JEE MAIN QUESTION PAPER

1. English : 1 Set : 10 Hindi : 1 Set : 10
PART A — PHYSICS
1. Match List - I (Event) with List - II (Order
of the time interval for happening of the
event) and select the correct option from
the options given below the lists.
(a)
Rotation period
of earth
(i) 105
s
(b)
Revolution
period of earth
(ii) 107
s
(c)
Period of a light
wave
(iii) 10215
s
(d)
Period of a
sound wave
(iv) 1023
s
List - I List - II
(1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(2) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
(3) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
(4) (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
Öæ» A — ÖæñçÌ·¤ çß™ææÙ
1. âê¿è-I(ƒæÅUÙæ) ·¤æð âê¿è-II (©â ƒæÅUÙæ ·ð¤ ãæðÙð ×´ð
Ü»ð â×Ø ¥‹ÌÚUæÜ ·¤è ·¤æðçÅU) âð âé×ðçÜÌ ·¤èçÁ°ð
¥æñÚU âêç¿Øæ´ð ·ð¤ ÕæÎ çÎØð »Øð çß·¤ËÂæ´ð ×ð´ âð âãè
çß·¤Ë ¿éçÙØðÐ
(a)
§ÐûÄÍ œ‰Ë ìËÏøËá¾
œ‰ËÁ
(i) 105
s
(b)
§ÐûÄÍ œ‰Ë §Ì¿Uœâ‰¼øË
œ‰ËÁ
(ii) 107
s
(c)
•œ‰ §âœ‰ËÅË ±¿™U
œ‰Ë œ‰ËÁ
(iii) 10215
s
(d)
•œ‰ çÄ̾ ±¿™U œ‰Ë
œ‰ËÁ
(iv) 1023
s
ÇϤÍ- I ÇϤÍ- II
(1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(2) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
(3) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
(4) (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)

2. English : 2 Set : 10 Hindi : 2 Set : 10
2. A bullet looses
th
1
n
 
 
 
of its velocity passing
through one plank. The number of such
planks that are required to stop the bullet
can be :
(1)
2
n
2n 12
(2)
2
2n
n 12
(3) Infinite
(4) n
3. A heavy box is to be dragged along a rough
horizontal floor. To do so, person A pushes
it at an angle 308 from the horizontal and
requires a minimum force FA, while person
B pulls the box at an angle 608 from the
horizontal and needs minimum force FB.
If the coefficient of friction between the box
and the floor is
3
5
, the ratio
F
A
F
B
is :
(1) 3
(2)
5
3
(3)
3
2
(4)
2
3
2. °· ÕéÜðÅU°·¤ÌÌð âð»éÁÚUÙð ×ð´ ¥ÂÙð ßð» ·ð¤
 
 
 
1
n
ßæ¡
·¤è ãæçÙ ·¤ÚUÌè ãñ´´Ð ÕéÜðÅU ·¤æð Âê‡æü çߟææ× ¥ßSÍæ ×´ð
ÜæÙð ·ð¤ çÜ°ð ç·¤ÌÙð §âè Âý·¤æÚU ·ð¤ ́Ìæð´ ·¤è
¥æßàØ·¤Ìæ ãæð»è Ñ
(1)
2
n
2n 12
(2)
2
2n
n 12
(3) ¥Ù‹Ì
(4) n
3. °·¤ ¹éÚUÎéÚðU ÿæñçÌÁ Ȥàæü ÂÚU °·¤ ÖæÚUè Õ€âð ·¤æð ¹è´¿æ
ÁæÌæ ãñÐ °ðâæ ·¤ÚUÙð ·ð¤ çÜØð, ÃØç€Ì A ·¤æð ÿæñçÌÁ âð
308 ·¤æð‡æ ÂÚU Ï€·¤æ Ü»æÙæ ÂǸÌæ ãñ ¥æñÚU ‹ØêÙÌ× ÕÜ
FA ·¤è ¥æßàØ·¤Ìæ ãæðÌè ãñ´ ÁÕ ç·¤ ÃØç€Ì B ·¤æð
ÿæñçÌÁ âð 608 ·¤æð‡æ ÂÚU ¹è´¿Ùæ ãæðÌæ ãñ ¥æñÚU ‹ØêÙÌ×
ÕÜ FB ·¤è ¥æßàØ·¤Ìæ ãæðÌè ãñ´Ð ØçΠȤàæü °ß´ Õ€âð
·ð¤ Õè¿ ƒæáü‡æ »é‡ææ¡·¤
3
5
ãñ´, ÌÕ ¥ÙéÂæÌ
F
A
F
B
ãñ´ :
(1) 3
(2)
5
3
(3)
3
2
(4)
2
3

3. English : 3 Set : 10 Hindi : 3 Set : 10
4. Consider a cylinder of mass M resting on
a rough horizontal rug that is pulled out
from under it with acceleration ‘a’
perpendicular to the axis of the cylinder.
What is Ffriction at point P ? It is assumed
that the cylinder does not slip.
(1) Mg
(2) Ma
(3)
Ma
2
(4)
Ma
3
4. °·¤ ¹éÚUÎéÚðU ÿæñçÌÁ ·¤æÜèÙ ÂÚU çߟææ× ¥ßSÍæ ×ð´
ÎýÃØ×æÙ M ·ð¤ °·¤ ÕðÜÙ ÂÚU çß¿æÚU ·¤èçÁ°ðÐ ÕðÜÙ
·¤è ¥ÿæ ·ð¤ ܐÕßÌ ˆßÚU‡æ ‘a’ âð ·¤æÜèÙ ·¤æð ¹è´¿
çÜØæ ÁæÌæ ãñ´Ð çÕ‹Îé P ÂÚU Fƒæáü‡æ €Øæ ãñ´? Øã ×æÙ Üð´
ç·¤ ÕðÜÙ çȤâÜÌæ Ùãè´ ãñ´Ð
(1) Mg
(2) Ma
(3)
Ma
2
(4)
Ma
3

4. English : 4 Set : 10 Hindi : 4 Set : 10
5.
A particle is released on a vertical smooth
semicircular track from point X so that OX
makes angle u from the vertical (see figure).
The normal reaction of the track on the
particle vanishes at point Y where OY
makes angle f with the horizontal. Then :
(1) sin f5cos u
(2) sin f5
1
2
cos u
(3) sin f5
2
3
cos u
(4) sin f5
3
4
cos u
5.
°·¤ ª¤ŠßæüÏÚU ç¿·¤Ùð ¥hüßëžæèØ ÂÍ ·ð¤ çÕ‹Îé X âð
°·¤ ·¤‡æ ·¤æð §â Âý·¤æÚU ÀUæðǸæ ÁæÌæ ãñ´ ç·¤ OX ª¤ŠßæüÏÚU
âð ·¤æð‡æ u ÕÙæÌæ ãñ´ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ »Øæ ãñ´Ð
·¤‡æ ·ð¤ ª¤ÂÚU ÂÍ ·¤è ¥çÖÜÕ ÂýçÌç·ý¤Øæ çÕ‹Îé Y
ÂÚU â×æ# ãæð ÁæÌè ãñ´ Áãæ¡ OY ÿæñçÌÁ âð ·¤æð‡æ f
ÕÙæÌæ ãñÐ ÌÕ Ñ
(1) sin f5cos u
(2) sin f5
1
2
cos u
(3) sin f5
2
3
cos u
(4) sin f5
3
4
cos u

5. English : 5 Set : 10 Hindi : 5 Set : 10
6. A ball of mass 160 g is thrown up at an
angle of 608 to the horizontal at a speed of
10 ms21. The angular momentum of the
ball at the highest point of the trajectory
with respect to the point from which the
ball is thrown is nearly (g510 ms22)
(1) 1.73 kg m2/s
(2) 3.0 kg m2/s
(3) 3.46 kg m2/s
(4) 6.0 kg m2/s
7. The gravitational field in a region is
given by g
r
5 ˆ5N/kg i 1 ˆ12 N/kg j . The
change in the gravitational potential
energy of a particle of mass 2 kg when it is
taken from the origin to a point
(7 m,23 m) is :
(1) 71 J
(2) 13 58 J
(3) 271 J
(4) 1 J
6. ÿæñçÌÁ âð 608 ·ð¤ ·¤æð‡æ ÂÚU 10 ms21 ·¤è ¿æÜ âð
160 g ÎýÃØ×æÙ ·¤è °·¤ »ð´Î ª¤ÂÚU ·¤è ¥æðÚU Èð´¤·¤è
ÁæÌè ãñ´Ð ÂÍ ·ð¤ ©“æÌ× çÕ‹Îé ÂÚU ©â çÕ‹Îé ·ð¤ âæÂðÿæ,
Áãæ¡ âð »ð´Î Èð´¤·¤è »§ü ãñ´, »ð´Î ·¤æ ·¤æð‡æèØ â´ßð» ֻܻ
ãñ (g510 ms22)
(1) 1.73 kg m2/s
(2) 3.0 kg m2/s
(3) 3.46 kg m2/s
(4) 6.0 kg m2/s
7. °·¤ ÿæð˜æ ×ð´ »éL¤ˆßæ·¤áü‡æ ÿæð˜æ §â Âý·¤æÚU çÎØæ ÁæÌæ ãñ´
g
r
5 ˆ5N/kg i 1 ˆ12 N/kg j ÎýÃØ×æÙ 2 kg ·ð¤
°·¤ ·¤‡æ ·¤æð ×êÜ çÕ‹Îé âð çÕ‹Îé (7 m,23 m) Üð
ÁæÙð ×ð´ »éL¤ˆßèØ çSÍçÌÁ ª¤Áæü ×ð´ ÂçÚUßÌüÙ ãñ´ :
(1) 71 J
(2) 13 58 J
(3) 271 J
(4) 1 J

6. English : 6 Set : 10 Hindi : 6 Set : 10
8. The velocity of water in a river is
18 km/hr near the surface. If the river is
5 m deep , find the shearing stress between
the horizontal layers of water. The
co-efficient of viscosity of water51022
poise.
(1) 1021 N/m2
(2) 1022 N/m2
(3) 1023 N/m2
(4) 1024 N/m2
9.
In the diagram shown, the difference in
the two tubes of the manometer is 5 cm,
the cross section of the tube at A and B is
6 mm2 and 10 mm2 respectively. The rate
at which water flows through the tube is
(g510 ms22)
(1) 7.5 cc/s
(2) 8.0 cc/s
(3) 10.0 cc/s
(4) 12.5 cc/s
8. °·¤ ÙÎè ×ð´ âÌã ·ð¤ â×è ÂæÙè ·¤æ ßð» 18 km/hr
ãñ´Ð ØçÎ ÙÎè 5 m »ãÚUè ãñ, ÌÕ ÂæÙè ·¤è ÿæñçÌÁ ÂÚUÌæð´
·ð¤ Õè¿ ¥ÂL¤Â‡æ ÂýçÌÕÜ ·¤è »‡æÙæ ·¤èçÁ°ðÐ ÂæÙè
·¤æ àØæÙÌæ »é‡ææ¡·¤ 51022 ÂæØÁÐ
(1) 1021 N/m2
(2) 1022 N/m2
(3) 1023 N/m2
(4) 1024 N/m2
9.
ÎàææüØð »Øð 翘æ ×ð´, Îæð ÙçÜØæ´ð ·ð¤ ×ðÙæð×èÅUÚU ×ð´ ¥‹ÌÚU
5 cm ãñ´Ð A °ß´ B ÙçÜØæ𴠷𤠥ÙéÂýSÍ ·¤æÅU ·ý¤×àæÑ
6 mm2 °ß´ 10 mm2 ãñ´Ð ÙÜè ×ð´ ÂýßæçãÌ ÂæÙè ·¤è
ÎÚU ãñ´ (g510 ms22)
(1) 7.5 cc/s
(2) 8.0 cc/s
(3) 10.0 cc/s
(4) 12.5 cc/s

7. English : 7 Set : 10 Hindi : 7 Set : 10
10. A large number of liquid drops each of
radius r coalesce to from a single drop of
radius R. The energy released in the
process is converted into kinetic energy of
the big drop so formed. The speed of the
big drop is (given surface tension of liquid
T, density r)
(1)
 
 
 
T 1 1
r R
2
r
(2)
 
 
 
2T 1 1
r R
2
r
(3)
 
 
 
4T 1 1
r R
2
r
(4)
 
 
 
6T 1 1
r R
2
r
10. ÂýˆØð·¤ ç˜æ’Øæ r ·¤è ¥ˆØçÏ·¤ ⴁØæ ×ð´ Îýß ·¤è Õê¡Îð´
ç×Ü·¤ÚU ç˜æ’Øæ R ·¤è °·¤ Õê¡Î ÕÙæÌè ãñ´Ð Âýç·ý¤Øæ ×ð´
çÙ·¤Üè ª¤Áæü, ÕǸè Õê¡Î ·¤è »çÌÁ ª¤Áæü ×ð´ ÂçÚUßçÌüÌ
ãæð ÁæÌè ãñ´Ð ÕǸè Õê¡Î ·¤è ¿æÜ ã´ñ (çÎØæ ãñ´ Îýß ·¤æ
ÂëcÆU ÌÙæß T,ƒæÙˆß r)
(1)
 
 
 
T 1 1
r R
2
r
(2)
 
 
 
2T 1 1
r R
2
r
(3)
 
 
 
4T 1 1
r R
2
r
(4)
 
 
 
6T 1 1
r R
2
r

8. English : 8 Set : 10 Hindi : 8 Set : 10
11. A black coloured solid sphere of radius R
and mass M is inside a cavity with vacuum
inside. The walls of the cavity are
maintained at temperature T0. The initial
temperature of the sphere is 3T0. If the
specific heat of the material of the sphere
varies as aT3 per unit mass with the
temperature T of the sphere, where a is a
constant, then the time taken for the sphere
to cool down to temperature 2T0 will be
(s is Stefan Boltzmann constant)
(1) ln
 
 
 
2
M 3
4 R
a
p
(2) ln
 
 
 
2
M 16
4 R
a
p
(3) ln
 
 
 
2
M 16
16 R
a
p
(4) ln
 
 
 
2
M 3
16 R
a
p
12. A gas is compressed from a volume of
2 m3 to a volume of 1 m3 at a constant
pressure of 100 N/m2. Then it is heated at
constant volume by supplying 150 J of
energy. As a result, the internal energy of
the gas :
(1) Increases by 250 J
(2) Decreases by 250 J
(3) Increases by 50 J
(4) Decreases by 50 J
11. °·¤ »éãæ, çÁâ×ð´ çÙßæüÌ ãñ´, ·ð¤ ¥‹ÎÚU ÎýÃØ×æÙ M °ß´
ç˜æ’Øæ R ·ð¤ °·¤ ·¤æÜð Ú´U» ·ð¤ ÆUæðâ »æðÜð ·¤æð ÚU¹æ »Øæ
ãñ´Ð »éãæ ·¤è ÎèßæÚUæð´ ·¤æ ÌæÂ×æÙ T0 ÂÚ ¥ÙéÚUçÿæÌ ç·¤Øæ
»Øæ ãñ´Ð »æðÜð ·¤æ ÂýæÚUçÖ·¤ ÌæÂ×æÙ 3T0 ãñ´Ð ØçÎ »æðÜð
·ð¤ ÂÎæÍü ·¤è çßçàæcÅU ª¤c×æ ÂýçÌ §·¤æ§ü ÎýÃØ×æÙ »æðÜð
·ð¤ ÌæÂ×æÙ T âð aT3 ·ðð U ¥ÙéâæÚU ÂçÚUßçÌüÌ ãæðÌè ãñ´,
Áãæ¡ a °·¤ çSÍÚUæ¡·¤ ãñ´, ÌÕ »æðÜð ·ð¤ ÌæÂ×æÙ ·¤æð 2T0
Ì·¤ ÆU´ÇUæ ãæðÙð ×ð´ â×Ø Ü»ð»æ (s SÅUèȤ٠ÕæðËÅUÁ×æÙ
çSÍÚUæ¡·¤ ãñ´)
(1) ln
 
 
 
2
M 3
4 R
a
p
(2) ln
 
 
 
2
M 16
4 R
a
p
(3) ln
 
 
 
2
M 16
16 R
a
p
(4) ln
 
 
 
2
M 3
16 R
a
p
12. °·¤ »ñâ 100 N/m2 ·ð¤ çSÍÚU ÎæÕ ÂÚU ¥æØÌÙ
2 m3 âð 1 m3 ×ð´ â´ÂèçÇUÌ ·¤è ÁæÌè ãñ´Ð çȤÚU §âð
çSÍÚU ¥æØÌÙ ÂÚU 150 J ·¤è ª¤Áæü âð »×ü ç·¤Øæ ÁæÌæ
ãñ´Ð ÂçÚU‡ææ×SßL¤Â »ñâ ·¤è ¥æ‹ÌçÚU·¤ ª¤Áæü Ñ
U
(1) 250 J âð Õɸð»è
(2) 250 J âð ƒæÅðU»è
(3) 50 J âð Õɸð»è
(4) 50 J âð ƒæÅðU»è

9. English : 9 Set : 10 Hindi : 9 Set : 10
13. A gas molecule of mass M at the surface
of the Earth has kinetic energy equivalent
to 08C. If it were to go up straight without
colliding with any other molecules, how
high it would rise ? Assume that the height
attained is much less than radius of the
earth. (kB is Boltzmann constant)
(1) 0
(2)
B273 k
2 Mg
(3)
B546 k
3 Mg
(4)
B819 k
2 Mg
14. A body is in simple harmonic motion with
time period half second (T50.5 s) and
amplitude one cm (A51 cm). Find the
average velocity in the interval in which it
moves from equilibrium position to half of
its amplitude.
(1) 4 cm/s
(2) 6 cm/s
(3) 12 cm/s
(4) 16 cm/s
13. Âë‰ßè ·ð¤ ÂëcÆU ÂÚU ÎýÃØ×æÙ M ·ð¤ °·¤ »ñâ ¥‡æé ·¤è
»çÌÁ ª¤Áæü 08C ·ð¤ â×ÌéËØ ãñ´Ð ØçÎ Øã çÕÙæ ç·¤âè
¥æñÚU ¥‡æé âð ÅU·¤ÚUæØð âèÏ𠪤ÂÚU ·¤è ¥æðÚU ÁæÌæ ãñ´, ÌÕ
Øã 緤⠪¡¤¿æ§ü Ì·¤ Áæ°ð»æ?(Øã ×æÙ Üð´ Øã ª¡¤¿æ§ü
Âë‰ßè ·¤è ç˜æ’Øæ âð ÕãéÌ ·¤× ãñ) (kB ÕæðËÅUÁ×æÙ
çSÍÚUæ¡·¤ ãñ´)
(1) 0
(2)
B273 k
2 Mg
(3)
B546 k
3 Mg
(4)
B819 k
2 Mg
14. °·¤ ßSÌé ¥æßÌü·¤æÜ ¥æÏð âñç·¤‡ÇU (T50.5 s)
¥æñÚ ¥æØæ× °·¤ âð´ÅUè×èÅUÚU (A51 cm) âðU âÚUÜ
¥æßÌü »çÌ ·¤ÚU ÚUãè ãñ´Ð ÁÕ Øã ¥ÂÙè âæØæßSÍæ
çSÍçÌ âð ¥ÂÙð ¥æÏð ¥æØæ× Ì·¤ Âãé¡¿Ìè ãñ´, ©â
¥‹ÌÚUæÜ ×ð´ ¥æñâÌ ßð» ·¤è »‡æÙæ ·¤èçÁ°ðÐ
(1) 4 cm/s
(2) 6 cm/s
(3) 12 cm/s
(4) 16 cm/s

10. English : 10 Set : 10 Hindi : 10 Set : 10
15. The total length of a sonometer wire
between fixed ends is 110 cm. Two bridges
are placed to divide the length of wire in
ratio 6 : 3 : 2. The tension in the wire is
400 N and the mass per unit length is
0.01 kg/m. What is the minimum common
frequency with which three parts can
vibrate ?
(1) 1100 Hz
(2) 1000 Hz
(3) 166 Hz
(4) 100 Hz
16. The electric field in a region of space is
given by, o oE E 2 Ei j
→ ∧ ∧
5 1 where
E05100 N/C. The flux of this field through
a circular surface of radius 0.02 m parallel
to the Y-Z plane is nearly :
(1) 0.125 Nm2/C
(2) 0.02 Nm2/C
(3) 0.005 Nm2/C
(4) 3.14 Nm2/C
15. SÍæØè çâÚUæ´ð ·ð¤ Õè¿ °·¤ âæðÙæð×æÂè ÌæÚU ·¤è ·é¤Ü
ܐÕæ§ü 110 cm ãñ´Ð §â·¤è ܐÕæ§ü ·¤æð ¥ÙéÂæÌ
6 : 3 : 2 ×ð´ çßÖæçÁÌ ·¤ÚUÙð ·ð¤ çÜØð Îæð âðÌé ÚU¹ð »Øð
ãñ´Ð ÌæÚU ×ð´ ÌÙæß 400 N ãñ´ ¥æñÚU ÂýçÌ §·¤æ§ü ܐÕæ§ü,
ÎýÃØ×æÙ 0.01 kg/m ãñ´Ð ßã ‹ØêÙÌ× ©ÖØçÙcÆU
¥æßëçžæ, çÁââð ç·¤ ÌèÙæð´ Öæ» ·¤ÂÙ ·¤ÚU â·ð´¤»ð´, ãñ´
(1) 1100 Hz
(2) 1000 Hz
(3) 166 Hz
(4) 100 Hz
16. ×é€Ì ¥æ·¤æàæ ·ð¤ °·¤ ÿæð˜æ ×ð´ çßléÌ ÿæð˜æ çÎØæ ÁæÌæ ãñ´
o oE E 2 Ei j
→ ∧ ∧
5 1 Áãæ¡ E05100 N/CÐ
Y-Z ÌÜ ·ð¤ â×æ‹ÌÚU 0.02 m ç˜æ’Øæ ·ð¤ ßëžæèØ ÂëcÆU
âð »éÁÚUÙð ÂÚU §â çßléÌ ÿæð˜æ ·¤æ Ü€â ֻܻ ãñ´ Ñ
(1) 0.125 Nm2/C
(2) 0.02 Nm2/C
(3) 0.005 Nm2/C
(4) 3.14 Nm2/C

11. English : 11 Set : 10 Hindi : 11 Set : 10
17. The gap between the plates of a parallel
plate capacitor of area A and distance
between plates d, is filled with a dielectric
whose permittivity varies linearly from Î1
at one plate to Î2 at the other. The
capacitance of capacitor is :
(1) Î0(Î11Î2)A/d
(2) Î0(Î21Î1)A/2d
(3) Î0A/[d ln(Î2/Î1)]
(4) Î0(Î22Î1)A/[d ln(Î2/Î1)]
18.
Four bulbs B1, B2, B3 and B4 of 100 W each
are connected to 220 V main as shown in
the figure. The reading in an ideal ammeter
will be :
(1) 0.45 A
(2) 0.90 A
(3) 1.35 A
(4) 1.80 A
17. °·¤ â×æ‹ÌÚU ŒÜðÅU â´ÏæçÚU˜æ ·¤è ÂýˆØð·¤ ŒÜðÅU ·¤æ ÿæð˜æȤÜ
A ãñ´ ¥æñÚU ŒÜðÅUæð´ ·ð¤ Õè¿ ÎêÚUè d ãñ´Ð ŒÜðÅUæð´ ·ð¤ Õè¿
SÍæÙ ·¤æð °·¤ ÂÚUæßñléÌ âð ÖÚUæ »Øæ ãñ çÁâ·¤è
çßléÌàæèÜÌæ °·¤ ŒÜðÅU ÂÚU Î1 âð ÎêâÚUè ŒÜðÅU ÂÚU Î2
Ì·¤ ÚðUç¹·¤ M¤Â ×ð´ ÂçÚUßçÌüÌ ãæðÌè ãñÐ â´ÏæçÚU˜æ ·¤è
ÏæçÚUÌæ ãñ´ Ñ
(1) Î0(Î11Î2)A/d
(2) Î0(Î21Î1)A/2d
(3) Î0A/[d ln(Î2/Î1)]
(4) Î0(Î22Î1)A/[d ln(Î2/Î1)]
18.
ÂýˆØð·¤ 100 W ·ð¤ ¿æÚU ÕËÕ B1, B2, B3 °ß´ B4
220 V ×ð‹â âð ÁæðǸð »Øð ãñ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ
»Øæ ãñ´Ð °·¤ ¥æÎàæü ÏæÚUæ×æÂè ×ð´ ×æÂÙ ãæð»æ Ñ
(1) 0.45 A
(2) 0.90 A
(3) 1.35 A
(4) 1.80 A

12. English : 12 Set : 10 Hindi : 12 Set : 10
19.
A square frame of side 10 cm and a long
straight wire carrying current 1 A are in
the plane of the paper. Starting from close
to the wire, the frame moves towards the
right with a constant speed of 10 ms21 (see
figure). The e.m.f induced at the time the
left arm of the frame is at x510 cm from
the wire is :
(1) 2 mV
(2) 1 mV
(3) 0.75 mV
(4) 0.5 mV
19.
10 cm ÖéÁæ ·¤æ °·¤ ß»æü·¤æÚU Èðý¤× ¥æñÚU ÏæÚUæ 1 A âð
ÂýßæçãÌ °·¤ ܐÕæ âèÏæ ÌæÚU ·¤æ»$Á ·ð¤ ÌÜ ×ð´ ÚU¹ð
ãñ´Ð ÌæÚU ·ð¤ â×è âð, Èýð¤× Îæ¡Øè ¥æðÚU °·¤ çSÍÚU ¿æÜ
10 ms21 âð »çÌ ·¤ÚUÌæ ãñ´Ð (翘æ Îð¹ð´)Ð ÌæÚU âð
ÁÕ Èýð¤× ·¤è Õæ¡Øè ÖéÁæ x510 cm ÂÚU ãñ´ ÌÕ ©â
â×Ø ÂýðçÚUÌ çßléÌ ßæã·¤ ÕÜ ãñ´ Ñ
(1) 2 mV
(2) 1 mV
(3) 0.75 mV
(4) 0.5 mV

13. English : 13 Set : 10 Hindi : 13 Set : 10
20. An example of a perfect diamagnet is a
superconductor. This implies that when a
superconductor is put in a magnetic field
of intensity B, the magnetic field Bs inside
the superconductor will be such that :
(1) Bs52B
(2) Bs50
(3) Bs5B
(4) BsB but Bs ≠ 0
20. ¥çÌ¿æÜ·¤ ¥æÎàæü ¥Ùé¿éÕ·¤ ·¤æ °·¤ ©ÎæãÚU‡æ ãñÐ
§â·¤æ ¥Íü ãñ ç·¤ ÁÕ ÌèßýÌæ B ·ð¤ °·¤ ¿éÕ·¤èØ ÿæð˜æ
×ð´ ¥çÌ¿æÜ·¤ ·¤æð ÚU¹æ ÁæÌæ ãñ´, ÌÕ ¥çÌ¿æÜ·¤ ·ð¤
¥‹ÎÚU ¿éÕ·¤èØ ÿæð˜æ Bs §â Âý·¤æÚU ãæð»æ Ñ
(1) Bs52B
(2) Bs50
(3) Bs5B
(4) BsB ÂÚ´UÌé Bs ≠ 0

14. English : 14 Set : 10 Hindi : 14 Set : 10
21.
Figure shows a circular area of radius R
where a uniform magnetic field B
→
is going
into the plane of paper and increasing in
magnitude at a constant rate. In that case,
which of the following graphs, drawn
schematically, correctly shows the
variation of the induced electric field
E(r) ?
(1)
(2)
21.
翘æ ç˜æ’Øæ R ·ð¤ °·¤ ßëžæèØ ÿæð˜æÈ¤Ü ·¤æð ÎàææüÌæ ãñ
Áãæ¡ °·¤ °·¤â×æÙ ¿éÕ·¤èØ ÿæð˜æ B
→
·¤æ»$Á ·ð¤ ÌÜ
×ð´ ãñ´ ¥æñÚU §â·¤è çSÍÚU ÎÚU âð ÂçÚU×æ‡æ ×ð´ ßëçh ãæð ÚUãè
ãñ´Ð §â ¥ßSÍæ ×ð´, âæ´·ð¤çÌ·¤ M¤Â âð ¹è´¿æ »Øæ,
·¤æñÙ-âæ »ýæȤ ÂýðçÚUÌ çßléÌ ÿæð˜æ E(r) ·ð¤ ÂçÚUßÌüÙ ·¤æð
âãè Îàææü°ð»æ?
(1)
(2)

15. English : 15 Set : 10 Hindi : 15 Set : 10
(3)
(4)
22. If denote microwaves, X rays, infrared,
gamma rays, ultra-violet, radio waves and
visible parts of the electromagnetic
spectrum by M, X, I, G, U, R and V, the
following is the arrangement in ascending
order of wavelength :
(1) R, M, I, V, U, X and G
(2) M, R, V, X, U, G and I
(3) G, X, U, V, I, M and R
(4) I, M, R, U, V, X and G
(3)
(4)
22. ØçÎ çßléÌ ¿éÕ·¤èØ SÂð€ÅþU× ·ð¤ Öæ» âêÿ× ÌÚ´U»ð´, X
ç·¤ÚU‡æð´, ¥ßÚU€Ì, »æ×æ ç·¤ÚU‡æð´, ÂÚUæÕñ´»Ùè, ÚðUçÇUØæð ÌÚ´U»ð´
¥æñÚU ÎëàØ Âý·¤æàæ ·ý¤×àæÑ M, X, I, G, U, R ¥æñÚU V
âð ç¿ç‹ãÌ ç·¤Øð ÁæØð, ÌÕ ÌÚ´U»ÎñƒØü ·ð¤ ©žæÚUæðžæÚU ·ý¤×
×ð´ çß‹Øæâ çِÙçÜç¹Ì ãæð»æ Ñ
(1) R, M, I, V, U, X ¥æñÚU G
(2) M, R, V, X, U, G ¥æñÚU I
(3) G, X, U, V, I, M ¥æñÚU R
(4) I, M, R, U, V, X ¥æñÚU G

16. English : 16 Set : 10 Hindi : 16 Set : 10
23. A ray of light is incident from a denser to
a rarer medium. The critical angle for total
internal reflection is uiC and the Brewster’s
angle of incidence is uiB, such that
sinuiC/sinuiB5h51.28. The relative
refractive index of the two media is :
(1) 0.2
(2) 0.4
(3) 0.8
(4) 0.9
24. The diameter of the objective lens of
microscope makes an angle b at the focus
of the microscope. Further, the medium
between the object and the lens is an oil of
refractive index n. Then the resolving
power of the microscope.
(1) Increases with decreasing value of n
(2) Increases with decreasing value of b
(3) Increases with increasing value of
n sin 2b
(4) Increases with increasing value of
1
n sin 2b
23. °·¤ âƒæÙ âð çßÚUÜ ×æŠØ× ×ð´ Âý·¤æàæ ·¤è ç·¤ÚU‡æ
¥æÂçÌÌ ãñ´Ð Âê‡æü ¥æ‹ÌçÚU·¤ ÂÚUæßÌüÙ ·ð¤ çÜØð ·ý¤æç‹Ì·¤
·¤æð‡æ uiC ãñ ¥æñÚU ¥æÂÌÙ ·¤æ ÕýêSÅUÚU ·¤æð‡æ uiB §â
Âý·¤æÚU ãñ´ ç·¤ sinuiC/sinuiB5h51.28Ð ÎæðÙæð´
×æŠØ×æ´ð ·¤æ ¥æÂðçÿæ·¤ ¥ÂßÌüÙæ¡·¤ ãñ´ Ñ
(1) 0.2
(2) 0.4
(3) 0.8
(4) 0.9
24. °·¤ âêÿ×Îàæèü ·ð¤ ¥çÖÎëàØ·¤ Üð‹â ·¤æ ÃØæâ
âêÿ×Îàæèü ·ð¤ Ȥæð·¤â ÂÚU ·¤æð‡æ b ÕÙæÌæ ãñ ; ßSÌé °ß´
Üð‹â ·ð¤ Õè¿ ·¤æ ×æŠØ× ¥ÂßÌüÙæ¡·¤ n ·¤æ °·¤ ÌðÜ
ãñ´Ð ÌÕ âêÿ×Îàæèü ·¤è çßÖðÎÙ ÿæ×Ìæ Ñ
(1) n ·¤æ ×æÙ ƒæÅUÙð âð Õɸð»è
(2) b ·¤æ ×æÙ ƒæÅUÙð âð Õɸð»è
(3) n sin 2b ·¤æ ×æÙ ÕɸÙð âð Õɸð»è
(4)
1
n sin 2b
·¤æ ×æÙ ÕɸÙð âð Õɸð»è

17. English : 17 Set : 10 Hindi : 17 Set : 10
25. In a Young’s double slit experiment, the
distance between the two identical slits is
6.1 times larger than the slit width. Then
the number of intensity maxima observed
within the central maximum of the single
slit diffraction pattern is :
(1) 3
(2) 6
(3) 12
(4) 24
25. Ø´» ·ð¤ çmçÀUÎý ÂýØæð» ×ð´, Îæð âßüâ×M¤Âè çSÜÅUæð´ ·ð¤
Õè¿ ÎêÚUè çSÜÅU ¿æñǸæ§ü ·¤è 6.1 »éÙæ ãñ´Ð ÌÕ °·¤Ü
çSÜÅU çßßÌüÙ ç¿˜æ ·ð¤ ·ð¤‹ÎýèØ ×ãžæ× ·ð¤ ¥‹ÎÚU
ÃØçÌ·¤ÚU‡æ ç¿˜æ ·¤è ¥çÏ·¤Ì× ÌèßýÌæ¥æð´ ·¤è ⴁØæ
ãñ´ Ñ
(1) 3
(2) 6
(3) 12
(4) 24

18. English : 18 Set : 10 Hindi : 18 Set : 10
26. Match List - I (Experiment performed)
with List - II (Phenomena discovered/
associated) and select the correct option
from the options given below the lists :
(a)
Davisson
and Germer
Experiment
(i)
Wave nature of
electrons
(b)
Millikan’s oil
drop
experiment
(ii)
Charge of an
electron
(c)
Rutherford
experiment
(iii)
Quantisation of
energy levels
(d)
Franck -
Hertz
experiment
(iv)
Existence of
nucleus
List - I List - II
(1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(2) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
(3) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(4) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
26. âê¿è-I (ç·¤Øæ »Øæ ÂýØæð») ·¤æð âê¿è-II (çâhæ‹Ì
¹æðÁæ »Øæ ãñ/âÕçhÌ ãñ´) âð âé×ðçÜÌ ·¤èçÁ°ð ¥æñÚ
âêç¿Øæð´ ·ð¤ Ùè¿ð çÎØð »Øð çß·¤ËÂæ´ð âð âãè çß·¤ËÂ
¿éçÙ°ð Ñ
(a)
¬ÕUÄÍǾ ŠËÖ¿U ¦¼á¿U
§â½ËÕ
(i)
ŒÁÕþªãU˾ËÕ™ œ‰Ë ±¿™U
§âœ‰Ë¿U
(b)
̼ÌÁœ‰Ë¾ œ‰Ë ³âÄ
œÕ‰ Ì ¿U¾Õ œ‰Ë §â½ËÕ
(ii)
ŒÁÕþªãU˾ œ‰Ë
ŠËÄÕÅË
(c) ¿U³¿U­‰ËÕ¬áU §â½ËÕ (iii)
‰¦Ëá S±¿U œ‰Ë
þÄËøªÍœ‰¿UøË
(d)
­Ö♉œ‰ - ȪáU¦
§â½ËÕ
(iv)
¾ËÌ»œ‰ œ‰Ë
ŠÌS±íÄ
ÇÏ¤Í - I ÇÏ¤Í - II
(1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(2) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
(3) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(4) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

19. English : 19 Set : 10 Hindi : 19 Set : 10
27. A piece of wood from a recently cut tree
shows 20 decays per minute. A wooden
piece of same size placed in a museum
(obtained from a tree cut many years back)
shows 2 decays per minute. If half life of
C14 is 5730 years, then age of the wooden
piece placed in the museum is
approximately :
(1) 10439 years
(2) 13094 years
(3) 19039 years
(4) 39049 years
28.
Given : A and B are input terminals.
Logic 1 5 5 V
Logic 0 5 1 V
Which logic gate operation, the following
circuit does ?
(1) AND Gate
(2) OR Gate
(3) XOR Gate
(4) NOR Gate
27. °·¤ ÌæÁð ·¤æÅðU »Øð ÂðǸ ·¤è Ü·¤Ç¸è ·ð¤ ÅéU·¤Ç¸ð âð ÂýçÌ
ç×ÙÅU 20 ÿæØ ãæðÌð ãñ´Ð ©âè ¥æ·¤æÚU ·¤æ Ü·¤Ç¸è ·¤æ
ÅéU·¤Ç¸æ °·¤ ØêçÁØ× âð ÂýæŒÌ ãæðÌæ ãñ´ (Áæð ç·¤ Ü·¤Ç¸è
·¤§ü ßáü ÂéÚUæÙè ·¤ÅUè ãé§ü ãñ) Áæð ç·¤ ÂýçÌ ç×ÙÅU 2 ÿæØ
ÎàææüÌæ ãñ ; ØçÎ C14 ·¤è ¥Ïü ¥æØé 5730 ßáü ãñ´, ÌÕ
ØêçÁØ× âð ÂýæŒÌ Ü·¤Ç¸è ·ð¤ ÅéU·¤Ç¸ð ·¤è ¥æØé ãñ´
ֻܻ Ñ
(1) 10439 ßáü
(2) 13094 ßáü
(3) 19039 ßáü
(4) 39049 ßáü
28.
çÎØæ ãñ´ Ñ A °ß´ B çÙßðàæ ÅUç×üÙÜ ãñ´Ð
ÜæçÁ·¤ 1 5 5 V
ÜæçÁ·¤ 0 5 1 V
çِÙçÜç¹Ì ÂçÚUÂÍ ·¤æñÙ-âð ÜæçÁ·¤ »ðÅU ·¤æ ·¤æØü
·¤ÚU ÚUãæ ãñ´?
(1) AND »ðÅU
(2) OR »ðÅU
(3) XOR »ðÅU
(4) NOR »ðÅU

20. English : 20 Set : 10 Hindi : 20 Set : 10
29. Long range radio transmission is possible
when the radiowaves are reflected from
the ionosphere. For this to happen the
frequency of the radiowaves must be in the
range :
(1) 80 - 150 MHz
(2) 8 - 25 MHz
(3) 1 - 3 MHz
(4) 150 - 500 kHz
29. ܐÕè ÚðU‹Á ×ð´ ÚðUçÇUØæð Âýðá‡æ âÖß ãñ´ ÁÕ ¥æØÙæðSȤèØÚU
âð ÚðUçÇUØæð ÌÚ´U»ð´ ÂÚUæßçÌüÌ ãæðÌè ãñ´Ð §â·ð¤ âÖß ãæðÙð
·ð¤ çÜØð ÚðUçÇUØæð ÌÚ´U»æð´ ·¤è ¥æßëçžæ §â ÚðU‹Á ×ð´ ¥ßàØ
ãæðÙè ¿æçã°ð Ñ
(1) 80 - 150 MHz
(2) 8 - 25 MHz
(3) 1 - 3 MHz
(4) 150 - 500 kHz

21. English : 21 Set : 10 Hindi : 21 Set : 10
30.
In an experiment for determining the
gravitational acceleration g of a place with
the help of a simple pendulum, the
measured time period square is plotted
against the string length of the pendulum
in the figure.
What is the value of g at the place ?
(1) 9.81 m/s2
(2) 9.87 m/s2
(3) 9.91 m/s2
(4) 10.0 m/s2
30.
°·¤ âÚUÜ ÜæðÜ·¤ ·¤è âãæØÌæ âð °·¤ SÍæÙ ÂÚU
»éL¤ˆßèØ ˆßÚU‡æ g ·ð¤ ×æÂÙ ·ð¤ ÂýØæð» ×ð´, ÙæÂð »Øð
¥æßÌü ·¤æÜ ·ð¤ ß»ü ·¤æ ÂçÚUßÌüÙ ÜæðÜ·¤ ·¤è ÇUæðÚUè ·¤è
ܐÕæ§ü ·ð¤ âæÍ ç¿˜æ ×ð´ ÎàææüØæ »Øæ ãñ Ñ
§â SÍæÙ ÂÚU g ·¤æ ×æÙ ãñ´Ð
(1) 9.81 m/s2
(2) 9.87 m/s2
(3) 9.91 m/s2
(4) 10.0 m/s2

22. English : 22 Set : 10 Hindi : 22 Set : 10
PART B — CHEMISTRY
31. Ionization energy of gaseous Na atoms is
495.5 kJmol21. The lowest possible
frequency of light that ionizes a sodium
atom is (h56.626310234 Js,
NA56.02231023 mol21)
(1) 7.503104 s21
(2) 4.7631014 s21
(3) 3.1531015 s21
(4) 1.2431015 s21
32. Choose the correct statement with respect
to the vapour pressure of a liquid among
the following :
(1) Increases linearly with increasing
temperature
(2) Increases non-linearly with
increasing temperature
(3) Decreases linearly with increasing
temperature
(4) Decreases non-linearly with
increasing temperature
Öæ» B — ÚUâæØÙ çß™ææÙ
31. »ñâèØ âæðçÇUØ× ÂÚU×æ‡æé¥æð´ ·¤è ¥æØÙÙ ª¤Áæü ·¤æ ×æÙ
495.5 kJ ×æðÜ21 ãñÐ âæðçÇUØ× ÂÚU×æ‡æé ·¤æ ¥æØÙÙ
·¤ÚUÙð ·ð¤ çÜØð Âý·¤æàæ ·¤è âÖß ‹ØêÙÌ× ¥æßëçÌ
(frequency) €Øæ ãæð»è? (h56.626310234 Js,
NA56.02231023 ×æðÜ21)
(1) 7.503104 s21
(2) 4.7631014 s21
(3) 3.1531015 s21
(4) 1.2431015 s21
32. ç·¤âè Îýß ·ð¤ ßæc ÎæÕ ·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ ×ð´
âð âãè °·¤ ·¤ÍÙ ·¤æð ¿éçÙ° Ñ
(1) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
ÕɸÌæ ãñÐ
(2) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ Ù âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
ÕɸÌæ ãñÐ
(3) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
ƒæÅUÌæ ãñÐ
(4) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ Ù âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
ƒæÅUÌæ ãñÐ

23. English : 23 Set : 10 Hindi : 23 Set : 10
33. Which one of the following molecules is
paramagnetic ?
(1) N2
(2) NO
(3) CO
(4) O3
34. Zirconium phosphate [Zr3(PO4)4]
dissociates into three zirconium cations of
charge 14 and four phosphate anions of
charge 23. If molar solubility of zirconium
phosphate is denoted by S and its solubility
product by Ksp then which of the following
relationship between S and Ksp is
correct ?
(1) S5{Ksp/(6912)1/7}
(2) S5{Ksp/144}1/7
(3) S5(Ksp/6912)1/7
(4) S5{Ksp/6912}7
33. çِ٠¥‡æé¥æð´ ×ð´ âð ·¤æñÙ ¥Ùé¿éÕ·¤èØ ãñ?
(1) N2
(2) NO
(3) CO
(4) O3
34. çÁÚU·¤æðçÙØ× $ȤæS$Èð¤ÅU [Zr3(PO4)4] çßØæðçÁÌ ãæð·¤ÚU
14 ¥æßðàæ ÂýçÌ ·ð¤ÅUæØÙ ·ð¤ ÌèÙ çÁÚU·¤æðçÙØ× ·ð¤ÅUæØÙ
¥æñÚU 23 ¥æßðàæ ÂýçÌÑ °ÙæØÙ ·ð¤ ¿æÚU $ȤæS$Èð¤ÅU °ÙæØÙ
ÎðÌæ ãñÐ ØçÎ çÁÚU·¤æðçÙØ× $ȤæS$Èð¤ÅU ·¤è ×æðÜÚU çßÜðØÌæ
·¤æð S âð ¥æñÚU §â·ð¤ çßÜðØÌæ »é‡æÙÈ¤Ü ·¤æð Ksp âð
âêç¿Ì ç·¤Øæ ÁæØð Ìæð çِ٠âÕ‹Ïæð´ âð ·¤æñÙ-âæ
S ¥æñÚU Ksp ·¤æ âÕ‹Ï âãè ×æÙæ ÁæØð»æ?
(1) S5{Ksp/(6912)1/7}
(2) S5{Ksp/144}1/7
(3) S5(Ksp/6912)1/7
(4) S5{Ksp/6912}7

24. English : 24 Set : 10 Hindi : 24 Set : 10
35. For the decomposition of the compound,
represented as
NH2COONH4(s)ì 2NH3(g)1CO2(g)
the Kp52.931025 atm3.
If the reaction is started with 1 mol of the
compound, the total pressure at
equilibrium would be :
(1) 1.9431022 atm
(2) 5.8231022 atm
(3) 7.6631022 atm
(4) 38.831022 atm
36. For the reaction,
3A12B ® C1D,
the differential rate law can be written
as :
(1)
[ ] [ ]
[ ] [ ]n md A d C1
k A B
3 dt dt
5 5
(2)
[ ] [ ]
[ ] [ ]n md A d C
k A B
dt dt
2 5 5
(3)
[ ] [ ]
[ ] [ ]n md A d C1
k A B
3 dt dt
1 52 5
(4)
[ ] [ ]
[ ] [ ]n md A d C1
k A B
3 dt dt
2 5 5
35. NH2COONH4(s)ì 2NH3(g)1CO2(g)
âð âêç¿Ì Øæñç»·¤ ·ð¤ çßØæðÁÙ ·ð¤ çÜØð
Kp52.931025 atm3
ãæðÌæ ãñÐ ØçÎ ¥çÖç·ý¤Øæ ·¤æð Øæñç»·¤ ·ð¤ 1 ×æðÜ âð
¥æÚUÖ ç·¤Øæ ÁæØð Ìæð âæØ ¥ßSÍæ ×ð´ â·¤Ü ÎæÕ
·¤æ ×æÙ ãæð»æ Ñ
(1) 1.9431022 atm
(2) 5.8231022 atm
(3) 7.6631022 atm
(4) 38.831022 atm
36. ¥çÖç·ý¤Øæ
3A12B ® C1D
·ð¤ çÜØð ¥ß·¤Ü ÎÚU çÙØ× çܹæ Áæ â·¤Ìæ ãñ Ñ
(1)
[ ] [ ]
[ ] [ ]n md A d C1
k A B
3 dt dt
5 5
(2)
[ ] [ ]
[ ] [ ]n md A d C
k A B
dt dt
2 5 5
(3)
[ ] [ ]
[ ] [ ]n md A d C1
k A B
3 dt dt
1 52 5
(4)
[ ] [ ]
[ ] [ ]n md A d C1
k A B
3 dt dt
2 5 5

25. English : 25 Set : 10 Hindi : 25 Set : 10
37. Sulphur dioxide and oxygen were allowed
to diffuse through a porous partition.
20 dm3 of SO2 diffuses through the porous
partition in 60 seconds. The volume of O2
in dm3 which diffuses under the similar
condition in 30 seconds will be (atomic
mass of sulphur532 u) :
(1) 7.09
(2) 14.1
(3) 10.0
(4) 28.2
38. The observed osmotic pressure for a
0.10 M solution of Fe(NH4)2(SO4)2 at 258C
is 10.8 atm. The expected and
experimental (observed) values of Van’t
Hoff factor (i) will be respectively :
(R50.082 L atm k2mol21)
(1) 5 and 4.42
(2) 4 and 4.00
(3) 5 and 3.42
(4) 3 and 5.42
37. °·¤ âÚ´UÏý ÂÚUÎð âð âË$ȤÚU ÇU槥æ€âæ§ÇU ¥æñÚU ¥æ€âèÁÙ
·¤æð çßâçÚUÌ ãæðÙð çÎØæ »Øæ ãñÐ §â âÚ´UÏý ÂÚUÎð âð
20 dm3 SO2 ·ð¤ çßâçÚUÌ ãæðÙð ·¤æ â×Ø 60 âñ·¤‹ÇU
ãæðÌæ ãñÐ °ðâè ãè ¥ßSÍæ ×ð´ çßâçÚUÌ ãæðÙð ßæÜè O2
·¤æ ¥æØÌÙ dm3 ×ð´ 30 âñ·¤‹ÇU ·ð¤ çÜØð ãæð»æ (âË$ȤÚU
·ð¤ ÂÚU×æ‡æé ·¤æ ÎýÃØ×æÙ532 ×æ˜æ·¤) Ñ
(1) 7.09
(2) 14.1
(3) 10.0
(4) 28.2
38. 258 C ÂÚU Fe(NH4)2(SO4)2 ·ð¤ 0.10 M çßÜØÙ
·¤æ ¥æâ×æçÅU·¤ (ÂÚUæâÚU‡æ) ÎæÕ 10.8 atm Îð¹æ
»ØæÐ ßæ´ÅU ãæȤ »é‡æ·¤ ·ð¤ ¥æàææ ¥ÙéâæÚU ¥æñÚU ÂýæØæðç»·¤
(×æçÂÌ) ×æÙ ·ý¤×æÙéâæÚU ãæð´»ð Ñ
(R50.082 L atm k2×æðÜ21)
(1) 5 ¥æñÚU 4.42
(2) 4 ¥æñÚU 4.00
(3) 5 ¥æñÚU 3.42
(4) 3 ¥æñÚU 5.42

26. English : 26 Set : 10 Hindi : 26 Set : 10
39. The total number of octahedral void(s) per
atom present in a cubic close packed
structure is :
(1) 2
(2) 4
(3) 1
(4) 3
40. For an ideal solution of two components
A and B, which of the following is true ?
(1) DHmixing 0 (zero)
(2) DHmixing 0 (zero)
(3) A2B interaction is stronger than
A2A and B2B interactions
(4) A2A, B2B and A2B interactions
are identical
41. Consider the reaction :
4 2
2 3(aq) (aq) 2 ( ) (aq) 4(aq) (aq)H SO Sn H O Sn HSO 3Hl →1 1 2 1
1 1 1 1
Which of the following statements is
correct ?
(1) Sn41 is the oxidizing agent because
it undergoes oxidation
(2) Sn41is the reducing agent because
it undergoes oxidation
(3) H2SO3 is the reducing agent because
it undergoes oxidation
(4) H2SO3 is the reducing agent because
it undergoes reduction
39. ƒæÙæ·¤æÚU âéâ´·é¤çÜÌ (çÙçÕǸ) â´ÚU¿Ùæ ×ð´ ©ÂçSÍÌ
ÂýçÌ ÂÚU×æ‡æé ¥cÅUȤܷ¤èØ çÚUç€ÌØæð´ ·¤è â·¤Ü â´Øæ
ãæð»è Ñ
(1) 2
(2) 4
(3) 1
(4) 3
40. Îæð ƒæÅU·¤æð´ A ¥æñÚU B ·ð¤ ¥æÎàæü çßÜØÙ ·ð¤ çÜØð çِÙæð´
×ð´ âð ·¤æñÙ âãè ãæð»æ?
(1) DHçןæ‡æ 0 (zero)
(2) DHçןæ‡æ 0 (zero)
(3) A2A ¥æñÚU B2B ·¤è ÂÚUSÂÚU ÂýÖæß âð
A2B ·¤æ ÂÚUSÂÚU ÂýÖæß ¥çÏ·¤ ÂýÕÜ ãæð»æÐ
(4) A2A, B2B ¥æñÚU A2B âÖè ÂÚUSÂÚU ÂýÖæß
°·¤ â×æÙ ãñ´Ð
41. ¥çÖç·ý¤Øæ
4 2
2 2 ( )3 4
H SO Sn H O Sn HSO 3Hl →1 1 2 11 1 1 1(¦Áͽ) (¦Áͽ) (¦Áͽ) (¦Áͽ) (¦Áͽ)
·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ ×ð´ âð ·¤æñÙ-âæ âãè ãñ?
(1) Sn41 ¥æ€âè·¤æÚU·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ
ãæðÌæ ãñÐ
(2) Sn41¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ
ãæðÌæ ãñÐ
(3) H2SO3 ¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ
ãæðÌæ ãñÐ
(4) H2SO3 ¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ¥Â¿ØÙ
ãæðÌæ ãñÐ

27. English : 27 Set : 10 Hindi : 27 Set : 10
42. Which one of the following has largest
ionic radius ?
(1) Li1
(2)
2
2O
2
(3) B31
(4) F2
43. An octahedral complex with molecular
composition M.5NH3.Cl.SO4 has two
isomers, A and B. The solution of A gives
a white precipitate with AgNO3 solution
and the solution of B gives white
precipitate with BaCl2 solution. The type
of isomerism exhibited by the complex is :
(1) Linkage isomerism
(2) Ionisation isomerism
(3) Coordinate isomerism
(4) Geometrical isomerism
44. How many electrons are involved in the
following redox reaction ?
Cr2O7
221Fe211 2
2 4C O 2
® Cr311Fe311CO2 (Unbalanced)
(1) 3
(2) 4
(3) 6
(4) 5
42. çِÙæð´ ×ð´ âð ç·¤â·¤è ¥æØçÙ·¤ ç˜æ’Øæ ¥çÏ·¤Ì× ãñ?
(1) Li1
(2)
2
2O
2
(3) B31
(4) F2
43. ¥‡æé â´ÚU¿Ùæ M.5 NH3.Cl.SO4 ßæÜð ¥cÅU Ȥܷ¤èØ
â´·¤ÚU ·ð¤ Îæð â×æßØÌè A ¥æñÚU B ãñ´Ð A ·¤æ çßÜØÙ
AgNO3 ·ð¤ çßÜØÙ ·ð¤ âæÍ â$Èð¤Î ¥ßÿæð ÎðÌæ ãñ
¥æñÚU B ·¤æ çßÜØÙ BaCl2 ·ð¤ çßÜØÙ ·ð¤ âæÍ â$Èð¤Î
¥ßÿæð ÎðÌæ ãñÐ §â â´·¤ÚU mæÚUæ ÂýÎçàæüÌ â×-¥ßØßÌæ
·¤æ Âý·¤æÚU ãæð»æ Ñ
(1) çÜ´·ð¤Á (â´Øæð»è) â×-¥ßØßÌæ
(2) ¥æØÙè â×-¥ßØßÌæ
(3) â׋ßØè â×-¥ßØßÌæ
(4) ’Øæç×çžæØ â×-¥ßØßÌæ
44. çِ٠¥Â¿ØÙ-©Â¿ØÙ ¥çÖç·ý¤Øæ ×ð´ ç·¤ÌÙð §Üð€ÅþUæÙ
âãÖæ»è ãñ´?
Cr2O7
221Fe211 2
2 4C O 2
® Cr311Fe311CO2 (¥â´ÌéçÜÌ)
(1) 3
(2) 4
(3) 6
(4) 5

28. English : 28 Set : 10 Hindi : 28 Set : 10
45. Amongst LiCl, RbCl, BeCl2 and MgCl2 the
compounds with the greatest and the least
ionic character, respectively are :
(1) LiCl and RbCl
(2) RbCl and BeCl2
(3) MgCl2 and BeCl2
(4) RbCl and MgCl2
46. Nickel(Z528) combines with a
uninegative monodentate ligand to form
a diamagnetic complex [NiL4]22. The
hybridisation involved and the number of
unpaired electrons present in the complex
are respectively :
(1) sp3, two
(2) dsp2, zero
(3) dsp2, one
(4) sp3, zero
47. Which of these statements is not true ?
(1) NO1 is not isoelectronic with O2
(2) B is always covalent in its
compounds
(3) In aqueous solution, the Tl1 ion is
much more stable than Tl (III)
(4) LiAlH4 is a versatile reducing agent
in organic synthesis.
45. LiCl, RbCl, BeCl2 ¥æñÚU MgCl2 ×ð´ âð ¥çÏ·¤Ì×
¥æñÚU ‹ØêÙÌ× ¥æØÙè çßàæðáÌæ ÚU¹Ùð ßæÜð Øæñç»·¤
·ý¤×æÙéâæÚU ãñ´ Ñ
(1) LiCl ¥æñÚU RbCl
(2) RbCl ¥æñÚU BeCl2
(3) MgCl2 ¥æñÚU BeCl2
(4) RbCl ¥æñÚU MgCl2
46. çÙ·¤Ü (Z528) °·¤ «¤‡æè °·¤ ΋̷¤ çÜ»ñ´ÇU âð
Øæð» ·¤ÚU °·¤ ÂýçÌ¿éÕ·¤èØ â´·¤ÚU [NiL4]22, ÕÙæÌæ
ãñÐ §â â´·¤ÚU âð âÕç‹ÏÌ â´·¤ÚU‡æ Âý·¤æÚU ¥æñÚU
¥Øé»ç×Ì §Üñ€ÅþUæÙæð´ ·¤è ⴁØæ ·ý¤×æÙéâæÚU ãñ´ Ñ
(1) sp3, Îæð
(2) dsp2, àæê‹Ø
(3) dsp2, °·¤
(4) sp3, àæê‹Ø
47. §Ù ·¤ÍÙæð´ ×ð´ âð ·¤æñÙ-âæ ·¤ÍÙ âˆØ Ùãè´ ãñ?
(1) NO1 ÌÍæ O2 âקÜð€ÅþUæÙè Ùãè´ ãñ´Ð
(2) ÕæðÚUæÙ ¥ÂÙð Øæñç»·¤æð´ ×ð´ âÎñß âãâ´ØæðÁè ãæðÌæ
ãñÐ
(3) ÁÜèØ çßÜØÙ ×ð´, Tl (III) ·¤è ¥Âðÿææ Tl1
¥æØÙ ¥ˆØæçÏ·¤ SÍæØè ãæðÌæ ãñÐ
(4) LiAlH4 ·¤æÕüçÙ·¤ â´àÜðá‡ææð´ ×ð´ ÂýØæð» ãæðÙð
ßæÜæ °·¤ Õãé×é¹è ¥Â¿æØ·¤ ãñÐ

29. English : 29 Set : 10 Hindi : 29 Set : 10
48. Example of a three-dimensional silicate
is :
(1) Zeolites
(2) Ultramarines
(3) Feldspars
(4) Beryls
49. Amongst the following, identify the
species with an atom in 16 oxidation
state :
(1) [MnO4]2
(2) [Cr(CN)6]32
(3) Cr2O3
(4) CrO2Cl2
50. Which one of the following ores is known
as Malachite :
(1) Cu2O
(2) Cu2S
(3) CuFeS2
(4) Cu(OH)2.CuCO3
51. The major product formed when 1, 1, 12
trichloro - propane is treated with aqueous
potassium hydroxide is :
(1) Propyne
(2) 1 - Propanol
(3) 2 - Propanol
(4) Propionic acid
48. ç˜æ-çß×èØ çâçÜ·ð¤ÅUæ𴠷𤠩ÎæãÚU‡æ ãñ´ Ñ
(1) ç$ÁØæðÜæ§Åð´U
(2) ¥ËÅþUæ×ñÚUèÙð´
(3) Èð¤ËÇUSÂæÚð´U
(4) ÕðçÚUÜð´
49. çِÙæð´ ×ð´ 16 ©Â¿ØÙ ¥ßSÍæ ·ð¤ ÂÚU×æ‡æé ßæÜð
SÂèàæè$Á ·¤è Âã¿æÙ ·¤èçÁØðÐ
(1) [MnO4]2
(2) [Cr(CN)6]32
(3) Cr2O3
(4) CrO2Cl2
50. çِ٠×ð´ âð ·¤æñÙ ×ñÜæ·¤æ§ÅU ¥ØS·¤ Ùæ× âð ÁæÙè
ÁæÌè ãñ Ñ
(1) Cu2O
(2) Cu2S
(3) CuFeS2
(4) Cu(OH)2.CuCO3
51. ÁÕ 1, 1, 12 ÅþU槀ÜæðÚUæðÂýæðÂðÙ ·¤è ÁÜèØ ÂæðÅñUçàæØ×
ãæÇþUæ€âæ§ÇU âð ç·ý¤Øæ ·¤è ÁæÌè ãñ Ìæð ÂýæŒÌ ãé§ü Õɸè
×æ˜ææ ·¤æ ç·ý¤Øæ È¤Ü ãæðÌæ ãñ Ñ
(1) ÂýæðÂæ§Ù
(2) 1 - ÂýæðÂðÙæòÜ
(3) 2 - ÂýæðÂðÙæòÜ
(4) ÂýæðçÂØæçÙ·¤ °ðçâÇU

30. English : 30 Set : 10 Hindi : 30 Set : 10
52. Which one of the following is an example
of thermosetting polymers ?
(1) Neoprene
(2) Buna -N
(3) Nylon 6, 6
(4) Bakelite
53. The correct IUPAC name of the following
compound
is :
(1) 4 - methyl - 3 - ethylhexane
(2) 3 - ethyl - 4 - methylhexane
(3) 3, 4 - ethylmethylhexane
(4) 4 - ethyl - 3 - methylhexane
54. Which one of the following substituents at
para-position is most effective in
stabilizing the phenoxide ,
ion ?
(1) 2CH3
(2) 2OCH3
(3) 2COCH3
(4) 2CH2OH
52. §Ù ×ð´ âð ·¤æñÙ ÌæÂÎëɸ ÕãéÜ·¤ ãñ?
(1) çÙØæðÂýèÙ
(2) ÕêÙæ - N
(3) Ùæ§ÜæÙ 6, 6
(4) Õñ·ð¤Üæ§ÅU
53. §â Øæñç»·¤
·¤æ âãè IUPAC Ùæ× ãñ Ñ
(1) 4 - ×ðçÍÜ - 3 - °çÍÜãñ€âðÙ
(2) 3 - °çÍÜ - 4 - ×ðçÍÜãñ€âðÙ
(3) 3, 4 - °çÍÜ×ðçÍÜãñ€âðÙ
(4) 4 - °çÍÜ - 3 - ×ðçÍÜãñ€âðÙ
54. çِ٠ÂýçÌSÍæ·¤æð´ ×ð´ âð ·¤æñÙ Èñ¤Ùæ€âæ§ÇU ¥æØÙ
, ·ð¤ ÂñÚUæ SÍæÙ ÂÚU ãæðÙð âð §âð
¥çÏ·¤Ì× SÍæØè ÕÙæÙð ×ð´ ÂýÖæßè ãæðÌæ ãñ?
(1) 2CH3
(2) 2OCH3
(3) 2COCH3
(4) 2CH2OH

31. English : 31 Set : 10 Hindi : 31 Set : 10
55. The final product formed when Methyl
amine is treated with NaNO2 and HCl
is :
(1) Diazomethane
(2) Methylalcohol
(3) Methylcyanide
(4) Nitromethane
56. Which one of the following compounds
will not be soluble in sodium
bicarbonate ?
(1) 2, 4, 6 - Trinitrophenol
(2) Benzoic acid
(3) o - Nitrophenol
(4) Benzene sulphonic acid
57. Williamson synthesis of ether is an example
of :
(1) Nucleophilic addition
(2) Electrophilic addition
(3) Electrophilic substitution
(4) Nucleophilic substitution
55. ×ðçÍÜ °×èÙ ·¤è NaNO2 ¥æñÚU HCl ·ð¤ âæÍ ç·ý¤Øæ
·¤ÚUÙð ÂÚU ©ÂÜŽÏ ¥ç‹Ì× ¥çÖç·ý¤Øæ È¤Ü ãæðÌæ ãñ Ñ
(1) ÇU槰ð$Áæð×èÍðÙ
(2) ×ðçÍÜ °ðË·¤æðãæÜ
(3) ×ðçÍÜçâØæÙæ§ÇU
(4) Ùæ§ÅþUæð×èÍðÙ
56. §Ù×ð´ âð ·¤æñÙ-âæ Øæñç»·¤ âæðçÇUØ× Õ槷¤æÕæðüÙðÅU ×ð´
Ùãè´ ƒæéÜð»æ?
(1) 2, 4, 6 - ÅþUæ§üÙæ§ÅþUæðç$ȤÙæòÜ
(2) Õñ‹$Áæ𧷤 °ðçâÇU
(3) o - Ùæ§ÅþUæðç$ȤÙæòÜ
(4) Õñ‹$ÁèÙ âË$ȤæçÙ·¤ °ðçâÇU
57. §üÍÚU ·¤æ çßçÜØ×âÙ â´àÜðá‡æ §Ù×ð´ âð 緤⠷¤æ
©ÎæãÚU‡æ ãñ?
(1) ‹Øêç€ÜØæðç$ȤçÜ·¤ â´·¤ÜÙ
(2) §Üñ€ÅþUæðç$ȤçÜ·¤ â´·¤ÜÙ
(3) §Üñ€ÅþUæðç$ȤçÜ·¤ ÂýçÌSÍæÂÙ
(4) ‹Øêç€ÜØæðç$ȤçÜ·¤ ÂýçÌSÍæÂÙ

32. English : 32 Set : 10 Hindi : 32 Set : 10
58. The reason for double helical structure of
DNA is the operation of :
(1) Electrostatic attractions
(2) van der Waals forces
(3) Dipole - Dipole interactions
(4) Hydrogen bonding
59. Among the following organic acids, the
acid present in rancid butter is :
(1) Pyruvic acid
(2) Lactic acid
(3) Butyric acid
(4) Acetic acid
58. §Ù×ð´ âð ·¤æñÙ-âè ç·ý¤Øæ DNA ·¤è ÎæðãÚUè ·é¤‡ÇUÜèÎæÚU
â´ÚU¿Ùæ ·¤æ ·¤æÚU‡æ ãæðÌè ãñ?
(1) çSÍÚUßñléÌ ¥æ·¤áü‡æ
(2) ßæÙÇUÚU ßæÜ ·ð¤ ÕÜ
(3) çmÏýéß - çmÏýéß ÂÚUSÂÚU ç·ý¤Øæ
(4) ãæ§ÇþUæðÁÙ ¥æÕ‹ÏÙ
59. Îé»ü‹Ïè ×€¹Ù ×ð´ ÂæØæ ÁæÙð ßæÜæ °ðçâÇU çِ٠°ðçâÇUæð´
×ð´ âð ·¤æñÙ-âæ ãæðÌæ ãñ?
(1) Âæ§L¤çß·¤ °ðçâÇU
(2) Üñç€ÅU·¤ °ðçâÇU
(3) ŽØéÅUèçÚU·¤ °ðçâÇU
(4) °âèçÅU·¤ °ðçâÇU

33. English : 33 Set : 10 Hindi : 33 Set : 10
60. In a set of reactions p - nitrotoluene yielded
a product E
The product E would be :
(1)
(2)
(3)
(4)
60. ¥çÖç·ý¤Øæ¥æ𴠷𤠧⠷ý¤× ×ð´
p - Ùæ§ÅþUæðÅUæËØé§üÙ âð ÂýæŒÌ ç·ý¤ØæÈ¤Ü E ãæð»æ Ñ
(1)
(2)
(3)
(4)

34. English : 34 Set : 10 Hindi : 34 Set : 10
PART C — MATHEMATICS
61. Let f : R®R be defined by f(x)5
1
1
x
x
2
1
then f is :
(1) both one - one and onto
(2) one - one but not onto
(3) onto but not one - one
(4) neither one - one nor onto.
62. For all complex numbers z of the form
11ia, a e R, if z25x1iy, then :
(1) y224x1250
(2) y214x2450
(3) y224x1450
(4) y214x1250
63. The equation 2
3 5x x1 1 5x23, where x
is real, has :
(1) no solution
(2) exactly one solution
(3) exactly two solutions
(4) exactly four solutions.
Öæ» C — »ç‡æÌ
61. ×æÙæ f : R®R , f(x)5
1
1
x
x
2
1
mæÚUæ ÂçÚUÖæçáÌ ãñ,
Ìæð f :
(1) °·ñ¤·¤è ÌÍæ ¥æ‘ÀUæÎè ÎæðÙæð´ ãñ´Ð
(2) °·ñ¤·¤è ãñ ÂÚ ¥æ‘ÀUæÎè Ùãè´ ãñÐ
(3) ¥æ‘ÀUæÎè ãñ ÂÚU °·ñ¤·¤è Ùãè´ ãñÐ
(4) Ù Ìæð °·ñ¤·¤è ãñ ¥æñÚU Ù ãè ¥æ‘ÀUæÎè ãñÐ
62. 11ia, a e R ·¤è Âý·¤æÚU ·¤è âÖè âç×Ÿæ ⴁØæ¥æð´
z ·ð¤ çÜØð, ØçÎ z25x1iy ãñ, Ìæð :
(1) y224x1250
(2) y214x2450
(3) y224x1450
(4) y214x1250
63. â×è·¤ÚU‡æ 2
3 5x x1 1 5x23, Áãæ¡ x ßæSÌçß·¤
ãñ, ·¤æ / ·ð¤ :
(1) ·¤æð§ü ãÜ Ùãè´ ãñ´Ð
(2) ÆUè·¤ °·¤ ãÜ ãñÐ
(3) ÆUè·¤ Îæð ãÜ ãñ´Ð
(4) ÆUè·¤ ¿æÚU ãÜ ãñ´Ð

35. English : 35 Set : 10 Hindi : 35 Set : 10
64. Let A and B be any two 333 matrices. If
A is symmetric and B is skewsymmetric,
then the matrix AB2BA is :
(1) skewsymmetric
(2) symmetric
(3) neither symmetric nor
skewsymmetric
(4) I or 2I, where I is an identity matrix.
65. If
( ) ( ) ( )( )
r
2
r 2r 1 3r 2
n
n 1 a
2
1 1
n n 1 n 1 n 1 3n 4
2 2
2 2
D 5 2
2 2 2 1 ,
then the value of ∑
n 1
r
r 1
2
D
5
:
(1) depends only on a
(2) depends only on n
(3) depends both on a and n
(4) is independent of both a and n.
64. ×æÙæ A ÌÍæ B ·¤æð§ü Îæð 333 ·ð¤ ¥æÃØêã ãñ´Ð ØçÎ A
â×ç×Ì ãñ ÌÍæ B çßá× â×ç×Ì ãñ, Ìæð ¥æÃØêã
AB2BA :
(1) çßá× â×ç×Ì ãñ
(2) â×ç×Ì ãñ
(3) Ù Ìæð â×ç×Ì ãñ´ ¥æñÚU Ù ãè çßá× â×ç×Ì ãñ
(4) I ¥Íßæ 2I ãñ´, Áãæ¡ I °·¤ ̈â×·¤ ¥æÃØêã
ãñÐ
65. ØçÎ
( ) ( ) ( )( )
r
2
r 2r 1 3r 2
n
n 1 a
2
1 1
n n 1 n 1 n 1 3n 4
2 2
2 2
D 5 2
2 2 2 1
ãñ´, Ìæð ∑
n 1
r
r 1
2
D
5
·¤æ ×æÙ :
(1) ·ð¤ßÜ a ÂÚU çÙÖüÚU ãñ
(2) ·ð¤ßÜ n ÂÚU çÙÖüÚU ãñ
(3) a ÌÍæ n ÎæðÙæð´ ÂÚU çÙÖüÚU ãñ´
(4) a ÌÍæ n ÎæðÙæð´ âð SßÌ´˜æ ãñ´Ð

36. English : 36 Set : 10 Hindi : 36 Set : 10
66. Two women and some men participated
in a chess tournament in which every
participant played two games with each
of the other participants. If the number of
games that the men played between them-
selves exceeds the number of games that
the men played with the women by 66,
then the number of men who participated
in the tournament lies in the interval :
(1) [8, 9]
(2) [10, 12)
(3) (11, 13]
(4) (14, 17)
67. The coefficient of x1012 in the expansion of
(11xn1x253)10, (where n £ 22 is any
positive integer), is :
(1) 1
(2) 10C4
(3) 4n
(4) 253C4
66. àæÌÚ´UÁ ·¤è °·¤ ÂýçÌØæðç»Ìæ ×ð´ Îæð ×çãÜæ¥æð´ ÌÍæ ·é¤ÀU
ÂéL¤áæð´ Ùð Öæ» çÜØæ çÁâ×ð´ ÂýˆØð·¤ ÂýçÌØæð»è Ùð àæðá
ÂýˆØð·¤ ÂýçÌØæð»è âð Îæð ÕæçÚUØæ´ ¹ðÜèÐ ØçÎ ÂéL¤áæð´ Ùð
¥æÂâ ×ð´ çÁÌÙè ÕæçÚUØæ´ ¹ðÜè ©Ù·¤è ⴁØæ ÂéL¤áæð´
mæÚUæ ×çãÜæ¥æð´ ·ð¤ âæÍ ¹ðÜè ÕæçÚUØæð´ ·¤è ⴁØæ âð 66
¥çÏ·¤ ãñ´, Ìæð ÂéL¤áæð´ ·¤è ⴁØæ, çÁ‹ãæð´Ùðð ÂýçÌØæð»èÌæ ×ð´
Öæ» çÜØæ, çِ٠¥´ÌÚUæÜ ×ð´ ãñ´ Ñ
(1) [8, 9]
(2) [10, 12)
(3) (11, 13]
(4) (14, 17)
67. (11xn1x253)10, (Áã¡æ n £ 22 ·¤æð§ü ÏÙ Âê‡ææZ·¤
ãñ´)·ð¤ ÂýâæÚU ×ð´ x1012 ·¤æ »é‡ææ´·¤ ãñ´ Ñ
(1) 1
(2) 10C4
(3) 4n
(4) 253C4

37. English : 37 Set : 10 Hindi : 37 Set : 10
68. The number of terms in an A.P. is even;
the sum of the odd terms in it is 24 and
that the even terms is 30. If the last term
exceeds the first term by 10
1
2
, then the
number of terms in the A.P. is :
(1) 4
(2) 8
(3) 12
(4) 16
69. Let f(n) 5
n
n
 
  
1 3
3 100
1 , where [n] denotes
the greatest integer less than or equal to n.
Then ( )f n∑
56
n 15
is equal to :
(1) 56
(2) 689
(3) 1287
(4) 1399
68. ç·¤âè â×æ´ÌÚU Ÿæðɸè ×ð´ ÂÎæð´ ·¤è ⴁØæ â× ãñÐ §â·ð¤
çßá× ÂÎæð´ ·¤æ Øæð» 24 ãñ ÌÍæ â× ÂÎæð´ ·¤æ Øæð» 30
ãñÐ ØçÎ ¥´çÌ× ÂÎ, ÂýÍ× ÂÎ âð 10
1
2
¥çÏ·¤ ãñ, Ìæð
â×æ´ÌÚU Ÿæðɸè ×ð´ ÂÎæð´ ·¤è ⴁØæ ãñ Ñ
(1) 4
(2) 8
(3) 12
(4) 16
69. ×æÙæ f(n)5
n
n
 
  
1 3
3 100
1 , Áãæ¡ [n] °·¤ ×ãžæ×
Âê‡ææZ·¤, Áæð n âð ÀUæðÅUæ ¥Íßæ ÕÚUæÕÚU ãñ, Ìæð
( )f n∑
56
n 15
ÕÚUæÕÚU ãñ Ñ
(1) 56
(2) 689
(3) 1287
(4) 1399

38. English : 38 Set : 10 Hindi : 38 Set : 10
70. If the function
( )2
2 cos 1
,
( )
k ,
x
x
f x x
x

≠



1 2
p
5 p 2
5p
is continuous at x5p, then k equals :
(1) 0
(2)
1
2
(3) 2
(4)
1
4
71. Let f: R ® R be a function such that
?f(x)? £ x2, for all x e R. Then, at x50, f is :
(1) continuous but not differentiable
(2) continuous as well as differentiable
(3) neither continuous nor differentiable
(4) differentiable but not continuous.
70. ØçΠȤÜÙ ( )2
2 cos 1
,
( )
k ,
x
x
f x x
x

≠



1 2
p
5 p 2
5p
x5p ÂÚU âÌÌ ãñ, Ìæð k ÕÚUæÕÚU ãñ :
(1) 0
(2)
1
2
(3) 2
(4)
1
4
71. ×æÙæ f: R ® R °·¤ °ðâæ ȤÜÙ ãñ ç·¤ âÖè x e R ·ð¤
çÜ° ?f(x)? £ x2 ãñ, Ìæð x50 ÂÚU f :
(1) âÌÌ ãñ ÂÚU ¥ß·¤ÜÙèØ Ùãè´ ãñ
(2) âÌÌ ÌÍæ ¥ß·¤ÜÙèØ ÎæðÙæð´ ãñ´
(3) Ù Ìæð âÌÌ ãñ ¥æñÚU Ù ãè ¥ß·¤ÜÙèØ ãñ
(4) ¥ß·¤ÜÙèØ ãñ ÂÚU âÌÌ Ùãè´ ãñÐ

39. English : 39 Set : 10 Hindi : 39 Set : 10
72. If non-zero real numbers b and c are such
that min f(x) max g(x), where
f(x)5x212bx12c2 and
g(x)52x222cx1b2 (x e R) ;
then
c
b
lies in the interval :
(1)
1
0,
2
 
 
 
(2)


 
1 1
,
2 2
(3)
1
, 2
2
 
 
 
(4) ( )2,∞
73. If the volume of a spherical ball is
increasing at the rate of 4p cc/sec, then
the rate of increase of its radius
(in cm/sec), when the volume is 288p cc,
is :
(1)
1
6
(2)
1
9
(3)
1
36
(4)
1
24
72. ØçÎ àæê‹ØðÌÚU ßæSÌçß·¤ ⴁØæ°¡ b ÌÍæ c °ðâè ãñ´ ç·¤
min f(x) max g(x), Áãæ¡ f(x)5x212bx12c2
ÌÍæ g(x)52x222cx1b2 (x e R) ãñ´,
Ìæð
c
b
çÁâ ¥´ÌÚUæÜ ×ð´ ãñ, ßã ãñ :
(1)
1
0,
2
 
 
 
(2)


 
1 1
,
2 2
(3)
1
, 2
2
 
 
 
(4) ( )2 ,∞
73. ØçÎ °·¤ »æðÜæ·¤æÚU »ð´Î ·¤æ ¥æØÌÙ 4p ƒæÙ âð×è/âñ.
·¤è ÎÚU âð Õɸ ÚUãæ ãñ, Ìæð ÁÕ ¥æØÌÙ 288p ƒæÙ âð×è
ãñ, Ìæð ç˜æ’Øæ çÁâ ÎÚU (âð×è/âñ. ×ð´) âð Õɸ ÚUãè ãñ, ßã
ãñ :
(1)
1
6
(2)
1
9
(3)
1
36
(4)
1
24

40. English : 40 Set : 10 Hindi : 40 Set : 10
74. If m is a non - zero number and
( )
5 1 4 1
32
2
d ( ) c
1
m m
m m
x x
x f x
x x
∫
2 2
1
5 1
1 1
,
then f(x) is :
(1)
( )
5
22
2 1
m
m m
x
m x x1 1
(2)
( )
4
22
2 1
m
m m
x
m x x1 1
(3)
( )
( )
5 4
22
2
1
m m
m m
m x x
x x
1
1 1
(4)
( )
( )
5 4
22
2 1
m m
m m
x x
m x x
2
1 1
74. ØçÎ m °·¤ àæê‹ØðÌÚU ⴁØæ ãñ ÌÍæ
( )
5 1 4 1
32
2
d ( ) c
1
m m
m m
x x
x f x
x x
∫
2 2
1
5 1
1 1
ãñ, Ìæð f(x) ãñ :
(1)
( )
5
22
2 1
m
m m
x
m x x1 1
(2)
( )
4
22
2 1
m
m m
x
m x x1 1
(3)
( )
( )
5 4
22
2
1
m m
m m
m x x
x x
1
1 1
(4)
( )
( )
5 4
22
2 1
m m
m m
x x
m x x
2
1 1

41. English : 41 Set : 10 Hindi : 41 Set : 10
75. Let function F be defined as
t
1
e
( ) dt , 0
t
x
F x x ∫5 then the value of
the integral
x
∫
t
1
e
dt
t a1
, where
a 0, is :
(1) ea[F(x)2F(11a)]
(2) e2a[F(x1a)2F(a)]
(3) ea[F(x1a)2F(11a)]
(4) e2a[F(x1a)2F(11a)]
76. The area of the region above the x-axis
bounded by the curve y5tan x, 0 £ x £
2
p
and the tangent to the curve at x5
4
p
is :
(1)
1 1
log 2
2 2
 
 
 
2
(2)
1 1
log 2
2 2
 
 
 
1
(3) ( )
1
1 log 2
2
2
(4) ( )
1
1 log 2
2
1
75. ×æÙæ ȤÜÙ F,
t
1
e
( ) dt , 0
t
x
F x x ∫5 mæÚUæ
ÂçÚUÖæçáÌ ãñ, Ìæð â×æ·¤Ü
x
∫
t
1
e
dt
t a1
, Áãæ¡
a 0 ãñ, ·¤æ ×æÙ ãñ :
(1) ea[F(x)2F(11a)]
(2) e2a[F(x1a)2F(a)]
(3) ea[F(x1a)2F(11a)]
(4) e2a[F(x1a)2F(11a)]
76. ß·ý¤ y5tan x, 0 £ x £
2
p
ÌÍæ ß·ý ÂÚU x5
4
p
ÂÚU ¹è´¿è »§ü SÂàæü ÚðU¹æ mæÚUæ çƒæÚðU ÿæð˜æ, Áæð x ¥ÿæ âð
ª¤ÂÚU ãñ, ·¤æ ÿæð˜æÈ¤Ü ãñ :
(1)
1 1
log 2
2 2
 
 
 
2
(2)
1 1
log 2
2 2
 
 
 
1
(3) ( )
1
1 log 2
2
2
(4) ( )
1
1 log 2
2
1

42. English : 42 Set : 10 Hindi : 42 Set : 10
77. If
y
x
d
d
1y tan x5sin 2x and y(0)51, then
y(p) is equal to :
(1) 1
(2) 21
(3) 25
(4) 5
78. The circumcentre of a triangle lies at the
origin and its centroid is the mid point of
the line segment joining the points
(a211, a211) and (2a, 22a), a ¹ 0. Then
for any a, the orthocentre of this triangle
lies on the line :
(1) y22ax50
(2) y2(a211)x50
(3) y1x50
(4) (a21)2x2(a11)2y50
77. ØçÎ
y
x
d
d
1y tan x5sin 2x ÌÍæ y(0)51 ãñ Ìæð
y(p) ÕÚUæÕÚU ãñ :
(1) 1
(2) 21
(3) 25
(4) 5
78. °·¤ ç˜æÖéÁ ·¤æ ÂçÚU·ð´¤Îý ×êÜ çÕ‹Îé ÂÚU ãñ ÌÍæ ©â·¤æ
·ð¤‹Îý·¤, çÕ‹Îé¥æð´ (a211, a211) ÌÍæ (2a, 22a),
a ¹ 0 ·¤æð ç×ÜæÙð ßæÜð ÚðU¹æ¹´ÇU ·¤æ ×ŠØ çÕ´Îé ãñ, Ìæð
ç·¤âè a ·¤ð çÜ° §â ç˜æÖéÁ ·¤æ Ü´Õ ·ð¤‹Îý çÁâ ÚðU¹æ
ÂÚU çSÍÌ ãñ, ßã ãñ Ñ
(1) y22ax50
(2) y2(a211)x50
(3) y1x50
(4) (a21)2x2(a11)2y50

43. English : 43 Set : 10 Hindi : 43 Set : 10
79. If a line L is perpendicular to the line
5x2y51, and the area of the triangle
formed by the line L and the coordinate
axes is 5, then the distance of line L from
the line x15y50 is :
(1)
7
5
(2)
5
13
(3)
7
13
(4)
5
7
80. The equation of the circle described on the
chord 3x1y1550 of the circle
x21y2516 as diameter is :
(1) x21y213x1y21150
(2) x21y213x1y1150
(3) x21y213x1y2250
(4) x21y213x1y22250
79. ØçÎ °·¤ ÚðU¹æ L, ÚðU¹æ 5x2y51 ÂÚU Ü´ÕßÌ ãñ ÌÍæ
ÚðU¹æ L ÌÍæ çÙÎðüàææ´·¤ ¥ÿææð´ mæÚUæ ÕÙè ç˜æÖéÁ ·¤æ ÿæð˜æȤÜ
5 ãñ, Ìæð ÚðU¹æ L ·¤è ÚðU¹æ x15y50 âð ÎêÚUè ãñ :
(1)
7
5
(2)
5
13
(3)
7
13
(4)
5
7
80. ßëžæ x21y2516 ·¤è °·¤ Áèßæ 3x1y1550
·¤æð ÃØæâ ×æÙ·¤Ú ¹è´¿ð »° ßëžæ ·¤æ â×è·¤ÚU‡æ ãñ :
(1) x21y213x1y21150
(2) x21y213x1y1150
(3) x21y213x1y2250
(4) x21y213x1y22250

44. English : 44 Set : 10 Hindi : 44 Set : 10
81. A chord is drawn through the focus of the
parabola y256x such that its distance from
the vertex of this parabola is
5
2
, then its
slope can be :
(1)
5
2
(2)
3
2
(3)
2
5
(4)
2
3
82. The tangent at an extremity (in the first
quadrant) of latus rectum of the hyperbola
22
1
4 5
yx
2 5 ,meets x - axis and y - axis
at A and B respectively. Then
(OA)22(OB)2, where O is the origin,
equals :
(1)
20
9
2
(2)
16
9
(3) 4
(4)
4
3
2
81. ÂÚUßÜØ y256x ·¤è ÙæçÖ âð ãæð·¤ÚU ÁæÌè °·¤ Áèßæ
¹è´¿è »§ü ãñ çÁâ·¤è ÂÚUßÜØ ·ð¤ àæèáü âð ÎêÚUè
5
2
ãñ,
Ìæð §â·¤è ÉUæÜ ãæð â·¤Ìè ãñ :
(1)
5
2
(2)
3
2
(3)
2
5
(4)
2
3
82. ¥çÌÂÚUßÜØ
22
1
4 5
yx
2 5 ·ð¤ ÙæçÖÜ´Õ ·ð¤ °·¤
çâÚðU (Áæð ÂýÍ× ¿ÌéÍæZàæ ×ð´ ãñ) ÂÚU ¹è´¿è »§ü SÂàæü
ÚðU¹æ x-¥ÿæ ÌÍæ y-¥ÿæ ·¤æð ·ý ×àæ çÕ‹Îé¥æð´ A ÌÍæ B
ÂÚU ç×ÜÌè ãñ´, Ìæð (OA)22(OB)2, Áãæ¡ O ×êÜ çÕ´Îé
ãñ, ÕÚUæÕÚU ãñ :
(1)
20
9
2
(2)
16
9
(3) 4
(4)
4
3
2

45. English : 45 Set : 10 Hindi : 45 Set : 10
83. Equation of the line of the shortest distance
between the lines
yx z
1 1 1
5 5
2
and
yx z11
0 2 1
12
5 5
2
is :
(1)
yx z
1 1 2
5 5
2 2
(2)
yx z11
1 1 2
12
5 5
2 2
(3)
yx z11
1 1 1
12
5 5
2
(4)
yx z
2 1 2
5 5
2
84. If the angle between the line
2(x11)5y5z14 and the plane
2x2y1 l z1450 is
6
p
, then the value
of l is :
(1)
135
7
(2)
45
11
(3)
45
7
(4)
135
11
83. ÚðU¹æ¥æð´
yx z
1 1 1
5 5
2
ÌÍæ
yx z11
0 2 1
12
5 5
2
·ð¤ Õè¿ ‹ØêÙÌ× ÎêÚUè
ßæÜè ÚðU¹æ ·¤æ â×è·¤ÚU‡æ ãñ :
(1)
yx z
1 1 2
5 5
2 2
(2)
yx z11
1 1 2
12
5 5
2 2
(3)
yx z11
1 1 1
12
5 5
2
(4)
yx z
2 1 2
5 5
2
84. ØçÎ ÚðU¹æ 2(x11)5y5z14 ÌÍæ â×ÌÜ
2x2y1 l z1450 ·ð¤ Õè¿ ·¤æ ·¤æð‡æ 6
p
ãñ, Ìæð
l ·¤æ ×æÙ ãñ :
(1)
135
7
(2)
45
11
(3)
45
7
(4)
135
11

46. English : 46 Set : 10 Hindi : 46 Set : 10
85. If x i j kˆˆ ˆ3 65 2 2
r
, y i j kˆˆ ˆ4 35 1 2
r
and z i j kˆˆ ˆ3 4 125 2 2
r
, then the
magnitude of the projection of x y3
r r
on z
r
is :
(1) 12
(2) 15
(3) 14
(4) 13
86. Let A and E be any two events with
positive probabilities :
Statement - 1 : P(E/A) ³ P(A/E)P(E)
Statement - 2 : P(A/E) ³ P(AÇE).
(1) Both the statements are true
(2) Both the statements are false
(3) Statement - 1 is true, Statement - 2 is
false
(4) Statement - 1 is false, Statement - 2
is true.
85. ØçÎ x i j kˆˆ ˆ3 65 2 2
r
, y i j kˆˆ ˆ4 35 1 2
r
ÌÍæ z i j kˆˆ ˆ3 4 125 2 2
r
ãñ´ Ìæð x y3
r r
·ð¤ z
r
ÂÚU
Âýÿæð ·¤æ ÂçÚU×æ‡æ ãñ :
(1) 12
(2) 15
(3) 14
(4) 13
86. ×æÙæ A ÌÍæ E ·¤æð§ü Îæð °ðâè ƒæÅUÙæ°¡ ãñ çÁÙ·¤è
ÂýæçØ·¤Ìæ°¡ ÏÙæˆ×·¤ ãñ´ Ñ
·¤ÍÙ-1 : P(E/A) ³ P(A/E)P(E)
·¤ÍÙ-2 : P(A/E) ³ P(AÇE).
(1) ÎæðÙæð´ ·¤ÍÙ âˆØ ãñ´
(2) ÎæðÙæð´ ·¤ÍÙ ¥âˆØ ãñ´
(3) ·¤ÍÙ-1 âˆØ ãñ, ·¤ÍÙ-2 ¥âˆØ ãñ
(4) ·¤ÍÙ-1 ¥âˆØ ãñ, ·¤ÍÙ-2 âˆØ ãñÐ

47. English : 47 Set : 10 Hindi : 47 Set : 10
87. Let x , M and s 2 be respectively the mean,
mode and variance of n observations
x1, x2, ..., xn and di52xi2a, i51, 2, ..., n,
where a is any number.
Statement I : Variance of d1, d2, ..., dn is
s2.
Statement II : Mean and mode of
d1, d2, ..., dn are 2 x 2a and 2M2a,
respectively
(1) Statement I and Statement II are
both false
(2) Statement I and Statement II are
both true
(3) Statement I is true and Statement II
is false
(4) Statement I is false and Statement II
is true
88. The function f x x x( ) sin 4 cos 25 1 , is a
periodic function with period :
(1) 2p
(2) p
(3)
2
p
(4)
4
p
87. ×æÙæ n Âýðÿæ‡ææð´ x1, x2, ..., xn·ð¤ ×æŠØ ÕãéÜ·¤ ÌÍæ
ÂýâÚU‡æ ·ý¤×àæÑ x , M ÌÍæ s 2 ÌÍæ di52xi2a,
i51, 2, ..., n ãñ´, Áãæ¡ a ·¤æð§ü ⴁØæ ãñ´Ð
·¤ÍÙ I : d1, d2, ..., dn ·¤æ ÂýâÚU‡æ s2 ãñ´
·¤ÍÙ II : d1, d2, ..., dn ·ð¤ ×æŠØ ÌÍæ ÕãéÜ·¤
·ý¤×æàæÑ 2 x 2a ÌÍæ 2M2a ãñ
(1) ·¤ÍÙ I ÌÍæ ·¤ÍÙ II ÎæðÙæð´ ¥âˆØ ãñ´Ð
(2) ·¤ÍÙ I ÌÍæ ·¤ÍÙ II ÎæðÙæð´ âˆØ ãñ´Ð
(3) ·¤ÍÙ I âˆØ ãñ ÌÍæ ·¤ÍÙ II ¥âˆØ ãñÐ
(4) ·¤ÍÙ I ¥âˆØ ãñ ÌÍæ ·¤ÍÙ II âˆØ ãñÐ
88. ȤÜÙ f x x x( ) sin 4 cos 25 1 °·¤ ¥æßçÌü
ȤÜÙ ãñ çÁâ·¤æ ¥æßÌü ·¤æÜ ãñ :
(1) 2p
(2) p
(3)
2
p
(4)
4
p

48. English : 48 Set : 10 Hindi : 48 Set : 10
89. The principal value of
1 43
tan cot
4
 
 
 
2 p
is :
(1)
3
4
p
2
(2)
3
4
p
(3)
4
p
2
(4)
4
p
90. The contrapositive of the statement “if I
am not feeling well, then I will go to the
doctor” is :
(1) If I am feeling well, then I will not
go to the doctor
(2) If I will go to the doctor, then I am
feeling well
(3) If I will not go to the doctor, then I
am feeling well
(4) If I will go to the doctor, then I am
not feeling well.
- o 0 o -
89.
1 43
tan cot
4
 
 
 
2 p
·¤æ ×éØ×æÙ ãñ :
(1)
3
4
p
2
(2)
3
4
p
(3)
4
p
2
(4)
4
p
90. ·¤ÍÙ ÒÒØçÎ ×ñ´ ¥SßSÍ ã¡ê, Ìæð ×ñ´ ÇUæ€ÅUÚU ·ð¤ Âæâ
Á檡¤»æÓÓ ·¤æ ÂýçÌÏÙæˆ×·¤ ãñ
(1) ØçÎ ×ñ´ SßSÍ ã¡ê, Ìæð ÇUæ€ÅUÚU ·ð¤ Âæâ Ùãè´ Á檡¤»æ
(2) ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Á檡¤»æ, Ìæð ×ñ´ SßSÍ ã¡ê
(3) ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Ùãè´ Á檡¤»æ, Ìæð ×ñ´
SßSÍ ã¡ê
(4) ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Á檡¤»æ, Ìæð ×ñ´ SßSÍ
Ùãè´ ã¡êÐ
- o 0 o -