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·¤ çßææÙ ÜÕæ§ü L ·ð¤ °·¤ âÚUÜ ÜæðÜ·¤ ·¤æ ÂýØæð» ·¤ÚU »éL¤ßèØ ßÚUæ 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 æǸUè âð ×æÂæ ÁæÌæ ãñ ¥æñÚ ×æÙ 90.0 âð·´¤ÇU ãñÐ ÜÕæ§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¤ çÙÏüæÚUæ ×ð´ æéçÅU ãæð»è Ñ (1)
1.7%
(2)
2.7%
(3)
4.4%
(4)
2.27%
×êÜ çÕÎé 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 ·¤æðæ 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 æÙß5103 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¤ °·¤ Üæ·¤ A ·¤æð °·¤ ÎêâÚðU ÎýÃØ×æÙ 5 kg ·ð¤ °·¤ Üæ·¤ B ·ð¤ ª¤ÂÚU ÚU¹æ ãñ ¥æñÚU Üæ·¤ B °·¤ ç¿·¤Ùè ÿæñçÌÁ ×ðÁ ÂÚU çßææ× ¥ßSÍæ ×ð´ ÚU¹æ ãñÐ ØçÎ Üæ·¤ A ÂÚU ßã ØêÙÌ× ÕÜ, çÁââð ç·¤ ÎæðÙæ´ð Üæ·¤ °·¤ âæÍ »çÌàæèÜ ãæð´, 12 N ãñ ÌÕ Üæ·¤ B ÂÚU Ü»æØæ »Øæ ¥çÏ·¤Ì× ÕÜ, çÁââð ç·¤ ÎæðÙæ´ð Üæ·¤ »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¤ßæüÏÚU ·¤×æÙè mæÚUæ ç¿æ ·ð¤ ¥ÙéâæÚU ÁæðǸUè »Øè ãñ´Ð ¥ËÂÌÚU ÎýÃØ×æÙ ·¤æðæèØ ¥æßëçæ 25 rad/s °ß´ ¥æØæ× 1.6 cm ·¤è âÚUÜ ¥æßÌü »çÌ ·¤ÚU ÚUãæ ãñ ÁÕç·¤ ÕëãæÚU 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¤ çÕÎé¥æð´ A °ß´ B ÂÚU ÚU¹æ »Øæ ãñÐ (ç¿æ Îð¹ð´) Ð ØçÎ ßð çÕÙæ çȤâÜð ¥æÙÌ ÌÜ ÂÚU §â Âý·¤æÚU Üéɸ·¤Ìð ãñ´ ç·¤ ©Ù·ð¤ ßÚUæ °·¤ 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.
Indias 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 Earths orbit is ae51.531011 m, that of Mars orbit a m 52.28310 11 m, taken Keplers laws give the estimate of time for Mangalyan to reach Mars from
ÖæÚUÌ ·¤æ ×´»ÜØæÙ ×´»Ü »ýã ·ð¤ çÜØð âêØü ·ð¤ ¿æÚUæð´ ¥æðÚU SÍæÙæÌÚUæ ·¤ÿæ EOM ×ð´ ÂýÿæðçÂÌ ç·¤Øæ »ØæÐ §âÙð Âëßè ·¤æð E ÂÚU ÀUæðÇ¸æ ¥æñÚU ×´»Ü »ýã âð Øã M ÂÚU ç×ÜÌæ ãñÐ ØçÎ Âëßè ·¤è ¥hü-Îèæü ¥ÿæ ae51.531011 m ãñ ¥æñÚU ×´»Ü »ýã ·¤è ¥hü-Îèæü ¥ÿæ am52.2831011 m ãñ, ÌÕ ·ð¤ÂÜÚU ·ð¤ çÙØ× ·ð¤ ¥ÙéâæÚU Âëßè 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 çßçÖÙ ÂýØæSÍÌæ »éææ¡·¤æð´ ·ð¤ ÂçÚU×ææ ·¤æ âãè ·ý¤× ãñ Ñ
elastic modulii is : (1)
Youngs modulii < shear modulii
(1)
< bulk modulii. (2)
Bulk modulii < shear modulii
(2)
< Youngs modulii. (3)
Shear modulii < Youngs modulii
(3)
< bulk modulii. (4)
Bulk modulii < Youngs modulii
(4)
< shear modulii. 9.
Ø´» ÂýØæSÍÌæ »éææ¡·¤ < ¥ÂM¤Âæ ÂýØæSÍÌæ »éææ¡·¤ < ¥æØÌÙ ÂýØæSÍÌæ »éææ¡·¤. ¥æØÌÙ Âý ØæSÍÌæ »é ææ¡ · ¤ < ¥ÂM¤Âæ ÂýØæSÍÌæ »éææ¡·¤ < Ø´» ÂýØæSÍÌæ »éææ¡·¤. ¥ÂM¤Âæ ÂýØæSÍÌæ »éææ¡·¤ < Ø´» ÂýØæSÍÌæ »éææ¡·¤ < ¥æØÌÙ ÂýØæSÍÌæ »éææ¡·¤. ¥æØÌÙ ÂýØæSÍÌæ »éææ¡·¤ < Ø´» ÂýØæSÍÌæ »éææ¡·¤ < ¥ÂM¤Âæ ÂýØæSÍÌæ »éææ¡·¤.
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·¤ æÅU ÁæÌæ ãñ Ð Øã ×æÙ Üð´ ç·¤ SÅUæð·¤ ·¤æ çÙØ× âãè ãñ ¥æñÚU ßæØé ·¤æ ·¤æÕüÙ ÇUæ§ü¥æòâæ§Ç âð àØæÙÌæ »éææ´·¤ ·¤æ ¥ÙéÂæÌ 1.3 ãñ, ÌÕ ·¤æÕüÙ ÇUæ§ü ¥æòâæ§ÇU ×ð´ §â ÜæðÜ·¤ ·ð¤ ¥æØæ× ·¤æð 10 cm âð 5 cm Ì·¤ æÅUÙð ×ð ´ Ü»æ â×Ø Ü»Ö» 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ßæüÏÚU ÂæÙè ×ð´ ÇéUÕæðØæ ÁæÌæ ãñ ¥æñÚU ÌÕ ÂæÙè ·ð¤ SÌÖ ·¤è ª¡¤¿æ§ü x ãæð ÁæÌè ãñÐ ÁÕ §â çßØæâ ·¤æð °·¤ »ãÚUæ§ü d ßæÜè °·¤ ¹æÙ ×ð´ Üð ÁæØæ ÁæÌæ ãñ, ÌÕ ÂæÙè ·ð¤ SÌÖ ·¤è ª¡¤¿æ§ü y ãñÐ ØçÎ Âëßè ·¤è çæØæ 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
°·¤ ÕÎ Âææ ×ð´ 2 L ¥æØÌÙ ÂæÙè ·¤æð 1 kW ·¤è ·é¤ÇUÜè âð »×ü ç·¤Øæ ÁæÌæ ãñÐ ÁÕ ÂæÙè »×ü ãæð ÚUãæ ãñ, ÌÕ Âææ 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 Âææ ·¤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·¤ÚUæ PV5nRT1aV âð çÎØæ ÁæÌæ ãñ, Áãæ¡ n ×æðÜ ·¤è â´Øæ ãñ ¥æñÚU a °·¤ ÏÙæ×·¤ çSÍÚUæ¡·¤ ãñÐ °·¤ ÕðÜÙ ×ð´ ÚU¹ð »ñ⠷𤠰·¤ ×æðÜ ·¤æ ÂýæÚUçÖ·¤ 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 ·¤×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 â´Øæ 5631023 ×æðÜ21 ÜðÌð ãéØð °·¤ çÙßæüçÌÌ ÕÌüÙ ×ð´ »ñ⠷𤠥æé¥æ´ð ·ð¤ Õè¿ ×æØ 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 ÜÕßÌ÷ 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»ÎñØü ·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 ,
Âëßè ·ð¤ ÂëcÆU âð ÁÚUæ ª¤ÂÚU ßæÌæßÚUæ ×ð´ âæÏæÚUæÌØæ ©ÂçSÍÌ ¥æñ â Ì çßlé Ì ÿæð æ ·¤æ ÂçÚU×ææ 150 N/C ·ð¤ ֻܻ ãñ çÁâ·¤è çÎàææ Âëßè ·ð¤ ·ð¤Îý ·¤è ¥æðÚU ¥ÌÚU×é¹è ãñÐ Øã Âëßè mæÚUæ ßæã·¤ ÂçÚUææ×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 :
ÂýØð·¤ 3 mF ·ð¤ ÌèÙ â´ÏæçÚUæ çÎØð »Øð ãñ´Ð §Ù·¤æ ç·¤âè Öè Âý·¤æÚU ·¤æ â´ØæðÁÙ çÙÙ ×ð´ âð ·¤æñÙ âæ ÂçÚUææ×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 ×éØ âÜæ§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)
àæêØ
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´ ÜÕæ§ü d ·ð¤ Îæð ÌÙé ¿éÕ·¤èØ çmÏéýßæ´ð ·ð¤ ×Ø çÕÎé¥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 × Ø Úð U ¹ æ ÂÚU Âë ßè ·ð ¤ ¿é Õ·¤èØ ÿæð æ ·¤æ ×æ٠ֻܻ 431025 T ãñÐ Âëßè ·¤è çæØæ 6.43106 m ãñÐ ÌÕ Âëßè ·¤æ çmÏýéß ¥ææêæü ֻܻ §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 ØæßÌèü ÏæÚU æ ææð Ì âð Áé Ç ¸ ð æð æè LCR ÂçÚUÂÍ ×ð´ ÂýðÚU·¤ß L â´ÏæçÚUÌ C ¥æñÚU ÂýçÌÚUæðÏ·¤ R ÂÚU ×æÂð »Øð ß»ü - ×æØ-×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 ÂýØæßÌèü ÏæÚUæ oýæðÌ ·¤è ß»ü-×æØ-×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 ¿éÕ·¤èØ SÂðÅþU× ·¤è ÌÚ´U»ÎñØü ÚðUÁ) ·¤æð âê¿è II (§Ù ÌÚ´U»æð´ ·ð¤ çÙ×æüæ ·¤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 øËÎËÕ Ä §¿U¼ËøËÎËÕ Õ §¾ ÇÕ §¿U¼ËøËÎËÕ Õ Ëü±Ì¿U ÅËÖÁ ÁÕþªãU˾ËÕ Í ¦Ëá S±¿U ÇÕ Ì¾¤ÁÕ S±¿U Í Ì± ÇÕ ¾ËÌ» Õ ¿ÕU̬U½ËÕ ÇÌâ½ 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 divers eyes are 15 cm below 3 the surface of water. Then the radius of
°·¤ »æðÌæ¹æðÚU ÂæÙè ·ð¤ ¥ÎÚU âð ÕæãÚU ·¤è ÎéçÙØæ ·¤æð °·¤ ßëæèØ 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 ßëæ ·¤è çæØæ 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 Youngs double slit experiment in three ways as shown. If she observes that y5b9, the wavelength
ÌÚ´U»ÎñØü l ·ð¤ °·¤ßæèü Âý·¤æàæ ·ð¤ ÂýØæð» âð °·¤ ßñææçÙ·¤ 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»ÎñØü 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´ Ùðçæ·¤æ Üðâ ·¤è $Ȥæð·¤â ÜÕæ§Øæ¡ ·ý¤×àæÑ 30 cm °ß´ 3.0 cm ãñÐ ÎêÚUÎàæèü Ùðçæ·¤æ Üðâ âð âéSÂcÅU ÎàæüÙ ·¤è ØêÙÌ× ÎêÚUè ÂÚU °·¤ ¥ØÌ ÎêÚU ·¤è ßSÌé ·¤æ ¥æÖæâè, âèÏæ ÂýçÌçÕÕ ÕÙæÌæ ãñÐ §â çSÍçÌ ×ð´, »ñçÜçÜØÙ ÎêÚUÎàæèü ·¤è ¥æßÏüÙ ÿæ×Ìæ ãæð»è Ñ
(1)
111.2
(2)
211.2
(1)
111.2
(3)
28.8
(2)
211.2
(4)
18.8
(3)
28.8
(4)
18.8
For which of the following particles will it be most difficult to experimentally verify 26. the de-Broglie relationship ? (1)
an electron
(2)
a proton
(3)
an a-particle
(4)
a dust particle
English : 17
Set : 01
çÙÙçÜç¹Ì ·¤ææð ´ ×ð ´ âð 緤⠷¤æ ·ð ¤ çÜØð ÇUè-ÕýæÜè âÕÏ ·¤æ ÂýæØæðç»·¤ âØæÂÙ ¥ØçÏ·¤ ×éçà·¤Ü ãæð»æ? (1) °·¤ §ÜðÅþUæÙ$ (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×ææé ×ð´ §ÜðÅþUæÙ ·¤è ÕÏÙ ª¤Áæü 13.6 eV ãñ, ÌÕ Li11 ·¤è ÂýÍ× ©æðçÁÌ ¥ßSÍæ âð §ÜðÅþUæÙ 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 Âýðáæ °çÅUÙæ ·¤è ª¡¤¿æ§ü 32 m ãñ ¥æñÚU ¥çÖ»ýæãè °çÅUÙæ ·¤è ª¡¤¿æ§ü 50 m ãñÐ ÎëçcÅUÚðU¹èØ (LOS) ×æðÇU ×ð´ â´ÌæðáÂýÎ â´¿ÚUæ ·ð¤ çÜ° ÎæðÙæ´ð °çÅUÙæ ·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 æçÁSÅUÚU ×ð ´ ÌèÙ ¿æÜ·¤ ÌæÚU A, B °ß´ C ãñ´Ð »èÜè ¥´»éçÜØæð´ âð B °ß´ C ·¤æð ÁæðǸÙð ÂÚU, °·¤ ÏæÚUæ×æÂè ·¤æð ÏÙæ×·¤ ¿æÜ·¤ ÌæÚU ·¤æð A âð ÁæðǸÙð ÂÚU ¥æñÚU ÏæÚUæ×æÂè ·¤è «¤ææ×·¤ ¿æÜ·¤ ÌæÚU ·¤æð C âð ÁæðǸÙð ÂÚU °·¤ Âýðÿæ·¤ ¥ØçÏ·¤ çßÿæð ÂæÌæ ãñÐ ÌÕ A, B °ß´ C ·¤æ â´ÎÖü ·ý¤×àæÑ §Ùâð ãñ Ñ (1) ©âÁü·¤, ¥æÏæÚU °ß´ â´»ýæãè (2) ¥æÏæÚU, ©âÁü·¤ °ß´ â´»ýæãè (3) ¥æÏæÚU, â´»ýæãè °ß´ ©âÁü·¤ (4) â´»ýæãè, ©âÁü·¤ °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 çßææÙ °·¤ Ȥܷ¤ ·ð¤çÎýÌ æÙæ·¤æÚU ÁæÜ·¤ ×ð´ A ·ð¤¤ ÂÚU×ææé ·¤æðÙæð´ ·ð¤ çÕÎé¥æð´ ÂÚU ãñ´ ¥æñÚU B ·ð¤ ÂÚU×ææé Ȥܷ¤ ·ð¤Îýæð´ ÂÚU ãñ´Ð ØçÎ B ÂÚU×ææé °·¤ Ȥܷ¤ ·ð¤Îý ÂÚU Ù ãæð Ìæð ¥æØçÙ·¤ Øæñç»·¤ ·¤æ âêæ 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 Waals 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·¤ÚUæ ¥æÎàæü »ñâ â×è·¤ÚUæ ·¤æ
This equation reduces to the perfect gas equation, p 5
°·¤ »ñâ ·ð¤ çÜØð ßæÇUÚU ßæÜ â×è·¤ÚUæ
both temperature and pressure are
M¤Â,
p5
nRT V
ÏæÚUæ ·¤ÚU Üð»æ ÁÕ Ñ
(1)
Ìæ ÂØæüÌ ©¿ ãæð»æ ¥æñÚU ÎæÕ ØêÙ ãæð»æÐ
(2)
Ìæ ÂØæüÌ 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¤ SÅñUÇUÇüU (×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 âæØÂÚU ·ð¤ßÜ 50% HI, H2 ¥æñÚU I2 ×ð´ çßÖæçÁÌ ãæðÌæ ãñÐ âæØ 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× ×æææ ·¤æð 1000 »ýæ× ÁÜ ×ð´ ææðÜÙð ÂÚU ÂýæÌ ãé° çßÜØÙ ·¤æ æÙß 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 °·¤ æÅUæ Âà¿æÌ÷ ÂÎæÍü ·¤è àæðá ÚUãè ×æææ ãæð»è Ñ
(1)
1
4 of the original amount
(1)
ÂýæÚUçÖ·¤ ×æææ ·¤æ
1
(2)
1
8 of the original amount
(2)
ÂýæÚUçÖ·¤ ×æææ ·¤æ
1
(3)
1
16 of the original amount
(3)
ÂýæÚUçÖ·¤ ×æææ ·¤æ
1
(4)
1
32 of the original amount
(4)
ÂýæÚUçÖ·¤ ×æææ ·¤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¤ çÂæÜð ãé° Üßæ ÏæÚU·¤ §ÜñÅþUæðçÜçÅU·¤ âñÜ ×ð´ âð 2.00 æÅðU ·ð¤ çÜØð 10.0 A ·¤è çßléÌ ÏæÚUæ ¿ÜæÙð ÂÚU 0.250 ×æðÜ X ÏæÌé ·¤æ Á×æß ãé¥æÐ çÂæÜð ãé° Üßæ ×ð´ ÏæÌé X ·¤è ¥æâè·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´ §ÜñÅþUæÙ ·¤è ª¤Áæü 213.6 eV ãñÐ Li 21 ·¤è ©æðçÁÌ ¥ßSÍæ ×ð´ §ÜñÅþUæÙ ·¤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×ææé
ÌæÂ, çÁâ ÂÚU ¥æòâèÁÙ ¥æé¥æð´ ·¤è ß»ü ×æØ×êÜ SÂèÇU ·¤æ ×æÙ ßãè ãæðÌæ ãñ Áæð ãèçÜØ× ÂÚU×ææé¥æð´ ·¤æ 300 K ÂÚU ãæðÌæ ãñ, (ÂÚU×ææé ÎýÃØ×æÙ Ñ He54 ×ææ·¤, O516 ×ææ·¤) 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 × ææé ¥ 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´ ¥æòâèÁÙ ·¤è ×æææ 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 âæÎý H2SO4 ·ð¤ âæÍ »ÚU× ·¤ÚUÙð âð ÂýæÌ 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§ÇþUæðÜæðçâçÜçâ·¤ °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×ææê ·ý¤×æ´·¤523) §â ßñÙðçÇUØ× ÜæðÚUæ§ÇU ·¤æ âêæ 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 ææðÜ ·¤è H2S ·ð¤ âæÍ ¥çÖç·ý¤Øæ ãæðÙð ÂÚU çÙÙæð´ ×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 §ÜñÅþUæÙ 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¿éÕ·¤èØ ãæðÌæ ãñÐ §â â´·¤ÚU ·ð¤ ÕÙÙð âð âÕçÏÌ â´·¤ÚUæ 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¤ çÙÙ âðÅUæð´ ×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´ ¥æÕÏæð´ ·¤è â´Øæ °ß´ Âý·¤æÚU çÙÙ ·¤æñÙâè ãñ? (1) °·¤ s ¥æÕÏ ¥æñÚU °·¤ p2¥æÕÏ (2) °·¤ s ¥æÕÏ ¥æñÚU Îæð p2¥æÕÏ (3) Îæð s ¥æÕÏ ¥æñÚU Îæð p2¥æÕÏ (4) Îæð s ¥æÕÏ ¥æñÚU °·¤ p2¥æÕÏ
CaC2
Ûææð´·¤æ Ö^è âð ÂýæÌ 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¤ ¿éÕ·¤èØ »éææð´ ·¤æ ØÍæÍü çßßÚUæ 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¿éÕ·¤èØ ãñ´Ð ÎæðÙæð´ ÂýçÌ ¿éÕ·¤èØ ãñ´Ð [Fe(CN)6]32 ÂýçÌ¿éÕ·¤èØ ¥æñÚU [FeF6]32¥Ùé¿éÕ·¤èØ ãñÐ [Fe (CN)6]32¥Ùé¿éÕ·¤èØ ¥æñÚU [FeF6]32 ÂýçÌ¿éÕ·¤èØ ãñÐ
§Ù ¥çÖç·ý¤Øæ¥æð´ ×ð´ âð ç·¤â ×ð´ ·¤æÕüÙ - ·¤æÕüÙ ¥æÕÏ Ùãè´ ÂýæÌ ãæð»æ?
carbon bond ?
52.
(1)
Reimer-Tieman reaction
(1)
(2)
Friedel Crafts 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-¥æòâè·¤ÚUæ ¥çÖç·ý¤Øæ ×ð´ 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 ×éØ
(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 ÜÕæ§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´ çÙÙ ÂÎæÍæðZ âð ·¤æñÙ ÃØßSÍæ ·¤æ â´ÂêUæü 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.
ØêçÜØâ SÙðãè ¥ÎÜ ÕÎÜ ¥çÖç·ý¤Øæ Ñ
(4)
In which of the following pairs A is more 57.
çÙÙ Øé×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 ×æææ ×ð´ ç·ý Øæ È¤Ü ÂýæÌ ãæðÌæ ãñ ÁÕ °ðâèÅUæðÙ ·¤æð ¥æØæðÇUèÙ ¥æñÚU ÂæðÅñUçàæØ× ãæ§ÇþUæâæ§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·¤ÚUæ âð ·¤æñÙâæ çÙÙ Âý·¤æÚU ·¤æ Øæñç»·¤ ÂýæÌ 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×æ â´Øæ ãñ, Ìæð âÖè âç×æ â´Øæ¥æð´ z ·¤æ â×éæØ, Áæð ç·¤âè ßæSÌçß·¤ â´Øæ k ·ð¤ çÜ°, â×è·¤ÚUæ 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 »çæÌ ×æÙ P âÖè ßæSÌçß·¤ â´Øæ¥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 ÂÚUÌé â´·ý¤æ×·¤ ãñÐ (2) SßÌéËØ ÌÍæ â´·ý¤æ×·¤ ãñ ÂÚUÌé â×ç×Ì ãñÐ (3) â×ç×Ì ÌÍæ â´·ý¤æ×·¤ ãñ ÂÚUÌé SßÌéËØ ãñÐ (4) °·¤ ÌéËØÌæ â´Õ´Ï ãñÐ
a common root, then a : b : c equals :
â×è·¤ÚUææð ´ 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·¤ÚUæ 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 àæêØðÌÚU ßæSÌçß·¤ â´Øæ°¡ ãñ´ ÌÍæ ØçÎ â×è·¤ÚUæ 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 °·¤ ¥ÌéÀU 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 â´Øæ 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 units place of 68.
°ðâæ
B250
ãñ, Ìæð
·ð¤ x ·¤è ææÌæð´ ×ð´ ÂýâæÚU
â´Øæ¥æð´ 3, 4, 5 ÌÍæ 6 ·ð¤ ÂýØæð» âð, çÕÙæ ·¤æð§ü â´Øæ ÎæðãÚUæ°, ÕÙÙð ßæÜè âÖè ¿æÚU ¥´·¤æð´ ·¤è â´Øæ¥æ𴠷𤠧·¤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 æðÉ¸è ·ð¤ âÖè ÂÎ ÏÙÂêææZ·¤ 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 Rolles 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·¤ÚUæ 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 ÿæðæ A ·¤æ ÿæðæÈ¤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 ßëææ𴠷𤠷é¤Ü, Áæð x-¥ÿæ ·¤æð ×êÜ çÕ´Îé ÂÚU SÂàæü ·¤ÚUÌð ãñ ´ , ·¤æ ¥ß·¤Ü â×è·¤ÚUæ (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 â´Øæ°¡ 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 Øð · ¤ ¥Ïü ¥ÿæ5 2 ãñÐ °·¤ ¥çÌÚU  ÚU ß ÜØ ÂÚU , çÁâ·¤æ Âý Øð · ¤ ¥Ïü ¥ÿæ52 ãñÐ °·¤ ßëæ ÂÚU, çÁâ·¤è çæØæ52 ãñÐ °·¤ ßëæ ÂÚU, çÁâ·¤è çæØæ5 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) ßëæ x21y226x210y1p50 ·ð¤ ¥ÌÑ Öæ» ×ð´ çSÍÌ ãñ ÌÍæ ßëæ, çÙÎðüàææ´·¤ ¥ÿææð´ ·¤æð Ù Ìæð SÂàæü ·¤ÚUÌæ ãñ, ¥æñÚU Ù ãè ·¤æÅUÌæ ãññ, Ìæð p ·ð¤ âÖè â´Öß ×æÙæð´ ·¤æ â×é¿Ø çÙÙ ¥Ì´ÚUæÜ ãñ Ñ (1) (2) (3) (4)
(0, 25) (25, 39) (9, 25) (25, 29)
ØçÎ OB, °·¤ Îèæüßëæ ·¤æ ¥Ïü Üæé¥ÿæ ãñ, F1 ÌÍæ F2 ©â·¤è ÙæçÖØæ¡ ãñ´ ÌÍæ F1B ÌÍæ F2B ·ð¤ Õè¿ ·¤æ ·¤æðæ °·¤ â×·¤æðæ ãñ, Ìæð Îèæüßëæ ·¤è ©·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·¤ÚUæ, 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¤ ÂýçÌÀðUÎÙ 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.
çæçß×èØ ¥æ·¤æàæ
p an angle u 0 < u [ with both the 2
ÎæðÙæ´ð ¥ÿææð´ ·ð¤ âæÍ ·¤æðæ u 0 < u [
x and y axes. Then the set of all values of
Ìæð u ·ð¤ âÖè ×æÙæð´ ·¤æ â×é¿Ø çÙÙ ¥´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 Âýðÿæææð´ ·ð¤ â×é¿Ø ×ð´, ©Ù âÖè Âýðÿæææð´, Áæð âÖè Âýðÿæææð´ ·ð¤ ×æØ·¤ âð ·¤× ãñ´, ÂýØð·¤ ·¤æð 5 âð Õɸæ çÎØæ »Øæ ÌÍæ àæðá âÖè Âðýÿæææð´ ×´ð ÂýØð·¤ ·¤æð 3 âð ·¤× ·¤ÚU çÎØæ »Øæ, Ìæð Âýðÿæææð´ ·ð¤ Ù° â×é¿Ø ·¤æ ×æØ 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 æÅU ÁæÌæ ãñÐ 2 âð æÅU ÁæÌæ ãñÐ 2 âð Õɸ ÁæÌæ ãñÐ
A ÌÍæ B Îæð °ðâè æÅUÙæ°¡ ãñ´ ç·¤ P(AÈB)5P(AÇB)
ãñ, Ìæð çÙÙ ·¤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 â´Øæ, 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 ÂýçÌÏÙæ×·¤ (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
