JEE Main 2014 Question Paper

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

(1) 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

English : 1 Set : 01 Hindi : 1 Set : 01

3. Water is flowing at a speed of 1.5 ms21 3. 1022 m2 ·ð¤ ¥ÙéÂýSÍ ·¤æÅU ßæÜè ÿæñçÌÁ ÙÜè âð
through a horizontal tube of 1.5 ms21 ·¤è »çÌ âð ÂæÙè ÂýßæçãÌ ãæð ÚUãæ ãñ ¥æñÚU
cross-sectional area 1022 m2 and you are ¥æ ¥ÂÙè ãÍðÜè âð Õãæß ·¤æð ÚUæð·¤Ùð ·¤æ ÂýØæâ ·¤ÚU
trying to stop the flow by your palm. ÚUãð ãñ´Ð Øã ×æÙÌð ãéØð ç·¤ ÂæÙè ãÍðÜè âð ÅU·¤ÚUæÌð ãè
Assuming that the water stops L¤·¤ ÁæÌæ ãñ, ¥æ·¤æð ¥ÂÙè ãÍðÜè âð ·¤× âð ·¤×
immediately after hitting the palm, the §ÌÙæ ÕÜ Ü»æÙæ ÂǸ ð » æÐ ( ÂæÙè ·¤æ
minimum force that you must exert should ƒæوß5103 kgm23).
be (density of water5103 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

4. A block A of mass 4 kg is placed on 4. ÎýÃØ×æÙ 4 kg ·ð¤ °·¤ ŽÜæ·¤ A ·¤æð °·¤ ÎêâÚðU ÎýÃØ×æÙ
another block B of mass 5 kg, and the block 5 kg ·ð¤ °·¤ ŽÜæ·¤ B ·ð¤ ª¤ÂÚU ÚU¹æ ãñ ¥æñÚU ŽÜæ·¤ B
B rests on a smooth horizontal table. If °·¤ ç¿·¤Ùè ÿæñçÌÁ ×ðÁ ÂÚU çߟææ× ¥ßSÍæ ×ð´ ÚU¹æ
the minimum force that can be applied on ãñÐ ØçÎ ŽÜæ·¤ A ÂÚU ß㠋ØêÙÌ× ÕÜ, çÁââð ç·¤
A so that both the blocks move together is ÎæðÙæ´ð ŽÜæ·¤ °·¤ âæÍ »çÌàæèÜ ãæð´, 12 N ãñ ÌÕ
12 N, the maximum force that can be ŽÜæ·¤ B ÂÚU Ü»æØæ »Øæ ¥çÏ·¤Ì× ÕÜ, çÁââð ç·¤
applied on B for the blocks to move 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. ÎýÃØ×æÙ 1 kg °ß´ 4 kg ·¤è Îæð ßSÌé°ð´ °·¤ ª¤ŠßæüÏÚU
connected to a vertical spring, as shown ·¤×æÙè mæÚUæ ç¿˜æ ·ð¤ ¥ÙéâæÚU ÁæðǸUè »Øè ãñ´Ð ¥ËÂÌÚU
in the figure. The smaller mass executes ÎýÃØ×æÙ ·¤æð‡æèØ ¥æßëçžæ 25 rad/s °ß´ ¥æØæ×
simple harmonic motion of angular 1.6 cm ·¤è âÚUÜ ¥æßÌü »çÌ ·¤ÚU ÚUãæ ãñ ÁÕç·¤
frequency 25 rad/s, and amplitude 1.6 cm ÕëãžæÚU ÎýÃØ×æÙ çSÍÚU ÚUãÌæ ãñÐ çÙ·¤æØ mæÚUæ Ȥàæü ÂÚU
while the bigger mass remains stationary Ü»æØæ »Øæ ¥çÏ·¤Ì× ÕÜ ãñ
on the ground. The maximum force (g510 ms22 Üð´).
exerted by the system on the floor is
(take g510 ms22).

(1) 20 N
(2) 10 N
(1) 20 N
(3) 60 N
(2) 10 N
(4) 40 N
(3) 60 N
(4) 40 N

English : 3 Set : 01 Hindi : 3 Set : 01

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

8
(1)
8 7
(1)
7
15
(2)
15 14
(2)
14
8
(3)
8 7
(3)
7 15
(4)
15 14
(4)
14

English : 4 Set : 01 Hindi : 4 Set : 01

7. India’s Mangalyan was sent to the Mars 7. ÖæÚUÌ ·¤æ ×´»ÜØæÙ ×´»Ü »ýã ·ð¤ çÜØð âêØü ·ð¤ ¿æÚUæð´
by launching it into a transfer orbit EOM ¥æðÚU SÍæÙæ‹ÌÚU‡æ ·¤ÿæ EOM ×ð´ ÂýÿæðçÂÌ ç·¤Øæ »ØæÐ
around the sun. It leaves the earth at E §âÙð Âë‰ßè ·¤æð E ÂÚU ÀUæðÇ¸æ ¥æñÚU ×´»Ü »ýã âð Øã M
and meets Mars at M. If the semi-major ÂÚU ç×ÜÌæ ãñÐ ØçÎ Âë‰ßè ·¤è ¥hü-Îèƒæü ¥ÿæ
axis of Earth’s orbit is ae51.531011 m, ae51.531011 m ãñ ¥æñÚU ×´»Ü »ýã ·¤è ¥hü-Îèƒæü
that of Mar’s orbit a m 52.28310 11 m, ¥ÿæ am52.2831011 m ãñ, ÌÕ ·ð¤ÂÜÚU ·ð¤ çÙØ×
taken Kepler’s laws give the estimate of ·ð¤ ¥ÙéâæÚU Âë‰ßè âð ×´»Ü»ýã Ì·¤ ×´»ÜØæÙ ·ð¤ Âãé¡¿Ùð
time for Mangalyan to reach Mars from ·¤æ â×Ø Ü»Ö» ãæð»æ Ñ
Earth to be close to :

(1) 500 days (1) 500 çÎÙ
(2) 320 days (2) 320 çÎÙ
(3) 260 days (3) 260 çÎÙ
(4) 220 days (4) 220 çÎÙ

English : 5 Set : 01 Hindi : 5 Set : 01

8. In materials like aluminium and copper, 8. °ËØéç×çÙØ× °ß´ Ìæ¡Õð Áñâð ÂÎæÍæðü´ ·ð¤ çÜØð çßç֋Ù
the correct order of magnitude of various ÂýˆØæSÍÌæ »é‡ææ¡·¤æð´ ·ð¤ ÂçÚU×æ‡æ ·¤æ âãè ·ý¤× ãñ Ñ
elastic modulii is :
(1) Young’s modulii < shear modulii (1) Ø´» ÂýˆØæSÍÌæ »é‡ææ¡·¤ < ¥ÂM¤Â‡æ ÂýˆØæSÍÌæ
< bulk modulii. »é‡ææ¡·¤ < ¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤.
(2) Bulk modulii < shear modulii (2) ¥æØÌÙ Âý ˆ ØæSÍÌæ »é ‡ ææ¡ · ¤ < ¥ÂM¤Â‡æ
< Young’s modulii. ÂýˆØæSÍÌæ »é‡ææ¡·¤ < Ø´» ÂýˆØæSÍÌæ »é‡ææ¡·¤.
(3) Shear modulii < Young’s modulii (3) ¥ÂM¤Â‡æ ÂýˆØæSÍÌæ »é‡ææ¡·¤ < Ø´» ÂýˆØæSÍÌæ
< bulk modulii. »é‡ææ¡·¤ < ¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤.
(4) Bulk modulii < Young’s modulii (4) ¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤ < Ø´» ÂýˆØæSÍÌæ
< shear modulii. »é‡ææ¡·¤ < ¥ÂM¤Â‡æ ÂýˆØæSÍÌæ »é‡ææ¡·¤.

9. The amplitude of a simple pendulum, 9. ßæØé ×ð´ ÎæðÜÙ ·¤ÚU ÚUãð °·¤ ÌÙé »æðÜèØ ÕæÕ ßæÜð âÚUÜ
oscillating in air with a small spherical bob, ÜæðÜ·¤ ·¤æ ¥æØæ× 40 âð·´¤ÇU ×ð´ 10 cm âð 8 cm
decreases from 10 cm to 8 cm in 40 seconds. Ì·¤ ƒæÅU ÁæÌæ ãñ Ð Øã ×æÙ Üð´ ç·¤ SÅUæð·¤ ·¤æ çÙØ×
Assuming that Stokes law is valid, and âãè ãñ ¥æñÚU ßæØé ·¤æ ·¤æÕüÙ ÇUæ§ü¥æò€âæ§Ç âð àØæÙÌæ
ratio of the coefficient of viscosity of air to »é‡ææ´·¤ ·¤æ ¥ÙéÂæÌ 1.3 ãñ, ÌÕ ·¤æÕüÙ ÇUæ§ü ¥æò€âæ§ÇU
that of carbon dioxide is 1.3, the time in ×ð´ §â ÜæðÜ·¤ ·ð¤ ¥æØæ× ·¤æð 10 cm âð 5 cm Ì·¤
which amplitude of this pendulum will ƒæÅUÙð ×ð ´ Ü»æ â×Ø Ü»Ö» ãæð » æ
reduce from 10 cm to 5 cm in (ln 551.601, ln 250.693).
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. °·¤ ·ð¤àæÙçÜ·¤æ ·¤æ𠪤ŠßæüÏÚU ÂæÙè ×ð´ ÇéUÕæðØæ ÁæÌæ ãñ
water and the height of the water column ¥æñÚU ÌÕ ÂæÙè ·ð¤ SÌÖ ·¤è ª¡¤¿æ§ü x ãæð ÁæÌè ãñÐ ÁÕ
is x. When this arrangement is taken into §â çߋØæâ ·¤æð °·¤ »ãÚUæ§ü d ßæÜè °·¤ ¹æÙ ×ð´ Üð
a mine of depth d, the height of the water ÁæØæ ÁæÌæ ãñ, ÌÕ ÂæÙè ·ð¤ SÌÖ ·¤è ª¡¤¿æ§ü y ãñÐ
column is y. If R is the radius of earth, the ØçÎ Âë‰ßè ·¤è ç˜æ’Øæ R ãñ, ÌÕ ¥ÙéÂæÌ x ãñ Ñ
x y
ratio is :
y
 d  d
(1)  12  (1)  12 
 R R

 2d   2d 
(2)  12  (2)  12 
R R

 R 2d   R 2d 
(3)  R 1d  (3)  R 1d 

 R 1d   R 1d 
(4)  R 2d  (4)  R 2d 

11. Water of volume 2 L in a closed container 11. °·¤ ՋΠÂæ˜æ ×ð´ 2 L ¥æØÌÙ ÂæÙè ·¤æð 1 kW ·¤è
is heated with a coil of 1 kW. While water ·é¤‡ÇUÜè âð »×ü ç·¤Øæ ÁæÌæ ãñÐ ÁÕ ÂæÙè »×ü ãæð ÚUãæ
is heated, the container loses energy at a ãñ, ÌÕ Âæ˜æ 160 J/s ·¤è ÎÚU â𠪤Áæü ·¤æ ÿæØ ·¤ÚU ÚUãæ
rate of 160 J/s. In how much time will the ãñÐ ç·¤ÌÙð â×Ø ×ð´ ÂæÙè ·¤æ ÌæÂ×æÙ 278C âð
temperature of water rise from 278C to 778C Âãé ¡ ¿ ð » æ? ( ÂæÙè ·¤è çßçàæcÅU ª¤c×æ
778C ? (Specific heat of water is 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) 8 ç×ÙÅU 20 âð·´¤ÇU
(2) 6 min 2 s (2) 6 ç×ÙÅU 2 âð·´¤ÇUU
(3) 7 min (3) 7 ç×ÙÅU
(4) 14 min (4) 14 ç×ÙÅU

English : 7 Set : 01 Hindi : 7 Set : 01

12. The equation of state for a gas is given by 12. °·¤ »ñâ ·¤è ¥ßSÍæ ·¤æ â×è·¤ÚU‡æ PV5nRT1aV
PV5nRT1aV, where n is the number of âð çÎØæ ÁæÌæ ãñ, Áãæ¡ n ×æðÜ ·¤è ⴁØæ ãñ ¥æñÚU a °·¤
moles and a is a positive constant. The ÏÙæˆ×·¤ çSÍÚUæ¡·¤ ãñÐ °·¤ ÕðÜÙ ×ð´ ÚU¹ð »ñ⠷𤠰·¤
initial temperature and pressure of one ×æðÜ ·¤æ ÂýæÚUçÖ·¤ ÌæÂ×æÙ °ß´ ÎæÕ ·ý¤×àæÑ To °ß´
mole of the gas contained in a cylinder are Po ãñÐ ÁÕ §â·¤æ ÌæÂ×æÙ â×ÎæÕ ÂÚU Îæð»éÙæ ãæð
To and Po respectively. The work done by Áæ°ð»æ, ÌÕ »ñâ mæÚUæ ç·¤Øæ »Øæ ·¤æØü ãæð»æ Ñ
the gas when its temperature doubles
isobarically will be :

Po To R Po To R
(1) (1)
Po 2a Po 2a

Po To R Po To R
(2) (2)
Po 1a Po 1a

(3) Po To R ln 2 (3) Po To R ln 2
(4) P o To R (4) Po To R

13. Modern vacuum pumps can evacuate a 13. ¥æÏéçÙ·¤ çÙßæüÌ ÂÂ ·¤×ÚðU ·ð¤ ÌæÂ×æÙ (300 K) ÂÚU
vessel down to a pressure of 4.0310215 atm. 4.0310215 °ÅUU×æSȤèØÚU ÎæÕ Ì·¤ °·¤ ÕÌüÙ ·¤æð
at room temperature (300 K). Taking çÙßæüçÌÌ ·¤ÚU â·¤Ìæ ãñÐ R58.3 JK21 ×æðÜ21,
R58.3 JK21 mole21, 1 atm5105 Pa and 1 °ÅU×æSȤèØÚU5105 ÂæS·¤Ü ¥æñÚU °ßæð»ðÇþUæð ⴁØæ
N Avogadro 56310 23 mole 21 , the mean 5631023 ×æðÜ21 ÜðÌð ãéØð °·¤ çÙßæüçÌÌ ÕÌüÙ ×ð´
distance between molecules of gas in an »ñ⠷𤠥‡æé¥æ´ð ·ð¤ Õè¿ ×æŠØ ÎêÚUè ·¤æ ×æ٠ֻܻ
evacuated vessel will be of the order of : §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

English : 8 Set : 01 Hindi : 8 Set : 01

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

(1)
(1)

(2)
(2)

(3)
(3)

(4)
(4)

English : 9 Set : 01 Hindi : 9 Set : 01

15. A transverse wave is represented by : 15. °·¤ ¥ÙéÂýSÍ ÌÚ´U» §ââð ÎàææüØè ÁæÌè ãñ Ñ
10 2p 2p  10 2p 2p 
y5 sin  t2 x y5 sin  t2 x
p  T l  p  T l 
For what value of the wavelength the ÌÚ´U»ÎñŠØü ·ð¤ ç·¤â ×æÙ ·ð¤ çÜ°ð ÌÚ´U» ßð» ·¤æ ×æÙ
wave velocity is twice the maximum ¥çÏ·¤Ì× ·¤‡æ ßð» ·¤æ Îæð»éÙæ ãæð»æ?
particle velocity ?
(1) 40 cm (1) 40 cm
(2) 20 cm (2) 20 cm
(3) 10 cm (3) 10 cm
(4) 60 cm (4) 60 cm

16. The magnitude of the average electric field 16. Âë‰ßè ·ð¤ ÂëcÆU âð ÁÚUæ ª¤ÂÚU ßæÌæßÚU‡æ ×ð´ âæÏæÚU‡æÌØæ
normally present in the atmosphere just ©ÂçSÍÌ ¥æñ â Ì çßlé Ì ÿæð ˜ æ ·¤æ ÂçÚU×æ‡æ
above the surface of the Earth is about 150 N/C ·ð¤ ֻܻ ãñ çÁâ·¤è çÎàææ Âë‰ßè ·ð¤ ·ð¤‹Îý
150 N/C, directed inward towards the ·¤è ¥æðÚU ¥‹ÌÚU×é¹è ãñÐ Øã Âë‰ßè mæÚUæ ßæã·¤ ÂçÚU‡ææ×è
center of the Earth. This gives the total ÂëcÆU ¥æßðàæ Îð»æ Ñ
net surface charge carried by the Earth to [ çÎØæ ãñ e o 58.85310 212 C 2 /N-m 2 ,
be : RE56.373106 m]
[Given e o 58.85310 212 C 2 /N-m 2 ,
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. Three capacitances, each of 3 mF, are 17. ÂýˆØð·¤ 3 mF ·ð¤ ÌèÙ â´ÏæçÚU˜æ çÎØð »Øð ãñ´Ð §Ù·¤æ
provided. These cannot be combined to ç·¤âè Öè Âý·¤æÚU ·¤æ â´ØæðÁÙ çِ٠×ð´ âð ·¤æñÙ âæ
provide the resultant capacitance of : 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

18. A d.c. main supply of e.m.f. 220 V is 18. çßléÌ ßæã·¤ ÕÜ 220 V ·¤è °·¤ çÎcÅU ÏæÚUæ ×éØ
connected across a storage battery of âŒÜæ§ü ·¤æð °·¤ 1 V ·¤ð¤ ÂýçÌÚUæðÏ mæÚUæ çßléÌ ßæã·¤
e.m.f. 200 V through a resistance of 1 V. ÕÜ 200 V ·¤è °·¤ â´ÖæçÚUÌ ÕñÅUÚè âð ÁæðǸæ ÁæÌæ ãñÐ
The battery terminals are connected to an ÕñÅUÚUè ·ð¤ ÅUç×üÙÜ ·¤æð °·¤ Õæ±Ø ÂýçÌÚUæðÏ ‘R’ âð ÁæðǸæ
external resistance ‘R’. The minimum ÁæÌæ ãñÐ ‘R’ ·¤æ ‹ØêÙÌ× ×æÙ, çÁââð ç·¤ ÕñÅUÚUè ×ð´
value of ‘R’, so that a current passes 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. ¥ÿæèØ çSÍçÌ ×ð´ ܐÕæ§ü d ·ð¤ Îæð ÌÙé ¿éÕ·¤èØ çmÏéýßæ´ð
dipoles of length d in end-on positions, are ·ð¤ ×ŠØ çՋÎé¥æð´ ·¤æð x ÎêÚUè ÂÚU ÚU¹æ »Øæ ãñ (x >>d)Ð
separated by a distance x, (x >> d). The ÎæðÙæð´ ·ð¤ Õè¿ ÕÜ x2n ·¤ð¤ â×æÙéÂæÌè ãñ, Áãæ¡ n ãñ :
force between them is proportional to
x2n where n is :

(1) 1
(2) 2
(1) 1
(3) 3
(2) 2
(4) 4
(3) 3
(4) 4
20. 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
20. The magnetic field of earth at the equator 6.43106 m ãñÐ ÌÕ Âë‰ßè ·¤æ çmÏýéß ¥æƒæê‡æü ֻܻ
is approximately 431025 T. The radius §â ·¤æðçÅU ·¤æ ãæð»æ Ñ
of earth is 6.43106 m. Then the dipole
moment of the earth will be nearly of the (1) 1023 A m2
order of :
(2) 1020 A m2
(1) 1023 A m2
(3) 1016 A m2
(2) 1020 A m2
(4) 1010 A m2
(3) 1016 A m2
(4) 1010 A m2

English : 12 Set : 01 Hindi : 12 Set : 01

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

English : 13 Set : 01 Hindi : 13 Set : 01

22. Match List I (Wavelength range of 22. âê¿è I (çßléÌ ¿éÕ·¤èØ SÂð€ÅþU× ·¤è ÌÚ´U»ÎñŠØü ÚðU‹Á)
electromagnetic spectrum) with List II. ·¤æð âê¿è II (§Ù ÌÚ´U»æð´ ·ð¤ çÙ×æü‡æ ·¤è çßçÏ) âð âé×ðçÜÌ
(Method of production of these waves) ·¤èçÁ°ð ¥æñÚU âê¿è ·ð¤ Ùè¿ð çÎØð »Øð çß·¤ËÂæ´ð ×ð´ âð
and select the correct option from the âãè çß·¤Ë ¿éçÙ°Ð
options given below the lists.
ÇÏ¤Í I ÇÏ¤Í II
List I List II 700 nm ÇÕ ŠøËΊËՙ •Ä™ §¿U¼ËøËΊËՙ œÕ‰
(a) (i)
(a)
700 nm to
(i)
Vibration of atoms 1 mm œ‰ƒ§¾ ÇÕ
1 mm and molecules.
§¿U¼ËøËΊËՙ œÕ‰ ŠËü±Ì¿Uœ‰ ÅËÖÁ
Inner shell electrons 1 nm ÇÕ
(b) (ii) ŒÁÕþªãU˾Ëՙ œ‰Í •œ‰ ‰¦Ëá S±¿U
1 nm to in atoms moving from 400 nm
(b) (ii) ÇÕ Ì¾¤ÁÕ S±¿U œ‰Í ̱ ÇÕ
400 nm one energy level to a
lower level.
¾ËÌ»œ‰ œÕ‰ ¿ÕU̬U½ËÕ Ç̜≽
(c) < 1023 nm (iii)
(c) < 10 23 nm (iii)
Radioactive decay of ä˽ ÇÕ
the nucleus.
1 mm ÇÕ
(d) (iv) ¼Öó¾ÕªUã ˾
† ÄË°Ä ÇÕ
1 mm to 0.1 m
(d) (iv) Magnetron valve.
0.1 m
(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. °·¤ »æðÌæ¹æðÚU ÂæÙè ·ð¤ ¥‹ÎÚU âð ÕæãÚU ·¤è ÎéçÙØæ ·¤æð
the outside world contained in a circular °·¤ ßëžæèØ ÿæñçÌÁ ×ð´ çÙçãÌ Îð¹Ìæ ãñÐ ÂæÙè ·¤æ
horizon. The refractive index of water is ¥ÂßÌüÙæ¡·¤ 4 ãñ ¥æñÚU »æðÌæ¹æðÚU ·¤è ¥æ¡¹ ÂæÙè ·ð¤
4 3
3
, and the diver’s eyes are 15 cm below ÂëcÆU âð 15 cm Ùè¿ð ãñ´Ð ÌÕ ßëžæ ·¤è ç˜æ’Øæ ãñ Ñ
the surface of water. Then the radius of
the circle is :

(1) 15333 5 cm (1) 15333 5 cm

(2) 1533 7 cm (2) 1533 7 cm

153 7 153 7
(3) cm (3) cm
3 3

153 3 153 3
(4) cm (4) cm
7 7

English : 15 Set : 01 Hindi : 15 Set : 01

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

English : 16 Set : 01 Hindi : 16 Set : 01

(1) 520 nm (1) 520 nm
(2) 540 nm (2) 540 nm
(3) 560 nm (3) 560 nm
(4) 580 nm (4) 580 nm

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

English : 17 Set : 01 Hindi : 17 Set : 01

27. If the binding energy of the electron in a 27. ØçÎ ãæ§ÇþUæðÁÙ ÂÚU×æ‡æé ×ð´ §Üð€ÅþUæÙ ·¤è ՋÏÙ ª¤Áæü
hydrogen atom is 13.6 eV, the energy 13.6 eV ãñ, ÌÕ Li11 ·¤è ÂýÍ× ©žæðçÁÌ ¥ßSÍæ
required to remove the electron from the âð §Üð€ÅþUæÙ ÕæãÚU çÙ·¤æÜÙð ×ð´ ¥æßàØ·¤ ª¤Áæü ãñ Ñ
first excited state of Li11 is :
(1) 122.4 eV (1) 122.4 eV
(2) 30.6 eV (2) 30.6 eV
(3) 13.6 eV (3) 13.6 eV
(4) 3.4 eV (4) 3.4 eV

28. Identify the gate and match A, B, Y in
bracket to check. 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) (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)
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
29. °·¤ ×èÙæÚU ·ð¤ àæèáü ÂÚU Âýðá‡æ °ç‹ÅUÙæ ·¤è ª¡¤¿æ§ü 32 m
maximum distance between them for ãñ ¥æñÚU ¥çÖ»ýæãè °ç‹ÅUÙæ ·¤è ª¡¤¿æ§ü 50 m ãñÐ
satisfactory communication in line of sight ÎëçcÅUÚðU¹èØ (LOS) ×æðÇU ×ð´ â´ÌæðáÂýÎ â´¿ÚU‡æ ·ð¤ çÜ°
(LOS) mode ? 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. °·¤ n-p-n Åþ U æç‹ÁSÅUÚU ×ð ´ ÌèÙ ¿æÜ·¤ ÌæÚU
A, B and C. Connecting B and C by moist A, B °ß´ C ãñ´Ð »èÜè ¥´»éçÜØæð´ âð B °ß´ C ·¤æð
fingers, A to the positive lead of an ÁæðǸÙð ÂÚU, °·¤ ÏæÚUæ×æÂè ·¤æð ÏÙæˆ×·¤ ¿æÜ·¤ ÌæÚU
ammeter, and C to the negative lead of the ·¤æð A âð ÁæðǸÙð ÂÚU ¥æñÚU ÏæÚUæ×æÂè ·¤è «¤‡ææˆ×·¤
ammeter, one finds large deflection. Then, ¿æÜ·¤ ÌæÚU ·¤æð C âð ÁæðǸÙð ÂÚU °·¤ Âýðÿæ·¤ ¥ˆØçÏ·¤
A, B and C refer respectively to : çßÿæð ÂæÌæ ãñÐ ÌÕ A, B °ß´ C ·¤æ â´ÎÖü ·ý¤×àæÑ
§Ùâð ãñ Ñ
(1) Emitter, base and collector (1) ©ˆâÁü·¤, ¥æÏæÚU °ß´ â´»ýæãè
(2) Base, emitter and collector (2) ¥æÏæÚU, ©ˆâÁü·¤ °ß´ â´»ýæãè
(3) Base, collector and emitter (3) ¥æÏæÚU, â´»ýæãè °ß´ ©ˆâÁü·¤
(4) Collector, emitter and base. (4) â´»ýæãè, ©ˆâÁü·¤ °ß´ ¥æÏæÚU

English : 19 Set : 01 Hindi : 19 Set : 01

PART B — CHEMISTRY Öæ» B — ÚUâæØÙ çߙææÙ
31. In a face centered cubic lattice atoms A 31. °·¤ Ȥܷ¤ ·ð¤ç‹ÎýÌ ƒæÙæ·¤æÚU ÁæÜ·¤ ×ð´ A ·ð¤¤ ÂÚU×æ‡æé
are at the corner points and atoms B at ·¤æðÙæð´ ·ð¤ çՋÎé¥æð´ ÂÚU ãñ´ ¥æñÚU B ·ð¤ ÂÚU×æ‡æé Ȥܷ¤
the face centered points. If atom B is ·ð¤‹Îýæð´ ÂÚU ãñ´Ð ØçÎ B ÂÚU×æ‡æé °·¤ Ȥܷ¤ ·ð¤‹Îý ÂÚU Ù
missing from one of the face centered ãæð Ìæð ¥æØçÙ·¤ Øæñç»·¤ ·¤æ âê˜æ ãæð»æ Ñ
points, the formula of the ionic compound
is : (1) AB2
(1) AB 2 (2) A 5B 2
(2) A 5B2 (3) A 2B 3
(3) A 2B3 (4) A 2B 5
(4) A 2B5

32. °·¤ »ñâ ·ð¤ çÜØð ßæ‹ÇUÚU ßæÜ â×è·¤ÚU‡æ
32. Van der Waal’s equation for a gas is stated 2
nRT  n
as, p5 2a   .
V 2 nb  V
2
nRT  n ãæðÌæ ãñÐ Øã â×è·¤ÚU‡æ ¥æÎàæü »ñâ â×è·¤ÚU‡æ ·¤æ
p5 2a   .
V 2 nb  V
nRT
This equation reduces to the perfect gas
M¤Â, p5 V ÏæÚU‡æ ·¤ÚU Üð»æ ÁÕ Ñ
nRT
equation, p 5 when ,
V
(1) Ìæ ÂØæüŒÌ ©‘¿ ãæð»æ ¥æñÚU ÎæÕ ‹ØêÙ ãæð»æÐ
(1) temperature is sufficiently high and
pressure is low.
(2) Ìæ ÂØæüŒÌ ‹ØêÙ ãæð»æ ¥æñÚU ÎæÕ ©‘¿ ãæð»æÐ
(2) temperature is sufficiently low and
pressure is high.
(3) Ìæ ¥æñÚU ÎæÕ ÎæðÙæð´ ÕãéÌ ©‘¿ ãæð´»ðÐ
(3) both temperature and pressure are
very high.
(4) Ìæ ¥æñÚU ÎæÕ ÎæðÙæð´ ÕãéÌ ‹ØêÙ ãæð´»ðÐ
(4) both temperature and pressure are
very low.

English : 20 Set : 01 Hindi : 20 Set : 01

33. The standard electrode potentials 33. ¿æÚU ÏæÌé¥æð´ A, B, C ¥æñÚU D ·ð¤ SÅñU‹ÇUÇüU (×æÙ·¤)

(E ) of four metals A, B, C and D are
o
M /M
1 §Üñ € Åþ U æð Ç U çßÖß (E )
o
1
M /M ·ý × æÙé â æÚU
21.2 V , 0.6 V, 0.85 V and 20.76 V, 21.2 V, 0.6 V, 0.85 V ¥æñÚU 20.76 V ãñ´Ð çßÖß
respectively. The sequence of deposition Üæ»ê ·¤ÚUÙð ÂÚU ÏæÌé Á×Ùð ·¤æ ·ý¤× ãæð»æ Ñ
of metals on applying potential is :
(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

34. At a certain temperature, only 50% HI is 34. °·¤ Ìæ çßàæðá âæØÂÚU ·ð¤ßÜ 50% HI, H2 ¥æñÚU
dissociated into H2 and I2 at equilibrium. I2 ×ð´ çßÖæçÁÌ ãæðÌæ ãñÐ âæØ çSÍÚUæ´·¤ ·¤æ ×æÙ ãæð»æ Ñ
The equilibrium constant is :
(1) 1.0 (1) 1.0
(2) 3.0 (2) 3.0
(3) 0.5 (3) 0.5
(4) 0.25 (4) 0.25

35. Dissolving 120 g of a compound of 35. °·¤ Øæñç»·¤ (¥‡æéÖæÚU 60) ·¤è 120 »ýæ× ×æ˜ææ ·¤æð
(mol. wt. 60) in 1000 g of water gave a 1000 »ýæ× ÁÜ ×𴠃ææðÜÙð ÂÚU ÂýæŒÌ ãé° çßÜØÙ ·¤æ
solution of density 1.12 g/mL. The ƒæÙˆß 1.12 »ýæ× ÂýçÌ ç×çÜ çÜÅUÚU ãñÐ çßÜØÙ ·¤è
molarity of the solution is : ×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

English : 21 Set : 01 Hindi : 21 Set : 01

36. The half-life period of a first order reaction 36. °·¤ ÂýÍ× ·¤æðçÅU ·¤è ¥çÖç·ý¤Øæ ·¤æ ¥Ïü-¥æØé ·¤æÜ
is 15 minutes. The amount of substance 15 ç×ÙÅU ãñÐ °·¤ ƒæ‡ÅUæ Âà¿æÌ÷ ÂÎæÍü ·¤è àæðá ÚUãè
left after one hour will be : ×æ˜ææ ãæð»è Ñ
(1) 1 ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ 1 4 Öæ»
4 of the original amount (1)

(2) 1 ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ 1 8 Öæ»
8 of the original amount (2)

(3) 1 ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ 1 16 Öæ»
16 of the original amount (3)

(4) 1 ÂýæÚUçÖ·¤ ×æ˜ææ ·¤æ 1 32 Öæ»
32 of the original amount (4)

37. A current of 10.0 A flows for 2.00 h 37. ÏæÌé X ·ð¤ çƒæÜð ãé° Ü߇æ ÏæÚU·¤ §Üñ€ÅþUæðçÜçÅU·¤
through an electrolytic cell containing a âñÜ ×ð´ âð 2.00 ƒæ‡ÅðU ·ð¤ çÜØð 10.0 A ·¤è çßléÌ
molten salt of metal X. This results in the ÏæÚUæ ¿ÜæÙð ÂÚU 0.250 ×æðÜ X ÏæÌé ·¤æ Á×æß ãé¥æÐ
decomposition of 0.250 mol of metal X at çƒæÜð ãé° Ü߇æ ×ð´ ÏæÌé X ·¤è ¥æ€âè·ë¤Ì ¥ßSÍæ
the cathode. The oxidation state of X in 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. The energy of an electron in first Bohr orbit 38. H-ÂÚU×æ‡æé ·ð¤ ÂýÍ× ÕæðãÚU ¥æçÕüÅU ×ð´ §Üñ€ÅþUæÙ ·¤è
of H - atom is 213.6 eV. The energy value ª¤Áæü 213.6 eV ãñÐ Li 21 ·¤è ©žæðçÁÌ ¥ßSÍæ ×ð´
of electron in the excited state of Li21 is : §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

39. The temperature at which oxygen 39. ÌæÂ, çÁâ ÂÚU ¥æò€âèÁÙ ¥‡æé¥æð´ ·¤è ß»ü ×æŠØ×êÜ
molecules have the same root mean square SÂèÇU ·¤æ ×æÙ ßãè ãæðÌæ ãñ Áæð ãèçÜØ× ÂÚU×æ‡æé¥æð´ ·¤æ
speed as helium atoms have at 300 K is : 300 K ÂÚU ãæðÌæ ãñ,
(Atomic masses : He54 u, O516 u) (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

40. The standard enthalpy of formation of 40. NH3 ÕÙÙð ·¤è ×æÙ·¤ ª¤Áæü 246.0 kJ/×æðÜ ãñÐ
NH3 is 246.0 kJ/mol. If the enthalpy of ØçÎ ¥ÂÙð ÂÚU × æ‡æé ¥ æð ´ âð H 2 ÕÙÙð ·¤è ª¤Áæü
formation of H 2 from its atoms is 2436 kJ/×æðÜ ¥æñÚU N2 ·¤è 2712 kJ/×æðÜ ãæð Ìæð
2436 kJ/mol and that of N 2 is N2H ·¤è NH3 ×ð´ ¥æñâÌ Õæ¡ÇU ª¤Áæü ãæð»è Ñ
2712 kJ/mol, the average bond enthalpy
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 :
(1) 115.2 g (1) 115.2 »ýæ×
(2) 57.6 g (2) 57.6 »ýæ×
(3) 28.8 g (3) 28.8 »ýæ×
(4) 18.4 g (4) 18.4 »ýæ×

42. The gas evolved on heating CaF2 and SiO2 42. CaF2 ¥æñÚU SiO2 ·¤æð âæ‹Îý H2SO4 ·ð¤ âæÍ »ÚU×
with concentrated H2SO4, on hydrolysis ·¤ÚUÙð âð ÂýæŒÌ ãé§ü »ñâ ãæ§ÇþUæÜðçââ ÂÚU °·¤ â$Èð¤Î
gives a white gelatinous precipitate. The ÁñÜ Áñâæ ¥ßÿæð ÎðÌè ãñÐ Øã ¥ßÿæð ãæð»æ Ñ
precipitate is :
(1) hydrofluosilicic acid (1) ãæ§ÇþUæðÜæðçâçÜçâ·¤ °ðçâÇU
(2) silica gel (2) çâçÜ·¤æ ÁñÜ
(3) silicic acid (3) çâçÜçâ·¤ °ðçâÇ
(4) calciumfluorosilicate (4) ·ñ¤çËàæØ׍ÜæðÚUæðçâçÜ·ð¤ÅU

43. Chloro compound of Vanadium has only 43. ßñÙðçÇUØ× ·¤æ °·¤ €ÜæðÚUæð Øæñç»·¤ 1.73 BM ·¤æ ·ð¤ßÜ
spin magnetic moment of 1.73 BM. This çSÂÙ ×ñ ‚ Ùð ç ÅU·¤ ×æð × ñ ‹ ÅU ÚU¹Ìæ ãñ
Vanadium chloride has the formula : (V ·¤æ ÂÚU×æ‡æê ·ý¤×æ´·¤523) §â ßñÙðçÇUØ× €ÜæðÚUæ§ÇU
(at. no. of V523) ·¤æ âê˜æ ãæðÌæ ãñ Ñ
(1) VCl2 (1) VCl2
(2) VCl4 (2) VCl4
(3) VCl3 (3) VCl3
(4) VCl5 (4) VCl5

English : 24 Set : 01 Hindi : 24 Set : 01

44. An octahedral complex of Co 31 is 44. Co31 ·¤æ °·¤ ¥cÅȤËæ·¤èØ â´·¤ÚU ÂýçÌ¿éÕ·¤èØ
diamagnetic. The hybridisation involved ãæðÌæ ãñÐ §â â´·¤ÚU ·ð¤ ÕÙÙð âð âÕç‹ÏÌ â´·¤ÚU‡æ
in the formation of the complex is : ãæð»æ Ñ
(1) sp3d2 (1) sp3d2
(2) dsp2 (2) dsp2
(3) d2sp3 (3) d2sp3
(4) dsp3d (4) dsp3d

45. Which of the following is not formed when 45. ¥ÜèØ K2Cr2O7 ƒææðÜ ·¤è H2S ·ð¤ âæÍ ¥çÖç·ý¤Øæ
H 2S reacts with acidic K 2 Cr 2 O 7 ãæðÙð ÂÚU çِÙæð´ ×ð´ âð ·¤æñÙ Ùãè´ ÕÙÌæ?
solution ? (1) CrSO 4
(1) CrSO 4 (2) Cr2(SO4)
3
(2) Cr2(SO4) (3) K2SO 4
3
(3) K2SO 4 (4) S
(4) S

46. §Ù ×ð´ âð ç·¤â ×ð´ ¥Øéç‚×Ì §Üñ€ÅþUæÙ ãæðÌæ ãñ Øæ ãæðÌð
46. Which of the following has unpaired ãñ´ ?
electron(s) ? (1) N2
(1) N2
(2) O2
2
(2) O2
2
(3) N 221
(3) N 221
(4) O 222
(4) O 222

English : 25 Set : 01 Hindi : 25 Set : 01

47. In the following sets of reactants which 47. ç·ý¤Øæ ·¤æÚU·¤æð´ ·ð¤ çِ٠âðÅUæð´ ×ð´ âð ç·¤â Îæð ×ð´
two sets best exhibit the amphoteric Al2O3 . xH2O ·¤æ ©ÖØ Ï×èü ÃØßãæÚU Îð¹æ ÁæÌæ
character of Al2O3 . xH2O ? ãñ?
2 2
Set 1 : Al2O3 . xH2O (s) and OH (aq) Set 1 : Al2O3 . xH2O (s) ¥æñÚU OH (ÁÜèØ)
Set 2 : Al2O3 . xH2O (s) and H2O (l) Set 2 : Al2O3 . xH2O (s) ¥æñÚU H2O (Îýß)
1 1
Set 3 : Al2O3 . xH2O (s) and H (aq) Set 3 : Al2O3 . xH2O (s) ¥æñÚU H (ÁÜèØ)
Set 4 : Al2O3 . xH2O (s) and NH3 (aq) Set 4 : Al2O3 . xH2O (s) ¥æñÚU NH3 (ÁÜèØ)
(1) 1 and 2 (1) 1 ¥æñÚU 2
(2) 1 and 3 (2) 1 ¥æñÚU 3
(3) 2 and 4 (3) 2 ¥æñÚU 4
(4) 3 and 4 (4) 3 ¥æñÚU 4

48. The number and type of bonds in C 222 ion 48. CaC2 ·ð C 222 ¥æØÙ ×ð´ ¥æՋÏæð´ ·¤è ⴁØæ °ß´
in CaC2 are : Âý·¤æÚU çِ٠·¤æñÙâè ãñ?
(1) One s bond and one p2bond (1) °·¤ s ¥æÕ‹Ï ¥æñÚU °·¤ p2¥æՋÏ
(2) One s bond and two p2bonds (2) °·¤ s ¥æÕ‹Ï ¥æñÚU Îæð p2¥æՋÏ
(3) Two s bonds and two p2bonds (3) Îæð s ¥æÕ‹Ï ¥æñÚU Îæð p2¥æՋÏ
(4) Two s bonds and one p2bond (4) Îæð s ¥æÕ‹Ï ¥æñÚU °·¤ p2¥æՋÏ

49. The form of iron obtained from blast 49. Ûææð´·¤æ Ö^è âð ÂýæŒÌ ãé° Üæðãð ·¤æ M¤Â ·¤ãÜæÌæ ãñ Ñ
furnace is :
(1) Steel (1) §SÂæÌ (Steel)
(2) Cast Iron (2) ÉUÜßæ¡ Üæðãæ (Cast Iron)
(3) Pig Iron (3) ·¤‘¿æ Üæðãæ (Pig Iron)
(4) Wrought Iron (4) çÂÅUßæ´ Üæðãæ (Wrought Iron)

English : 26 Set : 01 Hindi : 26 Set : 01

50. The correct statement about the magnetic 50. [Fe(CN)6]32 ¥æñÚU [FeF6]32 ·ð¤ ¿éÕ·¤èØ »é‡ææð´
properties of [Fe(CN)6]32 and [FeF6]32 ·¤æ ØÍæÍü çßßÚU‡æ ãñ Ñ (Z526).
is : (Z526).
(1) both are paramagnetic. (1) ÎæðÙæ´ð ¥Ùé¿éÕ·¤èØ ãñ´Ð
(2) both are diamagnetic. (2) ÎæðÙæð´ ÂýçÌ ¿éÕ·¤èØ ãñ´Ð
(3) [Fe(CN) 6 ] 32 is diamagnetic, (3) [Fe(CN)6]32 ÂýçÌ¿éÕ·¤èØ ¥æñÚU
[FeF6]32 is paramagnetic. [FeF6]32¥Ùé¿éÕ·¤èØ ãñÐ
(4) [Fe(CN) 6 ] 32 is paramagnetic, (4) [Fe (CN)6]32¥Ùé¿éÕ·¤èØ ¥æñÚU [FeF6]32
[FeF6]32 is diamagnetic. ÂýçÌ¿éÕ·¤èØ ãñÐ

51. Which one of the following reactions will 51. §Ù ¥çÖç·ý¤Øæ¥æð´ ×ð´ âð ç·¤â ×ð´ ·¤æÕüÙ - ·¤æÕüÙ
not result in the formation of carbon- ¥æÕ‹Ï Ùãè´ ÂýæŒÌ ãæð»æ?
carbon bond ?
(1) Reimer-Tieman reaction (1) ÚUæð×ÚU - ÅUè×Ù ¥çÖç·ý¤ØæÐ
(2) Friedel Craft’s acylation (2) Èý¤èÇUÜ ·ý¤æȤÅU °ðâèÜðàæÙÐ
(3) Wurtz reaction (3) ßéÅüU$Á ¥çÖç·ý¤ØæÐ
(4) Cannizzaro reaction (4) ·ñ¤Ùè$ÁñÚUæð ¥çÖç·ý¤ØæÐ

52. In the hydroboration - oxidation reaction 52. ÂýæðÂèÙ ·ð¤ ÇUæ§ÕæðÚðUÙ, H2O2 ¥æñÚU NaOH ·ð¤ âæÍ
of propene with diborane, H 2 O 2 and ãæ§ÇþUæðÕæðÚðUàæÙ-¥æò€âè·¤ÚU‡æ ¥çÖç·ý¤Øæ ×ð́ ÕÙæ ·¤æÕüçÙ·¤
NaOH, the organic compound formed is : Øæñç»·¤ ãñ Ñ
(1) CH3CH2OH (1) CH3CH2OH
(2) CH3CHOHCH3 (2) CH3CHOHCH3
(3) CH3CH2CH2OH (3) CH3CH2CH2OH
(4) (CH3) COH (4) (CH3) COH
3 3

English : 27 Set : 01 Hindi : 27 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
→ ·¤æ ×éØ

is : ç·ý¤Øæ È¤Ü ãñ Ñ

(1)
(1)

(2)
(2)

(3)
(3)

(4)
(4)

54. For the compounds
CH3Cl, CH3Br, CH3I and CH3F,
54. Øæñç»·¤æð´
the correct order of increasing C-halogen
CH3Cl,CH3Br,CH3I ¥æñÚU CH3F
bond length is :
×ð´ ·¤æÕüÙ-ãñÜæðÁÙ Õæ¡ÇU ·¤è ÕɸÌè ܐÕæ§ü ·¤æ ÆUè·¤
(1) CH3F < CH3Cl < CH3Br < CH3I
·ý¤× ãñ Ñ
(2) CH3F < CH3Br < CH3Cl < CH3I
(1) CH3F < CH3Cl < CH3Br < CH3I
(3) CH3F < CH3I < CH3Br < CH3Cl
(2) CH3F < CH3Br < CH3Cl < CH3I
(4) CH3Cl < CH3Br < CH3F < CH3I
(3) CH3F < CH3I < CH3Br < CH3Cl
(4) CH3Cl < CH3Br < CH3F < CH3I

English : 28 Set : 01 Hindi : 28 Set : 01

55. Allyl phenyl ether can be prepared by 55. °Üæ§Ü çȤÙæ§Ü §üÍÚU §‹ãð´ »ÚU× ·¤ÚU ÕÙæØæ Áæ â·¤Ìæ
heating : ãñ Ñ
(1) C6H5Br1CH25CH2CH22ONa (1) C6H5Br1CH25CH2CH22ONa
(2) CH25CH2CH22Br1C6H5ONa (2) CH25CH2CH22Br1C6H5ONa
(3) C6H52CH5CH2Br1CH32ONa (3) C6H52CH5CH2Br1CH32ONa
(4) CH25CH2Br1C6H52CH22ONa (4) CH25CH2Br1C6H52CH22ONa

56. In a nucleophilic substitution reaction : 56. ‹Øêç€ÜØâ SÙðãè ¥ÎÜ ÕÎÜ ¥çÖç·ý¤Øæ Ñ
DMF DMF
R2Br1Cl2 → R_Cl1Br2, R2Br1Cl2 → R_Cl1Br2,
which one of the following undergoes ×ð´ çِ٠ÂÎæÍæðZ âð ·¤æñÙ ÃØßSÍæ ·¤æ â´ÂêU‡æü ÕÎÜ ·¤ÚU
complete inversion of configuration ? ÜðÌæ ãñ ?
(1) C6H5CHC6H5Br (1) C6H5CHC6H5Br
(2) C6H5CH2Br (2) C6H5CH2Br
(3) C6H5CH CH3Br (3) C6H5CH CH3Br
(4) C6H5CCH3C6H5Br (4) C6H5CCH3C6H5Br

57. 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 B A B

(1) (1)

(2) (2)

(3) (3)

• • • •
(4) Ph3C , (CH3) C (4) Ph3C , (CH3) C
3 3

English : 29 Set : 01 Hindi : 29 Set : 01

58. Structure of some important polymers are 58. ·é¤ÀU Âýçâh ÕãéÜ·¤æð´ ·¤è â´ÚU¿Ùæ°´ Ùè¿ð Îè »§ü ãñ §Ù×ð´
given. Which one represents Buna-S ? âð ·¤æñÙ ÕêÙæ-S ·¤è âê¿·¤ ãñ?

(1) (1)

(2) (2)

(3) (3)

(4) (4)

59. Which is the major product formed when 59. ·¤æñÙ âè ÕǸè ×æ˜ææ ×ð´ ç·ý Øæ È¤Ü ÂýæŒÌ ãæðÌæ ãñ ÁÕ
acetone is heated with iodine and °ðâèÅUæðÙ ·¤æð ¥æØæðÇUèÙ ¥æñÚU ÂæðÅñUçàæØ× ãæ§ÇþUæ€âæ§ÇU
potassium hydroxide ? ·ð¤ âæÍ »ÚU× ç·¤Øæ ÁæÌæ ãñ?
(1) Iodoacetone (1) ¥æØæðÇUæð°ðâèÅUæðÙ
(2) Acetic acid (2) °âèçÅU·¤ °ðçâÇU
(3) Iodoform (3) ¥æØæðÇUæð$Ȥæ×ü
(4) Acetophenone (4) °ðâèÅUæð çȤÙæðÙ

60. Which one of the following class of 60. °çâçÅUÜèÙ ·ð¤ ÕãéÜ·¤è·¤ÚU‡æ âð ·¤æñÙâæ çِ٠Âý·¤æÚU
compounds is obtained by polymerization ·¤æ Øæñç»·¤ ÂýæŒÌ ãæðÌæ ãñ?
of acetylene ?
(1) Poly-yne (1) ÂæòÜè-¥æ§Ù
(2) Poly-ene (2) ÂæòÜè-§üÙ
(3) Poly-ester (3) ÂæòÜè-°ðSÅUÚU
(4) Poly-amide (4) ÂæòÜè-°×æ§ÇU

English : 30 Set : 01 Hindi : 30 Set : 01

PART C — MATHEMATICS Öæ» C — »ç‡æÌ
61. Let P be the relation defined on the set of 61. ×æÙ P âÖè ßæSÌçß·¤ ⴁØæ¥æð´ ÂÚU ÂçÚUÖæçáÌ °·¤
all real numbers such that °ðâæ â´Õ´Ï ãñ ç·¤
P5{(a, b) : sec2 a2tan2 b51}. Then P is : P5{(a, b) : sec2 a2tan2 b51} ãñ, Ìæð P Ñ
(1) reflexive and symmetric but not (1) SßÌéËØ ÌÍæ â×ç×Ì ãñ ÂÚU‹Ìé â´·ý¤æ×·¤ Ùãè´
transitive. ãñÐ
(2) reflexive and transitive but not (2) SßÌéËØ ÌÍæ â´·ý¤æ×·¤ ãñ ÂÚU‹Ìé â×ç×Ì Ùãè´
symmetric. ãñÐ
(3) symmetric and transitive but not (3) â×ç×Ì ÌÍæ â´·ý¤æ×·¤ ãñ ÂÚU‹Ìé SßÌéËØ Ùãè´
reflexive. ãñÐ
(4) an equivalence relation. (4) °·¤ ÌéËØÌæ â´Õ´Ï ãñÐ

62. Let w(Im w ¹ 0) be a complex number. 62. ×æÙæ w(Im w ¹ 0) °·¤ âç×Ÿæ ⴁØæ ãñ, Ìæð âÖè
Then the set of all complex numbers z âç×Ÿæ ⴁØæ¥æð´ z ·¤æ â×é“æØ, Áæð ç·¤âè ßæSÌçß·¤
satisfying the equation w2 w z5k (12z), ⴁØæ k ·ð¤ çÜ°, â×è·¤ÚU‡æ w2 w z5k (12z)
for some real number k, is : ·¤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}

63. If equations ax 2 1bx1c50, 63. ØçÎ â×è·¤ÚU‡ææð ´ ax 2 1bx1c50,
(a, b, c Î R, a ¹ 0) and 2x213x1450 have (a, b, c Î R, a ¹ 0) ÌÍæ 2x213x1450 ·¤æ
a common root, then a : b : c equals : °·¤ ×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

English : 31 Set : 01 Hindi : 31 Set : 01

1 1 1 1
64. If and are the roots of the 64. ØçÎ ÌÍæ b â×è·¤ÚU‡æ ax21bx1150
a b a
equation, ax21bx1150 (a ¹ 0, a, b Î R), (a ¹ 0, a, b Î R) ·ð ¤ ×ê Ü ãñ , Ìæð â×è·¤ÚU ‡ æ
then the equation, x(x1b3)1(a323abx)50 ·ð¤ ×êÜ ã´ñ Ñ
x(x1b3)1(a323abx)50 has roots :
3 3 3 3
(1) a 2 and b 2 (1) a 2 ÌÍæ b 2
1 1 1 1
(2) a b 2 and a 2 b (2) a b 2 ÌÍæ a 2 b

(3) a b and a b (3) a b ÌÍæ a b

223 23 23 23
(4) a and b 2 (4) a 2 ÌÍæ b 2

65. If a, b, c are non - zero real numbers and if 65. ØçÎ a, b, c àæê‹ØðÌÚU ßæSÌçß·¤ ⴁØæ°¡ ãñ´ ÌÍæ ØçÎ
the system of equations â×è·¤ÚU‡æ çÙ·¤æØ
(a21)x5y1z, (a21)x5y1z,
(b21)y5z1x, (b21)y5z1x,
(c21)z5x1y, (c21)z5x1y,
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. ØçÎ B °·¤ °ðâæ 333 ¥æÃØêã ãñ ç·¤ B250 ãñ, Ìæð
det. [(I1B)50250B] is equal to : det. [(I1B)50250B] ÕÚUæÕÚU ãñ Ñ
(1) 1 (1) 1
(2) 2 (2) 2
(3) 3 (3) 3
(4) 50 (4) 50

67. The number of terms in the expansion of 67. (11x)101 (11x22x)100 ·ð¤ x ·¤è ƒææÌæð´ ×ð´ ÂýâæÚU
(11x)101 (11x22x)100 in powers of x is : ×ð´ ÂÎæð´ ·¤è ⴁØæ ãñ Ñ
(1) 302 (1) 302
(2) 301 (2) 301
(3) 202 (3) 202
(4) 101 (4) 101

68. The sum of the digits in the unit’s place of 68. ⴁØæ¥æð´ 3, 4, 5 ÌÍæ 6 ·ð¤ ÂýØæð» âð, çÕÙæ ·¤æð§ü ⴁØæ
all the 4-digit numbers formed by using the ÎæðãÚUæ°, ÕÙÙð ßæÜè âÖè ¿æÚU ¥´·¤æð´ ·¤è ⴁØæ¥æð´ ·ð¤
numbers 3, 4, 5 and 6, without repetition, §·¤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. Îè »§ü °·¤ â×æ´ÌÚU ŸæðÉ¸è ·ð¤ âÖè ÂÎ ÏÙÂê‡ææZ·¤ ãñ´Ð
integers. The sum of its first nine terms is §â·ð¤ ÂýÍ× Ùæñ ÂÎæð´ ·¤æ Øæð» 200 âð ¥çÏ·¤ ÌÍæ
greater than 200 and less than 220. If the 220 âð ·¤× ãñÐ ØçÎ §â·¤æ ÎêâÚUæ ÂÎ 12 ãñ, Ìæð
second term in it is 12, then its 4th term §â·¤æ ¿æñÍæ ÂÎ ãñ Ñ
is :
(1) 8 (1) 8
(2) 16 (2) 16
(3) 20 (3) 20
(4) 24 (4) 24

70. If the sum 70. ØçÎ
3 5 7 3 5 7
1 2
2 2
1 2 1.......1 u p t o 1 2 1 2 1.......1 ·ð ¤ 20
1 1 12 1 1 2 2 1 32 1 2
1 12 2
1 1 2 2 1 32

k
20 terms is equal to , then k is equal to : ÂÎæð´ Ì·¤ ·¤æ Øæð» k ·ð¤ ÕÚUæÕÚU ãñ, Ìæð k ÕÚUæÕÚU ãñ Ñ
21 21
(1) 120 (1) 120
(2) 180 (2) 180
(3) 240 (3) 240
(4) 60 (4) 60

71. ( )
If f(x) is continuous and f 9 2 5 2 9 , then 71. ØçÎ f(x) âÌÌ ãñ ÌÍæ f ( 9 2 ) 5 2 9 ãñ, Ìæð
 12 cos 3x   12 cos 3x 
lim f   is equal to : lim f   ÕÚUæÕÚU ãñ Ñ
x→0  x2 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 Set : 01

 d2 y   d2 x   d2 y   d2 x 
72. If y5enx, then  2   2  is equal to : 72. ØçÎ y5enx ãñ, Ìæð  2   2  ÕÚUæÕÚU ãñ Ñ
 dx   dy   dx   dy 
(1) n enx (1) n enx
(2) n e2nx (2) n e2nx
(3) 1 (3) 1
(4) 2n e2nx (4) 2n e2nx

73. If the Rolle’s theorem holds for the 73. ØçΠȤÜÙ f(x)52x31ax21bx ·ð¤¤ çÜ° ¥´ÌÚUæÜ
function f(x)52x31ax21bx in the interval 1
[21, 1] ×ð´ çÕ´Îé c5 ÂÚU ÚUæðÜð ·¤æ Âý×ðØ Üæ»ê ãñ,
1 2
[21, 1] for the point c5 , then the value
2 Ìæð 2a1b ·¤æ ×æÙ ãñ Ñ
of 2a1b is :
(1) 1 (1) 1
(2) 21 (2) 21
(3) 2 (3) 2
(4) 22 (4) 22

3 x 4 x x x
74. If f (x )5  1  2 1 , x Î R, then the 74.
 5  5
ØçÎ f (x )5 3  1 4  2 1 , x Î R ãñ, Ìæð
5 5
equation f(x)50 has : â×è·¤ÚU‡æ f(x)50 ·¤æ/·ð¤ Ñ
(1) no solution (1) ·¤æð§ü ãÜ Ùãè´ ãñÐ
(2) one solution (2) °·¤ ãÜ ãñÐ
(3) two solutions (3) Îæð ãÜ ãñ´Ð
(4) more than two solutions (4) Îæð âð ¥çÏ·¤ ãÜ ãñ´Ð

English : 35 Set : 01 Hindi : 35 Set : 01

sin 8 x 2 cos8 x sin 8 x 2 cos8 x
75. ∫ (12 2 sin 2 x cos2 x ) dx is equal to : 75. ∫ (12 2 sin 2 x cos2 x ) dx ÕÚUæÕÚU ãñ Ñ
1 1
(1) sin 2x1c (1) sin 2x1c
2 2
1 1
(2) 2 sin 2x1c (2) 2 sin 2x1c
2 2
1 1
(3) 2 sin x1c (3) 2 sin x1c
2 2
(4) 2sin2 x1c (4) 2sin2 x1c

1 1
2 l n (11 2 x ) 2 l n (11 2 x )
76. The integral ∫ d x , equals : 76. â×æ·¤Ü ∫ d x , ÕÚUæÕÚU ãñ Ñ
0 11 4 x 2 0 11 4 x 2

p p
(1) ln 2 (1) ln 2
4 4
p p
(2) ln 2 (2) ln 2
8 8
p p
(3) ln 2 (3) ln 2
16 16
p p
(4) ln 2 (4) ln 2
32 32

77. Let A5{(x, y) : y2 [ 4x, y22x/24}. The 77. ×æÙæ A5{(x, y) : y2 [ 4x, y22x/24} ãñÐ
area (in square units) of the region A is : 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

English : 36 Set : 01 Hindi : 36 Set : 01

78. If the differential equation representing the 78. ØçÎ ©Ù âÖè ßëžææ𴠷𤠷é¤Ü, Áæð x-¥ÿæ ·¤æð ×êÜ çÕ´Îé
family of all circles touching x-axis at the ÂÚU SÂàæü ·¤ÚUÌð ãñ ´ , ·¤æ ¥ß·¤Ü â×è·¤ÚU‡æ
dy dy
origin is (x 22y 2) 5g(x) y, then g(x) (x22y2) 5g(x) y, ãñ, Ìæð g(x) ÕÚUæÕÚU ãñ Ñ
dx dx
equals :
1 1
(1) x (1) x
2 2
(2) 2x 2 (2) 2x 2
(3) 2x (3) 2x
1 2 1 2
(4) x (4) x
2 2

79. Let a and b be any two numbers satisfying 1 1 1
79. ×æÙ a ¥æñÚU b, 2
1 2 5 ·¤æð â´ÌécÅU ·¤ÚUÙð ßæÜè
4
1 1 1 a b
1 2 5 . Then, the foot of x y
a2
b 4 Îæð ⴁØæ°¡ ãñ´, Ìæð ¿ÚUÚðU¹æ, 1 51 ×êÜ çÕ´Îé âð
a b
perpendicular from the origin on the
x y ÇUæÜð »° Ü´Õ ·¤æ ÂæÎ, çSÍÌ ãñ Ñ
variable line, 1 51 , lies on :
a b
(1) °·¤ ¥çÌÂÚU ß ÜØ ÂÚU , çÁâ·¤æ Âý ˆ Øð · ¤
(1) a hyperbola with each ¥Ïü ¥ÿæ5 2 ãñÐ
semi-axis5 2 .
(2) °·¤ ¥çÌÚU  ÚU ß ÜØ ÂÚU , çÁâ·¤æ Âý ˆ Øð · ¤
(2) a hyperbola with each semi-axis52. ¥Ïü ¥ÿæ52 ãñÐ
(3) °·¤ ßëžæ ÂÚU, çÁâ·¤è ç˜æ’Øæ52 ãñÐ
(3) a circle of radius52
(4) °·¤ ßëžæ ÂÚU, çÁâ·¤è ç˜æ’Øæ5 2 ãñÐ
(4) a circle of radius5 2

English : 37 Set : 01 Hindi : 37 Set : 01

80. Given three points P, Q, R with P(5, 3) and 80. ÌèÙ çΰ »° çÕ´Îé¥æð´ P, Q, R ×ð´ P(5, 3) ãñ ÌÍæ R,
R lies on the x-axis. If equation of RQ is
x-¥ÿæ ÂÚU çSÍÌ ãñ Ð ØçÎ RQ ·¤æ â×è·¤ÚU ‡ æ
x22y52 and PQ is parallel to the x-axis,
then the centroid of DPQR lies on the x22y52 ãñ ÌÍæ PQ, x-¥ÿæ ·ð¤ â×æ´ÌÚU ãñ, Ìæð
line : DPQR ·¤æ ·ð´¤Îý·¤ çÁâ ÚðU¹æ ÂÚU çSÍÌ ãñ, ßã
(1) 2x1y2950 ãñ Ñ
(2) x22y1150 (1) 2x1y2950
(3) 5x22y50 (2) x22y1150
(4) 2x25y50 (3) 5x22y50
(4) 2x25y50
81. If the point (1, 4) lies inside the circle
x 2 1y 2 26x210y1p50 and the circle 81. ØçÎ çÕ´Îé (1, 4) ßëžæ x21y226x210y1p50
does not touch or intersect the coordinate ·ð¤ ¥‹ÌÑ Öæ» ×ð´ çSÍÌ ãñ ÌÍæ ßëžæ, çÙÎðüàææ´·¤ ¥ÿææð´ ·¤æð
axes, then the set of all possible values of p
is the interval : Ù Ìæð SÂàæü ·¤ÚUÌæ ãñ, ¥æñÚU Ù ãè ·¤æÅUÌæ ãññ, Ìæð p ·ð¤
(1) (0, 25) âÖè â´Öß ×æÙæð´ ·¤æ â×é‘¿Ø çِ٠¥Ì´ÚUæÜ ãñ Ñ
(2) (25, 39) (1) (0, 25)
(3) (9, 25) (2) (25, 39)
(4) (25, 29) (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
82. ØçÎ OB, °·¤ Îèƒæüßëžæ ·¤æ ¥Ïü ܃æé¥ÿæ ãñ, F1 ÌÍæ
F 1 B and F 2B is a right angle, then the F2 ©â·¤è ÙæçÖØæ¡ ãñ´ ÌÍæ F1B ÌÍæ F2B ·ð¤ Õè¿ ·¤æ
square of the eccentricity of the ellipse is : ·¤æð‡æ °·¤ â×·¤æð‡æ ãñ, Ìæð Îèƒæüßëžæ ·¤è ©ˆ·ð´¤ÎýÌæ ·¤æ
1 ß»ü ãñ Ñ
(1)
2 1
(1)
1 2
(2)
2 1
(2)
1 2
(3)
2 2 1
(3)
1 2 2
(4)
4 1
(4)
4

English : 38 Set : 01 Hindi : 38 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 ÌÍæ
x 21 y 2 2 z2 3 3 1 2
5 5 and
3 1 2 x 2 3 y 21 z2 2
5 5
x 2 3 y 21 z2 2 1 2 3
5 5
1 2 3 ·ð¤ Âýç̑ÀðUÎÙ çÕ´Îé âð ãæð ·¤ÚU ÁæÌæ ãñ, ÌÍæ ×êÜçÕ´Îé âð
and has the largest distance from the origin ¥çÏ·¤Ì× ÎêÚUè ÂÚU ãñ, ãñ Ñ
is :
(1) 7x12y14z554 (1) 7x12y14z554
(2) 3x14y15z549 (2) 3x14y15z549
(3) 4x13y15z550 (3) 4x13y15z550
(4) 5x14y13z557 (4) 5x14y13z557

84. A line in the 3-dimensional space makes 84. ç˜æçß×èØ ¥æ·¤æàæ (space) ×ð´ °·¤ ÚðU¹æ x ÌÍæ y,
p
an angle u  0 < u [  with both the ÎæðÙæ´ð ¥ÿææð´ ·ð¤ âæÍ ·¤æð‡æ u  0 < u [ p  ÕÙæÌè ãñ,
 2  2
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 :

 p  p
(1)  0 ,  (1)  0 , 
4 4
p p p p
(2)  6 , 3  (2)  6 , 3 

p p p p
(3)  4 , 2  (3)  4 , 2 

 p p  p p
(4)  ,  (4)  , 
3 2 3 2

English : 39 Set : 01 Hindi : 39 Set : 01

→ → → → → → → →
85. If ? a ?5 2, ? b ?5 3 and ?2 a 2 b ?5 5 , then 85. ØçÎ ? a ?5 2, ? b ?5 3 ÌÍæ ?2 a 2 b ?5 5 ãñ, Ìæð
→ → → →
?2 a 1 b ? equals : ?2 a 1 b ? ÕÚUæÕÚU ãñ Ñ
(1) 17 (1) 17
(2) 7 (2) 7
(3) 5 (3) 5
(4) 1 (4) 1

86. In a set of 2n distinct observations, each of 86. 2n çßçÖóæ Âýðÿæ‡ææð´ ·ð¤ â×é‘¿Ø ×ð´, ©Ù âÖè Âýðÿæ‡ææð´,
the observation below the median of all the Áæð âÖè Âýðÿæ‡ææð´ ·ð¤ ×æŠØ·¤ âð ·¤× ãñ´, ÂýˆØð·¤ ·¤æð 5 âð
observations is increased by 5 and each of Õɸæ çÎØæ »Øæ ÌÍæ àæðá âÖè Âðýÿæ‡ææð´ ×´ð ÂýˆØð·¤ ·¤æð 3
the remaining observations is decreased by âð ·¤× ·¤ÚU çÎØæ »Øæ, Ìæð Âýðÿæ‡ææð´ ·ð¤ Ù° â×é‘¿Ø ·¤æ
3. Then the mean of the new set of ×æŠØ Ñ
observations :
(1) increases by 1. (1) 1 âð Õɸ ÁæÌæ ãñÐ
(2) decreases by 1. (2) 1 âð ƒæÅU ÁæÌæ ãñÐ
(3) decreases by 2. (3) 2 âð ƒæÅU ÁæÌæ ãñÐ
(4) increases by 2. (4) 2 âð Õɸ ÁæÌæ ãñÐ

87. If A and B are two events such that 87. A ÌÍæ B Îæð °ðâè ƒæÅUÙæ°¡ ãñ´ ç·¤ P(AÈB)5P(AÇB)
P(AÈB)5P(AÇB), then the incorrect ãñ, Ìæð çِ٠·¤ÍÙæð´ ×ð´ âð ·¤æñÙ âæ ·¤ÍÙ »ÜÌ ãñ ?
statement amongst the following
statements is : (1) A ÌÍæ B â×â´ÖæçßÌ ã´ñ
(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 Set : 01

88. The number of values of a in [0, 2p] for 88. [0, 2p] ×ð´ a ·ð¤ ©Ù ×æÙæð´ ·¤è ⴁØæ, çÁÙ·ð¤ çÜ°
which 2 sin3 a27 sin2 a17 sin a52, is : 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

p1q p1q
89. If cosec u5
p2q
(p¹q¹0), then 89. ØçÎ cosec u5 (p¹q¹0) ãñ , Ìæð
p2q

 p u  p u
cot  1  is equal to :
 4 2 cot  1  ÕÚUæÕÚU ãñ Ñ
 4 2

p p
(1) (1)
q q

q q
(2) (2)
p p

(3) pq (3) pq
(4) pq (4) pq

90. The contrapositive of the statement “I go 90. ·¤ÍÙ ÒÒ×ñ´ S·ê¤Ü ÁæÌæ ã¡ê ØçÎ ßáæü Ùãè´ ãæðÌèÓÓ ·¤æ
to school if it does not rain” is : ÂýçÌÏÙæˆ×·¤ (Contrapositive) ·¤ÍÙ ãñ Ñ
(1) If it rains, I do not go to school. (1) ØçÎ ßáæü ãæðÌè ãñ, ×ñ´ S·ê¤Ü Ùãè´ ÁæÌæÐ
(2) If I do not go to school, it rains. (2) ØçÎ ×ñ´ S·ê¤Ü Ùãè´ ÁæÌæ, ßáæü ãæðÌè ãñÐ
(3) If it rains, I go to school. (3) ØçÎ ßáæü ãæðÌè ãñ, ×ñ´ S·ê¤Ü ÁæÌæ ã¡êÐ
(4) If I go to school, it rains. (4) ØçÎ ×ñ´ S·ê¤Ü ÁæÌæ ã¡ê, ßáæü ãæðÌè ãñÐ

-o0o- -o0o-

English : 41 Set : 01 Hindi : 41 Set : 01