JEE Main 2014 Question Paper 11 Apr

PART A — PHYSICS Öæ» A — ÖæñçÌ·¤ çߙææÙ
1. In terms of resistance R and time T, the 1. ÂýçÌÚUæðÏ R ¥æñÚU â×Ø T ·ð¤ ÂÎæð´ ×ð´, ¿éÕ·¤àæèÜÌæ m
m m
dimensions of ratio of the permeability °ß´ çßléÌàæèÜÌæ e ·ð¤ ¥ÙéÂæÌ ·¤è çß×æ ãñ Ñ
e e
m and permittivity e is :
(1) [RT22] (1) [RT22]
(2) [R2 T21] (2) [R2 T21]
(3) [R2] (3) [R2]
(4) [R2 T2] (4) [R2 T2]

2. The initial speed of a bullet fired from a 2. °·¤ ÚUæ§È¤Ü âð Îæ»è »§ü ÕéÜðÅU ·¤è ÂýæÚUçÖ·¤ ¿æÜ
rifle is 630 m/s. The rifle is fired at the 630 m/s ãñÐ ÜÿØ ·ð¤ SÌÚU ÂÚU ÜÿØ âð 700 m ÎêÚU
centre of a target 700 m away at the same ÜÿØ ·ð¤ ·ð¤‹Îý ÂÚU ÚUæ§È¤Ü Îæ»è ÁæÌè ãñÐ ÜÿØ ·¤æð
level as the target. How far above the Îæ»Ùð ·ð¤ çÜØð ÚUæ§È¤Ü ·¤æ çÙàææÙæ ÜÿØ ·ð¤ ·ð¤‹Îý âð
centre of the target the rifle must be aimed ç·¤ÌÙæ ª¤ÂÚU Ü»æÙæ ¿æçã°?
in order to hit the target ?
(1) 1.0 m (1) 1.0 m
(2) 4.2 m (2) 4.2 m
(3) 6.1 m (3) 6.1 m
(4) 9.8 m (4) 9.8 m

English : 1 Set : 11 Hindi : 1 Set : 11

3. A body of mass 5 kg under the action of 3. r ∧ ∧
çSÍÚU ÕÜ F5Fx i 1 Fy j ·ð¤ ·¤æÚU‡æ ÎýÃØ×æÙ
r ∧ ∧
constant force F5Fx i 1 Fy j has velocity
5 kg ·¤è °·¤ ßSÌé t50s ÂÚU ßð »
at t50s as
r
( ∧
)
∧
v 5 6 i 22 j m/s and at r
(
∧ ∧
)
v 5 6 i 22 j m/s âð »çÌàæèÜ ãñ ¥æñÚU t510 s
r ∧ r r ∧ r
t510 s as v516 j m/s. The force F is : ÂÚU ßð» v516 j m/s âð »çÌàæèÜ ãñÐ ÕÜ F ãñ :

(1) (23 i 14 j ) N
∧ ∧
(1) (23 i 14 j ) N
∧ ∧

 3 ∧ 4 ∧  3 ∧
(2) 2 i1 j N 4 ∧
 5 5  (2) 2 i1 j N
 5 5 

(3) (3 i 2 4 j ) N
∧ ∧
(3) (3 i 2 4 j ) N
∧ ∧

3∧ 4 ∧ 3∧
(4)  i 2 j N 4 ∧
5 5  (4)  i 2 j N
5 5 

English : 2 Set : 11 Hindi : 2 Set : 11

4. A small ball of mass m starts at a point A 4. ÎýÃØ×æÙ m ·¤è °·¤ ÀUæðÅUè »ð´Î çՋÎé A âð ¿æÜ vo âð
with speed v o and moves along a ÂýæÚUÖ ·¤ÚUÌè ãñ ¥æñÚU °·¤ ƒæáü‡æãèÙ ÂÍ AB ÂÚU
frictionless track AB as shown. The »çÌàæèÜ ãñ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ »Øæ ãñÐ ÂÍ BC
track BC has coefficient of friction m. The ·¤æ ƒæáü‡æ »é‡ææ¡·¤ m ãñÐ »ð´Î C ÂÚU ÎêÚUè L ¿ÜÙð ·ð¤
ball comes to stop at C after travelling a Âà¿æÌ÷ L¤·¤ ÁæÌè ãñ Áãæ¡ L ãñ :
distance L which is :

2h v2
(1) 1 o
2h v2 m 2m g
(1) 1 o
m 2m g
h v2
(2) 1 o
h v2 m 2m g
(2) 1 o
m 2m g
h v2
(3) 1 o
h v2 2m mg
(3) 1 o
2m mg
h v2
(4) 1 o
h v2 2m 2m g
(4) 1 o
2m 2m g

English : 3 Set : 11 Hindi : 3 Set : 11

5. The average mass of rain drops is 5. ßáæü ·¤è Õê´Îæð´ ·¤æ ¥æñâÌ ÎýÃØ×æÙ 3.031025 kg ãñ
3.031025 kg and their average terminal ¥æñÚU ©Ù·¤æ ¥æñâÌ âè×æ‹Ì ßð» 9 m/s ãñÐ çÁâ
velocity is 9 m/s. Calculate the energy SÍæÙ ÂÚU °·¤ ßáü ×ð´ 100 cm ßáæü ãæðÌè ãñ ©â SÍæÙ
transferred by rain to each square metre ·ð¤ ÂýçÌ ß»ü ×èÅUÚU ÂëcÆU ÂÚU ßáæü mæÚUæ SÍæÙæ‹ÌçÚUÌ ª¤Áæü
of the surface at a place which receives 100 ·¤è »‡æÙæ ·¤èçÁ°Ð
cm of rain in a year. (1) 3.53105 J
(1) 3.53105 J (2) 4.053104 J
(2) 4.053104 J (3) 3.03105 J
(3) 3.03105 J (4) 9.03104 J
(4) 9.03104 J 6. ܐÕæ§ü L ·¤è °·¤ ÂÌÜè ÀUǸ ·¤æ ÂýçÌ §·¤æ§ü ܐÕæ§ü
6. A thin bar of length L has a mass per unit ÎýÃØ×æÙ l ãñ Áæð ç·¤ °·¤ çâÚðU âð ÎêÚUè ·ð¤ ¥ÙéâæÚU
length l, that increases linearly with ÚñUç¹·¤ÌÑ ÕɸÌæ ãñÐ ØçÎ §â·¤æ ·é¤Ü ÎýÃØ×æÙ M ãñ
distance from one end. If its total mass ¥æñÚU ãË·ð¤ çâÚðU ÂÚU ÂýçÌ §·¤æ§ü ܐÕæ§ü ÎýÃØ×æÙ lo ãñ,
is M and its mass per unit length at the ÌÕ ãË·ð¤ çâÚðU âð ÎýÃØ×æÙ ·ð¤‹Îý ·¤è ÎêÚUè ãñ Ñ
lighter end is lo, then the distance of the
L l L2
centre of mass from the lighter end is : (1) 2 o
2 4M
L l L2 l L2
(1) 2 o L
1 o
2 4M (2)
3 8M
L l L2 l L2
(2) 1 o L
1 o
3 8M (3)
3 4M
L l L2 l L2
(3) 1 o 2L
2 o
3 4M (4)
3 6M
2L l L2
(4) 2 o
3 6M

English : 4 Set : 11 Hindi : 4 Set : 11

7. From a sphere of mass M and radius R, a 7. ç˜æ’Øæ R °ß´ Îý à Ø×æÙ M ·ð ¤ °·¤ »æð Ü ð âð ,
smaller sphere of radius R 2 is carved out ç˜æ’Øæ R 2 ·¤æ °·¤ ÀUæðÅUæ »æðÜæ §â Âý·¤æÚU çÙ·¤æÜ
such that the cavity made in the original çÜØæ ÁæÌæ ãñ ç·¤ ×êÜ »æðÜð ×ð´ ÕÙè »éãæ §â·ð¤ ·ð¤‹Îý
sphere is between its centre and the °ß´ ÂçÚUçÏ ·ð¤ Õè¿ ãñ (翘æ Îð¹ð´)Ð ç¿˜æ ·ð¤ çߋØæâ
periphery. (See figure). For the ·ð¤ ¥ÙéâæÚU ÁÕ ×êÜ »æðÜð ·ð¤ ·ð¤‹Îý ¥æñÚU ãÅUæØð »Øð
configuration in the figure where the »æðÜð ·ð¤ ·ð¤‹Îý ·ð¤ Õè¿ ÎêÚUè 3R ãñ, ÌÕ ÎæðÙæð »æðÜæð´ ·ð¤
distance between the centre of the original Õè¿ »éL¤ˆßæ·¤áü‡æ ÕÜ ãñ Ñ
sphere and the removed sphere is 3R, the
gravitational force between the two
spheres is :

41 GM 2
(1)
3600 R 2

41 GM 2
41 GM 2 (2)
(1) 450 R 2
3600 R 2
59 GM 2
41 GM 2 (3)
(2) 450 R 2
450 R 2
GM 2
59 GM 2 (4)
(3) 2 225 R 2
450 R

GM 2
(4)
225 R 2

English : 5 Set : 11 Hindi : 5 Set : 11

8. The Bulk moduli of Ethanol, Mercury and 8. °ÍÙæòÜ, ÂæÚUæ °ß´ ÂæÙè ·ð¤ ¥æØÌÙ ÂýˆØæSÍÌæ »é‡ææ¡·¤
water are given as 0.9, 25 and 2.2 109 Nm22 ·¤è §·¤æ§ü ×ð´ ·ý¤×àæÑ 0.9, 25 °ß´ 2.2
respectively in units of 109 Nm22. For a çÎØð ãéØð ãñ´Ð ÎæÕ ·ð¤ çÎØð ×æÙ ·ð¤ çÜ°, ¥æØÌÙ ×ð´
given value of pressure, the fractional 9
ç֋Ùæˆ×·¤ â´ÂèǸ٠ãñÐ §Ù ÌèÙ Îýßæð´ ·ð¤ çÜ°
9 V
compression in volume is . Which of
V 9
·ð¤ ÕæÚðU ×ð´ çِÙçÜç¹Ì ·¤ÍÙæð´ ×ð´ âð ·¤æñÙ âæ
9 V
the following statements about for
V âãè ãñ?
these three liquids is correct ?
(1) Ethanol > Water > Mercury (1) °ÍÙæòÜ > ÂæÙè > ÂæÚUæ
(2) Water > Ethanol > Mercury (2) ÂæÙè > °ÍÙæòÜ > ÂæÚUæ
(3) Mercury > Ethanol > Water (3) ÂæÚUæ > °ÍÙæòÜ > ÂæÙè
(4) Ethanol > Mercury > Water (4) °ÍÙæòÜ > ÂæÚUæ > ÂæÙè

9. A tank with a small hole at the bottom has 9. ÌÜè ×ð´ °·¤ ÀUæðÅðU çÀUÎý ßæÜð Åñ´U·¤ ·¤æð ÂæÙè °ß´ ç×^è ·ð¤
been filled with water and kerosene ÌðÜ (¥æÂðçÿæÌ ƒæÙˆß 0.8) âð ÖÚUæ »Øæ ãñÐ ÂæÙè ·¤è
(specific gravity 0.8). The height of water ª¡¤¿æ§ü 3 m ãñ ¥æñÚU ç×^è ·ð¤ ÌðÜ ·¤è 2 mÐ ÁÕ çÀUÎý
is 3 m and that of kerosene 2 m. When the ·¤æð ¹æðÜ çÎØæ ÁæÌæ ãñ, ÌÕ çÙ·¤ÜÙð ßæÜð Îýß ·¤è
hole is opened the velocity of fluid coming ¿æÜ Ü»Ö» ãæð » è : (g510 ms 22 Üð ¥æñ Ú U
out from it is nearly : (take g510 ms22 ÂæÙè ·¤æ ƒæÙˆß 5103 kg m23)
and density of water 5103 kg m23)
(1) 10.7 ms21 (1) 10.7 ms21
(2) 9.6 ms21 (2) 9.6 ms21
(3) 8.5 ms21 (3) 8.5 ms21
(4) 7.6 ms21 (4) 7.6 ms21

English : 6 Set : 11 Hindi : 6 Set : 11

10. An air bubble of radius 0.1 cm is in a liquid 10. ÂëcÆU ÌÙæß 0.06 N/m ¥æñÚU ƒæÙˆß 103 kg/m3
having surface tension 0.06 N/m and ßæÜð °·¤ Îýß ×ð´ ç˜æ’Øæ 0.1 cm ·¤æ °·¤ ßæØé ·¤æ
density 103 kg/m3. The pressure inside ÕéÜÕéÜæ ãñÐ ÕéÜÕéÜð ·ð¤ ¥‹ÎÚU ÎæÕ ßæØé×´ÇUÜèØ ÎæÕ
the bubble is 1100 Nm22 greater than the âð 1100 Nm22 ¥çÏ·¤ ãñÐ Îýß ·ð¤ ÂëcÆU âð ç·¤â
atmospheric pressure. At what depth is »ãÚUæ§ü ÂÚU ÕéÜÕéÜæ ãñ? (g59.8 ms22)
the bubble below the surface of the
liquid ? (g59.8 ms22)
(1) 0.1 m (1) 0.1 m
(2) 0.15 m (2) 0.15 m
(3) 0.20 m (3) 0.20 m
(4) 0.25 m (4) 0.25 m
11. A hot body, obeying Newton’s law of 11. ‹ØêÅUÙ ·ð¤ àæèÌÜÙ çÙØ× ·¤æ ÂæÜÙ ·¤ÚUÌè ãé§ü °·¤ »×ü
cooling is cooling down from its peak value ßSÌé ¥ÂÙð àæèáü ÌæÂ×æÙ 808C âð ÂçÚUßðàæ ÌæÂ×æÙ
808C to an ambient temperature of 308C. 308C Ì·¤ Æ´UÇUè ãæðÌè ãñÐ Øã 808C âð 408C Ì·¤
It takes 5 minutes in cooling down from Æ´UÇUæ ãæðÙð ×ð´ 5 ç×ÙÅU ÜðÌè ãñÐ Øã 628C âð 328C
808C to 408C. How much time will it take Ì·¤ Æ´UÇæ ãæðÙð ×ð´ ç·¤ÌÙæ â×Ø Üð»è?
to cool down from 628C to 328C ? (çÎØæ ãñ ln 250.693, ln 551.609)
(Given ln 250.693, ln 551.609) (1) 3.75 ç×ÙÅU
(1) 3.75 minutes (2) 8.6 ç×ÙÅU
(2) 8.6 minutes (3) 9.6 ç×ÙÅU
(3) 9.6 minutes (4) 6.5 ç×ÙÅU
(4) 6.5 minutes

English : 7 Set : 11 Hindi : 7 Set : 11

12. During an adiabatic compression, 830 J of 12. °·¤ L¤hæððc× â´ÂèǸ٠·ð¤ ÎæñÚUæÙ, °·¤ çmÂÚU×æ‡æé·¤ ¥æÎàæü
work is done on 2 moles of a diatomic ideal »ñâ ·ð¤ 2 ×æðÜ ·¤æ ¥æØÌÙ 50% ·¤× ç·¤Øð ÁæÙð ×ð´
gas to reduce its volume by 50%. The 830 J ·¤æ ·¤æØü ·¤ÚUÙæ ÂǸÌæ ãñÐ §â·ð¤ ÌæÂ×æÙ ×ð´
change in its temperature is nearly : ÂçÚUßÌüÙ ãñ ֻܻ Ñ (R58.3 JK21 mol21)
(R58.3 JK21 mol21)
(1) 40 K (1) 40 K
(2) 33 K (2) 33 K
(3) 20 K (3) 20 K
(4) 14 K (4) 14 K

English : 8 Set : 11 Hindi : 8 Set : 11

13. An ideal monoatomic gas is confined in a 13. °·¤ ÕðÜÙ ×ð´ ¥ÙéÂýSÍ ·¤æÅU 8.031023 m2 ·ð¤ °·¤
cylinder by a spring loaded piston of cross ·¤×æÙèÎæÚU ÖæçÚUÌ çÂSÅUÙ mæÚUæ °·¤ ¥æÎàæü °·¤ÂÚU×æ‡æé·¤
section 8.031023 m2. Initially the gas is at »ñâ ·¤æð ÚU¹æ »Øæ ãñÐ ÂýæÚUÖ ×ð´ »ñâ 300 K ÂÚU ãñ ¥æñÚU
300K and occupies a volume of 2.431023 m3 ¥æØÌÙ ÚU¹Ìè ãñ´ ¥æñÚU ·¤×æÙè ¥ÂÙè
2.4310 23 m 3 and the spring is in its çßoýæ´çÌ ¥ßSÍæ ×ð´ ãñ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ »Øæ ãñÐ
relaxed state as shown in figure. The gas is »ñâ ·¤æð °·¤ ÀUæðÅðU ãèÅUÚU mæÚUæ ÌÕ Ì·¤ »ÚU×U ç·¤Øæ ÁæÌæ
heated by a small heater until the piston ãñ ÁÕ Ì·¤ ç·¤ çÂSÅUÙ ÏèÚðU âð 0.1 m ·¤è »çÌ Ù ·¤ÚU
moves out slowly by 0.1 m. The force ÜðÐ ·¤×æÙè ·¤æ ÕÜ çÙØÌæ¡·¤ 8000 N/m ãñ ¥æñÚU
constant of the spring is 8000 N/m and the ßæØé×´ÇUÜèØ ÎæÕ 1.03105 N/m2 ãñÐ ÕðÜÙ °ß´
atmospheric pressure is 1.03105 N/m2. çÂSÅUÙ ª¤c×æÚUæÏð è ãñ́Ð çÂSÅUÙ °ß´ ·¤×æÙè ÎýÃØ×æÙçßãèÙ
The cylinder and the piston are thermally ãñ ¥æñÚU çÂSÅUÙ °ß´ ÕðÜÙ ·ð¤ Õè¿ ·¤æð§ü ƒæáü‡æ Ùãè´ ãñÐ
insulated. The piston and the spring are »ñâ ·¤æ ¥ç‹Ì× ÌæÂ×æÙ ãæð»æ Ñ
massless and there is no friction between (ãèÅUÚU ·ð¤ ÜèÇU ÌæÚUæð´ â𠪤Áæü ·¤è ãæçÙ Ù»‡Ø ×æÙð
the piston and the cylinder. The final ¥æñÚU ãèÅUÚU ·é¤‡ÇUÜè ·¤è ª¤c×æÏæçÚUÌæ Öè Ù»‡Ø ãñ) :
temperature of the gas will be :
(Neglect the heat loss through the lead
wires of the heater. The heat capacity of
the heater coil is also negligible)

(1) 300 K
(2) 800 K
(3) 500 K
(4) 1000 K
(1) 300 K
(2) 800 K
(3) 500 K
(4) 1000 K

English : 9 Set : 11 Hindi : 9 Set : 11

14. The angular frequency of the damped 14. °·¤ ¥ß×ç‹ÎÌ ÎæðÜ·¤ ·¤è ·¤æð‡æèØ ¥æßëçžæ §ââð Îè
oscillator is given by, ÁæÌè ãñ ,
k r2  k r2 
v5  2  where k is the spring v5  2  Áãæ¡ k ·¤×æÙè çSÍÚUæ¡·¤ ãñ,
m 4m 2  m 4m 2 
constant, m is the mass of the oscillator and m ÎæðÜ·¤ ·¤æ ÎýÃØ×æÙ ãñ ¥æñÚU r ¥ß׋ÎÙ çSÍÚUæ¡·¤ ãñÐ

r2
r is the damping constant. If the ratio ØçÎ ¥ÙéÂæÌ 5 8% ãñ, ÌÕ ¥Ùß×ç‹ÎÌ ÎæðÜ·¤
mk
r2
·ð¤ ×é·¤æÕÜð ¥æßÌü ·¤æÜ ×ð´ ÂçÚUßÌü٠ֻܻ ãæð»æ Ñ
is 8%, the change in time period
mk
compared to the undamped oscillator is
approximately as follows :
(1) increases by 1% (1) 1%âð ßëçh ãæð»è
(2) increases by 8% (2) 8%âð ßëçh ãæð»è
(3) decreases by 1% (3) 1%âð ƒæÅðU»æ
(4) decreases by 8% (4) 8%âð ƒæÅðU»æ

15. Two factories are sounding their sirens 15. Îæð Èñ¤€ÅUçÚUØæ¡ ¥ÂÙð âæØÚUÙ 800 Hz ÂÚU ŠßçÙÌ ·¤ÚUÌè
at 800 Hz. A man goes from one factory ãñ´Ð °·¤ ÃØç€Ì 2 m/s ·¤è ¿æÜ âð °·¤ Èñ¤€ÅUÚUè âð
to other at a speed of 2 m/s. The velocity Îê â ÚU è Èñ ¤ €ÅÚè Ì·¤ ÁæÌæ ãñ Ð ŠßçÙ ·¤æ ßð »
of sound is 320 m/s. The number of beats 320 m/s ãñÐ °·¤ âð·´¤ÇU ×ð´ ÃØç€Ì mæÚUæ âéÙè »§ü
heard by the person in one second will çßS‹Îæð´ ·¤è ⴁØæ ãñ Ñ
be :
(1) 2 (1) 2
(2) 4 (2) 4
(3) 8 (3) 8
(4) 10 (4) 10

English : 10 Set : 11 Hindi : 10 Set : 11

16. A cone of base radius R and height h is 16. ¥æÏæÚU ç˜æ•Øæ R °ß´ ª¡¤¿æ§ü h ßæÜæ °·¤ àæ´·é¤ ¥æÏæÚU
→ →
located in a uniform electric field E ·ð¤ â×æ‹ÌÚU °·¤â×æÙ çßléÌ ÿæð˜æ E ×ð´ çSÍÌ ãñÐ
parallel to its base. The electric flux àæ´·é¤ ×ð´ Âýßðàæ ·¤ÚUÙð ßæÜæ çßléÌ Ü€â ãñ :
entering the cone is :

1 1
(1) EhR (1) EhR
2 2

(2) EhR (2) EhR

(3) 2EhR (3) 2EhR

(4) 4EhR (4) 4EhR

English : 11 Set : 11 Hindi : 11 Set : 11

17. A parallel plate capacitor is made of two 17. °·¤ â×æ‹ÌÚU ŒÜðÅU â´ÏæçÚU˜æ Îæð ŒÜðÅUæð´ âð ÕÙæ ãñ çÁÙ·¤è
plates of length l, width w and separated ܐÕæ§ü l, ¿æñÇUæ§ü w ãñ´ ¥æñÚU °·¤ ÎéâÚðU âð d ÎêÚUè ÂÚU
by distance d. A dielectric slab (dielectric ãñÐ °·¤ ÂÚUæßñléÌ Â^è (ÂÚUæßñléÌæ´·¤ K) Áæð ç·¤ ŒÜðÅUæð´
constant K) that fits exactly between the ·ð¤ Õè¿ ÆUè·¤ âð â×æ ÁæÌè ãñ, ·¤æð ŒÜðÅUæð´ ·¤è çâÚðU ·ð¤
plates is held near the edge of the plates. Âæâ ·¤Ç¸ ·¤ÚU ÚU¹æ ãé¥æ ãñÐ §âð â´ÏæçÚU˜æ ·ð¤ ¥‹ÎÚU
It is pulled into the capacitor by a force ∂U
ÕÜ F 5 2 mæÚUæ ¹è´¿æ ÁæÌæ ãñ Áãæ¡ U â´ÏæçÚU˜æ
∂U ∂x
F5 2 where U is the energy of the
∂x ·¤è ÌÕ ª¤Áæü ãñ ÁÕ ÂÚUæßñléÌ â´ÏæçÚU˜æ ·ð¤ ¥‹ÎÚU x ÎêÚUè
capacitor when dielectric is inside the ÂÚU ãñÐ (翘æ Îð¹ð´)Ð ØçÎ â´ÏæçÚU˜æ ÂÚU ¥æßðàæ Q ãñ,
capacitor up to distance x (See figure). If
ÌÕ ÂÚUæßñléÌ ÂÚU ÕÜ, ÁÕ ßã çâÚðU ·ð¤ Âæâ ãñ, ãæð»æ Ñ
the charge on the capacitor is Q then the
force on the dielectric when it is near the
edge is :

Q2 d
(1) K
2 wl 2 eo
Q2 d
(1) K Q2 w
2 wl 2 eo (2) ( K21)
2 dl 2 eo
Q2 w
(2) ( K21) Q2 d
2 dl 2 eo (3) ( K21)
2 wl 2 eo
Q2 d
(3) ( K21) Q2 w
2 wl 2 eo (4) K
2 dl 2 eo
Q2 w
(4) K
2 dl 2 eo

English : 12 Set : 11 Hindi : 12 Set : 11

18. In the circuit shown, current (in A) 18. ÎàææüØð »Øð ÂçÚUÂÍ ×ð´, 50 V °ß´ 30 V ÕñÅUçÚUØæð´ ×ð´
through the 50 V and 30 V batteries are, ÏæÚUæ (A ×ð´) ·ý¤×àæÑ ãñ´ Ñ
respectively :

(1) 2.5 and 3 (1) 2.5 °ß´ 3
(2) 3.5 and 2 (2) 3.5 °ß´ 2
(3) 4.5 and 1 (3) 4.5 °ß´ 1
(4) 3 and 2.5 (4) 3 °ß´ 2.5
19. Three straight parallel current carrying 19. ÌèÙ âèÏð â×æ‹ÌÚU ÏæÚUæ ÂýßæçãÌ ¿æÜ·¤ 翘æ ×ð´ ÎàææüØð
conductors are shown in the figure. The »Øð ãñ´Ð ܐÕæ§ü 25 cm ·ð¤ Õè¿ ßæÜð ¿æÜ·¤ mæÚUæ
force experienced by the middle conductor ¥ÙéÖß ç·¤Øæ »Øæ ÕÜ ãñ :
of length 25 cm is :

(1) 331024 N toward right (1) 331024 N Îæ¡Øè ¥æðÚU
(2) 631024 N toward left (2) 631024 N Õæ¡Øè ¥æðÚU
(3) 931024 N toward left (3) 931024 N Õæ¡Øè ¥æðÚU
(4) Zero (4) àæê‹ØU

English : 13 Set : 11 Hindi : 13 Set : 11

20. Three identical bars A, B and C are made 20. ÌèÙ âßüâ×M¤Âè ÀUǸð A, B °ß´ C ÌèÙ çßç֋Ù
of different magnetic materials. When ¿éÕ·¤èØ ÂÎæÍæðZ âð ÕÙè ãñ´Ð ÁÕ §‹ãð´ °·¤ °·¤â×æÙ
kept in a uniform magnetic field, the field ¿éÕ·¤èØ ÿæð˜æ ×ð´ ÚU¹æ ÁæÌæ ãñ, ÌÕ §Ù ÂÚU ÿæð˜æ ÚðU¹æ°¡
lines around them look as follows : çِ٠Âý·¤æÚU âð çιÌè ãñ´ Ñ

Make the correspondence of these bars §Ù ÀUÇæ¸ ´ð ·ð¤ ÂÎæÍæðZ ·¤æð ÂýçÌ¿éÕ·¤èØ (D), Üæðã ¿éÕ·¤èØ
with their material being diamagnetic (D), (F) °ß´ ¥Ùé¿éÕ·¤èØ (P) ¥æÏæÚU ÂÚU â´»Ì ·¤ÚðU´ :
ferromagnetic (F) and paramagnetic (P) :
(1) A ↔ D, B ↔ P, C ↔ F (1) A ↔ D, B ↔ P, C ↔ F
(2) A ↔ F, B ↔ D, C ↔ P (2) A ↔ F, B ↔ D, C ↔ P
(3) A ↔ P, B ↔ F, C ↔ D (3) A ↔ P, B ↔ F, C ↔ D
(4) A ↔ F, B ↔ P, C ↔ D (4) A ↔ F, B ↔ P, C ↔ D

21. A coil of circular cross-section having 21. 1000 Èð¤ÚðU °ß´ 4 cm2 Ȥܷ¤ ÿæð˜æÈ¤Ü ßæÜè °·¤
1000 turns and 4 cm2 face area is placed ßëžæèØ ¥ÙéÂýSÍ ·¤æÅU ·¤è ·é´¤ÇUÜè ·¤æð §â·ð¤ ¥ÿæ ·ð¤
with its axis parallel to a magnetic field â×æ‹ÌÚU °·¤ ¿éÕ·¤èØ ÿæð˜æ ×ð´ ÚU¹æ »Øæ ãñ Áæð ç·¤
which decreases by 10 22 Wb m 22 in 1022 Wb m22 0.01 s ×𴠃æÅU ÁæÌæ ãñÐ ·é´¤‡ÇUÜè
0.01 s. The e.m.f. induced in the coil is : ×ð´ ÂýðçÚUÌ çßléÌ ßæã·¤ ÕÜ ãñ Ñ
(1) 400 mV (1) 400 mV
(2) 200 mV (2) 200 mV
(3) 4 mV (3) 4 mV
(4) 0.4 mV (4) 0.4 mV

English : 14 Set : 11 Hindi : 14 Set : 11

22. An electromagnetic wave of frequency 22. ¥æßëçžæ 131014 ãÅüUÁ ·¤è °·¤ çßléÌ ¿éÕ·¤èØ ÌÚ´U»
131014 hertz is propagating along z - axis. z - ¥ÿæ ÂÚU â´¿ÚU‡æ ·¤ÚU ÚUãè ãñÐ çßléÌ ÿæð˜æ ·¤æ
The amplitude of electric field is 4 V/m. If ¥æØæ× 4 V/m ãñÐ ØçÎ
e o58.8310 212 C 2/N-m 2, then average eo58.8310212 C2/N-m2, ÌÕ çßléÌ ÿæð˜æ ·¤æ
energy density of electric field will ¥æñâÌ ª¤Áæü ƒæÙˆß ãæð»æ :
be :
(1) 35.2310210 J/m3 (1) 35.2310210 J/m3
(2) 35.2310211 J/m3 (2) 35.2310211 J/m3
(3) 35.2310212 J/m3 (3) 35.2310212 J/m3
(4) 35.2310213 J/m3 (4) 35.2310213 J/m3
23. An object is located in a fixed position 23. °·¤ ÂÎðü ·ð¤ âæ×Ùð °·¤ çSÍÚU çSÍçÌ ×ð´ °·¤ ßSÌé çSÍÌ
in front of a screen. Sharp image is ãñÐ °·¤ ÂÌÜð Üð‹â ·¤è 10 cm ÎêÚUè ÂÚU Îæð çSÍçÌØæð´
obtained on the screen for two positions âð ÂÎðü ÂÚU SÂcÅU ÂýçÌçÕÕ ÕÙÌð ãñ´Ð ÎæðÙæð´ çSÍçÌØæð´ ×ð´
of a thin lens separated by 10 cm. The size ÂýçÌçՐÕæ𴠷𤠥淤æÚU ·¤æ ¥ÙéÂæÌ 3 : 2 ãñÐ ßSÌé °ß´
of the images in two situations are in the ÂÎðü ·ð¤ Õè¿ ÎêÚUè €Øæ ãñ?
ratio 3 : 2. What is the distance between
the screen and the object ?
(1) 124.5 cm (1) 124.5 cm
(2) 144.5 cm (2) 144.5 cm
(3) 65.0 cm (3) 65.0 cm
(4) 99.0 cm (4) 99.0 cm

English : 15 Set : 11 Hindi : 15 Set : 11

24. Two monochromatic light beams of 24. ÌèßýÌæ 16 °ß´ 9 §·¤æ§ü ßæÜè Îæð °·¤ß‡æèü Âý·¤æàæ Âé´Áæð´
intensity 16 and 9 units are interfering. ·ð¤ Õè¿ ÃØçÌ·¤ÚU‡æ ãæð ÚUãæ ãñÐ ÂçÚU‡ææ×è ç¿˜æ ·ð¤
The ratio of intensities of bright and dark ©ÁÜð ¥æñÚU ·¤æÜð çãSâæð´ ·¤è ÌèßýÌæ¥æð´ ·¤æ ¥ÙéÂæÌ
parts of the resultant pattern is : ãæð»æ Ñ
16 16
(1) (1)
9 9

4 4
(2) (2)
3 3

7 7
(3) (3)
1 1

49 49
(4) (4)
1 1

25. In a compound microscope the focal length 25. °·¤ â´Øé€Ì âêÿ×Îàæèü ×ð´ ¥çÖÎëàØ·¤ Üð‹â ·¤è Ȥæð·¤â
of objective lens is 1.2 cm and focal length ܐÕæ§ü 1.2 cm ¥æñÚU Ùðç˜æ·¤æ ·¤è Ȥæð·¤â ܐÕæ§ü
of eye piece is 3.0 cm. When object is kept 3.0 cm ãñ´Ð ÁÕ ßSÌé ·¤æð ¥çÖÎëàØ·¤ ·ð¤ âæ×Ùð
at 1.25 cm in front of objective, final image 1.25 cm ·¤è ÎêÚUè ÂÚU ÚU¹æ ÁæÌæ ãñ, ÌÕ ¥ç‹Ì×
is formed at infinity. Magnifying power ÂýçÌçÕÕ ¥Ù‹Ì ÂÚU ÕÙÌæ ãñÐ â´Øé€Ì âêÿ×Îàæèü ·¤è
of the compound microscope should be : ¥æßÏüÙ àæç€Ì ãæðÙè ¿æçã° Ñ
(1) 200 (1) 200
(2) 100 (2) 100
(3) 400 (3) 400
(4) 150 (4) 150

English : 16 Set : 11 Hindi : 16 Set : 11

26. A photon of wavelength l is scattered 26. çßoýæ× ¥ßSÍæ ·ð¤ °·¤ §Üð€ÅþUæÙ âð ÌÚ´U»ÎñƒØü l ·¤æ
from an electron, which was at rest. The °·¤ ȤæðÅUæÙ Âý·¤èç‡æüÌ ãæðÌæ ãñÐ ÌÚ´U»ÎñƒØü SÍæÙæ‹ÌÚU
wavelength shift Dl is three times of l and Dl ÌÚ´U»ÎñƒØü l ·¤æ ÌèÙ »éÙæ ãñ ¥æñÚU Âý·¤è‡æüÙ ·¤æð‡æ
the angle of scattering u is 608. The angle u5608 ãñÐ §Üð€ÅþUæÙ f ·¤æð‡æ ÂÚU ÂýçÌçÿæŒÌ ãæðÌæ ãñÐ
at which the electron recoiled is f. The tan f ·¤æ ×æÙ ãñ Ñ (§Üð€ÅþUæÙ ·¤è ¿æÜ Âý·¤æàæ ·¤è
value of tan f is : (electron speed is much ¿æÜ âð ·¤æÈ¤è ·¤× ãñ)
smaller than the speed of light)
(1) 0.16 (1) 0.16
(2) 0.22 (2) 0.22
(3) 0.25 (3) 0.25
(4) 0.28 (4) 0.28

27. A radioactive nuclei with decay constant 27. 100 ÙæçÖ·¤ ÂýçÌ âñç·¤‡ÇU ·¤è çSÍÚU ÎÚU âð ÿæØçSÍÚUæ¡·¤
0.5/s is being produced at a constant rate 0.5/s ßæÜð ÚðUçÇUØæðâç·ý¤Ø ÙæçÖ·¤ ©ˆÂ‹Ù ãæð ÚUãð ãñ´Ð
of 100 nuclei/s. If at t50 there were no ØçÎ t50 ÂÚU °·¤ Öè Ùæç×·¤ ©ÂçSÍÌ Ùãè´ Íæ, ÌÕ
nuclei, the time when there are 50 nuclei 50 ÙæçÖ·¤ ©ˆÂ‹Ù ãæðÙð ×ð´ Ü»æ â×Ø ãñ Ñ
is :
(1) 1s (1) 1s

4 4
(2) 2 ln   s (2) 2 ln   s
3 3
(3) ln 2 s (3) ln 2 s

4 4
(4) ln   s (4) ln   s
3 3

English : 17 Set : 11 Hindi : 17 Set : 11

28. A Zener diode is connected to a battery 28. °·¤ ÁðÙÚU ÇUæØæðÇU ·¤æð °·¤ ÕñÅUÚUè °ß´ °·¤ ÜæðÇU âð
and a load as shown below : ÁæðÇ¸æ »Øæ ãñ Áñâæ ç·¤ ÂçÚUÂÍ ×ð´ ÎàææüØæ »Øæ ãñÐ ÏæÚUæØð´
The currents I, IZ and IL are respectively I, IZ °ß´ IL ·ý¤×àæÑ ãñ´ Ñ

(1) 15 mA, 5 mA, 10 mA (1) 15 mA, 5 mA, 10 mA

(2) 15 mA, 7.5 mA, 7.5 mA (2) 15 mA, 7.5 mA, 7.5 mA

(3) 12.5 mA, 5 mA, 7.5 mA (3) 12.5 mA, 5 mA, 7.5 mA

(4) 12.5 mA, 7.5 mA, 5 mA (4) 12.5 mA, 7.5 mA, 5 mA

English : 18 Set : 11 Hindi : 18 Set : 11

29. Match the List - I (Phenomenon associated 29. âê¿è-I (çßléÌ ¿éÕ·¤èØ çßç·¤ÚU‡æ âð âÕh ƒæÅUÙæ°¡)
with electromagnetic radiation) with ·¤æð âê¿è-II (çßléÌ ¿éÕ·¤èØ SÂð€ÅþU× ·¤æ Öæ») âð
List - II (Part of electromagnetic spectrum) âé×ðçÜÌ ·¤èçÁ° ¥æñÚU âêç¿Øæð́ ·ð¤ Ùè¿ð çÎØð »Øð çß·¤ËÂæð́
and select the correct code from the ×´ð âð âãè çß·¤Ë ¿éçÙ° Ñ
choices given below the lists :

List - I List - II ÇÏ¤Í - I ÇÏ¤Í - II
Visible
I Doublet of sodium A
radiation
I ÇËÕ̬U½¼ œ‰Ë Ìmœ‰ A ³ÐŽ ÌÄ̜‰¿UøË

Wavelength
corresponding to ǃ§ÏøËá ǼÌcªU ¼Õ™ Ǽ³ÖÌ؉
II temperature associated B Microwave II ÌÄ̜‰¿UøË œ‰Õ‰»¿UÕU ÈËÕ¾Õ ÇÕ ÇƒºÌh± B ÇÏÏä¼ ±¿U™U
with the isotropic ±Ë§¼Ë¾ œ‰Õ‰ Ǚ™ ± ±¿U™U ³Öç½á
radiation filling all space

Wavelength emitted by Šü±¿U±Ë¿Uœ‰Í½ ŠËœ‰ËÅË ¼Õ™ §¿U¼ËøËÎ
Short
III atomic hydrogen in C III Èˌ¬UãUËÕ¦¾ mË¿UË ŽíÇ̦ᱠC ÁìËÎ ¿UÕU̬U½ËÕ ±¿U™U Õ
radiowave
interstellar space ±¿U™U ³Öç½á
Wavelength of radiation
Èˌ¬UãUËÕ¦¾ ¼Õ™ ³ËÕ Ç¼Í§ ‰¦Ëá S±¿U˙Õ
IV arising from two close D X - rays IV D X - ̜‰¿UøËՙ
energy levels in hydrogen ÇÕ Ì¾œ‰ÁÕ ÌÄ̜‰¿UøË œ‰Í ±¿U™U ³Öç½á

(1) (I)-(A), (II)-(B), (III)-(B), (IV)-(C) (1) (I)-(A), (II)-(B), (III)-(B), (IV)-(C)
(2) (I)-(A), (II)-(B), (III)-(C), (IV)-(C) (2) (I)-(A), (II)-(B), (III)-(C), (IV)-(C)
(3) (I)-(D), (II)-(C), (III)-(A), (IV)-(B) (3) (I)-(D), (II)-(C), (III)-(A), (IV)-(B)
(4) (I)-(B), (II)-(A), (III)-(D), (IV)-(A) (4) (I)-(B), (II)-(A), (III)-(D), (IV)-(A)

English : 19 Set : 11 Hindi : 19 Set : 11

30. In the circuit diagrams (A, B, C and D) 30. ÎàææüØð ÂçÚUÂÍ ç¿˜ææð´ (A, B, C °ß´ D) ×ð´, R °·¤ ¥‹Ø
shown below, R is a high resistance and S ©‘¿ ÂýçÌÚUæðÏ ãñ ¥æñÚU S »ñËßñÙæð×æÂè ÂýçÌÚUæðÏ G ·¤è
is a resistance of the order of galvanometer ·¤æðçÅU ·¤æ ÂýçÌÚUæðÏ ãñÐ »ñËßñÙæð×æÂè ·¤æ ÂýçÌÚUæðÏ °ß´
resistance G. The correct circuit, ÎÿæÌæ´·¤ çÙ·¤æÜÙð ·ð¤ ¥hü-çßÿæð‡æ çßçÏ ·ð¤ â´»Ì
corresponding to the half deflection âãè ÂçÚUÂÍ ç¿ç‹ãÌ ãñ §ââð Ñ
method for finding the resistance and
figure of merit of the galvanometer, is the
circuit labelled as :

(A)

(A)

(B)

(B)

(C)
(C)

English : 20 Set : 11 Hindi : 20 Set : 11

(D)
(D)

RS
(1) Circuit A with G5 ( RS
R 2 S)
(1) G5 (
R 2 S)
·ð¤ âæÍ ÂçÚUÂÍ A
(2) Circuit B with G5S
(2) G5S ·ð¤ âæÍ ÂçÚUÂÍ B
(3) Circuit C with G5S
(3) G5S ·ð¤ âæÍ ÂçÚUÂÍ C
RS
(4) Circuit D with G5 RS
R2 S (4) G5 ·ð¤ âæÍ ÂçÚUÂÍ D
R2 S

English : 21 Set : 11 Hindi : 21 Set : 11

PART B — CHEMISTRY Öæ» B — ÚUâæØÙ çߙææÙ
31. If lo and l be the threshold wavelength 31. ØçÎ lo ¥æñÚU l ÎãÜè$Áè ÌÚ´U»ÎñƒØü ¥æñÚU ¥æÂçÌÌ Âý·¤æàæ
and wavelength of incident light, the ·¤æ ÌÚ´U» ÎñƒØü ãæð´ Ìæð ÏæÌé SÍÜ âð çÙ·¤Üð Âý·¤æàæèØ
velocity of photoelectron ejected from the §Üð€ÅþUæÙæ´ð ·¤æ ßð» ãæð»æ Ñ
metal surface is :

2h 2h
(1) ( lo 2 l ) (1) ( lo 2 l )
m m

2hc 2hc
(2) ( lo 2 l ) (2) ( lo 2 l )
m m

2 h c  lo 2 l  2 h c  lo 2 l 
(3) m  l lo  (3) m  l lo 

2h  1 1 2h  1 1
(4)  2  (4)  2 
m  lo l m  lo l

32. The appearance of colour in solid alkali 32. ÆUæðâ ÿææÚU ÏæÌé ãðÜæ§ÇUæð´ ×ð´ Ú´U» ·ð¤ Îð¹ð ÁæÙð ·¤æ ·¤æÚU‡æ
metal halides is generally due to : ÂýæØÑ ãæðÌæ ãñ Ñ
(1) Schottky defect (1) àææòÅU·¤è Îæðá
(2) Frenkel defect (2) $Èýñ´¤·¤Ü Îæðá
(3) Interstitial position (3) ¥‹ÌÚUæÜè SÍæÙ
(4) F-centres (4) F-·ð¤‹Îý

English : 22 Set : 11 Hindi : 22 Set : 11

33. In the reaction of formation of sulphur 33. âÂ·ü¤ çßçÏ mæÚUæ âË$ȤÚU ÅþUæ§ü¥æ€âæ§ÇU ÕÙæÙð ·¤è
trioxide by contact process ¥çÖç·ý¤Øæ 2SO21O2 ì 2SO3 ×ð´ ¥çÖç·ý¤Øæ ·¤è
d [O2 ]
2SO21O2 ì 2SO3 the rate of reaction was ÎÚU ·¤æð 522.531024 ×æðÜ L21 s21
dt
measured as ·ð¤ M¤Â ×ð´ ×æÂæ »ØæÐ ¥çÖç·ý¤Øæ ÎÚU [SO2]·ð¤ M¤Â ×ð´
d [O 2 ]
dt
522.531024mol L21 s21. The ×æðÜ L21 s21 ×ð´ ãæð»è Ñ
rate of reaction in terms of [SO2] in mol
L21s21 will be :
(1) 21.25310 24 (1) 21.25310 24
(2) 22.50310 24 (2) 22.50310 24
(3) 23.75310 24 (3) 23.75310 24
(4) 25.00310 24 (4) 25.00310 24
34. Assuming that the degree of hydrolysis is 34. Øã ×æÙÌð ãé° ç·¤ ãæ§ÇþUæðÜðçââ ·¤æ ·ý¤×æ´·¤ (çÇU»ýè)
small, the pH of 0.1 M solution of sodium ‹Øê Ù ãñ , âæð ç ÇU Ø × °ð â èÅð U Å U ·ð ¤ 0.1M çßÜØÙ
acetate (Ka=1.031025) will be : (Ka=1.031025) ·¤æ pH ãæð»æ Ñ
(1) 5.0 (1) 5.0
(2) 6.0 (2) 6.0
(3) 8.0 (3) 8.0
(4) 9.0 (4) 9.0

English : 23 Set : 11 Hindi : 23 Set : 11

35. For the reaction, 2N2O5 → 4NO21O2, the 35. ¥çÖç·ý¤Øæ 2N2O5 → 4NO21O2, ·ð¤ çÜ° ÎÚU
rate equation can be expressed in two â×è·¤ÚU‡æ ·¤æð Îæð ÌÚUè·ð¤ âð çܹæ Áæ â·¤Ìæ ãñ
d[N2O5 ] d[N2O5 ]
ways 2 5 k [ N 2 O 5 ] and 2 5 k [ N 2 O 5 ] ¥æñÚU
dt dt
d [ NO 2 ] d [ NO 2 ]
1 5 k9 [ N 2 O 5 ] 1 5 k9 [ N 2 O 5 ]
dt dt
k and k’ are related as : k ¥æñÚU k’ ·¤æð çِ٠緤â M¤Â ×ð´ çܹæ ÁæØð»æ?
(1) k5k’ (1) k5k’
(2) 2k5k’ (2) 2k5k’
(3) k52k’ (3) k52k’
(4) k54k’ (4) k54k’
36. In some solutions, the concentration of
H3O1 remains constant even when small 36. ·é¤ÀU çßÜØÙæð´ ×ð´ ÂýÕÜ °ðçâÇU ¥Íßæ ÂýÕÜ ÿææÚU ·¤è
amounts of strong acid or strong base are ÍæðǸè ×æ˜ææ ç×ÜæÙð ÂÚU Öè H3O1 ·¤æ âæ‹Îý‡æ çSÍÚU ãè
added to them. These solutions are known ÚUãÌæ ãñÐ §Ù çßÜØÙæð´ ·¤æð Ùæ× çÎØæ ÁæÌæ ãñ Ñ
as :
(1) Ideal solutions
(2) Colloidal solutions (1) ¥æÎàæü çßÜØÙ
(3) True solutions (2) ·¤æðÜæØÇUè çßÜØÙ
(4) Buffer solutions (3) ßæSÌçß·¤ çßÜØÙ
(4) ÕȤÚU (Buffer) çßÜØÙ

English : 24 Set : 11 Hindi : 24 Set : 11

37. Given 37. çÎØæ »Øæ ãñ -
Fe31(aq)1 e2®Fe21(aq); E8=10.77 V Fe31(ÁÜèØ)1 e2®Fe21(ÁÜèØ); E8 =10.77 V
A l 3 1 ( a q ) 1 3 e2 ® A l ( s ) ; E 8 = 2 1 . 6 6 V Al31(ÁÜèØ)13 e2®Al(s); E8 = 21.66 V
2
Br2(aq)12 e2®2B r2 ; E8=11.09 V Br2(ÁÜèØ)12 e ®2B r2 ; E8 = 11.09 V
Considering the electrode potentials, §Üñ€ÅþUæðÇU çßÖßæ𴠷𤠥æÏæÚU ÂÚU çِÙæð´ ×ð´ âð ·¤æñÙ ·ý¤×
which of the following represents the ¥Â¿ØÙ àæç€ÌØæð´ ·¤æð âãè ÂýSÌéÌ ·¤ÚUÌæ ãñ?
correct order of reducing power ?
(1) Fe21< Al < B r2
(1) Fe21< Al < B r2
(2) B r2 < Fe21< Al
(2) B r2 < Fe21< Al
(3) Al < B r2 < Fe21
(3) Al < B r2 < Fe21
(4) Al < Fe21< B r2
(4) Al < Fe21< B r2 38. °·¤ »ñ â ·ð ¤ çâç܋ÇU Ú U ·¤æ Âý æ ÚU ç Ö·¤ ¥æØÌÙ
750.0 mL ãñÐ ØçÎ çâç܋ÇUÚU ·ð¤ Õè¿ ·¤è »ñâ ·¤æ
38. The initial volume of a gas cylinder is ÎæÕ 840.0 mm Hg âð ÕÎÜ ·¤ÚU 360.0 mm Hg
750.0 mL. If the pressure of gas inside the ãæð ÁæÌæ ãñ Ìæð »ñâ ·¤æ ¥ç‹Ì× ¥æØÌÙ ãæð»æ Ñ
cylinder changes from 840.0 mm Hg to
360.0 mm Hg, the final volume the gas will (1) 1.750 L
be : (2) 3.60 L
(1) 1.750 L (3) 4.032 L
(2) 3.60 L (4) 7.50 L
(3) 4.032 L
(4) 7.50 L

English : 25 Set : 11 Hindi : 25 Set : 11

39. The molar heat capacity (Cp) of CD2O is 39. CD2O ·¤è ×æðÜÚU ª¤c×æ ÏæçÚUÌæ (Cp) 1000 K ÂÚU
10 cals at 1000 K. The change in entropy 10 cals ãñÐ 32 g CD2O ßæc ·¤æð 1000 K âð
associated with cooling of 32 g of CD2O 100 K Ì·¤ çSÍÚU ÎæÕ ÂÚU ÆU‡ÇUæ ·¤ÚUÙð ÂÚU âÕh
vapour from 1000 K to 100 K at constant °ð‹ÅþUæÂè ÂçÚUßÌüÙ ãæð»æ Ñ
pressure will be : (D = çÇUØéÅUèçÚUØ×, ¥æñÚU §â·¤æ ÂÚU×æ‡æé ÎýÃØ×æÙ
(D = deuterium, at. mass = 2 u) = 2 ×æ˜æ·¤)
(1) 23.03 cal deg21 (1) 23.03 cal deg21
(2) 223.03 cal deg21 (2) 223.03 cal deg21
(3) 2.303 cal deg21 (3) 2.303 cal deg21
(4) 22.303 cal deg21 (4) 22.303 cal deg21
40. Based on the equation : 40. â×è·¤ÚU‡æ Ñ
 1 1   1 1 
(523 218 - 2 2 (523 218 - 2 2
 n 2
n 1   n 2
n 1 
2 2
the wavelength of the light that must be ·ð¤ ¥æÏæÚU ÂÚU ãæ§ÇþUæðÁÙ ·ð¤ §Üñ€ÅþUæÙ ·¤æð SÌÚU n=1 âð
absorbed to excite hydrogen electron from SÌÚU n=2 Ì·¤ ©žæðçÁÌ ·¤ÚUÙð ·ð¤ çÜØð Âý·¤æàæ, çÁâ
level n=1 to level n=2 will be : ·¤æ àææðá‡æ ¥æßàØ·¤ ãæð»æ, ·¤æ ÌÚ´U» ÎñƒØü §Ù×ð´ âð €Øæ
(h = 6.625310234 Js, C= 33108 ms21) ãæð»æ Ñ
(h = 6.625310234 Js, C = 33108 ms21)
(1) 1.325310 27 m (1) 1.325310 27 m
(2) 1.325310210 m (2) 1.325310210 m
(3) 2.650310 27 m (3) 2.650310 27 m
(4) 5.300310210 m (4) 5.300310210 m

English : 26 Set : 11 Hindi : 26 Set : 11

41. Which of the following series correctly 41. çِ٠âð ·¤æñÙ âæ âèÚUè$Á Îæð ̈ßæð´ X ¥æñÚU Y ·ð¤ Õè¿
represents relations between the elements ·ð¤ âÕ‹Ï ·¤æ âãè çÙM¤ÂÙ ·¤ÚUÌæ ãñ?
from X to Y ?
X ® Y X ® Y
(1) 3Li ® 19K Ionization enthalpy (1) 3Li ® 19K ¥æØÙè·¤ÚU‡æ ·¤è °ð‹ÍñËÂè ÕɸÌè
increases ãñ
(2) 9F ® 35Br Electron gain enthalpy (2) 9F ® 35Br §Üñ € Åþ U æ Ù ÜæÖ ·¤è °ð ‹ Íñ Ë Âè
with negative sign «¤‡ææˆ×·¤ 翋㠷ð¤ âæÍ ÕɸÌè
increases ãñ
(3) 6C ® 32Ge Atomic radii increases (3) 6C ® 32Ge ÂÚU×æ‡æé¥æð´ ·¤è ç˜æ’Øæ°¡ ÕɸÌè ãñ´ñ

(4) 18Ar ® 54Xe Noble character increases (4) 18Ar® 54Xe ©ˆ·ý¤C SßÖæß ÕɸÌæ ãñ

42. The correct order of bond dissociation 42. çِ٠ÃØßSÍæ¥æð´ ×ð´ âð ç·¤â ×ð´ N2, O2, O2
2
·¤è
energy among N2, O2, O2
2
is shown in ¥æÕ‹Ï çßØæðÁÙ ª¤Áæü ·ð¤ âãè ·ý¤× ·¤æð çιæØæ »Øæ
which of the following arrangements ? ãñ ?
(1) N2 > O2
2
> O2 (1) N2 > O2
2
> O2
2 2
(2) O 2 > O2 > N2 (2) O 2 > O2 > N2

(3) N2 > O2 > O2
2
(3) N2 > O2 > O2
2

(4) O2 > O2
2
> N2 (4) O2 > O2
2
> N2

English : 27 Set : 11 Hindi : 27 Set : 11

43. Which of the following statements about 43. Na2O2 ·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ âð ·¤æñÙ âæ ·¤ÍÙ
Na2O2 is not correct ? âãè Ùãè´ ãñ?
(1) It is diamagnetic in nature. (1) §â ·¤è Âýßëçžæ ÂýçÌ¿éÕ·¤èØ ãñÐ
(2) It is a derivative of H2O2. (2) Øã H2O2·¤æ °·¤ ÃØéˆÂ‹Ù ãñ
(3) Na2O2 oxidises Cr31 to CrO422 in (3) ¥æÜ ×æŠØ× ×ð ´ Na 2O 2 âð Cr 31 ·¤æ
acid medium. CrO422 ×𴠩¿ØÙ ãæð ÁæÌæ ãñÐ
(4) It is the super oxide of sodium. (4) Øã âæðçÇUØ× ·¤æ ÂÚUæ-¥æ€âæ§Ç ãñÐU

44. Which of the following statements about 44. ¥æðÁæðÙ SÌÚU ·ð¤ ƒæÅUÙð âÕ‹Ïè çِ٠·¤ÍÙæð´ ×ð´ âð ·¤æñÙ
the depletion of ozone layer is correct ? âæ âãè ãñ?
(1) The problem of ozone depletion is less (1) Ïýéßè ÿæð˜ææð´ ×ð´ ¥æð$ÁæðÙ ƒæÅUÙð ·¤è â×SØæ ·¤×
serious at poles because NO 2 ×ãˆß ÚU¹Ìè ãñ €Øæð´ç·¤ NO2 Á×·¤ÚU ÆUæðâ ÕÙ
solidifies and is not available for ÁæÌè ãñ ¥æñÚU ClO• ×êÜ·¤æð´ ·¤æð ãÅUæÙð ·ð¤ çÜØð
consuming ClO• radicals. ©ÂÜŽÏ Ùãè´ ãæðÌèÐ
(2) The problem of ozone depletion is (2) Ïýß é è ÿæð˜ææð́ ×ð́ ¥æðÁ
$ æðÙ ·ð¤ ƒæÅUÙð ·¤è â×SØæ ¥çÏ·¤
more serious at poles because ice ×ãˆß ÚU¹Ìè ãñ €Øæð´ç·¤ Ïýéßæð´ ÂÚU ÕæÎÜæð´ ×ð´ ÕÈü¤
crystals in the clouds over poles act ·ð¤ ç·ý¤SÅUÜæð´ ·ð¤ ãæðÙð âð Cl• ¥æñÚU ClO•
as catalyst for photochemical ÚðUçÇU·¤Üæð´ mæÚUæ ©ˆÂýðçÚUÌ ¥æð$ÁæðÙ çßØæðÁÙ ·¤è
reactions involving the Âý·¤æàæ-ÚUæâæØçÙ·¤ ¥çÖç·ý¤Øæ°¡ ãæð â·¤Ìè ãñÐ
decomposition of ozone by Cl• and
ClO• radicals.
(3) Freons, chlorofluorocarbons, are (3) çÈý¤¥æÙð´ (€ÜæðÚUæðÜæðÚUæð ·¤æÕüÙ) ÚUæâæØçÙ·¤ M¤Â
inert chemically, they do not react ×ð´ ¥ç·ý¤Ø ãæðÌè ãñ´Ð ß𠪤ÂÚUè ßæØéׇÇUÜ ×ð´
with ozone in stratosphere. ©ÂçSÍÌ ¥æð$ÁæðÙ âð ç·ý¤Øæ Ùãè´ ·¤ÚUÌè´Ð
(4) Oxides of nitrogen also do not react (4) ª¤ÂÚUè ßæØéׇÇUÜ ·¤è ¥æð$ÁæðÙ âð Ùæ§ÅUþUæðÁÙ ·ð¤
with ozone in stratosphere. ¥æ€âæ§ÇU Öè ç·ý¤Øæ Ùãè´ ·¤ÚUÌðÐ

English : 28 Set : 11 Hindi : 28 Set : 11

45. A gaseous compound of nitrogen and 45. Ùæ§ÅþUæðÁÙ ¥æñÚU ãæ§ÇþUæðÁÙ ·¤æ °·¤ »ñâèØ Øæñç»·¤
hydrogen contains 12.5%(by mass) of ÎýÃØ×æÙ âð 12.5% ãæ§ÇþUæðÁÙ ÚU¹Ìæ ãñÐ ãæ§ÇþUæðÁÙ
hydrogen. The density of the compound ·¤è ÌéÜÙæ ×ð´ §â Øæñç»·¤ ·¤æ ƒæÙˆß 16 ãñÐ Øæñç»·¤
relative to hydrogen is 16. The molecular ·¤æ ¥‡æéâê˜æ ãæð»æ Ñ
formula of the compound is :
(1) NH2 (1) NH2
(2) N3H (2) N3H
(3) NH3 (3) NH3
(4) N2H4 (4) N2H4
46. Shapes of certain interhalogen compounds 46. ·é¤ÀU ¥´ÌÑãñÜæðÁÙ Øæñç»·¤æ𴠷𤠥淤æÚU Ùè¿ð çܹ𠻰
are stated below. Which one of them is ãñ´Ð §Ù×ð´ âð ·¤æñÙ âæ ·¤ÍÙ âãè Ùãè´ ãñ?
not correctly stated ?
(1) IF7 : pentagonal bipyramid (1) IF7 : ´¿ÖéÁèØ çmçÂÚUæç×ÇU
(2) BrF5 : trigonal bipyramid (2) BrF5 : ç˜æ·¤æð‡æèØ çmçÂÚUæç×ÇU
(3) BrF3 : planar T-shaped (3) BrF3 : â×ÌÜèØ T-¥æ·¤æÚU ·¤æ
(4) ICl3 : planar dimeric (4) ICl3 : â×ÌÜèØ ÇUæ§×ðçÚU·¤ (Îæð ÃØßçSÍÌ)

47. Consider the following equilibrium 47. §â âæØ
1 1
AgCl ¯12NH3 ì Ag ( NH 3 )2  1 Cl2 AgCl ¯12NH3 ì Ag ( NH 3 )2  1 Cl2

White precipitate of AgCl appears on ·¤æð ŠØæÙ ÎèçÁ°Ð çِÙæð´ ×ð´ âð ç·¤âð ÇUæÜÙð ÂÚU AgCl
adding which of the following ? ·¤æ àßðÌ ¥ßÿæð ÕÙð»æ?
(1) NH3 (1) NH3
(2) aqueous NaCl (2) ÁÜèØ NaCl
(3) aqueous HNO3 (3) ÁÜèØ HNO3
(4) aqueous NH4Cl (4) ÁÜèØ NH4Cl

English : 29 Set : 11 Hindi : 29 Set : 11

48. Which of the following name formula 48. çِ٠Ùæ×-âê˜æ ÁæðǸæð ×ð´ âð ·¤æñÙ âãè Ùãè´ ãñ?
combinations is not correct ?

Formula Name ÇÏîË ¾Ë¼
Potassium
(1) K2[Pt(CN)4] (1) K2[Pt(CN)4] §ËÕªUËÌÅ˽¼ ªÖUªãUËÇ˽¾ËÕ åÁÖªU;ժU (II)
tetracyanoplatinate (II)

(2) [Mn(CN)5]22 Pentacyanomagnate (II) ion (2) [Mn(CN)5]22 §ÖüªUËÇ˽¾ËÕ ¼Ö™ ˾ժU(II) ŠË½¾
Potassium diammine §ËÕªÖUÌÅ˽¼
(3) K[Cr(NH3)2Cl4] (3) K[Cr(NH3)2Cl4]
tetrachlorochromate (III)
¬Uˌᕼ;ªÖUªãUËþÁËÕ¿UË՜â‰ËÕ¼ÕªU‰(III)
Tetraammine aquaiodo ªÖUªãUË •Õ¼Í¾ËՕþÄˊ˽ËÕ¬UË՜‰Ëպ˰ªU
(4) [Co(NH3)4(H2O)I]SO4 (4) [Co(NH3)4(H2O)I]SO4
cobalt (III) sulphate
(III) Ç°$$­Õ‰ªU

49. Consider the coordination compound, 49. â׋ßØè Øæñç»·¤ [Co(NH3)6]Cl3 ·¤æð ŠØæÙ ÎèçÁ°Ð
[Co(NH3)6]Cl3. In the formation of this §â â´·¤ÚUU ·ð¤ ÕÙæÙð ×ð´ ÂýØé€Ì ÂÎæÍü Áæð ËØé§â °ðçâÇU
complex, the species which acts as the (Lewis acid) ãñ, ãæð»æ Ñ
Lewis acid is :
(1) [Co(NH3)6]31 (1) [Co(NH3)6]31
(2) Cl2 (2) Cl2
(3) Co31 (3) Co31
(4) NH3 (4) NH3

50. Which one of the following does not have 50. çِÙæð´ ×ð´ âð 緤⠷¤æ M¤Â çÂÚUæç×ÇUèØ Ùãè´ ãñ?
a pyramidal shape ?
(1) (CH3)3 N (1) (CH3)3 N
(2) (SiH3)3 N (2) (SiH3)3 N
(3) P(CH3)3 (3) P(CH3)3
(4) P(SiH3)3 (4) P(SiH3)3

English : 30 Set : 11 Hindi : 30 Set : 11

51. The following reaction 51. ¥çÖç·ý¤Øæ

is known as : ·¤æð §Ù×ð´ âð ç·¤â Ùæ× âð ÁæÙæ ÁæÌæ ãñ?
(1) Perkin reaction (1) ÂÚUç·¤Ù ¥çÖç·ý¤Øæ
(2) Gattermann-Koch Formylation (2) »ñÅUÚU×Ù - ·¤æò¿ $ȤÚU×èÜðàæÙ
(3) Kolbe’s reaction (3) ·¤æðÜÕð ·¤è ¥çÖç·ý¤Øæ
(4) Gattermann reaction (4) »ñÅUÚU×Ù ¥çÖç·ý¤Øæ

52. The reagent needed for converting 52. ÂçÚUßÌüÙ

is : ·ð¤ çÜØð ¥æßàØ·¤ ¥çÖ·¤æÚU·¤ ãñ Ñ
(1) Cat. Hydrogenation (1) ·ñ¤ÅU. ãæ§ÇþUæðçÁÙðàæÙ
(2) H2/Lindlar Cat. (2) H2/çÜ´ÇUÜÚU ·ñ¤ÅU.
(3) Li/NH3 (3) Li/NH3
(4) LiAlH4 (4) LiAlH4
53. Complete reduction of benzene-diazonium 53. Zn/HCl ·ð¤ mæÚUæ Õñ‹$ÁèÙ ÇUæØæ$ÁæðçÙØ× €ÜæðÚUæ§ÇU
chloride with Zn/HCl gives : ·¤æ ÂêÚUæ ¥Â¿ØÙ ÎðÌæ ãñ Ñ
(1) Aniline (1) °ðÙèÜèÙ
(2) Phenylhydrazine (2) ç$ȤÙæ§Üãæ§ÇþUæ$ÁèÙ
(3) Azobenzene (3) °ð$ÁæðÕñ‹$ÁèÙ
(4) Hydrazobenzene (4) ãæ§ÇþU°ð$ÁæðÕñ‹$ÁèÙ

English : 31 Set : 11 Hindi : 31 Set : 11

54. An organic compound A, C5H8O; reacts 54. °·¤ ¥æÚU»ñçÙ·¤ Øæñç»·¤ A, C5H8O; çِ٠Âý·¤æÚU
with H 2 O, NH 3 and CH 3 COOH as H2O, NH3 ¥æñÚU CH3COOH ·ð¤ âæÍ ç·ý¤Øæ ·¤ÚUÌæ
described below : ãñ

A is : A ãñ Ñ

(1) (1)

(2) (2)

(3) (3)

(4) (4)

55. In allene (C 3 H 4 ), the type(s) of 55. C3H4 (°ÜèÙ) ×ð´ ·¤æÕüÙ ÂÚU×æ‡æé (ÂÚU×æ‡æé¥æð´) ·ð¤
hybridization of the carbon atoms is (are): â´·¤ÚU‡æ ·¤è çßçÏ ãæðÌè ãñ Ñ
(1) sp and sp3 (1) sp ¥æñÚU sp3

(2) sp2 and sp (2) sp2 ¥æñÚU sp

(3) only sp2 (3) ·ð¤ßÜ sp2

(4) sp2 and sp3 (4) sp2 ¥æñÚU sp3

English : 32 Set : 11 Hindi : 32 Set : 11

56. Chlorobenzne reacts with trichloro 56. H 2 SO 4 ·¤è ©ÂçSÍçÌ ×ð ´ €Üæð Ú Uæð Õ ñ ‹ $ Á èÙ ·¤è
acetaldehyde in the presence of H2SO4 ÅþU槀ÜæðÚUæð°ðçâÅU °ðçËÇUãæ§ÇU âð ¥çÖç·ý¤Øæ

The major product formed is : ×ð´ ÕÙÙð ßæÜè Âý×é¹ Øæñç»·¤ ãñ Ñ

(1) (1)

(2) (2)

(3) (3)

(4) (4)

57. Tischenko reaction is a modification of : 57. çÅUâ¿ñ‹·¤æð ¥çÖç·ý¤Øæ °·¤ ÕÎÜæ ãé¥æ M¤Â ãñ Ñ
(1) Aldol condensation (1) °ðËÇUæðÜ â´ƒæÙÙ ·¤æ
(2) Claisen condensation (2) €Üð$Á٠ⴃæÙÙ ·¤æ
(3) Cannizzaro reaction (3) ·ñ¤Ùè$ÁæÚUæð ¥çÖç·ý¤Øæ ·¤æ
(4) Pinacol-pinacolon reaction (4) çÂÙæ·¤æðÜ - çÂÙæ·¤æðÜæðÙ ¥çÖç·ý¤Øæ ·¤æ

English : 33 Set : 11 Hindi : 33 Set : 11

58. Which one of the following is used as 58. çِÙæð´ ×ð´ âð 緤⠰·¤ ·¤æð °ð‹ÅUè çãSÅUæ×èÙ ·ð¤ M¤Â ×ð´
Antihistamine ? ÂýØæð» ·¤ÚUÌð ãñ´?
(1) Omeprazole (1) ¥æð×èÂýæ$ÁæðÜ
(2) Chloranphenicol (2) €ÜæðÚðUÙ $Èñ¤çÙ·¤æðÜ
(3) Diphenhydramine (3) ÇUæ§Èñ¤Ùãæ§ÇþU°×èÙ
(4) Norethindrone (4) ÙæÚU°çÍÙÇþUæðÙ

59. Which one of the following statements is 59. çِ٠·¤ÍÙæð´ ×ð´ âð ·¤æñÙ âæ âãè Ùãè´ ãñ?
not correct ?
(1) Alcohols are weaker acids than (1) °ðË·¤æðãæÜð´ ÂæÙè ·¤è ÌéÜÙæ ×ð´ ÎéÕüÜ ¥Ü ãñ´
water
(2) Acid strength of alcohols decreases (2) °ðË·¤æðãæÜæð´ ·¤è ¥Ü àæç€Ì §â ·ý¤× ×𴠃æÅUÌè
in the following order ÁæÌè ãñ -
RCH2OH > R2CHOH > R3COH RCH2OH > R2CHOH > R3COH
(3) Carbon-oxygen bond length in (3) ×ñÍðÙæÜ, CH3OH ×ð´ ·¤æÕüÙ - ¥æ€âèÁÙ
methanol, CH3OH is shorter than ¥æÕ‹Ï ·¤è ܐÕæ§ü ç$ȤÙæÜ ×ð´ C2O ¥æՋÏ
that of C2O bond length in phenol. ·¤è ܐÕæ§ü âð ÀUæðÅUè ãæðÌè ãñÐ
(4) The bond angle in methanol (4) ×ðÍðÙæÜ ×ð´ ¥æÕ‹Ï ·¤æð‡æ 108.98
is 108.98 ãæðÌæ ãñÐ

60. The gas liberated by the electrolysis of 60. ÇUæ§ÂæðÅñUçàæØ× â€âèÙðÅU ·ð¤ çßÜØÙ ·ð¤ ßñléÌ çßÖæÁÙ
Dipotassium succinate solution is : ×ð´ ÂýæŒÌ »ñâ ãæðÌè ãñ Ñ
(1) Ethane (1) §üÍðÙ
(2) Ethyne (2) §üÍæ§Ù
(3) Ethene (3) §üÍèÙ
(4) Propene (4) ÂýæðÂèÙ

English : 34 Set : 11 Hindi : 34 Set : 11

PART C — MATHEMATICS Öæ» C — »ç‡æÌ
61. Let f be an odd function defined on the set 61. ×æÙæ f °·¤ çßá× È¤ÜÙ ãñ Áæð ç·¤ ßæSÌçß·¤ ⴁØæ¥æð´
of real numbers such that for x/0, ·ð¤ â×é‘¿Ø ÂÚU f(x)53 sin x14 cos x mæÚUæ
f(x)53 sin x14 cos x. 11p
ÂçÚUÖæçáÌ ãñ Áãæ¡ x/0 ãñ, Ìæð x 5 2 ÂÚU
6
11p
Then f(x) at x 5 2 is equal to : f(x) ÕÚUæÕÚU ãñ Ñ
6
3
(1) 12 3 3
2 (1) 12 3
2
3
(2) 2 12 3 3
2 (2) 2 12 3
2
3
(3) 22 3 3
2 (3) 22 3
2
3
(4) 2 22 3 3
2 (4) 2 22 3
2

62. If z1, z2 and z3, z4 are 2 pairs of complex
conjugate numbers, then 62. ØçÎ z1, z2 ÌÍæ z3, z4 âç×oý â´Øé‚×è ⴁØæ¥æð´ ·ð¤
Îæð Øé‚× ãñ´, Ìæð-
z  z 
arg  1  1 arg  2  equals : z  z 
 z4   z3  arg  1  1 arg  2  ÕÚUæÕÚU ãñ Ñ
 z4   z3 
(1) 0
(1) 0
p
(2) p
2 (2)
2
3p
(3) 3p
2 (3)
2
(4) p
(4) p

English : 35 Set : 11 Hindi : 35 Set : 11

63. If a and b are roots of the equation, 63. ØçÎ a ÌÍæ b ç·¤âè k ·ð ¤ çÜ°, â×è·¤ÚU‡æ
x 2 2 4 2 kx 1 2e 4 ln k2 1 5 0 for some k, x 2 2 4 2 kx 1 2e 4 ln k2 1 5 0 ·ð¤ ×êÜ ãñ´ ÌÍæ
and a21b2 5 66, then a31b3 is equal to : a21b2 5 66, ãñ, Ìæð a31b3 ÕÚUæÕÚU ãñ Ñ

(1) (1) 248 2
248 2
(2) (2) 280 2
280 2
(3) (3) 232 2
232 2
(4) (4) 2280 2
2280 2
64. Let A be a 333 matrix such that 64. ×æÙæ A °·¤ °ðâæ 333 ¥æÃØêã ãñ ç·¤

 1 2 3 0 0 1   1 2 3 0 0 1 
A 0 2 3  5  1 0 0 
  A 0 2 3  5  1 0 0 
 
ãñ, Ìæð
0 1 1  0 1 0  0 1 1  0 1 0 

Then A21 is : A21 ãñ Ñ

3 1 2  3 1 2 
3 0 2  3 0 2 
(1) (1)  
 
 1 0 1   1 0 1 

 3 2 1 3 2 1
3 2 0 3 2 0
(2) (2)  
 
 1 1 0   1 1 0 

0 1 3 0 1 3
0 2 3 0 2 3
(3) (3)  
 
 1 1 1   1 1 1 

 1 2 3 1 2 3
0 1 1 0 1 1
(4) (4)  
 
0 2 3  0 2 3 

English : 36 Set : 11 Hindi : 36 Set : 11

65. Let for i51, 2, 3, pi(x) be a polynomial of 65. ×æÙæ i51, 2, 3,·ð¤ çÜ° pi(x), x ×𴠃ææÌ 2 ·ð¤
degree 2 in x, pi’(x) and pi’’(x) be the first ÕãéÂÎ ãñ´, pi’(x) ÌÍæ pi’’(x) ·ý¤×àæÑ ÂýÍ× ·¤æðçÅU ÌÍæ
and second order derivatives of p i (x) çmÌèØ ·¤æðçÅU ·ð¤ ¥ß·¤ÜÁ ãñ´Ð
respectively. Let, ×æÙæ
 p1 ( x ) p19 ( x ) p10 ( x )   p1 ( x ) p19 ( x ) p10 ( x ) 
A( x ) 5  p2 ( x ) p29 ( x ) p20 ( x ) A( x ) 5  p2 ( x ) p29 ( x ) p20 ( x )
 p3 ( x ) p39 ( x ) p30 ( x )   p3 ( x ) p39 ( x ) p30 ( x ) 

and B(x) = [A(x)]T A(x). Then determinant ÌÍæ B(x) = [A(x)] T A(x) ãñ , Ìæð B(x) ·¤æ
of B(x) : âæÚUç‡æ·¤ Ñ
(1) is a polynomial of degree 6 in x. (1) x ×𴠃ææÌ 6 ·¤æ °·¤ ÕãéÂÎ ãñÐ
(2) is a polynomial of degree 3 in x. (2) x ×𴠃ææÌ 3 ·¤æ °·¤ ÕãéÂÎ ãñÐ
(3) is a polynomial of degree 2 in x. (3) x ×𴠃ææÌ 2 ·¤æ °·¤ ÕãéÂÎ ãñÐ
(4) does not depend on x. (4) x ÂÚU çÙÖüÚU Ùãè´ ·¤ÚUÌæÐ
66. An eight digit number divisible by 9 is to 66. 0 âð 9 Ì·¤ ·ð¤ ¥´·¤æð´ ·ð¤ ÂýØæð» âð, ¥´·¤æð´ ·¤æð ÎæðãÚUæ°
be formed using digits from 0 to 9 without çÕÙæ, °·¤ 9 âð Öæ’Ø, ¥æÆU ¥´·¤æð´ ·¤è ⴁØæ ÕÙæÙè
repeating the digits. The number of ways ãñÐ Øã çÁÌÙð ÌÚUè·¤æð´ âð ç·¤Øæ Áæ â·¤Ìæ ãñ, ßð ãñ´ Ñ
in which this can be done is :
(1) 72 (7!) (1) 72 (7!)
(2) 18 (7!) (2) 18 (7!)
(3) 40 (7!) (3) 40 (7!)
(4) 36 (7!) (4) 36 (7!)

English : 37 Set : 11 Hindi : 37 Set : 11

67. The coefficient of x 50 in the binomial 67. (11x) 1000 1 x(11x) 999 1x 2 (11x) 998 1
expansion of ......1x1000 ·ð¤ çmÂÎ ÂýâæÚU ×ð´ x50 ·¤æ »é‡ææ¡·¤ ãñ Ñ
(11x) 1000 1 x(11x) 999 1x 2 (11x) 998 1
......1x1000 is :

(1000) ! (1000) !
(1) (1)
(50) ! (950) ! (50) ! (950) !

(1000) ! (1000) !
(2) (2)
(49) ! (951) ! (49) ! (951) !

(1001) ! (1001) !
(3) (3)
(51) ! (950) ! (51) ! (950) !

(1001) ! (1001) !
(4) (4)
(50) ! (951) ! (50) ! (951) !

68. In a geometric progression, if the ratio of 68. °·¤ »é‡ææðžæÚU oýðɸè ×ð´ ØçÎ ÂãÜð 5 ÂÎæð´ ·ð¤ Øæð» ·¤æ
the sum of first 5 terms to the sum of their ©Ù·ð¤ ÃØ鈷ý¤×æð´ ·ð¤ Øæð» âð ¥ÙéÂæ̤ 49 ãñ ÌÍæ §â·ð¤
reciprocals is 49, and the sum of the first ÂãÜð ÌÍæ ÌèâÚðU ÂÎæð´ ·¤æ Øæð»U 35 ãñ, Ìæð §â »é‡ææðžæÚU
and the third term is 35. Then the first term oýðÉ¸è ·¤æ ÂýÍ× ÂÎ ãñ Ñ
of this geometric progression is :
(1) 7 (1) 7
(2) 21 (2) 21
(3) 28 (3) 28
(4) 42 (4) 42

English : 38 Set : 11 Hindi : 38 Set : 11

69. The sum of the first 20 terms common 69. oýðç‡æØæð´U 3171111151..... ÌÍæU
between the series 3171111151..... and 1161111161..... , ·ð¤ Õè¿ ©ÖØçÙcÆU ÂýÍ×
1161111161..... , is : 20 ÂÎæð´ ·¤æ Øæð» ãñ Ñ
(1) 4000 (1) 4000
(2) 4020 (2) 4020
(3) 4200 (3) 4200
(4) 4220 (4) 4220

70. If 70. ØçÎ
tan ( x 2 2 ){x 2 1 (k22)x 2 2k} tan ( x 2 2 ){x 2 1 (k22)x 2 2k}
lim 55 , lim 55
x →2 x 2 2 4x 1 4 x →2 x 2 2 4x 1 4
then k is equal to : ãñ, Ìæð k ÕÚUæÕÚU ãñ Ñ
(1) 0 (1) 0
(2) 1 (2) 1
(3) 2 (3) 2
(4) 3 (4) 3

71. Let f(x)5x?x?, g(x) = sin x and 71. ×æÙæ f(x)5x?x?, g(x) = sin x ÌÍæ
h(x) 5(gof )(x). Then h(x) 5(gof ) (x) ãñ, Ìæð
(1) h(x) is not differentiable at x50. (1) h(x), x50 ÂÚU ¥ß·¤ÜÙèØ Ùãè´ ãñÐ
(2) h(x) is differentiable at x50, but (2) h(x), x50 ÂÚU ¥ß·¤ÜÙèØ ãñ ÂÚU‹Ìé h’(x),
h’(x) is not continuous at x50. x50 ÂÚU âÌÌ Ùãè´ ãñÐ
(3) h’(x) is continuous at x50 but it is (3) h’(x), x50 ÂÚU âÌÌ ãñ, ÂÚU‹Ìé Øã x50 ÂÚU
not differentiable at x50. ¥ß·¤ÜÙèØ Ùãè´ ãñÐ
(4) h’(x) is differentiable at x50. (4) h’(x), x50 ÂÚU ¥ß·¤ÜÙèØ ãñÐ

English : 39 Set : 11 Hindi : 39 Set : 11

72. For the curve y = 3 sin u cos u, x5eu sin u, 72. ß·ý ¤ y = 3 sin u cos u, x5e u sin u,
0 [ u [ p, the tangent is parallel to x-axis 0 [ u [ p, ·ð¤ çÜ° SÂàæüÚðU¹æ x- ¥ÿæ ·ð¤ â×æ´ÌÚU ãñ,
when u is : ÁÕ u ÕÚUæÕÚU ãñ Ñ
(1) 3p (1) 3p
4 4

(2) p (2) p
2 2

(3) p (3) p
4 4

(4) p (4) p
6 6
73. Two ships A and B are sailing straight 73. Îæð Áãæ$Á A ÌÍæ B, °·¤ çÙçà¿Ì çÕ´Îé O âð ÎêÚU âèÏð
away from a fixed point O along routes ×æ»æðZ ÂÚU §â Âý·¤æÚU Áæ ÚUãð ãñ´ ç·¤ ÐAOB âÎæ 1208
such that ÐAOB is always 1208. At a ÚU ã Ìæ ãñ Ð ç·¤âè ÿæ‡æ, OA = 8 ç·¤×è ÌÍæ
certain instance, OA = 8 km, OB = 6 km OB = 6 ç·¤×è ãñ ÌÍæ Áãæ$Á A, 20 ç·¤×è/ƒæ´ÅUæ ·¤è
and the ship A is sailing at the rate of ¿æÜ âð ¿Ü ÚUãæ ãñ ÁÕç·¤ Áãæ$Á B, 30 ç·¤×è/ƒæ´ÅUæ
20 km/hr while the ship B sailing at the ·¤è ¿æÜ âð ¿Ü ÚUãæ ãñ, Ìæð A ÌÍæ B ·ð¤ Õè¿ ·¤è ÎêÚUè
rate of 30 km/hr. Then the distance çÁâ ÎÚU (ç·¤×è/ƒæ´ÅUæ ×ð´) âð ÕÎÜ ÚUãè ãñ, ßã ãñ Ñ
between A and B is changing at the rate
(in km/hr) :
(1) 260 37
(1) 260 37
(2) 260 37
(2) 260 37
(3) 80 37
(3) 80 37
(4) 80 37
(4) 80 37

English : 40 Set : 11 Hindi : 40 Set : 11

74. The volume of the largest possible right 74. ç˜æ’Øæ 3 ßæÜð »æðÜð ·ð¤ ¥´Ì»üÌ, ÕǸð âð ÕǸð Ü´Õ
circular cylinder that can be inscribed in a ßëžæèØ ÕðÜÙ ·¤æ ¥æØÌÙ ãñ Ñ
sphere of radius5 3 is :
4 4
(1) 3 p (1) 3 p
3 3
8 8
(2) 3 p (2) 3 p
3 3
(3) 4p (3) 4p
(4) 2p (4) 2p

 1 2 x2   2
75. The integral ∫ x cos21   dx (x > 0) 75. â×æ·¤Ü ∫ x cos21  1 2 x 2  dx , (x > 0) ÕÚUæÕÚU
 1 1 x2   11x 
is equal to : ãñ Ñ
(1) 2 x1(11x2) tan21 x1c (1) 2 x1(11x2) tan21 x1c
(2) x2 (11x2) cot21 x1c (2) x2 (11x2) cot21 x1c
(3) 2 x1(11x2) cot21 x1c (3) 2 x1(11x2) cot21 x1c
(4) x2 (11x2) tan21 x1c (4) x2 (11x2) tan21 x1c
e e
n
76. If for n/1, Pn 5 ∫ (log x ) d x , then 76. ØçÎ n/1 ·ð¤ çÜ°, Pn 5 ∫ (log x )n d x ãñ, Ìæð
1 1
P10290P8 is equal to : P10290P8 ÕÚUæÕÚU ãñ Ñ
(1) 29 (1) 29
(2) 10e (2) 10e
(3) 29e (3) 29e
(4) 10 (4) 10

English : 41 Set : 11 Hindi : 41 Set : 11

77. If the general solution of the differential 77. ØçÎ ç·¤âè ȤÜÙ F ·ð¤ çÜ° ¥ß·¤Ü â×è·¤ÚU‡æ
y x y x
equation y9 5 1 F  , for some y9 5 1 F  , ·¤æ ÃØæ·¤ ãÜ y ln ?cx?5x,
x y x y
function F, is given by mæÚUæ ÂýΞæ ãñ, Áãæ¡ c °·¤ Sßð‘ÀU ¥¿ÚU ãñ, Ìæð F(2)
y ln ?cx?5x, where c is an arbitrary ÕÚUæÕÚU ãñ Ñ
constant, then F (2) is equal to :
(1) 4 (1) 4
1 1
(2) (2)
4 4
(3) 24 (3) 24
1 1
(4) 2 (4) 2
4 4

78. A stair-case of length l rests against a 78. Ü´Õæ§ü l ·¤è °·¤ âèÉ¸è °·¤ ©ŠßæüÏÚU ÎèßæÚU ÌÍæ ·¤×ÚðU
vertical wall and a floor of a room,. Let P ·ð¤ Ȥàæü ·ð¤ âæÍ ¹Ç¸è ãñÐ ×æÙæ §â âèɸè ÂÚU °·¤
be a point on the stair-case, nearer to its çÕ´Îé P, Áæð §â·ð¤ ÎèßæÚU ·ð¤ âæÍ Ü»Ùð ßæÜð çâÚðU ·ð¤
end on the wall, that divides its length in çÙ·¤ÅU ãñ, §â Âý·¤æÚU ãñ ç·¤ Øã âèÉ¸è ·¤è Ü´Õæ§ü ·¤æð
the ratio 1 : 2. If the stair-case begins to 1 : 2 ·ð¤ ¥ÙéÂæÌ ×ð´ Õæ´ÅUÌæ ãñÐ ØçÎ âèɸè Ȥàæü ÂÚU
slide on the floor, then the locus of P is : âÚU·¤Ùð Ü»Ìè ãñ, Ìæð P ·¤æ çÕ´Îé ÂÍ ãñ Ñ
1
(1) an ellipse of eccentricity (1) ©ˆ·ð´¤ÎýÌæ 1 ßæÜæ °·¤ ÎèƒæüßëÌÐ
2 2

3 3
(2) an ellipse of eccentricity (2) ©ˆ·ð´¤ÎýÌæ ßæÜæ °·¤ ÎèƒæüßëÌ
2 2
l l
(3) a circle of radius
2
(3) ç˜æ’Øæ 2 ßæÜæ °·¤ ßëÌÐ

3 3
(4) a circle of radius
2
l (4) ç˜æ’Øæ l ßæÜæ °·¤ ßëÌÐ
2

English : 42 Set : 11 Hindi : 42 Set : 11

79. The base of an equilateral triangle is along 79. °·¤ â×Õæãé ç˜æÖéÁ ·¤æ ¥æÏæÚU ÚðU¹æ 3x14y = 9 ·ð¤
the line given by 3x14y = 9. If a vertex of ¥ÙéçÎàæ ãñÐ ØçÎ ç˜æÖéÁ ·¤æ °·¤ àæèáü (1, 2) ãñ Ìæð
the triangle is (1, 2), then the length of a ç˜æÖéÁ ·¤è °·¤ ÖéÁæ ·¤è Ü´Õæ§ü ãñ Ñ
side of the triangle is :

2 3 2 3
(1) (1)
15 15

4 3 4 3
(2) (2)
15 15

4 3 4 3
(3) (3)
5 5

2 3 2 3
(4) (4)
5 5

80. The set of all real values of l for which 80. l ·ð¤ âÖè ßæSÌçß·¤ ×æÙæð´ ·¤æ â×鑿Ø, çÁÙ·ð¤ çÜ°
exactly two common tangents can be ßëžææð´ x21y224x24y1650 ÌÍæ
drawn to the circles x 2 1y 2 210x210y1l50 ÂÚU ÆUè·¤ Îæð
x21y224x24y1650 and ©ÖØçÙcÆU SÂàæüÚðU¹æ°¡ ¹è´¿è Áæ â·¤Ìè ãæð´, ·¤æ Áæð
x21y2210x210y1l50 is the interval : ¥´ÌÚUæÜ ãñ, ßã ãñ Ñ
(1) (12, 32)
(1) (12, 32)
(2) (18, 42)
(2) (18, 42)
(3) (12, 24)
(3) (12, 24)
(4) (18, 48)
(4) (18, 48)

English : 43 Set : 11 Hindi : 43 Set : 11

81. Let L1 be the length of the common chord 81. ×æÙæ L1, ß·ý ¤ æð ´ x21y259 ÌÍæ y258x, ·¤è
of the curves x21y259 and y258x, and ©ÖØçÙcÆU Áèßæ ·¤è Ü´Õæ§ü ãñ, ÌÍæ L2, y258x ·ð¤
L2 be the length of the latus rectum of ÙæçÖÜ´Õ ·¤è Ü´Õæ§ü ãñ, Ìæð Ñ
y258x, then :
(1) L1 > L 2 (1) L1 > L2
(2) L15L2 (2) L15L2
(3) L1 < L 2 (3) L1 < L2
L1 L1
(4) 5 2 (4) 5 2
L2 L2

82. Let P (3 sec u, 2 tan u) and
x2 y2
82. ×æÙæ ¥çÌÂÚUßÜØ 2 5 1 ÂÚU Îæð çÖóæ çÕ´Îé
p 9 4
Q (3 sec f, 2 tan f) where u 1 f 5
, be
2 P (3 sec u, 2 tan u) ÌÍæ Q (3 sec f, 2 tan f)
two distinct points on the hyperbola p
2 2 ãñ´, Áãæ¡ u 1 f 5 2 ãñ, Ìæð P ÌÍæ Q ÂÚU ¹è´¿ð »°
x y
2 5 1 . Then the ordinate of the
9 4 ¥çÖÜ´Õæð´ ·ð¤ Âýç̑ÀðUÎÙ çÕ´Îé ·¤è ·¤æðçÅU (ordinate)
point of intersection of the normals at P ãñ Ñ
and Q is :
11 11
(1) (1)
3 3

11 11
(2) 2 (2) 2
3 3

13 13
(3) (3)
2 2

13 13
(4) 2 (4) 2
2 2

English : 44 Set : 11 Hindi : 44 Set : 11

83. Let A (2, 3, 5), B (21, 3, 2) and 83. ×æÙæ A (2, 3, 5), B (21, 3, 2) ÌÍæ
C (l, 5, m) be the vertices of a DABC. If the C (l, 5, m) °·¤ ç˜æÖéÁ ABC ·ð¤ àæèáü ãñ´Ð ØçÎ A
median through A is equally inclined to âð ãæð·¤ÚU ÁæÙð ßæÜè ×æçŠØ·¤æ, çÙÎðüàææ´·¤ ¥ÿææð´ ÂÚU
the coordinate axes, then : â×æÙ ·¤æð‡æ ÕÙæÌè ãñ, Ìæð Ñ
(1) 5l28m50 (1) 5l28m50
(2) 8l25m50 (2) 8l25m50
(3) 10l27m50 (3) 10l27m50
(4) 7l210m50 (4) 7l210m50

84. The plane containing the line
84. Úð U ¹ æ x 2 1 5 y 2 2 5 z 2 3 ·¤æ𠥋Ìçßü c ÅU
x 21 y 22 z 23 1 2 3
5 5 and parallel to
1 2 3 x y z
·¤ÚUÙð ßæÜæ ÌÍæ ÚðU¹æ 5 5 ·ð¤ â×æ´ÌÚU â×ÌÜ,
x y z 1 1 4
the line 5 5 passes through the
1 1 4 çÁâ çÕ´Îé âð ãæð·¤ÚU ÁæÌæ ãñ, ßã ãñ Ñ
point :
(1) (1,22, 5) (1) (1,22, 5)
(2) (1, 0, 5) (2) (1, 0, 5)
(3) (0, 3,25) (3) (0, 3,25)
(4) (21,23, 0) (4) (21,23, 0)
→ → ∧ ∧ ∧ → → → ∧ ∧ ∧ →
2
85. If ? c ? 5 60 and c 3( i12 j15 k )50 , 85. ØçÎ ? c ?2 5 60 ÌÍæ c 3( i12 j15 k )50 , ãñ,
→ ∧ ∧ ∧ → ∧ ∧ ∧
then a value of c . (2 7 i 1 2 j 1 3 k ) is : Ìæð c . (2 7 i 1 2 j 1 3 k ) ·¤æ °·¤ ×æÙ ãñ Ñ
(1) 4 2 (1) 4 2
(2) 12 (2) 12
(3) 24 (3) 24
(4) 12 2 (4) 12 2

English : 45 Set : 11 Hindi : 45 Set : 11

86. A set S contains 7 elements. A non-empty 86. °·¤ â×é“æØ S ×ð´ 7 ¥ßØß ãñ´Ð S ·¤æ °·¤ ¥çÚU€ˆæ
subset A of S and an element x of S are ©Ââ×é“æØ A ÌÍæ S ·¤æ °·¤ ¥ßØß x , ØæÎë‘ÀUØæ
chosen at random. Then the probability ¿éÙð »° , Ìæð xÎA ·¤è ÂýæçØ·¤Ìæ ãñ Ñ
that xÎA is :
1 1
(1) (1)
2 2
64 64
(2) (2)
127 127
63 63
(3) (3)
128 128
31 31
(4) (4)
128 128

87. If X has a binomial distribution, B(n, p) 87. ØçÎ X ·¤æ °ð â æ çmÂÎ Õ´ Å UÙ, B(n, p) ãñ ,
with parameters n and p such that Áãæ¡ n, p §â·ð¤ Âýæ¿Ü ãñ´, ¥æñÚU P(X52)5P(X53)
P(X52)5P(X53), then E(X), the mean of ãñ, Ìæð ¿ÚU X ·¤æ ×æŠØ E(X) ãñ Ñ
variable X, is :
(1) 22p (1) 22p
(2) 32p (2) 32p
p p
(3) 2 (3) 2
p p
(4) 3 (4) 3

English : 46 Set : 11 Hindi : 46 Set : 11

 p  p
88. If 2 cos u1sin u51 u ≠ 2  ,
 
88. ØçÎ 2 cos u1sin u51 u ≠ 2 
 
ãñ , Ìæð
then 7 cos u16 sin u is equal to : 7 cos u16 sin u ÕÚUæÕÚU ãñ Ñ

1 1
(1) (1)
2 2

(2) 2 (2) 2

11 11
(3) (3)
2 2

46 46
(4) (4)
5 5

89. The angle of elevation of the top of a 89. â×ÌÜ Öêç× ÂÚU °·¤ çÕ´Îé P âð °·¤ ª¤ŠßæüÏÚU ×èÙæÚU
vertical tower from a point P on the ·ð¤ çàæ¹ÚU ·¤æ ©‹ÙØÙ ·¤æð‡æ a ÂæØæ »ØæÐ P âð ×èÙæÚU
horizontal ground was observed to be a. ·ð¤ ÂæÎ ·¤è ¥æðÚU 2 ×è. ÁæÙð ÂÚU, ©‹ÙØÙ ·¤æð‡æ ÕÎÜ
After moving a distance 2 metres from P ·¤ÚU b ãæð ÁæÌæ ãñ, Ìæð (×è.×ð´) ×èÙæÚU ·¤è ª¡¤¿æ§ü ãñ Ñ
towards the foot of the tower, the angle of
elevation changes to b. Then the height (in
metres) of the tower is :

2 sin a sin b 2 sin a sin b
(1) sin (b2a ) (1) sin (b2a )

sin a sin b sin a sin b
(2) cos (b2a ) (2) cos (b2a )

2 sin (b2a ) 2 sin (b2a )
(3) (3)
sin a sin b sin a sin b

cos (b2a ) cos (b2a )
(4) (4)
sin a sin b sin a sin b

English : 47 Set : 11 Hindi : 47 Set : 11

90. The proposition ~ (pÚ ~ q)Ú ~ (pÚq) 90. âæŠØ ~(pÚ~q)Ú~(pÚq) Ìæç·ü¤·¤ M¤Â ×ð´ çÁâ·ð¤
is logically equivalent to : ÌéËØ ãñ, ßã ãñ Ñ
(1) p (1) p
(2) q (2) q
(3) ~p (3) ~p
(4) ~q (4) ~q

-o0o- -o0o-

English : 48 Set : 11 Hindi : 48 Set : 11