JEE MAIN EXAM 2015 CODE -ONLINE QUESTION PAPER DT.11.04.2015

1. Page 1 PHYSICS : English & Hindi 01
1. If electronic charge e, electron mass m,
speed of light in vacuum c and Planck’s
constant h are taken as fundamental
quantities, the permeability of vacuum m0
can be expressed in units of :
(1) 2
hc
me
 
 
 
(2) 2
h
me
 
 
 
(3) 2
h
ce
 
 
 
(4)
2
2
mc
he
 
  
 
2. A vector A
→
is rotated by a small angle Du
radians (Du<<1) to get a new vector B
→
.
In that case B A
→ →
2 is :
(1) 0
(2)
2
A 1
2
→  
  
 
Du
2
(3) A
→
Du
(4) B A
→ →
Du 2
1. ØçÎ §Üð€ÅþUæòÙ-¥æßðàæ e, §Üð€ÅþUæòÙ-ÎýÃØ×æÙ m, çÙßæüÌ÷
×ð´ Âý·¤æàæ ·ð¤ ßð» c ÌÍæ ŒÜæ¡·¤ çSÍÚUæ´·¤ h, ·¤æð ×êÜ
ÚUæçàæØæ¡ ×æÙ çÜØæ ÁæØ Ìæð, çÙßæüÌ÷ ·¤è ¿éÕ·¤àæèÜÌæ
m0 ·¤æ ×æ˜æ·¤ ãæð»æ Ñ
(1) 2
hc
me
 
 
 
(2) 2
h
me
 
 
 
(3) 2
h
ce
 
 
 
(4)
2
2
mc
he
 
  
 
2. ç·¤âè âçÎàæ A
→
·¤æð Du ÚðUçÇUØÙ (Du<<1) ƒæé×æ ÎðÙð
ÂÚU °·¤ ÙØæ âçÎàæ B
→
ÂýæŒÌ ãæðÌæ ãñÐ §â ¥ßSÍæ ×ð´
B A
→ →
2 ãæð»æ Ñ
(1) àæê‹Ø
(2)
2
A 1
2
→  
  
 
Du
2
(3) A
→
Du
(4) B A
→ →
Du 2

2. Page 2 PHYSICS : English & Hindi 01
3. A large number (n) of identical beads, each
of mass m and radius r are strung on a
thin smooth rigid horizontal rod of length
L (L>>r) and are at rest at random
positions. The rod is mounted between
two rigid supports (see figure). If one of
the beads is now given a speed v, the
average force experienced by each support
after a long time is (assume all collisions
are elastic) :
(1)
2
m
L nr
v
2
(2)
2
m
L 2nr
v
2
(3)
2
m
2(L nr)
v
2
(4) zero
4. A particle is moving in a circle of radius r
under the action of a force F5ar2 which
is directed towards centre of the circle.
Total mechanical energy (kinetic
energy1potential energy) of the particle
is (take potential energy50 for r50) :
(1) ar3
(2)
31
r
2
a
(3)
34
r
3
a
(4)
35
r
6
a
3. °·¤ ÂÌÜè ç¿·¤Ùè ÿæñçÌÁ ÀUǸ ÂÚU ·¤§ü (n) âßüâ×
×ç‡æ·¤æØð´ (ÕèÇU) çÂÚUæð§ü »§ü ãñ´ Áæð ÀUǸ ÂÚU ¥çÙØç×Ì
ÌÍæ çßÚUæ× ¥ßSÍæ ×ð´ ãñ´Ð ÂýˆØð·¤ ÕèÇU ·¤æ ÎýÃØ×æÙ
m ÌÍæ ç˜æ’Øæ r ãñ ¥æñÚU ÀUǸ ·¤è Ü´Õæ§ü L ãñ (L>>r)Ð
Øã ÀUǸ Îæð ÅðU·¤æð´ (¥æÏæÚUæð´) ÂÚU, ¥æÚðU¹ ×ð´ ÎàææüØð »Øð
¥ÙéâæÚU çÅU·¤è ãñÐ ØçÎ °·¤ ÕèÇU ·¤æð v ßð» ÂýÎæÙ
ç·¤Øæ ÁæØ Ìæð, °·¤ ܐÕð â×Ø ·ð¤ Âà¿æÌ÷ ÂýˆØð·¤
ÅðU·¤ (¥æÏæÚU) ÂÚU Ü»Ùð ßæÜð ¥æñâÌ ÕÜ ·¤æ ×æÙ
ãæð»æ (ØçÎ âÖè ÅU€·¤Úð´U ÂýˆØæSÍ ãñ´) Ñ
(1)
2
m
L nr
v
2
(2)
2
m
L 2nr
v
2
(3)
2
m
2(L nr)
v
2
(4) àæê‹Ø
4. ç·¤âè ÕÜ F5ar2 ·ð¤ ·¤æÚU‡æ, °·¤ ·¤‡æ r ç˜æ’Øæ ·ð¤
ßëžæ ×ð´ »çÌ ·¤ÚUÌæ ãñÐ ÕÜ ·¤è çÎàææ ßëžæ ·ð¤ ·ð¤‹Îý ·¤è
¥æðÚU ãñÐ ØçÎ, r50 ·ð¤ çÜØð çSÍçÌÁ ª¤Áæü ·¤æð àæê‹Ø
×æÙæ ÁæØ Ìæð, §â ·¤‡æ ·¤è ·é¤Ü Øæ´ç˜æ·¤ ª¤Áæü (»çÌÁ
ª¤Áæü1çSÍçÌÁ ª¤Áæü) ãæð»è Ñ
(1) ar3
(2)
31
r
2
a
(3)
34
r
3
a
(4)
35
r
6
a

3. Page 3 PHYSICS : English & Hindi 01
5. A uniform thin rod AB of length L has
linear mass density m(x)5
b
a
L
x
1 , where
x is measured from A. If the CM of the
rod lies at a distance of
7
L
12
 
 
 
from A,
then a and b are related as :
(1) a5b
(2) a52b
(3) 2a5b
(4) 3a52b
6. A particle of mass 2 kg is on a smooth
horizontal table and moves in a circular
path of radius 0.6 m. The height of the
table from the ground is 0.8 m. If the
angular speed of the particle is 12 rad s21,
the magnitude of its angular momentum
about a point on the ground right under
the centre of the circle is :
(1) 8.64 kg m2s21
(2) 11.52 kg m2s21
(3) 14.4 kg m2s21
(4) 20.16 kg m2s21
5. L ܐÕæ§ü ÌÍæ °·¤â×æÙ ÂÌÜè ÀUǸ AB, ·¤æ ÚñUç¹·¤
ÎýÃØ×æÙ ƒæÙˆß m(x)5
b
a
L
x
1 ãñ, Áãæ¡ x ·¤æð ÀUǸ
·ð¤ çâÚðUA âð ×æÂæ ÁæÌæ ãñÐ ØçÎ §â ÀUǸ ·¤æ ÎýÃØ×æÙ-
·ð¤‹Îý ÀUǸ ·ð¤ çâÚðU A âð
7
L
12
 
 
 
ÎêÚUè ÂÚU ãñ Ìæð,
a ÌÍæ b ·ð¤ Õè¿ â´Õ´Ï ãæð»æ Ñ
(1) a5b
(2) a52b
(3) 2a5b
(4) 3a52b
6. 2 kg ÎýÃØ×æÙ ·¤æ °·¤ ·¤‡æ, ç·¤âè ç¿·¤Ùð ÿæñçÌÁ
×ðÁ ÂÚU çSÍÌ ãñ ÌÍæ 0.6 m ç˜æ’Øæ ·ð¤ ßëžææ·¤æÚU ÂÍ
ÂÚU »çÌ ·¤ÚU ÚUãæ ãñÐ Öê-ÌÜ âð ×ðÁ ·¤è ª¡¤¿æ§ü 0.8 m
ãñÐ ØçÎ ·¤‡æ ·¤è ·¤æð‡æèØ ¿æÜ 12 rad s21 ãæð Ìæð,
ßëžæ ·ð¤ ·ð¤‹Îý ·ð¤ ÆUè·¤ Ùè¿ð Öê-ÌÜ ÂÚU ç·¤âè çÕ‹Îé ·ð¤
ÂçÚUÌÑ, §â ·¤‡æ ·¤æ ·¤æð‡æèØ â´ßð» ·¤æ ÂçÚU×æ‡æ ãæð»æ Ñ
(1) 8.64 kg m2s21
(2) 11.52 kg m2s21
(3) 14.4 kg m2s21
(4) 20.16 kg m2s21

4. Page 4 PHYSICS : English & Hindi 01
7. Which of the following most closely
depicts the correct variation of the
gravitation potential V(r) due to a large
planet of radius R and uniform mass
density ? (figures are not drawn to scale)
(1)
(2)
(3)
(4)
8. A cylindrical block of wood
(density5650 kg m23), of base area
30 cm2 and height 54 cm, floats in a liquid
of density 900 kg m23. The block is
depressed slightly and then released. The
time period of the resulting oscillations of
the block would be equal to that of a simple
pendulum of length (nearly) :
(1) 65 cm
(2) 52 cm
(3) 39 cm
(4) 26 cm
7. çِÙæ´ç·¤Ì ¥æÜð¹æð´ ×ð´ âð ·¤æñÙ âæ ¥æÜð¹ (»ýæȤ), R
ç˜æ’Øæ ÌÍæ °·¤â×æÙ ÎýÃØ×æÙ ƒæÙˆß ßæÜð ç·¤âè ÕǸð
»ý㠷𤠻éL¤ˆßèØ çßÖß V(r) ·ð¤ âãè çß¿ÚU‡æ
(ÂçÚUßÌüÙ) ·¤æ âßæüçÏ·¤ çÙ·¤ÅU 翘æ‡æ ·¤ÚUÌæ ãñ?
(¥æÚðU¹ ÆUè·¤ Âñ×æÙð ·ð¤ ¥ÙéâæÚU Ùãè´ ãñ´)
(1)
(2)
(3)
(4)
8. Ü·¤Ç¸è ·ð¤ ç·¤âè ÕðÜÙæ·¤æÚU »éÅU·ð¤ (ŽÜæò·¤) ·¤è ܐÕæ§ü
54 cm, ÌÍæ ƒæÙˆß 650 kg m23 ãñÐ §â·ð¤ ¥æÏæÚU
·¤æ ÿæð˜æÈ¤Ü 30 cm2 ãñ, ¥æñÚU Øã 900 kg m23
ƒæÙˆß ßæÜð Îýß ×ð´ ÌñÚU ÚUãæ ãñ (ŒÜß×æÙ ãñ)Ð §â
ŽÜæò·¤ ·¤æð ÍæðǸæ âæ Ùè¿ð ·¤è ¥æðÚU ÎÕæ·¤ÚU ÀUæðǸ çÎØæ
ÁæÌæ ãñÐ ÂçÚU‡ææ× SßM¤Â ©ˆÂóæ §â·ð¤ ÎæðÜÙæð´ ·¤æ
¥æßÌü·¤æÜ, ç·¤â ܐÕæ§ü (ֻܻ) ·ð¤ âÚUÜ ÜæðÜ·¤
·ð¤ ¥æßÌü·¤æÜ ·ð¤ ÕÚUæÕÚU ãæð»æ?
(1) 65 cm
(2) 52 cm
(3) 39 cm
(4) 26 cm

5. Page 5 PHYSICS : English & Hindi 01
9. ç·¤âè Õè·¤ÚU ×ð´ ÚU¹ð °·¤ Îýß ·¤æ ƒæÙˆß r kg/m3,
çßçàæcÅUU ª¤c×æ S J/kg8C ÌÍæ àØæÙÌæ h ãñÐ Øã
Õè·¤ÚU h ª¤¡¿æ§ü Ì·¤ Îýß âð ÖÚUæ ãñÐ Õè·¤ÚU ·¤æð °·¤
ÒãæòÅU ŒÜðÅUÓ ÂÚU ÚU¹Ùð ÂÚU, ©â×ð´ ÚU¹ð Îýß ·¤è âÕâð
ª¤ÂÚU ÌÍæ âÕâð Ùè¿ð ·¤è ÂÚUÌ ·ð¤ Õè¿ Ìæ ·¤æ ¥‹ÌÚU
Du (8C ×ð´) ãæðÌæ ãñÐ °·¤ çßlæÍèü ·ð¤ ¥ÙéâæÚ, §â
¥ßSÍæ ×ð´ â´ßãÙ mæÚUæ ÂýçÌ §·¤æ§ü ÿæð˜æÈ¤Ü ª¤c×æ ·¤æ
SÍæÙæ‹ÌÚU‡æ, ¥ÍæüÌ÷ (Q /A)
•
·¤æ ×æÙ h,
S 1
h g
  
  
   
Du
r
±²Ë ÂÚU çÙÖüÚU ·¤ÚUÙæ ¿æçãØð, Ìæð,
(Q/A)
•
·ð¤ ×æÙ ·ð¤ çÜØð âãè çß·¤Ë ãæð»æ Ñ
(1)
S
h
Du
h
(2)
S 1
h g
  
  
   
Du
h
r
(3)
S
h
Du
h
(4)
S 1
h g
  
  
   
Du
h r
10. ç·¤âè ÂýØæð» ×ð´ ç·¤âè ª¤c×·¤ (ãèÅUÚU) mæÚUæ °·¤â×æÙ
ÎÚU ÂÚU ª¤c×æ ÎðÙð ÂÚU, °·¤ Âæ˜æ ×ð´ ÚU¹ð ÁÜ ·¤æ ÌæÂ
08C âð 1008C Ì·¤ ÕɸæÙð ·ð¤ çÜØð 10 ç×ÙÅU ·¤æ
â×Ø Ü»Ìæ ãñÐ §âè Îýß ·¤æð Âê‡æüÌÑ ßæc ×ð´ M¤Âæ‹ÌçÚUÌ
·¤ÚUÙð ×ð´ 55 ç×ÙÅU ¥æñÚU Ü»Ìð ãñ´Ð Âæ˜æ ·¤è çßçàæcÅU
ª¤c×æ ·¤æð Ù»‡Ø ÌÍæ ÁÜ ·¤è çßçàæcÅUU ª¤c×æ ·¤æð
1 cal/g 8C ÜðÌð ãé°, §â ÂýØæ𻠷𤠥ÙéâæÚU ßæcÂÙ
·¤è ª¤c×æ ·¤æ ×æÙ ãæð»æ Ñ
(1) 530 cal/g
(2) 540 cal/g
(3) 550 cal/g
(4) 560 cal/g
9. A beaker contains a fluid of density
r kg/m3, specific heat S J/kg8C and
viscosity h. The beaker is filled up to height
h. To estimate the rate of heat transfer
per unit area (Q /A)
•
by convection when
beaker is put on a hot plate, a student
proposes that it should depend on h,
S 1
and
h g
  
  
   
Du
r
when Du (in 8C) is the
difference in the temperature between the
bottom and top of the fluid. In that
situation the correct option for (Q/A)
•
is :
(1)
S
h
Du
h
(2)
S 1
h g
  
  
   
Du
h
r
(3)
S
h
Du
h
(4)
S 1
h g
  
  
   
Du
h r
10. An experiment takes 10 minutes to raise
the temperature of water in a container
from 08C to 1008C and another 55 minutes
to convert it totally into steam by a heater
supplying heat at a uniform rate.
Neglecting the specific heat of the container
and taking specific heat of water to be
1 cal/g 8C, the heat of vapourization
according to this experiment will come out
to be :
(1) 530 cal/g
(2) 540 cal/g
(3) 550 cal/g
(4) 560 cal/g

6. Page 6 PHYSICS : English & Hindi 01
11. Using equipartition of energy, the specific
heat (in J kg21 K21) of aluminium at room
temperature can be estimated to be (atomic
weight of aluminium527)
(1) 25
(2) 410
(3) 925
(4) 1850
12. A pendulum with time period of 1s is
losing energy due to damping. At certain
time its energy is 45 J. If after completing
15 oscillations, its energy has become 15 J,
its damping constant (in s21) is :
(1)
1
3
30
ln
(2)
1
3
15
ln
(3) 2
(4)
1
2
11. ª¤Áæü ·ð¤ â×çßÖæÁÙ ·ð¤ ©ÂØæð» âð, ·¤ÿæ-Ìæ ÂÚU,
°ðÜéç×çÙØ× ·¤è çßçàæcÅU ª¤c×æ (J kg21 K21) ·¤æ
¥Ùé×æçÙÌ ×æÙ ãæð»æ, (°ðÜéç×çÙØ× ·¤æ ÂÚU×æ‡æé
ÖæÚU527)
(1) 25
(2) 410
(3) 925
(4) 1850
12. 1s ¥æßÌü·¤æÜ ·ð¤ ç·¤âè ÜæðÜ·¤ ·¤è ª¤Áæü ¥ß×´ÎÙ
·ð¤ ·¤æÚU‡æ ÿæØ ãæð ÚUãè ãñÐ ç·¤âè ÿæ‡æ §â·¤è ª¤Áæü
45 J ãñÐ ØçÎ 15 ÎæðÜÙ ÂêÚðU ·¤ÚUÙð ·ð¤ Âà¿æÌ÷ §â·¤è
ª¤Áæü 15 J ãæð ÁæÌè ãñ Ìæð, §â·ð¤ çÜØð ¥ß×´ÎÙ çSÍÚUæ´·¤
ãñ (s21 ×ð´) Ñ
(1)
1
3
30
ln
(2)
1
3
15
ln
(3) 2
(4)
1
2

7. Page 7 PHYSICS : English & Hindi 01
13. A source of sound emits sound waves at
frequency f0. It is moving towards an
observer with fixed speed vs(vs<v, where
v is the speed of sound in air). If the
observer were to move towards the source
with speed v0, one of the following two
graphs (A and B) will give the correct
variation of the frequency f heard by the
observer as v0 is changed.
The variation of f with v0 is given correctly
by :
(1) graph A with slope 0
s( )
f
v v
5
2
(2) graph A with slope 0
s( )
f
v v
5
1
(3) graph B with slope 0
s( )
f
v v
5
2
(4) graph B with slope 0
s( )
f
v v
5
1
13. ŠßçÙ ·ð¤ °·¤ dæðÌ âð f0 ¥æßëçžæ ·¤è ÌÚ´U»ð´ ©ˆâçÁüÌ
(©ˆÂóæ) ãæðÌè ãñ´Ð Øã dæðÌ ç·¤âè ŸææðÌæ ·¤è ¥æðÚU °·¤
çÙØÌ ¿æÜ vs âð ¿Ü ÚUãæ ãñ (vs< v, Áãæ¡ v ßæØé ×ð´
ŠßçÙ ·¤è ¿æÜ ãñ)Ð ØçÎ ŸææðÌæ v0 ¿æÜ âð dæðÌ ·¤è
¥æðÚU ¿ÜÙð Ü»ð, Ìæð v0 ×ð´ ÂçÚUßÌüÙ âð, ŸææðÌæ mæÚUæ âéÙè
»§ü ¥æßëçžæ ·ð¤ âãè çß¿ÚU‡æ (ÂçÚUßÌüÙ) ·¤æð çِÙæ´ç·¤Ì
»ýæȤ A Øæ B ×ð´ âð °·¤ »ýæȤ ÎàææüØð»æÐ
Ìæð, v0 ·ð¤ âæÍ f ·ð¤ çß¿ÚU‡æ (ÂçÚUßÌüÙ) ·¤æð âãè
ÎàææüÌæ ãñ Ñ
(1) »ýæȤ A Âý߇æÌæ 0
s( )
f
v v
5
2
·ð¤ âæÍ
(2) »ýæȤ A Âý߇æÌæ 0
s( )
f
v v
5
1
·ð¤ âæÍ
(3) »ýæȤ B Âý߇æÌæ 0
s( )
f
v v
5
2
·ð¤ âæÍ
(4) »ýæȤ B Âý߇æÌæ 0
s( )
f
v v
5
1
·ð¤ âæÍ

8. Page 8 PHYSICS : English & Hindi 01
14. A wire, of length L(520 cm), is bent into
a semi-circular arc. If the two equal halves,
of the arc, were each to be uniformly
charged with charges 6Q, [|Q|5103 e0
Coulomb where e0 is the permittivity (in
SI units) of free space] the net electric field
at the centre O of the semi-circular arc
would be :
(1) (503103 N/C) j
∧
(2) (253103 N/C) i
∧
(3) (253103 N/C) j
∧
(4) (503103 N/C) i
∧
15. An electric field
( ) 1
E 25 i 30 j NC
→ ∧ ∧
25 1 exists in a
region of space. If the potential at the
origin is taken to be zero then the potential
at x52 m, y52 m is :
(1) 2130 J
(2) 2120 J
(3) 2140 J
(4) 2110 J
14. L(520 cm) ܐÕæ§ü ·ð¤ °·¤ ÌæÚU ·¤æð °·¤ ¥Ïü ßëžææ·¤æÚU
¿æ ·ð¤ M¤Â ×ð´ ×æðǸ çÎØæ »Øæ ãñÐ ØçÎ §â ¿æ ·ð¤ Îæð
â×æÙ Öæ»æð´ ·¤æð 6Q ¥æßðàæ âð °·¤â×æÙ ¥æßðçàæÌ
·¤ÚU çÎØæ ÁæØ [|Q|5103 e0 ·ê¤Üæò× Áãæ¡ e0 (SI
×æ˜æ·¤ ×ð´) ×é€Ì ¥æ·¤æàæ ·¤è çßléÌàæèÜÌæ
(ÂÚUæßñléÌæ´·¤) ãñ ], Ìæð, ¥Ïüßëžææ·¤æÚU ¿æ ·ð¤ ·ð¤‹Îý O
ÂÚU ÙðÅU çßléÌ ÿæð˜æ ãæð»æ Ñ
(1) (503103 N/C) j
∧
(2) (253103 N/C) i
∧
(3) (253103 N/C) j
∧
(4) (503103 N/C) i
∧
15. ç·¤âè SÍæÙ ÂÚU °·¤ çßléÌ ÿæð˜æ,
( ) 1
E 25 i 30 j NC
→ ∧ ∧
25 1 , çßl×æÙ ãñÐ ØçÎ
×êÜçÕ‹Îé ÂÚU çßÖß ·¤æ ×æÙ àæê‹Ø ×æÙæ ÁæØ Ìæð,
x52 m, y52 m ÂÚU çßÖß ãæð»æ Ñ
(1) 2130 J
(2) 2120 J
(3) 2140 J
(4) 2110 J

9. Page 9 PHYSICS : English & Hindi 01
16. In figure is shown a system of four
capacitors connected across a 10 V battery.
Charge that will flow from switch S when
it is closed is :
(1) 5 mC from b to a
(2) 20 mC from a to b
(3) 5 mC from a to b
(4) zero
17. In the electric network shown, when no
current flows through the 4 V resistor in
the arm EB, the potential difference
between the points A and D will be :
(1) 3 V
(2) 4 V
(3) 5 V
(4) 6 V
16. Øãæ¡ ¥æÚðU¹ ×ð´ ¿æÚU â´ÏæçÚU˜ææ𴠷𤠰·¤ çÙ·¤æØ (Ì´˜æ)
·¤æð °·¤ 10 V ·¤è ÕñÅUÚUè âð ÁéǸæ ãé¥æ ÎàææüØæ »Øæ ãñÐ
çSß¿ S ·¤æð Õ´Î ·¤ÚUÙð ÂÚU ©ââð ÂýßæçãÌ ¥æßðàæ ãæð»æ Ñ
(1) 5 mC, b âð a ·¤æð
(2) 20 mC, a âð b ·¤æð
(3) 5 mC, a âð b ·¤æð
(4) àæê‹Ø
17. ÎàææüØð »Øð ÂçÚUÂÍ ÁæÜ ×ð´, ÖéÁæ EB ·ð¤ ÂýçÌÚUæðÏ 4 V
âð ØçÎ ·¤æð§ü ÏæÚUæ ÂýßæçãÌ Ùãè´ ãæð ÚUãè ãñ Ìæð, A ÌÍæ D
çÕ‹Îé¥æð´ ·ð¤ Õè¿ çßÖßæ‹ÌÚU ãæð»æ Ñ
(1) 3 V
(2) 4 V
(3) 5 V
(4) 6 V

10. Page 10 PHYSICS : English & Hindi 01
18. The value of the resistor, RS, needed in the
dc voltage regulator circuit shown here,
equals :
(1) (Vi2VL)/n IL
(2) (Vi1VL)/n IL
(3) (Vi2VL)/(n11) IL
(4) (Vi1VL)/(n11) IL
18. Øãæ¡ ÎàææüØð »Øð ÇUè.âè. (dc) ßæðËÅUÌæ çÙØ´˜æ·¤ ÂçÚUÂÍ
×ð´, ¥æßàØ·¤ ÂýçÌÚUæðÏ RS ·¤æ ×æÙ ãæð»æ Ñ
(1) (Vi2VL)/n IL
(2) (Vi1VL)/n IL
(3) (Vi2VL)/(n11) IL
(4) (Vi1VL)/(n11) IL

11. Page 11 PHYSICS : English & Hindi 01
19. Îæð ܐÕð, âèÏð, â×æ‹ÌÚU ÌæÚUæð´ ·ð¤ Õè¿ ·¤è ÎêÚUè d ãñÐ
§Ùâð I1 ÌÍæ I2 ÏæÚUæØð´ ÂýßæçãÌ ãæð ÚUãè ãñ´ (çÁÙ·ð¤ ×æÙ
â×æØæðçÁÌ ç·¤Øð Áæ â·¤Ìð ãñ´) ØçÎ §Ù ÌæÚUæð´ ·ð¤ Õè¿
ÂýçÌ·¤áü‡æ ãæðÙð ÂÚU §Ù·ð¤ Õè¿ ÕÜ ‘F’ ·¤æð ÒÏÙæˆ×·¤Ó
ÌÍæ §Ù ·ð¤ Õè¿ ¥æ·¤áü‡æ ãæðÙð ÂÚU ÕÜ F ·¤æ𠫤‡ææˆ×·¤
×æÙæ ÁæØ Ìæð, I1 ÌÍæ I2 ·ð¤ »é‡æÙÈ¤Ü (I1I2) ÂÚU ‘F’
·ð¤ çÙÖüÚU ãæðÙð ·¤æð ·¤æñÙ âæ »ýæȤ ÆUè·¤ (âãè) ÎàææüÌæ
ãñ?
(1)
(2)
(3)
(4)
19. Two long straight parallel wires, carrying
(adjustable) currents I1 and I2, are kept at
a distance d apart. If the force ‘F’ between
the two wires is taken as ‘positive’ when
the wires repel each other and ‘negative’
when the wires attract each other, the
graph showing the dependence of ‘F’, on
the product I1I2, would be :
(1)
(2)
(3)
(4)

12. Page 12 PHYSICS : English & Hindi 01
20. I ÏæÚUæßæãè °·¤ ÌæÚU, P ÌÍæ Q çÕ‹Îé¥æð´ ÂÚU Õ´Ïæ ãñ
¥æñÚU ¥ÂÙð ¥æâ-Âæâ ¿éÕ·¤èØ ÿæð˜æ B ·ð¤ ·¤æÚU‡æ (Áæð
xxx mæÚUæ ÎàææüØæ »Øæ ãñ ¥æñÚU §â ÂëcÆ ·ð¤ ܐÕßÌ÷ ãñ)
R ç˜æ’Øæ ·ð¤ ßëžææ·¤æÚU ¿æ ·ð¤ M¤Â ×ð´ ¥æ ÁæÌæ ãñÐ
ØçÎ Øã ÌæÚU, ©â ßëžæ ·ð¤ ·ð¤‹Îý ÂÚU çÁâ·¤æ Øã ¿æÂ
Öæ» ãñ, 2u0 ·¤æð‡æ ÕÙæÌæ ãñ Ìæð, ÌæÚU ×ð´ ÌÙæß ãæð»æ Ñ
(1) IBR
(2)
0
IBR
sinu
(3)
0
IBR
2sinu
(4)
0
0
IBR
sin
u
u
21. ç·¤âè ÀUæðÅðU âð δÇU ¿éÕ·¤ ·¤æð Âë‰ßè ·ð¤ ¿éÕ·¤èØ ÿæð˜æ
·ð¤ ¿éÕ·¤èØ ØæØæðžæÚU ×ð´ §â Âý·¤æÚU ÚU¹æ »Øæ ãñ ç·¤
©â·¤æ ©žæÚU Ïýéß, ©žæÚU ·¤è ¥æðÚU ãñÐ §â·ð¤ ·¤æÚU‡æ
¿éÕ·¤ ·ð¤ ׊ØçÕ‹Îé âð Âêßü-Âçà¿× çÎàææ ×𴠹贿è
»§ü âÚUÜ ÚðU¹æ ÂÚU, ©ÎæâèÙ çÕ‹Îé ÂýæŒÌ ãæðÌð ãñ´, çÁÙ·¤è
¿éÕ·¤ âð ÎêÚUè 30 cm ãñÐ Ìæð, ¿éÕ·¤ ·¤æ ¿éÕ·¤èØ
¥æƒæê‡æü (Am2 ×ð´) ãæð»æ ֻܻ Ñ
(çÎØæ ãñ, 70 10
4
2m
5
p
SI ×æ˜æ·¤ ×ð´ ÌÍæ BH5Âë‰ßè
·ð¤ ¿éÕ·¤èØ ÿæð˜æ ·¤æ ÿæñçÌÁ ƒæÅU·¤ 53.631025
Tesla.)
(1) 9.7
(2) 4.9
(3) 19.4
(4) 14.6
20. A wire carrying current I is tied between
points P and Q and is in the shape of a
circular arch of radius R due to a uniform
magnetic field B (perpendicular to the
plane of the paper, shown by xxx) in the
vicinity of the wire. If the wire subtends
an angle 2u0 at the centre of the circle (of
which it forms an arch) then the tension
in the wire is :
(1) IBR
(2)
0
IBR
sinu
(3)
0
IBR
2sinu
(4)
0
0
IBR
sin
u
u
21. A short bar magnet is placed in the
magnetic meridian of the earth with north
pole pointing north. Neutral points are
found at a distance of 30 cm from the
magnet on the East - West line, drawn
through the middle point of the magnet.
The magnetic moment of the magnet in
Am2 is close to :
(Given 70 10
4
2m
5
p
in SI units and
BH5Horizontal component of earth’s
magnetic field53.631025 Tesla.)
(1) 9.7
(2) 4.9
(3) 19.4
(4) 14.6

13. Page 13 PHYSICS : English & Hindi 01
22. Øãæ¡ ÎàææüØð »Øð LCR ÂçÚUÂÍ ×ð´, çßléÌÏæÚUæ, ¥æÚUæðçÂÌ
ßæðËÅUÌæ âð ¥»ý»æ×è (¥æ»ð) ÚUãÌè ãñÐ ÂçÚUÂÍ ×ð´ ÁéǸð
â´ÏæçÚU˜æ C ·ð¤ âæÍ °·¤ ¥çÌçÚU€Ì â´ÏæçÚU˜æ C9 ÁæðǸÙð
âð, §â ÂçÚUÂÍ ·¤æ àæç€Ì-»é‡æ·¤ §·¤æ§ü (°·¤·¤) ãæð
ÁæÌæ ãñÐ Ìæð, â´ÏæçÚU˜æ C9 ·¤æð ¥ßàØ ãè ÁæðÇ¸æ »Øæ
ãæð»æ Ñ
(1) C âð Ÿæð‡æè ·ý¤× ×ð´ ¥æñÚU ©â·¤æ ×æÙ ãæð»æ
2
2
1 LC
L
2 v
v
.
(2) C âð Ÿæð‡æè ·ý¤× ×ð´ ¥æñÚU ©â·¤æ ×æÙ ãæð»æ
2
C
( LC 1)v 2 .
(3) C âð â×æ´ÌÚU (Âæàßü) ·ý¤× ×ð´ ¥æñÚU ©â·¤æ ×æÙ
ãæð»æ 2
C
( LC 1)v 2 .
(4) C âð â×æ´ÌÚU ·ý¤× ×ð´ ¥æñÚU ©â·¤æ ×æÙ ãæð»æ
2
2
1 LC
L
2 v
v
.
23. z çÎàææ ×ð´ »×Ù ·¤ÚUÌè ãé§ü â×ÌÜ çßléÌ-¿éÕ·¤èØ
ÌÚ´U»æð´ ·ð¤ çÜØð, çِÙæ´ç·¤Ì â´ØæðÁÙæð´ ×ð´ ·¤æñÙ-âæ â´ØæðÁÙ
·ý¤×àæÑ E
→
ÌÍæ B
→
ÿæð˜ææð´ ·¤è âãè çÎàææ ÎàææüÌæ ãñ?
(1) ( )2i j
∧ ∧
1 ÌÍæ ( )2 i j
∧ ∧
2
(2) ( )2 3i j
∧ ∧
2 2 ÌÍæ ( )3 2i j
∧ ∧
2
(3) ( )2 3i j
∧ ∧
1 ÌÍæ ( )2i j
∧ ∧
1
(4) ( )3 4i j
∧ ∧
1 ÌÍæ ( )4 3i j
∧ ∧
2
22. For the LCR circuit, shown here, the
current is observed to lead the applied
voltage. An additional capacitor C9, when
joined with the capacitor C present in the
circuit, makes the power factor of the
circuit unity. The capacitor C9, must have
been connected in :
(1) series with C and has a magnitude
2
2
1 LC
L
2 v
v
.
(2) series with C and has a magnitude
2
C
( LC 1)v 2 .
(3) parallel with C and has a magnitude
2
C
( LC 1)v 2 .
(4) parallel with C and has a magnitude
2
2
1 LC
L
2 v
v
.
23. For plane electromagnetic waves
propagating in the z direction, which one
of the following combination gives the
correct possible direction for E
→
and B
→
field respectively ?
(1) ( )2i j
∧ ∧
1 and ( )2 i j
∧ ∧
2
(2) ( )2 3i j
∧ ∧
2 2 and ( )3 2i j
∧ ∧
2
(3) ( )2 3i j
∧ ∧
1 and ( )2i j
∧ ∧
1
(4) ( )3 4i j
∧ ∧
1 and ( )4 3i j
∧ ∧
2

14. Page 14 PHYSICS : English & Hindi 01
24. °·¤ ©žæÜ Üð´â ·¤æð, ¥æÚðU¹ ×ð´ ÎàææüØð »Øð ¥ÙéâæÚU
ç·¤âè â×ÌÜ ÎÂü‡æ ·ð¤ ª¤ÂÚU ÚU¹æ »Øæ ãñÐ Üð´â ·¤è
Ȥæð·¤â ÎêÚUè ‘f’ ãñÐ §â â´ØæðÁÙ âð ç·¤âè ßSÌé ·¤æð ‘a’
ÎêÚUè ÂÚU ÚU¹Ùð âð, ©â·¤æ ÂýçÌçÕÕ â´ØæðÁÙ ·ð¤ âæ×Ùð
a
3
ÎêÚUè ÂÚU ÕÙÌæ ãñÐ Ìæð, ‘a’ ·¤æ ×æÙ ãñ Ñ
(1) f
(2) 2f
(3) 3f
(4)
3
f
2
25. Ø´» ·ð¤ ç·¤âè çm-çÛæÚUè ÂýØæð» ×ð´, ÂýØé€Ì Âý·¤æàæ ·¤è
ÌÚ´U»ÎñƒØü l, çÛæçÚUØæð´ (çSÜÅUæð´) ·ð¤ Õè¿ ·¤è ÎêÚUè d,
ÌÍæ ÂÎðü ·¤è çÛæçÚUØæð´ âð ÎêÚUè D ãñÐ
Áãæ¡, D > > d > > lÐ ØçÎ, çÈý´¤Á ¿æñǸæ§ü b ãñ Ìæð,
¥çÏ·¤Ì× ÌèßýÌæ ·ð¤ çÕ‹Îé âð, ÎæðÙæð´ ¥æðÚU ·ð¤ ©Ù çÕ‹Îé¥æð´
·¤è ÎêÚUè, Áãæ¡ ÌèßýÌæ, ¥çÏ·¤Ì× âð ¥æÏè ãæð ÁæÌè ãñ,
ãæð»è Ñ
(1)
2
b
(2)
4
b
(3)
3
b
(4)
6
b
24. A thin convex lens of focal length ‘f’ is put
on a plane mirror as shown in the figure.
When an object is kept at a distance ‘a’
from the lens - mirror combination, its
image is formed at a distance
a
3
in front
of the combination. The value of ‘a’ is :
(1) f
(2) 2f
(3) 3f
(4)
3
f
2
25. In a Young’s double slit experiment with
light of wavelength l the separation of slits
is d and distance of screen is D such that
D > > d > > l. If the Fringe width is b, the
distance from point of maximum intensity
to the point where intensity falls to half of
maximum intensity on either side is :
(1)
2
b
(2)
4
b
(3)
3
b
(4)
6
b

15. Page 15 PHYSICS : English & Hindi 01
26. I0 ÌèßýÌæ ·¤æ ¥ÏýéçßÌ Âý·¤æàæ, ·¤æ¡¿ ·ð¤ ŽÜæò·¤ (»éÅU·ð¤)
·¤è âÌã (ÂëcÆU) ÂÚU, ÕýêSÅUÚU ·¤æð‡æ ÂÚU, ¥æÂçÌÌ ãæðÌæ
ãñÐ §â çSÍçÌ ·ð¤ çÜØð çِÙçÜç¹Ì ×ð´ âð ·¤æñÙâæ
·¤ÍÙ âãè (âˆØ) ãñ?
(1) ÂæÚU»Ì Âý·¤æàæ, ¥æ´çàæ·¤ ÏýéçßÌ ãæð»æ ¥æñÚU ©â·¤è
ÌèßýÌæ I0/2 ãæð»èÐ
(2) ÂæÚU»Ì Âý·¤æàæ Âê‡æüM¤Â âð ÏýéçßÌ ãæð»æ ¥æñÚU ©â·¤è
ÌèßýÌæ I0/2 âð ·¤× ãæð»èÐ
(3) ÂÚUæßçÌüÌ Âý·¤æàæ Âê‡æüÌÑ ÏýéçßÌ ãæð»æ ¥æñÚU ©â·¤è
ÌèßýÌæ I0/2 âð ·¤× ãæð»èÐ
(4) ÂÚUæßçÌüÌ Âý·¤æàæ Âê‡æüÌÑ ÏýéçßÌ ãæð»æ ¥æñÚU ©â·¤è
ÌèßýÌæ I0/2 ãæð»èÐ
27. n54 SÌÚU ÂÚU, ç·¤âè §Üð€ÅþUæòÙ âð â´Õh Îð-Õýæò‚Üè
ÌÚ´U»ÎñƒØü ãæð»è Ñ
(1) ‹ØêÙÌ× ª¤Áæü SÌÚU ÂÚU §Üð€ÅþUæòÙ ·¤è Îð-Õýæò‚Üè
ÌÚ´U»ÎñƒØü âð Îæð »éÙæÐ
(2) ‹ØêÙÌ× ª¤Áæü SÌÚU ÂÚU §Üð€ÅþUæòÙ ·¤è Îð-Õýæò‚Üè
ÌÚ´U»ÎñƒØü ·¤è ¿æÚU »éÙæÐ
(3) ‹ØêÙÌ× ª¤Áæü SÌÚU ÂÚU §Üð€ÅþUæòÙ ·¤è Îð-Õýæò‚Üè
ÌÚ´U»ÎñƒØü ·¤è ¥æÏèÐ
(4) ‹ØêÙÌ× ª¤Áæü SÌÚU ÂÚU §Üð€ÅþUæòÙ ·¤è Îð-Õýæò‚Üè
ÌÚ´U»ÎñƒØü ·¤è 1/4.
28. ØçÎ 1 »ýæ×
24
Na ÚðUçÇUØæð°ç€ÅUß ÙæçÖ·¤ (¥Ïü ¥æØé
15 ƒæ´ÅðU) mæÚUæ 7.5 ƒæ´ÅðU ×ð´ ©ˆâçÁüÌ b ·¤‡ææð´ ·¤è
ⴁØæ Nb ãæð Ìæð, Nb ·¤æ ×æÙ çÙ·¤ÅU ãæð»æ
(¥æßæð»æÎýUæð ⴁØæ 6.02331023/g. mol) :
(1) 6.231021
(2) 7.531021
(3) 1.2531022
(4) 1.7531022
26. Unpolarized light of intensity I0 is incident
on surface of a block of glass at Brewster’s
angle. In that case, which one of the
following statements is true ?
(1) transmitted light is partially
polarized with intensity I0/2.
(2) transmitted light is completely
polarized with intensity less than
I0/2.
(3) reflected light is completely polarized
with intensity less than I0/2.
(4) reflected light is partially polarized
with intensity I0/2.
27. The de - Broglie wavelength associated
with the electron in the n54 level is :
(1) two times the de-Broglie wavelength
of the electron in the ground state
(2) four times the de-Broglie wavelength
of the electron in the ground state
(3) half of the de-Broglie wavelength of
the electron in the ground state
(4) 1/4th of the de-Broglie wavelength
of the electron in the ground state
28. Let Nb be the number of b particles emitted
by 1 gram of
24
Na radioactive nuclei
(half life515 hrs) in 7.5 hours, Nb is close
to (Avogadro number 56.02331023/g.
mole) :
(1) 6.231021
(2) 7.531021
(3) 1.2531022
(4) 1.7531022

16. Page 16 PHYSICS : English & Hindi 01
29. ¥æÚðU¹ ×ð´ 2V ·¤è °·¤ ÕñÅUÚUè A ß B ·ð¤ Õè¿ ÁéǸè ãñÐ
ØçÎ ÂãÜè Îàææ ×ð´ ÕñÅUÚUè ·¤æ ÏÙæˆ×·¤ ÅUç×üÙÜ A âð
ÌÍæ ÎêâÚUè Îàææ ×ð´ ÏÙæˆ×·¤ ÅUç×üÙÜ B âð ÁéǸæ ãæð Ìæð,
§Ù ÎæðÙæð´ Îàææ¥æð´ ×ð´ ÕñÅUÚUè mæÚUæ ÂýΞæ çßléÌ ÏæÚUæ ·¤æ
×æÙ ·ý¤×àæÑ ãæð»æ Ñ
(1) 0.2 A ÌÍæ 0.1 A
(2) 0.4 A ÌÍæ 0.2 A
(3) 0.1 A ÌÍæ 0.2 A
(4) 0.2 A ÌÍæ 0.4 A
30. ç·¤âè ÂýçÌÚUæðÏ ·ð¤ çâÚUæð´ ·ð¤ Õè¿ AC (°.âè.) ßæðËÅUÌæ
·¤æð ×æÂæ Áæ â·¤Ìæ ãñ Ñ
(1) ÂæðÅðUç‹àæØæð×èÅUÚU (çßÖß×æÂè) mæÚUæ
(2) ¿Ü ·é´¤ÇUÜè ÏæÚUæ×æÂè (»ñËßðÙæð×èÅUÚU) mæÚUæ
(3) ¿Ü-¿éÕ·¤ »ñËßðÙæð×èÅUÚU mæÚUæ
(4) ÌŒÌ ÌæÚU ßæðËÅU×èÅUÚU mæÚUæ
29. A 2V battery is connected across AB as
shown in the figure. The value of the
current supplied by the battery when in
one case battery’s positive terminal is
connected to A and in other case when
positive terminal of battery is connected
to B will respectively be :
(1) 0.2 A and 0.1 A
(2) 0.4 A and 0.2 A
(3) 0.1 A and 0.2 A
(4) 0.2 A and 0.4 A
30. The AC voltage across a resistance can be
measured using a :
(1) potentiometer
(2) moving coil galvanometer
(3) moving magnet galvanometer
(4) hot wire voltmeter

17. Page 1 CHEMISTRY : English & Hindi 01
1. A12B13C ì AB2C3
Reaction of 6.0 g of A, 6.031023 atoms of
B, and 0.036 mol of C yields 4.8 g of
compound AB2C3. If the atomic mass of
A and C are 60 and 80 amu, respectively,
the atomic mass of B is (Avogadro
no.5631023) :
(1) 70 amu
(2) 60 amu
(3) 50 amu
(4) 40 amu
2. When does a gas deviate the most from its
ideal behaviour ?
(1) At low pressure and low
temperature
(2) At low pressure and high
temperature
(3) At high pressure and low
temperature
(4) At high pressure and high
temperature
3. At temperature T, the average kinetic
energy of any particle is
3
2
kT. The
de Broglie wavelength follows the order :
(1) Thermal proton > Visible photon >
Thermal electron
(2) Thermal proton > Thermal electron
> Visible photon
(3) Visible photon > Thermal electron >
Thermal neutron
(4) Visible photon > Thermal neutron >
Thermal electron
4. Molecule AB has a bond length of 1.617Å
and a dipole moment of 0.38 D. The
fractional charge on each atom (absolute
magnitude) is : (e054.802310210 esu)
(1) 0
(2) 0.05
(3) 0.5
(4) 1.0
1. A12B13C ì AB2C3
6.0 g A, 6.031023 ÂÚU×æ‡æé B ÌÍæ 0.036 ×æðÜ C
·ð¤ ¥çÖç·ý¤Øæ ·¤ÚUÙð ÂÚU 4.8 g AB2C3 ÂýæŒÌ ãæðÌæ ãñÐ
ØçÎ A ÌÍæ C ·ð¤ ÂÚU×æ‡æé ÎýÃØ×æÙ ·ý¤×àæÑ 60 ¥æñÚU
80 amu ãæð´, Ìæð B ·¤æ ÂÚU×æ‡æé ÎýÃØ×æÙ ãñ (¥æßæð»æÎýæð
ⴁØæ5631023) Ñ
(1) 70 amu
(2) 60 amu
(3) 50 amu
(4) 40 amu
2. °·¤ »ñâ ¥ÂÙð ¥æÎàæü ÃØßãæÚU âð âßæüçÏ·¤ çß¿ÜÙ
·¤Õ ÎàææüÌè ãñ?
(1) çِ٠ÎæÕ ¥æñÚU çِ٠Ìæ ÂÚU
(2) çِ٠ÎæÕ ¥æñÚU ©“æ Ìæ ÂÚU
(3) ©“æ ÎæÕ ¥æñÚU çِ٠Ìæ ÂÚU
(4) ©“æ ÎæÕ ¥æñÚU ©“æ Ìæ ÂÚU
3. Ìæ T ÂÚU, ç·¤âè Öè ·¤‡æ ·¤è ¥æñâÌ »çÌÁ ª¤Áæü
3
2
kT ãñÐ Îð Õýæò‚Üè ÌÚ´U»-ÎñƒØü ·¤æ âãè ·ý¤× ãñ Ñ
(1) ÌæÂèØ ÂýæðÅUæòÙ > ÎëàØ È¤æðÅUæòÙ > ÌæÂèØ §Üð€ÅþUæòÙ
(2) ÌæÂèØ ÂýæðÅUæòÙ > ÌæÂèØ §Üð€ÅþUæòÙ > ÎëàØ È¤æðÅUæòÙ
(3) ÎëàØ È¤æðÅUæòÙ > ÌæÂèØ §Üð€ÅþUæòÙ > ÌæÂèØ ‹ØêÅþUæòÙ
(4) ÎëàØ È¤æðÅUæòÙ > ÌæÂèØ ‹ØêÅþUæòÙ > ÌæÂèØ §Üð€ÅþUæòÙ
4. ¥‡æé AB ·¤è ¥æÕ´Ï Ü´Õæ§ü 1.617Å ãñ ¥æñÚU ©â·¤æ
çmÏýéß ¥æƒæê‡æü 0.38 D ãñÐ ÂýˆØð·¤ ÂÚU×æ‡æé ÂÚU ¥æ´çàæ·¤
¥æßðàæ (çÙÚUÂðÿæ ÂçÚU×æ‡æ) ãñ Ñ
(e054.802310210 esu)
(1) 0
(2) 0.05
(3) 0.5
(4) 1.0

18. Page 2 CHEMISTRY : English & Hindi 01
5. For the equilibrium, A(g)ì B(g), DH is
240 kJ/mol. If the ratio of the activation
energies of the forward (Ef ) and reverse
(Eb) reactions is
2
3
then :
(1) Ef560 kJ/mol ; Eb5100 kJ/mol
(2) Ef530 kJ/mol ; Eb570 kJ/mol
(3) Ef580 kJ/mol ; Eb5120 kJ/mol
(4) Ef570 kJ/mol ; Eb530 kJ/mol
6. Determination of the molar mass of acetic
acid in benzene using freezing point
depression is affected by :
(1) dissociation
(2) association
(3) partial ionization
(4) complex formation
7. The increase of pressure on iceì water
system at constant temperature will lead
to :
(1) no effect on the equilibrium
(2) a decrease in the entropy of the
system
(3) a shift of the equilibrium in the
forward direction
(4) an increase in the Gibbs energy of the
system
8. At 298 K, the standard reduction
potentials are 1.51 V for 2
4MnO Mn2 1 ,
1.36 V for Cl2?Cl2, 1.07 V for Br2?Br2, and
0.54 V for I2?I2. At pH53, permanganate
is expected to oxidize :
RT
0.059 V
F
 
 
 
5
(1) Cl2, Br2 and I2
(2) Cl2 and Br2
(3) Br2 and I2
(4) I2 only
5. §â âæØæßSÍæ ·ð¤ çÜ°, A(g) ì B(g), DH
240 kJ/mol ãñÐ ¥»ÚU ¥»ý (Ef ) ¥æñÚU Âà¿»æ×è
(Eb) ¥çÖç·ý¤Øæ¥æð´ ·ð¤ âç·ý¤Ø‡æ ª¤Áæü¥æð´ ·¤æ ¥ÙéÂæÌ
2
3
ãñ, ÌÕ Ñ
(1) Ef560 kJ/mol ; Eb5100 kJ/mol
(2) Ef530 kJ/mol ; Eb570 kJ/mol
(3) Ef580 kJ/mol ; Eb5120 kJ/mol
(4) Ef570 kJ/mol ; Eb530 kJ/mol
6. °ðçâçÅU·¤ ¥Ü ·¤æ ×æðÜÚU ÎýÃØ×æÙ Õð´$ÁèÙ ×ð´ çã×æ´·¤
¥ßÙ×Ù âð çÙ·¤æÜð ÁæÙð ÂÚU çÁââð ÂýÖæçßÌ ãæðÌæ ãñ
ßã ãñ Ñ
(1) çßØæðÁÙ
(2) â´»é‡æÙ
(3) ¥æ´çàæ·¤ ¥æØÙè·¤ÚU‡æ
(4) â´·é¤Ü çßÚU¿Ù
7. çSÍÚU Ìæ ÂÚU, ¥çÏ·¤ ÎæÕ ÇæÜÙð ÂÚU ÕÈü¤ìÁÜ
â×éÎæØ ×ð´ Ñ
(1) âæØæßSÍæ ÂÚU ·¤æð§ü ÂýÖæß Ùãè´ ãæðÌæ ãñÐ
(2) çÙ·¤æØ ·¤è °ð‹ÅþUæòÂè ƒæÅUÌè ãñÐ
(3) âæØæßSÍæ ¥»ý çÎàææ ×ð´ ¥»ýâÚU ãæðÌè ãñÐ
(4) çÙ·¤æØ ·¤è 绎Á ª¤Áæü ÕɸÌè ãñÐ
8. 298 K ÂÚU ×æÙ·¤ ¥Â¿ØÙ çßÖß, 2
4MnO Mn2 1
·¤æ 1.51 V, Cl2?Cl2 ·¤æ 1.36 V, Br2?Br2 ·¤æ
1.07 V ¥æñÚU I2?I2 ·¤æ 0.54 V ãñÐ pH53 ÂÚU
4MnO2
ç·¤Ù·¤æ ©Â¿ØÙ ·¤ÚðU»æ?
RT
0.059 V
F
 
 
 
5
(1) Cl2, Br2 ¥æñÚU I2
(2) Cl2 ¥æñÚU Br2
(3) Br2 ¥æñÚU I2
(4) I2 ×æ˜æ

19. Page 3 CHEMISTRY : English & Hindi 01
9. A12B ® C, the rate equation for this
reaction is given as
Rate5k[A][B].
If the concentration of A is kept the same
but that of B is doubled what will happen
to the rate itself ?
(1) halved
(2) the same
(3) doubled
(4) quadrupled
10. Under ambient conditions, which among
the following surfactants will form micelles
in aqueous solution at lowest molar
concentration ?
(1)
(2) CH32(CH2)132 3OSO2
Na1
(3)
(4)
11. Choose the incorrect formula out of the
four compounds for an element X below :
(1) X2Cl3
(2) X2O3
(3) X2(SO4)3
(4) XPO4
12. Calamine is an ore of :
(1) Aluminium
(2) Copper
(3) Iron
(4) Zinc
9. ¥çÖç·ý¤Øæ A12B ® C ·¤æ ÎÚU â×è·¤ÚU‡æ ãñ
ÎÚU5k[A][B].
A ·¤è âæ´ÎýÌæ çSÍÚU ÚU¹Ìð ãé° B ·¤è âæ´ÎýÌæ Îé»éÙè ·¤ÚUÙð
ÂÚU ßð» ·¤æ ×æÙ €Øæ ãæð»æ?
(1) ¥æÏæ ÚUã Áæ°»æ
(2) â×æÙ ÚUãð»æ
(3) Îé»éÙæ ãæð Áæ°»æ
(4) ¿æÚU »éÙæ ãæð Áæ°»æ
10. ÂçÚUßðàæ çSÍçÌ ÂÚU, ·¤æñÙ-ÂëcÆU â´ç·ý¤Ø·¤ ÁÜèØ çßÜØÙ
×ð´ âÕâð ·¤× ×æðÜèØ âæ´Îý‡æ ×ð´ ç×âðÜ ÕÙæ°»æ?
(1)
(2) CH32(CH2)132 3OSO2
Na1
(3)
(4)
11. Ìˆß X ·ð¤ ¿æÚU Øæñç»·¤æð´ ·ð¤ âê˜ææð´ ×ð´ âð »ÜÌ âê˜æ
¿éçÙ° Ñ
(1) X2Cl3
(2) X2O3
(3) X2(SO4)3
(4) XPO4
12. ·ñ¤Üæç×Ù çÁâ·¤æ ¥ØS·¤ ãñ, ßã ãñ Ñ
(1) °ðÜéç×çÙØ×
(2) ·¤æòÂÚU
(3) ¥æØÚUÙ
(4) çÁ´·¤

20. Page 4 CHEMISTRY : English & Hindi 01
13. Which physical property of dihydrogen is
wrong ?
(1) Colourless gas
(2) Odourless gas
(3) Tasteless gas
(4) Non-inflammable gas
14. Which of the alkaline earth metal halides
given below is essentially covalent in
nature ?
(1) MgCl2
(2) BeCl2
(3) SrCl2
(4) CaCl2
15. Which of the following compounds has a
P2P bond ?
(1) H4P2O5
(2) H4P2O6
(3) H4P2O7
(4) (HPO3)3
16. Chlorine water on standing loses its colour
and forms :
(1) HCl only
(2) HOCl and HOCl2
(3) HCl and HOCl
(4) HCl and HClO2
17. Which of the following statements is
false ?
(1)
2
4CrO
2
is tetrahedral in shape
(2) 2
72Cr O
2
has a Cr2O2Cr bond
(3) Na2Cr2O7 is a primary standard in
volumetry
(4) Na2Cr2O7 is less soluble than
K2Cr2O7
13. ÇUæ§ãæ§ÇþUæðÁÙ ·ð¤ â´ÎÖü ×ð´ ·¤æñÙ-âæ ÖæñçÌ·¤ »é‡æ »ÜÌ
ãñ?
(1) ߇æüãèÙ »ñâ
(2) »´ÏãèÙ »ñâ
(3) SßæÎãèÙ »ñâ
(4) ¥’ßÜÙàæèÜ »ñâ
14. çِÙçÜç¹Ì ÿææÚUèØ ×ëÎæ ÏæÌé ·ð¤ ãñÜæ§ÇUæð´ ×ð´ âð 緤ⷤæ
SßÖæß ßæSÌß ×ð´ âãâ´ØæðÁ·¤ ãñ?
(1) MgCl2
(2) BeCl2
(3) SrCl2
(4) CaCl2
15. çΰ »° Øæñç»·¤æð´ ×ð´ âð P2P Õ´Ï·¤ ç·¤â ×ð´ ãñ?
(1) H4P2O5
(2) H4P2O6
(3) H4P2O7
(4) (HPO3)3
16. €ÜæðÚUèÙ ÁÜ ·é¤ÀU â×Ø ·ð¤ Âà¿æÌ÷ ¥ÂÙæ Ú´U» ¹æð ÎðÌæ
ãñ ¥æñÚU ÕÙæÌæ ãñ Ñ
(1) ·ð¤ßÜ HCl
(2) HOCl ¥æñÚU HOCl2
(3) HCl ¥æñÚU HOCl
(4) HCl ¥æñÚU HClO2
17. çِ٠·¤ÍÙæð´ ×ð´ âð »ÜÌ ·¤ÍÙ ¿éçÙØð?
(1)
2
4CrO
2
¿ÌécȤܷ¤èØ ¥æ·¤æÚU ·¤æ ãñÐ
(2) 2
72Cr O
2
×ð´ °·¤ Cr2O2Cr ¥æÕ´Ï ãñÐ
(3) ¥æØÌÙè çßàÜðá‡æ ×ð´ Na2Cr2O7 °·¤
ÂýæÍç×·¤ ×æÙ·¤ ãñÐ
(4) Na2Cr2O7 ·¤è çßÜØÌæ K2Cr2O7 âð ·¤×
ãñÐ

21. Page 5 CHEMISTRY : English & Hindi 01
18. ÁÕ âæ´çÎýÌ HCl ·¤æð CoCl2 ·ð¤ ÁÜèØ ƒææðÜ ×ð´ ç×ÜæØæ
»Øæ, ÌÕ ©â·¤æ Ú´U» ÚU€ÌæÖ »éÜæÕè âð »æɸæ ÙèÜæ ãæð
»ØæÐ §â ¥çÖç·ý¤Øæ ×ð´ ·¤æñÙ âæ â´·é¤Ü ¥æØÙ ÙèÜð
Ú´U» ·¤æ ·¤æÚU‡æ ãñ?
(1) [CoCl6]42
(2) [CoCl6]32
(3) [CoCl4]22
(4) [Co(H2O)6]21
19. çِÙçÜç¹Ì â´·é¤Ü ¥æØÙæð´ ×ð´ âð 緤⠥æØÙ ·¤è t2g
¥æñÚU eg ·¤ÿæ·¤æð´ ×ð´ §Üð€ÅþUæòÙ â×ç×Ì M¤Â âð ÖÚðU ãñ´?
(1) [CoF6]32
(2) [Co(NH3)6]21
(3) [Mn(CN)6]42
(4) [FeF6]32
20. ȤæòSÈð¤ÅU Øé€Ì ©ßüÚU·¤æð´ ·ð¤ ç×ÜæÙð âð ÁÜæàæØæð´ ×ð´ Ñ
(1) àæñßæÜæð´ ·¤è ¥ˆØæçÏ·¤ ßëçh ãæðÌè ãñÐ
(2) ÁÜ ×ð´ çßÜèÙ ¥æò€âèÁÙ ·¤è ×æ˜ææ ÕɸÌè ãñÐ
(3) ·ñ¤çËâØ× È¤æòSÈð¤ÅU ·¤æ çÙÿæð‡æ ãæðÌæ ãñÐ
(4) ×ÀUçÜØæð´ ·¤è Áèß â´Øæ ×ð´ ßëçh ãæðÌè ãñÐ
21. ·¤æòÜ× - I ×ð´ çΰ »° ·¤æÕüçÙ·¤ Øæñç»·¤æð´ ·¤æð
·¤æòÜ× - II ×ð´ Üñâð´ ÅðUSÅU ·ð¤ ÂçÚU‡ææ×æð´ ·ð¤ âæÍ âé×ðçÜÌ
·¤èçÁ° Ñ
(A) •Õ¾ÍÁ; (i) FeCl3 œÕ‰ Ç˲ ÁËÁ ¿™U
(B) ºÕü¦Í¾
Ç°­‰ËÕ̾œ‰ ŠƒÁ
(ii) ÇËÕ̬U½¼ ¾ËŒªãUËÕ§âÏSÇËŒ¬U œÕ‰
Ç˲ ¦Ë¼Ï¾Í ¿™U
(C) ²Ö½ËÕ½ÏÌ¿U½Ë (iii) ¿U¼ ŠƒÁͽ FeSO4
ÌÄÁ½¾ œÕ‰ Ç˲ ¾ÍÁË ¿™U
œ‰Ë×Á¼ - I œ‰Ë×Á¼ - II
(1) (A) - (ii) ; (B) - (i) ; (C) - (iii)
(2) (A) - (iii) ; (B) - (ii) ; (C) - (i)
(3) (A) - (ii) ; (B) - (iii) ; (C) - (i)
(4) (A) - (iii) ; (B) - (i) ; (C) - (ii)
18. When concentrated HCl is added to an
aqueous solution of CoCl2, its colour
changes from reddish pink to deep blue.
Which complex ion gives blue colour in this
reaction ?
(1) [CoCl6]42
(2) [CoCl6]32
(3) [CoCl4]22
(4) [Co(H2O)6]21
19. Which of the following complex ions has
electrons that are symmetrically filled in
both t2g and eg orbitals ?
(1) [CoF6]32
(2) [Co(NH3)6]21
(3) [Mn(CN)6]42
(4) [FeF6]32
20. Addition of phosphate fertilisers to water
bodies causes :
(1) enhanced growth of algae
(2) increase in amount of dissolved
oxygen in water
(3) deposition of calcium phosphate
(4) increase in fish population
21. Match the organic compounds in
column - I with the Lassaigne’s test results
in column - II appropriately :
(A) Aniline (i) Red color with
FeCl3
(B) Benzene
sulfonic acid
(ii) Violet color with
sodium
nitroprusside
(C) Thiourea (iii) Blue color with hot
and acidic solution
of FeSO4
Column - I Column - II
(1) (A) - (ii) ; (B) - (i) ; (C) - (iii)
(2) (A) - (iii) ; (B) - (ii) ; (C) - (i)
(3) (A) - (ii) ; (B) - (iii) ; (C) - (i)
(4) (A) - (iii) ; (B) - (i) ; (C) - (ii)

22. Page 6 CHEMISTRY : English & Hindi 01
22. Which of the following pairs of
compounds are positional isomers ?
(1) CH32CH22CH22CH22CHO
and
(2) and
(3) and
(4) and
23. The number of structural isomers for C6H14
is :
(1) 3
(2) 4
(3) 5
(4) 6
22. çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ-âð Øæñç»·¤ Øé‚× â×êã
â×æßØßè ãñ´?
(1) CH32CH22CH22CH22CHO ¥æñÚU
(2) ¥æñÚU
(3) ¥æñÚU
(4) ¥æñÚU
23. C6H14 ·¤è â´ÚU¿Ùæˆ×·¤ â×æßØçßØæð´ ·¤è ⴁØæ ãñ Ñ
(1) 3
(2) 4
(3) 5
(4) 6

23. Page 7 CHEMISTRY : English & Hindi 01
24. What is the major product expected from
the following reaction ?
Where D is an isotope of Hydrogen.
(1)
(2)
(3)
(4)
25. In the reaction sequence
OH
32 CH CHO A B→ →
2
D ; the
product B is :
(1) CH32CH22CH22CH22OH
(2) CH32CH5CH2CHO
(3)
(4) CH32CH22CH22CH3
24. çِÙçÜç¹Ì ¥çÖç·ý¤Øæ ·¤æ Âý×é¹ ©ˆÂæÎ €Øæ ãñ?
Áãæ¡ D - ãæ§ÇþUæðÁÙ ·¤æ â×SÍæçÙ·¤ ãñÐ
(1)
(2)
(3)
(4)
25. çِÙçÜç¹Ì ¥çÖç·ý¤Øæ ·ý¤× ×ð´ ©ˆÂæÎ B ãñ Ñ
OH
32 CH CHO A B→ →
2
D
(1) CH32CH22CH22CH22OH
(2) CH32CH5CH2CHO
(3)
(4) CH32CH22CH22CH3

24. Page 8 CHEMISTRY : English & Hindi 01
26. Which compound exhibits maximum
dipole moment among the following ?
(1)
(2)
(3)
(4)
27. Which one of the following structures
represents the neoprene polymer ?
(1)
(2)
(3)
(4)
26. çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ-âæ Øæñç»·¤ âßæüçÏ·¤ çmÏýéß
¥æƒæê‡æü ÎàææüÌæ ãñ?
(1)
(2)
(3)
(4)
27. ÕãéÜ·¤ çÙØæðÂýèÙ ·¤è â´ÚU¿Ùæ çِÙçÜç¹Ì â´ÚU¿Ùæ¥æð´
×ð´ âð ·¤æñÙ-âè ãñ?
(1)
(2)
(3)
(4)

25. Page 9 CHEMISTRY : English & Hindi 01
28. ¥æðÁSßè ÃØæØæ× ·ð¤ ȤÜSßM¤Â, ×æ´âÂðçàæØæð´ ×ð´ ç·¤â
Øæñç»·¤ ·¤æ â´¿ØÙ ãæðÌæ ãñ?
(1) ‚Üê·¤æð$Á
(2) ‚Üñ·¤æð$ÁÙ
(3) L-Üñç€ÅU·¤ ¥Ü
(4) ÂñM¤çß·¤ ¥Ü
29. 緤⠷ë¤ç˜æ× ×ÏéÚU·¤ ×ð´ €ÜæðÚUèÙ ãñ?
(1) °ðSÂæÅðüU×
(2) âñ·¤ÚUèÙ
(3) âê·ý¤æÜæðâ
(4) °ðçÜÅðU×
30. °·¤ »éÜæÕè Ü߇æ, »ÚU× ·¤ÚUÙð ÂÚU ÙèÜæ ãæð ÁæÌæ ãñÐ
Ü߇æ ×ð´ ç·¤â ÏÙæØÙ ·ð¤ ãæðÙð ·¤è âßæüçÏ·¤ â´ÖæßÙæ
ãñ?
(1) Cu21
(2) Fe21
(3) Zn21
(4) Co21
- o 0 o -
28. Accumulation of which of the following
molecules in the muscles occurs as a result
of vigorous exercise ?
(1) Glucose
(2) Glycogen
(3) L-lactic acid
(4) Pyruvic acid
29. Which artificial sweetener contains
chlorine ?
(1) Aspartame
(2) Saccharin
(3) Sucralose
(4) Alitame
30. A pink coloured salt turns blue on heating.
The presence of which cation is most
likely ?
(1) Cu21
(2) Fe21
(3) Zn21
(4) Co21
- o 0 o -

26. Page 1 MATHEMATICS : English & Hindi 01
1. Let A5{x1, x2, ..., x7} and B5{y1, y2, y3}
be two sets containing seven and three
distinct elements respectively. Then the
total number of functions f : A ® B that
are onto, if there exist exactly three
elements x in A such that f(x)5y2, is equal
to :
(1) 14 . 7C2
(2) 16 . 7C3
(3) 12 . 7C2
(4) 14 . 7C3
2. If z is a non-real complex number, then
the minimum value of
5
5
Im
(Im )
z
z
is :
(1) 21
(2) 22
(3) 24
(4) 25
3. If the two roots of the equation,
(a21)(x41x211)1(a11)(x21x11)250
are real and distinct, then the set of all
values of ‘a’ is :
(1)
1
, 0
2
 
 
 
2
(2) (2:, 22) È (2, :)
(3)
1 1
, 0 0,
2 2
   
∪   
   
2
(4)
1
0,
2
 
 
 
4. If A is a 333 matrix such that ?5. adjA?55,
then ?A? is equal to :
(1)
1
5
6
(2) 65
(3) 61
(4)
1
25
6
1. ×æÙæ A5{x1, x2, ..., x7} ÌÍæ B5{y1, y2, y3}
°ðâð Îæð â×é“æØ ãñ´ çÁÙ×ð´ ·ý¤×àæÑ âæÌ ÌÍæ ÌèÙ çßçÖóæ
¥ßØß ãñ´ ; Ìæð °ðâð ȤÜÙæð´ f : A ® B ·¤è ·é¤Ü
ⴁØæ, Áæð ç·¤ ¥æ‘ÀUæη¤ ãñ´, ØçÎ A ×ð´ °ðâð ÆUè·¤ ÌèÙ
x ¥ßØß ãñ´ çÁÙ·ð¤ çÜ° f(x)5y2 ãñ, ãñ Ñ
(1) 14 . 7C2
(2) 16 . 7C3
(3) 12 . 7C2
(4) 14 . 7C3
2. ØçÎ z °·¤ ¥ßæSÌçß·¤ âç×Ÿæ ⴁØæ ãñ, Ìæð
5
5
Im
(Im )
z
z
·¤æ ‹ØêÙÌ× ×æÙ ãñ Ñ
(1) 21
(2) 22
(3) 24
(4) 25
3. ØçÎ â×è·¤ÚU‡æ
(a21)(x41x211)1(a11)(x21x11)250
·ð¤ Îæð ×êÜ ßæSÌçß·¤ ÌÍæ çßçÖóæ ãñ´, Ìæð ‘a’ ·ð¤ âÖè
×æÙæð´ ·¤æ â×êã ãñ Ñ
(1)
1
, 0
2
 
 
 
2
(2) (2:, 22) È (2, :)
(3)
1 1
, 0 0,
2 2
   
∪   
   
2
(4)
1
0,
2
 
 
 
4. ØçÎ A °·¤ °ðâæ 333 ¥æÃØêã ãñ ç·¤ ?5. adjA?55
ãñ, Ìæð ?A? ÕÚUæÕÚU ãñ Ñ
(1)
1
5
6
(2) 65
(3) 61
(4)
1
25
6

27. Page 2 MATHEMATICS : English & Hindi 01
5. If
2
2
2
1 2
a 122 3 1 3 3 3
2 3 2 1 2 1
x x x x
xx x x x
x x x x
1 1 2
5 21 2 2
1 1 2 2
,
then ‘a’ is equal to :
(1) 12
(2) 24
(3) 212
(4) 224
6. If in a regular polygon the number of
diagonals is 54, then the number of sides
of this polygon is :
(1) 10
(2) 12
(3) 9
(4) 6
7. The term independent of x in the binomial
expansion of
8
5 21 1
1 3 2x x
x x
   
   
   
2 1 2 is :
(1) 400
(2) 496
(3) 2400
(4) 2496
8. The sum of the 3rd and the 4th terms of a
G.P. is 60 and the product of its first three
terms is 1000. If the first term of this G.P.
is positive, then its 7th term is :
(1) 7290
(2) 320
(3) 640
(4) 2430
5. ØçÎ
2
2
2
1 2
a 122 3 1 3 3 3
2 3 2 1 2 1
x x x x
xx x x x
x x x x
1 1 2
5 21 2 2
1 1 2 2
ãñ, Ìæð ‘a’ ÕÚUæÕÚU ãñ Ñ
(1) 12
(2) 24
(3) 212
(4) 224
6. ØçÎ °·¤ çÙØç×Ì ÕãéÖéÁ ·ð¤ çß·¤‡ææðZ ·¤è ⴁØæ 54
ãñ, Ìæð ÕãéÖéÁ ·ð¤ ÖéÁæ¥æð´ ·¤è ⴁØæ ãñ Ñ
(1) 10
(2) 12
(3) 9
(4) 6
7.
8
5 21 1
1 3 2x x
x x
   
   
   
2 1 2 ·ð¤ çmÂÎ ÂýâæÚU
×ð´ x âð SßÌ´˜æ ÂÎ ãñ Ñ
(1) 400
(2) 496
(3) 2400
(4) 2496
8. °·¤ »é‡ææðžæÚU Ÿæðɸè (G.P.) ·ð¤ ÌèâÚðU ÌÍæ ¿æñÍð ÂÎæð´ ·¤æ
Øæð» 60 ãñ ÌÍæ §â·ð¤ ÂýÍ× ÌèÙ ÂÎæð´ ·¤æ »é‡æÙȤÜ
1000 ãñÐ ØçÎ §â »é‡ææðžæÚU ŸæðÉ¸è ·¤æ ÂýÍ× ÂÎ ÏÙæˆ×·¤
ãñ, Ìæð §â·¤æ âæÌßæ´ ÂÎ ãñ Ñ
(1) 7290
(2) 320
(3) 640
(4) 2430

28. Page 3 MATHEMATICS : English & Hindi 01
9. If
5
n 1
1 k
n(n 1)(n 2)(n 3) 35
S 5
1 1 1
, then k is
equal to :
(1)
55
336
(2)
17
105
(3)
1
6
(4)
19
112
10. Let k be a non-zero real number. If
2
(e 1)
, 0
( ) sin log 1
k 4
12 , 0
x
x
x x
f x
x

≠
    
    
   

2
5 1
5
is a continuous function, then the value of
k is :
(1) 1
(2) 2
(3) 3
(4) 4
11. The equation of a normal to the curve,
sin sin
3
y x y
 
 
 
p
5 1 at x50, is :
(1) 2 3 0x y1 5
(2) 2 3 0y x2 5
(3) 2 3 0y x1 5
(4) 2 3 0x y2 5
9. ØçÎ
5
n 1
1 k
n(n 1)(n 2)(n 3) 35
S 5
1 1 1
ãñ, Ìæð k
ÕÚUæÕÚU ãñ Ñ
(1)
55
336
(2)
17
105
(3)
1
6
(4)
19
112
10. ×æÙæ k °·¤ àæê‹ØðÌÚU ßæSÌçß·¤ ⴁØæ ãñÐ ØçÎ
2
(e 1)
, 0
( ) sin log 1
k 4
12 , 0
x
x
x x
f x
x

≠
    
    
   

2
5 1
5
°·¤ â´ÌÌ È¤ÜÙ ãñ, Ìæð k ·¤æ ×æÙ ãñ Ñ
(1) 1
(2) 2
(3) 3
(4) 4
11. x50 ÂÚU ß·ý¤ sin sin
3
y x y
 
 
 
p
5 1 ·ð¤
¥çÖÜ´Õ ·¤æ â×è·¤ÚU‡æ ãñ Ñ
(1) 2 3 0x y1 5
(2) 2 3 0y x2 5
(3) 2 3 0y x1 5
(4) 2 3 0x y2 5

29. Page 4 MATHEMATICS : English & Hindi 01
12. Let k and K be the minimum and the
maximum values of the function
0.6
0.6
(1 )
( )
1
x
f x
x
1
5
1
in [0, 1] respectively,
then the ordered pair (k, K) is equal to :
(1) (1, 20.6)
(2) (220.4, 20.6)
(3) (220.6, 1)
(4) (220.4, 1)
13. From the top of a 64 metres high tower, a
stone is thrown upwards vertically with
the velocity of 48 m/s. The greatest height
(in metres) attained by the stone, assuming
the value of the gravitational acceleration
g532 m/s2, is :
(1) 100
(2) 88
(3) 128
(4) 112
14. If
( ) ( )
2
2
2
t 1 tlog 1
dt g (t) C
21 t
∫
1 1
5 1
1
,
where C is a constant, then g(2) is equal
to :
(1) ( )2log 2 51
(2) ( )log 2 51
(3) ( )
1
log 2 5
5
1
(4) ( )
1
log 2 5
2
1
12. ×æÙæ k ÌÍæ K, ȤÜÙ
0.6
0.6
(1 )
( )
1
x
f x
x
1
5
1
·ð¤
[0, 1] ×ð´ ·ý¤×àæÑ ‹ØêÙÌ× ÌÍæ ¥çÏ·¤Ì× ×æÙ ãñ´, Ìæð
·ý¤ç×Ì Øé‚× (k, K) ÕÚUæÕÚU ãñ Ñ
(1) (1, 20.6)
(2) (220.4, 20.6)
(3) (220.6, 1)
(4) (220.4, 1)
13. 64 ×èÅUÚU ª¡¤¿è °·¤ ×èÙæÚU ·ð¤ çàæ¹ÚU âð 48 ×è./âð.
·¤è »çÌ âð ©ŠßæüÏÚU ª¤ÂÚU ·¤è çÎàææ ×ð´ °·¤ ˆÍÚU
Èð´¤·¤æ »ØæÐ Øã ×æÙÌð ãé° ç·¤ »éL¤ˆßæ·¤áü‡æ ˆßÚU‡æ
g532 ×è./âð.2 ãñ, ßã ¥çÏ·¤Ì× ª¡¤¿æ§ü
(×èÅUÚUæð´ ×ð´) Áãæ¡ Ì·¤ ˆÍÚU Âã¡é¿Ìæ ãñ, ãñ Ñ
(1) 100
(2) 88
(3) 128
(4) 112
14. ØçÎ
( ) ( )
2
2
2
t 1 tlog 1
dt g (t) C
21 t
∫
1 1
5 1
1
ãñ, Áãæ¡ C °·¤ ¥¿ÚU ãñ, Ìæð g(2) ÕÚUæÕÚU ãñ Ñ
(1) ( )2log 2 51
(2) ( )log 2 51
(3) ( )
1
log 2 5
5
1
(4) ( )
1
log 2 5
2
1

30. Page 5 MATHEMATICS : English & Hindi 01
15. ×æÙæ f : R ® R °·¤ °ðâæ ȤÜÙ ãñ, ç·¤ âÖè x e R
·ð¤ çÜ°, f (22x)5f (21x) ÌÍæ f (42x)5
f (41x) ãñ ¥æñÚU
2
0
( ) d 5f x x∫ 5 ãñ, Ìæð
50
10
( ) df x x∫
·¤æ ×æÙ ãñ Ñ
(1) 80
(2) 100
(3) 125
(4) 200
16. ×æÙæ f : (21, 1) ® R °·¤ â´ÌÌ È¤ÜÙ ãñÐ ØçÎ
sin
0
3
(t) dt
2
x
f x∫ 5 ãñ, Ìæð
3
2
f
 
 
 
ÕÚUæÕÚU ãñ Ñ
(1)
3
2
(2) 3
(3)
3
2
(4)
1
2
17. x5f(y) ¥ß·¤Ü â×è·¤ÚU‡æ
ydx2(x12y2)dy50 ·¤æ ãÜ ãñÐ
ØçÎ f(21)51 ãñ, Ìæð f(1) ÕÚUæÕÚU ãñ Ñ
(1) 4
(2) 3
(3) 2
(4) 1
15. Let f : R ® R be a function such that
f (22x)5f (21x) and f (42x)5f (41x),
for all x e R and
2
0
( ) d 5f x x∫ 5 . Then the
value of
50
10
( ) df x x∫ is :
(1) 80
(2) 100
(3) 125
(4) 200
16. Let f : (21, 1) ® R be a continuous
function. If
sin
0
3
(t) dt
2
x
f x∫ 5 , then
3
2
f
 
 
 
is equal to :
(1)
3
2
(2) 3
(3)
3
2
(4)
1
2
17. The solution of the differential equation
ydx2(x12y2)dy50 is x5f(y).
If f(21)51, then f(1) is equal to :
(1) 4
(2) 3
(3) 2
(4) 1

31. Page 6 MATHEMATICS : English & Hindi 01
18. A straight line L through the point (3, 22)
is inclined at an angle of 608 to the line
3 1x y1 5 . If L also intersects the
x-axis, then the equation of L is :
(1) 3 2 3 3 0y x1 1 2 5
(2) 3 2 3 3 0y x2 1 1 5
(3) 3 3 2 3 0y x2 1 1 5
(4) 3 3 2 3 0y x1 2 1 5
19. If the incentre of an equilateral triangle is
(1, 1) and the equation of its one side is
3x14y1350, then the equation of the
circumcircle of this triangle is :
(1) x21y222x22y2250
(2) x21y222x22y21450
(3) x21y222x22y1250
(4) x21y222x22y2750
20. If a circle passing through the point
(21, 0) touches y-axis at (0, 2), then the
length of the chord of the circle along the
x-axis is :
(1)
3
2
(2)
5
2
(3) 3
(4) 5
18. çÕ´Îé (3, 22) âð ãæð·¤ÚU ÁæÙð ßæÜè °·¤ âÚUÜ ÚðU¹æ L,
ÚUð¹æ 3 1x y1 5 ·ð¤ âæÍ 608 ·¤æ ·¤æð‡æ ÕÙæÌè
ãñÐ ØçÎ L, x-¥ÿæ ·¤æð Öè ·¤æÅUÌè ãñ, Ìæð L ·¤æ
â×è·¤ÚU‡æ ãñ Ñ
(1) 3 2 3 3 0y x1 1 2 5
(2) 3 2 3 3 0y x2 1 1 5
(3) 3 3 2 3 0y x2 1 1 5
(4) 3 3 2 3 0y x1 2 1 5
19. ØçÎ °·¤ â×Õæãé ç˜æÖéÁ ·¤æ ¥´ÌÑ·ð´¤Îý (1, 1) ãñ ÌÍæ
§â·¤è °·¤ ÖéÁæ ·¤æ â×è·¤ÚU‡æ 3x14y1350 ãñ,
Ìæð §â ç˜æÖéÁ ·ð¤ ÂçÚUßëžæ ·¤æ â×è·¤ÚU‡æ ãñ Ñ
(1) x21y222x22y2250
(2) x21y222x22y21450
(3) x21y222x22y1250
(4) x21y222x22y2750
20. ØçÎ çÕ´Îé (21, 0) âð ãæð·¤ÚU ÁæÙð ßæÜæ °·¤ ßëžæ
y-¥ÿæ ·¤æð (0, 2) ÂÚU SÂàæü ·¤ÚUÌæ ãñ, Ìæð x-¥ÿæ ·¤è
çÎàææ ×ð´ ßëžæ ·¤è Áèßæ ·¤è Ü´Õæ§ü ãñ Ñ
(1)
3
2
(2)
5
2
(3) 3
(4) 5

32. Page 7 MATHEMATICS : English & Hindi 01
21. If the distance between the foci of an ellipse
is half the length of its latus rectum, then
the eccentricity of the ellipse is :
(1)
1
2
(2)
2 2 1
2
2
(3) 2 12
(4)
2 1
2
2
22. Let PQ be a double ordinate of the
parabola, y2524x, where P lies in the
second quadrant. If R divides PQ in the
ratio 2 : 1, then the locus of R is :
(1) 9y254x
(2) 9y2524x
(3) 3y252x
(4) 3y2522x
23. The shortest distance between the z-axis
and the line
x1y12z235052x13y14z24, is :
(1) 1
(2) 2
(3) 3
(4) 4
24. A plane containing the point (3, 2, 0) and
the line
21 3
1 5 4
yx z22 2
5 5 also
contains the point :
(1) (0, 23, 1)
(2) (0, 7, 10)
(3) (0, 7, 210)
(4) (0, 3, 1)
21. °·¤ Îèƒæüßëžæ ·¤è ÙæçÖØæð´ ·ð¤ Õè¿ ·¤è ÎêÚUè, §â·ð¤
ÙæçÖÜ´Õ ·¤è Ü´Õæ§ü ·¤è ¥æÏè ãñ, Ìæð Îèƒæüßëžæ ·¤è
©ˆ·ð´¤ÎýÌæ ãñ Ñ
(1)
1
2
(2)
2 2 1
2
2
(3) 2 12
(4)
2 1
2
2
22. ×æÙæ PQ ÂÚUßÜØ y2524x ·¤è °·¤ çm·¤æðçÅU
(double ordinate) ãñ, ÁÕç·¤ P çmÌèØ ¿ÌéÍæZàæ ×ð´
ãñÐ ØçÎ R, PQ ·¤æð 2 : 1 ·ð¤ ¥ÙéÂæÌ ×ð´ Õæ´ÅUÌæ ãñ, Ìæð
R ·¤æ çÕ´ÎéÂÍ ãñ Ñ
(1) 9y254x
(2) 9y2524x
(3) 3y252x
(4) 3y2522x
23. ÚðU¹æ x1y12z235052x13y14z24 ÌÍæ
z-¥ÿæ ·ð¤ Õè¿ ·¤è ‹ØêÙÌ× ÎêÚUè ãñ Ñ
(1) 1
(2) 2
(3) 3
(4) 4
24. °·¤ â×ÌÜ çÁâ ÂÚU çÕ´Îé (3, 2, 0) ÌÍæ ÚðU¹æ
21 3
1 5 4
yx z22 2
5 5 çSÍÌ ãñ´, ÂÚU çِ٠çÕ´Îé
Öè çSÍÌ ãñ Ñ
(1) (0, 23, 1)
(2) (0, 7, 10)
(3) (0, 7, 210)
(4) (0, 3, 1)

33. Page 8 MATHEMATICS : English & Hindi 01
25. In a parallelogram ABCD, 5a,
5b and 5c, then has the
value :
(1) ( )2 2 21
a b c
2
2 1
(2) ( )2 2 21
a b c
4
1 2
(3) ( )2 2 21
b c a
3
1 2
(4) ( )2 2 21
a b c
2
1 1
26. If the lengths of the sides of a triangle are
decided by the three throws of a single fair
die, then the probability that the triangle
is of maximum area given that it is an
isosceles triangle, is :
(1)
1
26
(2)
1
27
(3)
1
21
(4)
1
15
27. If the mean and the variance of a binomial
variate X are 2 and 1 respectively, then the
probability that X takes a value greater
than or equal to one is :
(1)
1
16
(2)
9
16
(3)
3
4
(4)
15
16
25. °·¤ â×æ´ÌÚU ¿ÌéÖéüÁ ABCD ×ð´, 5a, 5b
ÌÍæ 5c ãñ, Ìæð ·¤æ ×æÙ ãñ Ñ
(1) ( )2 2 21
a b c
2
2 1
(2) ( )2 2 21
a b c
4
1 2
(3) ( )2 2 21
b c a
3
1 2
(4) ( )2 2 21
a b c
2
1 1
26. °·¤ ¥ÙçÖÙÌ Âæâð ·¤æð ÌèÙ ÕæÚU Èð´¤·¤ ·¤ÚU °·¤ ç˜æÖéÁ
·¤è ÖéÁæ¥æð´ ·¤è Ü´Õæ§Øæ¡ çÙÏæüçÚUÌ ·¤è ÁæÌè ãñ, Ìæð
ç˜æÖéÁ ·ð¤ ¥çÏ·¤Ì× ÿæð˜æÈ¤Ü ·ð¤ ãæðÙð ·¤è ÂýæçØ·¤Ìæ,
ÁÕ ç·¤ çÎØæ ãñ ç·¤ ç˜æÖéÁ â×çmÕæãé ãñ, ãñ Ñ
(1)
1
26
(2)
1
27
(3)
1
21
(4)
1
15
27. ØçÎ °·¤ çmÂÎ ¿ÚU X ·ð¤ ×æŠØ ÌÍæ ÂýâÚU‡æ ·ý¤×àæÑ 2
ÌÍæ 1 ãñ´, Ìæð X ·¤æ ×æÙ 1 Øæ §ââð ¥çÏ·¤ ãæðÙð ·¤è
ÂýæçØ·¤Ìæ ãñ Ñ
(1)
1
16
(2)
9
16
(3)
3
4
(4)
15
16

34. Page 9 MATHEMATICS : English & Hindi 01
28. If
3
cos cos
2
a 1 b 5 and
1
sin sin
2
a 1 b 5
and u is the arithmetic mean of a and b,
then sin2u1cos2u is equal to :
(1)
3
5
(2)
4
5
(3)
7
5
(4)
8
5
29. Let 10 vertical poles standing at equal
distances on a straight line, subtend the
same angle of elevation a at a point O on
this line and all the poles are on the same
side of O. If the height of the longest pole
is ‘h’ and the distance of the foot of the
smallest pole from O is ‘a’ ; then the
distance between two consecutive poles,
is :
(1)
h sin a cos
9 sin
a 1 a
a
(2)
h cos a sin
9 cos
a 2 a
a
(3) h cos a sin
9 sin
a 2 a
a
(4)
h sin a cos
9 cos
a 1 a
a
28. ØçÎ
3
cos cos
2
a 1 b 5 ÌÍæ
1
sin sin
2
a 1 b 5 ãñ´, ÌÍæ a ÌÍæ b ·¤æ â×æ´ÌÚU
×æŠØ u ãñ, Ìæð sin2u1cos2u ÕÚUæÕÚU ãñ Ñ
(1)
3
5
(2)
4
5
(3)
7
5
(4)
8
5
29. ×æÙæ °·¤ âÚUÜ ÚðU¹æ ÂÚU â×æÙ ÎêçÚUØæð´ ÂÚU ¹Ç¸ð 10
©ŠßæüÏÚU ¹´Öð §â âÚUÜ ÚðU¹æ ·ð¤ °·¤ çÕ´Îé O ÂÚU
â×æÙ ©óæØÙ ·¤æð‡æ a ÕÙæÌð ãñ´, ÁÕç·¤ âÖè ¹´Öð O
·ð¤ °·¤ ãè ¥æðÚU çSÍÌ ãñ´Ð ØçÎ âÕâð ÕǸ𠹴Öð ·¤è
ª¡¤¿æ§ü ‘h’ ãñ ÌÍæ âÕâð ÀUæðÅðU ¹´Öð ·ð¤ ÂæÎ ·¤è O âð
ÎêÚUè ‘a’ ãñ ; Ìæð Îæð ·ý¤×æ»Ì ¹´Öæð´ ·ð¤ Õè¿ ·¤è ÎêÚUè ãñ Ñ
(1)
h sin a cos
9 sin
a 1 a
a
(2)
h cos a sin
9 cos
a 2 a
a
(3) h cos a sin
9 sin
a 2 a
a
(4)
h sin a cos
9 cos
a 1 a
a

35. Page 10 MATHEMATICS : English & Hindi 01
30. Consider the following statements :
P : Suman is brilliant.
Q : Suman is rich.
R : Suman is honest.
The negation of the statement,
“Suman is brilliant and dishonest if and
only if Suman is rich” can be equivalently
expressed as :
(1) ~ Q « ~ P Ù R
(2) ~ Q « ~ P Ú R
(3) ~ Q « P Ú ~ R
(4) ~ Q « P Ù ~ R
- o 0 o -
30. çِ٠·¤ÍÙæð´ ÂÚU çß¿æÚU ·¤èçÁ° Ñ
P : âé×Ù ÂýçÌÖæàææÜè ãñÐ
Q : âé×Ù ¥×èÚU ãñÐ
R : âé×Ù §ü×æÙÎæÚU ãñÐ
·¤ÍÙ ÒÒâé×Ù ÂýçÌÖæàææÜè ÌÍæ Õð§ü×æÙ ãñ ØçÎ ¥æñÚU
·ð¤ßÜ ØçÎ âé×Ù ¥×èÚU ãñÓÓ ·¤æ çÙáðÏ çِ٠Âý·¤æÚU âð
ÃØ€Ì ç·¤Øæ Áæ â·¤Ìæ ãñ Ñ
(1) ~ Q « ~ P Ù R
(2) ~ Q « ~ P Ú R
(3) ~ Q « P Ú ~ R
(4) ~ Q « P Ù ~ R
- o 0 o -