PART A — PHYSICS
1.
Match List - I (Event) with List - II (Order 1.
of the time interval for happening of the
event) and select the correct option from
the options given below the lists.
List - I
Öæ» A — ÖæñçÌ·¤ çߙææÙ
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
List - II
(a)
Rotation period
(i) 10 5 s
of earth
(a)
(b)
Revolution
period of earth
(b)
(c)
Period of a light
(iii) 10 215 s
wave
(c)
(d)
Period of a
sound wave
(d)
(ii) 10 7 s
(iv) 10 23 s
ÇϤÍ- I
§ÐûÄÍ œ‰Ë ìËÏøËá¾
œ‰ËÁ
§ÐûÄÍ œ‰Ë §Ì¿Uœâ‰¼øË
œ‰ËÁ
•œ‰ §âœ‰ËÅË ±¿™U œ‰Ë œ‰ËÁ
•œ‰ çÄ̾ ±¿™U œ‰Ë
œ‰ËÁ
ÇϤÍ- II
(i) 105 s
(ii) 107 s
(iii) 10215 s
(iv) 1023 s
(1)
(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(1)
(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(2)
(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
(2)
(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
(3)
(a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
(3)
(a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
(4)
(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
(4)
(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
English : 1
Set : 10
Hindi : 1
Set : 10
th
2.
1
A bullet looses   of its velocity passing 2.
n
through one plank. The number of such
planks that are required to stop the bullet
can be :
3.
1
°· ÕéÜðÅU °·¤ ́Ìð âð »éÁÚUÙð ×ð´ ¥ÂÙð ßð» ·ð¤  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)
n2
2n21
(1)
n2
2n21
(2)
2n 2
n21
(2)
2n 2
n21
(3)
Infinite
(3)
¥Ù‹Ì
(4)
n
(4)
n
A heavy box is to be dragged along a rough 3.
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
°·¤ ¹éÚUÎéÚðU ÿæñçÌÁ Ȥàæü ÂÚU °·¤ ÖæÚUè Հâð ·¤æð ¹è´¿æ
ÁæÌæ ãñÐ °ðâæ ·¤ÚUÙð ·ð¤ çÜØð, ÃØç€Ì A ·¤æð ÿæñçÌÁ âð
308 ·¤æð‡æ ÂÚU π·¤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´ Հâð
·ð¤ Õè¿ ƒæáü‡æ »é‡ææ¡·¤
F
A
3
, the ratio F is :
5
B
(1)
3
(1)
3
(2)
5
3
(2)
5
3
(3)
3
2
(3)
3
2
(4)
2
3
(4)
2
3
English : 2
Set : 10
Hindi : 2
3
5
ãñ´, ÌÕ ¥ÙéÂæÌ
F
A
F
B
ãñ´ :
Set : 10
4.
What is Ffriction at point P ? It is assumed
°·¤ 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 çՋÎé P ÂÚU Fƒæáü‡æ €Øæ ãñ´? Øã ×æÙ Üð´
ç·¤ ÕðÜÙ çȤâÜÌæ Ùãè´ ãñ´Ð
(1)
Mg
(1)
Mg
(2)
Ma
(2)
Ma
(3)
Ma
2
(3)
Ma
2
(4)
Ma
3
(4)
Ma
3
Consider a cylinder of mass M resting on 4.
a rough horizontal rug that is pulled out
from under it with acceleration ‘a’
perpendicular to the axis of the cylinder.
that the cylinder does not slip.
English : 3
Set : 10
Hindi : 3
Set : 10
5.
5.
makes angle f with the horizontal. Then :
°·¤ ª¤ŠßæüÏÚU ç¿·¤Ùð ¥hüßëžæèØ ÂÍ ·ð¤ çՋÎé 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 çՋÎé Y
ÂÚU â×æ# ãæð ÁæÌè ãñ´ Áãæ¡ OY ÿæñçÌÁ âð ·¤æð‡æ f
ÕÙæÌæ ãñÐ ÌÕ Ñ
(1)
sin f5cos u
(1)
sin f5cos u
(2)
sin f5
1
cos u
2
(2)
sin f5
1
cos u
2
(3)
sin f5
2
cos u
3
(3)
sin f5
2
cos u
3
(4)
sin f5
3
cos u
4
(4)
sin f5
3
cos u
4
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
English : 4
Set : 10
Hindi : 4
Set : 10
6.
A ball of mass 160 g is thrown up at an 6.
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)
7.
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× çՋÎé ÂÚU ©â çՋÎé ·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
(1)
1.73 kg m2/s
(2)
3.0 kg m2/s
(2)
3.0 kg m2/s
(3)
3.46 kg m2/s
(3)
3.46 kg m2/s
(4)
6.0 kg m2/s
(4)
6.0 kg m2/s
The gravitational field in a region is 7.
r
given by g 5 5N/kg iˆ 1 12 N/kg ˆj . The
change in the gravitational potential
energy of a particle of mass 2 kg when it is
°·¤ ÿæð˜æ ×ð´ »éL¤ˆßæ·¤áü‡æ ÿæð˜æ §â Âý·¤æÚU çÎØæ ÁæÌæ ãñ´
r
g 5 5N/kg iˆ 1 12 N/kg ˆj ÎýÃØ×æÙ 2 kg ·ð¤
°·¤ ·¤‡æ ·¤æð ×êÜ çՋÎé âð çՋÎé (7 m,23 m) Üð
ÁæÙð ×ð´ »éL¤ˆßèØ çSÍçÌÁ ª¤Áæü ×ð´ ÂçÚUßÌüÙ ãñ´ :
taken from the origin to a point
(7 m,23 m) is :
(1)
71 J
(1)
71 J
(2)
13 58 J
(2)
13 58 J
(3)
271 J
(3)
271 J
(4)
1J
(4)
1J
English : 5
Set : 10
Hindi : 5
Set : 10
8.
The velocity of water in a river is 8.
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 water510 22
°·¤ 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
poise.
(1)
1021 N/m2
(1)
1021 N/m2
(2)
1022 N/m2
(2)
1022 N/m2
(3)
1023 N/m2
(3)
1023 N/m2
(4)
1024 N/m2
(4)
1024 N/m2
9.
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
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)
at which water flows through the tube is
(g510 ms22)
(1)
7.5 cc/s
(1)
7.5 cc/s
(2)
8.0 cc/s
(2)
8.0 cc/s
(3)
10.0 cc/s
(3)
10.0 cc/s
(4)
12.5 cc/s
(4)
12.5 cc/s
English : 6
Set : 10
Hindi : 6
Set : 10
10.
A large number of liquid drops each of 10.
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
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)
big drop is (given surface tension of liquid
T, density r)
(1)
T1
1
 2 
R
rr
(1)
T1
1
 2 
R
rr
(2)
2T  1
1
 2 
r r
R
(2)
2T  1
1
 2 
r r
R
(3)
4T  1
1
 2 
r r
R
(3)
4T  1
1
 2 
r r
R
(4)
6T  1
1
 2 
r r
R
(4)
6T  1
1
 2 
r r
R
English : 7
Set : 10
Hindi : 7
Set : 10
11.
A black coloured solid sphere of radius R 11.
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 aT 3 per unit mass with the
temperature T of the sphere, where a is a
constant, then the time taken for the sphere
°·¤ »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´)
to cool down to temperature 2T0 will be
(s is Stefan Boltzmann constant)
12.
(1)
Ma
3
ln  
2
4 pR

(1)
Ma
3
ln  
2
4 pR

(2)
Ma
 16 
ln  
2
4 pR
 
(2)
Ma
 16 
ln  
2
4 pR
 
(3)
Ma
 16 
ln  
2
16 pR
 
(3)
Ma
 16 
ln  
2
16 pR
 
(4)
Ma
3
ln  
16 pR 2

(4)
Ma
3
ln  
16 pR 2

A gas is compressed from a volume of 12.
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 :
°·¤ »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)
Increases by 250 J
(1)
(2)
Decreases by 250 J
(2)
(3)
Increases by 50 J
(3)
(4)
Decreases by 50 J
(4)
English : 8
Set : 10
âð Õɸð»è
250 J âð ƒæÅðU»è
50 J âð Õɸð»è
50 J âð ƒæÅðU»è
250 J
Hindi : 8
Set : 10
13.
attained is much less than radius of the
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´)
earth. (kB is Boltzmann constant)
(1) 0
(1)
0
A gas molecule of mass M at the surface 13.
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
14.
(2)
273 k B
2 Mg
(2)
273 k B
2 Mg
(3)
546 k B
3 Mg
(3)
546 k B
3 Mg
(4)
819 k B
2 Mg
(4)
819 k B
2 Mg
A body is in simple harmonic motion with 14.
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
°·¤ 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
its amplitude.
(1)
4 cm/s
(1)
4 cm/s
(2)
6 cm/s
(2)
6 cm/s
(3)
12 cm/s
(3)
12 cm/s
(4)
16 cm/s
(4)
16 cm/s
English : 9
Set : 10
Hindi : 9
Set : 10
15.
The total length of a sonometer wire 15.
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
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 ß㠋ØêÙÌ× ©ÖØçÙcÆU
¥æßëçžæ, çÁââð ç·¤ ÌèÙæð´ Öæ» ·¤ÂÙ ·¤ÚU â·ð´¤»ð´, ãñ´
frequency with which three parts can
vibrate ?
16.
(1)
1100 Hz
(1)
1100 Hz
(2)
1000 Hz
(2)
1000 Hz
(3)
166 Hz
(3)
166 Hz
(4)
100 Hz
(4)
100 Hz
The electric field in a region of space is 16.
given
by,
→
∧
∧
E 5 Eo i 1 2 Eo j
where
E05100 N/C. The flux of this field through
a circular surface of radius 0.02 m parallel
×é€Ì ¥æ·¤æàæ ·ð¤ °·¤ ÿæð˜æ ×ð´ çßléÌ ÿæð˜æ çÎØæ ÁæÌæ ãñ´
→
∧
∧
E 5 Eo i 1 2 Eo j
Áãæ¡
E 0 5100 N/C Ð
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
to the Y-Z plane is nearly :
(1)
0.125 Nm2/C
(1)
0.125 Nm2/C
(2)
0.02 Nm2/C
(2)
0.02 Nm2/C
(3)
0.005 Nm2/C
(3)
0.005 Nm2/C
(4)
3.14 Nm2/C
(4)
3.14 Nm2/C
English : 10
Set : 10
Hindi : 10
Set : 10
17.
at one plate to Î 2 at the other. The
capacitance of capacitor is :
°·¤ 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
(1)
Î0(Î11Î2)A/d
(2)
Î0(Î21Î1)A/2d
(2)
Î0(Î21Î1)A/2d
(3)
Î0A/[d
(3)
Î0A/[d
(4)
Î0(Î22Î1)A/[d
(4)
Î0(Î22Î1)A/[d
ÂýˆØð·¤
100 W
The gap between the plates of a parallel 17.
plate capacitor of area A and distance
between plates d, is filled with a dielectric
whose permittivity varies linearly from Î1
ln(Î2/Î1)]
ln(Î2/Î1)]
18.
ln(Î2/Î1)]
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
·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
will be :
(1)
0.45 A
(1)
0.45 A
(2)
0.90 A
(2)
0.90 A
(3)
1.35 A
(3)
1.35 A
(4)
1.80 A
(4)
1.80 A
English : 11
Set : 10
Hindi : 11
Set : 10
19.
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
10 cm ÖéÁæ
·¤æ °·¤ ß»æü·¤æÚU Èðý¤× ¥æñÚU ÏæÚUæ 1 A âð
ÂýßæçãÌ °·¤ ܐÕæ âèÏæ ÌæÚU ·¤æ»$Á ·ð¤ ÌÜ ×ð´ ÚU¹ð
ãñ´Ð ÌæÚU ·ð¤ â×è âð, Èýð¤× Îæ¡Øè ¥æðÚU °·¤ çSÍÚU ¿æÜ
10 ms21 âð »çÌ ·¤ÚUÌæ ãñ´Ð (翘æ Îð¹ð´)Ð ÌæÚU âð
ÁÕ Èýð¤× ·¤è Õæ¡Øè ÖéÁæ x510 cm ÂÚU ãñ´ ÌÕ ©â
â×Ø ÂýðçÚUÌ çßléÌ ßæã·¤ ÕÜ ãñ´ Ñ
left arm of the frame is at x510 cm from
the wire is :
(1)
2 mV
(1)
2 mV
(2)
1 mV
(2)
1 mV
(3)
0.75 mV
(3)
0.75 mV
(4)
0.5 mV
(4)
0.5 mV
English : 12
Set : 10
Hindi : 12
Set : 10
20.
of intensity B, the magnetic field Bs inside
¥çÌ¿æÜ·¤ ¥æÎàæü ¥Ùé¿éÕ·¤ ·¤æ °·¤ ©ÎæãÚU‡æ ãñÐ
§â·¤æ ¥Íü ãñ ç·¤ ÁÕ ÌèßýÌæ B ·ð¤ °·¤ ¿éÕ·¤èØ ÿæð˜æ
×ð´ ¥çÌ¿æÜ·¤ ·¤æð ÚU¹æ ÁæÌæ ãñ´, ÌÕ ¥çÌ¿æÜ·¤ ·ð¤
¥‹ÎÚU ¿éÕ·¤èØ ÿæð˜æ Bs §â Âý·¤æÚU ãæð»æ Ñ
(1)
Bs52B
(1)
Bs52B
(2)
Bs50
(2)
Bs50
(3)
Bs5B
(3)
Bs5B
(4)
Bs<B but Bs ≠ 0
(4)
An example of a perfect diamagnet is a 20.
superconductor. This implies that when a
superconductor is put in a magnetic field
the superconductor will be such that :
English : 13
Set : 10
Bs<B ÂÚ´UÌé Bs ≠ 0
Hindi : 13
Set : 10
21.
21.
Figure shows a circular area of radius R
→
where a uniform magnetic field B is going
into the plane of paper and increasing in
magnitude at a constant rate. In that case,
which of the following graphs, drawn
schematically, correctly shows the
翘æ ç˜æ’Øæ R ·ð¤ °·¤ ßëžæèØ ÿæð˜æÈ¤Ü ·¤æð ÎàææüÌæ ãñ
→
Áãæ¡ °·¤ °·¤â×æÙ ¿éÕ·¤èØ ÿæð˜æ B ·¤æ»$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?
variation of the induced electric field
E(r) ?
(1)
(1)
(2)
(2)
English : 14
Set : 10
Hindi : 14
Set : 10
22.
(3)
(3)
(4)
(4)
If denote microwaves, X rays, infrared, 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´ çߋØæâ çِÙçÜç¹Ì ãæð»æ Ñ
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
(1)
(2)
M, R, V, X, U, G and I
(2)
(3)
G, X, U, V, I, M and R
(3)
(4)
I, M, R, U, V, X and G
(4)
English : 15
Set : 10
¥æñÚU G
M, R, V, X, U, G ¥æñÚU I
G, X, U, V, I, M ¥æñÚU R
I, M, R, U, V, X ¥æñÚU G
R, M, I, V, U, X
Hindi : 15
Set : 10
23.
A ray of light is incident from a denser to
a rarer medium. The critical angle for total 23.
internal reflection is uiC and the Brewster’s
angle of incidence is u iB , such that
sinu iC /sinu iB 5h51.28. The relative
refractive index of the two media is :
24.
°·¤ 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
(1)
0.2
(3)
0.8
(2)
0.4
(4)
0.9
(3)
0.8
(4)
0.9
The diameter of the objective lens of
microscope makes an angle b at the focus 24.
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.
°·¤ âê ÿ ×Îàæèü ·ð ¤ ¥çÖÎë à Ø·¤ 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)
Increases with decreasing value of n
(2)
Increases with decreasing value of b
(1)
(3)
Increases with increasing value of
(2)
n sin 2b
(3)
(4)
n ·¤æ
×æÙ ƒæÅUÙð âð Õɸð»è
b ·¤æ ×æÙ ƒæÅUÙð âð Õɸð»è
n sin 2b ·¤æ ×æÙ ÕɸÙð âð Õɸð»è
Increases with increasing value of
1
n sin 2b
English : 16
(4)
Set : 10
Hindi : 16
1
n sin 2b
·¤æ ×æÙ ÕɸÙð âð Õɸð»è
Set : 10
25.
In a Young’s double slit experiment, the 25.
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
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
slit diffraction pattern is :
(1)
3
(1)
3
(2)
6
(2)
6
(3)
12
(3)
12
(4)
24
(4)
24
English : 17
Set : 10
Hindi : 17
Set : 10
26.
Match List - I (Experiment performed) 26.
with List - II (Phenomena discovered/
associated) and select the correct option
from the options given below the lists :
List - I
Davisson
(a) and Germer
Experiment
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
ÇÏ¤Í - I
List - II
(i)
Wave nature of
electrons
Millikan’s oil
Charge of an
(b) drop
(ii)
electron
experiment
ÇÏ¤Í - II
(a)
¬ÕUÄÍǾ ŠËÖ¿U ¦¼á¿U
§â½ËÕ (i)
ŒÁÕþªãU˾Ëՙ œ‰Ë ±¿™U §âœ‰Ë¿U
(b)
̼ÌÁœ‰Ë¾ œ‰Ë ³âÄ
œÕ‰ Ì ¿U¾Õ œ‰Ë §â½ËÕ (ii)
ŒÁÕþªãU˾ œ‰Ë
ŠËÄÕÅË
Rutherford
experiment
(iii)
Quantisation of
energy levels
(c)
¿U³¿U­‰ËÕ¬áU §â½ËÕ (iii)
‰¦Ëá S±¿U œ‰Ë
þÄËøªÍœ‰¿UøË
Franck (d) Hertz
experiment
(iv)
Existence of
nucleus
(d)
­Ö♉œ‰ - ȪáU¦
§â½ËÕ (iv)
¾ËÌ»œ‰ œ‰Ë
ŠÌS±íÄ
(c)
(1)
(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(1)
(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(2)
(a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
(2)
(a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
(3)
(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(3)
(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(4)
(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
(4)
(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
English : 18
Set : 10
Hindi : 18
Set : 10
27.
A piece of wood from a recently cut tree 27.
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
°·¤ 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
approximately :
(1)
10439 years
(1)
10439
(2)
13094 years
(2)
13094
(3)
19039 years
(3)
19039
(4)
39049 years
(4)
39049
ßáü
ßáü
ßáü
ßáü
28.
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
English : 19
Set : 10
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
Hindi : 19
Set : 10
29.
Long range radio transmission is possible 29.
when the radiowaves are reflected from
the ionosphere. For this to happen the
frequency of the radiowaves must be in the
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
range :
(1)
80 - 150 MHz
(1)
80 - 150 MHz
(2)
8 - 25 MHz
(2)
8 - 25 MHz
(3)
1 - 3 MHz
(3)
1 - 3 MHz
(4)
150 - 500 kHz
(4)
150 - 500 kHz
English : 20
Set : 10
Hindi : 20
Set : 10
30.
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
°·¤ 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
against the string length of the pendulum
in the figure.
What is the value of g at the place ?
§â SÍæÙ ÂÚU g ·¤æ ×æÙ ãñ´Ð
(1)
9.81 m/s2
(1)
9.81 m/s2
(2)
9.87 m/s2
(2)
9.87 m/s2
(3)
9.91 m/s2
(3)
9.91 m/s2
(4)
10.0 m/s2
(4)
10.0 m/s2
English : 21
Set : 10
Hindi : 21
Set : 10
PART B — CHEMISTRY
31.
Ionization energy of gaseous Na atoms is 31.
495.5 kJmol 21 . The lowest possible
frequency of light that ionizes a sodium
atom is (h56.626310234 Js,
NA56.02231023 mol21)
32.
Öæ» B — ÚUâæØÙ çߙææÙ
»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
(1)
7.503104 s21
(2)
4.7631014 s21
(2)
4.7631014 s21
(3)
3.1531015 s21
(3)
3.1531015 s21
(4)
1.2431015 s21
(4)
1.2431015 s21
Choose the correct statement with respect 32.
to the vapour pressure of a liquid among
ç·¤âè Îýß ·ð¤ ßæc ÎæÕ ·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ ×ð´
âð âãè °·¤ ·¤ÍÙ ·¤æð ¿éçÙ° Ñ
the following :
(1)
Increases linearly with increasing
(1)
temperature
(2)
Increases
non-linearly
with
(2)
Decreases linearly with increasing
(3)
increasing temperature
(3)
temperature
(4)
Decreases
non-linearly
with
increasing temperature
English : 22
Set : 10
(4)
ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
ÕɸÌæ ãñÐ
ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ Ù âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
ÕɸÌæ ãñÐ
ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
ƒæÅUÌæ ãñÐ
ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ Ù âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
ƒæÅUÌæ ãñÐ
Hindi : 22
Set : 10
33.
Which one of the following molecules is 33.
çِ٠¥‡æé¥æð´ ×ð´ âð ·¤æñÙ ¥Ùé¿éÕ·¤èØ ãñ?
paramagnetic ?
34.
(1)
N2
(1)
N2
(2)
NO
(2)
NO
(3)
CO
(3)
CO
(4)
O3
(4)
O3
Zirconium
phosphate
[Zr 3 (PO 4 ) 4 ] 34.
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 K sp
correct ?
is
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}
(1)
S5{Ksp/(6912)1/7}
(2)
S5{Ksp/144}1/7
(2)
S5{Ksp/144}1/7
(3)
S5(Ksp/6912)1/7
(3)
S5(Ksp/6912)1/7
(4)
S5{Ksp/6912}7
(4)
S5{Ksp/6912}7
English : 23
Set : 10
Hindi : 23
Set : 10
35.
For the decomposition of the compound, 35.
represented as
NH2COONH4(s) ì 2NH3(g)1CO2(g)
âð âêç¿Ì Øæñç»·¤ ·ð¤ çßØæðÁÙ ·ð¤ çÜØð
the Kp52.931025 atm3.
If the reaction is started with 1 mol of the
Kp52.931025 atm3
compound,
the
total
pressure
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
at
equilibrium would be :
36.
NH2COONH4(s) ì 2NH3(g)1CO2(g)
(1)
1.9431022 atm
(1)
1.9431022 atm
(2)
5.8231022 atm
(2)
5.8231022 atm
(3)
7.6631022 atm
(3)
7.6631022 atm
(4)
38.831022 atm
(4)
38.831022 atm
For the reaction,
36.
¥çÖç·ý¤Øæ
3A12B ® C1D,
3A12B ® C1D
the differential rate law can be written
·ð¤ çÜØð ¥ß·¤Ü ÎÚU çÙØ× çܹæ Áæ â·¤Ìæ ãñ Ñ
as :
(1)
d [C ]
1 d [A ]
n
m
5
5 k [A ] [ B ]
3 dt
dt
(1)
d [C]
1 d [A ]
n
m
5
5 k [A ] [ B ]
3 dt
dt
(2)
2
d [A ]
d [C ]
n
m
5
5 k [A ] [ B ]
dt
dt
(2)
2
d [A ]
d [C ]
n
m
5
5 k [A ] [ B ]
dt
dt
(3)
1
d [C ]
1 d [A ]
n
m
52
5 k [A ] [ B ]
3 dt
dt
(3)
1
d [C]
1 d [A ]
n
m
52
5 k [A ] [ B ]
3 dt
dt
(4)
2
d [C ]
1 d [A ]
n
m
5
5 k [A ] [ B ]
3 dt
dt
(4)
2
d [C]
1 d [A ]
n
m
5
5 k [A ] [ B ]
3 dt
dt
English : 24
Set : 10
Hindi : 24
Set : 10
37.
Sulphur dioxide and oxygen were allowed 37.
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
°·¤ 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
mass of sulphur532 u) :
38.
(1)
7.09
(1)
7.09
(2)
14.1
(2)
14.1
(3)
10.0
(3)
10.0
(4)
28.2
(4)
28.2
The observed osmotic pressure for a 38.
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
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
258 C
Hoff factor (i) will be respectively :
(R50.082 L atm k2mol21)
(R50.082 L atm k2×æðÜ21)
(1)
5 and 4.42
(1)
(2)
4 and 4.00
(2)
(3)
5 and 3.42
(3)
(4)
3 and 5.42
(4)
English : 25
Set : 10
¥æñÚU 4.42
4 ¥æñÚU 4.00
5 ¥æñÚU 3.42
3 ¥æñÚU 5.42
5
Hindi : 25
Set : 10
39.
structure is :
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
(1)
2
(2)
4
(2)
4
(3)
1
(3)
1
(4)
3
(4)
3
The total number of octahedral void(s) per 39.
atom present in a cubic close packed
40.
A and B, which of the following is true ?
Îæð ƒæÅU·¤æð´ A ¥æñÚU B ·ð¤ ¥æÎàæü çßÜØÙ ·ð¤ çÜØð çِÙæð´
×ð´ âð ·¤æñÙ âãè ãæð»æ?
(1)
DHmixing < 0 (zero)
(1)
(2)
DHmixing > 0 (zero)
(2)
(3)
A2B interaction is stronger than
(3)
For an ideal solution of two components 40.
A2A and B2B interactions
(4)
A2A, B2B and A2B interactions
are identical
41.
Consider the reaction :
41.
41
21
H 2 SO 3(aq)1Sn (aq)
1H 2 O (l ) → Sn (aq)
1HSO24(aq)13H1(aq)
Which of the following statements is
¥æñ Ú U B2B ·¤è ÂÚU S ÂÚU Âý Ö æß âð
A2B ·¤æ ÂÚUSÂÚU ÂýÖæß ¥çÏ·¤ ÂýÕÜ ãæð»æÐ
(4) A2A, B2B ¥æñÚU A2B âÖè ÂÚUSÂÚU ÂýÖæß
°·¤ â×æÙ ãñ´Ð
¥çÖç·ý¤Øæ
Sn41 is the oxidizing agent because
·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ ×ð´ âð ·¤æñÙ-âæ âãè ãñ?
(1)
it undergoes oxidation
(2)
Sn41is the reducing agent because
(2)
it undergoes oxidation
(3)
H2SO3 is the reducing agent because
(3)
H2SO3 is the reducing agent because
(4)
it undergoes oxidation
(4)
it undergoes reduction
English : 26
Set : 10
A2A
41
21
H 2 SO 3(¦Áͽ)1Sn(¦Áͽ)
1H 2 O(l ) → Sn(¦Áͽ)
1HSO24(¦Áͽ)13H1
(¦Áͽ)
correct ?
(1)
DHçןæ‡æ < 0 (zero)
DHçןæ‡æ > 0 (zero)
Sn41 ¥æ€âè·¤æÚU·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ
ãæðÌæ ãñÐ
Sn41¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ
ãæðÌæ ãñÐ
H2SO3 ¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ
ãæðÌæ ãñÐ
H2SO3 ¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ¥Â¿ØÙ
ãæðÌæ ãñÐ
Hindi : 26
Set : 10
42.
Which one of the following has largest 42.
çِÙæð´ ×ð´ âð ç·¤â·¤è ¥æØçÙ·¤ ç˜æ’Øæ ¥çÏ·¤Ì× ãñ?
ionic radius ?
43.
(1)
Li1
(1)
Li1
(2)
O2
(2)
O2
(3)
B31
(3)
B31
(4)
F2
(4)
F2
22
An octahedral complex with molecular 43.
composition M.5NH 3 .Cl.SO 4 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 :
44.
22
¥‡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)
Linkage isomerism
(1)
(2)
Ionisation isomerism
(2)
(3)
Coordinate isomerism
(3)
(4)
Geometrical isomerism
(4)
çÜ´·ð¤Á (â´Øæð»è) â×-¥ßØßÌæ
¥æØÙè â×-¥ßØßÌæ
â׋ßØè â×-¥ßØßÌæ
’Øæç×çžæØ â×-¥ßØßÌæ
following redox reaction ?
çِ٠¥Â¿ØÙ-©Â¿ØÙ ¥çÖç·ý¤Øæ ×ð´ ç·¤ÌÙð §Üð€ÅþUæÙ
âãÖæ»è ãñ´?
Cr2O7221Fe211 C 2 O 242
Cr2O7221Fe211 C 2 O 242
How many electrons are involved in the 44.
®
Cr311Fe311CO2 (Unbalanced)
®
(1)
3
(1)
3
(2)
4
(2)
4
(3)
6
(3)
6
(4)
5
(4)
5
English : 27
Set : 10
Hindi : 27
Cr311Fe311CO2
(¥â´ÌéçÜÌ)
Set : 10
45.
Amongst LiCl, RbCl, BeCl2 and MgCl2 the 45.
compounds with the greatest and the least
ionic character, respectively are :
46.
(1)
LiCl and RbCl
(2)
(3)
RbCl and BeCl2
MgCl2 and BeCl2
(4)
RbCl and MgCl2
Nickel(Z528)
combines
with
a 46.
uninegative monodentate ligand to form
a diamagnetic complex [NiL 4 ] 22 . The
hybridisation involved and the number of
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
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
unpaired electrons present in the complex
are respectively :
47.
(1)
sp3, two
(1)
sp3, Îæð
(2)
dsp2, zero
(2)
dsp2,
(3)
dsp2, one
(3)
(4)
sp3, zero
(4)
Which of these statements is not true ?
(1)
(2)
NO1 is not isoelectronic with O2
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.
English : 28
Set : 10
47.
àæê‹Ø
dsp2, °·¤
sp3, àæê‹Ø
§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
Hindi : 28
Set : 10
48.
Example of a three-dimensional silicate 48.
ç˜æ-çß×èØ çâçÜ·ð¤ÅUæ𴠷𤠩ÎæãÚU‡æ ãñ´ Ñ
is :
49.
(1)
Zeolites
(2)
Ultramarines
(3)
Feldspars
(4)
Beryls
ç$ÁØæðÜæ§Åð´U
(2) ¥ËÅþUæ×ñÚUèÙð´
(3) Èð¤ËÇUSÂæÚð´U
(4) ÕðçÚUÜð´
çِÙæð´ ×ð´ 16 ©Â¿ØÙ ¥ßSÍæ ·ð¤ ÂÚU×æ‡æé ßæÜð
SÂèàæè$Á ·¤è Âã¿æÙ ·¤èçÁØðÐ
(1)
Amongst the following, identify the 49.
species with an atom in 16 oxidation
state :
50.
51.
(1)
[MnO4]2
(1)
[MnO4]2
(2)
[Cr(CN)6]32
(2)
[Cr(CN)6]32
(3)
Cr2O 3
(3)
Cr2O3
(4)
CrO2Cl2
(4)
CrO2Cl2
as Malachite :
çِ٠×ð´ âð ·¤æñÙ ×ñÜæ·¤æ§ÅU ¥ØS·¤ Ùæ× âð ÁæÙè
ÁæÌè ãñ Ñ
(1)
Cu 2O
(1)
Cu 2O
(2)
Cu 2S
(2)
Cu2S
(3)
CuFeS2
(3)
CuFeS2
(4)
Cu(OH)2.CuCO3
(4)
Cu(OH)2.CuCO3
Which one of the following ores is known 50.
The major product formed when 1, 1, 12 51.
trichloro - propane is treated with aqueous
potassium hydroxide is :
(1)
Propyne
(2)
1 - Propanol
(3)
2 - Propanol
(4)
Propionic acid
English : 29
Set : 10
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
Hindi : 29
Set : 10
52.
Which one of the following is an example 52.
§Ù ×ð´ âð ·¤æñÙ ÌæÂÎëɸ ÕãéÜ·¤ ãñ?
of thermosetting polymers ?
53.
(1)
Neoprene
(1)
(2)
Buna -N
(2)
(3)
Nylon 6, 6
(3)
(4)
Bakelite
(4)
The correct IUPAC name of the following 53.
çÙØæðÂýèÙ
ÕêÙæ - N
Ùæ§ÜæÙ 6, 6
Õñ·ð¤Üæ§ÅU
§â Øæñç»·¤
compound
is :
54.
(1)
4 - methyl - 3 - ethylhexane
(2)
3 - ethyl - 4 - methylhexane
(3)
3, 4 - ethylmethylhexane
(4)
4 - ethyl - 3 - methylhexane
Which one of the following substituents at 54.
·¤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
çِ٠ÂýçÌSÍæ·¤æð´ ×ð´ âð ·¤æñÙ Èñ¤Ùæ€âæ§ÇU ¥æØÙ
para-position is most effective in
,
stabilizing the phenoxide
,
·ð ¤ Âñ Ú U æ SÍæÙ ÂÚU ãæð Ù ð âð §âð
¥çÏ·¤Ì× SÍæØè ÕÙæÙð ×ð´ ÂýÖæßè ãæðÌæ ãñ?
ion ?
(1)
2CH3
(1)
2CH3
(2)
2OCH3
(2)
2OCH3
(3)
2COCH3
(3)
2COCH3
(4)
2CH2OH
(4)
2CH2OH
English : 30
Set : 10
Hindi : 30
Set : 10
55.
amine is treated with NaNO2 and HCl
×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)
Diazomethane
(1)
(2)
Methylalcohol
(2)
(3)
Methylcyanide
(3)
(4)
Nitromethane
(4)
The final product formed when Methyl 55.
is :
56.
Which one of the following compounds 56.
will
not
be
soluble
in
sodium
ÇU槰ð$Áæð×èÍðÙ
×ðçÍÜ °ðË·¤æðãæÜ
×ðçÍÜçâØæÙæ§ÇU
Ùæ§ÅþUæð×èÍðÙ
§Ù×ð´ âð ·¤æñÙ-âæ Øæñç»·¤ âæðçÇUØ× Õ槷¤æÕæðüÙðÅU ×ð´
Ùãè´ ƒæéÜð»æ?
bicarbonate ?
57.
(1)
2, 4, 6 - Trinitrophenol
(1)
(2)
Benzoic acid
(2)
(3)
o - Nitrophenol
(3)
(4)
Benzene sulphonic acid
(4)
Williamson synthesis of ether is an example 57.
of :
(1)
Nucleophilic addition
(2)
Electrophilic addition
(3)
Electrophilic substitution
(4)
Nucleophilic substitution
English : 31
Set : 10
ÅþUæ§üÙæ§ÅþUæðç$ȤÙæòÜ
Õñ‹$Áæ𧷤 °ðçâÇU
o - Ùæ§ÅþUæðç$ȤÙæòÜ
Õñ‹$ÁèÙ âË$ȤæçÙ·¤ °ðçâÇU
2, 4, 6 -
§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
Hindi : 31
Set : 10
58.
The reason for double helical structure of 58.
DNA is the operation of :
59.
(1)
Electrostatic attractions
(2)
van der Waals forces
(3)
Dipole - Dipole interactions
(4)
Hydrogen bonding
Among the following organic acids, the 59.
acid present in rancid butter is :
(1)
Pyruvic acid
(2)
Lactic acid
(3)
Butyric acid
(4)
Acetic acid
English : 32
Set : 10
§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 ¥æՋÏÙ
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
Hindi : 32
Set : 10
60.
In a set of reactions p - nitrotoluene yielded 60.
¥çÖç·ý¤Øæ¥æ𴠷𤠧⠷ý¤× ×ð´
a product E
The product E would be :
p - Ùæ§ÅþUæðÅUæËØé§üÙ
(1)
(1)
(2)
(2)
(3)
(3)
(4)
(4)
English : 33
Set : 10
Hindi : 33
âð ÂýæŒÌ ç·ý¤ØæÈ¤Ü E ãæð»æ Ñ
Set : 10
Öæ» C — »ç‡æÌ
PART C — MATHEMATICS
61.
62.
Let f : R®R be defined by f(x)5
×æÙæ f : R®R , f(x)5
then f is :
Ìæð
(1)
both one - one and onto
(1)
(2)
one - one but not onto
(2)
(3)
onto but not one - one
(3)
(4)
neither one - one nor onto.
(4)
For all complex numbers z of the form 62.
11ia, a e R, if
63.
x 21
61.
x 11
z25x1iy,
then :
°·ñ¤·¤è ÌÍæ ¥æ‘ÀUæÎè ÎæðÙæð´ ãñ´Ð
°·ñ¤·¤è ãñ ÂÚ ¥æ‘ÀUæÎè Ùãè´ ãñÐ
¥æ‘ÀUæÎè ãñ ÂÚU °·ñ¤·¤è Ùãè´ ãñÐ
Ù Ìæð °·ñ¤·¤è ãñ ¥æñÚU Ù ãè ¥æ‘ÀUæÎè ãñÐ
11ia, a e R ·¤è
z ·ð¤
çÜØð, ØçÎ
Âý·¤æÚU ·¤è âÖè âç×Ÿæ ⴁØæ¥æð´
ãñ, Ìæð :
z25x1iy
y 2 24x1250
(1)
y 224x1250
(2)
y 2 14x2450
(2)
y 214x2450
(3)
y 2 24x1450
(3)
y 224x1450
(4)
y 2 14x1250
(4)
y 214x1250
3x 21x15 5x23, where x 63.
is real, has :
(1)
no solution
(2)
exactly one solution
(3)
exactly two solutions
(4)
exactly four solutions.
English : 34
Set : 10
mæÚUæ ÂçÚUÖæçáÌ ãñ,
f :
(1)
The equation
x 21
x 11
â×è·¤ÚU‡æ 3x 21x15 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
Hindi : 34
Set : 10
64.
A is symmetric and B is skewsymmetric,
×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
then the matrix AB2BA is :
AB2BA :
(1)
skewsymmetric
(1)
(2)
symmetric
(2)
(3)
neither
Let A and B be any two 333 matrices. If 64.
symmetric
nor
(3)
I or 2I, where I is an identity matrix.
(4)
çßá× â×ç×Ì ãñ
â×ç×Ì ãñ
Ù Ìæð â×ç×Ì ãñ´ ¥æñÚU Ù ãè çßá× â×ç×Ì ãñ
skewsymmetric
(4)
65. If
65.
Dr 5
r
n
2
1
n ( n 2 1)
2
2r 2 1
3r 2 2
n2 1
a
( n 2 1 )2
then the value of
n2 1
∑
r5 1
1
( n 2 1 )( 3n 1 4 ) ,
2
Dr :
ØçÎ
Dr 5
ãñ´, Ìæð
depends only on a
(2)
depends only on n
(1)
(3)
depends both on a and n
(2)
(4)
is independent of both a and n.
(3)
(4)
Set : 10
2r 2 1
3r 2 2
n2 1
a
( n 2 1 )2
1
( n 2 1 )( 3n 1 4 )
2
r
n
2
1
n ( n 2 1)
2
(1)
English : 35
¥Íßæ 2I ãñ´, Áãæ¡ I °·¤ ̈â×·¤ ¥æÃØêã
ãñÐ
I
n2 1
∑
r5 1
Dr
·¤æ ×æÙ :
·ð¤ßÜ a ÂÚU çÙÖüÚU ãñ
·ð¤ßÜ n ÂÚU çÙÖüÚU ãñ
a ÌÍæ n ÎæðÙæð´ ÂÚU çÙÖüÚU ãñ´
a ÌÍæ n ÎæðÙæð´ âð SßÌ´˜æ ãñ´Ð
Hindi : 35
Set : 10
66.
Two women and some men participated 66.
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 themselves exceeds the number of games that
the men played with the women by 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´Ùð ÂýçÌØæð»èÌæ ×ð´
Öæ» çÜØæ, çِ٠¥´ÌÚUæÜ ×ð´ ãñ´ Ñ
then the number of men who participated
in the tournament lies in the interval :
67.
(1)
[8, 9]
(1)
[8, 9]
(2)
[10, 12)
(2)
[10, 12)
(3)
(11, 13]
(3)
(11, 13]
(4)
(14, 17)
(4)
(14, 17)
The coefficient of x1012 in the expansion of 67.
(11x n 1x 253 ) 10 ,
(where n £ 22 is any
(11xn1x253)10,
ãñ´)·ð¤ ÂýâæÚU ×ð´
(Áã¡æ n £ 22 ·¤æð§ü ÏÙ Âê‡ææZ·¤
»é‡ææ´·¤ ãñ´ Ñ
x1012 ·¤æ
positive integer), is :
(1)
1
(2)
10C
(3)
4n
(4)
253C
English : 36
4
4
Set : 10
(1)
1
(2)
10C
(3)
4n
(4)
253C
Hindi : 36
4
4
Set : 10
68.
The number of terms in an A.P. is even; 68.
the sum of the odd terms in it is 24 and
that the even terms is 30. If the last term
1
ãñÐ ØçÎ ¥´çÌ× ÂÎ, ÂýÍ× ÂÎ âð 10 2 ¥çÏ·¤ ãñ, Ìæð
1
, then the
2
number of terms in the A.P. is :
exceeds the first term by 10
69.
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
â×æ´ÌÚU Ÿæðɸè ×ð´ ÂÎæð´ ·¤è ⴁØæ ãñ Ñ
(1)
4
(1)
4
(2)
8
(2)
8
(3)
12
(3)
12
(4)
16
(4)
16
3n 
1
n , where [n] denotes 69.
Let f(n) 5  1
100 
3
×æÙæ f(n)5  3 1 100  n , Áãæ¡
1
the greatest integer less than or equal to n.
Âê ‡ ææZ · ¤, Áæð
Then
56
∑ f ( n ) is equal to :
n5 1
56
∑ f ( n)
n5 1
(1)
56
(1)
56
(2)
689
(2)
689
(3)
1287
(3)
1287
(4)
1399
(4)
1399
English : 37
Set : 10
Hindi : 37
n
3n 
[n]
°·¤ ×ãžæ×
âð ÀU æ ð Å U æ ¥Íßæ ÕÚU æ ÕÚU ãñ , Ìæð
ÕÚUæÕÚU ãñ Ñ
Set : 10
70.
If the function
 2 1 cos x2 1
, x ≠p

2
f (x ) 5  ( p 2 x )
k
, x5p

71.
70.
ØçΠȤÜÙ
is continuous at x5p, then k equals :
x5p ÂÚU
(1)
0
(1)
0
(2)
1
2
(2)
1
2
(3)
2
(3)
2
(4)
1
4
(4)
1
4
Let f: R ® R be a function such that 71.
?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.
English : 38
Set : 10
 2 1 cos x2 1
, x ≠p

2
f (x ) 5  ( p 2 x )
k
, x5p

âÌÌ ãñ, Ìæð k ÕÚUæÕÚU ãñ :
×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
Hindi : 38
Set : 10
72.
If non-zero real numbers b and c are such 72.
that min f(x) > max g(x), where
f(x)5x212bx12c2 and
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´,
g(x)52x222cx1b2 (x e R) ;
73.
then
c
lies in the interval :
b
Ìæð
(1)
 1
 0, 
 2
(1)
 1
 0, 
 2
(2)
1 1 
2 , 2 


(2)
1 1 
2 , 2 


(3)
 1

 2 , 2


(3)
 1

 2 , 2


(4)
(
(4)
(
2 ,∞
)
If the volume of a spherical ball is 73.
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,
c
b
çÁâ ¥´ÌÚUæÜ ×ð´ ãñ, ßã ãñ :
2 ,∞
)
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 :
is :
(1)
1
6
(1)
1
6
(2)
1
9
(2)
1
9
(3)
1
36
(3)
1
36
(4)
1
24
(4)
1
24
English : 39
Set : 10
Hindi : 39
Set : 10
74.
If m is a non - zero number and 74.
∫
x 5m21 1 2 x 4 m21
(
)
x 2 m 1 x m 11
3
∫
d x5 f ( x )1c ,
(2)
(
x 5m
)
2m x 2m 1 x m 1 1
(
x 4m
)
2m x 2m 1 x m 1 1
(
(3)
(4)
( x 5m 2 x 4 m )
2
2 m ( x 2 m 1 x m 1 1)
2 m x 5m 1 x 4m
English : 40
(
)
Set : 10
3
d x5 f ( x )1c
f(x) ãñ :
(
x 5m
)
2
)
2
2m x 2m 1 x m 1 1
(2)
2
°·¤ àæê ‹ Øð Ì ÚU â´  Øæ ãñ ÌÍæ
x 2 m 1 x m 11
(1)
2
)
2
( x2m 1 xm 1 1)
m
x 5m21 12 x 4 m21
ãñ, Ìæð
then f(x) is :
(1)
ØçÎ
(
x 4m
2m x 2m 1 x m 1 1
(
(3)
)
2
( x2m 1 xm 1 1)
(4)
( x 5m 2 x 4 m )
2
2 m ( x 2 m 1 x m 1 1)
Hindi : 40
2 m x 5m 1 x 4m
Set : 10
75.
Let
function
F( x ) 5
the
F
be
defined
as 75.
et
∫1 t dt , x > 0 then the value of
x
integral
et
∫1 t 1 a dt ,
x
et
dt , x > 0
1 t
×æÙæ ȤÜÙ F , F( x ) 5 ∫
x
x
et
ÂçÚUÖæçáÌ ãñ, Ìæð â×æ·¤Ü ∫1
t1 a
a > 0 ãñ,
where
dt
mæÚUæ
, Áãæ¡
·¤æ ×æÙ ãñ :
a > 0, is :
76.
(1)
ea[F(x)2F(11a)]
(1)
ea[F(x)2F(11a)]
(2)
e2a[F(x1a)2F(a)]
(2)
e2a[F(x1a)2F(a)]
(3)
ea[F(x1a)2F(11a)]
(3)
ea[F(x1a)2F(11a)]
(4)
e2a[F(x1a)2F(11a)]
(4)
e2a[F(x1a)2F(11a)]
The area of the region above the x-axis 76.
bounded by the curve y5tan x, 0 £ x £
and the tangent to the curve at x5
p
2
p
is :
4
ß·ý¤ y5tan x, 0 £ x £
x5
p
4
ª¤ÂÚU ãñ, ·¤æ ÿæð˜æÈ¤Ü ãñ :
1
1
 log 2 2 
2
2
(1)
1
1
 log 2 2 
2
2
(2)
1
1
 log 2 1 
2
2
(2)
1
1
 log 2 1 
2
2
(3)
1
( 1 2 log 2 )
2
(3)
1
( 1 2 log 2 )
2
(4)
1
( 1 1 log 2 )
2
(4)
1
( 1 1 log 2 )
2
Set : 10
ÌÍæ ß·ý ÂÚU
ÂÚU ¹è´¿è »§ü SÂàæü ÚðU¹æ mæÚUæ çƒæÚðU ÿæð˜æ, Áæð x ¥ÿæ âð
(1)
English : 41
p
2
Hindi : 41
Set : 10
77.
78.
dy
1y tan x5sin 2x and y(0)51, then 77.
dx
y(p) is equal to :
If
dy
1y tan x5sin 2x
dx
y(p) ÕÚUæÕÚU ãñ :
ØçÎ
(1)
1
(1)
1
(2)
21
(2)
21
(3)
25
(3)
25
(4)
5
(4)
5
The circumcentre of a triangle lies at the 78.
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
ÌÍæ y(0)51 ãñ Ìæð
°·¤ ç˜æÖéÁ ·¤æ ÂçÚU·ð´¤Îý ×êÜ çՋÎé ÂÚU ãñ ÌÍæ ©â·¤æ
·ð¤‹Îý·¤, çՋÎé¥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
lies on the line :
(1)
y22ax50
(1)
y22ax50
(2)
y2(a211)x50
(2)
y2(a 211)x50
(3)
y1x50
(3)
y1x50
(4)
(a21)2x2(a11) 2y50
English : 42
(4)
Set : 10
(a21) 2x2(a11) 2y50
Hindi : 42
Set : 10
79.
If a line L is perpendicular to the line 79.
5x2y51, and the area of the triangle
formed by the line L and the coordinate
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 :
axes is 5, then the distance of line L from
the line x15y50 is :
80.
(1)
7
5
(1)
7
5
(2)
5
13
(2)
5
13
(3)
7
13
(3)
7
13
(4)
5
7
(4)
5
7
The equation of the circle described on the 80.
chord
3x1y1550
x21y2516
of
the
circle
ßëžæ x21y2516 ·¤è °·¤ Áèßæ 3x1y1550
·¤æð ÃØæâ ×æÙ·¤Ú ¹è´¿ð »° ßëžæ ·¤æ â×è·¤ÚU‡æ ãñ :
as diameter is :
(1)
x 21y 213x1y21150
(1)
x 21y 213x1y21150
(2)
x 21y 213x1y1150
(2)
x 2 1y 2 13x1y1150
(3)
x 21y 213x1y2250
(3)
x 2 1y 2 13x1y2250
(4)
x 21y 213x1y22250
(4)
x 21y 213x1y22250
English : 43
Set : 10
Hindi : 43
Set : 10
81.
A chord is drawn through the focus of the 81.
parabola y256x such that its distance from
ÂÚUßÜØ y256x ·¤è ÙæçÖ âð ãæð·¤ÚU ÁæÌè °·¤ Áèßæ
¹è´¿è »§ü ãñ çÁâ·¤è ÂÚUßÜØ ·ð¤ àæèáü âð ÎêÚUè
5
, then its
the vertex of this parabola is
2
5
2
ãñ,
Ìæð §â·¤è ÉUæÜ ãæð â·¤Ìè ãñ :
slope can be :
82.
(1)
5
2
(1)
5
2
(2)
3
2
(2)
3
2
(3)
2
5
(3)
2
5
(4)
2
3
(4)
2
3
y2
x2
2
5 1 ·ð¤
4
5
The tangent at an extremity (in the first 82.
¥çÌÂÚUßÜØ
quadrant) of latus rectum of the hyperbola
çâÚðU (Áæð ÂýÍ× ¿ÌéÍæZàæ ×ð´ ãñ) ÂÚU ¹è´¿è »§ü SÂàæü
y2
x2
2
5 1 ,meets x - axis and y - axis
4
5
ÚðU¹æ x-¥ÿæ ÌÍæ y-¥ÿæ ·¤æð ·ý ×àæ çՋÎé¥æð´ A ÌÍæ B
at A and B
respectively. Then
(OA) 2 2(OB) 2 , where O is the origin,
equals :
(1)
2
(2)
16
9
(3)
4
(4)
2
English : 44
20
9
4
3
Set : 10
ÙæçÖÜ´Õ ·ð¤ °·¤
ÂÚU ç×ÜÌè ãñ´, Ìæð (OA)22(OB)2, Áãæ¡ O ×êÜ çÕ´Îé
ãñ, ÕÚUæÕÚU ãñ :
(1)
2
(2)
16
9
(3)
4
(4)
2
Hindi : 44
20
9
4
3
Set : 10
83.
Equation of the line of the shortest distance 83.
between the lines
y
x
z
5
5
and
1
21
1
y11
x21
z
5
5
22
0
1
y11
x21
z
5
5 is :
0
22
1
84.
y
x
z
5
5
1
21
1
Úð U ¹æ¥æð ´
·ð¤ Õè¿ ‹ØêÙÌ× ÎêÚUè
ßæÜè ÚðU¹æ ·¤æ â×è·¤ÚU‡æ ãñ :
(1)
y
x
z
5
5
1
21
22
(1)
y
x
z
5
5
1
21
22
(2)
y11
x21
z
5
5
21
22
1
(2)
y11
x21
z
5
5
21
22
1
(3)
y11
x21
z
5
5
21
1
1
(3)
y11
x21
z
5
5
1
21
1
(4)
y
x
z
5 5
22
1
2
(4)
y
x
z
5 5
22
1
2
If
the
angle
2(x11)5y5z14
between
and
the
the
line 84.
plane
p
2x2y1 l z1450 is
, then the value
6
of l is :
ØçÎ Úð U ¹æ
l ·¤æ
×æÙ ãñ :
135
7
(1)
135
7
(2)
45
11
(2)
45
11
(3)
45
7
(3)
45
7
(4)
135
11
(4)
135
11
Set : 10
2(x11)5y5z14
2x2y1 l z1450
(1)
English : 45
ÌÍæ
Hindi : 45
ÌÍæ â×ÌÜ
·ð¤ Õè¿ ·¤æ ·¤æð‡æ
p
ãñ,
6
Ìæð
Set : 10
85.
r
r
If x 5 3iˆ 2 6 ˆj 2 kˆ , y 5 iˆ 1 4 ˆj 2 3kˆ 85.
and
r
z 5 3iˆ 2 4 ˆj 2 12kˆ ,
ØçÎ
ÌÍæ
then the
r r
r
magnitude of the projection of x 3y on z
r
r
x 5 3iˆ 2 6 ˆj 2 kˆ , y 5 iˆ 1 4 ˆj 2 3kˆ
r r
r
r
z 5 3iˆ 2 4 ˆj 2 12kˆ ãñ´ Ìæð x 3y ·ð¤ z ÂÚU
Âýÿæð ·¤æ ÂçÚU×æ‡æ ãñ :
is :
86.
(1)
12
(1)
12
(2)
15
(2)
15
(3)
14
(3)
14
(4)
13
(4)
13
Let A and E be any two events with 86.
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
×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
false
(4)
Statement - 1 is false, Statement - 2
(4)
·¤ÍÙ-1 ¥âˆØ ãñ, ·¤ÍÙ-2 âˆØ ãñÐ
is true.
English : 46
Set : 10
Hindi : 46
Set : 10
87.
Let x , M and s 2 be respectively the mean, 87.
mode and variance of n observations
×æÙæ n Âýðÿæ‡ææð´
ÂýâÚU‡æ ·ý¤×àæÑ
x1, x2, ..., xn·ð¤ ×æŠØ ÕãéÜ·¤ ÌÍæ
x , M ÌÍæ s 2 ÌÍæ di52xi2a,
x1, x2, ..., xn and di52xi2a, i51, 2, ..., n,
where a is any number.
i51, 2, ..., n ãñ´,
Statement I : Variance of d1, d2, ..., dn is
s2.
·¤ÍÙ I : d1, d2, ..., dn ·¤æ ÂýâÚU‡æ
Statement II : Mean and mode of
·¤ÍÙ II : d1, d2, ..., dn ·ð¤ ×æŠØ ÌÍæ ÕãéÜ·¤
·ý¤×æàæÑ 2 x 2a ÌÍæ 2M2a ãñ
d 1 , d 2 , ..., d n are 2 x 2a and 2M2a,
respectively
(1)
Statement I and Statement II are
Áãæ¡ a ·¤æð§ü ⴁØæ ãñ´Ð
s2 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
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.
periodic function with period :
ȤÜÙ f ( x )5 sin 4x 1 cos 2x °·¤ ¥æßçÌü
ȤÜÙ ãñ çÁâ·¤æ ¥æßÌü ·¤æÜ ãñ :
(1)
2p
(1)
2p
(2)
p
(2)
p
(3)
p
2
(3)
p
2
(4)
p
4
(4)
p
4
The function f ( x )5 sin 4x 1 cos 2 x , is a 88.
English : 47
Set : 10
Hindi : 47
Set : 10
89.
90.
43p 
21 
 is : 89.
The principal value of tan  cot
4 

3p
4
(1)
2
(2)
3p
4
(3)
2
(4)
p
4
p
4
The contrapositive of the statement “if I 90.
am not feeling well, then I will go to the
43p 

tan21  cot

4 

·¤æ ×éØ×æÙ ãñ :
3p
4
(1)
2
(2)
3p
4
(3)
2
(4)
p
4
p
4
·¤ÍÙ ÒÒØçÎ ×ñ´ ¥SßSÍ ã¡ê, Ìæð ×ñ´ ÇUæ€ÅUÚU ·ð¤ Âæâ
Á檡¤»æÓÓ ·¤æ ÂýçÌÏÙæˆ×·¤ ãñ
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.
(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
ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Á檡¤»æ, Ìæð ×ñ´ SßSÍ
Ùãè´ ã¡êÐ
(4)
-o0o-
English : 48
-o0o-
Set : 10
Hindi : 48
Set : 10

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