PUBDET 2018 Question Paper Physics

PUBDET-2018 81250001
Subject: Physics (Booklet Number)

Duration: 90 minutes Full Marks: 100

Instructions
1. All questions are of objective type having four answer options for each. Only one option is
correct. Correct answer will carry full marks 2. In case of incorrect answer or any combination
of more than one answer, ½ marks will be deducted.
2. Questions must be answered on OMR sheet by darkening the appropriate bubble marked A, B,
C, or D.
3. Use only Black/Blue ball point pen to mark the answer by complete filling up of the respective
bubbles.
4. Do not make any stray mark on the OMR.
5. Write question booklet number and your roll number carefully in the specified locations of the
OMR. Also fill appropriate bubbles.
6. Write your name (in block letter), name of the examination centre and put your full signature in
appropriate boxes in the OMR.
7. The OMRs will be processed by electronic means. Hence it is liable to become invalid if there
is any mistake in the question booklet number or roll number entered or if there is any mistake
in filling corresponding bubbles. Also it may become invalid if there is any discrepancy in the
name of the candidate, name of the examination centre or signature of the candidate vis-a-vis
what is given in the candidate’s admit card. The OMR may also become invalid due to folding
or putting stray marks on it or any damage to it. The consequence of such invalidation due to
incorrect marking or careless handling by the candidate will be sole responsibility of candidate.
8. Candidates are not allowed to carry any written or printed material, calculator, pen, docu-pen,
log table, any communication device like mobile phones etc. inside the examination hall. Any
candidate found with such items will be reported against & his/her candidature will be
summarily cancelled.
9. Rough work must be done on the question paper itself. Additional blank pages are given in the
question paper for rough work.
10. Hand over the OMR to the invigilator before leaving the Examination Hall.
11. This paper contains questions in both English and Bengali. Necessary care and precaution were
taken while framing the Bengali version. However, if any discrepancy(ies) is /are found
between the two versions, the information provided in the English version will stand and will
be treated as final

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1. A force acting on a particle of mass m first grows to a maximum F0 and then decreases to zero. The
force varies with time according to a linear law and the force acts for a total time T. The velocity of
the particle after time T (assume initial velocity of the particle is zero) is
m i−ll HL¢V LZ¡l Efl f¢lhaÑen£m hm fË−u¡N Ll¡ qmz fËb−j hm¢Vl j¡e hª¢Ü −f−u Qlj
j¡e F0 −a −f±yR¡u Hhw a¡lfl qÊ¡Ê p −f−u n§eÉ qu, hm¢V pj−ul p¡−b plm°l¢ML i¡−h f¢lh¢aÑa
qu Hhw −j¡V T pju d−l LZ¡¢Vl Efl fËkš ¤ ² quz T pju f−l LZ¡¢Vl −hN q−h (d−l e¡J hÙ¹¥¢Vl
fË¡l¢ñL −hN n§eÉ)
F0 F0 T F0 T F0 T 2
(A) (B) (C) (D)
m m 2m 2m

2. Two identical particles moving at right angles to each other possess de Broglie wavelengths λ and
2λ . The de Broglie wavelength in their centre of mass frame is
c¤¢V Ae¤l©f LZ¡ flØf−ll p−‰ pj−L¡−Z N¢an£m Hhw a¡−cl cÉ-hËu al‰°cOÑÉ kb¡œ²−j λ J 2λ
z pwÙÛ¡¢Vl il−L−¾cÊl p¡−f−r cÉ-hËu al‰°cOÑÉ q−h
λ 4λ λ
(A) (B) λ (C) (D)
3 5 2

3. A point source is placed midway between two converging mirrors having equal focal length 10 cm.
The mirrors are separated by a distance L. The value of L for which only one image is formed is
pj¡e −g¡L¡p °cOÑÉ 10 cm-Hl c¤¢V Ešm cfÑ−el A−rl jdÉ¢h¾c¥−a HL¢V ¢h¾c¥ Evp l¡M¡ B−Rz
c¤¢V cfÑ−el j−dÉL¡l c§laÆ L. Evp¢Vl HL¢Vj¡œ fË¢a¢hð °a¢l q−m L-Hl j¡e q−h
(A) 10 cm (B) 20 cm (C) 40 cm (D) 5 cm

4. ∞

∞ ∞

∞
Infinite number of conducting rings, each carrying current I in alternative directions as shown in the
figure are placed concentrically in the same plane. The radii of rings are R, 2R, 4R, 8R, …..∞. The
magnetic field at the centre of the rings will be
Ap£j pwMÉL f¢lh¡q£ hªš¡L¡l ¢lw-Hl BL¡−l pj−L¾cÊ£u i¡−h HLC pja−m p¢‹a B−Rz fË¢a¢V
f¢lh¡q£l jdÉ ¢c−u fËh¡qj¡œ¡ I J fËh¡qj¡œ¡l A¢ij¤M ¢Q−œ fËc¢nÑaz hªš¡L¡l f¢lh¡q£l hÉ¡p¡dÑ…¢m
kb¡œ²−j R, 2R, 4R, 8R, …..∞ −L−¾cÊ Evfæ −Q±ðL−r−œl j¡e qm,
µ0 I µ0 I µ0 I
(A) zero (B) (C) (D)
R 3R 2R

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5. A radioactive source emits both α and β particles with 1600 years and 400 years as respective half –
1
lives. The time after which th of the material remain undecayed is
4
(A) 320 years (B) 640 years (C) 1600 years (D) 200 years
HL¢V −aS¢ûu Evp −b−L α J β LZ¡ ¢expªa quz HC c¤C fÜ¢a−a AdÑ¡u¤ kb¡œ²−j 1600 hRl
1
J 400 hRlz La pju f−l Ev−pl Awn Ah¢nø b¡L−h?
4
(A) 320 hRl (B) 640 hRl (C) 1600 hRl (D) 200 hRl

6.
× ×
×
B ×
B
θ v × ×

A particle of mass m and charge +q enters a region of uniform magnetic field of intensity B pointing
inward into the page with uniform velocity v as shown in figure. For how much time the particle will
stay inside the magnetic field?
¢Q−œ fËc¢nÑa m i−ll +q a¢sa¡d¡e k¤š² HL¢V LZ¡ f¡a¡l ¢ia−ll ¢c−L mði¡−h ¢e−cÑ¢na B
fË¡h−mÉl HL¢V p¤¤oj −Q±ðL−r−œl j−dÉ v p¤¤oj N¢a−h−N fË−hn L−lz −Q±ðL−r−œl j−dÉ LZ¡¢V
Lare pju A¢ah¡¢qa Ll−h?

m(π − θ) m( π − 2θ) 2πm 2m
(A) (B) (C) (D) ( π − θ)
qB qB qB qB

7. An atomic Nucleus of mass m emits a γ -ray photon of frequency υ . The net loss in the
internal energy of the parent nucleus is
HL¢V m i−ll f¡lj¡Z¢hL ¢eE¢LÓu¡p −b−L υ LÇf¡−ˆl HL¢V γ l¢nÈ −g¡Ve ¢eNÑa quz Hl SeÉ
¢eE¢LÓu¡−pl −k f¢lj¡Z B¿¹xn¢š² L−j a¡ qm
 hυ   hυ 
(A) zero (B) hυ (C) hυ  1 +  (D) hυ  1 + 2 
 2mc2   mc 

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8. Consider a region where electric field E is in the z- direction and magnetic field B points
Eˆ
in the x-direction. A particle of charge q is released from the origin with velocity v = j.
B
The equation of the trajectory of the charged particle is
HL¢V ÙÛ¡−e z-Ar hl¡hl a¢sv−rœ E Hhw x-Ar hl¡hl −Q±ðL−rœ B ¢œ²u¡n£mz q Bd¡ek¤š²
Eˆ
HL¢V LZ¡ j§m¢h¾c¥ −b−L v = j −h−N k¡œ¡ öl¦ Llmz Bd¡e¢Vl p’¡lf−bl pj£LlZ q−h
B
E 2 E E
(A) y(t) = t (B) y(t) = t (C) y(t) = 0 (D) y(t) = t
2B B 2B

9. The ratio of dimensions of Planck’s constant h and moment of Inertia (I) has the dimension
of
(A) velocity (B) angular momentum (C) time (D) frequency

fÔÉ¡ˆ dË¥hL (h) Hhw Ssa¡ ï¡j−Ll (I) j¡œ¡l Ae¤f¡−al j¡œ¡ ¢e−Ql −L¡eÚ l¡¢nl j¡œ¡l pj¡e ?
(A) −hN (B) −L±¢eL il−hN (C) pju (D) LÇf¡ˆ

10. Two resistors A and B having resistances R1 and R2 respectively at 00C and temperature coefficients
α1 and α2 are joined in series. If this combination gives the same resistance at all temperatures, then
(A) A is a metal , B is a semiconductor
(B) Both A and B are metals
(C) Both A and B are semi conductors
(D) Not enough information is given for conclusion

00C a¡fj¡œ¡u A Hhw B c¤C −l¡d−Ll −l¡d R1 J R2 Hhw a¡fj¡œ¡ …Z¡ˆ α1J α2 z A Hhw B
−nËe£ pjh¡−u pwk¤š²z k¢c HC pwÙÛ¡ pLm a¡fj¡œ¡u HLC −l¡d fËcnÑe L−l, a−h

(A) A HL¢V d¡a¥, B HL¢V AdÑf¢lh¡q£z
(B) A Hhw B EiuC d¡a¥z
(C) A Hhw B EiuC AdÑf¢lh¡q£z
(D) ¢pÜ¡−¿¹l SeÉ fË−u¡Se£u abÉ −cJu¡ −eCz

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11. ρ
A spherical ball of radius R and density ρ released in a liquid of density , attains a terminal
2
velocity v. Then another ball of radius 2R and density 1.5 ρ , released in the same liquid will attain a
terminal velocity
ρ
HL¢V R hÉ¡p¡−dÑl J ρ Oe−aÆl −N¡mL−L Oe−aÆl al−m ¢ej¢‹a Ll−m −N¡mL¢V v fË¡¿¹£u −hN
2
ASÑe L−lz AeÉ HL¢V 2R hÉ¡p¡−dÑl J 1.5 ρ Oe−aÆl −N¡mL−L I HLC al−m ¢ej¢‹a Ll−m
a¡l fË¡¿¹£u −hN q−h

(A) v (B) 2v (C) 3v (D) 8v

12. One measures the specific resistance of a wire of circular cross-section by measuring length ( ℓ ),
diameter (d) and resistance (R). The recorded data are: R = 100 ± 0.01Ω, d = 0.50 ± 0.01 mm and
ℓ = 100 ± 0.01 cm . The maximum percentage of error in the measurement of its specific resistance
will be
HL¢V hªš¡L¡l fËÙÛ−µR−cl p¤¤oj a¡−ll −l¡d¡ˆ ¢eZÑu Ll¡l SeÉ a¡−ll °cOÑÉ ( ℓ ), hÉ¡p (d) J −l¡d
(R) ¢eZÑu Ll¡ qmz fl£r¡mì j¡e…¢m qm: R = 100 ± 0.01Ω, d = 0.50 ± 0.01 mm Hhw
ℓ = 100 ± 0.01 cm . HC fl£r¡u −l¡d¡ˆ ¢eZÑ−ul p−hÑ¡µQ naLl¡ œ¥¢Vl j¡e

(A) 4.02% (B) 2.02% (C) 1.01% (D) 0.06%

13.  2abxt + b2 t 2 + a 2 x 2 
Equation of a travelling wave is given by y ( x, t ) = A exp  −  , Where A, a, b, c
 c2 
are all positive constants of proper dimensions. The speed of the wave is

 
HL¢V Qmal−‰l pj£LlZ qm y ( x, t ) = A exp  − 2abxt + b 2t + a x  , −kM¡−e A, a, b, c l¡¢n…¢m
2 2 2 2

 c 
p¢WL j¡œ¡k¤š² de¡aÈL dË¥hL z Eš² al−‰l −hN

b 2b cb b
(A) (B) (C) (D)
a a a 2a

14. 1 mole of O2 and 1 mole of He are present in a mixture. The heat required to raise its temperature
from 00C to 1000 C at constant volume is (universal gas constant R = 8.31 Joules / mole k)
HL¢V ¢jnË−e 1 −j¡m O2 Hhw 1 −j¡m He B−Rz ¢jnËZ¢Vl a¡fj¡œ¡ ¢ÙÛl Bua−e 00C −b−L 1000C
Ll−a fË−u¡Se£u a¡−fl f¢lj¡Z (p¡hÑSe£e NÉ¡p dË¥hL R = 8.31 Joules /mole k)
(A) 3.324 x 103 J (B) 2.50 x 103 J (C) 3.00 x 103 J (D) 6.648 x 103 J

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15. a
A charge q is placed at a distance above the centre of a horizontal, square plate of side ‘a’. The
2
flux of electric field through the square face will be
a
HL¢V a¢sa¡d¡e q −L Ae¤i¨¢jL a−m l¡M¡ HL¢V a h¡ý ¢h¢nø hNÑ−r−œl jdÉ¢h¾c¥ −b−L EµQa¡u
2
l¡M¡ qmz hNÑ−r−œl jdÉ ¢c−u a¢sv gÓ¡„ q−h
q q q
(A) (B) (C) (D) 0
∈0 2 ∈0 6 ∈0

16. A ball of mass m, moving with a velocity v collides elastically with a wall of mass M moving with
velocity 2v towards the ball. Considering M → ∞ , the work done during this collision is
v −h−N N¢an£m m i−ll HL¢V hm a¡l ¢hfl£a¢c−L 2v N¢a−h−N Qmj¡e M i−ll HL¢V
−cJu¡−ml p¡−b ¢ÙÛ¢aÙÛ¡fL pwOoÑ OV¡uz M → ∞ q−m HC pwO−oÑ L«aL¡−kÑl f¢lj¡Z
(A) 12mv2 (B) 4 mv2 (C) Infinite (D) mv2

17. R
V

V C
I
2V
3R
In the given circuit with steady state current (I), the potential drop across the capacitor must be
¢Q−œ fËcš haÑe£u jdÉ ¢c−u Af¢lhaÑ£ fËh¡q (I) q−m d¡l−Ll f¡aà−ul j−dÉ ¢hih fË−ic qm
v v v
(A) (B) v (C) (D)
3 2 4

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18.
k

2kg

k

A mass of 2 kg is fixed between two springs, each of spring constant k = 200 N / m as shown in the
diagram. Initially the springs are un-stretched. If the mass is released and the springs are allowed to
expand or contract under the influence of the mass, what would be the acceleration of the mass at its
lowest position? Take g = 10 m / s2
Ef−ll ¢Q−œ −cM¡−e¡ 2 kg i−ll hÙ¹¥¢V HLC ¢ØfËw dËh¥ L k-l c¤¢V ¢ØfËw-Hl j¡TM¡−e l¡M¡ B−Rz
¢ØfËw c¤¢V fË¡b¢jLi¡−h AfËp¡¢la AhÙÛ¡u l¡M¡ B−Rz HC AhÙÛ¡u hÙ¹¢¥ V−L −R−s ¢c−m hÙ¹¥¢Vl phÑ¢ejÀ
AhÙÛ¡u aÆlZ ¢L? k = 200 N / m , g = 10 m / s2
(A) 5 m/sec2 upwards (FÜÑj§M£) (B) 10 m/sec2 upwards (FÜÑj§M£)
(C) 5 m/sec2 downwards (¢ejÀj§M£) (D) 100 m/sec2 upwards (FÜÑj§M£)

19. Each of 1000 small spherical water drops of radius ‘r’ carry a charge ‘q’. If these are combined to
Φ
form a large spherical drop, then the ratio of s , where Φ s is the electrostatic potential of each
Φℓ
small drop and Φ ℓ is that of the large drop, is

fË¢a¢V ‘r’ hÉ¡p¡−dÑl 1000 ¢V −N¡m¡L¡l Sm¢h¾c¥ HL¢œa q−u HL¢V hªqšl Sm¢h¾c¥ N¢Wa qmz fË¢a¢V
Φs
r¥â Sm¢h¾c¥l °hc¤É¢ae Bd¡e ‘q’ J ¢hih Φ s . p¢Çj¢ma Sm¢h¾c¥¢Vl a¢sv ¢hih Φ ℓ qC−m
Φℓ
Ae¤f¡a¢Vl j¡e
1 1
(A) (B) (C) 100 (D) 1000
1000 100

20. Two identical small mercury spheres, each of radius ‘r’, are fused to make a bigger sphere. The ratio
of the total surface energy of the two smaller spheres to that of the bigger sphere will be
fË¢a¢V ‘r’ hÉ¡p¡−dÑl c¤C¢V f¡l−cl −N¡mL ¢j−n ¢N−u HL¢V hs −N¡mL °al£ Llmz c¤¢V r¥â
−N¡m−Ll p¢Çj¢ma fªùn¢š² J hs −N¡mL¢Vl fªùn¢š²l Ae¤f¡a
1 1
(A) 1: 2 3 (B) 2 3 :1 (C) 2 :1 (D) 1: 2

21. Two coherent sources of intensities 9 watt/m2 and 4 watt/m2 produce interference fringes. The ratio
of maximum to minimum intensity of the fringe system is
9 watt/m2 J 4 watt/m2 a£hËa¡l c¤C¢V cn¡pðå B−m¡L Ev−pl à¡l¡ N¢Wa hÉ¢aQ¡l f¢Vl p−îÑ¡Q J
pîÑ¢ejÀ a£hËa¡l Ae¤f¡a
(A) 4 : 9 (B) 9 : 4 (C) 25 : 1 (D) 5 : 1

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22. A brass sphere of 10 cms radius is electrified to a potential of 80 units. It is then connected by a wire
to another uncharged brass sphere when its potential drops to 20 units. What is the radius of the
second sphere?
10 cm hÉ¡p¡−dÑl HL¢V B¢qa ¢fa−ml −N¡m−Ll °hc¤É¢aL ¢hih 80 HLLz HL¢V a¡−ll p¡q¡−kÉ HC
−N¡mL¢V−L Bl HL¢V Ae¡¢qa ¢fa−ml −N¡m−Ll p¢qa k¤š² Ll−m fËbj −N¡mL¢Vl °hc¤É¢aL
¢hih 20 HLL q−u k¡uz ¢àa£u −N¡mL¢Vl hÉ¡p¡dÑ La?
(A) 30 cms (B) 35 cms (C) 40 cms (D) 45 cms

23. A glass slab of refractive index 1.5 is immersed in a liquid of refractive index 1.35. What is the
polarizing angle for a light ray entering the glass slab from the liquid?
1.5 fË¢apl¡−ˆl HL¢V L¡y−Ql Mä 1.35 fË¢apl¡−ˆl HL¢V al−ml j−dÉ ¢ej¢‹a B−Rz alm q−a
L¡y−Ql M−ä fË−hnL¡l£ −L¡e B−m¡Ll¢nÈl pjhaÑ−el −L¡Z (dË¥hZ −L¡Z) ¢L q−h?
(A) tan −1 0.99 (B) tan −1 1.11 (C) tan −1 1.32 (D) tan −1 1.41

24. A monatomic ideal gas expands at constant pressure after addition of an amount of heat Q. The
fraction of heat goes into work done by the gas is
HL¢V HLflj¡e¤L BcnÑ NÉ¡−p Q f¢lj¡Z a¡f −cJu¡l fl NÉ¡p¢V ¢ÙÛl Q¡−f fËp¡¢la qmz fËcš
a¡−fl −k Awn NÉ¡p LaÑ«L L«aL¡−kÑ l©f¡¿¹¢la qm, a¡ qm
2 2 3
(A) (B) (C) (D) 1
5 3 5

25.
p
A
2P0

P0 B
v
V0 2V0
n mole ideal gas undergoes a process A → B as shown in the P–V diagram. At what volume the
temperature of the gas will be maximum?
3
(A) V0 (B) V0 (C) 2V0 (D) There is no maximum value of temperature.
2
‘n’ −j¡m f¢lj¡Z HL¢V BcnÑ NÉ¡p−L P–V ¢Qœ¡e¤p¡−l A → B HL¢V fË¢œ²u¡l jdÉ ¢c−u ¢e−u k¡Ju¡
qmz Bua−el −L¡eÚ j¡−e NÉ¡−pl a¡fj¡œ¡ p−hÑ¡µQ q−h?
3
(A) V0 (B) V0 (C) 2V0 (D) HM¡−e a¡fj¡œ¡l −L¡e p−hÑ¡µQ j¡e −eCz
2

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26. The magnetic flux linking a conducting ring varies with time as φ(t) = 4t 3 −12 t 2 Tm 2 . The
resistance of the ring is 2Ω. Maximum current induced in the ring during time interval 0 to 2 sec is
HL¢V f¢lh¡q£ L¥äm£l p¢qa S¢sa −Q±ðL fËh¡q pj−ul p−‰ φ(t) = 4t 3 −12 t 2 Tm 2 i¡−h f¢lh¢aÑa
quz L¥äm£¢Vl −l¡d 2Ω q−m 0 −b−L 2 −p−Lä pj−ul hÉhd¡−e L¥äm£−a B¢hø a¢svfËh¡−ql
p−hÑ¡µQ j¡e q−h

(A) 2 Amp (B) 1 Amp (C) 8 Amp (D) 6Amp

27. An electron in a hydrogen atom makes a transition from ground state to first excited state. The
magnetic dipole moment due to the circulating electron will
(A) increase by two times (B) decrease by two times
(C) decrease four times (D) remain same

q¡C−XÊ¡−Se flj¡Z¤l HL¢V C−mƒÊe ¢ejÀaj Ù¹l (ground state) −b−L fËbj EµQal Ù¹l (first excited
state) H ÙÛ¡e¡¿¹¢la q−m O§ZÑ¡uj¡e C−mƒÊ−el −Q±ðL ¢à−jl¦ ï¡jL
(A) 2…Z hª¢Ü f¡−h (B) 2 …Z L−j k¡−h
(C) 4…Z L−j k¡−h (D) HLC b¡L−h

28. A car is moving from rest with a constant acceleration f1 for some time, then the car retards with a
constant retardation f2 for some time and finally comes to rest. What is the average acceleration of
the car during its entire journey?
HL¢V N¡¢s ¢ÙÛl¡hÙÛ¡ −b−L f1 pjaÆl−Z ¢LR¥rZ −Nm, a¡lfl f2 pjj¾c−e ¢LR¥rZ k¡Ju¡l fl
¢ÙÛl¡hÙÛ¡u Hmz pÇf¨ZÑ k¡œ¡f−b N¡¢s¢Vl Ns aÆlZ La?
f1f 2 f1 + f 2 f12 − f 2 2 f12 + f 2 2
(A) (B) (C) (D)
f1 + f 2 2 f1 f 2 f1 f 2

29. Two point sources of sound are separated by a distance 1.50 m and they emit sound waves in phase
at wave length λ = 0.6m . If a sound detector is moved along a circle centered at the midpoint
between sources, the number of points on the circle where two waves arrive in phase is
c¤¢V në Evp 1.50 m ag¡−a Ah¢ÙÛa Hhw Evpàu pjcn¡u λ = 0.6m al‰°cOÑÉ ¢explZ L−lz
HL¢V në NË¡qL k¿»−L c¤¢V në Ev−pl jdÉ¢h¾c¥−L −L¾cÊ L−l HL¢V hªš¡L¡l f−b −O¡l¡−m hª−šl
Efl La…¢m ¢h¾c¥−a nëal‰àu pjcn¡u ¢j¢ma q−h?
(A) 10 (B) 8 (C) 6 (D) 14

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30. The P-V diagram of an ideal gas undergoing a reversible cyclic process is an ellipse as shown in the
figure. In this process
p

3P0/2

P0/2
v
V0/2 3V0/2
πP0 V0
(A) The work done per cycle is πP0 V0 (B) The work done per cycle is 2

2π 2π
(C) The efficiency is η = (D) The efficiency is η =
π+5 π+8

¢Q−œ BcnÑ NÉ¡−pl SeÉ HL¢V f§ZÑ fËaÉ¡haÑL Efhªš¡L¡l P-V fË¢œ²u¡ −cM¡−e¡ q−u−Rz HC
fË¢œ²u¡u
πP0 V0
(A) fË¢a f§ZÑ BhaÑ−e L«aL¡kÑ πP0 V0 (B) fË¢a f§ZÑ BhaÑ−e L«aL¡kÑ
2
2π 2π
(C) LjÑcra¡ η = (D) LjÑcra¡ η =
π+5 π+8

31. A particle is projected at time t=0 from a point on the ground with certain velocity at an angle with
the horizontal. The work done W by the gravitational force plotted against time t is best represented
by the curve
t=0 pj−u HL¢V LZ¡−L i¨¢j −b−L HL¢V ¢e¢cÑø −L¡−Z HL¢V ¢e¢cÑø N¢a−h−N −R¡ys¡ qmz pj−ul
p¡−f−r A¢iLoÑS hm à¡l¡ hÙ¹¢¥ Vl Efl L«aL¡kÑ W Hl f¢lhaÑe ¢e−Ql −L¡eÚ¢Vl Ae¤l©f?

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

t t t t

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32. Two ideal monatomic gases at absolute temperatures T1 and T2 are mixed. No energy is lost during
the process of mixing. If the masses of the molecules are m1 and m2 and the number of molecules in
the gases are μ1 and μ2 respectively, then final temperature of the mixture will be

T1J T2flj a¡fj¡œ¡u b¡L¡ c¤¢V BcnÑ NÉ¡p−L −jn¡−e¡ qmz NÉ¡−pl HC ¢jnËZ fË¢œ²u¡l −L¡e n¢š²
ru qu¢ez k¢c NÉ¡p c¤¢Vl AZ¤l il kb¡œ²−j m1 J m2 Hhw AZ¤l pwMÉ¡ kb¡œ²−j μ1J μ2 qu
a¡q−m ¢jnË−Zl a¡fj¡œ¡ q−h

µ1T2 + µ 2 T1 T1 + T2 µ1T1 + µ 2 T2
(A) (B) T1T2 (C) (D)
T1 + T2 2 µ1 + µ 2

33. A massless string can carry a maximum mass 6 kg. What maximum mass can this string raise up to a
height 10 m in 2 seconds with a constant acceleration?  g = 10m / s 2 

HL¢V ilq£e p¤¤−a¡ p−hÑ¡µQ 6 kg i−ll hÙ¹¥ hqe Ll−a f¡−lz p¤−¤ a¡¢V pjaÆl−Z 2 −p−L−ä p−hÑ¡µQ
La i−ll hÙ¹¥−L 10m EµQa¡u a¥m−a f¡l−h?
(A) 12 kg (B) 6 kg (C) 3 kg (D) 4 kg

x
34. −
The mass density of a linear rod of length L varies as ρ ( x ) = ρ 0 e L , where ‘x’ is the distance from
the left end of the rod and ρ 0 is a constant. Centre of mass of the rod lies at a distance

L 2 2
(A) from left end (B) ρ0 L  1 −  from left end
2  e
L  1 
(C) from right end (D) L  1 −  from right end
e −1  e −1
x
−
L °cOÑÉ¢h¢nø HL¢V plm°l¢ML c−äl ilOeaÆ ρ ( x ) = ρ 0 e L ¢q−p−h f¢lh¢aÑa quz −kM¡−e ‘x’
qm cä¢Vl h¡j¢cL −b−L c§l−aÆl f¢lj¡f J ρ 0 qm HL¢V dË¥hLz cä¢Vl il−L−¾cÊl AhÙÛ¡e
c−äl
 2
(A) h¡j¢cL −b−L L c§l−aÆ (B) h¡j¢cL −b−L ρ0 L2  1 −  c§l−aÆ
 e
2
L  1 
(C) X¡e¢cL −b−L c§l−aÆ (D) X¡e¢cL −b−L L  1 −  c§l−aÆ
e −1  e −1

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35. The density of sea water at the sea surface is ρ0 and the bulk modulus of the water is B. What will be
the density of water at a depth ‘d’ in the sea? g denotes the acceleration due to gravity. Assume
B ≫ dρ0 g

pj¤âa−m pj¤âS−ml OeaÆ ρ 0 Hhw HC S−ml Buae ¢hL«¢a …Z¡ˆ B. pj¤−âl Ef¢lam −b−L d
Ni£la¡u pj¤â S−ml OeaÆ La? g qm A¢iLoÑ£u aÆlZz d−l e¡J B ≫ dρ0 g

(A) ρ0 (1 + Bρ0 g d) (B) ρ0 (1 + B−1ρ0 g d) (C) ρ0 (1 − B−1ρ0 g d) (D) ρ 0 g d

36. An electric field in x-y plane is given by E = y ˆi + x ˆj .The equipotential surface corresponding to the
electric field is
(A) Parabola (B) Straight line (C) Hyperbola (D) Ellipse

x-y pja−m HL¢V a¢sv−r−œl fË¡hmÉ E = y ˆi + x ˆj . HC a¢sv−rœ¢Vl pj¢hih am qm

(A) A¢dhªš (B) plm −lM¡ (C) fl¡hªš (D) Efhªš

37. 1
A convex mirror of focal length ‘f’ produces a real image of the size of the object. The distance
n th
of the object from the mirror is
1
f −g¡L¡p °c−OÑÉl HL¢V Ešm cfÑZ HL¢V hÙ¹¥l BL¡−ll BL¡−ll fË¢a¢hð NWe Llmz cfÑZ
n th
−b−L hÙ¹¥l c§laÆ qm
f
(A) (B) (n-1) f (C) (n+1) f (D) nf
n

38. Two sound waves of wavelengths λ1 and λ 2 (λ 2 > λ1 ) produce n beats per second. The speed of
sound is
λ1 J λ 2 al‰°c−OÑÉl c¤¢V në al‰ fË¢a −p−L−ä n pwMÉL ülLÇf °al£ L−lz d−l e¡J λ 2 > λ1 z
−p−r−œ n−ël N¢a−hN q−h
λ 2 − λ1 λ1λ 2
(A) n (B) ( λ 2 − λ1 )n (C) n (D) n ( λ1 + λ 2 )
λ1λ 2 λ 2 − λ1

39. Two wires are of the same material. Their lengths are in the ratio 1:2 and their diameters are in the
ratio 2:1. If they are pulled by the same force, their increase in length will be in the ratio
HLC fc¡−bÑl °al£ c¤¢V a¡−ll °cOÑÉ J hÉ¡−pl Ae¤f¡a kb¡œ²−j 1:2 J 2:1z c¤¢Vl Efl HLC hm
fË−u¡N Ll−m, a¡−cl °cOÑÉ hª¢Ül Ae¤f¡a q−h
(A) 1:1 (B) 1:2 (C) 1:4 (D) 1:8

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40. Suppose a body at an absolute temperature 3T is placed in surroundings of absolute temperature T.
The time required for its temperature to decrease by T is proportional to
(A) ln (l/3) (B) 2T (C) 1/T (D) ln (2)

j−e Ll 3T flj Eo·a¡ ¢h¢nø HL¢V hÙ¹−¥ L T flj Eo·a¡ ¢h¢nø f¢lf¡¢nÄÑL j¡dÉ−j l¡M¡ qm z
hÙ¹¥¢Vl a¡fj¡œ¡ T f¢lj¡Z Lj−a −k pju m¡N−h a¡
(A) ln (l/3) Hl pj¡e¤f¡¢aL (B) 2T-Hl pj¡e¤f¡¢aL
(C) 1/T-Hl pj¡e¤f¡¢aL (D) ln (2) -Hl pj¡e¤f¡¢aL

41. Suppose a straight wire is hanging from a ceiling. The wire is pulled in such a way that its length
becomes l1 and its tension becomes T1. On further pulling , the length becomes l2 and corresponding
tension becomes T2. The original length of the wire is

j−e Ll HL¢V GS¥ a¡l R¡c −b−L T¥m−Rz a¡l¢V−L Hjei¡−h V¡e¡ qm −k a¡l¢Vl °cOÑÉ −h−s l1
qu Hhw HC V¡e T1 quz Hh¡l a¡l¢V−L B−l¡ −S¡−l V¡e¡l g−m a¡l¢Vl °cOÑÉ l2 J V¡e T2 qmz
a¡l¢Vl fËL«a °cOÑÉ qm
l1 + l2 T2 l2 − T1l1 T2 l1 − T1l2
(A) l1l2 (B) (C) (D)
2 T2 − T1 T2 − T1

42. The acceleration of an electron at an instant in a magnetic field B = ˆi + y ˆj + 13kˆ is a = 2iˆ + 3jˆ − 2kˆ .
The value of y is
B = ˆi + y ˆj + 13kˆ −Q±ðL−r−œ −L¡e HL j¤ý−aÑ HL¢V C−mƒÊ−el aÆlZ a = 2iˆ + 3jˆ − 2kˆ q−m y Hl j¡e
q−h
28
(A) 7 (B) 24 (C) (D) 8
3

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43. A particle of mass ‘m’ moves along the x-axis under a potential v(x)=a+bx+cx2 , where a, b, c are all
positive constants. Its motion will be
m
(A) simple harmonic with period 2π
2c

ma
(B) simple harmonic with period 2π
2b 2
(C) One of constant velocity
(D) One of constant acceleration

’m’ i−ll HL¢V LZ¡ v(x)=a+bx+cx2 ¢hi−hl fËi¡−h x-Ar hl¡hl Q¢m−a−Rz Cq¡l N¢al fËL«¢a

m
(A) 2π fkÑ¡uL¡m ¢h¢nø plm −c¡mL N¢a
2c

ma
(B) 2π fkÑ¡uL¡m ¢h¢nø plm −c¡mL N¢a
2b 2
(C) pj−h−N N¢a
(D) pjaÆl−Z N¢a

44. 1020 photons of wavelength 660 nm are being emitted every second by an electric bulb. What is its
power?
−L¡e °hc¤¢aL h¡¢a −b−L fË¢a −p−L−ä 660 nm al‰°c−OÑÉl 1020 −g¡Ve ¢eNÑa q−µRz h¡¢a¢Vl
rja¡ La ?
(A) 30W (B) 60W (C) 100W (D) 500W

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45. A closed cubical tank is completely filled with liquid and is accelerated horizontally with an
acceleration a = 2 m / s towards right. The pressure at any point inside liquid is a function of depth
2

h and distance l from the front wall. Variation of pressure with l is shown in the figure.

P (N)
h
a 45O
l
P(h,l)
l (m)
L L

The density of the liquid is
(A) 1 kg/m3 (B) 0.5 kg/m3
(C) 0.1 kg/m3 (D) sufficient information is not given

HL¢V hÜ OeL¡L«¢a VÉ¡ˆ (tank) pÇf¨ZÑi¡−h alm ¢c−u i¢aÑ Hhw Cq¡−L Ae¤i¢¨ jLi¡−h X¡e¢c−L
a = 2m / s 2 pjaÆl−Z aÆl¡¢eÄa Ll¡ qmz al−ml j−dÉ −k −L¡e ¢h¾c¥−a Q¡f, Ni£la¡ h J p¡j−el
−cJu¡m −b−L c§laÆ l Hl A−frLz l Hl p¢qa Q¡f P Hl f¢lhaÑe ¢Q−œ −cM¡−e¡ q−u−Rz alm¢Vl
OeaÆ qm
(A) 1 kg/m3 (B) 0.5 kg/m3
(C) 0.1 kg/m3 (D) Eš−ll SeÉ fË−u¡Se£u abÉ −cJu¡ −eC

46. A ray of light passes from a medium of refractive index μ1 to a medium of refractive index μ2 (μ2>
μ1). If the angle of incidence is twice the angle of refraction, then the angle of incidence is

j−e Ll HL¢V B−m¡Ll¢nÈ µ1 fË¢apl¡−ˆl HL¢V j¡dÉj −b−L µ 2 fË¢apl¡−ˆl Afl HL¢V j¡dÉ−j
−Nmz −kM¡−e µ 2 > µ1 z k¢c Bfae −L¡Z fË¢aplZ −L¡−Zl ¢à…Z qu a¡q−m Bfae −L¡−Zl j¡e
q−h
µ  µ   µ   µ 
(A) 2 cos −1  2  (B) cos −1  2  (C) 2 cos −1  1  (D) cos −1  1 
 2µ1   2µ1   2µ 2   2µ 2 

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47. In which of the following systems will the wavelengths of the photon emitted in the transition of an
electron from n=2 to n=1 state be a minimum?
(A) hydrogen atom (B) deuterium atom
(C) single ionized helium (D) doubly ionized lithium

¢ejÀ¢m¢Ma −L¡e −r−œ n=2 −b−L n=1 AhÙÛ¡¿¹−l ¢eNÑa −g¡V−el al‰°cOÑÉ e§Éeaj q−h?
(A) q¡C−XÊ¡−Se flj¡Z¤ (B) ¢XE−V¢lu¡j flj¡Z¤
(C) HLh¡l Bu¢ea ¢q¢mu¡j flj¡Z¤ (D) c¤h¡l Bu¢ea ¢m¢bu¡j flj¡Z¤

48. The velocity of sound in a gas of diatomic molecules is v and the rms velocity of gas molecules is c.
v
Then is
c
HL¢V ¢àflj¡Z¤ ¢h¢nø NÉ¡−pl ¢ia−l n−ël N¢a−hN v. HC NÉ¡−pl Ae¤…¢ml j§m Ns hNÑ−hN c.
v
a¡q−m -l j¡e
c
15 7 3 7
(A) (B) (C) (D)
7 15 7 3

49. A planet is at a distance d from the sun and its average temperature is T. Suppose the planet receives
energy only from the sun and loses energy from its surface by the process of radiation. If we ignore
all atmospheric effects then
p§kÑ −b−L HL¢V NË−ql c§laÆ d J NË−ql Ns a¡fj¡œ¡ Tz j−e Ll NËq¢V −Lhmj¡œ p§kÑ −b−L n¢š²
NËqZ Ll−R Hhw ¢h¢Ll−Zl j¡dÉ−j a¡l fªùam −b−L n¢š² hSÑe Ll−Rz k¢c pjÙ¹ h¡u¤jäm£u fËi¡h
ANË¡qÉ L¢l a¡q−m
1 1
(A) T∝ (B) T∝ (C) T∝ d (D) T∝ d
d d

50. A driver in his car notices a change in frequency of his horn from 550 Hz to 770 Hz when moving
towards a vertical wall. The frequency changes due to reflection from the wall. The speed of the car
is (velocity of sound in air is 330 m/s)
HL¢V Eõð −cJu¡−ml A¢ij¤−M ANËpl qJu¡l pju N¡¢sl Q¡mL mrÉ L−l −cJu¡−m n−ël
fË¢agm−el SeÉ N¡¢sl q−ZÑl LÇf¡ˆ 550 Hz −b−L 770 Hz H f¢lh¢aÑa quz N¡¢sl N¢a−hN qm
(h¡a¡−p n−ël −hN 330 m/s)
(A) 65 m/s (B) 14.7 m/s (C) 55 m/s (D) 110 m/s

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PUBDET-2018
Subject: Physics

pju: 90 ¢j¢eV phÑ¡¢dL eðl: 100

¢e−cÑn¡hm£
1. HC fËnÀf−œl ph fËnÀC Ah−S¢ƒi fËnÀ Hhw fË¢a¢V fË−nÀl Q¡l¢V pñ¡hÉ Ešl −cJu¡
B−R k¡l HL¢V j¡œ p¢WLz p¢WL Ešl ¢c−m 2 eðl f¡−hz i¥m Ešl ¢c−m Abh¡
HL¡¢dL Ešl ¢c−m ½ eðl L¡V¡ k¡−hz
2. OMR f−œ A,B,C,D ¢Q¢q²a p¢WL Ol¢V il¡V L−l Ešl ¢c−a q−hz
3. OMR f−œ Ešl ¢c−a öd¤j¡œ L¡−m¡ h¡ e£m hm f−u¾V −fe hÉ¡hq¡l Ll−hz
4. OMR f−œ ¢e¢cÑø ÙÛ¡e R¡s¡ AeÉ −L¡b¡J −L¡e c¡N −c−h e¡z
5. OMR f−œ ¢e¢cÑø ÙÛ¡−e fËnÀf−œl eðl Hhw ¢e−Sl −l¡m eðl A¢a p¡hd¡ea¡l p¡−b
¢mM−a q−h Hhw fË−u¡Se£u Ol…¢m f§lZ Ll−a q−hz
6. OMR f−œ ¢e¢cÑø ÙÛ¡−e ¢e−Sl e¡j J fl£r¡ −L−¾cÊl e¡j ¢mM−a q−h Hhw ¢e−Sl pÇf¨ZÑ
p¡rl ¢c−a q−hz
7. OMR Ešlfœ¢V C−mLVÊ¢eL k−¿»l p¡q¡−kÉ fs¡ q−hz p¤a
¤ l¡w fËnÀ−fœl eðl h¡ −l¡m
eðl i¥m ¢mM−m Abh¡ i¥m Ol il¡V Ll−m Ešlfœ¢V A¢eh¡kÑ L¡l−Z h¡¢am q−a
f¡−lz HR¡s¡ fl£r¡bÑ£l e¡j, fl£r¡ −L−¾cÊl e¡j h¡ p¡r−l −L¡e i¥m b¡L−mJ Ešl fœ
h¡¢am q−u −k−a f¡−lz OMR Ešlfœ¢V i¡yS q−m h¡ a¡−a Ae¡hnÉL c¡N fs−mJ
h¡¢am q−u −k−a f¡−lz fl£r¡bÑ£l HC dl−el i¥m h¡ ApaÑLa¡l SeÉ Ešlfœ h¡¢am
q−m HLj¡œ fl£r¡bÑ£ ¢e−SC a¡l SeÉ c¡u£ b¡L−hz
8. −j¡h¡Cm−g¡e, LÉ¡mL¥−mVl, pÔ¡CXl¦m, mN−Vhm, −lM¡¢Qœ, NË¡g h¡ −L¡e dl−Zl a¡¢mL¡
fl£r¡ L−r Be¡ k¡−h e¡z Be−m −p¢V h¡−Su¡ç q−h Hhw fl£r¡bÑ£l JC fl£r¡
h¡¢am Ll¡ q−hz
9. fËnÀf−œl −n−o l¡g L¡S Ll¡l SeÉ gy¡L¡ S¡uN¡ −cJu¡ B−Rz AeÉ −L¡e L¡NS HC
L¡−S hÉhq¡l Ll−h e¡z
10. fl£r¡ Lr R¡s¡l B−N OMR fœ AhnÉ C f¢lcnÑL−L ¢c−u k¡−hz
11. HC fËnÀf−œ Cwl¡S£ J h¡wm¡ Eiu i¡o¡−aC fËnÀ −cJu¡ B−Rz h¡wm¡ j¡dÉ−j fËnÀ °al£l
pju fË−u¡Se£u p¡hd¡ea¡ J paLÑa¡ Ahmðe Ll¡ q−u−Rz a¡ p−šÄJ k¢c −L¡e Ap‰¢a
mr Ll¡ k¡u, −p−r−œ Cwl¡S£ j¡dÉ−j −cJu¡ fËnÀ ¢WL J Q¨s¡¿¹ h−m ¢h−h¢Qa q−hz

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