PART A — PHYSICS
1.
An experiment is performed to obtain the 1.
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 :
2.
(1)
1.7%
(2)
2.7%
(3)
4.4%
(4)
2.27%
2.
The position of a projectile launched from
the
→
origin
∧
at
∧
r 5(40 i 1 50 j ) m
t50
is
given
at t52s.
by
If the
projectile was launched at an angle u from
the horizontal, then u is (take g510 ms22).
Öæ» A — ÖæñçÌ·¤ çߙææÙ
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 ×𴠘æéçÅU ãæð»è Ñ
(1)
1.7%
(2)
2.7%
(3)
4.4%
(4)
2.27%
×êÜ çՋÎé âð
t50 ÂÚU
→
(1)
tan21 2 3
tan21 2 3
(2)
tan21 3 2
(2)
tan21 3 2
(3)
tan21 7 4
(3)
tan21 7 4
(4)
tan21 4 5
(4)
tan21 4 5
Set : 01
ÂýÿæðçÂÌ °·¤ Âýÿæð ·¤è çSÍçÌ
∧
ÂÚU r 5(40 i 1 50 j ) m âð Îè ÁæÌè ãñÐ
ØçÎ Âýÿæð ÿæñçÌÁ âð u ·¤æð‡æ ÂÚU ÂýÿæðçÂÌ ç·¤Øæ »Øæ
Íæ, ÌÕ u ãñ (g510 ms22 Üð´).
t52s
(1)
English : 1
∧
Hindi : 1
Set : 01
3.
Water is flowing at a speed of 1.5 ms21 3.
through
a
horizontal
cross-sectional area
1022
m2
tube
of
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).
4.
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 ÂǸ ð » æÐ ( ÂæÙè ·¤æ
ƒæوß5103 kgm23).
(1)
15 N
(1)
15 N
(2)
22.5 N
(2)
22.5 N
(3)
33.7 N
(3)
33.7 N
(4)
45 N
(4)
45 N
A block A of mass 4 kg is placed on 4.
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
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 ß㠋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
together will be :
(1)
30 N
(1)
30 N
(2)
25 N
(2)
25 N
(3)
27 N
(3)
27 N
(4)
48 N
(4)
48 N
English : 2
Set : 01
Hindi : 2
Set : 01
5.
Two bodies of masses 1 kg and 4 kg are 5.
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
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´).
exerted by the system on the floor is
(take g510 ms22).
(1)
20 N
(2)
10 N
(3)
60 N
(4)
40 N
English : 3
Set : 01
(1)
20 N
(2)
10 N
(3)
60 N
(4)
40 N
Hindi : 3
Set : 01
6.
A cylinder of mass Mc and sphere of mass 6.
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
sin uc
the ratio
is :
sin us
8
7
(1)
15
14
(2)
(3)
(4)
8
7
15
14
English : 4
Set : 01
ÎýÃØ×æÙ Mc ·ð¤ °·¤ ÕðÜÙ °ß´ ÎýÃØ×æÙ Ms ·ð¤ °·¤
»æðÜð ·¤æð ·ý¤×àæÑ Îæð ¥æÙÌ ÌÜæð´ ·ð¤ çՋÎé¥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
(1)
8
7
(2)
15
14
(3)
8
7
(4)
15
14
Hindi : 4
sin uc
sin us
ãñ :
Set : 01
7.
India’s Mangalyan was sent to the Mars 7.
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 a m 52.28310 11 m,
taken Kepler’s laws give the estimate of
time for Mangalyan to reach Mars from
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
Earth to be close to :
(1)
500 days
(1)
500
(2)
320 days
(2)
320
(3)
260 days
(3)
260
(4)
220 days
(4)
220
English : 5
Set : 01
Hindi : 5
çÎÙ
çÎÙ
çÎÙ
çÎÙ
Set : 01
8.
In materials like aluminium and copper, 8.
the correct order of magnitude of various
°ËØéç×çÙØ× °ß´ Ìæ¡Õð Áñâð ÂÎæÍæðü´ ·ð¤ çÜØð çßç֋Ù
ÂýˆØæSÍÌæ »é‡ææ¡·¤æð´ ·ð¤ ÂçÚU×æ‡æ ·¤æ âãè ·ý¤× ãñ Ñ
elastic modulii is :
(1)
Young’s modulii < shear modulii
(1)
< bulk modulii.
(2)
Bulk modulii < shear modulii
(2)
< Young’s modulii.
(3)
Shear modulii < Young’s modulii
(3)
< bulk modulii.
(4)
Bulk modulii < Young’s modulii
(4)
< shear modulii.
9.
Ø´» ÂýˆØæSÍÌæ »é‡ææ¡·¤ < ¥ÂM¤Â‡æ ÂýˆØæSÍÌæ
»é‡ææ¡·¤ < ¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤.
¥æØÌÙ Âý ˆ ØæSÍÌæ »é ‡ ææ¡ · ¤ < ¥ÂM¤Â‡æ
ÂýˆØæSÍÌæ »é‡ææ¡·¤ < Ø´» ÂýˆØæSÍÌæ »é‡ææ¡·¤.
¥ÂM¤Â‡æ ÂýˆØæSÍÌæ »é‡ææ¡·¤ < Ø´» ÂýˆØæSÍÌæ
»é‡ææ¡·¤ < ¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤.
¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤ < Ø´» ÂýˆØæSÍÌæ
»é‡ææ¡·¤ < ¥ÂM¤Â‡æ ÂýˆØæSÍÌæ »é‡ææ¡·¤.
which amplitude of this pendulum will
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
ֻܻ ãæð » æ
reduce from 10 cm to 5 cm in
(ln 551.601, ln 250.693).
The amplitude of a simple pendulum, 9.
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
carbondioxide will be close to (ln 551.601,
ln 250.693).
(1)
231 s
(1)
231 s
(2)
208 s
(2)
208 s
(3)
161 s
(3)
161 s
(4)
142 s
(4)
142 s
English : 6
Set : 01
Hindi : 6
Set : 01
10.
A capillary tube is immersed vertically in 10.
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
x
ratio
is :
y
d

(1)  12 

R
11.
°·¤ ·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 çߋØæâ ·¤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 ãñ Ñ
y
(1)
d

 12 
R
(2)
2d 

 12 
R
(2)
2d 

 12 
R
(3)
 R 2d 
 R 1d 
(3)
 R 2d 
 R 1d 
(4)
 R 1d 
 R 2d 
(4)
 R 1d 
 R 2d 
Water of volume 2 L in a closed container 11.
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
°·¤ ՋΠÂæ˜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)
4.2 kJ/kg and that of the container is
negligible).
(1)
8 min 20 s
(1)
(2)
6 min 2 s
(2)
(3)
7 min
(3)
(4)
14 min
(4)
English : 7
Set : 01
ç×ÙÅU 20 âð·´¤ÇU
6 ç×ÙÅU 2 âð·´¤ÇUU
7 ç×ÙÅU
14 ç×ÙÅU
8
Hindi : 7
Set : 01
12.
The equation of state for a gas is given by 12.
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
°·¤ »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
the gas when its temperature doubles
isobarically will be :
13.
(1)
Po To R
Po 2a
(1)
Po To R
Po 2a
(2)
Po To R
Po 1a
(2)
Po To R
Po 1a
(3)
Po To R ln 2
(3)
(4)
P o To R
(4)
Po To R ln 2
Po To R
evacuated vessel will be of the order of :
¥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
(1)
0.2 mm
(2)
0.2 mm
(2)
0.2 mm
(3)
0.2 cm
(3)
0.2 cm
(4)
0.2 nm
(4)
0.2 nm
Modern vacuum pumps can evacuate a 13.
vessel down to a pressure of 4.0310215 atm.
at room temperature (300 K). Taking
R58.3 JK21 mole21, 1 atm5105 Pa and
N Avogadro 56310 23 mole 21 , the mean
distance between molecules of gas in an
English : 8
Set : 01
Hindi : 8
Set : 01
14.
A particle which is simultaneously 14.
subjected to two perpendicular simple
harmonic motions represented by ;
x5a1 cos vt and y5a2 cos 2vt traces a
curve given by :
°·¤ ·¤‡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)
(1)
(2)
(2)
(3)
(3)
(4)
(4)
English : 9
Set : 01
Hindi : 9
Set : 01
15.
A transverse wave is represented by :
y5
15.
10
2p
2p 
sin 
x
t2
 T
p
l 
°·¤ ¥ÙéÂýSÍ ÌÚ´U» §ââð ÎàææüØè ÁæÌè ãñ Ñ
y5
10
2p
2p 
sin 
x
t2
 T
p
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?
For what value of the wavelength the
wave velocity is twice the maximum
particle velocity ?
16.
(1)
40 cm
(1)
40 cm
(2)
20 cm
(2)
20 cm
(3)
10 cm
(3)
10 cm
(4)
60 cm
(4)
60 cm
The magnitude of the average electric field 16.
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
e o 58.85310 212
C 2 /N-m 2 ,
Âë‰ßè ·ð¤ ÂëcÆU âð ÁÚUæ ª¤ÂÚU ßæÌæßÚU‡æ ×ð´ âæÏæÚU‡æÌØæ
©ÂçSÍÌ ¥æñ â Ì çßlé Ì 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 e o 58.85310 212 C 2 /N-m 2 ,
RE56.373106 m]
RE56.373106 m]
(1)
1670 kC
(1)
1670 kC
(2)
2670 kC
(2)
2670 kC
(3)
2680 kC
(3)
2680 kC
(4)
1680 kC
(4)
1680 kC
English : 10
Set : 01
Hindi : 10
Set : 01
17.
provide the resultant capacitance of :
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
(1)
1 mF
(2)
2 mF
(2)
2 mF
(3)
4.5 mF
(3)
4.5 mF
(4)
6 mF
(4)
6 mF
Three capacitances, each of 3 mF, are 17.
provided. These cannot be combined to
18.
A d.c. main supply of e.m.f. 220 V is 18.
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
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
through the battery to charge it is :
(1)
7V
(1)
7V
(2)
9V
(2)
9V
(3)
11 V
(3)
11 V
(4)
Zero
(4)
àæê‹Ø
English : 11
Set : 01
Hindi : 11
Set : 01
19.
The mid points of two small magnetic 19.
dipoles of length d in end-on positions, are
separated by a distance x, (x >> d). The
¥ÿæèØ çSÍçÌ ×ð´ ܐÕæ§ü d ·ð¤ Îæð ÌÙé ¿éÕ·¤èØ çmÏéýßæ´ð
·ð¤ ×ŠØ çՋÎé¥æð´ ·¤æð x ÎêÚUè ÂÚU ÚU¹æ »Øæ ãñ (x >>d)Ð
ÎæðÙæð´ ·ð¤ Õè¿ ÕÜ x2n ·¤ð¤ â×æÙéÂæÌè ãñ, Áãæ¡ n ãñ :
force between them is proportional to
x2n where n is :
20.
(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
(2)
1020
(3)
1016
(4)
1010 A m2
English : 12
A
m2
A
m2
A
m2
Set : 01
(1)
1
(2)
2
(3)
3
(4)
4
Öê × ŠØ Úð U ¹ æ 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
Hindi : 12
Set : 01
21.
VL : VC : VR51 : 2 : 3. If the rms voltage
of the AC source is 100 V, then VR is close
°·¤ Âý ˆ ØæßÌèü ÏæÚU æ Ÿææð Ì âð Áé Ç ¸ ð Ÿæð ‡ æè LCR
ÂçÚUÂÍ ×ð´ ÂýðÚU·¤ˆß L â´ÏæçÚUÌ C ¥æñÚU ÂýçÌÚUæðÏ·¤ R ÂÚU
×æÂð »Øð ß»ü - ×æŠØ-×ê Ü ßæð Ë ÅUÌæ°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
(1)
50 V
(2)
70 V
(2)
70 V
(3)
90 V
(3)
90 V
(4)
100 V
(4)
100 V
When the rms voltages VL, VC and VR are 21.
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
to :
English : 13
Set : 01
Hindi : 13
Set : 01
22.
Match
List I (Wavelength range of 22.
electromagnetic spectrum) with List II.
(Method of production of these waves)
and select the correct option from the
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
options given below the lists.
List I
ÇÏ¤Í I
List II
Vibration of atoms
700 nm to
(i)
(a)
and molecules.
1 mm
1 nm to
(b)
400 nm
Inner shell electrons
in atoms moving from
(ii)
one energy level to a
lower level.
(c) < 10 23 nm (iii)
1 mm to
(d)
0.1 m
Radioactive decay of
the nucleus.
(a)
700 nm ÇÕ
(b)
1 nm ÇÕ
1 mm
400 nm
(i)
(ii)
(c) < 1023 nm (iii)
(d)
(iv) Magnetron valve.
1 mm ÇÕ
0.1 m
ÇÏ¤Í II
ŠøËΊËՙ •Ä™ §¿U¼ËøËΊËՙ œÕ‰
œ‰ƒ§¾ ÇÕ
§¿U¼ËøËΊËՙ œÕ‰ ŠËü±Ì¿Uœ‰ ÅËÖÁ
ŒÁÕþªãU˾Ëՙ œ‰Í •œ‰ ‰¦Ëá S±¿U
ÇÕ Ì¾¤ÁÕ S±¿U œ‰Í ̱ ÇÕ
¾ËÌ»œ‰ œÕ‰ ¿ÕU̬U½ËÕ Ç̜≽
ä˽ ÇÕ
(iv) ¼Öó¾ÕªUã ˾
†
ÄË°Ä ÇÕ
(1)
(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
(1)
(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
(2)
(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(2)
(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(3)
(a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)
(3)
(a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)
(4)
(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(4)
(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
English : 14
Set : 01
Hindi : 14
Set : 01
23.
A diver looking up through the water sees 23.
the outside world contained in a circular
horizon. The refractive index of water is
4
, and the diver’s eyes are 15 cm below
3
the surface of water. Then the radius of
°·¤ »æðÌæ¹æðÚU ÂæÙè ·ð¤ ¥‹ÎÚU âð ÕæãÚU ·¤è ÎéçÙØæ ·¤æð
°·¤ ßëžæèØ ÿæñçÌÁ ×ð´ çÙçãÌ Îð¹Ìæ ãñÐ ÂæÙè ·¤æ
¥ÂßÌüÙæ¡·¤ 4 ãñ ¥æñÚU »æðÌæ¹æðÚU ·¤è ¥æ¡¹ ÂæÙè ·ð¤
3
ÂëcÆU âð 15 cm Ùè¿ð ãñ´Ð ÌÕ ßëžæ ·¤è ç˜æ’Øæ ãñ Ñ
the circle is :
(1)
15333 5 cm
(1)
15333 5 cm
(2)
1533 7 cm
(2)
1533 7 cm
(3)
153 7
cm
3
(3)
153 7
cm
3
(4)
153 3
cm
7
(4)
153 3
cm
7
English : 15
Set : 01
Hindi : 15
Set : 01
24.
Using monochromatic light of wavelength 24.
l, an experimentalist sets up the Young’s
double slit experiment in three ways as
shown.
If she observes that y5b9, the wavelength
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
of light used is :
English : 16
Set : 01
Hindi : 16
Set : 01
25.
(1)
520 nm
(1)
520 nm
(2)
540 nm
(2)
540 nm
(3)
560 nm
(3)
560 nm
(4)
580 nm
(4)
580 nm
The focal lengths of objective lens and eye
lens of a Gallelian Telescope are 25.
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 :
26.
°·¤ »ñçÜçÜØÙ ÎêÚUÎàæèü ·ð¤ ¥çÖÎëàØ·¤ °ß´ Ùðç˜æ·¤æ
Üð‹â ·¤è $Ȥæð·¤â ܐÕæ§Øæ¡ ·ý¤×àæÑ 30 cm °ß´
3.0 cm ãñÐ ÎêÚUÎàæèü Ùðç˜æ·¤æ Üð‹â âð âéSÂcÅU ÎàæüÙ
·¤è ‹ØêÙÌ× ÎêÚUè ÂÚU °·¤ ¥ˆØ‹Ì ÎêÚU ·¤è ßSÌé ·¤æ
¥æÖæâè, âèÏæ ÂýçÌçÕÕ ÕÙæÌæ ãñÐ §â çSÍçÌ ×ð´,
»ñçÜçÜØÙ ÎêÚUÎàæèü ·¤è ¥æßÏüÙ ÿæ×Ìæ ãæð»è Ñ
(1)
111.2
(2)
211.2
(1)
111.2
(3)
28.8
(2)
211.2
(4)
18.8
(3)
28.8
(4)
18.8
For which of the following particles will it
be most difficult to experimentally verify 26.
the de-Broglie relationship ?
(1)
an electron
(2)
a proton
(3)
an a-particle
(4)
a dust particle
English : 17
Set : 01
çِÙçÜç¹Ì ·¤‡ææð ´ ×ð ´ âð 緤⠷¤‡æ ·ð ¤ çÜØð
ÇUè-Õýæ‚Üè âÕ‹Ï ·¤æ ÂýæØæðç»·¤ âˆØæÂÙ ¥ˆØçÏ·¤
×éçà·¤Ü ãæð»æ?
(1) °·¤ §Üð€ÅþUæÙ$
(2) °·¤ ÂýæðÅUæòÙ
(3) °·¤ a-·¤‡æ
(4) °·¤ ÏêÜ ·¤æ ·¤‡æ
Hindi : 17
Set : 01
27.
28.
29.
If the binding energy of the electron in a 27.
hydrogen atom is 13.6 eV, the energy
required to remove the electron from the
first excited state of Li11 is :
ØçÎ ãæ§ÇþUæðÁÙ ÂÚU×æ‡æé ×ð´ §Üð€ÅþUæÙ ·¤è ՋÏÙ 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
(1)
122.4 eV
(2)
30.6 eV
(2)
30.6 eV
(3)
13.6 eV
(4)
3.4 eV
(3)
13.6 eV
(4)
3.4 eV
Identify the gate and match A, B, Y in
28.
bracket to check.
»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)
(1)
AND (A51, B51, Y51)
(3)
NOT (A51, B51, Y51)
(2)
OR (A51, B51, Y50)
(4)
XOR (A50, B50, Y50)
(3)
NOT (A51, B51, Y51)
(4)
XOR (A50, B50, Y50)
A transmitting antenna at the top of a
tower has a height 32 m and the height of
29.
the receiving antenna is 50 m. What is the
maximum distance between them for
satisfactory communication in line of sight
(LOS) mode ?
°·¤ ×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
(1)
55.4 km
(2)
45.5 km
(2)
45.5 km
(3)
54.5 km
(3)
54.5 km
(4)
455 km
(4)
455 km
English : 18
Set : 01
Hindi : 18
Set : 01
30.
An n-p-n transistor has three leads 30.
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.
English : 19
Set : 01
°·¤
Åþ U æç‹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
n-p-n
Hindi : 19
Set : 01
PART B — CHEMISTRY
31.
In a face centered cubic lattice atoms A 31.
are at the corner points and atoms B at
the face centered points. If atom B is
missing from one of the face centered
Öæ» B — ÚUâæØÙ çߙææÙ
°·¤ Ȥܷ¤ ·ð¤ç‹ÎýÌ ƒæÙæ·¤æÚU ÁæÜ·¤ ×ð´ A ·ð¤¤ ÂÚU×æ‡æé
·¤æðÙæð´ ·ð¤ çՋÎé¥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
points, the formula of the ionic compound
is :
AB2
(1)
AB 2
(2)
(2)
A 5B2
A 5B 2
(3)
(3)
A 2B3
A 2B 3
(4)
(4)
A 2B5
A 2B 5
32.
32.
(1)
Van der Waal’s equation for a gas is stated
as,
p5
2
nRT
 n
2a   .
 V
V 2 nb
(1)
nRT
when ,
V
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)
2
nRT
 n
p5
2a   .
 V
V 2 nb
ãæðÌæ ãñÐ Øã â×è·¤ÚU‡æ ¥æÎàæü »ñâ â×è·¤ÚU‡æ ·¤æ
This equation reduces to the perfect gas
equation, p 5
°·¤ »ñâ ·ð¤ çÜØð ßæ‹ÇUÚU ßæÜ â×è·¤ÚU‡æ
both temperature and pressure are
M¤Â,
p5
nRT
V
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´»ðÐ
very low.
English : 20
Set : 01
Hindi : 20
Set : 01
33.
The
standard
electrode
potentials 33.
(E ) of four metals A, B, C and D are
o
1
M /M
¿æÚU ÏæÌé¥æð´
A, B, C
§Üñ € Åþ U æð Ç U
çßÖß
¥æñÚU
·ð¤ SÅñU‹ÇUÇüU (×æÙ·¤)
D
(E )
o
1
M /M
·ý × æÙé â æÚU
21.2 V, 0.6 V, 0.85 V ¥æñÚU 20.76 V ãñ´Ð
21.2 V , 0.6 V, 0.85 V and 20.76 V,
Üæ»ê ·¤ÚUÙð ÂÚU ÏæÌé Á×Ùð ·¤æ ·ý¤× ãæð»æ Ñ
respectively. The sequence of deposition
çßÖß
of metals on applying potential is :
34.
(1)
A, C, B, D
(1)
A, C, B, D
(2)
B, D, C, A
(2)
B, D, C, A
(3)
C, B, D, A
(3)
C, B, D, A
(4)
D, A, B, C
(4)
D, A, B, C
At a certain temperature, only 50% HI is 34.
dissociated into H2 and I2 at equilibrium.
The equilibrium constant is :
35.
°·¤ 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
(1)
1.0
(2)
3.0
(2)
3.0
(3)
0.5
(3)
0.5
(4)
0.25
(4)
0.25
molarity of the solution is :
°·¤ Øæñç»·¤ (¥‡æéÖæÚU 60) ·¤è 120 »ýæ× ×æ˜ææ ·¤æð
1000 »ýæ× ÁÜ ×𴠃ææðÜÙð ÂÚU ÂýæŒÌ ãé° çßÜØÙ ·¤æ
ƒæÙˆß 1.12 »ýæ× ÂýçÌ ç×çÜ çÜÅUÚU ãñÐ çßÜØÙ ·¤è
×æðÜñçÚUÅUè ãæð»è Ñ
(1)
1.00 M
(1)
1.00 M
(2)
2.00 M
(2)
2.00 M
(3)
2.50 M
(3)
2.50 M
(4)
4.00 M
(4)
4.00 M
Dissolving 120 g of a compound of 35.
(mol. wt. 60) in 1000 g of water gave a
solution of density 1.12 g/mL.
English : 21
The
Set : 01
Hindi : 21
Set : 01
36.
The half-life period of a first order reaction 36.
is 15 minutes. The amount of substance
left after one hour will be :
37.
°·¤ 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)
1
4 of the original amount
(1)
ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ
1
(2)
1
8 of the original amount
(2)
ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ
1
(3)
1
16 of the original amount
(3)
ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ
1
(4)
1
32 of the original amount
(4)
ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ
1
A current of 10.0 A flows for 2.00 h 37.
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
4
Öæ»
8
Öæ»
16
Öæ»
32
Öæ»
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)
the molten salt is : (F596,500 C)
(1)
11
(1)
11
(2)
21
(2)
21
(3)
31
(3)
31
(4)
41
(4)
41
English : 22
Set : 01
Hindi : 22
Set : 01
38.
of electron in the excited state of Li21 is :
·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
(1)
227.2 eV
(2)
30.6 eV
(2)
30.6 eV
(3)
230.6 eV
(3)
230.6 eV
(4)
27.2 eV
(4)
27.2 eV
The energy of an electron in first Bohr orbit 38.
of H - atom is 213.6 eV. The energy value
39.
The temperature at which oxygen 39.
molecules have the same root mean square
speed as helium atoms have at 300 K is :
(Atomic masses : He54 u, O516 u)
40.
H-ÂÚU×æ‡æé
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
(1)
300 K
(2)
600 K
(2)
600 K
(3)
1200 K
(3)
1200 K
(4)
2400 K
(4)
2400 K
The standard enthalpy of formation of 40.
NH3 is 246.0 kJ/mol. If the enthalpy of
formation of H 2 from its atoms is
2436 kJ/mol and that of N 2 is
2712 kJ/mol, the average bond enthalpy
ÕÙÙð ·¤è ×æÙ·¤ ª¤Áæü 246.0 kJ/×æðÜ ãñÐ
ØçÎ ¥ÂÙð ÂÚU × æ‡æé ¥ æð ´ âð H 2 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
NH3
of N2H bond in NH3 is :
(1)
21102 kJ/mol
(1)
21102 kJ/×æðÜ
(2)
2964 kJ/mol
(2)
2964 kJ/×æðÜ
(3)
1352 kJ/mol
(3)
1352 kJ/×æðÜ
(4)
11056 kJ/mol
(4)
11056 kJ/×æðÜ
English : 23
Set : 01
Hindi : 23
Set : 01
41.
The amount of oxygen in 3.6 moles of water 41.
3.6 ×æðÜ
ÁÜ ×ð´ ¥æò€âèÁÙ ·¤è ×æ˜ææ ãæðÌè ãñ Ñ
is :
42.
(1)
115.2 g
(1)
(2)
57.6 g
(2)
(3)
28.8 g
(3)
(4)
18.4 g
(4)
The gas evolved on heating CaF2 and SiO2 42.
with concentrated H2SO4, on hydrolysis
gives a white gelatinous precipitate. The
»ýæ×
57.6 »ýæ×
28.8 »ýæ×
18.4 »ýæ×
115.2
¥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
CaF2
precipitate is :
43.
(1)
hydrofluosilicic acid
(1)
(2)
silica gel
(2)
(3)
silicic acid
(3)
(4)
calciumfluorosilicate
(4)
ãæ§ÇþUæðÜæðçâçÜçâ·¤ °ðçâÇU
çâçÜ·¤æ ÁñÜ
çâçÜçâ·¤ °ðçâÇ
·ñ¤çËàæØ׍ÜæðÚUæðçâçÜ·ð¤ÅU
(at. no. of V523)
ßñÙðçÇUØ× ·¤æ °·¤ €ÜæðÚUæð Øæñç»·¤ 1.73 BM ·¤æ ·ð¤ßÜ
çSÂÙ ×ñ ‚ Ùð ç ÅU·¤ ×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
(1)
VCl2
(2)
VCl4
(2)
VCl4
(3)
VCl3
(3)
VCl3
(4)
VCl5
(4)
VCl5
Chloro compound of Vanadium has only 43.
spin magnetic moment of 1.73 BM. This
Vanadium chloride has the formula :
English : 24
Set : 01
Hindi : 24
Set : 01
44.
An octahedral complex of Co 31 is 44.
diamagnetic. The hybridisation involved
in the formation of the complex is :
45.
(1)
sp3d2
(1)
sp3d2
(2)
dsp2
(2)
dsp2
(3)
d2sp3
(3)
d2sp3
(4)
dsp3d
(4)
dsp3d
Which of the following is not formed when 45.
H 2S
reacts
with
solution ?
acidic
K 2 Cr 2 O 7
¥ÜèØ K2Cr2O7 ƒææðÜ ·¤è H2S ·ð¤ âæÍ ¥çÖç·ý¤Øæ
ãæðÙð ÂÚU çِÙæð´ ×ð´ âð ·¤æñÙ Ùãè´ ÕÙÌæ?
(1)
CrSO 4
(1)
CrSO 4
(2)
(2)
Cr2(SO4)
Cr2(SO4)
(3)
(3)
K2SO 4
K2SO 4
(4)
S
(4)
S
3
3
Which of the following has unpaired
§Ù ×ð´ âð ç·¤â ×ð´ ¥Øéç‚×Ì §Üñ€ÅþUæÙ ãæðÌæ ãñ Øæ ãæðÌð
ãñ´ ?
electron(s) ?
(1)
N2
(2)
O2
2
(3)
N 221
(4)
O 222
46.
46.
·¤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
Co31
(1)
N2
(2)
O2
2
(3)
N 221
(4)
O 222
English : 25
Set : 01
Hindi : 25
Set : 01
47.
In the following sets of reactants which 47.
two sets best exhibit the amphoteric
character of Al2O3 . xH2O ?
2
Set 1 : Al2O3 . xH2O (s) and OH (aq)
Set 2 : Al2O3 . xH2O (s) and H2O (l)
1
Set 3 : Al2O3 . xH2O (s) and H (aq)
Set 4 : Al2O3 . xH2O (s) and NH3 (aq)
(1) 1 and 2
48.
49.
(2)
1 and 3
(3)
2 and 4
(4)
3 and 4
The number and type of bonds in C 222 ion 48.
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
The form of iron obtained from blast 49.
ç·ý¤Øæ ·¤æÚU·¤æð´ ·ð¤ çِ٠âðÅUæð´ ×ð´ âð ç·¤â Îæð ×ð´
Al2O3 . xH2O ·¤æ ©ÖØ Ï×èü ÃØßãæÚU Îð¹æ ÁæÌæ
ãñ?
2
Set 1 : Al2O3 . xH2O (s) ¥æñÚU OH (ÁÜèØ)
Set 2 : Al2O3 . xH2O (s) ¥æñÚU H2O (Îýß)
1
Set 3 : Al2O3 . xH2O (s) ¥æñÚU H (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
·ð C 222 ¥æØÙ ×ð´ ¥æՋÏæð´ ·¤è ⴁØæ °ß´
Âý·¤æÚU çِ٠·¤æñÙâè ãñ?
(1) °·¤ s ¥æÕ‹Ï ¥æñÚU °·¤ p2¥æՋÏ
(2) °·¤ s ¥æÕ‹Ï ¥æñÚU Îæð p2¥æՋÏ
(3) Îæð s ¥æÕ‹Ï ¥æñÚU Îæð p2¥æՋÏ
(4) Îæð s ¥æÕ‹Ï ¥æñÚU °·¤ p2¥æՋÏ
CaC2
Ûææð´·¤æ Ö^è âð ÂýæŒÌ ãé° Üæðãð ·¤æ M¤Â ·¤ãÜæÌæ ãñ Ñ
furnace is :
(1)
Steel
(1)
(2)
Cast Iron
(2)
(3)
Pig Iron
(3)
(4)
Wrought Iron
(4)
English : 26
Set : 01
§SÂæÌ (Steel)
ÉUÜßæ¡ Üæðãæ (Cast Iron)
·¤‘¿æ Üæðãæ (Pig Iron)
çÂÅUßæ´ Üæðãæ (Wrought Iron)
Hindi : 26
Set : 01
50.
The correct statement about the magnetic 50.
properties of [Fe(CN)6]32 and [FeF6]32
¥æñÚU [FeF6]32 ·ð¤ ¿éÕ·¤èØ »é‡ææð´
·¤æ ØÍæÍü çßßÚU‡æ ãñ Ñ (Z526).
[Fe(CN)6]32
is : (Z526).
(1)
both are paramagnetic.
(1)
(2)
both are diamagnetic.
(2)
(3)
[Fe(CN) 6 ] 32
(3)
is
diamagnetic,
[FeF6]32 is paramagnetic.
(4)
[Fe(CN) 6 ] 32 is
paramagnetic,
(4)
[FeF6]32 is diamagnetic.
51.
Which one of the following reactions will 51.
not result in the formation of carbon-
ÎæðÙæ´ð ¥Ùé¿éÕ·¤èØ ãñ´Ð
ÎæðÙæð´ ÂýçÌ ¿éÕ·¤èØ ãñ´Ð
[Fe(CN)6]32 ÂýçÌ¿éÕ·¤èØ ¥æñÚU
[FeF6]32¥Ùé¿éÕ·¤èØ ãñÐ
[Fe (CN)6]32¥Ùé¿éÕ·¤èØ ¥æñÚU [FeF6]32
ÂýçÌ¿éÕ·¤èØ ãñÐ
§Ù ¥çÖç·ý¤Øæ¥æð´ ×ð´ âð ç·¤â ×ð´ ·¤æÕüÙ - ·¤æÕüÙ
¥æÕ‹Ï Ùãè´ ÂýæŒÌ ãæð»æ?
carbon bond ?
52.
(1)
Reimer-Tieman reaction
(1)
(2)
Friedel Craft’s acylation
(2)
(3)
Wurtz reaction
(3)
(4)
Cannizzaro reaction
(4)
ÚUæð×ÚU - ÅUè×Ù ¥çÖç·ý¤ØæÐ
Èý¤èÇUÜ ·ý¤æȤÅU °ðâèÜðàæÙÐ
ßéÅüU$Á ¥çÖç·ý¤ØæÐ
·ñ¤Ùè$ÁñÚUæð ¥çÖç·ý¤ØæÐ
of propene with diborane, H 2 O 2 and
NaOH, the organic compound formed is :
ÂýæðÂèÙ ·ð¤ ÇUæ§ÕæðÚðUÙ, H2O2 ¥æñÚU NaOH ·ð¤ âæÍ
ãæ§ÇþUæðÕæðÚðUàæÙ-¥æò€âè·¤ÚU‡æ ¥çÖç·ý¤Øæ ×ð́ ÕÙæ ·¤æÕüçÙ·¤
Øæñç»·¤ ãñ Ñ
(1)
CH3CH2OH
(1)
CH3CH2OH
(2)
CH3CHOHCH3
(2)
CH3CHOHCH3
(3)
CH3CH2CH2OH
(3)
CH3CH2CH2OH
(4)
(CH3) COH
(4)
(CH3) COH
In the hydroboration - oxidation reaction 52.
English : 27
3
Set : 01
Hindi : 27
3
Set : 01
53.
The major product of the reaction
53.
¥çÖç·ý¤Øæ
NaNO /H SO
NaNO /H SO
2
2
4

→
2
2
4

→
ç·ý¤Øæ È¤Ü ãñ Ñ
is :
(1)
(1)
(2)
(2)
(3)
(3)
(4)
54.
·¤æ ×éØ
(4)
For the compounds
CH3Cl, CH3Br, CH3I and CH3F,
54.
the correct order of increasing C-halogen
bond length is :
(3)
CH3F < CH3Cl < CH3Br < CH3I
CH3F < CH3Br < CH3Cl < CH3I
CH3F < CH3I < CH3Br < CH3Cl
(4)
CH3Cl < CH3Br < CH3F < CH3I
(1)
(2)
English : 28
Set : 01
Øæñç»·¤æð´
¥æñÚU CH3F
×ð´ ·¤æÕüÙ-ãñÜæðÁÙ Õæ¡ÇU ·¤è ÕɸÌè ܐÕæ§ü ·¤æ ÆUè·¤
·ý¤× ãñ Ñ
CH3Cl,CH3Br,CH3I
(1)
(3)
CH3F < CH3Cl < CH3Br < CH3I
CH3F < CH3Br < CH3Cl < CH3I
CH3F < CH3I < CH3Br < CH3Cl
(4)
CH3Cl < CH3Br < CH3F < CH3I
(2)
Hindi : 28
Set : 01
55.
56.
heating :
°Üæ§Ü çȤÙæ§Ü §üÍÚU §‹ãð´ »ÚU× ·¤ÚU ÕÙæØæ Áæ â·¤Ìæ
ãñ Ñ
(1)
C6H5Br1CH25CH2CH22ONa
(1)
C6H5Br1CH25CH2CH22ONa
(2)
CH25CH2CH22Br1C6H5ONa
(2)
CH25CH2CH22Br1C6H5ONa
(3)
C6H52CH5CH2Br1CH32ONa
(3)
C6H52CH5CH2Br1CH32ONa
(4)
CH25CH2Br1C6H52CH22ONa
(4)
CH25CH2Br1C6H52CH22ONa
Allyl phenyl ether can be prepared by 55.
In a nucleophilic substitution reaction :
DMF
56.
DMF
R2Br1Cl2 → R_Cl1Br2,
R2Br1Cl2 → R_Cl1Br2,
which one of the following undergoes
×ð´ çِ٠ÂÎæÍæðZ âð ·¤æñÙ ÃØßSÍæ ·¤æ â´ÂêU‡æü ÕÎÜ ·¤ÚU
ÜðÌæ ãñ ?
complete inversion of configuration ?
(1)
C6H5CHC6H5Br
(1)
C6H5CHC6H5Br
(2)
C6H5CH2Br
(2)
C6H5CH2Br
(3)
C6H5CH CH3Br
C6H5CCH3C6H5Br
(3)
C6H5CH CH3Br
C6H5CCH3C6H5Br
(4)
57.
‹Øêç€ÜØâ SÙðãè ¥ÎÜ ÕÎÜ ¥çÖç·ý¤Øæ Ñ
(4)
In which of the following pairs A is more 57.
çِ٠Øé‚×æð´ ×ð´ âð ç·¤â×ð´ A, ¥çÏ·¤ SÍæ§ü ãñ B âð ?
stable than B ?
A
A
B
(1)
(1)
(2)
(2)
(3)
(3)
(4)
•
•
Ph3C , (CH3) C
3
English : 29
(4)
Set : 01
B
•
•
Ph3C , (CH3) C
3
Hindi : 29
Set : 01
58.
59.
given. Which one represents Buna-S ?
·é¤ÀU Âýçâh ÕãéÜ·¤æð´ ·¤è â´ÚU¿Ùæ°´ Ùè¿ð Îè »§ü ãñ §Ù×ð´
âð ·¤æñÙ ÕêÙæ-S ·¤è âê¿·¤ ãñ?
(1)
(1)
(2)
(2)
(3)
(3)
(4)
(4)
Which is the major product formed when 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
Structure of some important polymers are 58.
acetone is heated with iodine and
potassium hydroxide ?
60.
(1)
Iodoacetone
(2)
Acetic acid
(3)
Iodoform
(4)
Acetophenone
Which one of the following class of 60.
compounds is obtained by polymerization
°çâçÅUÜèÙ ·ð¤ ÕãéÜ·¤è·¤ÚU‡æ âð ·¤æñÙâæ çِ٠Âý·¤æÚU
·¤æ Øæñç»·¤ ÂýæŒÌ ãæðÌæ ãñ?
of acetylene ?
(1)
Poly-yne
(1)
(2)
Poly-ene
(2)
(3)
Poly-ester
(3)
(4)
Poly-amide
(4)
English : 30
Set : 01
ÂæòÜè-¥æ§Ù
ÂæòÜè-§üÙ
ÂæòÜè-°ðSÅUÚU
ÂæòÜè-°×æ§ÇU
Hindi : 30
Set : 01
PART C — MATHEMATICS
61.
Let P be the relation defined on the set of 61.
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)
62.
an equivalence relation.
°·¤
Ùãè´
Ùãè´
Ùãè´
for some real number k, is :
×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 w z5k (12z)
·¤æð â´ÌécÅU ·¤ÚUÌæ ãñ, ãñ Ñ
(1)
{z : ?z?51}
(1)
{z : ?z?51}
(2)
{z : z5 z }
(2)
{z : z5 z }
(3)
{z : z ¹ 1}
(3)
{z : z ¹ 1}
(4)
{z : ?z?51, z ¹ 1}
(4)
{z : ?z?51, z ¹ 1}
If
equations
Let w(Im w ¹ 0) be a complex number. 62.
Then the set of all complex numbers z
satisfying the equation w2 w z5k (12z),
63.
Öæ» C — »ç‡æÌ
×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×·¤
ãñÐ
(2) SßÌéËØ ÌÍæ â´·ý¤æ×·¤ ãñ ÂÚU‹Ìé â×ç×Ì
ãñÐ
(3) â×ç×Ì ÌÍæ â´·ý¤æ×·¤ ãñ ÂÚU‹Ìé SßÌéËØ
ãñÐ
(4) °·¤ ÌéËØÌæ â´Õ´Ï ãñÐ
a common root, then a : b : c equals :
â×è·¤ÚU‡ææð ´
ax 2 1bx1c50,
(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
(1)
1:2:3
(2)
2:3:4
(2)
2:3:4
(3)
4:3:2
(3)
4:3:2
(4)
3:2:1
(4)
3:2:1
ax 2 1bx1c50, 63.
(a, b, c Î R, a ¹ 0) and 2x213x1450 have
English : 31
Set : 01
ØçÎ
Hindi : 31
Set : 01
64.
ØçÎ
then
x(x1b3)1(a323abx)50
the
x(x1b3)1(a323abx)50
a 2 and b 2
(2)
a b 2 and a 2 b
(4)
equation,
1
1
a b and a b
223
a
·ð¤ ×êÜ ã´ñ Ñ
has roots :
3
3
(1)
(3)
65.
1
1
ÌÍæ b â×è·¤ÚU‡æ ax21bx1150
a
(a ¹ 0, a, b Î R) ·ð ¤ ×ê Ü ãñ , Ìæð â×è·¤ÚU ‡ æ
1
1
and
are the roots of the 64.
a
b
equation, ax21bx1150 (a ¹ 0, a, b Î R),
If
223
and b
3
ÌÍæ b
(1)
a 2
(2)
ab 2
(3)
ab
(4)
1
223
a
3
2
1
ÌÍæ
a 2 b
ÌÍæ a b
ÌÍæ
223
b
the system of equations
ØçÎ a, b, c àæê‹ØðÌÚU ßæSÌçß·¤ ⴁØæ°¡ ãñ´ ÌÍæ ØçÎ
â×è·¤ÚU‡æ çÙ·¤æØ
(a21)x5y1z,
(a21)x5y1z,
(b21)y5z1x,
(b21)y5z1x,
(c21)z5x1y,
(c21)z5x1y,
If a, b, c are non - zero real numbers and if 65.
has
a
non-trivial
solution,
then
·¤æ °·¤ ¥Ìé‘ÀU ãÜ ãñ, Ìæð ab1bc1ca ÕÚUæÕÚU ãñ Ñ
ab1bc1ca equals :
(1)
a1b1c
(1)
a1b1c
(2)
abc
(2)
abc
(3)
1
(3)
1
(4)
21
(4)
21
English : 32
Set : 01
Hindi : 32
Set : 01
66.
If B is a 333 matrix such that B250, then 66.
det. [(I1B)50250B] is equal to :
67.
B °·¤
¥æÃØêã ãñ ç·¤
det. [(I1B)50250B] ÕÚUæÕÚU ãñ Ñ
(1)
1
(1)
1
(2)
2
(2)
2
(3)
3
(3)
3
(4)
50
(4)
50
The number of terms in the expansion of 67.
(11x)101
68.
ØçÎ
(11x22x)100
in powers of x is :
×ð´ ÂÎæð´ ·¤è ⴁØæ ãñ Ñ
302
(1)
302
(2)
301
(2)
301
(3)
202
(3)
202
(4)
101
(4)
101
all the 4-digit numbers formed by using the
numbers 3, 4, 5 and 6, without repetition,
333
(11x)101 (11x22x)100
(1)
The sum of the digits in the unit’s place of 68.
°ðâæ
B250
ãñ, Ìæð
·ð¤ x ·¤è ƒææÌæð´ ×ð´ ÂýâæÚU
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
is :
(1)
432
(1)
432
(2)
108
(2)
108
(3)
36
(3)
36
(4)
18
(4)
18
English : 33
Set : 01
Hindi : 33
Set : 01
69.
Given an A.P. whose terms are all positive 69.
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
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
is :
70.
(1)
8
(1)
8
(2)
16
(2)
16
(3)
20
(3)
20
(4)
24
(4)
24
If the sum
70.
3
5
7
1 2
1 2
1.......1 u p t o
2
1
1 12
1 1 2 2 1 32
3
5
7
1 2
1 2
1.......1
2
1
1 12
1 1 2 2 1 32
2
20 terms is equal to
71.
ØçÎ
2
k
, then k is equal to :
21
ÂÎæð´ Ì·¤ ·¤æ Øæð»
(1)
120
(1)
120
(2)
180
(2)
180
(3)
240
(3)
240
(4)
60
(4)
60
( )
k
21
·ð¤ ÕÚUæÕÚU ãñ, Ìæð k ÕÚUæÕÚU ãñ Ñ
If f(x) is continuous and f 9 2 5 2 9 , then 71.
ØçÎ f(x) âÌÌ ãñ ÌÍæ
 12 cos 3x 
lim f 
 is equal to :
x→0 
x2
 12 cos 3x 
lim f 

x→0 
x2
(1)
9/2
(1)
9/2
(2)
2/9
(2)
2/9
(3)
0
(3)
0
(4)
8/9
(4)
8/9
English : 34
Set : 01
Hindi : 34
·ð ¤ 20
( )
f 9 2 52 9
ãñ, Ìæð
ÕÚUæÕÚU ãñ Ñ
Set : 01
72.
73.
If
y5enx,
 d2 y   d2 x 
then  2   2  is equal to : 72.
 dx   dy 
 d2 y   d2 x 
 2   2
 dx   dy 
Ìæð
(1)
n enx
(1)
n enx
(2)
n e2nx
(2)
n e2nx
(3)
1
(3)
1
(4)
2n e2nx
(4)
2n e2nx
If the Rolle’s theorem holds for the 73.
function f(x)52x31ax21bx in the interval
1
[21, 1] for the point c5 , then the value
2
of 2a1b is :
74.
ØçÎ
y5enx ãñ,
ØçΠȤÜÙ f(x)52x31ax21bx ·ð¤¤ çÜ° ¥´ÌÚUæÜ
1
[21, 1] ×ð´
çÕ´Îé c5 ÂÚU ÚUæðÜð ·¤æ Âý×ðØ Üæ»ê ãñ,
2
Ìæð 2a1b ·¤æ ×æÙ ãñ Ñ
(1)
1
(1)
1
(2)
21
(2)
21
(3)
2
(3)
2
(4)
22
(4)
22
3 x
4 x
If f (x )5  1  2 1 , x Î R, then the 74.
 5
 5
ØçÎ f (x )5 3 
equation f(x)50 has :
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
(1)
no solution
(2)
one solution
(3)
two solutions
(4)
more than two solutions
English : 35
Set : 01
ÕÚUæÕÚU ãñ Ñ
5
Hindi : 35
x
x
 4
1  2 1 , x Î R ãñ,
 5
Ìæð
Set : 01
75.
76.
77.
∫
sin 8 x 2 cos8 x
(12 2 sin 2 x cos 2 x )
(1)
1
sin 2x1c
2
(2)
2
(3)
2
(4)
2sin2 x1c
dx is equal to :
75.
∫
sin 8 x 2 cos8 x
(12 2 sin 2 x cos 2 x )
(1)
1
sin 2x1c
2
1
sin 2x1c
2
(2)
2
1
sin 2x1c
2
1
sin x1c
2
(3)
2
1
sin x1c
2
(4)
2sin2 x1c
The integral
1
2
∫0
l n (11 2 x )
11 4 x
2
d x , equals :
76.
1
2
â×æ·¤Ü ∫
0
l n (11 2 x )
11 4 x 2
(1)
p
ln 2
4
(1)
p
ln 2
4
(2)
p
ln 2
8
(2)
p
ln 2
8
(3)
p
ln 2
16
(3)
p
ln 2
16
(4)
p
ln 2
32
(4)
p
ln 2
32
dx
ÕÚUæÕÚU ãñ Ñ
d x , ÕÚUæÕÚU
ãñ Ñ
area (in square units) of the region A is :
×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
(1)
8
(2)
9
(2)
9
(3)
10
(3)
10
(4)
11
(4)
11
Let A5{(x, y) : y2 [ 4x, y22x/24}. The 77.
English : 36
Set : 01
Hindi : 36
Set : 01
78.
If the differential equation representing the 78.
family of all circles touching x-axis at the
origin is (x 22y 2)
dy
5g(x) y, then g(x)
dx
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)
dy
5g(x) y, ãñ,
dx
Ìæð
g(x)
ÕÚUæÕÚU ãñ Ñ
equals :
79.
(1)
1
x
2
(1)
1
x
2
(2)
2x 2
(2)
2x 2
(3)
2x
(3)
2x
(4)
1 2
x
2
(4)
1 2
x
2
Let a and b be any two numbers satisfying
1
1
1
1 2 5 . Then, the foot of
4
a
b
perpendicular from the origin on the
2
variable line,
(1)
hyperbola
semi-axis5 2 .
(2)
a hyperbola with each semi-axis52.
(3)
a circle of radius52
(4)
a circle of radius5 2
English : 37
with
×æÙ a ¥æñÚU b,
Îæð ⴁØæ°¡ ãñ´,
1
1
1
1 2 5 ·¤æð â´ÌécÅU ·¤ÚUÙð ßæÜè
4
a
b
x y
Ìæð ¿ÚUÚðU¹æ, 1 51 ×êÜ çÕ´Îé âð
a b
2
ÇUæÜð »° Ü´Õ ·¤æ ÂæÎ, çSÍÌ ãñ Ñ
x y
1 51 , lies on :
a b
a
79.
each
(1)
(2)
(3)
(4)
Set : 01
°·¤ ¥çÌÂÚU ß ÜØ ÂÚU , çÁâ·¤æ Âý ˆ Øð · ¤
¥Ïü ¥ÿæ5 2 ãñÐ
°·¤ ¥çÌÚU  ÚU ß ÜØ ÂÚU , çÁâ·¤æ Âý ˆ Øð · ¤
¥Ïü ¥ÿæ52 ãñÐ
°·¤ ßëžæ ÂÚU, çÁâ·¤è ç˜æ’Øæ52 ãñÐ
°·¤ ßëžæ ÂÚU, çÁâ·¤è ç˜æ’Øæ5 2 ãñÐ
Hindi : 37
Set : 01
80.
81.
82.
Given three points P, Q, R with P(5, 3) and 80.
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
If the point (1, 4) lies inside the circle
x 2 1y 2 26x210y1p50 and the circle 81.
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)
If OB is the semi-minor axis of an ellipse,
82.
F1 and F2 are its foci and the angle between
F 1 B and F 2B is a right angle, then the
square of the eccentricity of the ellipse is :
(1)
(2)
(3)
(4)
1
2
(1)
(2)
(3)
(4)
2x1y2950
x22y1150
5x22y50
2x25y50
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)
(2)
(3)
(4)
(0, 25)
(25, 39)
(9, 25)
(25, 29)
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 2
(3)
1
4
English : 38
ÌèÙ çΰ »° çÕ´Îé¥æð´ P, Q, R ×ð´ P(5, 3) ãñ ÌÍæ R,
x-¥ÿæ ÂÚU çSÍÌ ãñ Ð 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
(4)
Set : 01
Hindi : 38
1
2
1
2
1
2 2
1
4
Set : 01
83.
Equation of the plane which passes 83.
©â â×ÌÜ ·¤æ â×è·¤ÚU‡æ, Áæð ÚðU¹æ¥æð´
through the point of intersection of lines
x 21 y 2 2 z2 3
5
5
3
1
2
x 21 y 2 2 z2 3
5
5
and
3
1
2
ÌÍæ
x 2 3 y 21 z2 2
5
5
1
2
3
x 2 3 y 21 z2 2
5
5
1
2
3
·ð¤ Âýç̑ÀðUÎÙ çÕ´Îé âð ãæð ·¤ÚU ÁæÌæ ãñ, ÌÍæ ×êÜçÕ´Îé âð
¥çÏ·¤Ì× ÎêÚUè ÂÚU ãñ, ãñ Ñ
and has the largest distance from the origin
is :
84.
(1)
7x12y14z554
(1)
7x12y14z554
(2)
3x14y15z549
(2)
3x14y15z549
(3)
4x13y15z550
(3)
4x13y15z550
(4)
5x14y13z557
(4)
5x14y13z557
A line in the 3-dimensional space makes 84.
ç˜æçß×èØ ¥æ·¤æàæ
p
an angle u  0 < u [  with both the

2
ÎæðÙæ´ð ¥ÿææð´ ·ð¤ âæÍ ·¤æð‡æ u  0 < u [
x and y axes. Then the set of all values of
Ìæð u ·ð¤ âÖè ×æÙæð´ ·¤æ â×é‘¿Ø çِ٠¥´ÌÚUæÜ ãñ Ñ
u is the interval :

(1)
 p
 0 , 
4
(1)
 p
 0 , 
4
(2)
p p
 6 , 3 
(2)
p p
 6 , 3 
(3)
p p
 4 , 2 
(3)
p p
 4 , 2 
(4)
 p p
 , 
3 2
(4)
 p p
 , 
3 2
English : 39
Set : 01
(space)
Hindi : 39
×ð´ °·¤ ÚðU¹æ
p

2
x
ÌÍæ y,
ÕÙæÌè ãñ,
Set : 01
85.
→
86.
→
→
→
→
If ? a ?5 2, ? b ?5 3 and ?2 a 2 b ?5 5 , then 85.
→
ØçÎ
→
→
? a ?5 2, ? b ?5 3
→
→
?2 a 1 b ? equals :
?2 a 1 b ?
(1)
17
(1)
17
(2)
7
(2)
7
(3)
5
(3)
5
(4)
1
(4)
1
In a set of 2n distinct observations, each of 86.
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
ÌÍæ
→
→
?2 a 2 b ?5 5
ãñ, Ìæð
ÕÚUæÕÚU ãñ Ñ
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
2n
observations :
87.
(1)
increases by 1.
(1)
(2)
decreases by 1.
(2)
(3)
decreases by 2.
(3)
(4)
increases by 2.
(4)
If A and B are two events such that 87.
P(AÈB)5P(AÇB), then the incorrect
statement
amongst
the
1 âð
Õɸ ÁæÌæ ãñÐ
1 âð ƒæÅU ÁæÌæ ãñÐ
2 âð ƒæÅU ÁæÌæ ãñÐ
2 âð Õɸ ÁæÌæ ãñÐ
A ÌÍæ B Îæð °ðâè ƒæÅUÙæ°¡ ãñ´ ç·¤ P(AÈB)5P(AÇB)
ãñ, Ìæð çِ٠·¤ÍÙæð´ ×ð´ âð ·¤æñÙ âæ ·¤ÍÙ »ÜÌ ãñ ?
following
statements is :
(1)
A ÌÍæ B â×â´ÖæçßÌ
(1)
A and B are equally likely
(2)
P(AÇB9)50
(2)
P(AÇB9)50
(3)
P(A9ÇB)50
(3)
P(A9ÇB)50
(4)
P(A)1P(B)51
(4)
P(A)1P(B)51
English : 40
Set : 01
Hindi : 40
ã´ñ
Set : 01
88.
The number of values of a in [0, 2p] for 88.
which 2 sin3 a27 sin2 a17 sin a52, is :
89.
©Ù ×æÙæð´ ·¤è ⴁØæ, çÁÙ·ð¤ çÜ°
2 sin3 a27 sin2 a17 sin a52 ãñ, ãñ Ñ
(1)
6
(1)
6
(2)
4
(2)
4
(3)
3
(3)
3
(4)
1
(4)
1
If
cosec u5
ØçÎ
cosec u5
p1q
p2q
(p¹q¹0),
then 89.
 p u
cot  1  is equal to :
 4 2
 p u
cot  1 
 4 2
(1)
p
q
(1)
p
q
(2)
q
p
(2)
q
p
(3)
pq
(3)
pq
(4)
90.
[0, 2p] ×ð´ a ·ð¤
pq
(4)
The contrapositive of the statement “I go 90.
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.
(p¹q¹0)
ãñ ,
Ìæð
ÕÚUæÕÚU ãñ Ñ
pq
·¤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
-o0oEnglish : 41
p1q
p2q
-o0oSet : 01
Hindi : 41
Set : 01