JEE MAIN EXAM 2015 CODE -A QUESTION PAPER DT.04.04.2015

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×ãžßÂê‡æü çÙÎðüàæ Ñ
1. ÂÚUèÿææ ÂéçSÌ·¤æ ·ð¤ §â ÂëcÆU ÂÚU ¥æßàØ·¤ çßßÚU‡æ ÙèÜð / ·¤æÜð ÕæòÜ
Œß槴ÅU ÂðÙ âð ̈·¤æÜ ÖÚð´Ð Âðç‹âÜ ·¤æ ÂýØæð» çÕË·é¤Ü ßçÁüÌ ãñÐ
2. ©žæÚU Â˜æ §â ÂÚUèÿææ ÂéçSÌ·¤æ ·ð¤ ¥‹ÎÚU ÚU¹æ ãñÐ ÁÕ ¥æ·¤æð ÂÚUèÿææ ÂéçSÌ·¤æ
¹æðÜÙð ·¤æð ·¤ãæ Áæ°, Ìæð ©žæÚU ˜æ çÙ·¤æÜ ·¤ÚU âæßÏæÙèÂêßü·¤ çßßÚU‡æ ÖÚð´UÐ
3. ÂÚUèÿææ ·¤è ¥ßçÏ 3 ƒæ´ÅðU ãñÐ
4. §â ÂÚUèÿææ ÂéçSÌ·¤æ ×ð´ 90 ÂýàÙ ãñ´Ð ¥çÏ·¤Ì× ¥´·¤ 360 ãñ´Ð
5. §â ÂÚUèÿææ ÂéçSÌ·¤æ ×ð´ ÌèÙ Öæ» A, B, C ãñ´, çÁâ·ð¤ ÂýˆØð·¤ Öæ» ×ð´
ÖæñçÌ·¤ çß™ææÙ, ÚUâæØÙ çß™ææÙ °ß´ »ç‡æÌ ·ð¤ 30 ÂýàÙ ãñ´ ¥æñÚU âÖè
ÂýàÙæ𴠷𤠥´·¤ â×æÙ ãñ´Ð ÂýˆØð·¤ ÂýàÙ ·ð¤ âãè ©žæÚU ·ð¤ çÜ° 4 (¿æÚU)
¥´·¤ çÙÏæüçÚUÌ ç·¤Øð »Øð ãñ´Ð
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çÙÎðüàææÙéâæÚU ¥´·¤ çÎØð ÁæØð´»ðÐ ÂýˆØð·¤ ÂýàÙ ·ð¤ »ÜÌ ©žæÚU ·ð¤ çÜØð
¼ ßæ´ Öæ» ·¤æÅU çÜØæ ÁæØð»æÐ ØçÎ ©žæÚU ˜æ ×ð´ ç·¤âè ÂýàÙ ·¤æ ©žæÚU
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7. ÂýˆØð·¤ ÂýàÙ ·¤æ ·ð¤ßÜ °·¤ ãè âãè ©žæÚU ãñÐ °·¤ âð ¥çÏ·¤ ©žæÚU ÎðÙð ÂÚU
©âð »ÜÌ ©žæÚU ×æÙæ ÁæØð»æ ¥æñÚU ©ÂÚUæð€Ì çÙÎðüàæ 6 ·ð¤ ¥ÙéâæÚU ¥´·¤ ·¤æÅU
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·¤ÚUÙð ãðÌé ·ð¤ßÜ ÙèÜð/·¤æÜð ÕæòÜ Œß槴ÅUU ÂðÙ ·¤æ ãè ÂýØæð» ·¤Úð´UÐ
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9. ÂÚUèÿææÍèü mæÚUæ ÂÚUèÿææ ·¤ÿæ/ãæòÜ ×ð´ Âýßðàæ ·¤æÇüU ·ð¤ ¥Üæßæ ç·¤âè Öè Âý·¤æÚU
·¤è ÂæÆ÷UØ âæ×»ýè, ×éçÎýÌ Øæ ãSÌçÜç¹Ì, ·¤æ»Á ·¤è Âç¿üØæ¡, ÂðÁÚU, ×æðÕæ§Ü
ȤæðÙ Øæ ç·¤âè Öè Âý·¤æÚU ·ð¤ §Üð€ÅþUæòçÙ·¤ ©Â·¤ÚU‡ææð´ Øæ ç·¤âè ¥‹Ø Âý·¤æÚU ·¤è
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10. ÚUȤ ·¤æØü ÂÚUèÿææ ÂéçSÌ·¤æ ×ð´ ·ð¤ßÜ çÙÏæüçÚUÌ Á»ã ÂÚU ãè ·¤èçÁ°Ð Øã
Á»ã ÂýˆØð·¤ ÂëcÆU ÂÚU Ùè¿ð ·¤è ¥æðÚU ¥æñÚU ÂéçSÌ·¤æ ·ð¤ ¥´Ì ×ð´ °·¤ ÂëcÆU ÂÚU
(ÂëcÆU 39) Îè »§ü ãñÐ
11. ÂÚUèÿææ â×æŒÌ ãæðÙð ÂÚU, ÂÚUèÿææÍèü ·¤ÿæ/ãæòÜ ÀUæðǸÙð âð Âêßü ©žæÚU Â˜æ ·¤ÿæ
çÙÚUèÿæ·¤ ·¤æð ¥ßàØ âæñ´Â Îð´Ð ÂÚUèÿææÍèü ¥ÂÙð âæÍ §â ÂÚUèÿææ ÂéçSÌ·¤æ
·¤æð Üð Áæ â·¤Ìð ãñ´Ð
12. §â ÂéçSÌ·¤æ ·¤æ â´·ð¤Ì A ãñÐ Øã âéçÙçà¿Ì ·¤ÚU Üð´ ç·¤ §â ÂéçSÌ·¤æ ·¤æ
â´·ð¤Ì, ©žæÚU Â˜æ ·ð¤ ÂëcÆU-2 ÂÚU ÀUÂð â´·ð¤Ì âð ç×ÜÌæ ãñ ¥æñÚU Øã Öè
âéçÙçà¿Ì ·¤ÚU Üð´ ç·¤ ÂÚUèÿææ ÂéçSÌ·¤æ, ©žæÚU ˜æ ÂÚU ·ý¤× ⴁØæ ç×ÜÌè ãñÐ
¥»ÚU Øã çÖóæ ãæð Ìæð ÂÚUèÿææÍèü ÎêâÚUè ÂÚUèÿææ ÂéçSÌ·¤æ ¥æñÚU ©žæÚU ˜æ ÜðÙð
·ð¤ çÜ° çÙÚUèÿæ·¤ ·¤æð ÌéÚU‹Ì ¥ß»Ì ·¤ÚUæ°¡Ð
13. ©žæÚU Â˜æ ·¤æð Ù ×æðǸ𴠰ߴ Ù ãè ©â ÂÚU ¥‹Ø çÙàææ٠ܻ氡Ð
Test Booklet Code
ÂÚèÿææ ÂéçSÌ·¤æ â´·ð¤Ì
A
PAPER - 1 : PHYSICS, CHEMISTRY & MATHEMATICS
ÂýàÙÂéçSÌ·¤æ - 1 : ÖæñçÌ·¤ çß™ææÙ, ÚUâæØÙ çß™ææÙ ÌÍæ »ç‡æÌ
LMN

2. A/Page 2 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
PART A — PHYSICS Öæ» A — ÖæñçÌ·¤ çß™ææÙ
1. Two stones are thrown up simultaneously
from the edge of a cliff 240 m high with
initial speed of 10 m/s and 40 m/s
respectively. Which of the following graph
best represents the time variation of
relative position of the second stone with
respect to the first ?
(Assume stones do not rebound after
hitting the ground and neglect air
resistance, take g510 m/s2)
(The figures are schematic and not drawn to
scale)
(1)
(2)
(3)
(4)
1. ç·¤âè 240 m ª¡¤¿è ¿æðÅUè ·ð¤ °·¤ ç·¤ÙæÚðU âð, Îæð
ˆÍÚUæð´ ·¤æð °·¤âæÍ ª¤ÂÚU ·¤è ¥æðÚU Èð´¤·¤æ »Øæ ãñ, §Ù·¤è
ÂýæÚ´UçÖ·¤ ¿æÜ ·ý¤×àæÑ 10 m/s ÌÍæ 40 m/s ãñ, Ìæð,
çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙâæ »ýæȤ (¥æÜð¹) ÂãÜð ˆÍÚU
·ð¤ âæÂðÿæ ÎêâÚðU ˆÍÚU ·¤è çSÍçÌ ·ð¤ â×Ø çß¿ÚU‡æ
(ÂçÚUßÌüÙ) ·¤æð âßæüçÏ·¤ âãè ÎàææüÌæ ãñ?
(×æÙ ÜèçÁ° ç·¤, ˆÍÚU Á×èÙ âð ÅU·¤ÚUæÙð ·ð¤ Âà¿æÌ
ª¤ÂÚU ·¤è ¥æðÚU Ùãè´ ©ÀUÜÌð ãñ´ ÌÍæ ßæØé ·¤æ ÂýçÌÚUæðÏ
Ù»‡Ø ãñ, çÎØæ ãñ g510 m/s2)
(Øãæ¡ »ýæȤ ·ð¤ßÜ ÃØßSÍæ ¥æÚðU¹ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤
¥ÙéâæÚU Ùãè´ ãñ´)
(1)
(2)
(3)
(4)

3. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 3
2. The period of oscillation of a simple
pendulum is
L
T 2
g
5 p . Measured value
of L is 20.0 cm known to 1 mm accuracy
and time for 100 oscillations of the
pendulum is found to be 90 s using a wrist
watch of 1s resolution. The accuracy in
the determination of g is :
(1) 2%
(2) 3%
(3) 1%
(4) 5%
3.
Given in the figure are two blocks A and B
of weight 20 N and 100 N, respectively.
These are being pressed against a wall by
a force F as shown. If the coefficient of
friction between the blocks is 0.1 and
between block B and the wall is 0.15, the
frictional force applied by the wall on block
B is :
(1) 100 N
(2) 80 N
(3) 120 N
(4) 150 N
2. ç·¤âè âÚUÜ ÜæðÜ·¤ ·¤æ ¥æßÌü, L
T 2
g
5 p ãñÐ
L ·¤æ ×æçÂÌ ×æÙ 20.0 cm ãñ, çÁâ·¤è ØÍæÍüÌæ
1 mm ãñÐ §â ÜæðÜ·¤ ·ð¤ 100 ÎæðÜÙæð´ ·¤æ â×Ø
90 s ãñ, çÁâð 1s çßÖðÎÙ ·¤è ƒæǸè âð ÙæÂæ »Øæ ãñÐ Ìæð,
g ·ð¤ çÙÏæüÚU‡æ ×ð´ ØÍæÍüÌæ ãæð»è Ñ
(1) 2%
(2) 3%
(3) 1%
(4) 5%
3.
Øãæ¡ ¥æÚðU¹ ×ð´ Îæð ŽÜæò·¤ (»éÅU·ð¤) A ¥æñÚU B ÎàææüØð »Øð
ãñ´ çÁÙ·ð¤ ÖæÚU ·ý¤×àæÑ 20 N ÌÍæ 100 N ãñ´Ð §‹ãð´,
°·¤ ÕÜ F mæÚUæ ç·¤âè ÎèßæÚU ÂÚU ÎÕæØæ Áæ ÚUãæ ãñÐ
ØçÎ ƒæáü‡æ »é‡ææ´·¤ ·¤æ ×æÙ, A ÌÍæ B ·ð¤ Õè¿ 0.1
ÌÍæ B ¥æñÚU ÎèßæÚU ·ð¤ Õè¿ 0.15 ãñ Ìæð, ÎèßæÚU mæÚUæ
ŽÜæò·¤ B ÂÚU Ü»æ ÕÜ ãæð»æ Ñ
(1) 100 N
(2) 80 N
(3) 120 N
(4) 150 N

4. A/Page 4 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
4. A particle of mass m moving in the
x direction with speed 2v is hit by another
particle of mass 2m moving in the
y direction with speed v. If the collision is
perfectly inelastic, the percentage loss in
the energy during the collision is close to :
(1) 44%
(2) 50%
(3) 56%
(4) 62%
5. Distance of the centre of mass of a solid
uniform cone from its vertex is z0. If the
radius of its base is R and its height is h
then z0 is equal to :
(1)
2
h
4R
(2)
3h
4
(3)
5h
8
(4)
2
3h
8R
4. x-çÎàææ ×ð´ 2v ¿æÜ âð ¿ÜÌð ãé° m ÎýÃØ×æÙ ·ð¤ °·¤
·¤‡æ âð, y-çÎàææ ×ð´ v ßð» âð ¿ÜÌæ ãé¥æ 2m ÎýÃØ×æÙ
·¤æ °·¤ ·¤‡æ, ÅU·¤ÚUæÌæ ãñÐ ØçÎ Øã â´ƒæÅ÷UÅU (ÅU€·¤ÚU)
Âê‡æüÌÑ ¥ÂýˆØæSÍ ãñ Ìæð, ÅU€·¤ÚU ·ð¤ ÎæñÚUæÙ ª¤Áæü ·¤æ ÿæØ
(ãæçÙ) ãæð»è Ñ
(1) 44%
(2) 50%
(3) 56%
(4) 62%
5. ç·¤âè °·¤â×æÙ ÆUæðâ àæ´·é¤ ·ð¤ ÎýÃØ×æÙ ·ð¤‹Îý ·¤è
©â·ð¤ àæèáü âð ÎêÚUè z0 ãñÐ ØçÎ àæ´·é¤ ·ð¤ ¥æÏæÚU ·¤è
ç˜æ’Øæ R ÌÍæ àæ´·é¤ ·¤è ª¡¤¿æ§ü h ãæð Ìæð z0 ·¤æ ×æÙ
çِÙæ´ç·¤Ì ×ð´ âð ç·¤â·ð¤ ÕÚUæÕÚU ãæð»æ?
(1)
2
h
4R
(2)
3h
4
(3)
5h
8
(4)
2
3h
8R

5. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 5
6. From a solid sphere of mass M and radius
R a cube of maximum possible volume is
cut. Moment of inertia of cube about an
axis passing through its center and
perpendicular to one of its faces is :
(1)
2
MR
32 2p
(2)
2
MR
16 2p
(3)
2
4MR
9 3p
(4)
2
4MR
3 3p
7. From a solid sphere of mass M and radius
R, a spherical portion of radius
R
2
is
removed, as shown in the figure. Taking
gravitational potential V50 at r5:, the
potential at the centre of the cavity thus
formed is :
(G5 gravitational constant)
(1)
GM
2R
2
(2)
GM
R
2
(3)
2GM
3R
2
(4)
2GM
R
2
6. ç·¤âè ÆUæðâ »æðÜð ·¤æ ÎýÃØ×æÙ M ÌÍæ §â·¤è ç˜æ’Øæ
R ãñÐ §â×ð´ âð ¥çÏ·¤Ì× â´Öß ¥æØÌÙ ·¤æ °·¤
€ØêÕ (ƒæÙ) ·¤æÅU çÜØæ ÁæÌæ ãñÐ §â €ØêÕ ·¤æ
ÁǸˆß ¥æƒæê‡æü ç·¤ÌÙæ ãæð»æ, ØçÎ, §â·¤è ƒæê‡æüÙ-¥ÿæ,
§â·ð¤ ·ð¤‹Îý âð ãæð·¤ÚU »é$ÁÚUÌè ãñ ÌÍæ §â·ð¤ ç·¤âè °·¤
Ȥܷ¤ ·ð¤ ܐÕßÌ÷U ãñ?
(1)
2
MR
32 2p
(2)
2
MR
16 2p
(3)
2
4MR
9 3p
(4)
2
4MR
3 3p
7. °·¤ ÆUæðâ »æðÜð ·¤æ ÎýÃØ×æÙ M ÌÍæ ç˜æ’Øæ R ãñÐ
§ââð
R
2
ç˜æ’Øæ ·¤æ °·¤ »æðÜèØ Öæ», ¥æÚðU¹ ×ð´ ÎàææüØð
»Øð ¥ÙéâæÚU ·¤æÅU çÜØæ ÁæÌæ ãñÐ r5:(¥Ù‹Ì) ÂÚU
»éL¤ˆßèØ çßÖß ·ð¤ ×æÙ V ·¤æð àæê‹Ø (V50) ×æÙÌð
ãé°, §â Âý·¤æÚU ÕÙð ·¤æðÅUÚU (·ñ¤çßÅUè) ·ð¤ ·ð¤‹Îý ÂÚU,
»éL¤ˆßèØ çßÖß ·¤æ ×æÙ ãæð»æ Ñ
(G5 »éL¤ˆßèØ çSÍÚUæ¡·¤ ãñ )
(1)
GM
2R
2
(2)
GM
R
2
(3)
2GM
3R
2
(4)
2GM
R
2

6. A/Page 6 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
8. A pendulum made of a uniform wire of
cross sectional area A has time period T.
When an additional mass M is added to
its bob, the time period changes to TM. If
the Young’s modulus of the material of the
wire is Y then
1
Y
is equal to :
(g5gravitational acceleration)
(1)
2
MT A
1
T Mg
  
  
   
2
(2)
2
M MgT
1
T A
  
  
   
2
(3)
2
MT A
1
T Mg
  
  
   
2
(4)
2
M
T A
1
T Mg
  
  
   
2
9. Consider a spherical shell of radius R at
temperature T. The black body radiation
inside it can be considered as an ideal gas
of photons with internal energy per unit
volume 4U
u T
V
5 ; and pressure
1 U
p
3 V
 
 
 
5 . If the shell now undergoes
an adiabatic expansion the relation
between T and R is :
(1) T ; e2R
(2) T ; e23R
(3)
1
T
R
;
(4) 3
1
T
R
;
8. ç·¤âè °·¤â×æÙ ÌæÚU ·¤è ¥ÙéÂýSÍ·¤æÅU ·¤æ ÿæð˜æȤÜ
‘A’ ãñÐ §ââð ÕÙæØð »Øð °·¤ ÜæðÜ·¤ ·¤æ ¥æßÌü·¤æÜ
T ãñÐ §â ÜæðÜ·¤ ·ð¤ »æðÜ·¤ âð °·¤ ¥çÌçÚU€Ì M
ÎýÃØ×æÙ ÁæðǸ ÎðÙð âð ÜæðÜ·¤ ·¤æ ¥æßÌü·¤æÜ ÂçÚUßçÌüÌ
ãæð·¤ÚU TM ãæð ÁæÌæ ãñÐ ØçÎ §â ÌæÚU ·ð¤ ÂÎæÍü ·¤æ Ø´»
»é‡ææ´·¤ ‘Y’ ãæð Ìæð
1
Y
·¤æ ×æÙ ãæð»æ Ñ
(g5»éL¤ˆßèØ ˆßÚU‡æ)
(1)
2
MT A
1
T Mg
  
  
   
2
(2)
2
M MgT
1
T A
  
  
   
2
(3)
2
MT A
1
T Mg
  
  
   
2
(4)
2
M
T A
1
T Mg
  
  
   
2
9. ç·¤âè »æðÜèØ ·¤æðàæ (àæñÜ) ·¤è ç˜æ’Øæ R ãñ ¥æñÚU §â·¤æ
Ìæ T ãñÐ §â·ð¤ ÖèÌÚU ·ë¤çc‡æ·¤æ çßç·¤ÚU‡ææð´ ·¤æð ȤæðÅUæòÙæð´
·¤è °·¤ °ðâè ¥æÎàæü »ñâ ×æÙæ Áæ â·¤Ìæ ãñ çÁâ·¤è
ÂýçÌ §·¤æ§ü ¥æØÌÙ ¥æ‹ÌçÚU·¤ ª¤Áæü, 4U
u T
V
5 ;
ÌÍæ ÎæÕ,
1 U
p
3 V
 
 
 
5 ãñÐ ØçÎ §â ·¤æðàæ ×ð´ L¤Î÷Ïæðc×
ÂýâæÚU ãæð Ìæð, T ÌÍæ R ·ð¤ Õè¿ â´Õ´Ï ãæð»æ Ñ
(1) T ; e2R
(2) T ; e23R
(3)
1
T
R
;
(4) 3
1
T
R
;

7. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 7
10. A solid body of constant heat capacity
1 J/8C is being heated by keeping it in
contact with reservoirs in two ways :
(i) Sequentially keeping in contact with
2 reservoirs such that each reservoir
supplies same amount of heat.
(ii) Sequentially keeping in contact with
8 reservoirs such that each reservoir
supplies same amount of heat.
In both the cases body is brought from
initial temperature 1008C to final
temperature 2008C. Entropy change of the
body in the two cases respectively is :
(1) ln2, 4ln2
(2) ln2, ln2
(3) ln2, 2ln2
(4) 2ln2, 8ln2
11. Consider an ideal gas confined in an
isolated closed chamber. As the gas
undergoes an adiabatic expansion, the
average time of collision between
molecules increases as V
q
, where V is the
volume of the gas. The value of q is :
p
v
C
C
 
 
 
g 5
(1)
3 5
6
g 1
(2)
3 5
6
g 2
(3) 1
2
g 1
(4)
1
2
g 2
10. °·¤ ÆUæðâ ç´ÇU (ßSÌé) ·¤è çSÍÚU ª¤c×æ ÏæçÚUÌæ
1 J/8C ãñÐ §â·¤æ𠪤c×·¤æð´ (ª¤c×æ Ö´ÇUæÚUæð´) ·ð¤ âÂ·ü¤
×ð´ ÚU¹·¤ÚU çِ٠Îæð Âý·¤æÚU âð »×ü ç·¤Øæ ÁæÌæ ãñ,
(i) ¥Ùé·ý¤ç×·¤ M¤Â âð 2 ª¤c×·¤æð´ ·ð¤ âÂ·ü¤ ×ð´
§â Âý·¤æÚU ÚU¹·¤ÚU ç·¤ ÂýˆØð·¤ ª¤c×·¤ â×æÙ
×æ˜ææ ×ð´ ª¤c×æ ÎðÌæ ãñ,
(ii) ¥Ùé·ý¤ç×·¤ M¤Â âð 8 ª¤c×·¤æð´ ·ð¤ âÂ·ü¤ ×ð´
§â Âý·¤æÚU ÚU¹·¤ÚU ç·¤ ÂýˆØð·¤ ª¤c×·¤ â×æÙ
×æ˜ææ ×ð´ ª¤c×æ ÎðÌæ ãñ,
ÎæðÙæð´ çSÍçÌØæð´ ×ð´ ç´ÇU ·¤æ ÂýæÚ´UçÖ·¤ Ìæ 1008C ÌÍæ
¥ç‹Ì× Ìæ 2008C ãñÐ Ìæð, §Ù Îæð çSÍçÌØæð´ ×ð´ ç´ÇU
·¤è °‹ÅþUæòÂè ×ð´ ÂçÚUßÌüÙ ãæð»æ, ·ý¤×àæÑ
(1) ln2, 4ln2
(2) ln2, ln2
(3) ln2, 2ln2
(4) 2ln2, 8ln2
11. °·¤ ¥æÎàæü »ñâ ç·¤âè Õ‹Î (â´ßëÌ), çßØé€Ì
(çßÜç»Ì) ·¤ÿæ ×ð´ âèç×Ì (ÚU¹è) ãñÐ §â »ñâ ×´ð´
L¤Î÷Ïæðc× ÂýâæÚU ãæðÙð ÂÚU, §â·ð¤ ¥‡æé¥æð´ ·ð¤ Õè¿ ÅU€·¤ÚU
·¤æ ¥æñâÌ ·¤æÜ (â×Ø) V
q
·ð¤ ¥ÙéâæÚU Õɸ ÁæÌæ ãñ,
Áãæ¡ V »ñâ ·¤æ ¥æØÌÙ ãñÐ Ìæð q ·¤æ ×æÙ ãæð»æ :
p
v
C
C
 
 
 
g 5
(1)
3 5
6
g 1
(2)
3 5
6
g 2
(3) 1
2
g 1
(4)
1
2
g 2

8. A/Page 8 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
12. For a simple pendulum, a graph is plotted
between its kinetic energy (KE) and
potential energy (PE) against its
displacement d. Which one of the
following represents these correctly ?
(graphs are schematic and not drawn to scale)
(1)
(2)
(3)
(4)
13. A train is moving on a straight track with
speed 20 ms21. It is blowing its whistle at
the frequency of 1000 Hz. The percentage
change in the frequency heard by a person
standing near the track as the train passes
him is (speed of sound5320 ms21) close
to :
(1) 6%
(2) 12%
(3) 18%
(4) 24%
12. ç·¤âè âÚUÜ ÜæðÜ·¤ ·ð¤ çÜØð, ©â·ð¤ çßSÍæÂÙ d ÌÍæ
©â·¤è »çÌÁ ª¤Áæü ·ð¤ Õè¿ ¥æñÚU çßSÍæÂÙ d ÌÍæ
©â·¤è çSÍçÌÁ ª¤Áæü ·ð¤ Õè¿ »ýæȤ ¹è´¿ð »Øð ãñ´Ð
çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙ âæ »ýæȤ (¥æÜð¹) âãè ãñ?
(Øãæ¡ »ýæȤ ·ð¤ßÜ ÃØßSÍæ ¥æÚðU¹ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤
¥ÙéâæÚU Ùãè´ ãñ´)
(1)
(2)
(3)
(4)
13. °·¤ ÅþðUÙ (ÚðUÜ»æǸè) âèÏè ÂÅUçÚUØæð´ ÂÚU 20 ms21 ·¤è
¿æÜ âð »çÌ ·¤ÚU ÚUãè ãñÐ §â·¤è âèÅUè ·¤è ŠßçÙ ·¤è
¥æßëçžæ 1000 Hz ãñÐ ØçÎ ŠßçÙ ·¤è ßæØé ×ð´ ¿æÜ
320 ms21 ãæð Ìæð, ÂÅUçÚUØæð´ ·ð¤ çÙ·¤ÅU ¹Ç¸ð ÃØç€Ì ·ð¤
Âæâ âð ÅþðUÙ ·ð¤ »éÁÚUÙð ÂÚU, ©â ÃØç€Ì mæÚUæ âéÙè »§ü
âèÅUè ·¤è ŠßçÙ ·¤è ¥æßëçžæ ×ð´ ÂýçÌàæÌ ÂçÚUßÌüÙ ãæð»æ
ֻܻ Ñ
(1) 6%
(2) 12%
(3) 18%
(4) 24%

9. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 9
14. A long cylindrical shell carries positive
surface charge s in the upper half and
negative surface charge 2s in the lower
half. The electric field lines around the
cylinder will look like figure given in :
(figures are schematic and not drawn to scale)
(1)
(2)
(3)
(4)
15. A uniformly charged solid sphere of radius
R has potential V0 (measured with respect
to :) on its surface. For this sphere the
equipotential surfaces with potentials
0 0 03V 5V 3V
, ,
2 4 4
and 0V
4
have radius R1,
R2, R3 and R4 respectively. Then
(1) R150 and R2 > (R42R3)
(2) R1 ¹ 0 and (R22R1) > (R42R3)
(3) R150 and R2 < (R42R3)
(4) 2R < R4
14. ç·¤âè ܐÕð ÕðÜÙæ·¤æÚU ·¤æðàæ ·ð¤ ª¤ÂÚUè Öæ» ×ð´ ÏÙæˆ×·¤
ÂëcÆU ¥æßðàæ s ÌÍæ çÙ¿Üð Öæ» ×ð´ «¤‡ææˆ×·¤ ÂëcÆU
¥æßðàæ 2s ãñ´Ð §â ÕðÜÙ (çâçÜ‹ÇUÚU) ·ð¤ ¿æÚUæð´
¥æðÚU çßléÌ ÿæð˜æ-ÚðU¹æØð´, Øãæ¡ ÎàææüØð »Øð ¥æÚð¹æð´ ×ð´ âð
緤⠥æÚðU¹ ·ð¤ â×æÙ ãæð´»è?
(Øã ¥æÚðU¹ ·ð¤ßÜ ÃØßSÍæ ¥æÚðU¹ ãñ ¥æñÚU S·ð¤Ü ·ð¤
¥ÙéâæÚU Ùãè´ ãñ)
(1)
(2)
(3)
(4)
15. R ç˜æ’Øæ ·ð¤ ç·¤âè °·¤â×æÙ ¥æßðçàæÌ ÆUæðâ »æðÜð ·ð¤
ÂëcÆU ·¤æ çßÖß V0 ãñ (: ·ð¤ âæÂðÿæ ×æÂæ »Øæ)Ð §â
»æðÜð ·ð¤ çÜØð, 0 0 03V 5V 3V
, ,
2 4 4
ÌÍæ 0V
4
çßÖßæð´
ßæÜð â×çßÖßè ÂëcÆUæð´ ·¤è ç˜æ’ØæØð´, ·ý¤×àæÑ
R1, R2, R3 ÌÍæ R4 ãñ´Ð Ìæð,
(1) R150 ÌÍæ R2 > (R42R3)
(2) R1 ¹ 0 ÌÍæ (R22R1) > (R42R3)
(3) R150 ÌÍæ R2 < (R42R3)
(4) 2R < R4

10. A/Page 10 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
16. In the given circuit, charge Q2 on the 2mF
capacitor changes as C is varied from 1mF
to 3mF. Q2 as a function of ‘C’ is given
properly by : (figures are drawn schematically
and are not to scale)
(1)
(2)
(3)
(4)
17. When 5V potential difference is applied
across a wire of length 0.1 m, the drift
speed of electrons is 2.531024 ms21. If
the electron density in the wire is
831028 m23, the resistivity of the material
is close to :
(1) 1.631028 Vm
(2) 1.631027 Vm
(3) 1.631026 Vm
(4) 1.631025 Vm
16. çÎØð »Øð ÂçÚUÂÍ ×ð´, C ·ð¤ ×æÙ ·ð¤ 1mF âð 3mF
ÂçÚUßçÌüÌ ãæðÙð âð, 2mF â´ÏæçÚU˜æ ÂÚU ¥æßðàæ Q2 ×ð´
ÂçÚUßÌüÙ ãæðÌæ ãñÐ ‘C’ ·ð¤ ȤÜÙ ·ð¤ M¤Â ×ð´ Q2 ·¤æð
·¤æñÙ âæ ¥æÜð¹ âãè ÎàææüÌæ ãñ? (¥æÜð¹ ·ð¤ßÜ
ÃØßSÍæ ¥æÚðU¹ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤ ¥ÙéâæÚU Ùãè´ ãñ´Ð)
(1)
(2)
(3)
(4)
17. 0.1 m Ü´Õð ç·¤âè ÌæÚU ·ð¤ çâÚUæð´ ·ð¤ Õè¿ 5V çßÖßæ´ÌÚUU
¥æÚUæðçÂÌ ·¤ÚUÙð âð §Üð€ÅþUæòÙæð´ ·¤è ¥Âßæã ¿æÜ
2.531024 ms21 ãæðÌè ãñÐ ØçÎ §â ÌæÚU ×ð´ §Üð€ÅþUæòÙ
ƒæÙˆß 831028 m23 ãæð Ìæð, §â ·ð¤ ÂÎæÍü ·¤è
ÂýçÌÚUæðÏ·¤Ìæ ãæð»è, ֻܻ Ñ
(1) 1.631028 Vm
(2) 1.631027 Vm
(3) 1.631026 Vm
(4) 1.631025 Vm

11. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 11
18.
In the circuit shown, the current in the 1V
resistor is :
(1) 1.3 A, from P to Q
(2) 0A
(3) 0.13 A, from Q to P
(4) 0.13 A, from P to Q
19. Two coaxial solenoids of different radii
carry current I in the same direction. Let
1F
→
be the magnetic force on the inner
solenoid due to the outer one and 2F
→
be
the magnetic force on the outer solenoid
due to the inner one. Then :
(1) 1 2F F 0
→ →
5 5
(2) 1F
→
is radially inwards and 2F
→
is
radially outwards
(3) 1F
→
is radially inwards and 2F
→
50
(4) 1F
→
is radially outwards and 2F
→
50
18.
ÎàææüØð »Øð ÂçÚUÂÍ ×ð´ 1V ÂýçÌÚUæðÏ·¤ âð ÂýßæçãÌ ÏæÚUæ
ãæð»è Ñ
(1) 1.3 A, P âð Q ·¤è ¥æðÚU
(2) 0 (àæê‹Ø) A
(3) 0.13 A, Q âð P ·¤æð
(4) 0.13 A, P âð Q ·¤æð
19. Îæð â×æÿæè ÂçÚUÙæçÜ·¤æ¥æð´ ×ð´, ÂýˆØð·¤ âð I ÏæÚUæ °·¤ ãè
çÎàææ ×ð´ ÂýßæçãÌ ãæð ÚUãè ãñÐ ØçÎ, ÕæãÚUè ÂçÚUÙæçÜ·¤æ
·ð¤ ·¤æÚU‡æ, ÖèÌÚUè ÂçÚUÙæçÜ·¤æ ÂÚU ¿éÕ·¤èØ ÕÜ
1F
→
ÌÍæ ÖèÌÚUè ÂçÚUÙæçÜ·¤æ ·ð¤ ·¤æÚU‡æ, ÕæãÚUè ÂçÚUÙæçÜ·¤æ
ÂÚU ¿éÕ·¤èØ ÕÜ 2F
→
ãæð Ìæð Ñ
(1) 1 2F F 0
→ →
5 5
(2) 1F
→
ÖèÌÚU ·¤è ¥æðÚU ß ¥ÚUèØ (ç˜æ’Ø) ãñ ¥æñÚU
2F
→
ÕæãÚU ·¤è ¥æðÚU ß ¥ÚUèØ ãñÐ
(3) 1F
→
ÖèÌÚU ·¤è ¥æðÚU ß ¥ÚUèØ ãñ ÌÍæ 2F
→
50
ãñÐ
(4) 1F
→
ÕæãÚU ·¤è ¥æðÚU ß ¥ÚUèØ ãñ ÌÍæ 2F
→
50
ãñÐ

12. A/Page 12 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
20.
Two long current carrying thin wires, both
with current I, are held by insulating
threads of length L and are in equilibrium
as shown in the figure, with threads
making an angle ‘u’ with the vertical. If
wires have mass l per unit length then the
value of I is :
(g5gravitational acceleration)
(1)
0
gL
sin
cos
pl
u
m u
(2)
0
gL
2sin
cos
pl
u
m u
(3)
0
gL
2 tan
p
u
m
(4)
0
gL
tan
pl
u
m
20.
Îæð ÂÌÜð ܐÕð ÌæÚUæð´ ×ð´ ÂýˆØð·¤ âð I ÏæÚUæ ÂýßæçãÌ ãæð ÚUãè
ãñÐ §‹ãð´ L ܐÕæ§ü ·ð¤ çßléÌÚUæðÏè Ïæ»æð´ âð ÜÅU·¤æØæ
»Øæ ãñÐ §Ù Ïæ»æð´ ×ð´ ÂýˆØð·¤ ·ð¤ mæÚUæ ª¤ŠßæüÏÚU çÎàææ âð
‘u’ ·¤æð‡æ ÕÙæÙð ·¤è çSÍçÌ ×ð´, Øð ÎæðÙæð´ ÌæÚU âæØæßSÍæ
×ð´ ÚUãÌð ãñ´Ð ØçÎ §Ù ÌæÚUæð´ ·¤è ÂýçÌ §·¤æ§ü ܐÕæ§ü
ÎýÃØ×æÙ l ãñ ÌÍæ g »éL¤ˆßèØ ˆßÚU‡æ ãñ Ìæð, I ·¤æ ×æÙ
ãæð»æ Ñ
(1)
0
gL
sin
cos
pl
u
m u
(2)
0
gL
2sin
cos
pl
u
m u
(3)
0
gL
2 tan
p
u
m
(4)
0
gL
tan
pl
u
m

13. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 13
21. A rectangular loop of sides 10 cm and
5 cm carrying a current I of 12 A is placed
in different orientations as shown in the
figures below :
(a)
(b)
(c)
(d)
If there is a uniform magnetic field of
0.3 T in the positive z direction, in which
orientations the loop would be in (i) stable
equilibrium and (ii) unstable equilibrium ?
(1) (a) and (b), respectively
(2) (a) and (c), respectively
(3) (b) and (d), respectively
(4) (b) and (c), respectively
21. 10 cm ÌÍæ 5 cm ÖéÁæ¥æ𴠷𤠰·¤ ¥æØÌæ·¤æÚU ÜêÂ
(Âæàæ) âð °·¤ çßléÌ ÏæÚUæ, I 5 12 A, ÂýßæçãÌ ãæðU
ÚUãè ãñÐ §â Âæàæ ·¤æð ¥æÚðU¹ ×ð´ ÎàææüØð »Øð ¥ÙéâæÚU
çßçÖóæ ¥çÖçß‹Øæâæð´ (çSÍçÌØæð´) ×ð´ ÚU¹æ »Øæ ãñÐ
(a)
(b)
(c)
(d)
ØçÎ ßãæ¡ 0.3 T ÌèßýÌæ ·¤æ ·¤æð§ü °·¤â×æÙ ¿éÕ·¤èØ
ÿæð˜æ, ÏÙæˆ×·¤ z çÎàææ ×ð´ çßl×æÙ ãñ Ìæð, ÎàææüØð »Øð
緤⠥çÖçß‹Øæâ ×ð´, Øã Âæàæ (ÜêÂ) (i) SÍæØè
â´ÌéÜÙ ÌÍæ (ii) ¥SÍæØè â´ÌéÜÙ ×ð´, ãæð»æ?
(1) ·ý¤×àæÑ (a) ÌÍæ (b) ×ð´
(2) ·ý¤×àæÑ (a) ÌÍæ (c) ×ð´
(3) ·ý¤×àæÑ (b) ÌÍæ (d) ×ð´
(4) ·ý¤×àæÑ (b) ÌÍæ (c) ×ð´

14. A/Page 14 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
22. An inductor (L50.03H) and a resistor
(R50.15 kV) are connected in series to a
battery of 15V EMF in a circuit shown
below. The key K1 has been kept closed
for a long time. Then at t50, K1 is opened
and key K2 is closed simultaneously.
At t51ms, the current in the circuit will
be : (e5@150)
(1) 100 mA
(2) 67 mA
(3) 6.7 mA
(4) 0.67 mA
23. A red LED emits light at 0.1 watt uniformly
around it. The amplitude of the electric
field of the light at a distance of 1 m from
the diode is :
(1) 1.73 V/m
(2) 2.45 V/m
(3) 5.48 V/m
(4) 7.75 V/m
22. ÎàææüØð »Øð ÂçÚUÂÍ ×ð´, °·¤ ÂýðÚU·¤ (L50.03H) ÌÍæ
°·¤ ÂýçÌÚUæðÏ·¤ (R50.15 kV) ç·¤âè 15V çßléÌ
ßæã·¤ ÕÜ (§ü.°×.°È¤) ·¤è ÕñÅUÚUè âð ÁéǸð ãñ´Ð ·é´¤Áè
K1 ·¤æð ÕãéÌ â×Ø Ì·¤ Õ‹Î ÚU¹æ »Øæ ãñÐ §â·ð¤
Âà¿æÌ÷ â×Ø t50 ÂÚU, K1 ·¤æð ¹æðÜ ·¤ÚU âæÍ ãè
âæÍ, K2 ·¤æð Õ‹Î ç·¤Øæ ÁæÌæ ãñÐ â×Ø t51ms
ÂÚU, ÂçÚUÂÍ ×ð´ çßléÌ ÏæÚUæ ãæð»è Ñ (e5@150)
(1) 100 mA
(2) 67 mA
(3) 6.7 mA
(4) 0.67 mA
23. °·¤ ÜæÜ Ú´U» ·¤æ °Ü.§ü.ÇUè. (Âý·¤æàæ ©ˆâÁü·¤ ÇUæØæðÇU)
0.1 ßæÅU ÂÚU, °·¤â×æÙ Âý·¤æàæ ©ˆâçÁüÌ ·¤ÚUÌæ ãñÐ
ÇUæØæðÇU âð 1 m ÎêÚUè ÂÚU, §â Âý·¤æàæ ·ð¤ çßléÌ ÿæð˜æ ·¤æ
¥æØæ× ãæð»æ Ñ
(1) 1.73 V/m
(2) 2.45 V/m
(3) 5.48 V/m
(4) 7.75 V/m

15. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 15
24. Monochromatic light is incident on a glass
prism of angle A. If the refractive index of
the material of the prism is m, a ray,
incident at an angle u, on the face AB
would get transmitted through the face AC
of the prism provided :
(1) 1 1 1
> sin sin A sin
   
   
    
2 2
u m 2
m
(2) 1 1 1
< sin sin A sin
   
   
    
2 2
u m 2
m
(3) 1 1 1
> cos sin A sin
   
   
    
2 2
u m 1
m
(4) 1 1 1
< cos sin A sin
   
   
    
2 2
u m 1
m
25. On a hot summer night, the refractive
index of air is smallest near the ground and
increases with height from the ground.
When a light beam is directed horizontally,
the Huygens’ principle leads us to conclude
that as it travels, the light beam :
(1) becomes narrower
(2) goes horizontally without any
deflection
(3) bends downwards
(4) bends upwards
24. ·¤æ¡¿ ·ð¤ ç·¤âè çÂý’× ·¤æ ·¤æð‡æ ‘A’ ãñÐ §â ÂÚU
°·¤ß‡æèü Âý·¤æàæ ¥æÂçÌÌ ãæðÌæ ãñÐ ØçÎ, çÂý’× ·ð¤
ÂÎæÍü ·¤æ ¥ÂßÌüÙæ´·¤ m ãñ Ìæð, çÂý’× ·ð¤ AB Ȥܷ¤
ÂÚU, u ·¤æð‡æ ¥æÂçÌÌ Âý·¤æàæ ·¤è ç·¤ÚU‡æ, çÂý’× ·ð¤
Ȥܷ¤ AC âð ÂæÚU»Ì ãæð»è ØçÎ Ñ
(1) 1 1 1
> sin sin A sin
   
   
    
2 2
u m 2
m
(2) 1 1 1
< sin sin A sin
   
   
    
2 2
u m 2
m
(3) 1 1 1
> cos sin A sin
   
   
    
2 2
u m 1
m
(4) 1 1 1
< cos sin A sin
   
   
    
2 2
u m 1
m
25. »ýèc× «¤Ìé ·¤è »×ü ÚUæç˜æ ×ð´, Öê-ÌÜ ·ð¤ çÙ·¤ÅU, ßæØé ·¤æ
¥ÂßÌüÙæ´·¤ ‹ØêÙÌ× ãæðÌæ ãñ ¥æñÚU Öê-ÌÜ â𠪡¤¿æ§ü ·ð¤
âæÍ ÕɸÌæ ÁæÌæ ãñÐ ØçÎ, ·¤æð§ü Âý·¤æàæ-ç·¤ÚU‡æ-´éÁ
ÿæñçÌÁ çÎàææ ×ð´ Áæ ÚUãæ ãæð Ìæð, ã槻ð‹â ·ð¤ çâhæ‹Ì âð
Øã ÂçÚU‡ææ× ÂýæŒÌ ãæðÌæ ãñ ç·¤, ¿ÜÌð ãé°
Âý·¤æàæ-ç·¤ÚU‡æ ´éÁ Ñ
(1) â´·é¤ç¿Ì (â´·¤è‡æü) ãæð ÁæØð»æÐ
(2) çÕÙæ çßÿæðçÂÌ ãé°, ÿæñçÌÁ çÎàææ ×ð´ ¿ÜÌæ
ÚUãð»æÐ
(3) Ùè¿ð ·¤è ¥æðÚU Ûæé·¤ ÁæØð»æÐ
(4) ª¤ÂÚU ·¤è ¥æðÚU Ûæé·¤ ÁæØð»æÐ

16. A/Page 16 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
26. Assuming human pupil to have a radius
of 0.25 cm and a comfortable viewing
distance of 25 cm, the minimum separation
between two objects that human eye can
resolve at 500 nm wavelength is :
(1) 1 mm
(2) 30 mm
(3) 100 mm
(4) 300 mm
27. As an electron makes a transition from an
excited state to the ground state of a
hydrogen - like atom/ion :
(1) its kinetic energy increases but
potential energy and total energy
decrease
(2) kinetic energy, potential energy and
total energy decrease
(3) kinetic energy decreases, potential
energy increases but total energy
remains same
(4) kinetic energy and total energy
decrease but potential energy
increases
26. ØçÎ ×æÙß Ùð˜æ ·¤è ÂéÌÜè ·¤è ç˜æ’Øæ 0.25 cm, ¥æñÚU
SÂcÅU âéçßÏæ ÁÙ·¤ Îð¹Ùð ·¤è ÎêÚUè 25 cm ãæð Ìæð,
500 nm ÌÚ´U»ÎñƒØü ·ð¤ Âý·¤æàæ ×ð´, Îæð ßSÌé¥æð´ ·ð¤ Õè¿
ç·¤ÌÙè ‹ØêÙÌ× ÎêÚUè Ì·¤ ×æÙß Ùð˜æ ©Ù ÎæðÙæð´ ·ð¤ Õè¿
çßÖðÎÙ ·¤ÚU â·ð¤»æ?
(1) 1 mm
(2) 30 mm
(3) 100 mm
(4) 300 mm
27. ÁÕ ·¤æð§ü §Üð€ÅþUæòÙ, ãæ§ÇþUæðÁÙ Áñâð ÂÚU×æ‡æé /¥æØÙ
·¤è ©žæðçÁÌ ¥ßSÍæ âð ‹ØêÙÌ× ª¤Áæü ¥ßSÍæ ×ð´
â´·ý¤×‡æ ·¤ÚUÌæ ãñ Ìæð ©â·¤è Ñ
(1) »çÌÁ ª¤Áæü ×ð´ ßëçh ÌÍæ çSÍçÌÁ ª¤Áæü ÌÍæ
·é¤Ü ª¤Áæü ×ð´ ·¤×è ãæðÌè ãñÐ
(2) »çÌÁ ª¤Áæü, çSÍçÌÁ ª¤Áæü ÌÍæ ·é¤Ü ª¤Áæü ×ð´
·¤×è ãæð ÁæÌè ãñÐ
(3) »çÌÁ ª¤Áæü ·¤× ãæðÌè ãñ, çSÍçÌÁ ª¤Áæü ÕɸÌè
ãñ ¥æñÚU ·é¤Ü ª¤Áæü ßãè ÚUãÌè ãñÐ
(4) »çÌÁ ª¤Áæü ß ·é¤Ü ª¤Áæü ·¤× ãæð ÁæÌè ãñ´
ç·¤‹Ìé, çSÍçÌÁ ª¤Áæü Õɸ ÁæÌè ãñÐ

17. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 17
28. âê¿è - I (×êÜ ÂýØæð») ·¤æ âê¿è - II (©â·ð¤ ÂçÚU‡ææ×)
·ð¤ âæÍ âé×ðÜÙ (×ñ¿) ·¤èçÁØð ¥æñÚU çِÙæ´ç·¤Ì
çß·¤ËÂæð´ ×ð´ âð âãè çß·¤Ë ·¤æ ¿ØÙ ·¤èçÁØð Ñ
ÇÏ¤Í - I ÇÏ¤Í - II
(A) ­âÕ™‰œ‰ ȪÜáÇ §â½ËÕ (i)
§âœ‰ËÅË œ‰Í œ‰ÌøËœ‰Ë
§âœÐ‰Ì±
(B) §âœ‰ËÅË ÌÄlα §â½ËÕ (ii)
ŠøËÎ œÕ‰ ÌÄÌÄþ±
‰¦Ëá S±¿U
(C) ¬ÕUÄÍǾ ¦¼á¿U §â½ËÕ (iii)
ŒÁÕþªãUË×¾ œ‰Í ±¿™U
§âœÐ‰Ì±
(iv) §¿U¼ËøËÎ œ‰Í Ç™¿U¤¾Ë
(1) (A) - (i) (B) - (iv) (C) - (iii)
(2) (A) - (ii) (B) - (iv) (C) - (iii)
(3) (A) - (ii) (B) - (i) (C) - (iii)
(4) (A) -(iv) (B) - (iii) (C)- (ii)
29. 5 kHz ¥æßëçžæ ·ð¤ ç·¤âè â´·ð¤Ì (çâ‚ÙÜ) ·¤æ
2 MHz ¥æßëçžæ ·¤è ßæã·¤ ÌÚ´U» ÂÚU ¥æØæ× ×æòÇéUÜÙ
ç·¤Øæ »Øæ ãñÐ Ìæð, ÂçÚU‡ææ×è çâ‚ÙÜ (â´·ð¤Ì) ·¤è
¥æßëçžæ ãæð»è Ñ
(1) 2 MHz ·ð¤ßÜ
(2) 2005 kHz, ÌÍæ 1995 kHz
(3) 2005 kHz, 2000 kHz ÌÍæ 1995 kHz
(4) 2000 kHz ÌÍæ 1995 kHz
28. Match List - I (Fundamental Experiment)
with List - II (its conclusion) and select
the correct option from the choices given
below the list :
List - I List - II
(A)
Franck-Hertz
Experiment.
(i)
Particle nature
of light
(B)
Photo-electric
experiment.
(ii)
Discrete energy
levels of atom
(C)
Davison - Germer
Experiment.
(iii)
Wave nature of
electron
(iv)
Structure of
atom
(1) (A) - (i) (B) - (iv) (C) - (iii)
(2) (A) - (ii) (B) - (iv) (C) - (iii)
(3) (A) - (ii) (B) - (i) (C) - (iii)
(4) (A) -(iv) (B) - (iii) (C) - (ii)
29. A signal of 5 kHz frequency is amplitude
modulated on a carrier wave of frequency
2 MHz. The frequencies of the resultant
signal is/are :
(1) 2 MHz only
(2) 2005 kHz, and 1995 kHz
(3) 2005 kHz, 2000 kHz and 1995 kHz
(4) 2000 kHz and 1995 kHz

18. A/Page 18 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
30. LCR (°Ü.âè.¥æÚU) ÂçÚUÂÍ ç·¤âè ¥ß×´çÎÌ ÜæðÜ·¤
·ð¤ ÌéËØ ãæðÌæ ãñÐ ç·¤âè LCR ÂçÚUÂÍ ×ð´ â´ÏæçÚU˜æ ·¤æð
Q0 Ì·¤ ¥æßðçàæÌ ç·¤Øæ »Øæ ãñ, ¥æñÚU çȤÚU §âð ¥æÚðU¹
×ð´ ÎàææüØð »Øð ¥ÙéâæÚU L ß R âð ÁæðÇ¸æ »Øæ ãñÐ
ØçÎ °·¤ çßlæÍèü L ·ð¤, Îæð çßçÖóæ ×æÙæð´, L1 ÌÍæ L2
(L1>L2) ·ð¤ çÜØð, â×Ø t ÌÍæ â´ÏæçÚU˜æ ÂÚU
¥çÏ·¤Ì× ¥æßðàæ ·ð¤ ß»ü 2
MaxQ ·ð¤ Õè¿ Îæð »ýæȤ
ÕÙæÌæ ãñ Ìæð çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙ âæ »ýæȤ âãè ãñ?
(ŒÜæòÅU ·ð¤ßÜ ÃØßSÍæ ŒÜæòÅU ãñ´ ÌÍæ S·ð¤Ü ·ð¤ ¥ÙéâæÚU
Ùãè´ ãñ´)
(1)
(2)
(3)
(4)
30. An LCR circuit is equivalent to a damped
pendulum. In an LCR circuit the capacitor
is charged to Q0 and then connected to
the L and R as shown below :
If a student plots graphs of the square of
maximum charge ( 2
MaxQ ) on the capacitor
with time(t) for two different values L1 and
L2 (L1>L2) of L then which of the following
represents this graph correctly ? (plots are
schematic and not drawn to scale)
(1)
(2)
(3)
(4)

19. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 19
31. The molecular formula of a commercial
resin used for exchanging ions in water
softening is C8H7SO3Na (Mol. wt. 206).
What would be the maximum uptake of
Ca21 ions by the resin when expressed in
mole per gram resin ?
(1)
1
103
(2)
1
206
(3)
2
309
(4)
1
412
32. Sodium metal crystallizes in a body centred
cubic lattice with a unit cell edge of 4.29Å.
The radius of sodium atom is
approximately :
(1) 1.86Å
(2) 3.22Å
(3) 5.72Å
(4) 0.93Å
33. Which of the following is the energy of a
possible excited state of hydrogen ?
(1) 113.6 eV
(2) 26.8 eV
(3) 23.4 eV
(4) 16.8 eV
31. °·¤ ßæç‡æ’Ø ÚðUç$ÁÙ ·¤æ ¥æç‡ß·¤ âê˜æ C8H7SO3Na
ãñ (¥æç‡ß·¤ ÖæÚU = 206) §â ÚðUç$ÁÙ ·¤è Ca21
¥æØÙ ·¤è ¥çÏ·¤Ì× ¥´Ì»ýüã‡æ ÿæ×Ìæ (×æðÜ ÂýçÌ
»ýæ× ÚðUç$ÁÙ) €Øæ ãñ?
(1)
1
103
(2)
1
206
(3)
2
309
(4)
1
412
32. âæðçÇUØ× ÏæÌé °·¤ ¥´ÌÑ·ð¤ç‹ÎýÌ ƒæÙèØ ÁæÜ·¤ ×ð´
ç·ý¤SÅUçÜÌ ãæðÌæ ãñ çÁâ·ð¤ ·¤æðÚU ·¤è Ü´Õæ§ü 4.29Å ãñÐ
âæðçÇUØ× ÂÚU×æ‡æé ·¤è ç˜æ’Øæ ֻܻ ãñ Ñ
(1) 1.86Å
(2) 3.22Å
(3) 5.72Å
(4) 0.93Å
33. çِÙçÜç¹Ì ×ð´ âð ãæ§üÇþUæðÁÙ ·¤è â´Öß ©žæðçÁÌ ¥ßSÍæ
·¤è ª¤Áæü ·¤æñÙ âè ãñ?
(1) 113.6 eV
(2) 26.8 eV
(3) 23.4 eV
(4) 16.8 eV
PART B — CHEMISTRY Öæ» B — ÚUâæØÙ çß™ææÙ

20. A/Page 20 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
34. The intermolecular interaction that is
dependent on the inverse cube of distance
between the molecules is :
(1) ion - ion interaction
(2) ion - dipole interaction
(3) London force
(4) hydrogen bond
35. The following reaction is performed at
298 K.
2 22NO(g) O (g) 2NO (g)1 ì
The standard free energy of formation of
NO(g) is 86.6 kJ/mol at 298 K. What is
the standard free energy of formation of
NO2(g) at 298 K? (Kp51.631012)
(1) R(298) ln(1.631012)286600
(2) 866001R(298) ln(1.631012)
(3)
12
n (1.6 10 )
86600
R (298)
l 3
2
(4) 0.5[2386,6002R(298) ln(1.631012)]
36. The vapour pressure of acetone at 208C is
185 torr. When 1.2 g of a non-volatile
substance was dissolved in 100 g of acetone
at 208C, its vapour pressure was 183 torr.
The molar mass (g mol21) of the substance
is :
(1) 32
(2) 64
(3) 128
(4) 488
34. ßã ¥´ÌÚUæ-¥‡æé·¤ ¥‹Øæð‹Ø ç·ý¤Øæ Áæ𠥇æé¥æð´ ·ð¤ Õè¿
·¤è ÎêÚUè ·ð¤ ÂýçÌÜæð× ƒæÙ ÂÚU çÙÖüÚU ãñ, ãñ Ñ
(1) ¥æØÙ - ¥æØÙ ¥‹Øæð‹Ø
(2) ¥æØÙ - çmÏýéß ¥‹Øæð‹Ø
(3) Ü´ÇUÙ ÕÜ
(4) ãæ§üÇþUæðÁÙ Õ´Ï·¤
35. çِÙçÜç¹Ì ¥çÖç·ý¤Øæ ·¤æð 298 K ÂÚU ç·¤Øæ »ØæÐ
2 22NO(g) O (g) 2NO (g)1 ì
298 K ÂÚU NO(g) ·ð¤ â´ÖßÙ ·¤è ×æÙ·¤ ×é€Ì ª¤Áæü
86.6 kJ/mol ãñÐ 298 K ÂÚU NO2(g) ·¤è ×æÙ·¤
×é€Ì ª¤Áæü €Øæ ãñ? (Kp51.631012)
(1) R(298) ln(1.631012)286600
(2) 866001R(298) ln(1.631012)
(3)
12
n (1.6 10 )
86600
R (298)
l 3
2
(4) 0.5[2386,6002R(298) ln(1.631012)]
36. 208C ÂÚU °ðçâÅUæðÙ ·¤è ßæc ÎæÕ 185 torr ãñÐ ÁÕ
208C ÂÚU, 1.2 g ¥ßæcÂàæèÜ ÂÎæÍü ·¤æð 100 g
°ðçâÅUæðÙ ×ð´ ƒææðÜæ »Øæ, ÌÕ ßæc ÎæÕ 183 torr ãæð
»ØæÐ §â ÂÎæÍü ·¤æ ×æðÜÚU ÎýÃØ×æÙ (g mol21 ×ð´)
ãñ Ñ
(1) 32
(2) 64
(3) 128
(4) 488

21. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 21
37. The standard Gibbs energy change at
300 K for the reaction 2A B C1ì is
2494.2 J. At a given time, the composition
of the reaction mixture is
1
[A]
2
5 , [B]52
and
1
[C]
2
5 . The reaction proceeds in
the : [R58.314 J/K/mol, e52.718]
(1) forward direction because Q > Kc
(2) reverse direction because Q > Kc
(3) forward direction because Q < Kc
(4) reverse direction because Q < Kc
38. Two Faraday of electricity is passed
through a solution of CuSO4. The mass of
copper deposited at the cathode is :
(at. mass of Cu563.5 amu)
(1) 0 g
(2) 63.5 g
(3) 2 g
(4) 127 g
39. Higher order (>3) reactions are rare due
to :
(1) low probability of simultaneous
collision of all the reacting species
(2) increase in entropy and activation
energy as more molecules are
involved
(3) shifting of equilibrium towards
reactants due to elastic collisions
(4) loss of active species on collision
37. 300 K ÂÚU ¥çÖç·ý¤Øæ 2A B C1ì ·¤è ×æÙ·¤
绎$Á ª¤Áæü 2494.2 J ãñÐ çΰ »° â×Ø ×ð´
¥çÖç·ý¤Øæ çןæ‡æ ·¤æ â´ƒæÅUÙ
1
[A]
2
5 ,
[B]52 ¥æñÚU
1
[C]
2
5 ãñÐ ¥çÖç·ý¤Øæ ¥»ýçâÌ ãæðÌè
ãñ Ñ [R58.314 J/K/mol, e52.718]
(1) ¥»ý çÎàææ ×ð´ €Øæð´ç·¤ Q > Kc
(2) çßÂÚUèÌ çÎàææ ×ð´ €Øæð´ç·¤ Q > Kc
(3) ¥»ý çÎàææ ×ð´ €Øæð´ç·¤ Q < Kc
(4) çßÂÚUèÌ çÎàææ ×ð´ €Øæð´ç·¤ Q < Kc
38. CuSO4 ·ð¤ °·¤ çßÜØÙ ×ð´, Îæð Èñ¤ÚUæÇðU çßléÌ ÂýßæçãÌ
·¤è »§üÐ ·ñ¤ÍæðÇU ÂÚU çÙÿæðçÂÌ Ìæ´Õð ·¤æ ÎýÃØ×æÙ ãñ :
(Cu ·¤æ ÂÚU×æç‡ß·¤ ÎýÃØ×æÙ 563.5 amu)
(1) 0 g
(2) 63.5 g
(3) 2 g
(4) 127 g
39. ©‘¿ ·¤æðçÅU ¥çÖç·ý¤Øæ (>3) ÎéÜüÖ ãñ €Øæð´ç·¤ Ñ
(1) ÂýçÌç·ý¤Øæ ×ð´ âÖè ÂýÁæçÌØæ𴠷𤠰·¤ âæÍ ÅU€·¤ÚU
·¤è â´ÖæßÙæ ·¤× ãæðÌè ãñÐ
(2) ¥çÏ·¤ ¥‡æé¥æð´ ·ð¤ àææç×Ü ãæðÙð âð °´ÅþUæÂè ¥æñÚU
â´ç·ý¤Ø‡æ ª¤Áæü ×ð´ ßëçh ãæðÌè ãñÐ
(3) Üæð¿ÎæÚU ÅU·¤ÚUæß ·ð¤ ·¤æÚU‡æ ¥çÖ·¤æÚU·¤æð´ ·¤è
çÎàææ ×ð´ âæØ ·¤æ SÍæÙæ´ÌÚU‡æ ãæðÌæ ãñÐ
(4) ÅU·¤ÚUæß âð âç·ý¤Ø SÂèàæè$Á ·¤æ ÿæØ ãæðÌæ ãñÐ

22. A/Page 22 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
40. 3 g of activated charcoal was added to
50 mL of acetic acid solution (0.06N) in a
flask. After an hour it was filtered and
the strength of the filtrate was found to be
0.042 N. The amount of acetic acid
adsorbed (per gram of charcoal) is :
(1) 18 mg
(2) 36 mg
(3) 42 mg
(4) 54 mg
41. The ionic radii (in Å) of N32, O22 and F2
are respectively :
(1) 1.36, 1.40 and 1.71
(2) 1.36, 1.71 and 1.40
(3) 1.71, 1.40 and 1.36
(4) 1.71, 1.36 and 1.40
42. In the context of the Hall - Heroult process
for the extraction of Al, which of the
following statements is false ?
(1) CO and CO2 are produced in this
process
(2) Al2O3 is mixed with CaF2 which
lowers the melting point of the
mixture and brings conductivity
(3) Al31 is reduced at the cathode to
form Al
(4) Na3AlF6 serves as the electrolyte
40. °·¤ ÜæS·¤ ×ð´ 0.06N °çâçÅU·¤ ¥Ü ·ð¤ 50 mL
çßÜØÙ ×ð´ 3 g âç·ý¤çØÌ÷ ·¤æcÆU ·¤æðØÜæ ç×ÜæØæ »ØæÐ
°·¤ ƒæ´ÅðU ·ð¤ Âà¿æÌ÷ ©âð ÀUæÙæ »Øæ ¥æñÚU çÙSØ´Î ·¤è
ÂýÕÜÌæ 0.042 N Âæ§ü »§üÐ ¥çÏàææðçáÌ °çâçÅU·¤
¥Ü ·¤è ×æ˜ææ (·¤æcÆU-·¤æðØÜæ ·ð¤ ÂýçÌ »ýæ× ÂÚU)
ãñ Ñ
(1) 18 mg
(2) 36 mg
(3) 42 mg
(4) 54 mg
41. N32, O22 ÌÍæ F2 ·¤è ¥æØçÙ·¤ ç˜æ’ØæØð´ (Å ×ð´)
·ý¤×àæÑ ãñ´ Ñ
(1) 1.36, 1.40 ÌÍæ 1.71
(2) 1.36, 1.71 ÌÍæ 1.40
(3) 1.71, 1.40 ÌÍæ 1.36
(4) 1.71, 1.36 ÌÍæ 1.40
42. ãæòÜ-ãðÚUæòËÅU Âý·ý¤× âð °ðÜéç×çÙØ× ·ð¤ çÙc·¤áü‡æ ·ð¤
â´ÎÖü ×ð´ ·¤æñÙ âæ ·¤ÍÙ »ÜÌ ãñ?
(1) §â Âý·ý¤× ×ð´ CO ÌÍæ CO2 ·¤æ ©ˆÂæÎÙ ãæðÌæ
ãñÐ
(2) CaF2 ·¤æð Al2O3 ×ð´ ç×ÜæÙð ÂÚU çןæ‡æ ·¤æ
»ÜÙæ´·¤ ·¤× ãæðÌæ ãñ ¥æñÚU ©â×ð´ ¿æÜ·¤Ìæ ¥æÌè
ãñÐ
(3) ·ñ¤ÍæðÇU ÂÚU Al31 ¥Â¿çØÌ ãæð ·¤ÚU Al ÕÙæÌæ
ãñÐ
(4) Na3AlF6 çßléÌ ¥ÂƒæÅ÷UØ ·¤æ ·¤æ× ·¤ÚUÌæ
ãñÐ

23. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 23
43. From the following statements regarding
H2O2, choose the incorrect statement :
(1) It can act only as an oxidizing agent
(2) It decomposes on exposure to light
(3) It has to be stored in plastic or wax
lined glass bottles in dark
(4) It has to be kept away from dust
44. Which one of the following alkaline earth
metal sulphates has its hydration enthalpy
greater than its lattice enthalpy ?
(1) CaSO4
(2) BeSO4
(3) BaSO4
(4) SrSO4
45. Which among the following is the most
reactive ?
(1) Cl2
(2) Br2
(3) I2
(4) ICl
43. H2O2 ·ð¤ â´ÎÖü ×ð´, çِÙçÜç¹Ì ·¤ÍÙæð´ ×ð´ âð »ÜÌ
·¤ÍÙ ¿éçÙ° Ñ
(1) Øã ·ð¤ßÜ ¥æò€âè·¤æÚU·¤ ãñ
(2) Âý·¤æàæ ×ð´ §â·¤æ ¥ÂƒæÅUÙ ãæðÌæ ãñ
(3) §âð ŒÜæçSÅU·¤ Øæ ×æð×¥ÅðU ·¤æ´¿ ÕæðÌÜæð´ ×ð´ ¥´ÏðÚðU
×ð´ â´»ýçãÌ ç·¤Øæ ÁæÌæ ãñ
(4) §âð ÏêÜ âð ÎêÚU ÚU¹Ùæ ¿æçã°
44. çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ âð ÿææÚUèØ ×ëÎæ ÏæÌé âËÈð¤ÅU
·¤è ÁÜØæðÁÙ °ð‹ÍæËÂè ©â·ð¤ ÁæÜ·¤ °ð‹ÍæËÂè âð
¥çÏ·¤ ãñ?
(1) CaSO4
(2) BeSO4
(3) BaSO4
(4) SrSO4
45. çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ âßæüçÏ·¤ ¥çÖç·ý¤ØæàæèÜ ãñ?
(1) Cl2
(2) Br2
(3) I2
(4) ICl

24. A/Page 24 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
46. Match the catalysts to the correct
processes :
Catalyst Process
(A) TiCl3 (i) Wacker process
(B) PdCl2 (ii) Ziegler - Natta
polymerization
(C) CuCl2 (iii) Contact process
(D) V2O5 (iv) Deacon’s process
(1) (A) - (iii), (B) - (ii), (C) - (iv), (D) - (i)
(2) (A) - (ii), (B) - (i), (C) - (iv), (D) - (iii)
(3) (A) - (ii), (B) - (iii), (C) - (iv), (D) - (i)
(4) (A) - (iii), (B) - (i), (C) - (ii), (D) - (iv)
47. Which one has the highest boiling point ?
(1) He
(2) Ne
(3) Kr
(4) Xe
48. The number of geometric isomers that can
exist for square planar [Pt (Cl) (py) (NH3)
(NH2OH)]1 is (py 5 pyridine) :
(1) 2
(2) 3
(3) 4
(4) 6
49. The color of KMnO4 is due to :
(1) M ® L charge transfer transition
(2) d 2 d transition
(3) L ® M charge transfer transition
(4) s 2 s* transition
46. çΰ »° ©ˆÂýðÚU·¤æð´ ·¤æð âãè Âý·ý¤× ·ð¤ âæÍ âé×ðçÜÌ
·¤Úð´U Ñ
©ˆÂýðÚU·¤ Âý·ý¤×
(A) TiCl3 (i) ßæò·¤ÚU Âý·ý¤×
(B) PdCl2 (ii) ˆâè‚ÜÚ-Ù^æ
ÕãéÜ·¤è·¤ÚU‡æU
(C) CuCl2 (iii) â´SÂàæü Âý·ý¤×
(D) V2O5 (iv) ÇUè·¤Ù Âý·ý¤×
(1) (A) - (iii), (B) - (ii), (C) - (iv), (D) - (i)
(2) (A) - (ii), (B) - (i), (C) - (iv), (D) - (iii)
(3) (A) - (ii), (B) - (iii), (C) - (iv), (D) - (i)
(4) (A) - (iii), (B) - (i), (C) - (ii), (D) - (iv)
47. çِÙçÜç¹Ì ×ð´ âð âßæüçÏ·¤ €ßÍÙæ´·¤ 緤ⷤæ ãñ?
(1) He
(2) Ne
(3) Kr
(4) Xe
48. ß»ü â×ÌÜèØ [Pt (Cl) (py) (NH3) (NH2OH)]1
(py 5 pyridine) ·ð¤ ’Øæç×ÌèØ â×æßØçßØæð´ ·¤è
ⴁØæ ãñ Ñ
(1) 2
(2) 3
(3) 4
(4) 6
49. KMnO4 ·ð¤ Ú´U» ·¤æ ·¤æÚU‡æ ãñ Ñ
(1) M ® L ¥æßðàæ SÍæÙæ´ÌÚU‡æ â´·ý¤×‡æ
(2) d 2 d â´·ý¤×‡æ
(3) L ® M ¥æßðàæ SÍæÙæ´ÌÚU‡æ â´·ý¤×‡æ
(4) s 2 s* â´·ý¤×‡æ

25. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 25
50. Assertion : Nitrogen and Oxygen are the
main components in the
atmosphere but these do not
react to form oxides of nitrogen.
Reason : The reaction between nitrogen
and oxygen requires high
temperature.
(1) Both assertion and reason are
correct, and the reason is the correct
explanation for the assertion
(2) Both assertion and reason are
correct, but the reason is not the
correct explanation for the assertion
(3) The assertion is incorrect, but the
reason is correct
(4) Both the assertion and reason are
incorrect
51. In Carius method of estimation of
halogens, 250 mg of an organic compound
gave 141 mg of AgBr. The percentage of
bromine in the compound is :
(at. mass Ag5108; Br580)
(1) 24
(2) 36
(3) 48
(4) 60
52. Which of the following compounds will
exhibit geometrical isomerism ?
(1) 1 - Phenyl - 2 - butene
(2) 3 - Phenyl - 1 - butene
(3) 2 - Phenyl - 1 - butene
(4) 1, 1 - Diphenyl - 1 - propane
50. ¥çÖ·¤ÍÙ Ñ Ùæ§ÅþUæðÁÙ ¥æñÚU ¥æò€âèÁÙ ßæÌæßÚU‡æ ·ð¤
×éØ ƒæÅU·¤ ãñ´ ÂÚU‹Ìé Øã ç·ý¤Øæ ·¤ÚU·ð¤
Ùæ§ÅþUæðÁÙ ·ð¤ ¥æò€âæ§ÇU Ùãè´ ÕÙæÌðÐ
Ì·ü¤ Ñ Ùæ§ÅþUæðÁÙ ¥æñÚU ¥æò€âèÁÙ ·ð¤ Õè¿
¥çÖç·ý¤Øæ ·ð¤ çÜ° ©“æ Ìæ ·¤è
¥æßàØ·¤Ìæ ãñÐ
(1) ¥çÖ·¤ÍÙ ¥æñÚU Ì·ü¤ ÎæðÙæð´ âãè ãñ´ ¥æñÚU Ì·ü¤
¥çÖ·¤ÍÙ ·¤æ âãè SÂcÅUè·¤ÚU‡æ ãñÐ
(2) ¥çÖ·¤ÍÙ ¥æñÚU Ì·ü¤ ÎæðÙæð´ âãè ãñ´ ÂÚU‹Ìé Ì·ü¤
¥çÖ·¤ÍÙ ·¤æ âãè SÂcÅUè·¤ÚU‡æ Ùãè´ ãñÐ
(3) ¥çÖ·¤ÍÙ »ÜÌ ãñ ÂÚU‹Ìé Ì·ü¤ âãè ãñÐ
(4) ¥çÖ·¤ÍÙ ß Ì·ü¤ ÎæðÙæð´ »ÜÌ ãñ´Ð
51. ãñÜæðÁÙ ·ð¤ ¥æ·¤ÜÙ ·¤è ·ñ¤çÚU¥â çßçÏ ×ð´ 250 mg
·¤æÕüçÙ·¤ Øæñç»·¤ 141 mg AgBr ÎðÌæ ãñÐ Øæñç»·¤
×ð´ Õýæð×èÙ ·¤è ÂýçÌàæÌÌæ ãñ :
(ÂÚU×æç‡ß·¤ ÎýÃØ×æÙ Ag5108; Br580)
(1) 24
(2) 36
(3) 48
(4) 60
52. çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ âæ Øæñç»·¤ ’Øæç×ÌèØ
â×æßØßÌæ ÎàææüÌæ ãñ?
(1) 1 - Èð¤çÙÜ - 2 - ŽØêÅUèÙ
(2) 3 - Èð¤çÙÜ - 1 - ŽØêÅUèÙ
(3) 2 - Èð¤çÙÜ - 1 - ŽØêÅUèÙ
(4) 1, 1 - ÇUæ§üÈð¤çÙÜ - 1 - ÂýæðÂðÙ

26. A/Page 26 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
53. Which compound would give
5 - keto - 2 - methyl hexanal upon
ozonolysis ?
(1)
(2)
(3)
(4)
54. The synthesis of alkyl fluorides is best
accomplished by :
(1) Free radical fluorination
(2) Sandmeyer’s reaction
(3) Finkelstein reaction
(4) Swarts reaction
53. ¥æð$ÁæðÙæðçÜçââ ·¤ÚUÙð ÂÚU ·¤æñÙ âæ Øæñç»·¤
5 - ·¤èÅUæð - 2 - ×ðçÍÜ ãð€âæÙñÜ ÎðÌæ ãñ?
(1)
(2)
(3)
(4)
54. ¥Ë·¤æ§Ü ÜæðÚUæ§ÇU ·ð¤ â´àÜðá‡æ ·ð¤ çÜ° âÕâð
ÕðãÌÚUèÙ çßçÏ ãñ Ñ
(1) ×é€Ì ×êÜ·¤ ÜæðçÚUÙðàæÙ
(2) âñ‹ÇU×æØÚU ¥çÖç·ý¤Øæ
(3) çÈ´¤·¤ÜSÅUæ§Ù ¥çÖç·ý¤Øæ
(4) SßæÅüUâ ¥çÖç·ý¤Øæ

27. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 27
55. çΰ »° ¥çÖç·ý¤Øæ ¥Ùé·ý¤× ×ð´ ©ˆÂæÎ C ãñ Ñ
4 2 2
4
KMnO SOCl H /Pd
BaSO
Toluene A B C→ → →
(1) C6H5COOH
(2) C6H5CH3
(3) C6H5CH2OH
(4) C6H5CHO
56. çΰ »° ¥çÖç·ý¤Øæ ×ð´ ©ˆÂæÎ E ãñ Ñ
2NaNO /HCl CuCN/KCN
20 5 C
D E N→ →
2 8 D
1
(1)
(2)
(3)
(4)
55. In the following sequence of reactions :
4 2 2
4
KMnO SOCl H /Pd
BaSO
Toluene A B C,→ → →
the product C is :
(1) C6H5COOH
(2) C6H5CH3
(3) C6H5CH2OH
(4) C6H5CHO
56. In the reaction
2NaNO /HCl CuCN/KCN
20 5 C
D E N→ →
2 8 D
1
the product E is :
(1)
(2)
(3)
(4)

28. A/Page 28 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
57. ç·¤â ÕãéÜ·¤ ·¤æ ©ÂØæð» ÂýÜð ¥æñÚU ÂýÜæÿæ ÕÙæÙð ×ð´
ãæðÌæ ãñ?
(1) Õð·ð¤Üæ§ÅU
(2) ç‚ÜŒÅUæÜ
(3) ÂæòçÜÂýæðÂèÙ
(4) ÂæòçÜ ßæ§çÙÜ €ÜæðÚUæ§ÇU
58. çِÙçÜç¹Ì çßÅUæç×Ùæð´ ×ð´ ÁÜ ×ð´ çßÜðØ ãæðÙð ßæÜæ
ãñ Ñ
(1) çßÅUæç×Ù C
(2) çßÅUæç×Ù D
(3) çßÅUæç×Ù E
(4) çßÅUæç×Ù K
59. çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ âæ Øæñç»·¤ ÂýçÌ¥Ü Ùãè´ ãñ?
(1) °ðÜéç×çÙØ× ãæ§ÇþUæ€âæ§ÇU
(2) çâ×ðçÅUÇUèÙ
(3) çȤÙçËÁÙ
(4) ÚñUçÙçÅUÇUèÙ
60. çΰ »° Øæñç»·¤æð´ ×ð´ ·¤æñÙ âð Øæñç»·¤ ·¤æ Ú´U» ÂèÜæ Ùãè´
ãñ?
(1) Zn2[Fe(CN)6]
(2) K3[Co(NO2)6]
(3) (NH4)3 [As (Mo3 O10)4]
(4) BaCrO4
57. Which polymer is used in the manufacture
of paints and lacquers ?
(1) Bakelite
(2) Glyptal
(3) Polypropene
(4) Poly vinyl chloride
58. Which of the vitamins given below is water
soluble ?
(1) Vitamin C
(2) Vitamin D
(3) Vitamin E
(4) Vitamin K
59. Which of the following compounds is not
an antacid ?
(1) Aluminium hydroxide
(2) Cimetidine
(3) Phenelzine
(4) Ranitidine
60. Which of the following compounds is not
colored yellow ?
(1) Zn2[Fe(CN)6]
(2) K3[Co(NO2)6]
(3) (NH4)3 [As (Mo3 O10)4]
(4) BaCrO4

29. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 29
PART C — MATHEMATICS Öæ» C — »ç‡æÌ
61. Let A and B be two sets containing four
and two elements respectively. Then the
number of subsets of the set A3B, each
having at least three elements is :
(1) 219
(2) 256
(3) 275
(4) 510
62. A complex number z is said to be
unimodular if ?z?51. Suppose z1 and z2
are complex numbers such that
1 2
1 2
2
2
z z
z z
2
2
is unimodular and z2 is not unimodular.
Then the point z1 lies on a :
(1) straight line parallel to x-axis.
(2) straight line parallel to y-axis.
(3) circle of radius 2.
(4) circle of radius 2 .
63. Let a and b be the roots of equation
x226x2250. If an5an2bn, for n/1,
then the value of 10 8
9
a 2a
2a
2
is equal to :
(1) 6
(2) 26
(3) 3
(4) 23
61. ×æÙæ A ÌÍæ B Îæð â×é‘¿Ø ãñ´ çÁÙ×ð´ ·ý¤×àæÑ ¿æÚU ÌÍæ
Îæð ¥ßØß ãñ´, Ìæð â×é‘¿Ø A3B ·ð¤ ©Ù ©Ââ×é‘¿Øæð´
·¤è ⴁØæ, çÁÙ×ð´ ÂýˆØð·¤ ×ð´ ·¤× âð ·¤× ÌèÙ ¥ßØß
ãñ´, ãñ Ñ
(1) 219
(2) 256
(3) 275
(4) 510
62. °·¤ âç×Ÿæ ⴁØæ z °·¤×æÂæ´·¤è ·¤ãÜæÌè ãñ ØçÎ
?z?51 ãñÐ ×æÙæ z1 ÌÍæ z2 °ðâè âç×Ÿæ ⴁØæ°¡ ãñ´
ç·¤ 1 2
1 2
2
2
z z
z z
2
2
°·¤×æÂæ´·¤è ãñ ÌÍæ z2 °·¤×æÂæ´·¤è
Ùãè´ ãñ, Ìæð çÕ´Îé z1 çSÍÌ ãñ Ñ
(1) x-¥ÿæ ·ð¤ â×æ´ÌÚU °·¤ ÚðU¹æ ÂÚUÐ
(2) y-¥ÿæ ·ð¤ â×æ´ÌÚU °·¤ ÚðU¹æ ÂÚUÐ
(3) 2 ç˜æ’Øæ ßæÜð ßëžæ ÂÚUÐ
(4) 2 ç˜æ’Øæ ßæÜð ßëžæ ÂÚUÐ
63. ×æÙæ a ÌÍæ b çmƒææÌ â×è·¤ÚU‡æ x226x2250 ·ð¤
×êÜ ãñ´Ð ØçÎ n/1 ·ð¤ çÜ°, an5an2bn ãñ, Ìæð
10 8
9
a 2a
2a
2
·¤æ ×æÙ ãñ Ñ
(1) 6
(2) 26
(3) 3
(4) 23

30. A/Page 30 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
64. If
1 2 2
A 2 1 2
a 2 b
 
 
 
  
5 2 is a matrix satisfying
the equation AAT59I, where I is 333
identity matrix, then the ordered pair
(a, b) is equal to :
(1) (2, 21)
(2) (22, 1)
(3) (2, 1)
(4) (22, 21)
65. The set of all values of l for which the
system of linear equations :
2x122x21x35lx1
2x123x212x35lx2
2x112x2 5lx3
has a non-trivial solution,
(1) is an empty set.
(2) is a singleton.
(3) contains two elements.
(4) contains more than two elements.
66. The number of integers greater than 6,000
that can be formed, using the digits 3, 5, 6,
7 and 8, without repetition, is :
(1) 216
(2) 192
(3) 120
(4) 72
64. ØçÎ
1 2 2
A 2 1 2
a 2 b
 
 
 
  
5 2 °·¤ °ðâæ ¥æÃØêã ãñ Áæð
¥æÃØêã â×è·¤ÚU‡æ AAT59I, ·¤æð â´ÌécÅU ·¤ÚUÌæ ãñ,
Áãæ¡ I, 333 ·¤æ ̈â×·¤ ¥æÃØêã ãñ, Ìæð ·ý¤ç×Ì Øé‚×
(a, b) ·¤æ ×æÙ ãñ Ñ
(1) (2, 21)
(2) (22, 1)
(3) (2, 1)
(4) (22, 21)
65. l ·ð¤ âÖè ×æÙæð´ ·¤æ â×é‘¿Ø, çÁÙ·ð¤ çÜ° ÚñUç¹·¤
â×è·¤ÚU‡æ çÙ·¤æØ
2x122x21x35lx1
2x123x212x35lx2
2x112x2 5lx3
·¤æ °·¤ ¥Ìé‘ÀU ãÜ ãñ,
(1) °·¤ çÚU€Ì â×é‘¿Ø ãñÐ
(2) °·¤ °·¤Ü â×é‘¿Ø ãñÐ
(3) ×ð´ Îæð ¥ßØß ãñ´Ð
(4) ×ð´ Îæð âð ¥çÏ·¤ ¥ßØß ãñ´Ð
66. ¥´·¤æð´ 3, 5, 6, 7 ÌÍæ 8 ·ð¤ ÂýØæð» âð, çÕÙæ ÎæðãÚUæØð,
ÕÙÙð ßæÜð 6,000 âð ÕǸð Âê‡ææZ·¤æð´ ·¤è ⴁØæ ãñ Ñ
(1) 216
(2) 192
(3) 120
(4) 72

31. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 31
67. The sum of coefficients of integral powers
of x in the binomial expansion of
( )
50
1 2 x2 is :
(1) ( )501
3 1
2
1
(2) ( )501
3
2
(3) ( )501
3 1
2
2
(4) ( )501
2 1
2
1
68. If m is the A.M. of two distinct real
numbers l and n (l, n > 1) and G1, G2 and
G3 are three geometric means between l
and n, then 4 4 4
1 2 3G 2G G1 1 equals.
(1) 4 l2mn
(2) 4 lm2n
(3) 4 lmn2
(4) 4 l2m2n2
69. The sum of first 9 terms of the series
3 3 3 3 33
1 2 1 2 31
....
1 1 3 1 3 5
1 1 1
1 1 1
1 1 1
is :
(1) 71
(2) 96
(3) 142
(4) 192
67. ( )
50
1 2 x2 ·ð¤ çmÂÎ ÂýâæÚU ×ð´ x ·¤è Âê‡ææZ·¤èØ
ƒææÌæ𴠷𤠻é‡ææ´·¤æð´ ·¤æ Øæð» ãñ Ñ
(1) ( )501
3 1
2
1
(2) ( )501
3
2
(3) ( )501
3 1
2
2
(4) ( )501
2 1
2
1
68. ØçÎ Îæð çßçÖ‹Ù ßæSÌçß·¤ ⴁØæ¥æð´ l ÌÍæ n
(l, n > 1) ·¤æ â×æ´ÌÚU ×æŠØ (A.M.) m ãñ ¥æñÚU l ÌÍæ
n ·ð¤ Õè¿ ÌèÙ »é‡ææðžæÚU ×æŠØ (G.M.) G1, G2 ÌÍæ
G3 ãñ´, Ìæð 4 4 4
1 2 3G 2G G1 1 ÕÚUæÕÚU ãñ Ñ
(1) 4 l2mn
(2) 4 lm2n
(3) 4 lmn2
(4) 4 l2m2n2
69. Ÿæð‡æè
3 3 3 3 33
1 2 1 2 31
....
1 1 3 1 3 5
1 1 1
1 1 1
1 1 1
·ð¤
Âý‰æ× 9 ÂÎæð´ ·¤æ Øæð» ãñ Ñ
(1) 71
(2) 96
(3) 142
(4) 192

32. A/Page 32 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
70. ( )( )
0
1 cos 2 3 cos
tan 4x
x xlim
x x→
2 1
is equal to :
(1) 4
(2) 3
(3) 2
(4)
1
2
71. If the function.
1 , 0 3
g( )
m 2 , 3 < 5
k x x
x
x x



1 [ [
5
1 [
is differentiable, then the value of k1m is :
(1) 2
(2)
16
5
(3)
10
3
(4) 4
72. The normal to the curve, x212xy23y250,
at (1, 1) :
(1) does not meet the curve again.
(2) meets the curve again in the second
quadrant.
(3) meets the curve again in the third
quadrant.
(4) meets the curve again in the fourth
quadrant.
70. ( )( )
0
1 cos 2 3 cos
tan 4x
x xlim
x x→
2 1
ÕÚUæÕÚU ãñ Ñ
(1) 4
(2) 3
(3) 2
(4)
1
2
71. ØçΠȤÜÙ
1 , 0 3
g( )
m 2 , 3 < 5
k x x
x
x x



1 [ [
5
1 [
¥ß·¤ÜÙèØ ãñ, Ìæð k1m ·¤æ ×æÙ ãñ Ñ
(1) 2
(2)
16
5
(3)
10
3
(4) 4
72. ß·ý¤ x212xy23y250 ·ð¤ çÕ´Îé (1, 1) ÂÚU
¥çÖÜÕ Ñ
(1) ß·ý¤ ·¤æð ÎæððÕæÚUæ Ùãè´ ç×ÜÌæÐ
(2) ß·ý¤ ·¤æð ÎæðÕæÚUæ çmÌèØ ¿ÌéÍæZàæ ×ð´ ç×ÜÌæ ãñÐ
(3) ß·ý¤ ·¤æð ÎæðÕæÚUæ ÌëÌèØ ¿ÌéÍæZàæ ×ð´ ç×ÜÌæ ãñÐ
(4) ß·ý¤ ·¤æð ÎæðÕæÚUæ ¿ÌéÍü ¿ÌéÍæZàæ ×ð´ ç×ÜÌæ ãñÐ

33. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 33
73. Let f (x) be a polynomial of degree four
having extreme values at x51 and x52.
If 20
( )
1 3
x
f x
lim
x→
 
 
 
1 5 , then f (2) is equal
to :
(1) 28
(2) 24
(3) 0
(4) 4
74. The integral 3
42 4
d
( 1)
x
x x
∫ 1
equals :
(1)
1
44
4
1
c
x
x
 
 
 
 
1
1
(2)
1
44
( 1) cx 1 1
(3)
1
44
( 1) cx2 1 1
(4)
1
44
4
1
c
x
x
 
 
 
 
1
2 1
75. The integral
4 2
2 2
2
log
d
log log (36 12 )
x
x
x x x
∫ 1 2 1
is equal to :
(1) 2
(2) 4
(3) 1
(4) 6
73. ×æÙæ f (x) ƒææÌ 4 ·¤æ °·¤ ÕãéÂÎ ãñ çÁâ·ð¤
x51 ÌÍæ x52 ÂÚU ¿ÚU× ×æÙ ãñ´Ð ØçÎ
20
( )
1 3
x
f x
lim
x→
 
 
 
1 5 ãñ, Ìæð f (2) ÕÚUæÕÚU ãñ Ñ
(1) 28
(2) 24
(3) 0
(4) 4
74. â×æ·¤Ü 3
42 4
d
( 1)
x
x x
∫ 1
ÕÚUæÕÚU ãñ Ñ
(1)
1
44
4
1
c
x
x
 
 
 
 
1
1
(2)
1
44
( 1) cx 1 1
(3)
1
44
( 1) cx2 1 1
(4)
1
44
4
1
c
x
x
 
 
 
 
1
2 1
75. â×æ·¤Ü
4 2
2 2
2
log
d
log log (36 12 )
x
x
x x x
∫ 1 2 1
ÕÚUæÕÚU ãñ Ñ
(1) 2
(2) 4
(3) 1
(4) 6

34. A/Page 34 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
76. The area (in sq. units) of the region
described by
{(x, y) : y2 [ 2x and y / 4x 2 1} is :
(1)
7
32
(2)
5
64
(3)
15
64
(4)
9
32
77. Let y(x) be the solution of the differential
equation
d
( log ) 2 log , ( 1).
d
y
x x y x x x
x
1 5 /
Then y(e) is equal to :
(1) e
(2) 0
(3) 2
(4) 2e
78. The number of points, having both
co-ordinates as integers, that lie in the
interior of the triangle with vertices (0, 0),
(0, 41) and (41, 0), is :
(1) 901
(2) 861
(3) 820
(4) 780
76. {(x, y) : y2[ 2x ÌÍæ y / 4x 2 1} mæÚUæ ÂçÚUÖæçáÌ
ÿæð˜æ ·¤æ ÿæð˜æÈ¤Ü (ß»ü §·¤æ§Øæð´) ×ð´ ãñ Ñ
(1)
7
32
(2)
5
64
(3)
15
64
(4)
9
32
77. ×æÙæ ¥ß·¤Ü â×è·¤ÚU‡æ
d
( log ) 2 log , ( 1)
d
y
x x y x x x
x
1 5 /
·¤æ ãÜ y(x) ãñ, Ìæð y(e) ÕÚUæÕÚU ãñ Ñ
(1) e
(2) 0
(3) 2
(4) 2e
78. ç˜æÖéÁ, çÁâ·ð¤ àæèáü (0, 0), (0, 41) ÌÍæ (41, 0) ãñ´,
·ð¤ ¥æ´ÌçÚU·¤ Öæ» ×ð´ çSÍÌ ©Ù çÕ´Îé¥æð´ ·¤è ⴁØæ
çÁÙ·ð¤ ÎæðÙæð´ çÙÎðüàææ´·¤ Âê‡ææZ·¤ ãñ´, ãñ Ñ
(1) 901
(2) 861
(3) 820
(4) 780

35. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 35
79. Locus of the image of the point (2, 3) in
the line (2x23y14)1k (x22y13)50,
k e R, is a :
(1) straight line parallel to x-axis.
(2) straight line parallel to y-axis.
(3) circle of radius 2 .
(4) circle of radius 3 .
80. The number of common tangents to the
circles x21y224x26y21250 and
x21y216x118y12650, is :
(1) 1
(2) 2
(3) 3
(4) 4
81. The area (in sq. units) of the quadrilateral
formed by the tangents at the end points
of the latera recta to the ellipse
22
1
9 5
yx
1 5 , is :
(1)
27
4
(2) 18
(3)
27
2
(4) 27
82. Let O be the vertex and Q be any point on
the parabola, x258y. If the point P divides
the line segment OQ internally in the ratio
1 : 3, then the locus of P is :
(1) x25y
(2) y25x
(3) y252x
(4) x252y
79. çÕ´Îé (2, 3) ·ð¤ ÚðU¹æ
(2x23y14)1k (x22y13)50, k e R ×ð´
ÂýçÌçÕ´Õ ·¤æ çÕ´ÎéÂÍ °·¤ Ñ
(1) x-¥ÿæ ·ð¤ â×æ´ÌÚU ÚðU¹æ ãñÐ
(2) y-¥ÿæ ·ð¤ â×æ´ÌÚU ÚðU¹æ ãñÐ
(3) 2 ç˜æ’Øæ ·¤æ ßëžæ ãñÐ
(4) 3 ç˜æ’Øæ ·¤æ ßëžæ ãñÐ
80. ßëžææð´ x21y224x26y21250 ÌÍæ
x21y216x118y12650 ·¤è ©ÖØçÙcÆU SÂàæü
ÚðU¹æ¥æð´ ·¤è ⴁØæ ãñ Ñ
(1) 1
(2) 2
(3) 3
(4) 4
81. Îèƒæüßëžæ
22
1
9 5
yx
1 5 ·ð¤ ÙæçÖܐÕæð´ ·ð¤ çâÚUæð´ ÂÚU
¹è´¿è »§ü SÂàæü ÚðU¹æ¥æð´ mæÚUæ çÙç×üÌ ¿ÌéÖéüÁ ·¤æ ÿæð˜æȤÜ
(ß»ü §·¤æ§Øæð´ ×ð´) ãñ Ñ
(1)
27
4
(2) 18
(3)
27
2
(4) 27
82. ×æÙæ ÂÚUßÜØ x258y ·¤æ àæèáü O ÌÍæ ©â ÂÚU ·¤æð§ü
çÕ´Îé Q ãñÐ ØçÎ çÕ´Îé P, ÚðU¹æ¹´ÇU OQ ·¤æð
1 : 3 ·ð¤ ¥æ´ÌçÚU·¤ ¥ÙéÂæÌ ×ð´ Õæ¡ÅUÌæ ãñ, Ìæð P ·¤æ
çÕ´ÎéÂÍ ãñ Ñ
(1) x25y
(2) y25x
(3) y252x
(4) x252y

36. A/Page 36 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
83. The distance of the point (1, 0, 2) from the
point of intersection of the line
12 2
3 4 12
yx z12 2
5 5 and the plane
x2y1z516, is :
(1) 2 14
(2) 8
(3) 3 21
(4) 13
84. The equation of the plane containing the
line 2x25y1z53; x1y14z55, and
parallel to the plane, x13y16z51, is :
(1) 2x16y112z513
(2) x13y16z527
(3) x13y16z57
(4) 2x16y112z5213
85. Let a , b and c
→→ →
be three non-zero vectors
such that no two of them are collinear and
1
( a b ) c acb
3
→ →→ → →→
3 3 5 . If u is the
angle between vectors b
→
and c
→
, then a
value of sinu is :
(1)
2 2
3
(2)
2
3
2
(3)
2
3
(4)
2 3
3
2
83. ÚðU¹æ
12 2
3 4 12
yx z12 2
5 5 ÌÍæ â×ÌÜ
x2y1z516 ·ð¤ ÂýçÌ‘ÀðUÎ çÕ´Îé ·¤è, çÕ´Îé (1, 0, 2)
âð ÎêÚUè ãñ Ñ
(1) 2 14
(2) 8
(3) 3 21
(4) 13
84. ÚðU¹æ 2x25y1z53, x1y14z55 ·¤æð ¥´ÌçßücÅU
·¤ÚUÙð ßæÜð â×ÌÜ, Áæð â×ÌÜ x13y16z51 ·ð¤
â×æ´ÌÚU ãñ, ·¤æ â×è·¤ÚU‡æ ãñ Ñ
(1) 2x16y112z513
(2) x13y16z527
(3) x13y16z57
(4) 2x16y112z5213
85. ×æÙæ a , b
→→
ÌÍæ c
→
ÌèÙ àæê‹ØðÌÚU °ðâð âçÎàæ ãñ´ ç·¤
©Ù×ð´ âð ·¤æð§ü Îæð â´ÚUð¹ Ùãè´ ã´ñ ÌÍæ
1
( a b ) c acb
3
→ →→ → →→
3 3 5 ãñÐ ØçÎ âçÎàææð´
b
→
ÌÍæ c
→
·ð¤ Õè¿ ·¤æ ·¤æð‡æ u ãñ, Ìæð sinu ·¤æ °·¤
×æÙ ãñ Ñ
(1)
2 2
3
(2)
2
3
2
(3)
2
3
(4)
2 3
3
2

37. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 37
86. If 12 identical balls are to be placed in 3
identical boxes, then the probability that
one of the boxes contains exactly 3 balls
is :
(1)
11
55 2
3 3
 
 
 
(2)
10
2
55
3
 
 
 
(3)
12
1
220
3
 
 
 
(4)
11
1
22
3
 
 
 
87. The mean of the data set comprising of 16
observations is 16. If one of the observation
valued 16 is deleted and three new
observations valued 3, 4 and 5 are added
to the data, then the mean of the resultant
data, is :
(1) 16.8
(2) 16.0
(3) 15.8
(4) 14.0
88. If the angles of elevation of the top of a
tower from three collinear points A, B and
C, on a line leading to the foot of the
tower, are 308, 458 and 608 respectively,
then the ratio, AB : BC, is :
(1) 3 : 1
(2) 3 : 2
(3) 1 : 3
(4) 2 : 3
86. ØçÎ 12 °·¤ Áñâè »ð´Îð´, 3 °·¤ Áñâð Õ€âæð´ ×ð´ ÚU¹è ÁæÌè
ãñ´, Ìæð §Ù×ð´ âð °·¤ Õ€âð ×ð´ ÆUè·¤ 3 »ð´Îð´ ãæðÙð ·¤è
ÂýæçØ·¤Ìæ ãñ Ñ
(1)
11
55 2
3 3
 
 
 
(2)
10
2
55
3
 
 
 
(3)
12
1
220
3
 
 
 
(4)
11
1
22
3
 
 
 
87. 16 Âýðÿæ‡ææð´ ßæÜð ¥æ¡·¤Ç¸æð´ ·¤æ ×æŠØ 16 ãñÐ ØçÎ °·¤
Âýðÿæ‡æ çÁâ·¤æ ×æÙ 16 ãñ, ·¤æð ãÅUæ ·¤ÚU, 3 ÙØð Âýðÿæ‡æ
çÁÙ·ð¤ ×æÙ 3, 4 ÌÍæ 5 ãñ´, ¥æ¡·¤Ç¸æð´ ×ð´ ç×Üæ çÎØð ÁæÌð
ãñ´, Ìæð ÙØð ¥æ¡·¤Ç¸æð´ ·¤æ ×æŠØ ãñ Ñ
(1) 16.8
(2) 16.0
(3) 15.8
(4) 14.0
88. ÌèÙ â´ÚðU¹ çÕ´Îé¥æð´ A, B ÌÍæ C, °·¤ °ðâè ÚðU¹æ ÂÚU
çSÍÌ ãñ´ Áæð °·¤ ×èÙæÚU ·ð¤ ÂæÎ ·¤è çÎàææ ×ð´ Üð ÁæÌè ãñ,
âð °·¤ ×èÙæÚU ·ð¤ çàæ¹ÚU ·ð¤ ©‹ÙØÙ ·¤æð‡æ ·ý¤×àæÑ
308, 458 ÌÍæ 608 ãñ´, Ìæð AB : BC ·¤æ ¥ÙéÂæÌ ãñ Ñ
(1) 3 : 1
(2) 3 : 2
(3) 1 : 3
(4) 2 : 3

38. A/Page 38 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
89. Let
1 1 1
2
2
tan tan tan ,
1
x
y x
x
 
 
 
2 2 2
5 1
2
where
1
<
3
x? ? . Then a value of y is :
(1)
3
2
3
1 3
x x
x
2
2
(2)
3
2
3
1 3
x x
x
1
2
(3)
3
2
3
1 3
x x
x
2
1
(4)
3
2
3
1 3
x x
x
1
1
90. The negation of ~ s Ú (~ r Ù s ) is equivalent
to :
(1) s Ù ~ r
(2) s Ù (r Ù ~ s)
(3) s Ú (r Ú ~ s)
(4) s Ù r
- o 0 o -
89. ×æÙæ
1 1 1
2
2
tan tan tan ,
1
x
y x
x
 
 
 
2 2 2
5 1
2
Áãæ¡
1
<
3
x? ? ãñ, Ìæð y ·¤æ °·¤ ×æÙ ãñ Ñ
(1)
3
2
3
1 3
x x
x
2
2
(2)
3
2
3
1 3
x x
x
1
2
(3)
3
2
3
1 3
x x
x
2
1
(4)
3
2
3
1 3
x x
x
1
1
90. ~ s Ú (~ r Ù s ) ·¤æ çÙáðÏ â×ÌéËØ ãñ Ñ
(1) s Ù ~ r
(2) s Ù (r Ù ~ s)
(3) s Ú (r Ú ~ s)
(4) s Ù r
- o 0 o -

39. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãA/Page 39
SPACE FOR ROUGH WORK / ÚȤ ·¤æØü ·ð¤ çÜ° Á»ã

40. Read the following instructions carefully :
1. The candidates should fill in the required particulars
on the Test Booklet and Answer Sheet (Side–1) with
Blue/Black Ball Point Pen.
2. For writing/marking particulars on Side–2 of the
Answer Sheet, use Blue/Black Ball Point Pen only.
3. The candidates should not write their Roll Numbers
anywhere else (except in the specified space) on the
Test Booklet/Answer Sheet.
4. Out of the four options given for each question, only
one option is the correct answer.
5. For each incorrect response, one–fourth (¼) of the total
marks allotted to the question would be deducted from
the total score. No deduction from the total score,
however, will be made if no response is indicated for
an item in the Answer Sheet.
6. Handle the Test Booklet and Answer Sheet with care,
as under no circumstances (except for discrepancy in
Test Booklet Code and Answer Sheet Code), another set
will be provided.
7. The candidates are not allowed to do any rough work
or writing work on the Answer Sheet. All calculations/
writing work are to be done in the space provided for
this purpose in the Test Booklet itself, marked ‘Space
for Rough Work’. This space is given at the bottom of
each page and in one page (i.e. Page 39) at the end of
the booklet.
8. On completion of the test, the candidates must hand
over the Answer Sheet to the Invigilator on duty in the
Room/Hall. However, the candidates are allowed to
take away this Test Booklet with them.
9. Each candidate must show on demand his/her Admit
Card to the Invigilator.
10. No candidate, without special permission of the
Superintendent or Invigilator, should leave his/her
seat.
11. The candidates should not leave the Examination Hall
without handing over their Answer Sheet to the
Invigilator on duty and sign the Attendance Sheet
again. Cases where a candidate has not signed the
Attendance Sheet second time will be deemed not to
have handed over the Answer Sheet and dealt with as
an unfair means case. The candidates are also required
to put their left hand THUMB impression in the space
provided in the Attendance Sheet.
12. Use of Electronic/Manual Calculator and any
Electronic device like mobile phone, pager etc. is
prohibited.
13. The candidates are governed by all Rules and
Regulations of the JAB/Board with regard to their
conduct in the Examination Hall. All cases of unfair
means will be dealt with as per Rules and Regulations
of the JAB/Board.
14. No part of the Test Booklet and Answer Sheet shall be
detached under any circumstances.
15. Candidates are not allowed to carry any textual
material, printed or written, bits of papers, pager,
mobile phone, electronic device or any other material
except the Admit Card inside the examination
room/hall.
çِÙçÜç¹Ì çÙÎðüàæ ŠØæÙ âð Âɸð´ Ñ
1. ÂÚUèÿææçÍüØæð´ ·¤æð ÂÚUèÿææ ÂéçSÌ·¤æ ¥æñÚU ©žæÚU ˜æ (ÂëD -1) ÂÚU ßæ´çÀUÌ
çßßÚU‡æ ÙèÜð/·¤æÜð ÕæòÜ Œß槴ÅU ÂðÙ âð ãè ÖÚUÙæ ãñÐ
2. ©žæÚU Â˜æ ·ð¤ ÂëD-2 ÂÚU çßßÚU‡æ çܹÙð/¥´ç·¤Ì ·¤ÚUÙð ·ð¤ çÜ° ·ð¤ßÜ
ÙèÜð/·¤æÜð ÕæòÜ Œß槴ÅU ÂðÙ ·¤æ ÂýØæð» ·¤Úð´UÐ
3. ÂÚUèÿææ ÂéçSÌ·¤æ/©žæÚU ˜æ ÂÚU çÙÏæüçÚUÌ SÍæÙ ·ð¤ ¥Üæßæ ÂÚUèÿææÍèü
¥ÂÙæ ¥ÙéR¤×æ´·¤ ¥‹Ø ·¤ãè´ Ùãè´ çܹð´Ð
4. ÂýˆØð·¤ ÂýàÙ ·ð¤ çÜØð çÎØð »Øð ¿æÚU çß·¤ËÂæð´ ×ð´ âð ·ð¤ßÜ °·¤ çß·¤ËÂ
âãè ãñÐ
5. ÂýˆØð·¤ »ÜÌ ©žæÚU ·ð¤ çÜ° ©â ÂýàÙ ·ð¤ çÜ° çÙÏæüçÚUÌ ·é¤Ü ¥´·¤æð´
×ð´ âð °·¤-¿æñÍæ§ü (¼) ¥´·¤ ·é¤Ü Øæð» ×ð´ âð ·¤æÅU çÜ° Áæ°¡»ðÐ
ØçÎ ©žæÚU ˜æ ×ð´ ç·¤âè ÂýàÙ ·¤æ ·¤æð§ü ©žæÚU Ùãè´ çÎØæ »Øæ ãñ, Ìæð
·é¤Ü Øæð» ×ð´ âð ·¤æð§ü ¥´·¤ Ùãè´ ·¤æÅðU Áæ°¡»ðÐ
6. ÂÚUèÿææ ÂéçSÌ·¤æ °ß´ ©žæÚU Â˜æ ·¤æ ŠØæÙÂêßü·¤ ÂýØæð» ·¤Úð´U €Øæð´ç·¤
ç·¤âè Öè ÂçÚUçSÍçÌ ×ð´ (·ð¤ßÜ ÂÚUèÿææ ÂéçSÌ·¤æ °ß´ ©žæÚU Â˜æ ·ð¤
â´·ð¤Ì ×ð´ çÖóæÌæ ·¤è çSÍçÌ ·¤æð ÀUæðǸ·¤ÚU), ÎêâÚUè ÂÚUèÿææ ÂéçSÌ·¤æ
©ÂÜŽÏ Ùãè´ ·¤ÚUæØè Áæ°»èÐ
7. ©žæÚU ˜æ ÂÚU ·¤æð§ü Öè ÚUȤ ·¤æØü Øæ çܹæ§ü ·¤æ ·¤æ× ·¤ÚUÙð ·¤è
¥Ùé×çÌ Ùãè´ ãñÐ âÖè »‡æÙæ °ß´ çܹæ§ü ·¤æ ·¤æ×, ÂÚUèÿææ ÂéçSÌ·¤æ
×ð´ çÙÏæüçÚUÌ Á»ã Áæð ç·¤ ÒÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãÓ mæÚUæ Ùæ×æ´ç·¤Ì
ãñ, ÂÚU ãè ç·¤Øæ Áæ°»æÐ Øã Á»ã ÂýˆØð·¤ ÂëD ÂÚU Ùè¿ð ·¤è ¥æðÚU ¥æñÚU
ÂéçSÌ·¤æ ·ð¤ ¥´Ì ×ð´ °·¤ ÂëD ÂÚU (ÂëD 39) Îè »§ü ãñÐ
8. ÂÚèÿææ âÂóæ ãæðÙð ÂÚU, ÂÚUèÿææÍèü ·¤ÿæ/ãæòÜ ÀUæðǸÙð âð Âêßü ©žæÚU ˜æ
·¤ÿæ çÙÚUèÿæ·¤ ·¤æð ¥ßàØ âæñ´Â Îð´Ð ÂÚUèÿææÍèü ¥ÂÙð âæÍ §â
ÂÚUèÿææ ÂéçSÌ·¤æ ·¤æð Üð Áæ â·¤Ìð ãñ´Ð
9. ×æ´»ð ÁæÙð ÂÚU ÂýˆØð·¤ ÂÚUèÿææÍèü çÙÚUèÿæ·¤ ·¤æð ¥ÂÙæ Âýßðàæ ·¤æÇü çι氡Ð
10. ¥Ïèÿæ·¤ Øæ çÙÚUèÿæ·¤ ·¤è çßàæðá ¥Ùé×çÌ ·ð¤ çÕÙæ ·¤æð§ü ÂÚUèÿææÍèü
¥ÂÙæ SÍæÙ Ù ÀUæðǸð´Ð
11. ·¤æØüÚUÌ çÙÚUèÿæ·¤ ·¤æð ¥ÂÙæ ©žæÚU ˜æ çΰ çÕÙæ °ß´ ©ÂçSÍçÌ Â˜æ
ÂÚU ÎéÕæÚUæ ãSÌæÿæÚU ç·¤° çÕÙæ ·¤æð§ü ÂÚUèÿææÍèü ÂÚUèÿææ ãæòÜ Ùãè´ ÀUæðǸð´»ðÐ
ØçÎ ç·¤âè ÂÚUèÿææÍèü Ùð ÎêâÚUè ÕæÚU ©ÂçSÍçÌ Â˜æ ÂÚU ãSÌæÿæÚU Ùãè´
ç·¤° Ìæð Øã ×æÙæ Áæ°»æ ç·¤ ©âÙð ©žæÚU ˜æ Ùãè´ ÜæñÅUæØæ ãñ çÁâð
¥Ùéç¿Ì âæÏÙ ÂýØæð» Ÿæð‡æè ×ð´ ×æÙæ Áæ°»æÐ ÂÚUèÿææÍèü ¥ÂÙð ÕæØð´
ãæÍ ·ð¤ ¥´»êÆðU ·¤æ çÙàææÙ ©ÂçSÍçÌ Â˜æ ×ð´ çΰ »° SÍæÙ ÂÚU
¥ßàØ Ü»æ°¡Ð
12. §Üð€ÅþUæòçÙ·¤/ãSÌ¿æçÜÌ ÂçÚU·¤Ü·¤ °ß´ ×æðÕæ§Ü ȤæðÙ, ÂðÁÚU §ˆØæçÎ
Áñâð ç·¤âè §Üð€ÅþUæòçÙ·¤ ©Â·¤ÚU‡æ ·¤æ ÂýØæð» ßçÁüÌ ãñÐ
13. ÂÚUèÿææ ãæòÜ ×ð´ ¥æ¿ÚU‡æ ·ð¤ çÜ° ÂÚUèÿææÍèü Á.°.Õ./ÕæðÇüU ·ð¤ âÖè
çÙØ×æð´ °ß´U çßçÙØ×æð´ mæÚUæ çÙØç×Ì ãæð´»ðÐ ¥Ùéç¿Ì âæÏÙ ÂýØæð» ·ð¤
âÖè ×æ×Üæð´ ·¤æ Èñ¤âÜæ Á.°.Õ./ÕæðÇüU ·ð¤ çÙØ×æð´ °ß´ çßçÙØ×æð´ ·ð¤
¥ÙéâæÚU ãæð»æÐ
14. ç·¤âè Öè çSÍçÌ ×ð´ ÂÚUèÿææ ÂéçSÌ·¤æ ÌÍæ ©žæÚU Â˜æ ·¤æ ·¤æð§ü Öè Öæ»
¥Ü» Ùãè´ ç·¤Øæ Áæ°»æÐ
15. ÂÚUèÿææÍèü mæÚUæ ÂÚUèÿææ ·¤ÿæ/ãæòÜ ×ð´ Âýßðàæ ·¤æÇüU ·ð¤ ¥Üæßæ
ç·¤âè Öè Âý·¤æÚU ·¤è ÂæÆ÷UØ âæ×»ýè, ×éçÎýÌ Øæ ãSÌçÜç¹Ì,
·¤æ»Á ·¤è Âç¿üØæ¡, ÂðÁÚU, ×æðÕæ§Ü ȤæðÙ Øæ ç·¤âè Öè Âý·¤æÚU
·ð¤ §Üð€ÅþUæòçÙ·¤ ©Â·¤ÚU‡ææð´ Øæ ç·¤âè ¥‹Ø Âý·¤æÚU ·¤è âæ×»ýè
·¤æð Üð ÁæÙð Øæ ©ÂØæð» ·¤ÚUÙð ·¤è ¥Ùé×çÌ Ùãè´ ãñÐ
A/Page 40