 1010 lg tla yß;m%o wkqjla
W;af;ackh fõ kï by; (iii) ys .Kkh l< w.hg wod,j W;af;ackh jk
yß;m%o wkq iS>%;djh .Kkh lrkak'
(v) r;= wdf,dalhg wkqrEm Yla;s wjfYdaIK iS>%;djfha m%;sY;h" yß;m%o wkqj,
iM, mDIaÀl j¾.M,h ks,a wdf,dalfhka w.fhkau fõ kï r;= yd ks,a
wdf,dal j,g wkqrEm f*dafgdak iS>%;djhkaf.a fjki .Kkh lrkak'