m%Yak wxlh
ms
m%Yak wxlh
ms
3
(26)
4
(2)
5
(27)
4
(3)
3
(28)
5
(4)
5
(29)
3
(5)
1
(30)
(6)
4
(31)
(7)
5
(32)
(8)
3
(33)
(9)
2
(34)
(10)
2
(11)
2
(12)
5
(13)
3
(14)
3
m
(1)
4
wa
.co
3 2 4 5 4
(36)
5
(37)
2
(38)
4
(39)
1
1
(40)
4
5
(41)
3
5
(42)
2
1
(43)
2
(19)
4
(44)
2
(20)
4
(45)
4
(21)
5
(46)
3
(22)
2
(47)
5
(23)
3
(48)
3
(24)
3
(49)
2
(25)
4
(50)
5
(16) (17)
w.
(18)
vib
(15)
ha
(35)
ww
w'fmd'i' ^W'fm<& Wmldrl iïuka;%Kh - 2016 fN!;sl úoHdj - I m;%h ms
[2 jk mssgqj n,kak
-2fN!;sl úoHdj - II m;%h ms
A fldgi - jHqy.; rpkd
1. (a)
uhsfl%daógr bial=remamq wdudkh
(b)
uQ,dxl fodaIh we;a±hs m¯laId ls¯u
(c)
(a) - ndysr ykq (b) - ndysr ykq (c) - wNHka;r ykq
( )]
m
[a × b − π ( d2 ) ] t 2
wa
.co
ridhksl ;=,dj 2 (e) V = a × b − π d t 2 d =
^,l=Kq 1&
^ish,a,u y˙ kï ,l=Kq 2 $ folla y˙ kï ,l=Kq 1&
(d) bf,lafg%daksla ;=,dj
[
^,l=Kq 1&
m
^,l=Kq 1& ^,l=Kq 1&
^,l=Kq 1&
(f) (i) 0.01 mm
^,l=Kq 1&
3.42 mm 17.12 =
5
(iii)
follg" WmlrKfhka ñkqï .; yelafla oYuia:dk follg neúks'
2. (a) we;a fodr
- A
ìysf∞r -
B
^,l=Kq 1& ^,l=Kq 1&
^,l=Kq 1&
fkdyel' l=àrh ;=< WIaK;ajh 100 C° mj;ajd .; fkdyels ksid oKAv yryd wkjr®: ;;a;ajhla mj;ajd .; fkdyels fõ' yqud, >k;ajh wvq ksid ie,lsh hq;= fõ,djla ;=< oKav r;alr .; yels ùu ^,l=Kq 1&
ww
(b)
3.42 mm
w.
ha
(ii) 3.05 + 3.51 + 3.52 + 3.51 + 3.53 = 17.12
vib
(c)
Out
In
^,l=Kq 1& [3 jk mssgqj n,kak
-3 (d)
Q t
(θ1 − θ2)
;dmh .,d hEfï iS>%;dj
x
WIAK;aj wkql%uh
^,l=Kq 1&
(e)
WIaK;aj udkj, mdGdxl fjkia fkdù mej;Su
^,l=Kq 1&
(f)
oKafâ yrialv úYalïNh T1 yd T2 w;r ≥r okakd ld,hloS tall k,hl .,d hk ;r, m˙udj$ ialkaOh
^,l=Kq 1& ^,l=Kq 1&
^,l=Kq 1&
m
x Q × 1 . t (θ1 − θ2) A
(g) k =
(h) c,h r;aùug ld,h m%udKj;a fkdjk ksid T3 ,T4 WIAK;ajudkj, mdGdxl ie,lsh hq;=
WIaK;aj udkj, mdGdxlj, ie,lsh hq;= ;rï fjkila we;s fkdùu'
wa
.co
fjkila fkdfmkaùu (i) fkdyel' = l
λ = 2l
√ mI
T = 1 2L m
√
I 1 f = 2 l m
√
1 2 (b) f 2 = y L = mT
(
2
2
w.
y
=
l
4L m
T
^,l=Kq 1&
= mx
ww
f
2
(
^,l=Kq 1&
vib
f=
^,l=Kq 1&
ha
λ 2
3. (a)
^,l=Kq 1&
^,l=Kq 1&
(c) (i) l †. wvq w.hl mj;ajd ta w;r lvodis wdfrdaylhla r|jd ixLHd;h olajd iriq, lïmkh lr èjks udk fmÜáh u; ;nd fia;= w;r mr;rh l%ufhka jeälr f.k hk úg lvodis wdfrdaylh úisjk fudfydf;ys l †. ,nd .kS' ^,l=Kq 1& (ii) B ys L †. lïmkh lrjd A ys lv∞is wdfrdaylfhka r|jd fia;= w;r mr;rh l=vd w.hl isg l%ufhka jeä lrf.k hk úg lv∞is wdfrdaylh úisjk fudfyd; tkï iqirjk wjia:dj ,nd .kak' tu wjia:dfõ° A lïìfha †. uekf.k tys mriamrh fidhd"
1/l
u.ska .kq ,efí' tu.ska rEmfha ±lafjk wdldrhg Bg wkqrem ixLHd;h ,nd 0
f
.; yel'
^,l=Kq 1&
[4 jk mssgqj n,kak
-4(d) f 2 0 wlaI ,l=Kq ls¯u yd yevh T (e) (i) wkql%uKh = =
m
1 2 m 4L 1 2 = wkql%uKh 4L
^,l=Kq 1&
m
^,l=Kq 1&
(ii) wvqu w.h f ∝ 1 ksid wvqu w.hg wod< †. fidhd .;aúg jeä w.hkg wod< †.j,a l uek.; yel' ^,l=Kq 1&
.co
= 480 f × 1 l 1 = k f l 100 480 = k 23.7 474 = k 100 l 480 = l 474 23.7 480 l = × 23.7 cm 474 (f) f A
^,l=Kq 1&
= 24 cm
vib
l
ha
wa
^,l=Kq 1&
^,l=Kq 1&
- t,jqï fldaIh
B
- iaúph ^talux&
C
- .e,ajfkdaógrfha wdrlaIl Wml%uh
D
- ueo ìx≥ .e,ajfkdaógrh
ww
w.
4. (i) A
(ii) A
- jeä fõ,djla tlu Odrdj iemhSug yels ùu'
D
- by< ixfõ°;djhla ;sîu'
(iii)
^,l=Kq 1&
E (< E0)
P S
(iv)
2 Vcm−1 200 0.01 Vcm−1
10 mVcm−1
^,l=Kq 1&
^,l=Kq 1& [5 jk mssgqj n,kak
-5100
(v) 200 × 4 × 10−1
=
2V
(vi) ke;' †. uekSfï Nd.sl f∞aIh jeähs'
^,l=Kq 1&
(vii) m%;sfrdaOh t,jqï fldaIhg fY%aKs.;j iïnkaO ls¯u
^,l=Kq 1&
(viii) 4 10
: 1996 : 399
3990 Ω
(ix) 200 × 4 = 80 cm 10 (x) F
1
= 1 4
F
=
2
1 800
F1 > F2 ys Nd.sl fodaIhg b;d l=vdhs'
^,l=Kq 1& ^,l=Kq 1&
wa
B fldgi - rpkd
ha
fndAÜgqfõ nr we;sjk Wvql=re f;rmqï n,hg iudk ùu' Wvql=re f;rmqï n,fha l%shd fr®Ldj yd nfr® l%shd fr®Ldj talfr®Çh ùu ^,l=Kq 1& u
vib
5. (a) (b)
^,l=Kq 1&
m
^,l=Kq 1&
.co
0.4 cm
^,l=Kq 1&
mg
w.
600 + 70 × 8 600 + 560 1160 kg 11600 N
ww
(c)
(d) (i) m%;sfrdaë n,h = 1160 × 0.6 N = 6960 N = 696 N (ii) F 696 696
696
696 50
= = = = =
mu (AVP) V 2 2 AV P 2 0.05 × 1000 × V 5 × 1000 × V2
=
50 × V
=
100
V
^,l=Kq 1&
^,l=Kq 1&
^,l=Kq 1& ^,l=Kq 1&
2
2
[6 jk mssgqj n,kak
-6-
3.73 ms
−1
=
V
=
V
(e) (i) P = FV 696 = 696 × 50
√
=
(ii) P
= FV × 100
^,l=Kq 1&
2596 W
40
√
696
^,l=Kq 1&
^,l=Kq 1&
=
696 × 50
=
6490 W
m
696 50
× 2.5
.co
√
=
11600 10000
jdhq nqn, iys; m%foaYfha° .sf,k m˙udj
=
11600 8000
wu;r m˙udj
1
wa
(f) (i) m
ha
V
1 ( 8000
= 11600 ×
vib
= =
^,l=Kq 1&
^,l=Kq 1&
−
1 10000
)
^,l=Kq 1&
2900
2000 8000 × 10000
11600
0.29 m3
4
^,l=Kq 1&
10
(ii) = 0.29 × 100 × 1 6 60 =
0.029 m3
ww
6. (a)
^,l=Kq 1&
w.
h
β 25 cm
α l
β α
= h l = h D
^,l=Kq 1&
^,l=Kq 1&
uE; ,laIHh jk D ≥r we;súg wefiys oDIaá ú;dkfha wdmd;sk fldaKh α > Bg wE;ska we;s ,laIHhl jia;=j we;s úg wefia wdmd; lrk fldaKh
α > β ∴ úYd,s; m%;sìïnh ,efí'
^,l=Kq 1&
[7 jk mssgqj n,kak
-7(b) mshú weiska n,k úg wefia oDIaá ú;dkfha wdmd; lrk fldaKh fuka wkaùlaIh ;=
Wmfk;
wjfk; l
fe
h
h1 α
f0
m
2f0
wjfk; ^,l=Kq 1& Wmfk; ^,l=Kq 1& ^Bysi iys;" O%ejh yryd hk lsrK iuÛ&
.co
h2
wa
α1 M = α
= me × mo
=
o
−1
)
^,l=Kq 1&
^,l=Kq 1&
( 252.5 + 1 ) ( 2022 − 1) (10 + 1)
(101 −1)
ww
11 × 100
w.
(d)
( Df + 1 ) ( lf e
vib
h h2 / D h h = 2 = 2 × 1 h h/D h1 h
^,l=Kq 1&
ha
h h /D h h M = 2 = 2 = 2 × 1 h h/D h1 h
1100
^,l=Kq 1&
(e) (i) <Û fkdfmkSu ^fyj;a ≥r oDIaál;ajh& ^,l=Kq 1& (ii) 1 − 1 = 1 V U f 1 1 + − 1 =− ^,l=Kq iïuq;sh yd ksjer† wdfoaYhg ,l=Kq 1& 25 2.5 U
1 1 + = 1 25 2.5 U 11 1 + = 25 U 25 U = cm 11 +
^,l=Kq 1& [8 jk mssgqj n,kak
-8kj U
1
=
25 11
175 81 × 11
= 81 × 25 + 175 81 × 11
=
2025 + 175 81 × 11
2200 81 × 11 200 = cm 81
= U
1
= 2.47 cm
1 −1 = 1 f V U 81 = − 1 1 − 200 V 2.5
1 = V
81 − 80 200
1 1 = 200 V V = 200 cm
^ksjer† wdfoaYhg ,l=Kq 1&
ha
81 − 80 200
vib
1 = V
ww
v
w.
(iii) 20.2 + 2.5 cm 22.7 cm 7. (a)
^,l=Kq 1&
wa
81 = − 1 1 − 200 V 2.5
m
+
.co
^,l=Kq 1&
^,l=Kq 1&
t
^,l=Kq 1&
(b) m%d:ñlhg jvd oaú;slfha fmdg .Kk jeä ùu m%d:ñlhg jvd oaú;slfha lïì uy; wvq ùu
^,l=Kq 1&
(c)
v
t
1 g jvd Wi jeä úh hq;=h'
^,l=Kq 1&
[9 jk mssgqj n,kak
-9vp Np
(d) (i)
Np Ns
vs Ns
vp vs
11000 = p Ns 250
=
N
44 = Np Ns 1
44 : 1 = Np : Ns
(ii)
Vrms =
=
vp
Vp
= 250
√2 √2
wa
= 353.5 V (iii) cQ,a ;dmh iq,O s drd ydksh
ha
ukaodhk ydksh
(iv) mdr.uH;dj jeä ls¯u yd i%dj ldka≥j wvq ls¯u I = F × l I
(ii) (iii)
BI (ab) N Cos θ
^,l=Kq 1&
=
V
20
√2
I
IR
= I × 100 =
1 5√2
I
=
=
1.6
5√2
^,l=Kq 1&
BI (ab) N
1 × 0.2 × 5√2 = 1.6 × √ 2 10
= 0.16 ×
20 × 10 ( 100 × 100
(
^,l=Kq 1&
^,l=Kq 1&
^,l=Kq 1&
= BIab N
ww
vib
(e) (i)
^,l=Kq 1&
w.
^,l=Kq 1&
Vrms
= 250 × 1.41
^,l=Kq 1&
m
^,l=Kq 1&
.co
=
× 400
Nm
^,l=Kq 1&
(iv) meΩï ú,s fyj;a kHdfoaYl fh†h hq;=h'
^,l=Kq 1&
√2
= 0.225 Nm
[10 jk mssgqj n,kak
- 10 I
=
6 πqrv
(F)
= MLT−2
6 πqrv
= [q] [r] [v]
= ML−2
= ML−1 T−1 L LT−1 = MLT−2
U
(b) U + F = mg 4 πr3pq + 6πqrv = 4 πdq 3 3
vib
^,l=Kq 1&
w.
(d)
^,l=Kq 1&
v
r
^,l=Kq 1&
wa
6πqrv + 4 πg (d − p)r3 3 v = 2 qr2g(d − p) 9
(c)
^,l=Kq 1&
mg
ha
F
3
^,l=Kq 1&
m
8. (a) F
t
.co
(f)
v = 2g (d − p) r v 9q
2
ww
(i)
= m
y
(ii) m
=
x
2g (d − p) r2 9η
^,l=Kq 1&
2g (d − p) 9m 2g (iii) η = (d − p) 9m
^,l=Kq 1&
= 2 × 10 (1240 − 700) 9 × 800
^wdfoaaYhg ,l=Kq 1&
η
=
60
= 2 × 540 9 × 80
[11 jk mssgqj n,kak
- 11
12 = 1.5 Nm−2 8
=
η (iv) v
= m
× r2 2 = 800 × 10 100
v
^,l=Kq 1&
( )
= 800 × 10 100
= 8 ms−1
(e)
^,l=Kq 1&
η
^,l=Kq 1&
40 × 1.5 × 8
=
60 × 8
=
480 N
(ii)
ha
=
F
V/ms−1
^,l=Kq 1&
^,l=Kq 1&
vib
wa
.co
θ (f) (i) F = η∆V d A F 8 = 1.5 × −1 −4 −3 400 × 10 1× 10
m
^,l=Kq 1&
8
(i)
p,kh jk bf,lafg%dak" bf,lafg%dak iu. .eàu;a mrudKq iu. .eàu;a ksid ydks jk pd,l Yla;sh u.ska ;dmh ckkh fõ' ^,l=Kq 1&
ww
9. (a)
w.
^yevhg ,l=Kq 1& d/ mm 0.1 ^tall iu`. ksjer†j wlaI ,l=Kq ls¯ug ,l=Kq 1&
(ii)
ú≥,s ia;%slalh" iQ;%sld n,anh
^,l=Kq 1&
(b) (A) fY%aKs.;j
R1 I
R2
r E [12 jk mssgqj n,kak
- 12 E = I ( r + R1 + R2 ) I =
(
E (r + R1 + R2)
)
^,l=Kq 1&
(ii) R yryd ;dm Yla;sh Wm†k iS>%;dj } I 2 R 1 1 2
R2 yryd ;dm Yla;sh Wm†k iS>%;dj } I R2
folgu
m
fuys° m%;sfrdaO ;=
ckkh jeä fõ'
iudka;r.;j
R1
.co
(B)
R2 r
I
ww
(
E R1 R2 R1 + R2
Rf = R1 R2 (R1 + R2) I =
E
ha
^iul m%;sfrdaOh fiùug& ^,l=Kq 1&
vib
wa
)
+r
w.
I × R2 R Odrdj I1 = 1 yryd (R1 + R2) R2 yryd Odrdj I2 =
R2 yryd ;dm Yla;sh Wm†k iS>%;dj =
I × R1 (R1 + R2)
R1 yryd ;dm Yla;sh Wm†k iS>%;dj =
^,l=Kq 1&
I 2 R22
(R1 + R2)2 I2 R21 (R1 + R2)2
^,l=Kq 1&
^,l=Kq 1&
× R1 = × R2 =
^,l=Kq 1&
I 2R2R1 (R1 + R2)2 I2R2R1 (R1 + R2)2
× R2
× R1
folgu ^,l=Kq 1&
R1 > R2 neúka R2 yryd ;dm Yla;s W;air®ck iS>%;dj jeäfõ'
^úl,aam l%uh } P } V2/ R wkqj ;r®llr we;akï o ,l=Kq ,nd †h yel'&
^,l=Kq 1&
[13 jk mssgqj n,kak
- 13 (c) (i)
P = I2 R
( )
2
(ii)
^,l=Kq 1&
R = r fõ'
^,l=Kq 1&
E . R (R + r)
=
( ) ( ) 2
P max
E . R (2r)
1
= 4
E (r)
2
. r
1 2 = 4 r
F
wa
(iii)
=
m
túg P max
vib
ha
R
9. (B) (a)
1
8
3
^,l=Kq 1&
^,l=Kq 1&
7
w.
2
.co
6
ww
4 5
^,l=Kq 1&
Vcal
+VS
−VA
VA
Vn
−VS
^,l=Kq 1&
[14 jk mssgqj n,kak
- 14 -
( ) ( ) (
(b) Vo = 10 V 1 R1 Vo = −
^,l=Kq 1&
10
R2 V2 ∴ Vo = − 10 V1 + 10 V1 R1 R2
^,l=Kq 1&
)
(c) 10 = 5 R1
^,l=Kq 1&
10 = 0.2 R2
(d)
(
V1 = 2 V0 = V
−(10)
V1 = 0
= 0
V2 = 5
V/V t1
1
t2
t3
(e) (i) A
B
C
0
0
1
0 0
0 1
F
0 0
1
ABC
1 0 1 1
A B C
0
ww
1
1
1
1
w.
0
1
^ld, mr;rj,g w.hka iuÛ&
^,l=Kq 3&
vib
)
t
ha
10 11
−1V
^,l=Kq 2&
wa
2
V0 =
.co
= 50 kΩ
m
10 100 R1 = 2 kΩ R2 = = 0.2 2
0 0
^,l=Kq 2&
1 1 1 ABC 1 F2 ABC + ABC + ABC (ii) ^,l=Kq 1& (iii)
^,l=Kq 2&
[15 jk mssgqj n,kak
- 15 10.(A) (a) tall m˙udjl we;s c,jdIam ialkaOh
^,l=Kq 1&
(b) tall m˙udjl we;s c,jdIam ialkaOh tu WIaK;ajfha ix;Dma; c, jdIam ialkaOhg ork wkqmd;h fõ'
^,l=Kq 1&
(c)
^,l=Kq 1&
(d) (i)
idfmalaI wdr®ø;dj
=
ksrfmalaI wdr®ø;dj ldur WIaK;ajfha ix'jd'mS'
.co
m
c,h >kSNjkh lr bj;a lrk ksid wjldYfha we;s c, jdIam idkaøKh wvqh' tneúka ksrfmalaI wdr®ø;dj wvqfõ' idfmalaI wdr®ø;dj jeä jkafka WIaK;ajh wvq lrk úg tu wjldYh ix;Dma; ùug wjYH c, jdIam ialkaOh wvq w.h ksid idfmalaI wdr®ø;dj by< hhs'
ksrfmalaI wdr®ø;dj 80 = 31. 70 100 = 80 × 31. 70 100 2536 = 10
wa
ksrfmalaI wdr®ø;dj
ha
= 25.36 Hgmm
^,l=Kq 1&
^,l=Kq 1&
^,l=Kq 1&
^,l=Kq 1&
(iii) 24 °C ° ;sìh hq;= m%udKh 22.3 Hgmm
^,l=Kq 1&
30 °C 24 °C meñfKk úg"
^,l=Kq 1&
PV = nRT
m RT M = PVM RT
ww
PV =
w.
m
vib
(ii) 25.36 Hgmm jkafka 26 °C ° tu ksid ;=Idr wxlh 26 °C
30 °C m30 = 25.36 × 13600 × 10 × 10 × 60 × 18 8.3 × 303 −3
24 °C m24 = 22.3 × 13600 × 10 × 10 × 60 × 18 8.3 × 297 −3
^,l=Kq 1&
^ksjer† wdfoaYhg& ^,l=Kq 1& ^,l=Kq 1&
[16 jk mssgqj n,kak
- 16 >kSNjkh jk c,jdIam = m − m + m24 30 24 2 ialkaOh (m)
2m30 − m24 = 2 =
=
[
=
13600 × 10 × 10 × 60 × 18 8.3
=
−3
−3
]
]
25.36 22.3 − 303 297
]
.co
[
25.36 22.3 − 303 297
13600 × 10 × 10 × 60 × 18 × (0.162392 − 0.075084) 8.3 −3
13600 × 10 × 10 × 60 × 18 8.3 −3
=
=
1633.52 g
=
1.634 Kg
× 0.092308
^,l=Kq 1&
ha
13600 × 10 × 10 × 60 × 18 8.3
]
(e) wjldYfha c, jdIam wvq lrk ksid m%dYajdi jd;h iuÛ c,h msg jqjo wdYajdi iuÛ th fkd,efí' tu ksid ffi,j, c, idkaøKh wvqfõ' nysiai%dù l%shdj ≥r®j, fõ' tu ksid c,h mdkh l< hq;=h' ^,l=Kq 1&
lef;davh
wefkdavh
ww
w.
10.(B)(a) (i)
vib
−3
wa
[ ][ [
25 − 3 × 2 22.3 − 297 303
13600 × 10 × 10 × 60 × 18 8.3
^,l=Kq 1&
m
μA
V
^,l=Kq 1&
(a) fldaIhg iïnkaO w.% fol udre ls¯u
^,l=Kq 1&
[17 jk mssgqj n,kak
- 17
m%ldY Odrdj
i ^,l=Kq 1&
B
^,l=Kq 1&
C
^,l=Kq 1&
V
^,l=Kq 1&
D
= hf
=
= hC λ
6.6 × 10−34 × 3 × 108 −9 660 × 10 16 −35
= 66 × 3 × 10 660
E
= 3 × 10−19
=
17
× 10
10
ha
3 × 10−19 = 30 16 1.6 × 10−19
15 = = 1.875 ev 8
vib
KE
.co
E E
wa
(b)
úNj wka;rh
m
A
= hf − Q
= 1.875 − 1 = 0.875 ev
= 0.875 × 1.6 × 10 = 1.4 × 10 J VS e
=
VS e
=
−19
^,l=Kq 1&
KEmax
ww
w.
−19
^,l=Kq 1&
0.875 ev
VS e = 0.875 ev
^,l=Kq 1&
[18 jk mssgqj n,kak
- 18 (c)
(i)
to
= 2 × 10−14 Hz
Q = 1.32 × 10 ev h = Δα (ii) Δλ
^,l=Kq 1&
−19
=
(iii)
−19
m
= 0.66 × 10−33
= 6.6 × 10 Js −34
^,l=Kq 1&
^,l=Kq 1&
.co
(iv)
1
2
3
4
wa
^,l=Kq 1&
(1.98 − 0.66) × 10−19 (5 − 3) × 1014
1.32 × 10 = 2 × 1014
^,l=Kq 1&
ha
1.35
ww
w.
vib
2.64
^,l=Kq 1&
