JEE MAIN QUESTION PAPER

1. English : 1 Set : 01 Hindi : 1 Set : 01
PART A — PHYSICS
1. An experiment is performed to obtain the
value of acceleration due to gravity g by
using a simple pendulum of length L. In
this experiment time for 100 oscillations is
measured by using a watch of 1 second
least count and the value is 90.0 seconds.
The length L is measured by using a meter
scale of least count 1 mm and the value is
20.0 cm. The error in the determination
of g would be :
(1) 1.7%
(2) 2.7%
(3) 4.4%
(4) 2.27%
2. The position of a projectile launched from
the origin at t50 is given by
r (40 50 ) mi j
→ ∧ ∧
5 1 at t52s. If the
projectile was launched at an angle u from
the horizontal, then u is (take g510 ms22).
(1) tan21 2
3
(2) tan21 3
2
(3) tan21 7
4
(4) tan21 4
5
Öæ» A — ÖæñçÌ·¤ çß™ææÙ
1. ܐÕæ§ü L ·ð¤ °·¤ âÚUÜ ÜæðÜ·¤ ·¤æ ÂýØæð» ·¤ÚU »éL¤ˆßèØ
ˆßÚU‡æ g ·¤æ ×æÙ çÙ·¤æÜÙð ·¤æ °·¤ ÂýØæð» ç·¤Øæ ÁæÌæ
ãñÐ §â ÂýØæð» ×ð´ 100 ÎæðÜÙæð´ ·¤æ â×Ø 1 âð·´¤ÇUU
¥ËÂÌ×æ¡·¤ ßæÜè ƒæǸUè âð ×æÂæ ÁæÌæ ãñ ¥æñÚ ×æÙ
90.0 âð·´¤ÇU ãñРܐÕæ§ü L 1 mm ¥ËÂÌ×æ¡·¤ ßæÜð
×èÅUÚU Âñ×æÙð âð ×æÂè ÁæÌè ãñ ¥æñÚU §â·¤æ ×æÙ
20.0 cm ãñÐ g ·ð¤ ×æÙ ·ð¤ çÙÏüæÚU‡æ ×ð´ ˜æéçÅU ãæð»è Ñ
(1) 1.7%
(2) 2.7%
(3) 4.4%
(4) 2.27%
2. ×êÜ çÕ‹Îé âð t50 ÂÚU ÂýÿæðçÂÌ °·¤ Âýÿæð ·¤è çSÍçÌ
t52s ÂÚU r (40 50 ) mi j
→ ∧ ∧
5 1 âð Îè ÁæÌè ãñÐ
ØçÎ Âýÿæð ÿæñçÌÁ âð u ·¤æð‡æ ÂÚU ÂýÿæðçÂÌ ç·¤Øæ »Øæ
Íæ, ÌÕ u ãñ (g510 ms22 Üð´).
(1) tan21 2
3
(2) tan21 3
2
(3) tan21 7
4
(4) tan21 4
5

2. English : 2 Set : 01 Hindi : 2 Set : 01
3. Water is flowing at a speed of 1.5 ms21
through a horizontal tube of
cross-sectional area 1022 m2 and you are
trying to stop the flow by your palm.
Assuming that the water stops
immediately after hitting the palm, the
minimum force that you must exert should
be (density of water5103 kgm23).
(1) 15 N
(2) 22.5 N
(3) 33.7 N
(4) 45 N
4. A block A of mass 4 kg is placed on
another block B of mass 5 kg, and the block
B rests on a smooth horizontal table. If
the minimum force that can be applied on
A so that both the blocks move together is
12 N, the maximum force that can be
applied on B for the blocks to move
together will be :
(1) 30 N
(2) 25 N
(3) 27 N
(4) 48 N
3. 1022 m2 ·ð¤ ¥ÙéÂýSÍ ·¤æÅU ßæÜè ÿæñçÌÁ ÙÜè âð
1.5 ms21 ·¤è »çÌ âð ÂæÙè ÂýßæçãÌ ãæð ÚUãæ ãñ ¥æñÚU
¥æ ¥ÂÙè ãÍðÜè âð Õãæß ·¤æð ÚUæð·¤Ùð ·¤æ ÂýØæâ ·¤ÚU
ÚUãð ãñ´Ð Øã ×æÙÌð ãéØð ç·¤ ÂæÙè ãÍðÜè âð ÅU·¤ÚUæÌð ãè
L¤·¤ ÁæÌæ ãñ, ¥æ·¤æð ¥ÂÙè ãÍðÜè âð ·¤× âð ·¤×
§ÌÙæ ÕÜ Ü»æÙæ ÂǸð»æÐ (ÂæÙè ·¤æ
ƒæÙˆß5103 kgm23).
(1) 15 N
(2) 22.5 N
(3) 33.7 N
(4) 45 N
4. ÎýÃØ×æÙ 4 kg ·ð¤ °·¤ ŽÜæ·¤ A ·¤æð °·¤ ÎêâÚðU ÎýÃØ×æÙ
5 kg ·ð¤ °·¤ ŽÜæ·¤ B ·ð¤ ª¤ÂÚU ÚU¹æ ãñ ¥æñÚU ŽÜæ·¤ B
°·¤ ç¿·¤Ùè ÿæñçÌÁ ×ðÁ ÂÚU çߟææ× ¥ßSÍæ ×ð´ ÚU¹æ
ãñÐ ØçÎ ŽÜæ·¤ A ÂÚU ßã ‹ØêÙÌ× ÕÜ, çÁââð ç·¤
ÎæðÙæ´ð ŽÜæ·¤ °·¤ âæÍ »çÌàæèÜ ãæð´, 12 N ãñ ÌÕ
ŽÜæ·¤ B ÂÚU Ü»æØæ »Øæ ¥çÏ·¤Ì× ÕÜ, çÁââð ç·¤
ÎæðÙæ´ð ŽÜæ·¤ »çÌàæèÜ ãæð´, ãæð»æ Ñ
(1) 30 N
(2) 25 N
(3) 27 N
(4) 48 N

3. English : 3 Set : 01 Hindi : 3 Set : 01
5. Two bodies of masses 1 kg and 4 kg are
connected to a vertical spring, as shown
in the figure. The smaller mass executes
simple harmonic motion of angular
frequency 25 rad/s, and amplitude 1.6 cm
while the bigger mass remains stationary
on the ground. The maximum force
exerted by the system on the floor is
(take g510 ms22).
(1) 20 N
(2) 10 N
(3) 60 N
(4) 40 N
5. ÎýÃØ×æÙ 1 kg °ß´ 4 kg ·¤è Îæð ßSÌé°ð´ °·¤ ª¤ŠßæüÏÚU
·¤×æÙè mæÚUæ ç¿˜æ ·ð¤ ¥ÙéâæÚU ÁæðǸUè »Øè ãñ´Ð ¥ËÂÌÚU
ÎýÃØ×æÙ ·¤æð‡æèØ ¥æßëçžæ 25 rad/s °ß´ ¥æØæ×
1.6 cm ·¤è âÚUÜ ¥æßÌü »çÌ ·¤ÚU ÚUãæ ãñ ÁÕç·¤
ÕëãžæÚU ÎýÃØ×æÙ çSÍÚU ÚUãÌæ ãñÐ çÙ·¤æØ mæÚUæ Ȥàæü ÂÚU
Ü»æØæ »Øæ ¥çÏ·¤Ì× ÕÜ ãñ
(g510 ms22 Üð´).
(1) 20 N
(2) 10 N
(3) 60 N
(4) 40 N

4. English : 4 Set : 01 Hindi : 4 Set : 01
6. A cylinder of mass Mc and sphere of mass
Ms are placed at points A and B of two
inclines, respectively. (See Figure). If they
roll on the incline without slipping such
that their accelerations are the same, then
the ratio c
s
sin
sin
u
u
is :
(1)
8
7
(2)
15
14
(3)
8
7
(4)
15
14
6. ÎýÃØ×æÙ Mc ·ð¤ °·¤ ÕðÜÙ °ß´ ÎýÃØ×æÙ Ms ·ð¤ °·¤
»æðÜð ·¤æð ·ý¤×àæÑ Îæð ¥æÙÌ ÌÜæð´ ·ð¤ çÕ‹Îé¥æð´ A °ß´ B
ÂÚU ÚU¹æ »Øæ ãñÐ (翘æ Îð¹ð´) Ð ØçÎ ßð çÕÙæ çȤâÜð
¥æÙÌ ÌÜ ÂÚU §â Âý·¤æÚU Üéɸ·¤Ìð ãñ´ ç·¤ ©Ù·ð¤ ˆßÚU‡æ
°·¤ â×æÙ ãñ, ÌÕ ¥ÙéÂæÌ c
s
sin
sin
u
u
ãñ :
(1)
8
7
(2)
15
14
(3)
8
7
(4)
15
14

5. English : 5 Set : 01 Hindi : 5 Set : 01
7. India’s Mangalyan was sent to the Mars
by launching it into a transfer orbit EOM
around the sun. It leaves the earth at E
and meets Mars at M. If the semi-major
axis of Earth’s orbit is ae51.531011 m,
that of Mar’s orbit am52.2831011 m,
taken Kepler’s laws give the estimate of
time for Mangalyan to reach Mars from
Earth to be close to :
(1) 500 days
(2) 320 days
(3) 260 days
(4) 220 days
7. ÖæÚUÌ ·¤æ ×´»ÜØæÙ ×´»Ü »ýã ·ð¤ çÜØð âêØü ·ð¤ ¿æÚUæð´
¥æðÚU SÍæÙæ‹ÌÚU‡æ ·¤ÿæ EOM ×ð´ ÂýÿæðçÂÌ ç·¤Øæ »ØæÐ
§âÙð Âë‰ßè ·¤æð E ÂÚU ÀUæðÇ¸æ ¥æñÚU ×´»Ü »ýã âð Øã M
ÂÚU ç×ÜÌæ ãñÐ ØçÎ Âë‰ßè ·¤è ¥hü-Îèƒæü ¥ÿæ
ae51.531011 m ãñ ¥æñÚU ×´»Ü »ýã ·¤è ¥hü-Îèƒæü
¥ÿæ am52.2831011 m ãñ, ÌÕ ·ð¤ÂÜÚU ·ð¤ çÙØ×
·ð¤ ¥ÙéâæÚU Âë‰ßè âð ×´»Ü»ýã Ì·¤ ×´»ÜØæÙ ·ð¤ Âãé¡¿Ùð
·¤æ â×Ø Ü»Ö» ãæð»æ Ñ
(1) 500 çÎÙ
(2) 320 çÎÙ
(3) 260 çÎÙ
(4) 220 çÎÙ

6. English : 6 Set : 01 Hindi : 6 Set : 01
8. In materials like aluminium and copper,
the correct order of magnitude of various
elastic modulii is :
(1) Young’s modulii < shear modulii
< bulk modulii.
(2) Bulk modulii < shear modulii
< Young’s modulii.
(3) Shear modulii < Young’s modulii
< bulk modulii.
(4) Bulk modulii < Young’s modulii
< shear modulii.
9. The amplitude of a simple pendulum,
oscillating in air with a small spherical bob,
decreases from 10 cm to 8 cm in 40 seconds.
Assuming that Stokes law is valid, and
ratio of the coefficient of viscosity of air to
that of carbon dioxide is 1.3, the time in
which amplitude of this pendulum will
reduce from 10 cm to 5 cm in
carbondioxide will be close to (ln 551.601,
ln 250.693).
(1) 231 s
(2) 208 s
(3) 161 s
(4) 142 s
8. °ËØéç×çÙØ× °ß´ Ìæ¡Õð Áñâð ÂÎæÍæðü´ ·ð¤ çÜØð çßçÖ‹Ù
ÂýˆØæSÍÌæ »é‡ææ¡·¤æð´ ·ð¤ ÂçÚU×æ‡æ ·¤æ âãè ·ý¤× ãñ Ñ
(1) Ø´» ÂýˆØæSÍÌæ »é‡ææ¡·¤ < ¥ÂM¤Â‡æ ÂýˆØæSÍÌæ
»é‡ææ¡·¤ < ¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤.
(2) ¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤ < ¥ÂM¤Â‡æ
ÂýˆØæSÍÌæ »é‡ææ¡·¤ < Ø´» ÂýˆØæSÍÌæ »é‡ææ¡·¤.
(3) ¥ÂM¤Â‡æ ÂýˆØæSÍÌæ »é‡ææ¡·¤ < Ø´» ÂýˆØæSÍÌæ
»é‡ææ¡·¤ < ¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤.
(4) ¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤ < Ø´» ÂýˆØæSÍÌæ
»é‡ææ¡·¤ < ¥ÂM¤Â‡æ ÂýˆØæSÍÌæ »é‡ææ¡·¤.
9. ßæØé ×ð´ ÎæðÜÙ ·¤ÚU ÚUãð °·¤ ÌÙé »æðÜèØ ÕæÕ ßæÜð âÚUÜ
ÜæðÜ·¤ ·¤æ ¥æØæ× 40 âð·´¤ÇU ×ð´ 10 cm âð 8 cm
Ì·¤ ƒæÅU ÁæÌæ ãñ Ð Øã ×æÙ Üð´ ç·¤ SÅUæð·¤ ·¤æ çÙØ×
âãè ãñ ¥æñÚU ßæØé ·¤æ ·¤æÕüÙ ÇUæ§ü¥æò€âæ§Ç âð àØæÙÌæ
»é‡ææ´·¤ ·¤æ ¥ÙéÂæÌ 1.3 ãñ, ÌÕ ·¤æÕüÙ ÇUæ§ü ¥æò€âæ§ÇU
×ð´ §â ÜæðÜ·¤ ·ð¤ ¥æØæ× ·¤æð 10 cm âð 5 cm Ì·¤
ƒæÅUÙð ×ð´ Ü»æ â×Ø Ü»Ö» ãæð»æ
(ln 551.601, ln 250.693).
(1) 231 s
(2) 208 s
(3) 161 s
(4) 142 s

7. English : 7 Set : 01 Hindi : 7 Set : 01
10. A capillary tube is immersed vertically in
water and the height of the water column
is x. When this arrangement is taken into
a mine of depth d, the height of the water
column is y. If R is the radius of earth, the
ratio
x
y
is :
(1)
d
1
R
 
  
2
(2)
2d
1
R
 
  
2
(3)
R d
R d
 
  
2
1
(4)
R d
R d
 
  
1
2
11. Water of volume 2 L in a closed container
is heated with a coil of 1 kW. While water
is heated, the container loses energy at a
rate of 160 J/s. In how much time will the
temperature of water rise from 278C to
778C ? (Specific heat of water is
4.2 kJ/kg and that of the container is
negligible).
(1) 8 min 20 s
(2) 6 min 2 s
(3) 7 min
(4) 14 min
10. °·¤ ·ð¤àæÙçÜ·¤æ ·¤æ𠪤ŠßæüÏÚU ÂæÙè ×ð´ ÇéUÕæðØæ ÁæÌæ ãñ
¥æñÚU ÌÕ ÂæÙè ·ð¤ SÌÖ ·¤è ª¡¤¿æ§ü x ãæð ÁæÌè ãñÐ ÁÕ
§â çß‹Øæâ ·¤æð °·¤ »ãÚUæ§ü d ßæÜè °·¤ ¹æÙ ×ð´ Üð
ÁæØæ ÁæÌæ ãñ, ÌÕ ÂæÙè ·ð¤ SÌÖ ·¤è ª¡¤¿æ§ü y ãñÐ
ØçÎ Âë‰ßè ·¤è ç˜æ’Øæ R ãñ, ÌÕ ¥ÙéÂæÌ x
y
ãñ Ñ
(1)
d
1
R
 
  
2
(2)
2d
1
R
 
  
2
(3)
R d
R d
 
  
2
1
(4)
R d
R d
 
  
1
2
11. °·¤ Õ‹Î Âæ˜æ ×ð´ 2 L ¥æØÌÙ ÂæÙè ·¤æð 1 kW ·¤è
·é¤‡ÇUÜè âð »×ü ç·¤Øæ ÁæÌæ ãñÐ ÁÕ ÂæÙè »×ü ãæð ÚUãæ
ãñ, ÌÕ Âæ˜æ 160 J/s ·¤è ÎÚU â𠪤Áæü ·¤æ ÿæØ ·¤ÚU ÚUãæ
ãñÐ ç·¤ÌÙð â×Ø ×ð´ ÂæÙè ·¤æ ÌæÂ×æÙ 278C âð
778C Âãé¡¿ð»æ? (ÂæÙè ·¤è çßçàæcÅU ª¤c×æ
4.2 kJ/kg ãñ ¥æñÚU Âæ˜æ ·¤è çßçàæcÅU ª¤c×æ Ù»‡Ø ãñ)
(1) 8 ç×ÙÅU 20 âð·´¤ÇU
(2) 6 ç×ÙÅU 2 âð·´¤ÇUU
(3) 7 ç×ÙÅU
(4) 14 ç×ÙÅU

8. English : 8 Set : 01 Hindi : 8 Set : 01
12. The equation of state for a gas is given by
PV5nRT1aV, where n is the number of
moles and a is a positive constant. The
initial temperature and pressure of one
mole of the gas contained in a cylinder are
To and Po respectively. The work done by
the gas when its temperature doubles
isobarically will be :
(1)
o o
o
P T R
P 2a
(2) o o
o
P T R
P 1a
(3) Po To R ln 2
(4) Po To R
13. Modern vacuum pumps can evacuate a
vesseldowntoapressureof4.0310215 atm.
at room temperature (300 K). Taking
R58.3 JK21 mole21, 1 atm5105 Pa and
NAvogadro5631023 mole21, the mean
distance between molecules of gas in an
evacuated vessel will be of the order of :
(1) 0.2 mm
(2) 0.2 mm
(3) 0.2 cm
(4) 0.2 nm
12. °·¤ »ñâ ·¤è ¥ßSÍæ ·¤æ â×è·¤ÚU‡æ PV5nRT1aV
âð çÎØæ ÁæÌæ ãñ, Áãæ¡ n ×æðÜ ·¤è ⴁØæ ãñ ¥æñÚU a °·¤
ÏÙæˆ×·¤ çSÍÚUæ¡·¤ ãñÐ °·¤ ÕðÜÙ ×ð´ ÚU¹ð »ñ⠷𤠰·¤
×æðÜ ·¤æ ÂýæÚUçÖ·¤ ÌæÂ×æÙ °ß´ ÎæÕ ·ý¤×àæÑ To °ß´
Po ãñÐ ÁÕ §â·¤æ ÌæÂ×æÙ â×ÎæÕ ÂÚU Îæð»éÙæ ãæð
Áæ°ð»æ, ÌÕ »ñâ mæÚUæ ç·¤Øæ »Øæ ·¤æØü ãæð»æ Ñ
(1)
o o
o
P T R
P 2a
(2) o o
o
P T R
P 1a
(3) Po To R ln 2
(4) Po To R
13. ¥æÏéçÙ·¤ çÙßæüÌ ÂÂ ·¤×ÚðU ·ð¤ ÌæÂ×æÙ (300 K) ÂÚU
4.0310215 °ÅUU×æSȤèØÚU ÎæÕ Ì·¤ °·¤ ÕÌüÙ ·¤æð
çÙßæüçÌÌ ·¤ÚU â·¤Ìæ ãñÐ R58.3 JK21 ×æðÜ21,
1 °ÅU×æSȤèØÚU5105 ÂæS·¤Ü ¥æñÚU °ßæð»ðÇþUæð ⴁØæ
5631023 ×æðÜ21 ÜðÌð ãéØð °·¤ çÙßæüçÌÌ ÕÌüÙ ×ð´
»ñ⠷𤠥‡æé¥æ´ð ·ð¤ Õè¿ ×æŠØ ÎêÚUè ·¤æ ×æ٠ֻܻ
§ÌÙæ ãæð»æ Ñ
(1) 0.2 mm
(2) 0.2 mm
(3) 0.2 cm
(4) 0.2 nm

9. English : 9 Set : 01 Hindi : 9 Set : 01
14. A particle which is simultaneously
subjected to two perpendicular simple
harmonic motions represented by ;
x5a1 cos vt and y5a2 cos 2vt traces a
curve given by :
(1)
(2)
(3)
(4)
14. °·¤ ·¤‡æ, çÁâ ÂÚU °·¤ âæÍ Îæð ܐÕßÌ÷ âÚUÜ ¥æßÌü
»çÌØæ¡ x5a1 cos vt ¥æñÚU y5a2 cos 2vt Ü» ÚUãè
ãñ´, §â ß·ý¤ ·¤æð ÎàææüØð»æ Ñ
(1)
(2)
(3)
(4)

10. English : 10 Set : 01 Hindi : 10 Set : 01
15. A transverse wave is represented by :
y5
10
p
sin
2 2
t
T
x
 
  
p p
2
l
For what value of the wavelength the
wave velocity is twice the maximum
particle velocity ?
(1) 40 cm
(2) 20 cm
(3) 10 cm
(4) 60 cm
16. The magnitude of the average electric field
normally present in the atmosphere just
above the surface of the Earth is about
150 N/C, directed inward towards the
center of the Earth. This gives the total
net surface charge carried by the Earth to
be :
[Given eo58.85310212 C2/N-m2,
RE56.373106 m]
(1) 1670 kC
(2) 2670 kC
(3) 2680 kC
(4) 1680 kC
15. °·¤ ¥ÙéÂýSÍ ÌÚ´U» §ââð ÎàææüØè ÁæÌè ãñ Ñ
y5
10
p
sin
2 2
t
T
x
 
  
p p
2
l
ÌÚ´U»ÎñŠØü ·ð¤ ç·¤â ×æÙ ·ð¤ çÜ°ð ÌÚ´U» ßð» ·¤æ ×æÙ
¥çÏ·¤Ì× ·¤‡æ ßð» ·¤æ Îæð»éÙæ ãæð»æ?
(1) 40 cm
(2) 20 cm
(3) 10 cm
(4) 60 cm
16. Âë‰ßè ·ð¤ ÂëcÆU âð ÁÚUæ ª¤ÂÚU ßæÌæßÚU‡æ ×ð´ âæÏæÚU‡æÌØæ
©ÂçSÍÌ ¥æñâÌ çßléÌ ÿæð˜æ ·¤æ ÂçÚU×æ‡æ
150 N/C ·ð¤ ֻܻ ãñ çÁâ·¤è çÎàææ Âë‰ßè ·ð¤ ·ð¤‹Îý
·¤è ¥æðÚU ¥‹ÌÚU×é¹è ãñÐ Øã Âë‰ßè mæÚUæ ßæã·¤ ÂçÚU‡ææ×è
ÂëcÆU ¥æßðàæ Îð»æ Ñ
[çÎØæ ãñ eo58.85310212 C2/N-m2,
RE56.373106 m]
(1) 1670 kC
(2) 2670 kC
(3) 2680 kC
(4) 1680 kC

11. English : 11 Set : 01 Hindi : 11 Set : 01
17. Three capacitances, each of 3 mF, are
provided. These cannot be combined to
provide the resultant capacitance of :
(1) 1 mF
(2) 2 mF
(3) 4.5 mF
(4) 6 mF
18. A d.c. main supply of e.m.f. 220 V is
connected across a storage battery of
e.m.f. 200 V through a resistance of 1 V.
The battery terminals are connected to an
external resistance ‘R’. The minimum
value of ‘R’, so that a current passes
through the battery to charge it is :
(1) 7 V
(2) 9 V
(3) 11 V
(4) Zero
17. ÂýˆØð·¤ 3 mF ·ð¤ ÌèÙ â´ÏæçÚU˜æ çÎØð »Øð ãñ´Ð §Ù·¤æ
ç·¤âè Öè Âý·¤æÚU ·¤æ â´ØæðÁÙ çِ٠×ð´ âð ·¤æñÙ âæ
ÂçÚU‡ææ×è ÏæçÚUÌæ Ùãè´ Îð»æ?
(1) 1 mF
(2) 2 mF
(3) 4.5 mF
(4) 6 mF
18. çßléÌ ßæã·¤ ÕÜ 220 V ·¤è °·¤ çÎcÅU ÏæÚUæ ×éØ
âŒÜæ§ü ·¤æð °·¤ 1 V ·¤ð¤ ÂýçÌÚUæðÏ mæÚUæ çßléÌ ßæã·¤
ÕÜ 200 V ·¤è °·¤ â´ÖæçÚUÌ ÕñÅUÚè âð ÁæðǸæ ÁæÌæ ãñÐ
ÕñÅUÚUè ·ð¤ ÅUç×üÙÜ ·¤æð °·¤ Õæ±Ø ÂýçÌÚUæðÏ ‘R’ âð ÁæðǸæ
ÁæÌæ ãñÐ ‘R’ ·¤æ ‹ØêÙÌ× ×æÙ, çÁââð ç·¤ ÕñÅUÚUè ×ð´
ÏæÚUæ ÂýßæçãÌ ãæð·¤ÚU ©âð ¥æßðçàæÌ ·¤ÚðU, ãñ Ñ
(1) 7 V
(2) 9 V
(3) 11 V
(4) àæê‹Ø

12. English : 12 Set : 01 Hindi : 12 Set : 01
19. The mid points of two small magnetic
dipoles of length d in end-on positions, are
separated by a distance x, (x >> d). The
force between them is proportional to
x2n where n is :
(1) 1
(2) 2
(3) 3
(4) 4
20. The magnetic field of earth at the equator
is approximately 431025 T. The radius
of earth is 6.43106 m. Then the dipole
moment of the earth will be nearly of the
order of :
(1) 1023 A m2
(2) 1020 A m2
(3) 1016 A m2
(4) 1010 A m2
19. ¥ÿæèØ çSÍçÌ ×ð´ ܐÕæ§ü d ·ð¤ Îæð ÌÙé ¿éÕ·¤èØ çmÏéýßæ´ð
·ð¤ ×ŠØ çÕ‹Îé¥æð´ ·¤æð x ÎêÚUè ÂÚU ÚU¹æ »Øæ ãñ (x >>d)Ð
ÎæðÙæð´ ·ð¤ Õè¿ ÕÜ x2n ·¤ð¤ â×æÙéÂæÌè ãñ, Áãæ¡ n ãñ :
(1) 1
(2) 2
(3) 3
(4) 4
20. Öê×ŠØ ÚðU¹æ ÂÚU Âë‰ßè ·ð¤ ¿éÕ·¤èØ ÿæð˜æ ·¤æ
×æ٠ֻܻ 431025 T ãñÐ Âë‰ßè ·¤è ç˜æ’Øæ
6.43106 m ãñÐ ÌÕ Âë‰ßè ·¤æ çmÏýéß ¥æƒæê‡æü ֻܻ
§â ·¤æðçÅU ·¤æ ãæð»æ Ñ
(1) 1023 A m2
(2) 1020 A m2
(3) 1016 A m2
(4) 1010 A m2

13. English : 13 Set : 01 Hindi : 13 Set : 01
21. When the rms voltages VL, VC and VR are
measured respectively across the inductor
L, the capacitor C and the resistor R in a
series LCR circuit connected to an
AC source, it is found that the ratio
VL : VC : VR51 : 2 : 3. If the rms voltage
of the AC source is 100 V, then VR is close
to :
(1) 50 V
(2) 70 V
(3) 90 V
(4) 100 V
21. °·¤ ÂýˆØæßÌèü ÏæÚUæ ŸææðÌ âð ÁéǸð Ÿæð‡æè LCR
ÂçÚUÂÍ ×ð´ ÂýðÚU·¤ˆß L â´ÏæçÚUÌ C ¥æñÚU ÂýçÌÚUæðÏ·¤ R ÂÚU
×æÂð »Øð ß»ü-×æŠØ-×êÜ ßæðËÅUÌæ°ð´ ·ý¤×àæÑ
VL, VC °ß´ VR ãñ´, ÌÕ Øã ÂæØæ ÁæÌæ ãñ ç·¤
VL : VC : VR51 : 2 : 3 Ð ØçÎ ÂýˆØæßÌèü ÏæÚUæ oýæðÌ
·¤è ß»ü-×æŠØ-×êÜ ßæðËÅUÌæ 100 V ãñ´, ÌÕ VR ·¤æ
×æ٠ֻܻ ãñ Ñ
(1) 50 V
(2) 70 V
(3) 90 V
(4) 100 V

14. English : 14 Set : 01 Hindi : 14 Set : 01
22. Match List I (Wavelength range of
electromagnetic spectrum) with List II.
(Method of production of these waves)
and select the correct option from the
options given below the lists.
(a)
700 nm to
1 mm
(i)
Vibration of atoms
and molecules.
(b)
1 nm to
400 nm
(ii)
Inner shell electrons
in atoms moving from
one energy level to a
lower level.
(c) < 1023
nm (iii)
Radioactive decay of
the nucleus.
(d)
1 mm to
0.1 m
(iv) Magnetron valve.
List I List II
(1) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
(2) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(3) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)
(4) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
22. âê¿è I (çßléÌ ¿éÕ·¤èØ SÂð€ÅþU× ·¤è ÌÚ´U»ÎñŠØü ÚðU‹Á)
·¤æð âê¿è II (§Ù ÌÚ´U»æð´ ·ð¤ çÙ×æü‡æ ·¤è çßçÏ) âð âé×ðçÜÌ
·¤èçÁ°ð ¥æñÚU âê¿è ·ð¤ Ùè¿ð çÎØð »Øð çß·¤ËÂæ´ð ×ð´ âð
âãè çß·¤Ë ¿éçÙ°Ð
(a)
700 nm ÇÕ
1 mm
(i)
ŠøËΊËÕ™ •Ä™ §¿U¼ËøËΊËÕ™ œÕ‰
œ‰ƒ§¾ ÇÕ
(b)
1 nm ÇÕ
400 nm
(ii)
§¿U¼ËøËΊËÕ™ œÕ‰ ŠËü±Ì¿Uœ‰ ÅËÖÁ
ŒÁÕþªãU˾ËÕ™ œ‰Í •œ‰ ‰¦Ëá S±¿U
ÇÕ Ì¾¤ÁÕ S±¿U œ‰Í ̱ ÇÕ
(c) < 1023
nm (iii)
¾ËÌ»œ‰ œÕ‰ ¿ÕU̬U½ËÕ Ç̜≽
ä˽ ÇÕ
(d)
1 mm ÇÕ
0.1 m
(iv) ¼Öó¾ÕªãUˆ¾ ÄË°Ä ÇÕ
ÇÏ¤Í I ÇÏ¤Í II
(1) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
(2) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(3) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)
(4) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)

15. English : 15 Set : 01 Hindi : 15 Set : 01
23. A diver looking up through the water sees
the outside world contained in a circular
horizon. The refractive index of water is
4
3
, and the diver’s eyes are 15 cm below
the surface of water. Then the radius of
the circle is :
(1) 15333 5 cm
(2) 1533 7 cm
(3)
15 7
cm
3
3
(4)
15 3
cm
7
3
23. °·¤ »æðÌæ¹æðÚU ÂæÙè ·ð¤ ¥‹ÎÚU âð ÕæãÚU ·¤è ÎéçÙØæ ·¤æð
°·¤ ßëžæèØ ÿæñçÌÁ ×ð´ çÙçãÌ Îð¹Ìæ ãñÐ ÂæÙè ·¤æ
¥ÂßÌüÙæ¡·¤ 4
3
ãñ ¥æñÚU »æðÌæ¹æðÚU ·¤è ¥æ¡¹ ÂæÙè ·ð¤
ÂëcÆU âð 15 cm Ùè¿ð ãñ´Ð ÌÕ ßëžæ ·¤è ç˜æ’Øæ ãñ Ñ
(1) 15333 5 cm
(2) 1533 7 cm
(3)
15 7
cm
3
3
(4)
15 3
cm
7
3

16. English : 16 Set : 01 Hindi : 16 Set : 01
24. Using monochromatic light of wavelength
l, an experimentalist sets up the Young’s
double slit experiment in three ways as
shown.
If she observes that y5b9, the wavelength
of light used is :
24. ÌÚ´U»ÎñƒØü l ·ð¤ °·¤ß‡æèü Âý·¤æàæ ·ð¤ ÂýØæð» âð °·¤ ßñ™ææçÙ·¤
Ø´» ·ð¤ çmçÀUÎý ÂýØæð» ·¤æð ÎàææüØð »Øð ÌèÙ Âý·¤æÚU âð
ÃØßçSÍÌ ·¤ÚUÌè ãñÐ
ØçÎ ßã ÂæÌè ãñ ç·¤ y5b9, ÌÕ ÂýØæð» ç·¤Øð »Øð
Âý·¤æàæ ·¤è ÌÚ´U»ÎñƒØü ãñ Ñ

17. English : 17 Set : 01 Hindi : 17 Set : 01
(1) 520 nm
(2) 540 nm
(3) 560 nm
(4) 580 nm
25. The focal lengths of objective lens and eye
lens of a Gallelian Telescope are
respectively 30 cm and 3.0 cm. Telescope
produces virtual, erect image of an object
situated far away from it at least distance
of distinct vision from the eye lens. In this
condition, the Magnifying Power of the
Gallelian Telescope should be :
(1) 111.2
(2) 211.2
(3) 28.8
(4) 18.8
26. For which of the following particles will it
be most difficult to experimentally verify
the de-Broglie relationship ?
(1) an electron
(2) a proton
(3) an a-particle
(4) a dust particle
(1) 520 nm
(2) 540 nm
(3) 560 nm
(4) 580 nm
25. °·¤ »ñçÜçÜØÙ ÎêÚUÎàæèü ·ð¤ ¥çÖÎëàØ·¤ °ß´ Ùðç˜æ·¤æ
Üð‹â ·¤è $Ȥæð·¤â ܐÕæ§Øæ¡ ·ý¤×àæÑ 30 cm °ß´
3.0 cm ãñÐ ÎêÚUÎàæèü Ùðç˜æ·¤æ Üð‹â âð âéSÂcÅU ÎàæüÙ
·¤è ‹ØêÙÌ× ÎêÚUè ÂÚU °·¤ ¥ˆØ‹Ì ÎêÚU ·¤è ßSÌé ·¤æ
¥æÖæâè, âèÏæ ÂýçÌçÕÕ ÕÙæÌæ ãñÐ §â çSÍçÌ ×ð´,
»ñçÜçÜØÙ ÎêÚUÎàæèü ·¤è ¥æßÏüÙ ÿæ×Ìæ ãæð»è Ñ
(1) 111.2
(2) 211.2
(3) 28.8
(4) 18.8
26. çِÙçÜç¹Ì ·¤‡ææð´ ×ð´ âð 緤⠷¤‡æ ·ð¤ çÜØð
ÇUè-Õýæ‚Üè âÕ‹Ï ·¤æ ÂýæØæðç»·¤ âˆØæÂÙ ¥ˆØçÏ·¤
×éçà·¤Ü ãæð»æ?
(1) °·¤ §Üð€ÅþUæÙ$
(2) °·¤ ÂýæðÅUæòÙ
(3) °·¤ a-·¤‡æ
(4) °·¤ ÏêÜ ·¤æ ·¤‡æ

18. English : 18 Set : 01 Hindi : 18 Set : 01
27. If the binding energy of the electron in a
hydrogen atom is 13.6 eV, the energy
required to remove the electron from the
first excited state of Li11 is :
(1) 122.4 eV
(2) 30.6 eV
(3) 13.6 eV
(4) 3.4 eV
28. Identify the gate and match A, B, Y in
bracket to check.
(1) AND (A51, B51, Y51)
(2) OR (A51, B51, Y50)
(3) NOT (A51, B51, Y51)
(4) XOR (A50, B50, Y50)
29. A transmitting antenna at the top of a
tower has a height 32 m and the height of
the receiving antenna is 50 m. What is the
maximum distance between them for
satisfactory communication in line of sight
(LOS) mode ?
(1) 55.4 km
(2) 45.5 km
(3) 54.5 km
(4) 455 km
27. ØçÎ ãæ§ÇþUæðÁÙ ÂÚU×æ‡æé ×ð´ §Üð€ÅþUæÙ ·¤è Õ‹ÏÙ ª¤Áæü
13.6 eV ãñ, ÌÕ Li11 ·¤è ÂýÍ× ©žæðçÁÌ ¥ßSÍæ
âð §Üð€ÅþUæÙ ÕæãÚU çÙ·¤æÜÙð ×ð´ ¥æßàØ·¤ ª¤Áæü ãñ Ñ
(1) 122.4 eV
(2) 30.6 eV
(3) 13.6 eV
(4) 3.4 eV
28. »ðÅU ·¤æð Âã¿æçÙ°ð ¥æñÚU ·¤æðcÅU·¤ ×ð´ A, B, Y ·ð¤ ×æÙ âð
âé×ðçÜÌ ·¤ÚU Áæ¡¿ ·¤èçÁ°ðÐ
(1) AND (A51, B51, Y51)
(2) OR (A51, B51, Y50)
(3) NOT (A51, B51, Y51)
(4) XOR (A50, B50, Y50)
29. °·¤ ×èÙæÚU ·ð¤ àæèáü ÂÚU Âýðá‡æ °ç‹ÅUÙæ ·¤è ª¡¤¿æ§ü 32 m
ãñ ¥æñÚU ¥çÖ»ýæãè °ç‹ÅUÙæ ·¤è ª¡¤¿æ§ü 50 m ãñÐ
ÎëçcÅUÚðU¹èØ (LOS) ×æðÇU ×ð´ â´ÌæðáÂýÎ â´¿ÚU‡æ ·ð¤ çÜ°
ÎæðÙæ´ð °ç‹ÅUÙæ ·ð¤ Õè¿ ¥çÏ·¤Ì× ÎêÚUè €Øæ ãñ?
(1) 55.4 km
(2) 45.5 km
(3) 54.5 km
(4) 455 km

19. English : 19 Set : 01 Hindi : 19 Set : 01
30. An n-p-n transistor has three leads
A, B and C. Connecting B and C by moist
fingers, A to the positive lead of an
ammeter, and C to the negative lead of the
ammeter, one finds large deflection. Then,
A, B and C refer respectively to :
(1) Emitter, base and collector
(2) Base, emitter and collector
(3) Base, collector and emitter
(4) Collector, emitter and base.
30. °·¤ n-p-n ÅþUæç‹ÁSÅUÚU ×ð´ ÌèÙ ¿æÜ·¤ ÌæÚU
A, B °ß´ C ãñ´Ð »èÜè ¥´»éçÜØæð´ âð B °ß´ C ·¤æð
ÁæðǸÙð ÂÚU, °·¤ ÏæÚUæ×æÂè ·¤æð ÏÙæˆ×·¤ ¿æÜ·¤ ÌæÚU
·¤æð A âð ÁæðǸÙð ÂÚU ¥æñÚU ÏæÚUæ×æÂè ·¤è «¤‡ææˆ×·¤
¿æÜ·¤ ÌæÚU ·¤æð C âð ÁæðǸÙð ÂÚU °·¤ Âýðÿæ·¤ ¥ˆØçÏ·¤
çßÿæð ÂæÌæ ãñÐ ÌÕ A, B °ß´ C ·¤æ â´ÎÖü ·ý¤×àæÑ
§Ùâð ãñ Ñ
(1) ©ˆâÁü·¤, ¥æÏæÚU °ß´ â´»ýæãè
(2) ¥æÏæÚU, ©ˆâÁü·¤ °ß´ â´»ýæãè
(3) ¥æÏæÚU, â´»ýæãè °ß´ ©ˆâÁü·¤
(4) â´»ýæãè, ©ˆâÁü·¤ °ß´ ¥æÏæÚU

20. English : 20 Set : 01 Hindi : 20 Set : 01
PART B — CHEMISTRY
31. In a face centered cubic lattice atoms A
are at the corner points and atoms B at
the face centered points. If atom B is
missing from one of the face centered
points, the formula of the ionic compound
is :
(1) AB2
(2) A5B2
(3) A2B3
(4) A2B5
32. Van der Waal’s equation for a gas is stated
as,
2
nRT n
p a
V nb V
 
  
5 2
2
.
This equation reduces to the perfect gas
equation,
nRT
p
V
5 when ,
(1) temperature is sufficiently high and
pressure is low.
(2) temperature is sufficiently low and
pressure is high.
(3) both temperature and pressure are
very high.
(4) both temperature and pressure are
very low.
Öæ» B — ÚUâæØÙ çß™ææÙ
31. °·¤ Ȥܷ¤ ·ð¤ç‹ÎýÌ ƒæÙæ·¤æÚU ÁæÜ·¤ ×ð´ A ·ð¤¤ ÂÚU×æ‡æé
·¤æðÙæð´ ·ð¤ çÕ‹Îé¥æð´ ÂÚU ãñ´ ¥æñÚU B ·ð¤ ÂÚU×æ‡æé Ȥܷ¤
·ð¤‹Îýæð´ ÂÚU ãñ´Ð ØçÎ B ÂÚU×æ‡æé °·¤ Ȥܷ¤ ·ð¤‹Îý ÂÚU Ù
ãæð Ìæð ¥æØçÙ·¤ Øæñç»·¤ ·¤æ âê˜æ ãæð»æ Ñ
(1) AB2
(2) A5B2
(3) A2B3
(4) A2B5
32. °·¤ »ñâ ·ð¤ çÜØð ßæ‹ÇUÚU ßæÜ â×è·¤ÚU‡æ
2
nRT n
p a
V nb V
 
  
5 2
2
.
ãæðÌæ ãñÐ Øã â×è·¤ÚU‡æ ¥æÎàæü »ñâ â×è·¤ÚU‡æ ·¤æ
M¤Â,
nRT
p
V
5 ÏæÚU‡æ ·¤ÚU Üð»æ ÁÕ Ñ
(1) Ìæ ÂØæüŒÌ ©‘¿ ãæð»æ ¥æñÚU ÎæÕ ‹ØêÙ ãæð»æÐ
(2) Ìæ ÂØæüŒÌ ‹ØêÙ ãæð»æ ¥æñÚU ÎæÕ ©‘¿ ãæð»æÐ
(3) Ìæ ¥æñÚU ÎæÕ ÎæðÙæð´ ÕãéÌ ©‘¿ ãæð´»ðÐ
(4) Ìæ ¥æñÚU ÎæÕ ÎæðÙæð´ ÕãéÌ ‹ØêÙ ãæð´»ððÐ

21. English : 21 Set : 01 Hindi : 21 Set : 01
33. The standard electrode potentials
( )M /M
o
E 1 of four metals A, B, C and D are
21.2 V , 0.6 V, 0.85 V and 20.76 V,
respectively. The sequence of deposition
of metals on applying potential is :
(1) A, C, B, D
(2) B, D, C, A
(3) C, B, D, A
(4) D, A, B, C
34. At a certain temperature, only 50% HI is
dissociated into H2 and I2 at equilibrium.
The equilibrium constant is :
(1) 1.0
(2) 3.0
(3) 0.5
(4) 0.25
35. Dissolving 120 g of a compound of
(mol. wt. 60) in 1000 g of water gave a
solution of density 1.12 g/mL. The
molarity of the solution is :
(1) 1.00 M
(2) 2.00 M
(3) 2.50 M
(4) 4.00 M
33. ¿æÚU ÏæÌé¥æð´ A, B, C ¥æñÚU D ·ð¤ SÅñU‹ÇUÇüU (×æÙ·¤)
§Üñ€ÅþUæðÇU çßÖß ( )M /M
o
E 1 ·ý×æÙéâæÚU
21.2 V, 0.6 V, 0.85 V ¥æñÚU 20.76 V ãñ´Ð çßÖß
Üæ»ê ·¤ÚUÙð ÂÚU ÏæÌé Á×Ùð ·¤æ ·ý¤× ãæð»æ Ñ
(1) A, C, B, D
(2) B, D, C, A
(3) C, B, D, A
(4) D, A, B, C
34. °·¤ Ìæ çßàæðá âæØÂÚU ·ð¤ßÜ 50% HI, H2 ¥æñÚU
I2 ×ð´ çßÖæçÁÌ ãæðÌæ ãñÐ âæØ çSÍÚUæ´·¤ ·¤æ ×æÙ ãæð»æ Ñ
(1) 1.0
(2) 3.0
(3) 0.5
(4) 0.25
35. °·¤ Øæñç»·¤ (¥‡æéÖæÚU 60) ·¤è 120 »ýæ× ×æ˜ææ ·¤æð
1000 »ýæ× ÁÜ ×ð´ ƒææðÜÙð ÂÚU ÂýæŒÌ ãé° çßÜØÙ ·¤æ
ƒæÙˆß 1.12 »ýæ× ÂýçÌ ç×çÜ çÜÅUÚU ãñÐ çßÜØÙ ·¤è
×æðÜñçÚUÅUè ãæð»è Ñ
(1) 1.00 M
(2) 2.00 M
(3) 2.50 M
(4) 4.00 M

22. English : 22 Set : 01 Hindi : 22 Set : 01
36. The half-life period of a first order reaction
is 15 minutes. The amount of substance
left after one hour will be :
(1) 1
4 of the original amount
(2) 1
8 of the original amount
(3) 1
16 of the original amount
(4) 1
32 of the original amount
37. A current of 10.0 A flows for 2.00 h
through an electrolytic cell containing a
molten salt of metal X. This results in the
decomposition of 0.250 mol of metal X at
the cathode. The oxidation state of X in
the molten salt is : (F596,500 C)
(1) 11
(2) 21
(3) 31
(4) 41
36. °·¤ ÂýÍ× ·¤æðçÅU ·¤è ¥çÖç·ý¤Øæ ·¤æ ¥Ïü-¥æØé ·¤æÜ
15 ç×ÙÅU ãñÐ °·¤ ƒæ‡ÅUæ Âà¿æÌ÷ ÂÎæÍü ·¤è àæðá ÚUãè
×æ˜ææ ãæð»è Ñ
(1) ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ 1
4 Öæ»
(2) ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ 1
8 Öæ»
(3) ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ 1
16 Öæ»
(4) ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ 1
32 Öæ»
37. ÏæÌé X ·ð¤ çƒæÜð ãé° Ü߇æ ÏæÚU·¤ §Üñ€ÅþUæðçÜçÅU·¤
âñÜ ×ð´ âð 2.00 ƒæ‡ÅðU ·ð¤ çÜØð 10.0 A ·¤è çßléÌ
ÏæÚUæ ¿ÜæÙð ÂÚU 0.250 ×æðÜ X ÏæÌé ·¤æ Á×æß ãé¥æÐ
çƒæÜð ãé° Ü߇æ ×ð´ ÏæÌé X ·¤è ¥æ€âè·ë¤Ì ¥ßSÍæ
ãæð»è Ñ (ÁÕç·¤ F596,500 C)
(1) 11
(2) 21
(3) 31
(4) 41

23. English : 23 Set : 01 Hindi : 23 Set : 01
38. The energy of an electron in first Bohr orbit
of H - atom is 213.6 eV. The energy value
of electron in the excited state of Li21 is :
(1) 227.2 eV
(2) 30.6 eV
(3) 230.6 eV
(4) 27.2 eV
39. The temperature at which oxygen
molecules have the same root mean square
speed as helium atoms have at 300 K is :
(Atomic masses : He54 u, O516 u)
(1) 300 K
(2) 600 K
(3) 1200 K
(4) 2400 K
40. The standard enthalpy of formation of
NH3 is 246.0 kJ/mol. If the enthalpy of
formation of H2 from its atoms is
2436 kJ/mol and that of N2 is
2712 kJ/mol, the average bond enthalpy
of N2H bond in NH3 is :
(1) 21102 kJ/mol
(2) 2964 kJ/mol
(3) 1352 kJ/mol
(4) 11056 kJ/mol
38. H-ÂÚU×æ‡æé ·ð¤ ÂýÍ× ÕæðãÚU ¥æçÕüÅU ×ð´ §Üñ€ÅþUæÙ ·¤è
ª¤Áæü 213.6 eV ãñÐ Li 21 ·¤è ©žæðçÁÌ ¥ßSÍæ ×ð´
§Üñ€ÅþUæÙ ·¤æ ª¤Áæü ×æÙ ãæð»æ Ñ
(1) 227.2 eV
(2) 30.6 eV
(3) 230.6 eV
(4) 27.2 eV
39. ÌæÂ, çÁâ ÂÚU ¥æò€âèÁÙ ¥‡æé¥æð´ ·¤è ß»ü ×æŠØ×êÜ
SÂèÇU ·¤æ ×æÙ ßãè ãæðÌæ ãñ Áæð ãèçÜØ× ÂÚU×æ‡æé¥æð´ ·¤æ
300 K ÂÚU ãæðÌæ ãñ,
(ÂÚU×æ‡æé ÎýÃØ×æÙ Ñ He54 ×æ˜æ·¤, O516 ×æ˜æ·¤)
ãæð»æ Ñ
(1) 300 K
(2) 600 K
(3) 1200 K
(4) 2400 K
40. NH3 ÕÙÙð ·¤è ×æÙ·¤ ª¤Áæü 246.0 kJ/×æðÜ ãñÐ
ØçÎ ¥ÂÙð ÂÚU×æ‡æé¥æð´ âð H2 ÕÙÙð ·¤è ª¤Áæü
2436 kJ/×æðÜ ¥æñÚU N2 ·¤è 2712 kJ/×æðÜ ãæð Ìæð
N2H ·¤è NH3 ×ð´ ¥æñâÌ Õæ¡ÇU ª¤Áæü ãæð»è Ñ
(1) 21102 kJ/×æðÜ
(2) 2964 kJ/×æðÜ
(3) 1352 kJ/×æðÜ
(4) 11056 kJ/×æðÜ

24. English : 24 Set : 01 Hindi : 24 Set : 01
41. The amount of oxygen in 3.6 moles of water
is :
(1) 115.2 g
(2) 57.6 g
(3) 28.8 g
(4) 18.4 g
42. The gas evolved on heating CaF2 and SiO2
with concentrated H2SO4, on hydrolysis
gives a white gelatinous precipitate. The
precipitate is :
(1) hydrofluosilicic acid
(2) silica gel
(3) silicic acid
(4) calciumfluorosilicate
43. Chloro compound of Vanadium has only
spin magnetic moment of 1.73 BM. This
Vanadium chloride has the formula :
(at. no. of V523)
(1) VCl2
(2) VCl4
(3) VCl3
(4) VCl5
41. 3.6 ×æðÜ ÁÜ ×ð´ ¥æò€âèÁÙ ·¤è ×æ˜ææ ãæðÌè ãñ Ñ
(1) 115.2 »ýæ×
(2) 57.6 »ýæ×
(3) 28.8 »ýæ×
(4) 18.4 »ýæ×
42. CaF2 ¥æñÚU SiO2 ·¤æð âæ‹Îý H2SO4 ·ð¤ âæÍ »ÚU×
·¤ÚUÙð âð ÂýæŒÌ ãé§ü »ñâ ãæ§ÇþUæÜðçââ ÂÚU °·¤ â$Èð¤Î
ÁñÜ Áñâæ ¥ßÿæð ÎðÌè ãñÐ Øã ¥ßÿæð ãæð»æ Ñ
(1) ãæ§ÇþUæðÜæðçâçÜçâ·¤ °ðçâÇU
(2) çâçÜ·¤æ ÁñÜ
(3) çâçÜçâ·¤ °ðçâÇ
(4) ·ñ¤çËàæØ׍ÜæðÚUæðçâçÜ·ð¤ÅU
43. ßñÙðçÇUØ× ·¤æ °·¤ €ÜæðÚUæð Øæñç»·¤ 1.73 BM ·¤æ ·ð¤ßÜ
çSÂÙ ×ñ‚ÙðçÅU·¤ ×æð×ñ‹ÅU ÚU¹Ìæ ãñ
(V ·¤æ ÂÚU×æ‡æê ·ý¤×æ´·¤523) §â ßñÙðçÇUØ× €ÜæðÚUæ§ÇU
·¤æ âê˜æ ãæðÌæ ãñ Ñ
(1) VCl2
(2) VCl4
(3) VCl3
(4) VCl5

25. English : 25 Set : 01 Hindi : 25 Set : 01
44. An octahedral complex of Co31 is
diamagnetic. The hybridisation involved
in the formation of the complex is :
(1) sp3d2
(2) dsp2
(3) d2sp3
(4) dsp3d
45. Which of the following is not formed when
H2S reacts with acidic K2Cr2O7
solution ?
(1) CrSO4
(2) Cr2(SO4)
3
(3) K2SO4
(4) S
46. Which of the following has unpaired
electron(s) ?
(1) N2
(2) 2O2
(3) 2
2N 1
(4) 2
2O 2
44. Co31 ·¤æ °·¤ ¥cÅȤËæ·¤èØ â´·¤ÚU ÂýçÌ¿éÕ·¤èØ
ãæðÌæ ãñÐ §â â´·¤ÚU ·ð¤ ÕÙÙð âð âÕç‹ÏÌ â´·¤ÚU‡æ
ãæð»æ Ñ
(1) sp3d2
(2) dsp2
(3) d2sp3
(4) dsp3d
45. ¥ÜèØ K2Cr2O7 ƒææðÜ ·¤è H2S ·ð¤ âæÍ ¥çÖç·ý¤Øæ
ãæðÙð ÂÚU çِÙæð´ ×ð´ âð ·¤æñÙ Ùãè´ ÕÙÌæ?
(1) CrSO4
(2) Cr2(SO4)
3
(3) K2SO4
(4) S
46. §Ù ×ð´ âð ç·¤â ×ð´ ¥Øéç‚×Ì §Üñ€ÅþUæÙ ãæðÌæ ãñ Øæ ãæðÌð
ãñ´ ?
(1) N2
(2) 2O2
(3) 2
2N 1
(4) 2
2O 2

26. English : 26 Set : 01 Hindi : 26 Set : 01
47. In the following sets of reactants which
two sets best exhibit the amphoteric
character of Al2O3 . xH2O ?
Set 1 : Al2O3 . xH2O (s) and OH
2
(aq)
Set 2 : Al2O3 . xH2O (s) and H2O (l)
Set 3 : Al2O3 . xH2O (s) and H
1
(aq)
Set 4 : Al2O3 . xH2O (s) and NH3 (aq)
(1) 1 and 2
(2) 1 and 3
(3) 2 and 4
(4) 3 and 4
48. The number and type of bonds in 2
2C 2 ion
in CaC2 are :
(1) One s bond and one p2bond
(2) One s bond and two p2bonds
(3) Two s bonds and two p2bonds
(4) Two s bonds and one p2bond
49. The form of iron obtained from blast
furnace is :
(1) Steel
(2) Cast Iron
(3) Pig Iron
(4) Wrought Iron
47. ç·ý¤Øæ ·¤æÚU·¤æð´ ·ð¤ çِ٠âðÅUæð´ ×ð´ âð ç·¤â Îæð ×ð´
Al2O3 . xH2O ·¤æ ©ÖØ Ï×èü ÃØßãæÚU Îð¹æ ÁæÌæ
ãñ?
Set 1 : Al2O3 . xH2O (s) ¥æñÚU OH
2
(ÁÜèØ)
Set 2 : Al2O3 . xH2O (s) ¥æñÚU H2O (Îýß)
Set 3 : Al2O3 . xH2O (s) ¥æñÚU H
1
(ÁÜèØ)
Set 4 : Al2O3 . xH2O (s) ¥æñÚU NH3 (ÁÜèØ)
(1) 1 ¥æñÚU 2
(2) 1 ¥æñÚU 3
(3) 2 ¥æñÚU 4
(4) 3 ¥æñÚU 4
48. CaC2 ·ð 2
2C 2 ¥æØÙ ×ð´ ¥æÕ‹Ïæð´ ·¤è ⴁØæ °ß´
Âý·¤æÚU çِ٠·¤æñÙâè ãñ?
(1) °·¤ s ¥æÕ‹Ï ¥æñÚU °·¤ p2¥æÕ‹Ï
(2) °·¤ s ¥æÕ‹Ï ¥æñÚU Îæð p2¥æÕ‹Ï
(3) Îæð s ¥æÕ‹Ï ¥æñÚU Îæð p2¥æÕ‹Ï
(4) Îæð s ¥æÕ‹Ï ¥æñÚU °·¤ p2¥æÕ‹Ï
49. Ûææð´·¤æ Ö^è âð ÂýæŒÌ ãé° Üæðãð ·¤æ M¤Â ·¤ãÜæÌæ ãñ Ñ
(1) §SÂæÌ (Steel)
(2) ÉUÜßæ¡ Üæðãæ (Cast Iron)
(3) ·¤‘¿æ Üæðãæ (Pig Iron)
(4) çÂÅUßæ´ Üæðãæ (Wrought Iron)

27. English : 27 Set : 01 Hindi : 27 Set : 01
50. The correct statement about the magnetic
properties of [Fe(CN)6]32 and [FeF6]32
is : (Z526).
(1) both are paramagnetic.
(2) both are diamagnetic.
(3) [Fe(CN)6]32 is diamagnetic,
[FeF6]32 is paramagnetic.
(4) [Fe(CN)6]32 is paramagnetic,
[FeF6]32 is diamagnetic.
51. Which one of the following reactions will
not result in the formation of carbon-
carbon bond ?
(1) Reimer-Tieman reaction
(2) Friedel Craft’s acylation
(3) Wurtz reaction
(4) Cannizzaro reaction
52. In the hydroboration - oxidation reaction
of propene with diborane, H2O2 and
NaOH, the organic compound formed is :
(1) CH3CH2OH
(2) CH3CHOHCH3
(3) CH3CH2CH2OH
(4) (CH3)
3
COH
50. [Fe(CN)6]32 ¥æñÚU [FeF6]32 ·ð¤ ¿éÕ·¤èØ »é‡ææð´
·¤æ ØÍæÍü çßßÚU‡æ ãñ Ñ (Z526).
(1) ÎæðÙæ´ð ¥Ùé¿éÕ·¤èØ ãñ´Ð
(2) ÎæðÙæð´ ÂýçÌ ¿éÕ·¤èØ ãñ´Ð
(3) [Fe(CN)6]32 ÂýçÌ¿éÕ·¤èØ ¥æñÚU
[FeF6]32¥Ùé¿éÕ·¤èØ ãñÐ
(4) [Fe (CN)6]32¥Ùé¿éÕ·¤èØ ¥æñÚU [FeF6]32
ÂýçÌ¿éÕ·¤èØ ãñÐ
51. §Ù ¥çÖç·ý¤Øæ¥æð´ ×ð´ âð ç·¤â ×ð´ ·¤æÕüÙ - ·¤æÕüÙ
¥æÕ‹Ï Ùãè´ ÂýæŒÌ ãæð»æ?
(1) ÚUæð×ÚU - ÅUè×Ù ¥çÖç·ý¤ØæÐ
(2) Èý¤èÇUÜ ·ý¤æȤÅU °ðâèÜðàæÙÐ
(3) ßéÅüU$Á ¥çÖç·ý¤ØæÐ
(4) ·ñ¤Ùè$ÁñÚUæð ¥çÖç·ý¤ØæÐ
52. ÂýæðÂèÙ ·ð¤ ÇUæ§ÕæðÚðUÙ, H2O2 ¥æñÚU NaOH ·ð¤ âæÍ
ãæ§ÇþUæðÕæðÚðUàæÙ-¥æò€âè·¤ÚU‡æ ¥çÖç·ý¤Øæ ×ð´ ÕÙæ ·¤æÕüçÙ·¤
Øæñç»·¤ ãñ Ñ
(1) CH3CH2OH
(2) CH3CHOHCH3
(3) CH3CH2CH2OH
(4) (CH3)
3
COH

28. English : 28 Set : 01 Hindi : 28 Set : 01
53. The major product of the reaction
2 2 4NaNO /H SO
→
is :
(1)
(2)
(3)
(4)
54. For the compounds
CH3Cl, CH3Br, CH3I and CH3F,
the correct order of increasing C-halogen
bond length is :
(1) CH3F < CH3Cl < CH3Br < CH3I
(2) CH3F < CH3Br < CH3Cl < CH3I
(3) CH3F < CH3I < CH3Br < CH3Cl
(4) CH3Cl < CH3Br < CH3F < CH3I
53. ¥çÖç·ý¤Øæ
2 2 4NaNO /H SO
→ ·¤æ ×éØ
ç·ý¤Øæ È¤Ü ãñ Ñ
(1)
(2)
(3)
(4)
54. Øæñç»·¤æð´
CH3Cl,CH3Br,CH3I ¥æñÚU CH3F
×ð´ ·¤æÕüÙ-ãñÜæðÁÙ Õæ¡ÇU ·¤è ÕɸÌè ܐÕæ§ü ·¤æ ÆUè·¤
·ý¤× ãñ Ñ
(1) CH3F < CH3Cl < CH3Br < CH3I
(2) CH3F < CH3Br < CH3Cl < CH3I
(3) CH3F < CH3I < CH3Br < CH3Cl
(4) CH3Cl < CH3Br < CH3F < CH3I

29. English : 29 Set : 01 Hindi : 29 Set : 01
55. Allyl phenyl ether can be prepared by
heating :
(1) C6H5Br1CH25CH2CH22ONa
(2) CH25CH2CH22Br1C6H5ONa
(3) C6H52CH5CH2Br1CH32ONa
(4) CH25CH2Br1C6H52CH22ONa
56. In a nucleophilic substitution reaction :
R2Br1Cl2 DMF
→ R_Cl1Br2,
which one of the following undergoes
complete inversion of configuration ?
(1) C6H5CHC6H5Br
(2) C6H5CH2Br
(3) C6H5CH CH3Br
(4) C6H5CCH3C6H5Br
57. In which of the following pairs A is more
stable than B ?
A B
(1)
(2)
(3)
(4) Ph3C
•
, (CH3)
3
C
•
55. °Üæ§Ü çȤÙæ§Ü §üÍÚU §‹ãð´ »ÚU× ·¤ÚU ÕÙæØæ Áæ â·¤Ìæ
ãñ Ñ
(1) C6H5Br1CH25CH2CH22ONa
(2) CH25CH2CH22Br1C6H5ONa
(3) C6H52CH5CH2Br1CH32ONa
(4) CH25CH2Br1C6H52CH22ONa
56. ‹Øêç€ÜØâ SÙðãè ¥ÎÜ ÕÎÜ ¥çÖç·ý¤Øæ Ñ
R2Br1Cl2 DMF
→ R_Cl1Br2,
×ð´ çِ٠ÂÎæÍæðZ âð ·¤æñÙ ÃØßSÍæ ·¤æ â´ÂêU‡æü ÕÎÜ ·¤ÚU
ÜðÌæ ãñ ?
(1) C6H5CHC6H5Br
(2) C6H5CH2Br
(3) C6H5CH CH3Br
(4) C6H5CCH3C6H5Br
57. çِ٠Øé‚×æð´ ×ð´ âð ç·¤â×ð´ A, ¥çÏ·¤ SÍæ§ü ãñ B âð ?
A B
(1)
(2)
(3)
(4) Ph3C
•
, (CH3)
3
C
•

30. English : 30 Set : 01 Hindi : 30 Set : 01
58. Structure of some important polymers are
given. Which one represents Buna-S ?
(1)
(2)
(3)
(4)
59. Which is the major product formed when
acetone is heated with iodine and
potassium hydroxide ?
(1) Iodoacetone
(2) Acetic acid
(3) Iodoform
(4) Acetophenone
60. Which one of the following class of
compounds is obtained by polymerization
of acetylene ?
(1) Poly-yne
(2) Poly-ene
(3) Poly-ester
(4) Poly-amide
58. ·é¤ÀU Âýçâh ÕãéÜ·¤æð´ ·¤è â´ÚU¿Ùæ°´ Ùè¿ð Îè »§ü ãñ §Ù×ð´
âð ·¤æñÙ ÕêÙæ-S ·¤è âê¿·¤ ãñ?
(1)
(2)
(3)
(4)
59. ·¤æñÙ âè ÕǸè ×æ˜ææ ×ð´ ç·ý Øæ È¤Ü ÂýæŒÌ ãæðÌæ ãñ ÁÕ
°ðâèÅUæðÙ ·¤æð ¥æØæðÇUèÙ ¥æñÚU ÂæðÅñUçàæØ× ãæ§ÇþUæ€âæ§ÇU
·ð¤ âæÍ »ÚU× ç·¤Øæ ÁæÌæ ãñ?
(1) ¥æØæðÇUæð°ðâèÅUæðÙ
(2) °âèçÅU·¤ °ðçâÇU
(3) ¥æØæðÇUæð$Ȥæ×ü
(4) °ðâèÅUæð çȤÙæðÙ
60. °çâçÅUÜèÙ ·ð¤ ÕãéÜ·¤è·¤ÚU‡æ âð ·¤æñÙâæ çِ٠Âý·¤æÚU
·¤æ Øæñç»·¤ ÂýæŒÌ ãæðÌæ ãñ?
(1) ÂæòÜè-¥æ§Ù
(2) ÂæòÜè-§üÙ
(3) ÂæòÜè-°ðSÅUÚU
(4) ÂæòÜè-°×æ§ÇU

31. English : 31 Set : 01 Hindi : 31 Set : 01
PART C — MATHEMATICS
61. Let P be the relation defined on the set of
all real numbers such that
P5{(a, b) : sec2 a2tan2 b51}. Then P is :
(1) reflexive and symmetric but not
transitive.
(2) reflexive and transitive but not
symmetric.
(3) symmetric and transitive but not
reflexive.
(4) an equivalence relation.
62. Let w(Im w ¹ 0) be a complex number.
Then the set of all complex numbers z
satisfying the equation w2 wz5k (12z),
for some real number k, is :
(1) {z : ?z?51}
(2) {z : z5 z }
(3) {z : z ¹ 1}
(4) {z : ?z?51, z ¹ 1}
63. If equations ax21bx1c50,
(a, b, c Î R, a ¹ 0) and 2x213x1450 have
a common root, then a : b : c equals :
(1) 1 : 2 : 3
(2) 2 : 3 : 4
(3) 4 : 3 : 2
(4) 3 : 2 : 1
Öæ» C — »ç‡æÌ
61. ×æÙ P âÖè ßæSÌçß·¤ ⴁØæ¥æð´ ÂÚU ÂçÚUÖæçáÌ °·¤
°ðâæ â´Õ´Ï ãñ ç·¤
P5{(a, b) : sec2 a2tan2 b51} ãñ, Ìæð P Ñ
(1) SßÌéËØ ÌÍæ â×ç×Ì ãñ ÂÚU‹Ìé â´·ý¤æ×·¤ Ùãè´
ãñÐ
(2) SßÌéËØ ÌÍæ â´·ý¤æ×·¤ ãñ ÂÚU‹Ìé â×ç×Ì Ùãè´
ãñÐ
(3) â×ç×Ì ÌÍæ â´·ý¤æ×·¤ ãñ ÂÚU‹Ìé SßÌéËØ Ùãè´
ãñÐ
(4) °·¤ ÌéËØÌæ â´Õ´Ï ãñÐ
62. ×æÙæ w(Im w ¹ 0) °·¤ âç×Ÿæ ⴁØæ ãñ, Ìæð âÖè
âç×Ÿæ ⴁØæ¥æð´ z ·¤æ â×é“æØ, Áæð ç·¤âè ßæSÌçß·¤
ⴁØæ k ·ð¤ çÜ°, â×è·¤ÚU‡æ w2 wz5k (12z)
·¤æð â´ÌécÅU ·¤ÚUÌæ ãñ, ãñ Ñ
(1) {z : ?z?51}
(2) {z : z5 z }
(3) {z : z ¹ 1}
(4) {z : ?z?51, z ¹ 1}
63. ØçÎ â×è·¤ÚU‡ææð´ ax21bx1c50,
(a, b, c Î R, a ¹ 0) ÌÍæ 2x213x1450 ·¤æ
°·¤ ×êÜ ©ÖØçÙcÅU ãñ, Ìæð a : b : c ÕÚUæÕÚU ãñ Ñ
(1) 1 : 2 : 3
(2) 2 : 3 : 4
(3) 4 : 3 : 2
(4) 3 : 2 : 1

32. English : 32 Set : 01 Hindi : 32 Set : 01
64. If
1
a
and
1
b
are the roots of the
equation, ax21bx1150 (a ¹ 0, a, b Î R),
then the equation,
x(x1b3)1(a323abx)50 has roots :
(1)
3
2a and
3
2b
(2) a
1
2b and
1
2a b
(3) a b and a b
(4)
3
2
2
a and
3
2
2
b
65. If a, b, c are non - zero real numbers and if
the system of equations
(a21)x5y1z,
(b21)y5z1x,
(c21)z5x1y,
has a non-trivial solution, then
ab1bc1ca equals :
(1) a1b1c
(2) abc
(3) 1
(4) 21
64. ØçÎ
1
a
ÌÍæ
1
b
â×è·¤ÚU‡æ ax21bx1150
(a ¹ 0, a, b Î R) ·ð¤ ×êÜ ãñ, Ìæð â×è·¤ÚU‡æ
x(x1b3)1(a323abx)50 ·ð¤ ×êÜ ã´ñ Ñ
(1)
3
2a ÌÍæ
3
2b
(2) a
1
2b ÌÍæ
1
2a b
(3) a b ÌÍæ a b
(4)
3
2
2
a ÌÍæ
3
2
2
b
65. ØçÎ a, b, c àæê‹ØðÌÚU ßæSÌçß·¤ ⴁØæ°¡ ãñ´ ÌÍæ ØçÎ
â×è·¤ÚU‡æ çÙ·¤æØ
(a21)x5y1z,
(b21)y5z1x,
(c21)z5x1y,
·¤æ °·¤ ¥Ìé‘ÀU ãÜ ãñ, Ìæð ab1bc1ca ÕÚUæÕÚU ãñ Ñ
(1) a1b1c
(2) abc
(3) 1
(4) 21

33. English : 33 Set : 01 Hindi : 33 Set : 01
66. If B is a 333 matrix such that B250, then
det. [(I1B)50250B] is equal to :
(1) 1
(2) 2
(3) 3
(4) 50
67. The number of terms in the expansion of
(11x)101 (11x22x)100 in powers of x is :
(1) 302
(2) 301
(3) 202
(4) 101
68. The sum of the digits in the unit’s place of
all the 4-digit numbers formed by using the
numbers 3, 4, 5 and 6, without repetition,
is :
(1) 432
(2) 108
(3) 36
(4) 18
66. ØçÎ B °·¤ °ðâæ 333 ¥æÃØêã ãñ ç·¤ B250 ãñ, Ìæð
det. [(I1B)50250B] ÕÚUæÕÚU ãñ Ñ
(1) 1
(2) 2
(3) 3
(4) 50
67. (11x)101 (11x22x)100 ·ð¤ x ·¤è ƒææÌæð´ ×ð´ ÂýâæÚU
×ð´ ÂÎæð´ ·¤è ⴁØæ ãñ Ñ
(1) 302
(2) 301
(3) 202
(4) 101
68. ⴁØæ¥æð´ 3, 4, 5 ÌÍæ 6 ·ð¤ ÂýØæð» âð, çÕÙæ ·¤æð§ü ⴁØæ
ÎæðãÚUæ°, ÕÙÙð ßæÜè âÖè ¿æÚU ¥´·¤æð´ ·¤è ⴁØæ¥æð´ ·ð¤
§·¤æ§ü ·ð¤ SÍæÙ ÂÚU ¥æÙð ßæÜð ¥´·¤æð´ ·¤æ Øæð» ãñ Ñ
(1) 432
(2) 108
(3) 36
(4) 18

34. English : 34 Set : 01 Hindi : 34 Set : 01
69. Given an A.P. whose terms are all positive
integers. The sum of its first nine terms is
greater than 200 and less than 220. If the
second term in it is 12, then its 4th term
is :
(1) 8
(2) 16
(3) 20
(4) 24
70. If the sum
2 2 2 2 2 2
3 5 7
1 1 2 1 2 3
.......1 1 1 1
1 1 1
upto
20 terms is equal to
k
21
, then k is equal to :
(1) 120
(2) 180
(3) 240
(4) 60
71. If f(x) is continuous and ( )9 2
2 9f ,5 then
20
1 cos 3
lim
x
x
f
x→
 
  
2
is equal to :
(1) 9/2
(2) 2/9
(3) 0
(4) 8/9
69. Îè »§ü °·¤ â×æ´ÌÚU ŸæðÉ¸è ·ð¤ âÖè ÂÎ ÏÙÂê‡ææZ·¤ ãñ´Ð
§â·ð¤ ÂýÍ× Ùæñ ÂÎæð´ ·¤æ Øæð» 200 âð ¥çÏ·¤ ÌÍæ
220 âð ·¤× ãñÐ ØçÎ §â·¤æ ÎêâÚUæ ÂÎ 12 ãñ, Ìæð
§â·¤æ ¿æñÍæ ÂÎ ãñ Ñ
(1) 8
(2) 16
(3) 20
(4) 24
70. ØçÎ
2 2 2 2 2 2
3 5 7
1 1 2 1 2 3
.......1 1 1 1
1 1 1
·ð¤20
ÂÎæð´ Ì·¤ ·¤æ Øæð» k
21
·ð¤ ÕÚUæÕÚU ãñ, Ìæð k ÕÚUæÕÚU ãñ Ñ
(1) 120
(2) 180
(3) 240
(4) 60
71. ØçÎ f(x) âÌÌ ãñ ÌÍæ ( )9 2
2 9f 5 ãñ, Ìæð
20
1 cos 3
lim
x
x
f
x→
 
  
2
ÕÚUæÕÚU ãñ Ñ
(1) 9/2
(2) 2/9
(3) 0
(4) 8/9

35. English : 35 Set : 01 Hindi : 35 Set : 01
72. If y5enx, then
2 2
2 2
d d
d d
y x
x y
   
   
   
is equal to :
(1) n enx
(2) n e2nx
(3) 1
(4) 2n e2nx
73. If the Rolle’s theorem holds for the
function f(x)52x31ax21bx in the interval
[21, 1] for the point c5
1
2
, then the value
of 2a1b is :
(1) 1
(2) 21
(3) 2
(4) 22
74. If
3 4
( ) 1
5 5
x x
f x
   
      
5 1 2 , x Î R, then the
equation f(x)50 has :
(1) no solution
(2) one solution
(3) two solutions
(4) more than two solutions
72. ØçÎ y5enx ãñ, Ìæð
2 2
2 2
d d
d d
y x
x y
   
   
   
ÕÚUæÕÚU ãñ Ñ
(1) n enx
(2) n e2nx
(3) 1
(4) 2n e2nx
73. ØçΠȤÜÙ f(x)52x31ax21bx ·ð¤¤ çÜ° ¥´ÌÚUæÜ
[21, 1] ×ð´ çÕ´Îé c5
1
2
ÂÚU ÚUæðÜð ·¤æ Âý×ðØ Üæ»ê ãñ,
Ìæð 2a1b ·¤æ ×æÙ ãñ Ñ
(1) 1
(2) 21
(3) 2
(4) 22
74. ØçÎ 3 4
( ) 1
5 5
x x
f x
   
      
5 1 2 , x Î R ãñ, Ìæð
â×è·¤ÚU‡æ f(x)50 ·¤æ/·ð¤ Ñ
(1) ·¤æð§ü ãÜ Ùãè´ ãñÐ
(2) °·¤ ãÜ ãñÐ
(3) Îæð ãÜ ãñ´Ð
(4) Îæð âð ¥çÏ·¤ ãÜ ãñ´Ð

36. English : 36 Set : 01 Hindi : 36 Set : 01
75.
8 8
2 2
sin cos
d
(1 2 sin cos )
x x
x
x x
∫
2
2
is equal to :
(1)
1
2
sin 2x1c
(2)
1
2
2 sin 2x1c
(3)
1
2
2 sin x1c
(4) 2sin2 x1c
76. The integral
1
2
0
2
(1 2 )
d
1 4
ln x
x
x
∫
1
1
, equals :
(1)
4
p
ln 2
(2)
8
p
ln 2
(3)
16
p
ln 2
(4)
32
p
ln 2
77. Let A5{(x, y) : y2 [ 4x, y22x/24}. The
area (in square units) of the region A is :
(1) 8
(2) 9
(3) 10
(4) 11
75.
8 8
2 2
sin cos
d
(1 2 sin cos )
x x
x
x x
∫
2
2
ÕÚUæÕÚU ãñ Ñ
(1)
1
2
sin 2x1c
(2)
1
2
2 sin 2x1c
(3)
1
2
2 sin x1c
(4) 2sin2 x1c
76. â×æ·¤Ü
1
2
0
2
(1 2 )
d
1 4
ln x
x
x
∫
1
1
, ÕÚUæÕÚU ãñ Ñ
(1)
4
p
ln 2
(2)
8
p
ln 2
(3)
16
p
ln 2
(4)
32
p
ln 2
77. ×æÙæ A5{(x, y) : y2 [ 4x, y22x/24} ãñÐ
ÿæð˜æ A ·¤æ ÿæð˜æÈ¤Ü (ß»ü §·¤æ§üØæð´ ×ð´) ãñ Ñ
(1) 8
(2) 9
(3) 10
(4) 11

37. English : 37 Set : 01 Hindi : 37 Set : 01
78. If the differential equation representing the
family of all circles touching x-axis at the
origin is (x22y2)
d
d
y
x
5g(x) y, then g(x)
equals :
(1)
1
2
x
(2) 2x2
(3) 2x
(4)
1
2
x2
79. Let a and b be any two numbers satisfying
2 2
1 1 1
4a b
1 5 . Then, the foot of
perpendicular from the origin on the
variable line, 1
a b
yx
1 5 , lies on :
(1) a hyperbola with each
semi-axis5 2 .
(2) a hyperbola with each semi-axis52.
(3) a circle of radius52
(4) a circle of radius5 2
78. ØçÎ ©Ù âÖè ßëžææ𴠷𤠷é¤Ü, Áæð x-¥ÿæ ·¤æð ×êÜ çÕ´Îé
ÂÚU SÂàæü ·¤ÚUÌð ãñ´, ·¤æ ¥ß·¤Ü â×è·¤ÚU‡æ
(x22y2)
d
d
y
x
5g(x) y, ãñ, Ìæð g(x) ÕÚUæÕÚU ãñ Ñ
(1)
1
2
x
(2) 2x2
(3) 2x
(4)
1
2
x2
79. ×æÙ a ¥æñÚU b, 2 2
1 1 1
4a b
1 5 ·¤æð â´ÌécÅU ·¤ÚUÙð ßæÜè
Îæð ⴁØæ°¡ ãñ´, Ìæð ¿ÚUÚðU¹æ, 1
a b
yx
1 5 ×êÜ çÕ´Îé âð
ÇUæÜð »° Ü´Õ ·¤æ ÂæÎ, çSÍÌ ãñ Ñ
(1) °·¤ ¥çÌÂÚUßÜØ ÂÚU, çÁâ·¤æ ÂýˆØð·¤
¥Ïü ¥ÿæ5 2 ãñÐ
(2) °·¤ ¥çÌÚUÂÚUßÜØ ÂÚU, çÁâ·¤æ ÂýˆØð·¤
¥Ïü ¥ÿæ52 ãñÐ
(3) °·¤ ßëžæ ÂÚU, çÁâ·¤è ç˜æ’Øæ52 ãñÐ
(4) °·¤ ßëžæ ÂÚU, çÁâ·¤è ç˜æ’Øæ5 2 ãñÐ

38. English : 38 Set : 01 Hindi : 38 Set : 01
80. Given three points P, Q, R with P(5, 3) and
R lies on the x-axis. If equation of RQ is
x22y52 and PQ is parallel to the x-axis,
then the centroid of DPQR lies on the
line :
(1) 2x1y2950
(2) x22y1150
(3) 5x22y50
(4) 2x25y50
81. If the point (1, 4) lies inside the circle
x21y226x210y1p50 and the circle
does not touch or intersect the coordinate
axes, then the set of all possible values of p
is the interval :
(1) (0, 25)
(2) (25, 39)
(3) (9, 25)
(4) (25, 29)
82. If OB is the semi-minor axis of an ellipse,
F1 and F2 are its foci and the angle between
F1B and F2B is a right angle, then the
square of the eccentricity of the ellipse is :
(1)
1
2
(2)
1
2
(3)
1
2 2
(4)
1
4
80. ÌèÙ çΰ »° çÕ´Îé¥æð´ P, Q, R ×ð´ P(5, 3) ãñ ÌÍæ R,
x-¥ÿæ ÂÚU çSÍÌ ãñÐ ØçÎ RQ ·¤æ â×è·¤ÚU‡æ
x22y52 ãñ ÌÍæ PQ, x-¥ÿæ ·ð¤ â×æ´ÌÚU ãñ, Ìæð
DPQR ·¤æ ·ð´¤Îý·¤ çÁâ ÚðU¹æ ÂÚU çSÍÌ ãñ, ßã
ãñ Ñ
(1) 2x1y2950
(2) x22y1150
(3) 5x22y50
(4) 2x25y50
81. ØçÎ çÕ´Îé (1, 4) ßëžæ x21y226x210y1p50
·ð¤ ¥‹ÌÑ Öæ» ×ð´ çSÍÌ ãñ ÌÍæ ßëžæ, çÙÎðüàææ´·¤ ¥ÿææð´ ·¤æð
Ù Ìæð SÂàæü ·¤ÚUÌæ ãñ, ¥æñÚU Ù ãè ·¤æÅUÌæ ãññ, Ìæð p ·ð¤
âÖè â´Öß ×æÙæð´ ·¤æ â×é‘¿Ø çِ٠¥Ì´ÚUæÜ ãñ Ñ
(1) (0, 25)
(2) (25, 39)
(3) (9, 25)
(4) (25, 29)
82. ØçÎ OB, °·¤ Îèƒæüßëžæ ·¤æ ¥Ïü ܃æé¥ÿæ ãñ, F1 ÌÍæ
F2 ©â·¤è ÙæçÖØæ¡ ãñ´ ÌÍæ F1B ÌÍæ F2B ·ð¤ Õè¿ ·¤æ
·¤æð‡æ °·¤ â×·¤æð‡æ ãñ, Ìæð Îèƒæüßëžæ ·¤è ©ˆ·ð´¤ÎýÌæ ·¤æ
ß»ü ãñ Ñ
(1)
1
2
(2)
1
2
(3)
1
2 2
(4)
1
4

39. English : 39 Set : 01 Hindi : 39 Set : 01
83. Equation of the plane which passes
through the point of intersection of lines
1 2 3
3 1 2
x y z2 2 2
5 5 and
3 1 2
1 2 3
x y z2 2 2
5 5
and has the largest distance from the origin
is :
(1) 7x12y14z554
(2) 3x14y15z549
(3) 4x13y15z550
(4) 5x14y13z557
84. A line in the 3-dimensional space makes
an angle 0 <
2
 
  
p
u u [ with both the
x and y axes. Then the set of all values of
u is the interval :
(1) 0
4
,
 
  
p
(2)
6 3
,
 
  
p p
(3)
4 2
,
 
  
p p
(4)
3 2
,
 
  
p p
83. ©â â×ÌÜ ·¤æ â×è·¤ÚU‡æ, Áæð ÚðU¹æ¥æð´
1 2 3
3 1 2
x y z2 2 2
5 5 ÌÍæ
3 1 2
1 2 3
x y z2 2 2
5 5
·ð¤ ÂýçÌ‘ÀðUÎÙ çÕ´Îé âð ãæð ·¤ÚU ÁæÌæ ãñ, ÌÍæ ×êÜçÕ´Îé âð
¥çÏ·¤Ì× ÎêÚUè ÂÚU ãñ, ãñ Ñ
(1) 7x12y14z554
(2) 3x14y15z549
(3) 4x13y15z550
(4) 5x14y13z557
84. ç˜æçß×èØ ¥æ·¤æàæ (space) ×ð´ °·¤ ÚðU¹æ x ÌÍæ y,
ÎæðÙæ´ð ¥ÿææð´ ·ð¤ âæÍ ·¤æð‡æ 0 <
2
 
  
p
u u [ ÕÙæÌè ãñ,
Ìæð u ·ð¤ âÖè ×æÙæð´ ·¤æ â×é‘¿Ø çِ٠¥´ÌÚUæÜ ãñ Ñ
(1) 0
4
,
 
  
p
(2)
6 3
,
 
  
p p
(3)
4 2
,
 
  
p p
(4)
3 2
,
 
  
p p

40. English : 40 Set : 01 Hindi : 40 Set : 01
85. If a 2, b 3
→→
? ?5 ? ?5 and 2 a b 5
→→
? 2 ?5 , then
2 a b
→→
? 1 ? equals :
(1) 17
(2) 7
(3) 5
(4) 1
86. In a set of 2n distinct observations, each of
the observation below the median of all the
observations is increased by 5 and each of
the remaining observations is decreased by
3. Then the mean of the new set of
observations :
(1) increases by 1.
(2) decreases by 1.
(3) decreases by 2.
(4) increases by 2.
87. If A and B are two events such that
P(AÈB)5P(AÇB), then the incorrect
statement amongst the following
statements is :
(1) A and B are equally likely
(2) P(AÇB9)50
(3) P(A9ÇB)50
(4) P(A)1P(B)51
85. ØçÎ a 2, b 3
→→
? ?5 ? ?5 ÌÍæ 2 a b 5
→→
? 2 ?5 ãñ, Ìæð
2 a b
→→
? 1 ? ÕÚUæÕÚU ãñ Ñ
(1) 17
(2) 7
(3) 5
(4) 1
86. 2n çßçÖóæ Âýðÿæ‡ææð´ ·ð¤ â×é‘¿Ø ×ð´, ©Ù âÖè Âýðÿæ‡ææð´,
Áæð âÖè Âýðÿæ‡ææð´ ·ð¤ ×æŠØ·¤ âð ·¤× ãñ´, ÂýˆØð·¤ ·¤æð 5 âð
Õɸæ çÎØæ »Øæ ÌÍæ àæðá âÖè Âðýÿæ‡ææð´ ×´ð ÂýˆØð·¤ ·¤æð 3
âð ·¤× ·¤ÚU çÎØæ »Øæ, Ìæð Âýðÿæ‡ææð´ ·ð¤ Ù° â×é‘¿Ø ·¤æ
×æŠØ Ñ
(1) 1 âð Õɸ ÁæÌæ ãñÐ
(2) 1 âð ƒæÅU ÁæÌæ ãñÐ
(3) 2 âð ƒæÅU ÁæÌæ ãñÐ
(4) 2 âð Õɸ ÁæÌæ ãñÐ
87. A ÌÍæB Îæð °ðâè ƒæÅUÙæ°¡ ãñ´ ç·¤ P(AÈB)5P(AÇB)
ãñ, Ìæð çِ٠·¤ÍÙæð´ ×ð´ âð ·¤æñÙ âæ ·¤ÍÙ »ÜÌ ãñ ?
(1) A ÌÍæ B â×â´ÖæçßÌ ã´ñ
(2) P(AÇB9)50
(3) P(A9ÇB)50
(4) P(A)1P(B)51

41. English : 41 Set : 01 Hindi : 41 Set : 01
88. The number of values of a in [0, 2p] for
which 2 sin3 a27 sin2 a17 sin a52, is :
(1) 6
(2) 4
(3) 3
(4) 1
89. If cosec
p q
p q
1
u5
2
(p¹q¹0), then
cot
4 2
 
  
p u
1 is equal to :
(1)
p
q
(2)
q
p
(3) pq
(4) pq
90. The contrapositive of the statement “I go
to school if it does not rain” is :
(1) If it rains, I do not go to school.
(2) If I do not go to school, it rains.
(3) If it rains, I go to school.
(4) If I go to school, it rains.
- o 0 o -
88. [0, 2p] ×ð´ a ·ð¤ ©Ù ×æÙæð´ ·¤è ⴁØæ, çÁÙ·ð¤ çÜ°
2 sin3 a27 sin2 a17 sin a52 ãñ, ãñ Ñ
(1) 6
(2) 4
(3) 3
(4) 1
89. ØçÎ cosec
p q
p q
1
u5
2
(p¹q¹0) ãñ, Ìæð
cot
4 2
 
  
p u
1 ÕÚUæÕÚU ãñ Ñ
(1)
p
q
(2)
q
p
(3) pq
(4) pq
90. ·¤ÍÙ ÒÒ×ñ´ S·ê¤Ü ÁæÌæ ã¡ê ØçÎ ßáæü Ùãè´ ãæðÌèÓÓ ·¤æ
ÂýçÌÏÙæˆ×·¤ (Contrapositive) ·¤ÍÙ ãñ Ñ
(1) ØçÎ ßáæü ãæðÌè ãñ, ×ñ´ S·ê¤Ü Ùãè´ ÁæÌæÐ
(2) ØçÎ ×ñ´ S·ê¤Ü Ùãè´ ÁæÌæ, ßáæü ãæðÌè ãñÐ
(3) ØçÎ ßáæü ãæðÌè ãñ, ×ñ´ S·ê¤Ü ÁæÌæ ã¡êÐ
(4) ØçÎ ×ñ´ S·ê¤Ü ÁæÌæ ã¡ê, ßáæü ãæðÌè ãñÐ
- o 0 o -