JEE Main 2015 Question Paper B.Tech

This booklet contains 40 printed pages. No. :
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PAPER - 1 : PHYSICS, CHEMISTRY & MATHEMATICS Test Booklet Code
ÂýàÙÂéçSÌ·¤æ - 1 : ÖæñçÌ·¤ çߙææÙ, ÚUâæØÙ çߙææÙ ÌÍæ »ç‡æÌ ÂÚèÿææ ÂéçSÌ·¤æ â´·ð¤Ì

A
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consisting of Physics, Chemistry and Mathematics having ÂýàÙæ𴠷𤠥´·¤ â×æÙ ãñ´Ð ÂýˆØð·¤ ÂýàÙ ·ð¤ âãè ©žæÚU ·ð¤ çÜ° 4 (¿æÚU)
30 questions in each part of equal weightage. Each question
is allotted 4 (four) marks for correct response.
¥´·¤ çÙÏæüçÚUÌ ç·¤Øð »Øð ãñ´Ð
6. Candidates will be awarded marks as stated above in instruction 6. ¥ØçÍüØæð´ ·¤æð ÂýˆØð·¤ âãè ©žæÚU ·ð¤ çÜ° ©ÂÚUæð€Ì çÙÎðüàæ٠ⴁØæ 5 ·ð¤
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will be deducted for indicating incorrect response of each question. ¼ ßæ´ Öæ» ·¤æÅU çÜØæ ÁæØð»æÐ ØçÎ ©žæÚU ˜æ ×ð´ ç·¤âè ÂýàÙ ·¤æ ©žæÚU
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up more than one response in any question will be treated as ©âð »ÜÌ ©žæÚU ×æÙæ ÁæØð»æ ¥æñÚU ©ÂÚUæð€Ì çÙÎðüàæ 6 ·ð¤ ¥ÙéâæÚU ¥´·¤ ·¤æÅU
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marking responses on Side-1 and Side–2 of the Answer Sheet. ·¤ÚUÙð ãðÌé ·ð¤ßÜ ÙèÜð/·¤æÜð ÕæòÜ Œß槴ÅU ÂðÙ ·¤æ ãè ÂýØæð» ·¤Úð´UÐ
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çÙÚUèÿæ·¤ ·¤æð ¥ßàØ âæñ´Â Îð´Ð ÂÚUèÿææÍèü ¥ÂÙð âæÍ §â ÂÚUèÿææ ÂéçSÌ·¤æ
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¥»ÚU Øã çÖóæ ãæð Ìæð ÂÚUèÿææÍèü ÎêâÚUè ÂÚUèÿææ ÂéçSÌ·¤æ ¥æñÚU ©žæÚU ˜æ ÜðÙð
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Name of the Candidate (in Capital letters ) :
ÂÚèÿææÍèü ·¤æ Ùæ× (ÕǸð ¥ÿæÚæð´ ×ð´) Ñ
Roll Number : in figures
¥Ùé·¤ý ×æ´·¤ Ñ ¥´·¤æð´ ×ð´
: in words
Ñ àæŽÎæð´ ×ð´
Examination Centre Number :
ÂÚèÿææ ·ð¤‹Îý ِÕÚU Ñ
Name of Examination Centre (in Capital letters) :
ÂÚUèÿææ ·ð¤‹Îý ·¤æ Ùæ× (ÕǸð ¥ÿæÚUæð´ ×ð´ ) Ñ
Candidate’s Signature : 1. Invigilator’s Signature :
ÂÚèÿææÍèü ·ð¤ ãSÌæÿæÚ Ñ çÙÚèÿæ·¤ ·ð¤ ãSÌæÿæÚ Ñ
2. Invigilator’s Signature :
çÙÚèÿæ·¤ ·ð¤ ãSÌæÿæÚ Ñ

PART A — PHYSICS Öæ» A — ÖæñçÌ·¤ çߙææÙ
1. Two stones are thrown up simultaneously 1. ç·¤âè 240 m ª¡¤¿è ¿æðÅUè ·ð¤ °·¤ ç·¤ÙæÚðU âð, Îæð
from the edge of a cliff 240 m high with ˆÍÚUæð´ ·¤æð °·¤âæÍ ª¤ÂÚU ·¤è ¥æðÚU Èð´¤·¤æ »Øæ ãñ, §Ù·¤è
initial speed of 10 m/s and 40 m/s ÂýæÚ´UçÖ·¤ ¿æÜ ·ý¤×àæÑ 10 m/s ÌÍæ 40 m/s ãñ, Ìæð,
respectively. Which of the following graph çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙâæ »ýæȤ (¥æÜð¹) ÂãÜð ˆÍÚU
best represents the time variation of ·ð¤ âæÂðÿæ ÎêâÚðU ˆÍÚU ·¤è çSÍçÌ ·ð¤ â×Ø çß¿ÚU‡æ
relative position of the second stone with (ÂçÚUßÌüÙ) ·¤æð âßæüçÏ·¤ âãè ÎàææüÌæ ãñ?
respect to the first ?

(Assume stones do not rebound after (×æÙ ÜèçÁ° ç·¤, ˆÍÚU Á×èÙ âð ÅU·¤ÚUæÙð ·ð¤ Âà¿æÌ
hitting the ground and neglect air ª¤ÂÚU ·¤è ¥æðÚU Ùãè´ ©ÀUÜÌð ãñ´ ÌÍæ ßæØé ·¤æ ÂýçÌÚUæðÏ
resistance, take g510 m/s2) Ù»‡Ø ãñ, çÎØæ ãñ g510 m/s2)
(The figures are schematic and not drawn to (Øãæ¡ »ýæȤ ·ð¤ßÜ ÃØßSÍæ ¥æÚðU¹ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤
scale) ¥ÙéâæÚU Ùãè´ ãñ´)

(1) (1)

(2) (2)

(3) (3)

(4) (4)

A/Page 2 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

2. The period of oscillation of a simple 2. ç·¤âè âÚUÜ ÜæðÜ·¤ ·¤æ ¥æßÌü, T 5 2p L ãñÐ
g
L
pendulum is T 5 2p . Measured value L ·¤æ ×æçÂÌ ×æÙ 20.0 cm ãñ, çÁâ·¤è ØÍæÍüÌæ
g
of L is 20.0 cm known to 1 mm accuracy 1 mm ãñÐ §â ÜæðÜ·¤ ·ð¤ 100 ÎæðÜÙæð´ ·¤æ â×Ø
and time for 100 oscillations of the 90 s ãñ, çÁâð 1s çßÖðÎÙ ·¤è ƒæǸè âð ÙæÂæ »Øæ ãñÐ Ìæð,
pendulum is found to be 90 s using a wrist g ·ð¤ çÙÏæüÚU‡æ ×ð´ ØÍæÍüÌæ ãæð»è Ñ
watch of 1s resolution. The accuracy in
the determination of g is :

(1) 2% (1) 2%

(2) 3% (2) 3%

(3) 1% (3) 1%

(4) 5% (4) 5%

3. 3.

Given in the figure are two blocks A and B Øãæ¡ ¥æÚðU¹ ×ð´ Îæð ŽÜæò·¤ (»éÅU·ð¤) A ¥æñÚU B ÎàææüØð »Øð
of weight 20 N and 100 N, respectively. ãñ´ çÁÙ·ð¤ ÖæÚU ·ý¤×àæÑ 20 N ÌÍæ 100 N ãñ´Ð §‹ãð´,
These are being pressed against a wall by °·¤ ÕÜ F mæÚUæ ç·¤âè ÎèßæÚU ÂÚU ÎÕæØæ Áæ ÚUãæ ãñÐ
a force F as shown. If the coefficient of ØçÎ ƒæáü‡æ »é‡ææ´·¤ ·¤æ ×æÙ, A ÌÍæ B ·ð¤ Õè¿ 0.1
friction between the blocks is 0.1 and ÌÍæ B ¥æñÚU ÎèßæÚU ·ð¤ Õè¿ 0.15 ãñ Ìæð, ÎèßæÚU mæÚUæ
between block B and the wall is 0.15, the ŽÜæò·¤ B ÂÚU Ü»æ ÕÜ ãæð»æ Ñ
frictional force applied by the wall on block
B is :

(1) 100 N (1) 100 N

(2) 80 N (2) 80 N

(3) 120 N (3) 120 N

(4) 150 N (4) 150 N

A/Page 3 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

4. A particle of mass m moving in the 4. x-çÎàææ ×ð´ 2v ¿æÜ âð ¿ÜÌð ãé° m ÎýÃØ×æÙ ·ð¤ °·¤
x direction with speed 2v is hit by another ·¤‡æ âð, y-çÎàææ ×ð´ v ßð» âð ¿ÜÌæ ãé¥æ 2m ÎýÃØ×æÙ
particle of mass 2m moving in the ·¤æ °·¤ ·¤‡æ, ÅU·¤ÚUæÌæ ãñÐ ØçÎ Øã ⴃæÅ÷UÅU (ÅU€·¤ÚU)
y direction with speed v. If the collision is Âê‡æüÌÑ ¥ÂýˆØæSÍ ãñ Ìæð, ÅU€·¤ÚU ·ð¤ ÎæñÚUæÙ ª¤Áæü ·¤æ ÿæØ
perfectly inelastic, the percentage loss in (ãæçÙ) ãæð»è Ñ
the energy during the collision is close to :

(1) 44% (1) 44%

(2) 50% (2) 50%

(3) 56% (3) 56%

(4) 62% (4) 62%

5. Distance of the centre of mass of a solid 5. ç·¤âè °·¤â×æÙ ÆUæðâ àæ´·é¤ ·ð¤ ÎýÃØ×æÙ ·ð¤‹Îý ·¤è
uniform cone from its vertex is z0. If the ©â·ð¤ àæèáü âð ÎêÚUè z0 ãñÐ ØçÎ àæ´·é¤ ·ð¤ ¥æÏæÚU ·¤è
radius of its base is R and its height is h ç˜æ’Øæ R ÌÍæ àæ´·é¤ ·¤è ª¡¤¿æ§ü h ãæð Ìæð z0 ·¤æ ×æÙ
then z0 is equal to : çِÙæ´ç·¤Ì ×ð´ âð ç·¤â·ð¤ ÕÚUæÕÚU ãæð»æ?

h2 h2
(1) (1)
4R 4R

3h 3h
(2) (2)
4 4

5h 5h
(3) (3)
8 8

3h 2 3h 2
(4) (4)
8R 8R

A/Page 4 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

6. From a solid sphere of mass M and radius 6. ç·¤âè ÆUæðâ »æðÜð ·¤æ ÎýÃØ×æÙ M ÌÍæ §â·¤è ç˜æ’Øæ
R a cube of maximum possible volume is R ãñÐ §â×ð´ âð ¥çÏ·¤Ì× â´Öß ¥æØÌÙ ·¤æ °·¤
cut. Moment of inertia of cube about an €ØêÕ (ƒæÙ) ·¤æÅU çÜØæ ÁæÌæ ãñÐ §â €ØêÕ ·¤æ
axis passing through its center and ÁǸˆß ¥æƒæê‡æü ç·¤ÌÙæ ãæð»æ, ØçÎ, §â·¤è ƒæê‡æüÙ-¥ÿæ,
perpendicular to one of its faces is : §â·ð¤ ·ð¤‹Îý âð ãæð·¤ÚU »é$ÁÚUÌè ãñ ÌÍæ §â·ð¤ ç·¤âè °·¤
Ȥܷ¤ ·ð¤ ܐÕßÌ÷U ãñ?
MR 2 MR 2
(1) (1)
32 2p 32 2p

MR 2 MR 2
(2) (2)
16 2p 16 2p

4MR 2 4MR 2
(3) (3)
9 3p 9 3p

4MR 2 4MR 2
(4) (4)
3 3p 3 3p

7. From a solid sphere of mass M and radius 7. °·¤ ÆUæðâ »æðÜð ·¤æ ÎýÃØ×æÙ M ÌÍæ ç˜æ’Øæ R ãñÐ
R R
R, a spherical portion of radius is §ââð ç˜æ’Øæ ·¤æ °·¤ »æðÜèØ Öæ», ¥æÚðU¹ ×ð´ ÎàææüØð
2 2
removed, as shown in the figure. Taking »Øð ¥ÙéâæÚU ·¤æÅU çÜØæ ÁæÌæ ãñÐ r5:(¥Ù‹Ì) ÂÚU
gravitational potential V50 at r5:, the »éL¤ˆßèØ çßÖß ·ð¤ ×æÙ V ·¤æð àæê‹Ø (V50) ×æÙÌð
potential at the centre of the cavity thus ãé°, §â Âý·¤æÚU ÕÙð ·¤æðÅUÚU (·ñ¤çßÅUè) ·ð¤ ·ð¤‹Îý ÂÚU,
formed is : »éL¤ˆßèØ çßÖß ·¤æ ×æÙ ãæð»æ Ñ
(G5 gravitational constant) (G5 »éL¤ˆßèØ çSÍÚUæ¡·¤ ãñ )

2 GM 2 GM
(1) (1)
2R 2R
2 GM 2 GM
(2) (2)
R R
2 2GM 2 2GM
(3) (3)
3R 3R
2 2GM 2 2GM
(4) (4)
R R

A/Page 5 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

8. A pendulum made of a uniform wire of 8. ç·¤âè °·¤â×æÙ ÌæÚU ·¤è ¥ÙéÂýSÍ·¤æÅU ·¤æ ÿæð˜æȤÜ
cross sectional area A has time period T. ‘A’ ãñÐ §ââð ÕÙæØð »Øð °·¤ ÜæðÜ·¤ ·¤æ ¥æßÌü·¤æÜ
When an additional mass M is added to T ãñÐ §â ÜæðÜ·¤ ·ð¤ »æðÜ·¤ âð °·¤ ¥çÌçÚU€Ì M
its bob, the time period changes to TM. If ÎýÃØ×æÙ ÁæðǸ ÎðÙð âð ÜæðÜ·¤ ·¤æ ¥æßÌü·¤æÜ ÂçÚUßçÌüÌ
the Young’s modulus of the material of the ãæð·¤ÚU TM ãæð ÁæÌæ ãñÐ ØçÎ §â ÌæÚU ·ð¤ ÂÎæÍü ·¤æ Ø´»
1 1
wire is Y then
Y
is equal to : »é‡ææ´·¤ ‘Y’ ãæð Ìæð Y ·¤æ ×æÙ ãæð»æ Ñ
(g5gravitational acceleration) (g5»éL¤ˆßèØ ˆßÚU‡æ)
 TM 2  A  TM 2  A
(1)   21 (1)   21
 T   Mg  T   Mg

 TM 2  Mg  TM 2  Mg
(2)   21 (2)   21
 T   A  T   A

 2 2
T   A  T   A
(3) 1 2  M   (3) 1 2  M  
  T   Mg   T   Mg

 2 2
 T   A   T   A
(4) 1 2    (4) 1 2   
  TM   Mg   TM   Mg
   

9. Consider a spherical shell of radius R at 9. ç·¤âè »æðÜèØ ·¤æðàæ (àæñÜ) ·¤è ç˜æ’Øæ R ãñ ¥æñÚU §â·¤æ
temperature T. The black body radiation Ìæ T ãñÐ §â·ð¤ ÖèÌÚU ·ë¤çc‡æ·¤æ çßç·¤ÚU‡ææð´ ·¤æð ȤæðÅUæòÙæð´
inside it can be considered as an ideal gas ·¤è °·¤ °ðâè ¥æÎàæü »ñâ ×æÙæ Áæ â·¤Ìæ ãñ çÁâ·¤è
of photons with internal energy per unit
ÂýçÌ §·¤æ§ü ¥æØÌÙ ¥æ‹ÌçÚU·¤ ª¤Áæü, u 5 U ; T 4
U V
volume u5 ; T4 and pressure
V 1 U
ÌÍæ ÎæÕ, p 5 3  V  ãñÐ ØçÎ §â ·¤æðàæ ×ð́ L¤Î÷Ïæðc×
1 U  
p5   . If the shell now undergoes
3 V ÂýâæÚU ãæð Ìæð, T ÌÍæ R ·ð¤ Õè¿ â´Õ´Ï ãæð»æ Ñ
an adiabatic expansion the relation
between T and R is :
(1) T ; e2R (1) T ; e2R
(2) T ; e23R (2) T ; e23R
1 1
(3) T; (3) T;
R R
1 1
(4) T; 3 (4) T;
R R3

A/Page 6 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

10. A solid body of constant heat capacity 10. °·¤ ÆUæðâ ç´ÇU (ßSÌé) ·¤è çSÍÚU ª¤c×æ ÏæçÚUÌæ
1 J/8C is being heated by keeping it in 1 J/8C ãñÐ §â·¤æ𠪤c×·¤æð´ (ª¤c×æ Ö´ÇUæÚUæð´) ·ð¤ âÂ·ü¤
contact with reservoirs in two ways : ×ð´ ÚU¹·¤ÚU çِ٠Îæð Âý·¤æÚU âð »×ü ç·¤Øæ ÁæÌæ ãñ,
(i) Sequentially keeping in contact with (i) ¥Ùé·ý¤ç×·¤ M¤Â âð 2 ª¤c×·¤æð´ ·ð¤ âÂ·ü¤ ×ð´
2 reservoirs such that each reservoir §â Âý·¤æÚU ÚU¹·¤ÚU ç·¤ ÂýˆØð·¤ ª¤c×·¤ â×æÙ
supplies same amount of heat. ×æ˜ææ ×ð´ ª¤c×æ ÎðÌæ ãñ,
(ii) Sequentially keeping in contact with (ii) ¥Ùé·ý¤ç×·¤ M¤Â âð 8 ª¤c×·¤æð´ ·ð¤ âÂ·ü¤ ×ð´
8 reservoirs such that each reservoir §â Âý·¤æÚU ÚU¹·¤ÚU ç·¤ ÂýˆØð·¤ ª¤c×·¤ â×æÙ
supplies same amount of heat. ×æ˜ææ ×ð´ ª¤c×æ ÎðÌæ ãñ,
In both the cases body is brought from ÎæðÙæð´ çSÍçÌØæð´ ×ð´ ç´ÇU ·¤æ ÂýæÚ´UçÖ·¤ Ìæ 1008C ÌÍæ
initial temperature 1008C to final ¥ç‹Ì× Ìæ 2008C ãñÐ Ìæð, §Ù Îæð çSÍçÌØæð´ ×ð´ ç´ÇU
temperature 2008C. Entropy change of the ·¤è °‹ÅþUæòÂè ×ð´ ÂçÚUßÌüÙ ãæð»æ, ·ý¤×àæÑ
body in the two cases respectively is :
(1) ln2, 4ln2 (1) ln2, 4ln2
(2) ln2, ln2 (2) ln2, ln2
(3) ln2, 2ln2 (3) ln2, 2ln2
(4) 2ln2, 8ln2 (4) 2ln2, 8ln2

11. Consider an ideal gas confined in an 11. °·¤ ¥æÎàæü »ñ â ç·¤âè ՋΠ(â´ ß ë Ì ), çßØé € Ì
isolated closed chamber. As the gas (çßÜç»Ì) ·¤ÿæ ×ð´ âèç×Ì (ÚU¹è) ãñÐ §â »ñâ ×´ð´
undergoes an adiabatic expansion, the L¤Î÷Ïæðc× ÂýâæÚU ãæðÙð ÂÚU, §â·ð¤ ¥‡æé¥æð´ ·ð¤ Õè¿ ÅU€·¤ÚU
average time of collision between ·¤æ ¥æñâÌ ·¤æÜ (â×Ø) Vq ·ð¤ ¥ÙéâæÚU Õɸ ÁæÌæ ãñ,
q
molecules increases as V , where V is the Áãæ¡ V »ñâ ·¤æ ¥æØÌÙ ãñÐ Ìæð q ·¤æ ×æÙ ãæð»æ :
volume of the gas. The value of q is :  Cp 
Cp  g 5 
  Cv 
g 5 
 Cv 

3g 1 5 3g 1 5
(1) (1)
6 6
3g 2 5 3g 2 5
(2) (2)
6 6

(3) g11 (3) g11
2 2
g21 g21
(4) (4)
2 2

A/Page 7 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

12. For a simple pendulum, a graph is plotted 12. ç·¤âè âÚUÜ ÜæðÜ·¤ ·ð¤ çÜØð, ©â·ð¤ çßSÍæÂÙ d ÌÍæ
between its kinetic energy (KE) and ©â·¤è »çÌÁ ª¤Áæü ·ð¤ Õè¿ ¥æñÚU çßSÍæÂÙ d ÌÍæ
potential energy (PE) against its ©â·¤è çSÍçÌÁ ª¤Áæü ·ð¤ Õè¿ »ýæȤ ¹è´¿ð »Øð ãñ´Ð
displacement d. Which one of the çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙ âæ »ýæȤ (¥æÜð¹) âãè ãñ?
following represents these correctly ? (Øãæ¡ »ýæȤ ·ð¤ßÜ ÃØßSÍæ ¥æÚðU¹ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤
(graphs are schematic and not drawn to scale) ¥ÙéâæÚU Ùãè´ ãñ´)

(1) (1)

(2) (2)

(3) (3)

(4) (4)

13. A train is moving on a straight track with 13. °·¤ ÅþðUÙ (ÚðUÜ»æǸè) âèÏè ÂÅUçÚUØæð´ ÂÚU 20 ms21 ·¤è
speed 20 ms21. It is blowing its whistle at ¿æÜ âð »çÌ ·¤ÚU ÚUãè ãñÐ §â·¤è âèÅUè ·¤è ŠßçÙ ·¤è
the frequency of 1000 Hz. The percentage ¥æßëçžæ 1000 Hz ãñÐ ØçÎ ŠßçÙ ·¤è ßæØé ×ð´ ¿æÜ
change in the frequency heard by a person 320 ms21 ãæð Ìæð, ÂÅUçÚUØæð´ ·ð¤ çÙ·¤ÅU ¹Ç¸ð ÃØç€Ì ·ð¤
standing near the track as the train passes Âæâ âð ÅþðUÙ ·ð¤ »éÁÚUÙð ÂÚU, ©â ÃØç€Ì mæÚUæ âéÙè »§ü
him is (speed of sound5320 ms21) close âèÅUè ·¤è ŠßçÙ ·¤è ¥æßëçžæ ×ð´ ÂýçÌàæÌ ÂçÚUßÌüÙ ãæð»æ
to : ֻܻ Ñ
(1) 6% (1) 6%
(2) 12% (2) 12%
(3) 18% (3) 18%
(4) 24% (4) 24%

A/Page 8 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

14. A long cylindrical shell carries positive 14. ç·¤âè ܐÕð ÕðÜÙæ·¤æÚU ·¤æðàæ ·ð¤ ª¤ÂÚUè Öæ» ×ð´ ÏÙæˆ×·¤
surface charge s in the upper half and ÂëcÆU ¥æßðàæ s ÌÍæ çÙ¿Üð Öæ» ×ð´ «¤‡ææˆ×·¤ ÂëcÆU
negative surface charge 2s in the lower ¥æßðàæ 2s ãñ´Ð §â ÕðÜÙ (çâç܋ÇUÚU) ·ð¤ ¿æÚUæð´
half. The electric field lines around the ¥æðÚU çßléÌ ÿæð˜æ-ÚðU¹æØð´, Øãæ¡ ÎàææüØð »Øð ¥æÚð¹æð´ ×ð´ âð
cylinder will look like figure given in : 緤⠥æÚðU¹ ·ð¤ â×æÙ ãæð´»è?
(figures are schematic and not drawn to scale) (Øã ¥æÚðU¹ ·ð¤ßÜ ÃØßSÍæ ¥æÚðU¹ ãñ ¥æñÚU S·ð¤Ü ·ð¤
¥ÙéâæÚU Ùãè´ ãñ)

(1) (1)

(2) (2)

(3) (3)

(4) (4)

15. A uniformly charged solid sphere of radius 15. R ç˜æ’Øæ ·ð¤ ç·¤âè °·¤â×æÙ ¥æßðçàæÌ ÆUæðâ »æðÜð ·ð¤
R has potential V0 (measured with respect ÂëcÆU ·¤æ çßÖß V0 ãñ (: ·ð¤ âæÂðÿæ ×æÂæ »Øæ)Ð §â
to :) on its surface. For this sphere the
V0
equipotential surfaces with potentials »æðÜð ·ð¤ çÜØð, 3V0 , 5V0 , 3V0 ÌÍæ çßÖßæð´
2 4 4 4
3V0 5V0 3V0
, ,
V
and 0 have radius R1, ßæÜð â×çßÖßè Âë c ÆU æ ð ´ ·¤è ç˜æ’ØæØð ´ , ·ý ¤ ×àæÑ
2 4 4 4 R1, R2, R3 ÌÍæ R4 ãñ´Ð Ìæð,
R2, R3 and R4 respectively. Then

(1) R150 and R2 > (R42R3) (1) R150 ÌÍæ R2 > (R42R3)
(2) R1 ¹ 0 and (R22R1) > (R42R3) (2) R1 ¹ 0 ÌÍæ (R22R1) > (R42R3)
(3) R150 and R2 < (R42R3) (3) R150 ÌÍæ R2 < (R42R3)
(4) 2R < R4 (4) 2R < R4

A/Page 9 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

16. In the given circuit, charge Q2 on the 2mF 16. çÎØð »Øð ÂçÚUÂÍ ×ð´, C ·ð¤ ×æÙ ·ð¤ 1mF âð 3mF
capacitor changes as C is varied from 1mF ÂçÚUßçÌüÌ ãæðÙð âð, 2mF â´ÏæçÚU˜æ ÂÚU ¥æßðàæ Q2 ×ð´
to 3mF. Q2 as a function of ‘C’ is given ÂçÚUßÌüÙ ãæðÌæ ãñÐ ‘C’ ·ð¤ ȤÜÙ ·ð¤ M¤Â ×ð´ Q2 ·¤æð
properly by : (figures are drawn schematically ·¤æñÙ âæ ¥æÜð¹ âãè ÎàææüÌæ ãñ? (¥æÜð¹ ·ð¤ßÜ
and are not to scale) ÃØßSÍæ ¥æÚðU¹ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤ ¥ÙéâæÚU Ùãè´ ãñ´Ð)

(1) (1)

(2) (2)

(3) (3)

(4) (4)

17. When 5V potential difference is applied 17. 0.1 m Ü´Õð ç·¤âè ÌæÚU ·ð¤ çâÚUæð´ ·ð¤ Õè¿ 5V çßÖßæ´ÌÚUU
across a wire of length 0.1 m, the drift ¥æÚUæðçÂÌ ·¤ÚUÙð âð §Üð€ÅþUæòÙæð´ ·¤è ¥Âßæã ¿æÜ
speed of electrons is 2.531024 ms21. If 2.531024 ms21 ãæðÌè ãñÐ ØçÎ §â ÌæÚU ×ð´ §Üð€ÅþUæòÙ
the electron density in the wire is ƒæÙˆß 831028 m23 ãæð Ìæð, §â ·ð¤ ÂÎæÍü ·¤è
831028 m23, the resistivity of the material ÂýçÌÚUæðÏ·¤Ìæ ãæð»è, ֻܻ Ñ
is close to :
(1) 1.631028 Vm (1) 1.631028 Vm
(2) 1.631027 Vm (2) 1.631027 Vm
(3) 1.631026 Vm (3) 1.631026 Vm
(4) 1.631025 Vm (4) 1.631025 Vm

A/Page 10 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

18. 18.

In the circuit shown, the current in the 1V ÎàææüØð »Øð ÂçÚUÂÍ ×ð´ 1V ÂýçÌÚUæðÏ·¤ âð ÂýßæçãÌ ÏæÚUæ
resistor is : ãæð»è Ñ
(1) 1.3 A, from P to Q (1) 1.3 A, P âð Q ·¤è ¥æðÚU

(2) 0A (2) 0 (àæê‹Ø) A

(3) 0.13 A, from Q to P (3) 0.13 A, Q âð P ·¤æð

(4) 0.13 A, from P to Q (4) 0.13 A, P âð Q ·¤æð

19. Two coaxial solenoids of different radii 19. Îæð â×æÿæè ÂçÚUÙæçÜ·¤æ¥æð´ ×ð´, ÂýˆØð·¤ âð I ÏæÚUæ °·¤ ãè
carry current I in the same direction. Let çÎàææ ×ð´ ÂýßæçãÌ ãæð ÚUãè ãñÐ ØçÎ, ÕæãÚUè ÂçÚUÙæçÜ·¤æ
→ ·ð¤ ·¤æÚU‡æ, ÖèÌÚUè ÂçÚUÙæçÜ·¤æ ÂÚU ¿éÕ·¤èØ ÕÜ
F1 be the magnetic force on the inner →
→ F1 ÌÍæ ÖèÌÚUè ÂçÚUÙæçÜ·¤æ ·ð¤ ·¤æÚU‡æ, ÕæãÚUè ÂçÚUÙæçÜ·¤æ
solenoid due to the outer one and F2 be
→
the magnetic force on the outer solenoid ÂÚU ¿éÕ·¤èØ ÕÜ F2 ãæð Ìæð Ñ
due to the inner one. Then :

→ → → →
(1) F1 5 F25 0 (1) F1 5 F25 0

→ → →
(2) F1 is radially inwards and F2 is (2) F1 ÖèÌÚU ·¤è ¥æðÚU ß ¥ÚUèØ (ç˜æ’Ø) ãñ ¥æñÚU
→
radially outwards F2 ÕæãÚU ·¤è ¥æðÚU ß ¥ÚUèØ ãñÐ

→ → → →
(3) F1 is radially inwards and F2 50 (3) F1 ÖèÌÚU ·¤è ¥æðÚU ß ¥ÚUèØ ãñ ÌÍæ F2 50
ãñÐ
→ → → →
(4) F1 is radially outwards and F2 50 (4) F1 ÕæãÚU ·¤è ¥æðÚU ß ¥ÚUèØ ãñ ÌÍæ F2 50
ãñÐ
A/Page 11 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

20. 20.

Two long current carrying thin wires, both Îæð ÂÌÜð ܐÕð ÌæÚUæð´ ×ð´ ÂýˆØð·¤ âð I ÏæÚUæ ÂýßæçãÌ ãæð ÚUãè
with current I, are held by insulating ãñÐ §‹ãð´ L ܐÕæ§ü ·ð¤ çßléÌÚUæðÏè Ïæ»æð´ âð ÜÅU·¤æØæ
threads of length L and are in equilibrium »Øæ ãñÐ §Ù Ïæ»æð´ ×ð´ ÂýˆØð·¤ ·ð¤ mæÚUæ ª¤ŠßæüÏÚU çÎàææ âð
as shown in the figure, with threads ‘u’ ·¤æð‡æ ÕÙæÙð ·¤è çSÍçÌ ×ð´, Øð ÎæðÙæð´ ÌæÚU âæØæßSÍæ
making an angle ‘u’ with the vertical. If ×ð´ ÚUãÌð ãñ´Ð ØçÎ §Ù ÌæÚUæð´ ·¤è ÂýçÌ §·¤æ§ü ܐÕæ§ü
wires have mass l per unit length then the ÎýÃØ×æÙ l ãñ ÌÍæ g »éL¤ˆßèØ ˆßÚU‡æ ãñ Ìæð, I ·¤æ ×æÙ
value of I is : ãæð»æ Ñ
(g5gravitational acceleration)

plgL plgL
(1) sinu (1) sinu
m0 cosu m0 cosu

plgL plgL
(2) 2sinu (2) 2sinu
m0 cosu m0 cosu

pgL pgL
(3) 2 tan u (3) 2 tan u
m0 m0

plgL plgL
(4) tan u (4) tan u
m0 m0

A/Page 12 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

21. A rectangular loop of sides 10 cm and 21. 10 cm ÌÍæ 5 cm ÖéÁæ¥æ𴠷𤠰·¤ ¥æØÌæ·¤æÚU ÜêÂ
5 cm carrying a current I of 12 A is placed (Âæàæ) âð °·¤ çßléÌ ÏæÚUæ, I 5 12 A, ÂýßæçãÌ ãæðU
in different orientations as shown in the ÚUãè ãñÐ §â Âæàæ ·¤æð ¥æÚðU¹ ×ð´ ÎàææüØð »Øð ¥ÙéâæÚU
figures below : çßçÖóæ ¥çÖçߋØæâæð´ (çSÍçÌØæð´) ×ð´ ÚU¹æ »Øæ ãñÐ

(a) (a)

(b) (b)

(c) (c)

(d) (d)

If there is a uniform magnetic field of ØçÎ ßãæ¡ 0.3 T ÌèßýÌæ ·¤æ ·¤æð§ü °·¤â×æÙ ¿éÕ·¤èØ
0.3 T in the positive z direction, in which ÿæð˜æ, ÏÙæˆ×·¤ z çÎàææ ×ð´ çßl×æÙ ãñ Ìæð, ÎàææüØð »Øð
orientations the loop would be in (i) stable 緤⠥çÖçߋØæâ ×ð´, Øã Âæàæ (ÜêÂ) (i) SÍæØè
equilibrium and (ii) unstable equilibrium ? â´ÌéÜÙ ÌÍæ (ii) ¥SÍæØè â´ÌéÜÙ ×ð´, ãæð»æ?
(1) (a) and (b), respectively (1) ·ý¤×àæÑ (a) ÌÍæ (b) ×ð´
(2) (a) and (c), respectively (2) ·ý¤×àæÑ (a) ÌÍæ (c) ×ð´
(3) (b) and (d), respectively (3) ·ý¤×àæÑ (b) ÌÍæ (d) ×ð´
(4) (b) and (c), respectively (4) ·ý¤×àæÑ (b) ÌÍæ (c) ×ð´
A/Page 13 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

22. An inductor (L50.03H) and a resistor 22. ÎàææüØð »Øð ÂçÚUÂÍ ×ð´, °·¤ ÂýðÚU·¤ (L50.03H) ÌÍæ
(R50.15 kV) are connected in series to a °·¤ ÂýçÌÚUæðÏ·¤ (R50.15 kV) ç·¤âè 15V çßléÌ
battery of 15V EMF in a circuit shown ßæã·¤ ÕÜ (§ü.°×.°È¤) ·¤è ÕñÅUÚUè âð ÁéǸð ãñ´Ð ·é´¤Áè
below. The key K1 has been kept closed K1 ·¤æð ÕãéÌ â×Ø Ì·¤ ՋΠÚU¹æ »Øæ ãñÐ §â·ð¤
for a long time. Then at t50, K1 is opened Âà¿æÌ÷ â×Ø t50 ÂÚU, K1 ·¤æð ¹æðÜ ·¤ÚU âæÍ ãè
and key K 2 is closed simultaneously. âæÍ, K2 ·¤æð ՋΠ緤Øæ ÁæÌæ ãñÐ â×Ø t51ms
At t51ms, the current in the circuit will ÂÚU, ÂçÚUÂÍ ×ð´ çßléÌ ÏæÚUæ ãæð»è Ñ (e5@150)
be : (e5@150)

(1) 100 mA (1) 100 mA

(2) 67 mA (2) 67 mA

(3) 6.7 mA (3) 6.7 mA

(4) 0.67 mA (4) 0.67 mA

23. A red LED emits light at 0.1 watt uniformly 23. °·¤ ÜæÜ Ú´U» ·¤æ °Ü.§ü.ÇUè. (Âý·¤æàæ ©ˆâÁü·¤ ÇUæØæðÇU)
around it. The amplitude of the electric 0.1 ßæÅU ÂÚU, °·¤â×æÙ Âý·¤æàæ ©ˆâçÁüÌ ·¤ÚUÌæ ãñÐ
field of the light at a distance of 1 m from ÇUæØæðÇU âð 1 m ÎêÚUè ÂÚU, §â Âý·¤æàæ ·ð¤ çßléÌ ÿæð˜æ ·¤æ
the diode is : ¥æØæ× ãæð»æ Ñ

(1) 1.73 V/m (1) 1.73 V/m

(2) 2.45 V/m (2) 2.45 V/m

(3) 5.48 V/m (3) 5.48 V/m

(4) 7.75 V/m (4) 7.75 V/m

A/Page 14 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

24. Monochromatic light is incident on a glass 24. ·¤æ¡¿ ·ð¤ ç·¤âè çÂý’× ·¤æ ·¤æð‡æ ‘A’ ãñÐ §â ÂÚU
prism of angle A. If the refractive index of °·¤ß‡æèü Âý·¤æàæ ¥æÂçÌÌ ãæðÌæ ãñÐ ØçÎ, çÂý’× ·ð¤
the material of the prism is m, a ray, ÂÎæÍü ·¤æ ¥ÂßÌüÙæ´·¤ m ãñ Ìæð, çÂý’× ·ð¤ AB Ȥܷ¤
incident at an angle u, on the face AB ÂÚU, u ·¤æð‡æ ¥æÂçÌÌ Âý·¤æàæ ·¤è ç·¤ÚU‡æ, çÂý’× ·ð¤
would get transmitted through the face AC Ȥܷ¤ AC âð ÂæÚU»Ì ãæð»è ØçÎ Ñ
of the prism provided :

   1      1  
(1) u > sin21 m sin  A 2 sin21     (1) u > sin21 m sin  A 2 sin21    
   m       m   

   1      1  
(2) u < sin21 m sin  A 2 sin21     (2) u < sin21 m sin  A 2 sin21    
   m       m   

   1      1  
(3) u > cos21 m sin  A 1 sin21     (3) u > cos21 m sin  A 1 sin21    
   m       m   

   1      1  
(4) u < cos21 m sin  A 1 sin21     (4) u < cos21 m sin  A 1 sin21    
   m       m   

25. On a hot summer night, the refractive 25. »ýèc× «¤Ìé ·¤è »×ü ÚUæç˜æ ×ð´, Öê-ÌÜ ·ð¤ çÙ·¤ÅU, ßæØé ·¤æ
index of air is smallest near the ground and ¥ÂßÌüÙæ´·¤ ‹ØêÙÌ× ãæðÌæ ãñ ¥æñÚU Öê-ÌÜ â𠪡¤¿æ§ü ·ð¤
increases with height from the ground. âæÍ ÕɸÌæ ÁæÌæ ãñÐ ØçÎ, ·¤æð§ü Âý·¤æàæ-ç·¤ÚU‡æ-´éÁ
When a light beam is directed horizontally, ÿæñçÌÁ çÎàææ ×ð´ Áæ ÚUãæ ãæð Ìæð, ã槻ð‹â ·ð¤ çâhæ‹Ì âð
the Huygens’ principle leads us to conclude Øã ÂçÚU‡ææ× Âý æ ŒÌ ãæð Ì æ ãñ ç·¤, ¿ÜÌð ãé °
that as it travels, the light beam : Âý·¤æàæ-ç·¤ÚU‡æ ´éÁ Ñ
(1) becomes narrower (1) â´·é¤ç¿Ì (â´·¤è‡æü) ãæð ÁæØð»æÐ
(2) goes horizontally without any (2) çÕÙæ çßÿæðçÂÌ ãé°, ÿæñçÌÁ çÎàææ ×ð´ ¿ÜÌæ
deflection ÚUã»ð æÐ
(3) bends downwards (3) Ùè¿ð ·¤è ¥æðÚU Ûæé·¤ ÁæØð»æÐ
(4) bends upwards (4) ª¤ÂÚU ·¤è ¥æðÚU Ûæé·¤ ÁæØð»æÐ
A/Page 15 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

26. Assuming human pupil to have a radius 26. ØçÎ ×æÙß Ùð˜æ ·¤è ÂéÌÜè ·¤è ç˜æ’Øæ 0.25 cm, ¥æñÚU
of 0.25 cm and a comfortable viewing SÂcÅU âéçßÏæ ÁÙ·¤ Îð¹Ùð ·¤è ÎêÚUè 25 cm ãæð Ìæð,
distance of 25 cm, the minimum separation 500 nm ÌÚ´U»ÎñƒØü ·ð¤ Âý·¤æàæ ×ð´, Îæð ßSÌé¥æð´ ·ð¤ Õè¿
between two objects that human eye can ç·¤ÌÙè ‹ØêÙÌ× ÎêÚUè Ì·¤ ×æÙß Ùð˜æ ©Ù ÎæðÙæð´ ·ð¤ Õè¿
resolve at 500 nm wavelength is : çßÖðÎÙ ·¤ÚU â·ð¤»æ?

(1) 1 mm (1) 1 mm

(2) 30 mm (2) 30 mm

(3) 100 mm (3) 100 mm

(4) 300 mm (4) 300 mm

27. As an electron makes a transition from an 27. ÁÕ ·¤æð§ü §Üð€ÅþUæòÙ, ãæ§ÇþUæðÁÙ Áñâð ÂÚU×æ‡æé /¥æØÙ
excited state to the ground state of a ·¤è ©žæðçÁÌ ¥ßSÍæ âð ‹ØêÙÌ× ª¤Áæü ¥ßSÍæ ×ð´
hydrogen - like atom/ion : â´·ý¤×‡æ ·¤ÚUÌæ ãñ Ìæð ©â·¤è Ñ

(1) its kinetic energy increases but (1) »çÌÁ ª¤Áæü ×ð´ ßëçh ÌÍæ çSÍçÌÁ ª¤Áæü ÌÍæ
potential energy and total energy ·é¤Ü ª¤Áæü ×ð´ ·¤×è ãæðÌè ãñÐ
decrease

(2) kinetic energy, potential energy and (2) »çÌÁ ª¤Áæü, çSÍçÌÁ ª¤Áæü ÌÍæ ·é¤Ü ª¤Áæü ×ð´
total energy decrease ·¤×è ãæð ÁæÌè ãñÐ

(3) kinetic energy decreases, potential (3) »çÌÁ ª¤Áæü ·¤× ãæðÌè ãñ, çSÍçÌÁ ª¤Áæü ÕɸÌè
energy increases but total energy ãñ ¥æñÚU ·é¤Ü ª¤Áæü ßãè ÚUãÌè ãñÐ
remains same

(4) kinetic energy and total energy (4) »çÌÁ ª¤Áæü ß ·é¤Ü ª¤Áæü ·¤× ãæð ÁæÌè ãñ´
decrease but potential energy ç·¤‹Ìé, çSÍçÌÁ ª¤Áæü Õɸ ÁæÌè ãñÐ
increases

A/Page 16 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

28. Match List - I (Fundamental Experiment) 28. âê¿è - I (×êÜ ÂýØæð») ·¤æ âê¿è - II (©â·ð¤ ÂçÚU‡ææ×)
with List - II (its conclusion) and select ·ð¤ âæÍ âé×ðÜÙ (×ñ¿) ·¤èçÁØð ¥æñÚU çِÙæ´ç·¤Ì
the correct option from the choices given çß·¤ËÂæð´ ×ð´ âð âãè çß·¤Ë ·¤æ ¿ØÙ ·¤èçÁØð Ñ
below the list :

List - I List - II ÇÏ¤Í - I ÇÏ¤Í - II
Franck-Hertz Particle nature §âœ‰ËÅË œ‰Í œ‰Ìø˜‰Ë
(A) (i) (A) ­âՙ‰œ‰ ȪÜáÇ §â½ËÕ (i)
Experiment. of light §âœÐ‰Ì±
Photo-electric Discrete energy ŠøËÎ œÕ‰ ÌÄÌÄþ±
(B) (ii) (B) §âœ‰ËÅË ÌÄlα §â½ËÕ (ii)
experiment. levels of atom ‰¦Ëá S±¿U
Davison - Germer Wave nature of ŒÁÕþªãUË×¾ œ‰Í ±¿™U
(C) (iii) (C) ¬ÕUÄÍǾ ¦¼á¿U §â½ËÕ (iii)
Experiment. electron §âœÐ‰Ì±
Structure of
(iv) (iv) §¿U¼ËøËÎ œ‰Í Ǚ¿U¤¾Ë
atom

(1) (A) - (i) (B) - (iv) (C) - (iii) (1) (A) - (i) (B) - (iv) (C) - (iii)

(2) (A) - (ii) (B) - (iv) (C) - (iii) (2) (A) - (ii) (B) - (iv) (C) - (iii)

(3) (A) - (ii) (B) - (i) (C) - (iii) (3) (A) - (ii) (B) - (i) (C) - (iii)

(4) (A) -(iv) (B) - (iii) (C) - (ii) (4) (A) -(iv) (B) - (iii) (C)- (ii)

29. A signal of 5 kHz frequency is amplitude 29. 5 kHz ¥æßëçžæ ·ð¤ ç·¤âè â´·ð¤Ì (çâ‚ÙÜ) ·¤æ
modulated on a carrier wave of frequency 2 MHz ¥æßëçžæ ·¤è ßæã·¤ ÌÚ´U» ÂÚU ¥æØæ× ×æòÇéUÜÙ
2 MHz. The frequencies of the resultant ç·¤Øæ »Øæ ãñÐ Ìæð, ÂçÚU‡ææ×è çâ‚ÙÜ (â´·ð¤Ì) ·¤è
signal is/are : ¥æßëçžæ ãæð»è Ñ

(1) 2 MHz only (1) 2 MHz ·ð¤ßÜ

(2) 2005 kHz, and 1995 kHz (2) 2005 kHz, ÌÍæ 1995 kHz

(3) 2005 kHz, 2000 kHz and 1995 kHz (3) 2005 kHz, 2000 kHz ÌÍæ 1995 kHz

(4) 2000 kHz and 1995 kHz (4) 2000 kHz ÌÍæ 1995 kHz

A/Page 17 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

30. An LCR circuit is equivalent to a damped 30. LCR (°Ü.âè.¥æÚU) ÂçÚUÂÍ ç·¤âè ¥ß×´çÎÌ ÜæðÜ·¤
pendulum. In an LCR circuit the capacitor ·ð¤ ÌéËØ ãæðÌæ ãñÐ ç·¤âè LCR ÂçÚUÂÍ ×ð´ â´ÏæçÚU˜æ ·¤æð
is charged to Q0 and then connected to Q0 Ì·¤ ¥æßðçàæÌ ç·¤Øæ »Øæ ãñ, ¥æñÚU çȤÚU §âð ¥æÚðU¹
the L and R as shown below : ×ð´ ÎàææüØð »Øð ¥ÙéâæÚU L ß R âð ÁæðÇ¸æ »Øæ ãñÐ

If a student plots graphs of the square of ØçÎ °·¤ çßlæÍèü L ·ð¤, Îæð çßçÖóæ ×æÙæð´, L1 ÌÍæ L2
2
maximum charge ( QMax ) on the capacitor (L 1 >L 2) ·ð ¤ çÜØð , â×Ø t ÌÍæ â´ Ï æçÚU ˜ æ ÂÚU
with time(t) for two different values L1 and ¥çÏ·¤Ì× ¥æßðàæ ·ð¤ ß»ü QMax 2
·ð¤ Õè¿ Îæð »ýæȤ
L2 (L1>L2) of L then which of the following
ÕÙæÌæ ãñ Ìæð çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙ âæ »ýæȤ âãè ãñ?
represents this graph correctly ? (plots are
(ŒÜæòÅU ·ð¤ßÜ ÃØßSÍæ ŒÜæòÅU ãñ´ ÌÍæ S·ð¤Ü ·ð¤ ¥ÙéâæÚU
schematic and not drawn to scale)
Ùãè´ ãñ´)

(1)
(1)

(2)
(2)

(3)
(3)

(4)
(4)

A/Page 18 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

PART B — CHEMISTRY Öæ» B — ÚUâæØÙ çߙææÙ
31. The molecular formula of a commercial 31. °·¤ ßæç‡æ’Ø ÚðUç$ÁÙ ·¤æ ¥æç‡ß·¤ âê˜æ C8H7SO3Na
resin used for exchanging ions in water ãñ (¥æç‡ß·¤ ÖæÚU = 206) §â ÚðUç$ÁÙ ·¤è Ca21
softening is C8H7SO3Na (Mol. wt. 206). ¥æØÙ ·¤è ¥çÏ·¤Ì× ¥´Ì»ýüã‡æ ÿæ×Ìæ (×æðÜ ÂýçÌ
What would be the maximum uptake of »ýæ× ÚðUç$ÁÙ) €Øæ ãñ?
Ca21 ions by the resin when expressed in
mole per gram resin ?

1 1
(1) (1)
103 103

1 1
(2) (2)
206 206

2 2
(3) (3)
309 309

1 1
(4) (4)
412 412

32. Sodium metal crystallizes in a body centred 32. âæðçÇUØ× ÏæÌé °·¤ ¥´ÌÑ·ð¤ç‹ÎýÌ ƒæÙèØ ÁæÜ·¤ ×ð´
cubic lattice with a unit cell edge of 4.29Å. ç·ý¤SÅUçÜÌ ãæðÌæ ãñ çÁâ·ð¤ ·¤æðÚU ·¤è Ü´Õæ§ü 4.29Å ãñÐ
The radius of sodium atom is âæðçÇUØ× ÂÚU×æ‡æé ·¤è ç˜æ’Øæ ֻܻ ãñ Ñ
approximately :

(1) 1.86Å (1) 1.86Å

(2) 3.22Å (2) 3.22Å

(3) 5.72Å (3) 5.72Å

(4) 0.93Å (4) 0.93Å

33. Which of the following is the energy of a 33. çِÙçÜç¹Ì ×ð´ âð ãæ§üÇþUæðÁÙ ·¤è â´Öß ©žæðçÁÌ ¥ßSÍæ
possible excited state of hydrogen ? ·¤è ª¤Áæü ·¤æñÙ âè ãñ?
(1) 113.6 eV (1) 113.6 eV

(2) 26.8 eV (2) 26.8 eV

(3) 23.4 eV (3) 23.4 eV

(4) 16.8 eV (4) 16.8 eV

A/Page 19 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

34. The intermolecular interaction that is 34. ßã ¥´ÌÚUæ-¥‡æé·¤ ¥‹Øæð‹Ø ç·ý¤Øæ Áæ𠥇æé¥æð´ ·ð¤ Õè¿
dependent on the inverse cube of distance ·¤è ÎêÚUè ·ð¤ ÂýçÌÜæð× ƒæÙ ÂÚU çÙÖüÚU ãñ, ãñ Ñ
between the molecules is :
(1) ion - ion interaction (1) ¥æØÙ - ¥æØÙ ¥‹Øæð‹Ø
(2) ion - dipole interaction (2) ¥æØÙ - çmÏýéß ¥‹Øæð‹Ø
(3) London force (3) Ü´ÇUÙ ÕÜ
(4) hydrogen bond (4) ãæ§üÇþUæðÁÙ Õ´Ï·¤

35. The following reaction is performed at 35. çِÙçÜç¹Ì ¥çÖç·ý¤Øæ ·¤æð 298 K ÂÚU ç·¤Øæ »ØæÐ
298 K.

2NO(g) 1 O 2 (g) ì 2NO 2 (g) 2NO(g) 1 O 2 (g) ì 2NO 2 (g)

The standard free energy of formation of 298 K ÂÚU NO(g) ·ð¤ â´ÖßÙ ·¤è ×æÙ·¤ ×é€Ì ª¤Áæü
NO(g) is 86.6 kJ/mol at 298 K. What is 86.6 kJ/mol ãñÐ 298 K ÂÚU NO2(g) ·¤è ×æÙ·¤
the standard free energy of formation of ×é€Ì ª¤Áæü €Øæ ãñ? (Kp51.631012)
NO2(g) at 298 K? (Kp51.631012)
(1) R(298) ln(1.6310 12)286600 (1) R(298) ln(1.6310 12)286600
(2) 866001R(298) ln(1.6310 12) (2) 866001R(298) ln(1.6310 12)

ln (1.6 3 1012 ) ln (1.6 3 1012 )
(3) 86600 2 (3) 86600 2
R (298) R (298)

(4) 0.5[2386,6002R(298) ln(1.631012)] (4) 0.5[2386,6002R(298) ln(1.631012)]

36. The vapour pressure of acetone at 208C is 36. 208C ÂÚU °ðçâÅUæðÙ ·¤è ßæc ÎæÕ 185 torr ãñÐ ÁÕ
185 torr. When 1.2 g of a non-volatile 208C ÂÚU, 1.2 g ¥ßæcÂàæèÜ ÂÎæÍü ·¤æð 100 g
substance was dissolved in 100 g of acetone °ðçâÅUæðÙ ×𴠃ææðÜæ »Øæ, ÌÕ ßæc ÎæÕ 183 torr ãæð
at 208C, its vapour pressure was 183 torr. »ØæÐ §â ÂÎæÍü ·¤æ ×æðÜÚU ÎýÃØ×æÙ (g mol21 ×ð´)
The molar mass (g mol21) of the substance ãñ Ñ
is :
(1) 32 (1) 32
(2) 64 (2) 64
(3) 128 (3) 128
(4) 488 (4) 488

A/Page 20 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

37. The standard Gibbs energy change at 37. 300 K ÂÚU ¥çÖç·ý¤Øæ 2A ì B 1 C ·¤è ×æÙ·¤
300 K for the reaction 2A ì B 1 C is 绎$ Á ª¤Áæü 2494.2 J ãñ Ð çΰ »° â×Ø ×ð ´
1
2494.2 J. At a given time, the composition ¥çÖç·ý ¤ Øæ çןæ‡æ ·¤æ â´ ƒ æÅUÙ [A] 5 2 ,
1 1
of the reaction mixture is [A] 5 , [B]52 [B]52 ¥æñÚU [C] 5 ãñÐ ¥çÖç·ý¤Øæ ¥»ýçâÌ ãæðÌè
2 2
1
and [C] 5
2
. The reaction proceeds in ãñ Ñ [R58.314 J/K/mol, e52.718]

the : [R58.314 J/K/mol, e52.718]
(1) forward direction because Q > Kc (1) ¥»ý çÎàææ ×𴠀Øæð´ç·¤ Q > Kc
(2) reverse direction because Q > Kc (2) çßÂÚUèÌ çÎàææ ×𴠀Øæð´ç·¤ Q > Kc
(3) forward direction because Q < Kc (3) ¥»ý çÎàææ ×𴠀Øæð´ç·¤ Q < Kc
(4) reverse direction because Q < Kc (4) çßÂÚUèÌ çÎàææ ×𴠀Øæð´ç·¤ Q < Kc

38. Two Faraday of electricity is passed 38. CuSO4 ·ð¤ °·¤ çßÜØÙ ×ð´, Îæð Èñ¤ÚUæÇðU çßléÌ ÂýßæçãÌ
through a solution of CuSO4. The mass of ·¤è »§üÐ ·ñ¤ÍæðÇU ÂÚU çÙÿæðçÂÌ Ìæ´Õð ·¤æ ÎýÃØ×æÙ ãñ :
copper deposited at the cathode is : (Cu ·¤æ ÂÚU×æç‡ß·¤ ÎýÃØ×æÙ 563.5 amu)
(at. mass of Cu563.5 amu)
(1) 0g (1) 0g
(2) 63.5 g (2) 63.5 g
(3) 2g (3) 2g
(4) 127 g (4) 127 g

39. Higher order (>3) reactions are rare due 39. ©‘¿ ·¤æðçÅU ¥çÖç·ý¤Øæ (>3) ÎéÜüÖ ãñ €Øæð´ç·¤ Ñ
to :
(1) low probability of simultaneous (1) ÂýçÌç·ý¤Øæ ×ð´ âÖè ÂýÁæçÌØæ𴠷𤠰·¤ âæÍ ÅU€·¤ÚU
collision of all the reacting species ·¤è â´ÖæßÙæ ·¤× ãæðÌè ãñÐ
(2) increase in entropy and activation (2) ¥çÏ·¤ ¥‡æé¥æð´ ·ð¤ àææç×Ü ãæðÙð âð °´ÅþUæÂè ¥æñÚU
energy as more molecules are â´ç·ý¤Ø‡æ ª¤Áæü ×ð´ ßëçh ãæðÌè ãñÐ
involved
(3) shifting of equilibrium towards (3) Üæð¿ÎæÚU ÅU·¤ÚUæß ·ð¤ ·¤æÚU‡æ ¥çÖ·¤æÚU·¤æð´ ·¤è
reactants due to elastic collisions çÎàææ ×ð´ âæØ ·¤æ SÍæÙæ´ÌÚU‡æ ãæðÌæ ãñÐ
(4) loss of active species on collision (4) ÅU·¤ÚUæß âð âç·ý¤Ø SÂèàæè$Á ·¤æ ÿæØ ãæðÌæ ãñÐ

A/Page 21 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

40. 3 g of activated charcoal was added to 40. °·¤ ÜæS·¤ ×ð´ 0.06N °çâçÅU·¤ ¥Ü ·ð¤ 50 mL
50 mL of acetic acid solution (0.06N) in a çßÜØÙ ×ð´ 3 g âç·ý¤çØÌ÷ ·¤æcÆU ·¤æðØÜæ ç×ÜæØæ »ØæÐ
flask. After an hour it was filtered and °·¤ ƒæ´ÅðU ·ð¤ Âà¿æÌ÷ ©âð ÀUæÙæ »Øæ ¥æñÚU çÙSØ´Î ·¤è
the strength of the filtrate was found to be ÂýÕÜÌæ 0.042 N Âæ§ü »§üÐ ¥çÏàææðçáÌ °çâçÅU·¤
0.042 N. The amount of acetic acid ¥Ü ·¤è ×æ˜ææ (·¤æcÆU-·¤æðØÜæ ·ð¤ ÂýçÌ »ýæ× ÂÚU)
adsorbed (per gram of charcoal) is : ãñ Ñ
(1) 18 mg (1) 18 mg

(2) 36 mg (2) 36 mg

(3) 42 mg (3) 42 mg

(4) 54 mg (4) 54 mg

41. The ionic radii (in Å) of N32, O22 and F2 41. N32, O22 ÌÍæ F2 ·¤è ¥æØçÙ·¤ ç˜æ’ØæØð´ (Å ×ð´)
are respectively : ·ý¤×àæÑ ãñ´ Ñ
(1) 1.36, 1.40 and 1.71 (1) 1.36, 1.40 ÌÍæ 1.71

(2) 1.36, 1.71 and 1.40 (2) 1.36, 1.71 ÌÍæ 1.40

(3) 1.71, 1.40 and 1.36 (3) 1.71, 1.40 ÌÍæ 1.36

(4) 1.71, 1.36 and 1.40 (4) 1.71, 1.36 ÌÍæ 1.40

42. In the context of the Hall - Heroult process 42. ãæòÜ-ãðÚUæòËÅU Âý·ý¤× âð °ðÜéç×çÙØ× ·ð¤ çÙc·¤áü‡æ ·ð¤
for the extraction of Al, which of the â´ÎÖü ×ð´ ·¤æñÙ âæ ·¤ÍÙ »ÜÌ ãñ?
following statements is false ?

(1) CO and CO2 are produced in this (1) §â Âý·ý¤× ×ð´ CO ÌÍæ CO2 ·¤æ ©ˆÂæÎÙ ãæðÌæ
process ãñÐ
(2) Al 2 O 3 is mixed with CaF 2 which (2) CaF2 ·¤æð Al2O3 ×ð´ ç×ÜæÙð ÂÚU çןæ‡æ ·¤æ
lowers the melting point of the »ÜÙæ´·¤ ·¤× ãæðÌæ ãñ ¥æñÚU ©â×ð´ ¿æÜ·¤Ìæ ¥æÌè
mixture and brings conductivity ãñÐ
(3) Al31 is reduced at the cathode to (3) ·ñ¤ÍæðÇU ÂÚU Al31 ¥Â¿çØÌ ãæð ·¤ÚU Al ÕÙæÌæ
form Al ãñÐ
(4) Na3AlF6 serves as the electrolyte (4) Na3AlF6 çßléÌ ¥ÂƒæÅ÷UØ ·¤æ ·¤æ× ·¤ÚUÌæ
ãñÐ
A/Page 22 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

43. From the following statements regarding 43. H2O2 ·ð¤ â´ÎÖü ×ð´, çِÙçÜç¹Ì ·¤ÍÙæð´ ×ð´ âð »ÜÌ
H2O2, choose the incorrect statement : ·¤ÍÙ ¿éçÙ° Ñ

(1) It can act only as an oxidizing agent (1) Øã ·ð¤ßÜ ¥æò€âè·¤æÚU·¤ ãñ

(2) It decomposes on exposure to light (2) Âý·¤æàæ ×ð´ §â·¤æ ¥ÂƒæÅUÙ ãæðÌæ ãñ

(3) It has to be stored in plastic or wax (3) §âð ŒÜæçSÅU·¤ Øæ ×æð×¥ÅðU ·¤æ´¿ ÕæðÌÜæð´ ×ð´ ¥´ÏðÚðU
lined glass bottles in dark ×ð´ â´»ýçãÌ ç·¤Øæ ÁæÌæ ãñ

(4) It has to be kept away from dust (4) §âð ÏêÜ âð ÎêÚU ÚU¹Ùæ ¿æçã°

44. Which one of the following alkaline earth 44. çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ âð ÿææÚUèØ ×ëÎæ ÏæÌé âËÈð¤ÅU
metal sulphates has its hydration enthalpy ·¤è ÁÜØæðÁÙ °ð‹ÍæËÂè ©â·ð¤ ÁæÜ·¤ °ð‹ÍæËÂè âð
greater than its lattice enthalpy ? ¥çÏ·¤ ãñ?

(1) CaSO 4 (1) CaSO 4

(2) BeSO4 (2) BeSO4

(3) BaSO4 (3) BaSO4

(4) SrSO 4 (4) SrSO 4

45. Which among the following is the most 45. çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ âßæüçÏ·¤ ¥çÖç·ý¤ØæàæèÜ ãñ?
reactive ?

(1) Cl2 (1) Cl2

(2) Br2 (2) Br2

(3) I2 (3) I2

(4) ICl (4) ICl

A/Page 23 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

46. Match the catalysts to the correct 46. çΰ »° ©ˆÂýðÚU·¤æð´ ·¤æð âãè Âý·ý¤× ·ð¤ âæÍ âé×ðçÜÌ
processes : ·¤Úð´U Ñ
Catalyst Process ©ˆÂýðÚU·¤ Âý·ý¤×
(A) TiCl3 (i) Wacker process (A) TiCl3 (i) ßæò·¤ÚU Âý·ý¤×
(B) PdCl2 (ii) Ziegler - Natta (B) PdCl2 (ii) ˆâè‚ÜÚ-Ù^æ
polymerization ÕãéÜ·¤è·¤ÚU‡æU
(C) CuCl2 (iii) Contact process (C) CuCl2 (iii) â´SÂàæü Âý·ý¤×
(D) V 2O 5 (iv) Deacon’s process (D) V 2O 5 (iv) ÇUè·¤Ù Âý·ý¤×
(1) (A) - (iii), (B) - (ii), (C) - (iv), (D) - (i) (1) (A) - (iii), (B) - (ii), (C) - (iv), (D) - (i)
(2) (A) - (ii), (B) - (i), (C) - (iv), (D) - (iii) (2) (A) - (ii), (B) - (i), (C) - (iv), (D) - (iii)
(3) (A) - (ii), (B) - (iii), (C) - (iv), (D) - (i) (3) (A) - (ii), (B) - (iii), (C) - (iv), (D) - (i)
(4) (A) - (iii), (B) - (i), (C) - (ii), (D) - (iv) (4) (A) - (iii), (B) - (i), (C) - (ii), (D) - (iv)

47. Which one has the highest boiling point ? 47. çِÙçÜç¹Ì ×ð´ âð âßæüçÏ·¤ €ßÍÙæ´·¤ 緤ⷤæ ãñ?
(1) He (1) He
(2) Ne (2) Ne
(3) Kr (3) Kr
(4) Xe (4) Xe

48. The number of geometric isomers that can 48. ß»ü â×ÌÜèØ [Pt (Cl) (py) (NH3) (NH2OH)]1
exist for square planar [Pt (Cl) (py) (NH3) (py 5 pyridine) ·ð¤ ’Øæç×ÌèØ â×æßØçßØæð´ ·¤è
(NH2OH)]1 is (py 5 pyridine) : ⴁØæ ãñ Ñ
(1) 2 (1) 2
(2) 3 (2) 3
(3) 4 (3) 4
(4) 6 (4) 6

49. The color of KMnO4 is due to : 49. KMnO4 ·ð¤ Ú´U» ·¤æ ·¤æÚU‡æ ãñ Ñ
(1) M ® L charge transfer transition (1) M ® L ¥æßðàæ SÍæÙæ´ÌÚU‡æ â´·ý¤×‡æ
(2) d 2 d transition (2) d 2 d â´·ý¤×‡æ
(3) L ® M charge transfer transition (3) L ® M ¥æßðàæ SÍæÙæ´ÌÚU‡æ â´·ý¤×‡æ
(4) s 2 s* transition (4) s 2 s* â´·ý¤×‡æ

A/Page 24 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

50. Assertion : Nitrogen and Oxygen are the 50. ¥çÖ·¤ÍÙ Ñ Ùæ§ÅþUæðÁÙ ¥æñÚU ¥æò€âèÁÙ ßæÌæßÚU‡æ ·ð¤
main components in the ×éØ ƒæÅU·¤ ãñ´ ÂÚU‹Ìé Øã ç·ý¤Øæ ·¤ÚU·ð¤
atmosphere but these do not Ùæ§ÅþUæðÁÙ ·ð¤ ¥æò€âæ§ÇU Ùãè´ ÕÙæÌðÐ
react to form oxides of nitrogen.
Reason : The reaction between nitrogen Ì·ü¤ Ñ Ùæ§ÅþUæðÁÙ ¥æñÚU ¥æò€âèÁÙ ·ð¤ Õè¿
and oxygen requires high ¥çÖç·ý ¤ Øæ ·ð ¤ çÜ° ©“æ Ìæ ·¤è
temperature. ¥æßàØ·¤Ìæ ãñÐ
(1) Both assertion and reason are (1) ¥çÖ·¤ÍÙ ¥æñÚU Ì·ü¤ ÎæðÙæð´ âãè ãñ´ ¥æñÚU Ì·ü¤
correct, and the reason is the correct ¥çÖ·¤ÍÙ ·¤æ âãè SÂcÅUè·¤ÚU‡æ ãñÐ
explanation for the assertion
(2) Both assertion and reason are (2) ¥çÖ·¤ÍÙ ¥æñÚU Ì·ü¤ ÎæðÙæð´ âãè ãñ´ ÂÚU‹Ìé Ì·ü¤
correct, but the reason is not the ¥çÖ·¤ÍÙ ·¤æ âãè SÂcÅUè·¤ÚU‡æ Ùãè´ ãñÐ
correct explanation for the assertion
(3) The assertion is incorrect, but the (3) ¥çÖ·¤ÍÙ »ÜÌ ãñ ÂÚU‹Ìé Ì·ü¤ âãè ãñÐ
reason is correct
(4) Both the assertion and reason are (4) ¥çÖ·¤ÍÙ ß Ì·ü¤ ÎæðÙæð´ »ÜÌ ãñ´Ð
incorrect

51. In Carius method of estimation of 51. ãñÜæðÁÙ ·ð¤ ¥æ·¤ÜÙ ·¤è ·ñ¤çÚU¥â çßçÏ ×ð´ 250 mg
halogens, 250 mg of an organic compound ·¤æÕüçÙ·¤ Øæñç»·¤ 141 mg AgBr ÎðÌæ ãñÐ Øæñç»·¤
gave 141 mg of AgBr. The percentage of ×ð´ Õýæð×èÙ ·¤è ÂýçÌàæÌÌæ ãñ :
bromine in the compound is : (ÂÚU×æç‡ß·¤ ÎýÃØ×æÙ Ag5108; Br580)
(at. mass Ag5108; Br580)
(1) 24 (1) 24
(2) 36 (2) 36
(3) 48 (3) 48
(4) 60 (4) 60

52. Which of the following compounds will 52. çِÙçÜç¹Ì ×ð ´ âð ·¤æñ Ù âæ Øæñ ç »·¤ ’Øæç×ÌèØ
exhibit geometrical isomerism ? â×æßØßÌæ ÎàææüÌæ ãñ?
(1) 1 - Phenyl - 2 - butene (1) 1 - Èð¤çÙÜ - 2 - ŽØêÅUèÙ
(2) 3 - Phenyl - 1 - butene (2) 3 - Èð¤çÙÜ - 1 - ŽØêÅUèÙ
(3) 2 - Phenyl - 1 - butene (3) 2 - Èð¤çÙÜ - 1 - ŽØêÅUèÙ
(4) 1, 1 - Diphenyl - 1 - propane (4) 1, 1 - ÇUæ§üÈð¤çÙÜ - 1 - ÂýæðÂðÙ

A/Page 25 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

53. Which compound would give 53. ¥æð $ Á æð Ù æð ç Üçââ ·¤ÚUÙð ÂÚU ·¤æñ Ù âæ Øæñ ç »·¤
5 - keto - 2 - methyl hexanal upon 5 - ·¤èÅUæð - 2 - ×ðçÍÜ ãð€âæÙñÜ ÎðÌæ ãñ?
ozonolysis ?

(1) (1)

(2) (2)

(3) (3)

(4) (4)

54. The synthesis of alkyl fluorides is best 54. ¥Ë·¤æ§Ü ÜæðÚUæ§ÇU ·ð¤ â´àÜðá‡æ ·ð¤ çÜ° âÕâð
accomplished by : ÕðãÌÚUèÙ çßçÏ ãñ Ñ

(1) Free radical fluorination (1) ×é€Ì ×êÜ·¤ ÜæðçÚUÙðàæÙ

(2) Sandmeyer’s reaction (2) âñ‹ÇU×æØÚU ¥çÖç·ý¤Øæ

(3) Finkelstein reaction (3) çÈ´¤·¤ÜSÅUæ§Ù ¥çÖç·ý¤Øæ

(4) Swarts reaction (4) SßæÅüUâ ¥çÖç·ý¤Øæ
A/Page 26 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

55. In the following sequence of reactions : 55. çΰ »° ¥çÖç·ý¤Øæ ¥Ùé·ý¤× ×ð´ ©ˆÂæÎ C ãñ Ñ
KMnO SOCl H /Pd KMnO SOCl H /Pd
Toluene →
4
A 
2
→ B 
2
→ C, Toluene →
4
A 
2
→ B 
2
→C
BaSO 4 BaSO 4

the product C is :

(1) C6H5COOH (1) C6H5COOH

(2) C6H5CH3 (2) C6H5CH3

(3) C6H5CH2OH (3) C6H5CH2OH

(4) C6H5CHO (4) C6H5CHO

56. In the reaction 56. çΰ »° ¥çÖç·ý¤Øæ ×ð´ ©ˆÂæÎ E ãñ Ñ

NaNO /HCl CuCN/KCN NaNO /HCl CuCN/KCN

2
→ D → E 1 N 2 
2
→ D 
→ E 1 N2
0258 C D 0258 C D

the product E is :

(1) (1)

(2) (2)

(3) (3)

(4) (4)

A/Page 27 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

57. Which polymer is used in the manufacture 57. ç·¤â ÕãéÜ·¤ ·¤æ ©ÂØæð» ÂýÜð ¥æñÚU ÂýÜæÿæ ÕÙæÙð ×ð´
of paints and lacquers ? ãæðÌæ ãñ?
(1) Bakelite (1) Õð·ð¤Üæ§ÅU
(2) Glyptal (2) ç‚ÜŒÅUæÜ
(3) Polypropene (3) ÂæòçÜÂýæðÂèÙ
(4) Poly vinyl chloride (4) ÂæòçÜ ßæ§çÙÜ €ÜæðÚUæ§ÇU

58. Which of the vitamins given below is water 58. çِÙçÜç¹Ì çßÅUæç×Ùæð´ ×ð´ ÁÜ ×ð´ çßÜðØ ãæðÙð ßæÜæ
soluble ? ãñ Ñ
(1) Vitamin C (1) çßÅUæç×Ù C
(2) Vitamin D (2) çßÅUæç×Ù D
(3) Vitamin E (3) çßÅUæç×Ù E
(4) Vitamin K (4) çßÅUæç×Ù K

59. Which of the following compounds is not 59. çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ âæ Øæñç»·¤ ÂýçÌ¥Ü Ùãè´ ãñ?
an antacid ?

(1) Aluminium hydroxide (1) °ðÜéç×çÙØ× ãæ§ÇþUæ€âæ§ÇU
(2) Cimetidine (2) çâ×ðçÅUÇUèÙ
(3) Phenelzine (3) çȤÙçËÁÙ
(4) Ranitidine (4) ÚñUçÙçÅUÇUèÙ

60. Which of the following compounds is not 60. çΰ »° Øæñç»·¤æð´ ×ð´ ·¤æñÙ âð Øæñç»·¤ ·¤æ Ú´U» ÂèÜæ Ùãè´
colored yellow ? ãñ?
(1) Zn2[Fe(CN)6] (1) Zn2[Fe(CN)6]

(2) K3[Co(NO2)6] (2) K3[Co(NO2)6]

(3) (NH4)3 [As (Mo3 O10)4] (3) (NH4)3 [As (Mo3 O10)4]

(4) BaCrO4 (4) BaCrO4

A/Page 28 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

PART C — MATHEMATICS Öæ» C — »ç‡æÌ
61. Let A and B be two sets containing four 61. ×æÙæ A ÌÍæ B Îæð â×é‘¿Ø ãñ´ çÁÙ×ð´ ·ý¤×àæÑ ¿æÚU ÌÍæ
and two elements respectively. Then the Îæð ¥ßØß ãñ´, Ìæð â×é‘¿Ø A3B ·ð¤ ©Ù ©Ââ×鑿Øæð´
number of subsets of the set A3B, each ·¤è ⴁØæ, çÁÙ×ð´ ÂýˆØð·¤ ×ð´ ·¤× âð ·¤× ÌèÙ ¥ßØß
having at least three elements is : ãñ´, ãñ Ñ
(1) 219 (1) 219

(2) 256 (2) 256

(3) 275 (3) 275

(4) 510 (4) 510

62. A complex number z is said to be 62. °·¤ âç×Ÿæ ⴁØæ z °·¤×æÂæ´·¤è ·¤ãÜæÌè ãñ ØçÎ
unimodular if ?z?51. Suppose z1 and z2 ?z?51 ãñÐ ×æÙæ z1 ÌÍæ z2 °ðâè âç×Ÿæ ⴁØæ°¡ ãñ´
z1 2 2 z2 z1 2 2 z2
are complex numbers such that ç·¤ °·¤×æÂæ´·¤è ãñ ÌÍæ z2 °·¤×æÂæ´·¤è
2 2 z1 z2 2 2 z1 z2
is unimodular and z2 is not unimodular. Ùãè´ ãñ, Ìæð çÕ´Îé z1 çSÍÌ ãñ Ñ
Then the point z1 lies on a :

(1) straight line parallel to x-axis. (1) x-¥ÿæ ·ð¤ â×æ´ÌÚU °·¤ ÚðU¹æ ÂÚUÐ

(2) straight line parallel to y-axis. (2) y-¥ÿæ ·ð¤ â×æ´ÌÚU °·¤ ÚðU¹æ ÂÚUÐ

(3) circle of radius 2. (3) 2 ç˜æ’Øæ ßæÜð ßëžæ ÂÚUÐ

(4) circle of radius 2. (4) 2 ç˜æ’Øæ ßæÜð ßëžæ ÂÚUÐ

63. Let a and b be the roots of equation 63. ×æÙæ a ÌÍæ b çmƒææÌ â×è·¤ÚU‡æ x226x2250 ·ð¤
x 2 26x2250. If a n 5a n 2b n , for n/1, ×êÜ ãñ´Ð ØçÎ n/1 ·ð¤ çÜ°, an5an2bn ãñ, Ìæð
a10 2 2a8 a10 2 2a8
then the value of is equal to : ·¤æ ×æÙ ãñ Ñ
2a9 2a9

(1) 6 (1) 6

(2) 26 (2) 26

(3) 3 (3) 3

(4) 23 (4) 23

A/Page 29 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

1 2 2  1 2 2 
 
64. If A 5  2 1 22  is a matrix satisfying 64. ØçÎ A 5  2 1 22  °·¤ °ðâæ ¥æÃØêã ãñ Áæð
 a 2 b   a 2 b 

the equation AA T 59I, where I is 333 ¥æÃØêã â×è·¤ÚU‡æ AAT59I, ·¤æð â´ÌécÅU ·¤ÚUÌæ ãñ,
identity matrix, then the ordered pair Áãæ¡ I, 333 ·¤æ ̈â×·¤ ¥æÃØêã ãñ, Ìæð ·ý¤ç×Ì Øé‚×
(a, b) is equal to : (a, b) ·¤æ ×æÙ ãñ Ñ

(1) (2, 21) (1) (2, 21)

(2) (22, 1) (2) (22, 1)

(3) (2, 1) (3) (2, 1)

(4) (22, 21) (4) (22, 21)

65. The set of all values of l for which the 65. l ·ð¤ âÖè ×æÙæð´ ·¤æ â×鑿Ø, çÁÙ·ð¤ çÜ° ÚñUç¹·¤
system of linear equations : â×è·¤ÚU‡æ çÙ·¤æØ
2x 122x21x 35lx 1 2x 122x21x 35lx 1

2x 123x 212x 35lx 2 2x 123x 212x 35lx 2

2x112x2 5lx3 2x112x2 5lx3

has a non-trivial solution, ·¤æ °·¤ ¥Ìé‘ÀU ãÜ ãñ,
(1) is an empty set. (1) °·¤ çÚU€Ì â×é‘¿Ø ãñÐ
(2) is a singleton. (2) °·¤ °·¤Ü â×é‘¿Ø ãñÐ
(3) contains two elements. (3) ×ð´ Îæð ¥ßØß ãñ´Ð
(4) contains more than two elements. (4) ×ð´ Îæð âð ¥çÏ·¤ ¥ßØß ãñ´Ð

66. The number of integers greater than 6,000 66. ¥´·¤æð´ 3, 5, 6, 7 ÌÍæ 8 ·ð¤ ÂýØæð» âð, çÕÙæ ÎæðãÚUæØð,
that can be formed, using the digits 3, 5, 6, ÕÙÙð ßæÜð 6,000 âð ÕǸð Âê‡ææZ·¤æð´ ·¤è ⴁØæ ãñ Ñ
7 and 8, without repetition, is :

(1) 216 (1) 216

(2) 192 (2) 192

(3) 120 (3) 120

(4) 72 (4) 72

A/Page 30 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

(1 2 2 x )
50
67. The sum of coefficients of integral powers 67. ·ð¤ çmÂÎ ÂýâæÚU ×ð´ x ·¤è Âê‡ææZ·¤èØ
of x in the binomial expansion of ƒææÌæ𴠷𤠻é‡ææ´·¤æð´ ·¤æ Øæð» ãñ Ñ
(1 2 2 x )
50
is :

(1)
2
(
1 50
3 11 ) (1)
2
(
1 50
3 11 )
(2)
2
( )
1 50
3 (2)
2
( )
1 50
3

(3)
2
(
1 50
3 21 ) (3)
2
(
1 50
3 21 )
(4)
2
(
1 50
2 11 ) (4)
2
(
1 50
2 11 )

68. If m is the A.M. of two distinct real 68. ØçÎ Îæð çßç֋٠ßæSÌçß·¤ â´  Øæ¥æð ´ l ÌÍæ n
numbers l and n (l, n > 1) and G1, G2 and (l, n > 1) ·¤æ â×æ´ÌÚU ×æŠØ (A.M.) m ãñ ¥æñÚU l ÌÍæ
G3 are three geometric means between l n ·ð¤ Õè¿ ÌèÙ »é‡ææðžæÚU ×æŠØ (G.M.) G1, G2 ÌÍæ
and n, then G14 1 2G24 1 G 34 equals. G3 ãñ´, Ìæð G14 1 2G24 1 G 34 ÕÚUæÕÚU ãñ Ñ

(1) 4 l2mn (1) 4 l2mn
(2) 4 lm2n (2) 4 lm2n
(3) 4 lmn2 (3) 4 lmn2
(4) 4 l2m2n2 (4) 4 l2m2n2

69. The sum of first 9 terms of the series 69. Ÿæð‡æè
13 13 1 2 3 13 1 2 3 1 3 3 13 13 1 2 3 13 1 2 3 1 3 3
1 1 1 .... is : 1 1 1 .... ·ð ¤
1 113 11 31 5 1 113 11 31 5
Âý‰æ× 9 ÂÎæð´ ·¤æ Øæð» ãñ Ñ
(1) 71 (1) 71
(2) 96 (2) 96
(3) 142 (3) 142
(4) 192 (4) 192

A/Page 31 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

70. lim ( 1 2 cos 2 x )( 3 1 cos x ) is equal to : 70. lim ( 1 2 cos 2 x )( 3 1 cos x ) ÕÚUæÕÚU ãñ Ñ
x→0 x tan 4 x x→0 x tan 4 x

(1) 4 (1) 4

(2) 3 (2) 3

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

71. If the function. 71. ØçΠȤÜÙ

 k x 1 1 , 0 [ x [ 3  k x 1 1 , 0 [ x [ 3
g( x ) 5  g( x ) 5 
 m x 1 2 , 3 < x [ 5  m x 1 2 , 3 < x [ 5

is differentiable, then the value of k1m is : ¥ß·¤ÜÙèØ ãñ, Ìæð k1m ·¤æ ×æÙ ãñ Ñ
(1) 2 (1) 2

16 16
(2) (2)
5 5

10 10
(3) (3)
3 3

(4) 4 (4) 4

72. The normal to the curve, x212xy23y250, 72. ß·ý ¤ x 2 12xy23y 250 ·ð ¤ çÕ´ Î é (1, 1) ÂÚU
at (1, 1) : ¥çÖÜÕ Ñ
(1) does not meet the curve again. (1) ß·ý¤ ·¤æð ÎæððÕæÚUæ Ùãè´ ç×ÜÌæÐ
(2) meets the curve again in the second (2) ß·ý¤ ·¤æð ÎæðÕæÚUæ çmÌèØ ¿ÌéÍæZàæ ×ð´ ç×ÜÌæ ãñÐ
quadrant.

(3) meets the curve again in the third (3) ß·ý¤ ·¤æð ÎæðÕæÚUæ ÌëÌèØ ¿ÌéÍæZàæ ×ð´ ç×ÜÌæ ãñÐ
quadrant.

(4) meets the curve again in the fourth (4) ß·ý¤ ·¤æð ÎæðÕæÚUæ ¿ÌéÍü ¿ÌéÍæZàæ ×ð´ ç×ÜÌæ ãñÐ
quadrant.

A/Page 32 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

73. Let f (x) be a polynomial of degree four 73. ×æÙæ f (x) ƒææÌ 4 ·¤æ °·¤ Õãé  Πãñ çÁâ·ð ¤
having extreme values at x51 and x52. x51 ÌÍæ x52 ÂÚU ¿ÚU× ×æÙ ãñ´Ð ØçÎ
 f ( x )  f ( x )
If lim 1 1  5 3 , then f (2) is equal
x →0  x2 
lim 1 1  5 3 ãñ, Ìæð f (2) ÕÚUæÕÚU ãñ Ñ
x →0  x2 
to :
(1) 28 (1) 28
(2) 24 (2) 24
(3) 0 (3) 0
(4) 4 (4) 4

dx dx
74. The integral ∫ 3
equals : 74. â×æ·¤Ü ∫ 3
ÕÚUæÕÚU ãñ Ñ
x 2 ( x 4 1 1) 4 x 2 ( x 4 1 1) 4

1 1
 x4 1 1  4  x4 1 1  4
(1)   1c (1)   1c
 x4   x4 
   
1 1
(2) ( x 411) 4 1 c (2) ( x 411) 4 1 c
1 1
(3) 2( x 4 1 1) 4 1 c (3) 2( x 4 1 1) 4 1 c

1 1
 x 41 1  4  x 41 1  4
(4) 2  1c (4) 2  1c
 x4   x4 
   

75. The integral 75. â×æ·¤Ü
4 4
log x 2 log x 2
∫ 2
1 log (36 2 12 x 1 x 2 )
dx ∫ 2
1 log (36 2 12 x 1 x 2 )
dx
2 log x 2 log x

is equal to : ÕÚUæÕÚU ãñ Ñ
(1) 2 (1) 2
(2) 4 (2) 4
(3) 1 (3) 1
(4) 6 (4) 6

A/Page 33 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

76. The area (in sq. units) of the region 76. {(x, y) : y2[ 2x ÌÍæ y / 4x 2 1} mæÚUæ ÂçÚUÖæçáÌ
described by ÿæð˜æ ·¤æ ÿæð˜æÈ¤Ü (ß»ü §·¤æ§Øæð´) ×ð´ ãñ Ñ
{(x, y) : y2 [ 2x and y / 4x 2 1} is :

7 7
(1) (1)
32 32

5 5
(2) (2)
64 64

15 15
(3) (3)
64 64

9 9
(4) (4)
32 32

77. Let y(x) be the solution of the differential 77. ×æÙæ ¥ß·¤Ü â×è·¤ÚU‡æ
equation

dy dy
( x log x ) 1 y 5 2 x log x , ( x / 1). ( x log x ) 1 y 5 2 x log x , ( x / 1)
dx dx
Then y(e) is equal to : ·¤æ ãÜ y(x) ãñ, Ìæð y(e) ÕÚUæÕÚU ãñ Ñ
(1) e (1) e

(2) 0 (2) 0

(3) 2 (3) 2

(4) 2e (4) 2e

78. The number of points, having both 78. ç˜æÖéÁ, çÁâ·ð¤ àæèáü (0, 0), (0, 41) ÌÍæ (41, 0) ãñ´,
co-ordinates as integers, that lie in the ·ð¤ ¥æ´ÌçÚU·¤ Öæ» ×ð´ çSÍÌ ©Ù çÕ´Îé¥æð´ ·¤è ⴁØæ
interior of the triangle with vertices (0, 0), çÁÙ·ð¤ ÎæðÙæð´ çÙÎðüàææ´·¤ Âê‡ææZ·¤ ãñ´, ãñ Ñ
(0, 41) and (41, 0), is :

(1) 901 (1) 901

(2) 861 (2) 861

(3) 820 (3) 820

(4) 780 (4) 780

A/Page 34 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

79. Locus of the image of the point (2, 3) in 79. çÕ´Îé (2, 3) ·ð¤ ÚðU¹æ
the line (2x23y14)1k (x22y13)50, (2x23y14)1k (x22y13)50, k e R ×ð ´
k e R, is a : ÂýçÌçÕ´Õ ·¤æ çÕ´ÎéÂÍ °·¤ Ñ
(1) straight line parallel to x-axis. (1) x-¥ÿæ ·ð¤ â×æ´ÌÚU ÚðU¹æ ãñÐ
(2) straight line parallel to y-axis. (2) y-¥ÿæ ·ð¤ â×æ´ÌÚU ÚðU¹æ ãñÐ
(3) circle of radius 2. (3) 2 ç˜æ’Øæ ·¤æ ßëžæ ãñÐ
(4) circle of radius 3. (4) 3 ç˜æ’Øæ ·¤æ ßëžæ ãñÐ

80. The number of common tangents to the 80. ßëžææð´ x21y224x26y21250 ÌÍæ
circles x 2 1y 2 24x26y21250 and x21y216x118y12650 ·¤è ©ÖØçÙcÆU SÂàæü
x21y216x118y12650, is : ÚðU¹æ¥æð´ ·¤è ⴁØæ ãñ Ñ
(1) 1 (1) 1
(2) 2 (2) 2
(3) 3 (3) 3
(4) 4 (4) 4

x2 y2
81. The area (in sq. units) of the quadrilateral 81. Îèƒæüßëžæ 1 5 1 ·ð¤ ÙæçÖܐÕæð´ ·ð¤ çâÚUæð´ ÂÚU
9 5
formed by the tangents at the end points ¹è´¿è »§ü SÂàæü ÚðU¹æ¥æð́ mæÚUæ çÙç×üÌ ¿ÌéÖéüÁ ·¤æ ÿæð˜æȤÜ
of the latera recta to the ellipse (ß»ü §·¤æ§Øæð´ ×ð´) ãñ Ñ
x2 y2
1 5 1 , is :
9 5
27 27
(1) (1)
4 4
(2) 18 (2) 18
27 27
(3) (3)
2 2
(4) 27 (4) 27

82. Let O be the vertex and Q be any point on 82. ×æÙæ ÂÚUßÜØ x258y ·¤æ àæèáü O ÌÍæ ©â ÂÚU ·¤æð§ü
the parabola, x258y. If the point P divides çÕ´ Î é Q ãñ Ð ØçÎ çÕ´ Î é P, Úð U ¹ æ¹´ Ç U OQ ·¤æð
the line segment OQ internally in the ratio 1 : 3 ·ð¤ ¥æ´ÌçÚU·¤ ¥ÙéÂæÌ ×ð´ Õæ¡ÅUÌæ ãñ, Ìæð P ·¤æ
1 : 3, then the locus of P is : çÕ´ÎéÂÍ ãñ Ñ
(1) x 2 5y (1) x 2 5y
(2) y 2 5x (2) y 2 5x
(3) y 2 52x (3) y 2 52x
(4) x 2 52y (4) x 2 52y

A/Page 35 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

x 22 y 11 z 22
83. The distance of the point (1, 0, 2) from the 83. Úð U ¹ æ5 5 ÌÍæ â×ÌÜ
3 4 12
point of intersection of the line x2y1z516 ·ð¤ Âýç̑ÀðUÎ çÕ´Îé ·¤è, çÕ´Îé (1, 0, 2)
x 22 y 11 z 22
5 5 and the plane âð ÎêÚUè ãñ Ñ
3 4 12
x2y1z516, is :
(1) 2 14 (1) 2 14
(2) 8 (2) 8
(3) 3 21 (3) 3 21
(4) 13 (4) 13

84. The equation of the plane containing the 84. ÚðU¹æ 2x25y1z53, x1y14z55 ·¤æð ¥´ÌçßücÅU
line 2x25y1z53; x1y14z55, and ·¤ÚUÙð ßæÜð â×ÌÜ, Áæð â×ÌÜ x13y16z51 ·ð¤
parallel to the plane, x13y16z51, is : â×æ´ÌÚU ãñ, ·¤æ â×è·¤ÚU‡æ ãñ Ñ
(1) 2x16y112z513 (1) 2x16y112z513
(2) x13y16z527 (2) x13y16z527
(3) x13y16z57 (3) x13y16z57
(4) 2x16y112z5213 (4) 2x16y112z5213

→ → → → → →
85. Let a , b and c be three non-zero vectors 85. ×æÙæ a , b ÌÍæ c ÌèÙ àæê‹ØðÌÚU °ðâð âçÎàæ ãñ´ ç·¤
such that no two of them are collinear and ©Ù×ð´ âð ·¤æð§ü Îæð â´ ÚU ð¹ Ùãè´ ã´ñ ÌÍæ
→ → → 1 → → → → → →
( a 3 b )3 c 5 b c a . If u is the 1 → → →
3 ( a 3 b )3 c 5 b c a ãñÐ ØçÎ âçÎàææð´
3
→ → → →
angle between vectors b and c , then a b ÌÍæ c ·ð¤ Õè¿ ·¤æ ·¤æð‡æ u ãñ, Ìæð sin u ·¤æ °·¤
value of sin u is : ×æÙ ãñ Ñ
2 2 2 2
(1) (1)
3 3
2 2 2 2
(2) (2)
3 3
2 2
(3) (3)
3 3
22 3 22 3
(4) (4)
3 3

A/Page 36 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

86. If 12 identical balls are to be placed in 3 86. ØçÎ 12 °·¤ Áñâè »ðδ ,´ð 3 °·¤ Áñâð Հâæð´ ×ð´ ÚU¹è ÁæÌè
identical boxes, then the probability that ãñ´, Ìæð §Ù×ð´ âð °·¤ Հâð ×ð´ ÆUè·¤ 3 »ð́Îð́ ãæðÙð ·¤è
one of the boxes contains exactly 3 balls ÂýæçØ·¤Ìæ ãñ Ñ
is :

55  2 11 55  2 11
(1)   (1)  
3 3 3 3
10 10
2 2
(2) 55   (2) 55  
3 3
12 12
1 1
(3) 220   (3) 220  
3 3
11 11
1 1
(4) 22   (4) 22  
3 3

87. The mean of the data set comprising of 16 87. 16 Âýðÿæ‡ææð´ ßæÜð ¥æ¡·¤Ç¸æð´ ·¤æ ×æŠØ 16 ãñÐ ØçÎ °·¤
observations is 16. If one of the observation Âýðÿæ‡æ çÁâ·¤æ ×æÙ 16 ãñ, ·¤æð ãÅUæ ·¤ÚU, 3 ÙØð Âýðÿæ‡æ
valued 16 is deleted and three new çÁÙ·ð¤ ×æÙ 3, 4 ÌÍæ 5 ãñ´, ¥æ¡·¤Ç¸æð´ ×ð´ ç×Üæ çÎØð ÁæÌð
observations valued 3, 4 and 5 are added ãñ´, Ìæð ÙØð ¥æ¡·¤Ç¸æð´ ·¤æ ×æŠØ ãñ Ñ
to the data, then the mean of the resultant
data, is :
(1) 16.8 (1) 16.8
(2) 16.0 (2) 16.0
(3) 15.8 (3) 15.8
(4) 14.0 (4) 14.0

88. If the angles of elevation of the top of a 88. ÌèÙ â´ÚðU¹ çÕ´Îé¥æð´ A, B ÌÍæ C, °·¤ °ðâè ÚðU¹æ ÂÚU
tower from three collinear points A, B and çSÍÌ ãñ´ Áæð °·¤ ×èÙæÚU ·ð¤ ÂæÎ ·¤è çÎàææ ×ð´ Üð ÁæÌè ãñ,
C, on a line leading to the foot of the âð °·¤ ×èÙæÚU ·ð¤ çàæ¹ÚU ·ð¤ ©‹ÙØÙ ·¤æð‡æ ·ý¤×àæÑ
tower, are 308, 458 and 608 respectively, 308, 458 ÌÍæ 608 ãñ´, Ìæð AB : BC ·¤æ ¥ÙéÂæÌ ãñ Ñ
then the ratio, AB : BC, is :
(1) 3:1 (1) 3:1
(2) 3: 2 (2) 3: 2
(3) 1: 3 (3) 1: 3
(4) 2:3 (4) 2:3

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89. Let 89. ×æÙæ
 2x   2x 
tan21 y 5 tan21 x 1 tan21  , tan21 y 5 tan21 x 1 tan21  ,
 1 2 x2   1 2 x2 
1 1
where ? x ? < . Then a value of y is : Áãæ¡ ?x? < ãñ, Ìæð y ·¤æ °·¤ ×æÙ ãñ Ñ
3 3

3 x 2 x3 3 x 2 x3
(1) (1)
1 2 3 x2 1 2 3 x2

3 x 1 x3 3 x 1 x3
(2) (2)
1 2 3 x2 1 2 3 x2

3 x 2 x3 3 x 2 x3
(3) (3)
1 1 3 x2 1 1 3 x2

3 x 1 x3 3 x 1 x3
(4) (4)
1 1 3 x2 1 1 3 x2

90. The negation of ~ s Ú (~ r Ù s ) is equivalent 90. ~ s Ú (~ r Ù s ) ·¤æ çÙáðÏ â×ÌéËØ ãñ Ñ
to :
(1) sÙ~r (1) sÙ~r
(2) s Ù (r Ù ~ s) (2) s Ù (r Ù ~ s)
(3) s Ú (r Ú ~ s) (3) s Ú (r Ú ~ s)
(4) sÙr (4) sÙr

-o0o- -o0o-

SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

A/Page 38 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã