PART A — PHYSICS
1.
From the following combinations of 1.
physical constants (expressed through
their usual symbols) the only combination,
that would have the same value in different
Öæ» A — ÖæñçÌ·¤ çߙææÙ
ÖæñçÌ·¤ çSÍÚUæ´·¤æð´ ·ð¤ çِÙçÜç¹Ì â´ØæðÁÙ âð (¥ÂÙð
âæÏæÚU‡æ ÂýØæð» ×ð´ çÜØð »Øð 翋ãæð´ mæÚUæ ÂýÎçàæüÌ),
·ð¤ßÜ ßã â´ØæðÁÙ, Áæð ç·¤ §·¤æ§Øæð´ ·ð¤ çßçÖóæ çÙ·¤æØæð´
×ð´ °·¤ ãè ×æÙ ÚU¹Ìæ ãñ, ãñ Ñ
systems of units, is :
(1)
(2)
2.
ch
e2
2peo Gm e 2
ch
(1)
2 peo2
(me5 mass of electron)
2 peo2
e2
(2)
2peo Gm e 2
(me5§Üð€ÅþUæòÙ
(3)
mo e o G
c2
h e2
(3)
mo eo G
c2
h e2
(4)
2 p mo eo h
G
ce 2
(4)
2 p mo eo h
G
ce 2
A person climbs up a stalled escalator 2.
in 60 s . If standing on the same but
escalator running with constant velocity
he takes 40 s. How much time is taken by
the person to walk up the moving
·¤æ ÎýÃØ×æÙ)
°·¤ ÃØç€ˆæ °·¤ SÍæçÂÌ °S·¤ÜðÅUÚU ·¤è ÎêÚUè 60 s ×ð´
¿É¸Ìæ ãñÐ ØçÎ ©â ÂÚU ¹Ç¸ð ãæð·¤ÚU ÂÚU‹Ìé çSÍÚU ßð» âð
°S·¤ÜðÅUÚU ·ð¤ ¿ÜÙð ÂÚU ßã 40 s ÜðÌæ ãñÐ ÃØ瀈æ
»çÌàæèÜ °S·¤ÜðÅUÚU ÂÚU ¿Ü·¤ÚU §âè ÎêÚUè ·¤æð ÌØ
·¤ÚUÙð ×ð´ ç·¤ÌÙæ â×Ø Üð»æ?
escalator ?
(1)
37 s
(1)
37 s
(2)
27 s
(2)
27 s
(3)
24 s
(3)
24 s
(4)
45 s
(4)
45 s
English : 1
Set : 06
Hindi : 1
Set : 06
3.
Three masses m, 2m and 3m are moving 3.
in x-y plane with speed 3u, 2u, and u
respectively as shown in figure. The three
masses collide at the same point at P and
stick together. The velocity of resulting
ÌèÙ ÎýÃØ×æÙ x-y ÌÜ ×ð´ ¿æÜ
·ý¤×àæÑ 3u, 2u, °ß´ u âð »çÌàæèÜ ãñ, Áñâæ ç·¤ 翘æ
×ð´ ÎàææüØæ »Øæ ãñÐ ÌèÙæð´ ÎýÃØ×æÙ °·¤ ãè çՋÎé ÂÚU
ⴃæ^ ·¤ÚUÌð ãñ´ ¥æñÚU °·¤ âæÍ ç¿Â·¤ ÁæÌð ãñ´Ð ÂçÚU‡ææ×è
ÎýÃØ×æÙ ·¤æ ßð» ãæð»æ Ñ
m, 2m
°ß´
3m ·ð¤
mass will be :
(1)
(2)
(3)
(4)
(
u ∧
i1
12
(
u ∧
i2
12
∧
3j
∧
3j
(
u ∧
2i 1
12
(
u ∧
2i 2
12
)
∧
u ∧
i 1 3j
12
)
(2)
u ∧
i 2
12
)
(3)
u ∧
2i 1
12
)
(4)
u ∧
2i 2
12
∧
3j
∧
3j
4.
4.
(
(1)
A 4 g bullet is fired horizontally with a
speed of 300 m/s into 0.8 kg block of wood
at rest on a table. If the coefficient of
friction between the block and the table is
(
∧
3j
)
)
∧
)
∧
)
(
3j
(
3j
°·¤ ×ð$Á ÂÚU çߟææ× ¥ßSÍæ ×ð´ çSÍÌ 0.8 kg Ü·¤Ç¸è
·ð¤ ŽÜæ·¤ ·¤æð 300 m/s ·¤è ¿æÜ âð °·¤ 4 g ·¤è
»æðÜè ÿæñçÌÁ Îæ»Ìè ãñÐ ØçÎ ×ð$Á °ß´ ŽÜæ·¤ ·ð¤ Õè¿
ƒæáü‡æ »é‡ææ´·¤ 0.3 ãñ, ÌÕ ŽÜæ·¤ ֻܻ ç·¤ÌÙè ÎêÚU
çȤâÜð»æ?
0.3, how far will the block slide
approximately ?
(1)
0.19 m
(1)
0.19 m
(2)
0.379 m
(2)
0.379 m
(3)
0.569 m
(3)
0.569 m
(4)
0.758 m
(4)
0.758 m
English : 2
Set : 06
Hindi : 2
Set : 06
5.
A spring of unstretched length l has a 5.
mass m with one end fixed to a rigid
support. Assuming spring to be made of a
uniform wire, the kinetic energy possessed
by it if its free end is pulled with uniform
çÕÙæ ÌæçÙÌ ÜÕæ§ü l ·¤è °·¤ ·¤×æÙè âð °·¤
ÎýÃØ×æÙ m §â Âý·¤æÚU ãñ ç·¤ §â·¤æ °·¤ çâÚUæ °·¤ Îëɸ
¥æÏæÚU ÂÚU Õ¡Ïæ ãñÐ Øã ×æÙÌð ãéØð ç·¤ ·¤×æÙè °·¤
°·¤â×æÙ ÌæÚU âð ÕÙè ãñ, §â×ð´ »çÌÁ ª¤Áæü ãæð»è ØçÎ
§â·¤æ Sß̋˜æ çâÚUæ °·¤â×æÙ ßð» v âð ¹è´¿æ Áæ° Ñ
velocity v is :
(1)
(2)
6.
1
m v2
2
mv 2
(1)
(2)
1
m v2
2
mv 2
(3)
1
m v2
3
(3)
1
m v2
3
(4)
1
m v2
6
(4)
1
m v2
6
A particle is moving in a circular path of 6.
radius a, with a constant velocity v as
shown in the figure. The center of circle is
marked by ‘C’. The angular momentum
°·¤ ·¤‡æ ç˜æ’Øæ a ·ð¤ °·¤ ßëžæèØ ÂÍ ÂÚU °·¤ çSÍÚU
ßð» v âð »çÌàæèÜ ãñ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ »Øæ ãñÐ
ßëžæ ·¤æ ·ð¤‹Îý ‘C’ âð ç¿ç‹ãÌ ç·¤Øæ »Øæ ãñÐ ×êÜ çՋÎé
O âð ·¤æð‡æèØ â´ßð» §â Âý·¤æÚU çܹæ Áæ â·¤Ìæ ãñ Ñ
from the origin O can be written as :
(1)
(1)
(2)
(3)
(4)
va(11cos 2u)
va(11cos u)
va cos 2u
va
English : 3
(2)
(3)
(4)
Set : 06
va(11cos 2u)
va(11cos u)
va cos 2u
va
Hindi : 3
Set : 06
7.
7.
Two hypothetical planets of masses m1 and
m 2 are at rest when they are infinite
distance apart. Because of the gravitational
force they move towards each other along
the line joining their centres. What is their
speed when their separation is ‘d’ ?
(Speed of m1 is v1 and that of m2 is v2)
(1) v 15v 2
(2)
(3)
(4)
v1 5 m 2
2G
d(m 11m 2 )
v2 5 m 1
2G
d(m 11m 2 )
v1 5 m 1
2G
d(m 11m 2 )
v2 5 m 2
2G
d(m 11m 2 )
v1 5 m 2
2G
m1
v2 5 m 1
2G
m2
English : 4
ÎýÃØ×æÙ m1 °ß´ m2 ·ð¤ Îæð ÂçÚU·¤çËÂÌ ©Â»ýã çߟææ×
¥ßSÍæ ×ð´ ãñ´ ÁÕ ßð °·¤ ÎêâÚðU â𠥋æ‹Ì ÎêÚUè ÂÚU ãñ´Ð
»éL¤ˆßæ·¤áü‡æ ÕÜ ·ð¤ ·¤æÚU‡æ ©Ù·ð¤ ·ð¤‹Îýæð´ ·¤æð ç×ÜæÙð
ßæÜè ÚðU¹æ ÂÚU °·¤ ÎêâÚðU ·¤è ¥æðÚU »çÌ ·¤ÚUÙæ ÂýæÚUÖ
·¤ÚUÌð ãñ´Ð ÁÕ ©‹æ·ð¤ Õè¿ ÎêÚUè ‘d’ ãñ, ÌÕ ©Ù·¤è ¿æÜ
€Øæ ãñ?
( m1 ·¤è ¿æÜ v1 °ß´ m2 ·¤è ¿æÜ v2 ãñ )
(1)
v 15v 2
(2)
v1 5 m 2
2G
d(m 11m 2 )
v2 5 m 1
2G
d(m 11m 2 )
v1 5 m 1
2G
d(m 11m 2 )
v2 5 m 2
2G
d(m 11m 2 )
v1 5 m 2
2G
m1
v2 5 m 1
2G
m2
(3)
(4)
Set : 06
Hindi : 4
Set : 06
8.
Steel
ruptures
when
a
shear
of 8.
3.5310 8 N m 22 is applied. The force
needed to punch a 1 cm diameter hole in
a steel sheet 0.3 cm thick is nearly :
9.
(1)
1.43104 N
(2)
SÅUèÜ È¤ÅU ÁæÌæ ãñ ÁÕ ©â ÂÚU 3.53108 Nm22
·¤æ ¥ÂM¤Â‡æ Ü»æØæ ÁæÌæ ãñÐ 0.3 cm ×æðÅUè SÅUèÜ
àæèÅU ×ð´ 1 cm ÃØæâ ·¤æ çÀUÎý ·¤ÚUÙð ×ð´ Ü»æØð ÁæÙð
ßæÜæ ÕÜ Ü»Ö» ãñ Ñ
(1)
1.43104 N
2.73104 N
(2)
2.73104 N
(3)
3.33104 N
(3)
3.33104 N
(4)
1.13104 N
(4)
1.13104 N
A cylindrical vessel of cross-section A 9.
contains water to a height h. There is a
hole in the bottom of radius ‘a’. The time
in which it will be emptied is :
(1)
(2)
(3)
(4)
2A
pa
2
h
g
(1)
h
g
(2)
2A
pa 2
2 2A
pa
h
g
2
A
2 pa
English : 5
¥ÙéÂýSÍ ·¤æÅU A ßæÜð °·¤ ÕðÜÙæ·¤æÚU ÕÌüÙ ×ð´ ÂæÙè
ª¡¤¿æ§ü h Ì·¤ ÖÚUæ ãñÐ §â·¤è ÌÜè ×ð´ ç˜æ’Øæ ‘a’ ·¤æ
°·¤ çÀUÎý ãñÐ ßã â×Ø, çÁâ×ð´ Øã ÕÌüÙ çÚU€ˆæ ãæð
Áæ°»æ, ãñ Ñ
2
(3)
h
g
(4)
Set : 06
Hindi : 5
2A
pa
2
h
g
2A
h
g
pa 2
2 2A
pa
h
g
2
A
2 pa
2
h
g
Set : 06
10.
Two soap bubbles coalesce to form a single 10.
bubble. If V is the subsequent change in
volume of contained air and S the change
in total surface area, T is the surface
tension and P atmospheric pressure, which
Îæð âæÕéÙ ·ð¤ ÕéÜÕéÜð ç×Ü·¤ÚU °·¤ ÕéÜÕéÜæ ÕÙæÌð ãñ´Ð
ØçÎ §Ù×ð´ çSÍÌ ßæØé ·ð¤ ¥æØÌÙ ×ð´ ÂÚUßÌèü ÂçÚUßÌüÙ
V ãñ ¥æñÚU âÂê‡æü ÂëcÆ ÿæð˜æÈ¤Ü ×ð´ ÂçÚUßÌüÙ S ãñ,
T ÂëcÆU ÌÙæß ãñ ¥æñÚU P ßæØé×´ÇUÜ ÎæÕ ãñ, ÌÕ
çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ-âæ âÕ‹Ï âãè ãñ?
of the following relation is correct ?
11.
(1)
4PV13ST50
(1)
4PV13ST50
(2)
3PV14ST50
(2)
3PV14ST50
(3)
2PV13ST50
(3)
2PV13ST50
(4)
3PV12ST50
(4)
3PV12ST50
Hot water cools from 608C to 508C in the 11.
first 10 minutes and to 428C in the next
10 minutes. The temperature of the
»×ü ÂæÙè 608C âð 508C ÂãÜð 10 ç×ÙÅU ×ð´ Æ´UÇUæ ãæðÌæ
ãñ ¥æñÚU 428C Ì·¤ ÎêâÚðU 10 ç×ÙÅU ×ð´ Æ´UÇUæ ãæðÌæ ãñÐ
ßæÌæßÚU‡æ ·¤æ ÌæÂ×æÙ ãñ Ñ
surroundings is :
12.
(1)
258C
(1)
258C
(2)
108C
(2)
108C
(3)
158C
(3)
158C
(4)
208C
(4)
208C
°ß´
40% °ß´
50% °ß´
70% °ß´
A Carnot engine absorbs 1000 J of heat 12.
energy from a reservoir at 1278C and rejects
600 J of heat energy during each cycle. The
efficiency of engine and temperature of
°·¤ ·¤æÙæðü §´ÁÙ °·¤ ·é´¤ÇU âð 1278C ÂÚU 1000 J
ª¤c×èØ ª¤Áæü ¥ßàææðçáÌ ·¤ÚUÌæ ãñ ¥æñÚU ÂýˆØð·¤ ¿·ý¤
×ð´ 600 J ª¤c×èØ ª¤Áæü ¥Sßè·¤æÚU ·¤ÚU ÎðÌæ ãñÐ §´ÁÙ
·¤è ÎÿæÌæ ¥æñÚU çâ´·¤ ·¤æ ÌæÂ×æÙ ãæð»æ Ñ
sink will be :
(1)
20% and 2438C
(1)
(2)
40% and 2338C
(2)
(3)
50% and 2208C
(3)
(4)
70% and 2108C
(4)
English : 6
Set : 06
20%
Hindi : 6
2438C
2338C
2208C
2108C
Set : 06
13.
1930 ms21. The gas is :
·¤×ÚðU ·ð¤ ÌæÂ×æÙ ÂÚU °·¤ çmÂÚU×æ‡æé·¤ »ñâ ·¤è
ß»ü-×æŠØ-×êÜ ¿æÜ 1930 ms21 ÂæØè ÁæÌè ãñÐ
»ñâ ãñ Ñ
(1)
H2
(1)
O2
(3)
At room temperature a diatomic gas is 13.
found to have an r.m.s. speed of
(2)
(3)
(4)
14.
Cl2
(2)
F2
(4)
Which of the following expressions 14.
corresponds to simple harmonic motion
along a straight line, where x is the
H2
Cl2
O2
F2
çِÙçÜç¹Ì ÃØ´Á·¤æð´ ×ð´ âð ·¤æñÙ âæ °·¤ âÚUÜ ÚðU¹æ
ÂÚU âÚUÜ ¥æßÌü »çÌ ·ð¤ â´»Ì ãñ, Áãæ¡ x çßSÍæÂÙ ãñ
¥æñÚU a, b, c ÏÙæˆ×·¤ çSÍÚUæ´·¤ ãñ ?
displacement and a, b, c are positive
constants ?
15.
(1)
a1bx2cx 2
(1)
a1bx2cx 2
(2)
bx2
(2)
bx2
(3)
a2bx1cx 2
(3)
a2bx1cx 2
(4)
2bx
(4)
2bx
A source of sound A emitting waves of 15.
frequency 1800 Hz is falling towards
ground with a terminal speed v. The
observer B on the ground directly beneath
the source receives waves of frequency
2150 Hz. The source A receives waves,
¥æßëçžæ 1800 Hz ·¤è Ì´ÚU»ð´ ©ˆâçÁüÌ ·¤ÚU ÚUãæ ŠßçÙ
dæðÌ A °·¤ âè×æ‹Ì ßð» v âð ÏÚUÌè ·¤è ¥æðÚU ç»ÚU ÚUãæ
ãñÐ dæðÌ ·ð¤ ÆUè·¤ Ùè¿ð ÏÚUÌè ÂÚU °·¤ Âýðÿæ·¤ B
¥æßëçžæ 2150 Hz ·¤è ÌÚ´U»ð´ ÂýæŒˆæ ·¤ÚUÌæ ãñÐ dæðÌ A,
ÏÚUÌè âð ÂÚUæßçÌüÌ Ü»Ö» §â ¥æßëçžæ ·¤è ÌÚ´U»ð´ Âý挈æ
·¤ÚðU»æ Ñ ( ŠßçÙ ·¤è ¿æÜ 5343 m/s)
reflected from ground, of frequency
nearly : (Speed of sound 5343 m/s)
(1)
2150 Hz
(1)
2150 Hz
(2)
2500 Hz
(2)
2500 Hz
(3)
1800 Hz
(3)
1800 Hz
(4)
2400 Hz
(4)
2400 Hz
English : 7
Set : 06
Hindi : 7
Set : 06
16.
A
spherically
symmetric
charge 16.
distribution is characterised by a charge
density having the following variation :
r

r(r)5ro  1 2  for r < R

R
°·¤ »æðÜèØ â×ç×Ìè ¥æßðàæ çßÌÚU‡æ ¥æßðàæ ƒæوß
·¤æ çِÙçÜç¹Ì çß¿ÚU‡æ ÚU¹Ìæ ãñ Ñ
r

r(r)5ro  1 2  r < R ·ð¤

R
çÜ°
Áãæ¡ r ¥æßðàæ çßÌÚU‡æ ·ð¤ ·ð¤‹Îý âð ÎêÚUè ãñ´ ¥æñÚU ro °·¤
çSÍÚUæ´·¤ ãñÐ °·¤ ¥‹ÌÑ çՋÎé (r < R) ÂÚU çßléÌ ÿæð˜æ
ãñ Ñ
r(r)50
r(r)50
for r / R
Where r is the distance from the centre of
the charge distribution and ro is a constant.
The electric field at an internal point
(r < R) is :
r / R ·ð¤
(1)
ro  r
r2 
 2

4eo  3
4R 
(1)
ro  r
r2 
 2

4e o  3
4R 
(2)
ro  r
r2 
2


4R 
eo  3
(2)
ro  r
r2 
 2

4R 
eo  3
(3)
ro  r
r2 
 2

3e o  3
4R 
(3)
ro  r
r2 
 2

3eo  3
4R 
(4)
ro  r
r2 
 2

12 eo  3
4R 
(4)
ro  r
r2 
 2

12 eo  3
4R 
English : 8
Set : 06
çÜ°
Hindi : 8
Set : 06
17.
The space between the plates of a parallel 17.
plate capacitor is filled with a ‘dielectric’
whose ‘dielectric constant’ varies with
distance as per the relation :
K(x)5Ko1lx (l5 a constant)
The capacitance C, of this capacitor, would
be related to its ‘vacuum’ capacitance Co
as per the relation :
°·¤ â×æ‹ÌÚU Âç^·¤æ â´ÏæçÚU˜æ ·¤è Âç^·¤æ¥æð´ ·ð¤ Õè¿
·¤æ SÍæÙ °·¤ ÂÚæßñléÌ âð ÖÚUæ ÁæÌæ ãñ çÁâ·¤æ ÂÚUæßñléÌ
çSÍÚUæ´·¤ ÎêÚUè ·ð¤ âæÍ çِ٠âÕ‹Ï ¥ÙéâæÚU ÂçÚUßçÌüÌ
ãæðÌæ ãñ Ñ
K(x)5Ko1lx (l5°·¤ çSÍÚUæ´·¤)
â´ÏæçÚU˜æ ·¤è ÏæçÚUÌæ C, §â·¤è çÙßæüÌ ÏæçÚUÌæ, Co ·ð¤
âæÍ çِ٠âÕ‹Ï ¥ÙéâæÚU âÕç‹ÏÌ ãæð»è Ñ
(1)
C5
ld
Co
l n (1 1 K o ld)
(1)
C5
ld
Co
l n (1 1 K o ld)
(2)
C5
l
Co
d. l n (1 1 K o ld)
(2)
C5
l
Co
d. l n (1 1 K o ld)
(3)
C5
ld
Co
l n (1 1 ld/K o )
(3)
C5
ld
Co
l n (1 1 ld/K o )
(4)
C5
l
Co
d. l n (1 1 K o /ld)
(4)
C5
l
Co
d. l n (1 1 K o /ld)
English : 9
Set : 06
Hindi : 9
Set : 06
18.
3 V, 9 V and 9 V and a capacitor 5.0 mF.
ÎàææüØð »Øð ÂçÚUÂÍ ×ð´ 8.0 V °ß´ 16.0 V ·¤è Îæð
ÕñÅUçÚUØæ¡ ¥æñÚU 3 V, 9 V °ß´ 9 V ·ð¤ ÌèÙ ÂýçÌÚUæðÏ ÌÍæ
5.0 mF ·¤æ °·¤ â´ÏæçÚU˜æ ãñÐ
How much is the current I in the circuit in
SÍæØè ¥ßSÍæ ×ð´ ÂçÚUÂÍ ×ð´ ÏæÚUæ I ·¤æ ×æÙ €Øæ ãñ?
The circuit shown here has two batteries 18.
of 8.0 V and 16.0 V and three resistors
steady state ?
19.
(1)
1.6 A
(1)
1.6 A
(2)
0.67 A
(2)
0.67 A
(3)
2.5 A
(3)
2.5 A
(4)
0.25 A
(4)
0.25 A
A positive charge ‘q’ of mass ‘m’ is moving 19.
along the 1x axis. We wish to apply a
uniform magnetic field B for time Dt so that
the charge reverses its direction crossing
the y axis at a distance d. Then :
ÎýÃØ×æÙ ‘m’ ·¤æ °·¤ ÏÙæˆ×·¤ ¥æßðàæ ‘q’, 1x ¥ÿæ
ÂÚU »çÌàæèÜ ãñÐ ã× °·¤ °·¤â×æÙ ¿éÕ·¤èØ ÿæð˜æ B
â×Ø Dt ·ð¤ çÜ° Ü»æÙæ ¿æãÌð ãñ´ çÁââð ç·¤ ¥æßðàæ
·¤è çÎàææ d ÎêÚUè ÂÚU y - ¥ÿæ ·¤æð ·¤æÅUÌð ãé° ÂýçÌÜæðç×Ì
ãæð Áæ°, ÌÕ Ñ
(1)
5
pd
mv
DQGDW5
qd
v
(1)
5
pd
mv
•Ä™ D W5
qd
v
(2)
5
mv
pd
DQG D W5
2 qd
2v
(2)
5
mv
pd
•Ä™ D W5
2 qd
2v
(3)
5
pd
2 mv
DQG D W5
qd
2v
(3)
5
pd
2 mv
•Ä™ D W5
qd
2v
(4)
5
pd
2 mv
DQG D W5
qd
v
(4)
5
pd
2 mv
•Ä™ D W5
qd
v
English : 10
Set : 06
Hindi : 10
Set : 06
20.
Consider two thin identical conducting 20.
wires covered with very thin insulating
material. One of the wires is bent into a
loop and produces magnetic field B1, at its
centre when a current I passes through it.
The second wire is bent into a coil with
three identical loops adjacent to each other
and produces magnetic field B 2 at the
centre of the loops when current I/3 passes
21.
Îæð ÂÌÜð âßü â×M¤Âè ¿æÜ·¤èØ ÌæÚU ÕãéÌ ÂÌÜð ÚUæðÏè
ÂÎæÍü âð ɸ·ð¤ ãé° ãñ´Ð °·¤ ÌæÚU ·¤æð ×æðǸ·¤ÚU °·¤ ÜêÂ
ÕÙæØæ ÁæÌæ ãñ Áæð ç·¤ ¥ÂÙð ·ð¤‹Îý ÂÚU ¿éÕ·¤èØ ÿæð˜æ
B1 ©ˆÂóæ ·¤ÚUÌæ ãñ ÁÕ §â×ð´ ÏæÚUæ I ÂýßæçãÌ ãæðÌè ãñÐ
ÎêâÚðU ÌæÚU ·¤æð ÌèÙ âßüâ×M¤Âè ÜêÂæð´ ×ð´ ×æðǸ·¤ÚU ¥æñÚU
°·¤ âæÍ ÚU¹·¤ÚU ·é¤‡ÇUÜè ÕÙæÌð ãñ´ Áæð ç·¤ ÜêÂæð´ ·ð¤
·ð¤‹Îý ÂÚU ¿éÕ·¤èØ ÿæð˜æ B2 ©ˆÂóæ ·¤ÚUÌæ ãñ ÁÕ §â×ð´
ÏæÚUæ I/3 ÂýßæçãÌ ãæðÌè ãñÐ ¥ÙéÂæÌ B1 : B2 ãñ Ñ
(1)
1:1
through it. The ratio B1 : B2 is :
(1) 1 : 1
(2)
1:3
(3)
1:9
(2)
1:3
(4)
9:1
(3)
1:9
(4)
9:1
21.
A sinusoidal voltage V(t)5100 sin (500t)
°·¤ ’ØæÃæ·ý¤èØ ßæðËÅUÌæ V(t)5100 sin (500t) °·¤
çßàæéh ÂýðÚU·¤ˆß L50.02 H ÂÚU Ü»æ§ü ÁæÌè ãñÐ
·é¤‡ÇUÜè âð ÂýßæçãÌ ÏæÚUæ ãñ Ñ
is applied across a pure inductance of
L50.02 H. The current through the coil
(1)
10 cos (500t)
is :
(2)
210 cos (500t)
(1)
10 cos (500t)
(3)
10 sin (500t)
(2)
210 cos (500t)
(4)
210 sin (500t)
(3)
10 sin (500t)
(4)
210 sin (500t)
English : 11
Set : 06
Hindi : 11
Set : 06
22.
A lamp emits monochromatic green light 22.
uniformly in all directions. The lamp is 3%
efficient in converting electrical power to
electromagnetic waves and consumes
100 W of power. The amplitude of the
electric
field
associated
with
the
°·¤ ÜðÂ âÖè çÎàææ¥æð´ ×ð´ °·¤â×æÙ M¤Â âð °·¤ß‡æèü
ãÚUæ Âý·¤æàæ ©ˆâçÁüÌ ·¤ÚU ÚUãæ ãñÐ ÜðÂ ·¤è çßléÌ
àæç€ˆæ ·¤æð çßléÌ ¿éÕ·¤èØ ÌÚ´U»æð´ ×ð´ ÂçÚUßÌüÙ ·¤ÚUÙð
·¤è ÎÿæÌæ 3% ãñ ¥æñÚU 100 W àæç€ˆæ ·¤è ¹ÂÌ ·¤ÚUÌæ
ãñÐ ÜðÂ âð 5 m ÎêÚUè ÂÚU çßléÌ ¿éÕ·¤èØ çßç·¤ÚU‡æ
âð âÕçhÌ çßléÌ ÿæð˜æ ·¤æ ¥æØæ× Ü»Ö» ãæð»æ Ñ
electromagnetic radiation at a distance of
(1)
1.34 V/m
5 m from the lamp will be nearly :
(2)
2.68 V/m
(1)
1.34 V/m
(3)
4.02 V/m
(2)
2.68 V/m
(4)
5.36 V/m
(3)
4.02 V/m
(4)
5.36 V/m
English : 12
Set : 06
Hindi : 12
Set : 06
23.
The refractive index of the material of a 23.
concave lens is m. It is immersed in a
medium of refractive index m1. A parallel
beam of light is incident on the lens. The
path of the emergent rays when m1 > m is :
°·¤ ¥ßÌÜ Üð‹â ·ð¤ ÂÎæÍü ·¤æ ¥ÂßÌüÙæ´·¤ m ãñÐ
§âð ¥ÂßÌüÙæ´·¤ m1 ·ð¤ ×æŠØ× ×ð´ ÇéUÕæðØæ ÁæÌæ ãñÐ
Âý·¤æàæ ·¤è °·¤ â×æ‹ÌÚU Âé´Á Üð‹â ÂÚU ¥æÂçÌÌ ãñÐ
ÁÕ m1 > m ãñ´, ÌÕ çÙ»üÌ ç·¤ÚU‡ææð´ ·¤æ ÂÍ ãñ Ñ
(1)
(1)
(2)
(2)
(3)
(3)
(4)
(4)
English : 13
Set : 06
Hindi : 13
Set : 06
24.
Interference pattern is observed at ‘P’ due 24.
to superimposition of two rays coming out
from a source ‘S’ as shown in the figure.
The value of ‘l’ for which maxima is
obtained at ‘P’ is :
°·¤ dæðÌ ’S’ âð çÙ·¤Ü ÚUãè Îæð ç·¤ÚU‡ææ𴠷𤠥ŠØæÚUæð‡æ
âð ‘P’ ÂÚU °·¤ ÃØçÌ·¤ÚU‡æ 翘æ ÂæØæ ÁæÌæ ãñ, Áñâæ ç·¤
翘æ ×ð´ ÎàææüØæ »Øæ ãñÐ ‘l’ ·¤æ ßã ×æÙ, çÁâ·ð¤ çÜ°
‘P’ ÂÚU Âý挈æ 翘æ ×ð´ ×ãžæ× ÌèßýÌæ ãñ, ãñ Ñ
(R °·¤ Âê‡æüÌØæ ÂÚUæßÌèü ÂëcÆU ãñ )
(R is perfect reflecting surface) :
(1)
(2)
(3)
(4)
l5
l5
l5
l5
2 nl
321
(2n21)l
2 ( 3 2 1)
(2n21)l 3
4 ( 22 3 )
(2n21)l
3 21
25.
25.
In an experiment of single slit diffraction
pattern, first minimum for red light
coincides with first maximum of some
2 nl
321
(1)
l5
(2)
l5
(2n21)l
2 ( 3 2 1)
(3)
l5
(2n21)l 3
4 ( 22 3 )
(4)
l5
(2n21)l
3 21
°·¤Ü çSÜÅU çßßÌüÙ ç¿˜æ ·ð¤ ÂýØæð» ×ð´, ÜæÜ Âý·¤æàæ
·¤æ ÂýÍ× ‹ØêÙÌ× °·¤ ÎêâÚUè ÌÚ´U»ÎñŠØü ·ð¤ ÂýÍ× ×ãžæ×
â´ÂæÌè ãñÐ ØçÎ ÜæÜ Âý·¤æàæ ·¤è ÌÚ´U»ÎñŠØü 6600 Å
ãñ, ÌÕ ÂýÍ× ×ãžæ× ·ð¤ â´»Ì ÌÚ´U»ÎñŠØü ãæð»è Ñ
other wavelength. If wavelength of red
light is 6600 Å , then wavelength of first
maximum will be :
(1)
3300 Å
(1)
3300 Å
(2)
4400 Å
(2)
4400 Å
(3)
5500 Å
(3)
5500 Å
(4)
6600 Å
(4)
6600 Å
English : 14
Set : 06
Hindi : 14
Set : 06
26.
A beam of light has two wavelengths 26.
4972 Å and 6216 Å with a total intensity
of 3.631023 Wm22 equally distributed
among the two wavelengths. The beam
falls normally on an area of 1 cm2 of a clean
metallic surface of work function 2.3 eV.
Assume that there is no loss of light by
reflection and that each capable photon
ejects one electron. The number of photo
electrons
liberated
in
2s
Îæð ÌÚ´U»ÎñŠØæðZ 4972Å °ß´ 6216 Å ßæÜð Âý·¤æàæ ·¤è
°·¤ Âé´Á ·¤è ·é¤Ü ÌèßýÌæ 3.631023 Wm22 ãñ Áæð
ç·¤ ÎæðÙæð´ ÌÚ´U»ÎñŠØæðZ ×ð´ °·¤ â×æÙ çßÌçÚUÌ ãñÐ 2.3 eV
·¤æØü È ¤ÜÙ ßæÜð °·¤ âæȤ ÏæÌé ·ð ¤ Âë c ÆU ·ð ¤
1 cm2 ÿæð˜æÈ¤Ü ÂÚU Øã Âé´Á ¥çÖܐÕßÌ÷ ¥æÂçÌÌ
ãñ´Ð Øã ×æÙ Üð´ ç·¤ ÂÚUæßÌüÙ mæÚUæ ç·¤âè Öè Âý·¤æàæ ·¤æ
Oæâ Ùãè´ ãæðÌæ ãñ ¥æñÚU ÂýˆØð·¤ ÿæç×Ì È¤æðÅUæÙ °·¤ §Üð€ÅþUæÙò
©ˆâçÁüÌ ·¤ÚUÌæ ãñÐ 2s ×ð´ ©ˆâçÁüÌ È¤æðÅUæð §Üð€ÅþUæòÙæð´
·¤è ⴁØæ ãñ ֻܻ Ñ
is
approximately :
27.
(1)
6310 11
(1)
6310 11
(2)
9310 11
(2)
9310 11
(3)
11310 11
(3)
11310 11
(4)
15310 11
(4)
15310 11
A piece of bone of an animal from a ruin 27.
is found to have
14 C
activity of
12 disintegrations per minute per gm of
its carbon content. The 14C activity of a
living animal is 16 disintegrations per
minute per gm. How long ago nearly did
the animal die ? (Given half life of
°·¤ ¹‡ÇUãÚU âð ÂýæŒˆæ °·¤ Âàæé ·¤è ãaè ·ð¤ ÅéU·¤Ç¸ð ·¤è
14C âç·ý¤ØÌæ §â·ð¤ ·¤æÕüÙ ¥´àæ ·¤è ÂýçÌ »ýæ× ÂýçÌ
ç×ÙÅU 12 ç߃æÅUÙ ãñÐ °·¤ ç’æ‹Îæ Âàæé ·¤è 14C âç·ý¤ØÌæ
16 ç߃æÅUÙ ÂýçÌ ç×ÙÅU ÂýçÌ »ýæ× ãñ Рֻܻ ç·¤ÌÙð
ßáü ÂãÜð Âàæé ·¤è ×ëˆØé ãé§ü? (çÎØæ ãñ 14C ·¤è ¥hü
¥æØé t1/255760 ßáü)
14C
is t1/255760 years)
(1) 1672 years
(1)
1672
(2)
2391 years
(2)
2391
(3)
3291 years
(3)
3291
(4)
4453 years
(4)
4453
English : 15
Set : 06
Hindi : 15
ßáü
ßáü
ßáü
ßáü
Set : 06
28.
For LED’s to emit light in visible region of 28.
electromagnetic light, it should have
energy band gap in the range of :
29.
(1)
0.1 eV to 0.4 eV
(2)
0.5 eV to 0.8 eV
(3)
0.9 eV to 1.6 eV
(4)
1.7 eV to 3.0 eV
For sky wave propagation, the radio 29.
waves must have a frequency range in
çßléÌ ¿éÕ·¤èØ Âý·¤æàæ ·ð¤ ÎëàØ ÿæð˜æ ×ð´
Âý·¤æàæ ©ˆâçÁüÌ ·¤ÚðU, §â·ð¤ çÜØð §Ù·¤è Õñ‹Ç ¥‹ÌÚUæÜ
§â ÚðU‹Á ×ð´ ãæðÙè ¿æçãØð Ñ
(1) 0.1 eV âð 0.4 eV
(2) 0.5 eV âð 0.8 eV
(3) 0.9 eV âð 1.6 eV
(4) 1.7 eV âð 3.0 eV
¥æ·¤æàæ ÌÚ´U» â´¿ÚU‡æ ·ð¤ çÜ°, ÚðUçÇUØæð ÌÚ´U»ð´ §â ¥æßëçžæ
ÚðU‹Á ·ð¤ Õè¿ ãæðÙè ¿æçã° Ñ
LED’s
between :
30.
(1)
1 MHz to 2 MHz
(1)
(2)
5 MHz to 25 MHz
(2)
(3)
35 MHz to 40 MHz
(3)
(4)
45 MHz to 50 MHz
(4)
In the experiment of calibration of 30.
voltmeter, a standard cell of e.m.f. 1.1 volt
is
balanced
against
440
cm
of
potentiometer wire. The potential
difference across the ends of resistance is
found to balance against 220 cm of the
âð 2 MHz
5 MHz âð 25 MHz
35 MHz âð 40 MHz
45 MHz âð 50 MHz
1 MHz
°·¤ ßæðËÅU×æÂè ·ð¤ ¥´àæàææðÏÙ ·ð¤ ÂýØæð» ×ð´, 1.1 ßæðËÅU
çßléÌßæã·¤ ÕÜ ·ð¤ °·¤ ×æÙ·¤ âñÜ ·ð¤ â´ÌéçÜÌ
440 cm ·¤æ çßÖß×æÂè ÌæÚU ÂæØæ ÁæÌæ ãñÐ °·¤
ÂýçÌÚUæðÏ ·ð¤ çâÚUæð´ ÂÚU çßÖßæ‹ÌÚU ÌæÚU ·ð¤ 220 cm ·ð¤
â´ÌéçÜÌ ÂæØæ ÁæÌæ ãñÐ ßæðËÅU×æÂè ·¤æ â´»Ì ÂÆUÙ
0.5 ßæðËÅU ãñÐ ßæðËÅU×æÂè ·ð¤ ÂÆUÙ ×𴠘æéçÅU ãæð»è Ñ
wire. The corresponding reading of
voltmeter is 0.5 volt. The error in the
reading of voltmeter will be :
(1)
20.15 volt
(1)
(2)
0.15 volt
(2)
(3)
0.5 volt
(3)
(4)
20.05 volt
(4)
English : 16
Set : 06
ßæðËÅU
0.15 ßæðËÅU
0.5 ßæðËÅU
20.05 ßæðËÅU
20.15
Hindi : 16
Set : 06
PART B — CHEMISTRY
31.
If m and e are the mass and charge of the 31.
revolving electron in the orbit of radius r
for hydrogen atom, the total energy of the
Öæ» B — ÚUâæØÙ çߙææÙ
ØçÎ ãæ§ÇþæðÁÙ ÂÚU×æ‡æé ·ð¤ ç˜æ’Øæ r ·¤è ¥æÚUçÕÅU ×ð´
ƒæê×Ùð ßæÜð §Üñ€ÅþUæòÙ ·¤æ ÎýÃØ×æÙ m ¥æñÚU ¥æßðàæ e ãæð´
Ìæð, ƒæê×Ùð ßæÜð §Üñ€ÅþUæòÙ ·¤è â·¤Ü ª¤Áæü ãæð»è Ñ
revolving electron will be :
32.
(1)
1 e2
2 r
(1)
1 e2
2 r
(2)
2
e2
r
(2)
2
(3)
me 2
r
(3)
me 2
r
(4)
2
(4)
2
1 e2
2 r
The de-Broglie wavelength of a particle of 32.
mass 6.63 g moving with a velocity of
100 ms21 is :
33.
e2
r
1 e2
2 r
ÎýÃØ×æÙ 6.63 g ·ð¤ ·¤‡æ ·¤æ ¥æßð» 100 ms21 âð
»çÌ×æÙ ãæðÙð ÂÚU Îè-Õýæ‚Üè ÌÚ´U»ÎñŠØü ãæð»è Ñ
(1)
10233 m
(1)
10233 m
(2)
10235 m
(2)
10235 m
(3)
10231 m
(3)
10231 m
(4)
10225 m
(4)
10225 m
What happens when an inert gas is added 33.
to an equilibrium keeping volume
unchanged ?
(1)
More product will form
(2)
Less product will form
(3)
More reactant will form
(4)
Equilibrium will remain unchanged
English : 17
Set : 06
âæØ ÚU¹Ùð ßæÜð ¥æØÌÙ ·¤æð ¥ÂçÚUßçÌüÌ ÚU¹Ùð ßæÜè
çSÍçÌ ×ð´ °·¤ ¥ç·ý¤Ø »ñâ ÇæÜÙð ÂÚU €Øæ ãæð»æ?
(1) ¥çÏ·¤ ç·ý¤Øæ È¤Ü Âý挈æ ãæð»æÐ
(2) ·¤× ç·ý¤Øæ È¤Ü Âý挈æ ãæð»æÐ
(3) ¥çÏ·¤ ¥çÖç·ý¤Øæ ãæð»èÐ
(4) âæØ ¥ÂçÚUßçÌüÌ ÚUãð»æÐ
Hindi : 17
Set : 06
34.
The amount of BaSO4 formed upon mixing 34.
100 mL of 20.8% BaCl 2 solution with
50 mL of 9.8% H2SO4 solution will be :
(Ba5137, Cl535.5, S532, H51 and
O516)
35.
ÁÕ
¥æñÚU
O516 ×æÙæ ÁæØð Ìæð 20.8% BaCl2 çßÜØÙ ·ð¤
100 mL ·¤æð 9.8%, H 2 SO 4 ·ð ¤ çßÜØÙ ·ð ¤
50 mL ×ð´ ç×ÜæÙð ÂÚU ç·¤ÌÙæ BaSO4 ÕÙð»æ?
Ba5137, Cl535.5, S532, H51
(1)
23.3 g
(1)
23.3 g
(2)
11.65 g
(2)
11.65 g
(3)
30.6 g
(3)
30.6 g
(4)
33.2 g
(4)
33.2 g
The rate coefficient (k) for a particular 35.
reactions is
and
1.331024
1.331023
M21
M21 s21
s21
at 1008C,
at 1508C. What
is the energy of activation (EA) (in kJ) for
this reaction ? (R5molar gas
constant58.314 JK21 mol21)
ÂÚU °·¤ çßàæðá ¥çÖç·ý¤Øæ ·¤æ ÎÚU çÙØÌæ´·¤ (k)
1.331024 M21 s21 ãñ ¥æñÚU 1508C ÂÚU §â·¤æ
×æÙ 1.331023 M21 s21 ãñÐ §â ¥çÖç·ý¤Øæ ·ð¤
çÜØð °ð€ÅUèßðàæÙ ª¤Áæü (EA) kJ ×ð´ ç·¤ÌÙè ãæð»è?
(R5×æðÜÚU »ñâ çÙØÌæ´·¤ 58.314 JK21 ×æðÜ 21)
1008C
(1)
16
(1)
16
(2)
60
(2)
60
(3)
99
(3)
99
(4)
132
(4)
132
English : 18
Set : 06
Hindi : 18
Set : 06
36.
How many electrons would be required to 36.
deposit 6.35 g of copper at the cathode
during the electrolysis of an aqueous
solution of copper sulphate ? (Atomic mass
of copper 5 63.5 u, N A 5Avogadro’s
constant) :
37.
·¤æÂÚU âË$Èð¤ÅUU ·ð¤ ÁÜèØ çßÜØÙ ·ð¤ §Üñ€ÅþUæòÜðçââ ×ð´
·ñ¤ÍæðÇ ÂÚU 6.35 »ýæ× ·¤æÂÚU ·ð¤ Á×æ¥æð´ ·ð¤ çÜØð
ç·¤ÌÙð §Üñ€ÅþUæòÙæð´ ·¤è ¥æßàØ·¤Ìæ ãæð»è? (·¤æÂÚU ·¤æ
ÂÚU×æ‡æé ÎýÃØ×æÙ 5 63.5 ×æ˜æ·¤, NA5 °ðßæð»æÎýæð
çÙØÌæ´·¤)
(1)
NA
20
(1)
NA
20
(2)
NA
10
(2)
NA
10
(3)
NA
5
(3)
NA
5
(4)
NA
2
(4)
NA
2
The entropy (S o ) of the following 37.
substances are :
CH4 (g) 186.2 J K21 mol21
O2
(g) 205.0 J K21 mol21
CO 2 (g) 213.6 J K21 mol21
H2O (l) 69.9
J K21 mol21
The entropy change (DSo) for the reaction
CH4(g)12O2(g) ® CO2(g)12H2O(l) is :
(1) 2312.5 J K21 mol21
(2)
(3)
(4)
2242.8 J K21 mol21
çِ٠ÂÎæÍæðZ ·ð¤ °ð‹ÅþUæÂè ×æÙ ãñ (So) ãñ´ Ñ
CH4 (g) 186.2 J K21 ×æðÜ21
O 2 (g) 205.0 J K21 ×æðÜ21
CO 2 (g) 213.6 J K21 ×æðÜ21
H2O (l) 69.9 J K21 ×æðÜ21
¥çÖç·ý¤Øæ
CH 4 (g)12O 2 (g) ® CO 2 (g)12H 2 O(l)
·ð¤ çÜØð °ð‹ÅþUæÂè ÂçÚUßÌüÙ (DSo) ·¤æ ×æÙ ãæð»æ Ñ
(1)
(2)
2108.1 J
K21
mol21
(3)
237.6 J
K21
mol21
(4)
English : 19
Set : 06
×æðÜ21
2242.8 J K21 ×æðÜ21
2108.1 J K21 ×æðÜ21
237.6 J K21 ×æðÜ21
2312.5 J K21
Hindi : 19
Set : 06
38.
39.
The conjugate base of hydrazoic acid is : 38.
(1)
N23
(2)
(1)
N23
N2
3
(2)
N2
3
(3)
N2
2
(3)
N2
2
(4)
HN2
3
(4)
HN2
3
In a monoclinic unit cell, the relation of 39.
sides and angles are respectively :
40.
ãæ§ÇþUæð$Áæ𧷤 °ðçâÇU ·¤æ â´Øé‚×è ÿææÚU ãñ Ñ
(1)
a5b ¹ c and a5b5g5908
(2)
a ¹ b ¹ c and a5b5g5908
(3)
a ¹ b ¹ c and b5g5908 ¹ a
(4)
a ¹ b ¹ c and a ¹ b ¹ g ¹ 908
The standard enthalpy of formation 40.
(D f H o 298 )
for
methane,
CH 4
is
274.9 kJ mol21. In order to calculate the
average energy given out in the formation
°·¤ ×æðÙæðç€ÜçÙ·¤ °·¤·¤ âñÜ ×ð´ Âÿææ𴠷𤠷¤æðÙæ çՋÎé¥æð´
âð âÕ‹Ï ·ý¤×æÙéâæÚU ãæðÌð ã´ñ Ñ
(1) a5b ¹ c ¥æñÚU a5b5g5908
(2) a ¹ b ¹ c ¥æñÚU a5b5g5908
(3) a ¹ b ¹ c ¥æñÚU b5g5908 ¹ a
(4) a ¹ b ¹ c ¥æñÚU a ¹ b ¹ g ¹ 908
×èÍðÙ,
CH4,
ÕÙÙð ·¤è ×æÙ·¤ °ð‹ÍñËÂè (DfHo298)
274.9 kJ ×æðÜ21 ãæðÌè ãñÐ §ââð C2H ¥æՋÏ
·¤è ׊Ø×æÙ ª¤Áæü ·¤æ ¥æ·¤ÜÙ ·¤ÚUÙð ·ð¤ çÜØð çِÙæð´
âð 緤⠰·¤ ·¤æð ÁæÙÙæ ¥æßàØ·¤ ãæð»æ?
of a C2H bond from this it is necessary to
know which one of the following ?
(1)
the dissociation energy of the
(1)
(2)
hydrogen molecule, H2.
the first four ionisation energies of
H2 ¥‡æé
(2)
·¤æÕüÙ ·¤è ÂãÜè ¿æÚU ¥æØÙÙ ª¤Áæü°¡Ð
(3)
H2 ·¤è
çßØæðÁÙ ª¤Áæü ¥æñÚU ·¤æÕüÙ (»ýð$Ȥæ§Å)U
·¤è ª¤ŠßüÂæÌÙ ª¤ÁæüÐ
(4)
·¤æÕüÙ ·¤è ÂýÍ× ¿æÚU ¥æØÙÙ ª¤Áæü°¡ ¥æñÚ
ãæ§ÇþUæðÁÙ ·¤è §Üñ€ÅþUæò٠ՋÏéÌæÐ
carbon.
(3)
the dissociation energy of H2 and
enthalpy of sublimation of carbon
(graphite).
(4)
the first four ionisation energies of
carbon and electron affinity of
·¤è çßØæðÁÙ ª¤ÁæüÐ
hydrogen.
English : 20
Set : 06
Hindi : 20
Set : 06
41.
hydrolysis of xenon fluorides ?
$ÁèÙæÙ ÜæðÚUæ§ÇUæð´ ·ð¤ ÁÜèØ ¥ÂƒæÅUÙ âð çِ٠$ÁèÙæÙ¥æ€âæð-Øæñç»·¤æð´ ×ð´ âð 緤ⷤæð Âý挈æ Ùãè´ ç·¤Øæ Áæ
â·¤Ìæ ãñ?
(1)
(1)
Which of the following xenon-OXO 41.
compounds may not be obtained by
(2)
(3)
(4)
42.
Xe O2F2
Xe O F4
(2)
Xe O3
Xe O4
(3)
(4)
Excited hydrogen atom emits light in the 42.
ultraviolet region at
2.4731015
Hz. With
this frequency, the energy of a single
Xe O2F2
Xe O F4
Xe O3
Xe O4
ÂÚU ÂÚUæÕñ´»Ùè ÿæð˜æ ×ð´ ©žæðçÁÌ
ãæ§ÇþUæðÁÙ ÂÚU×æ‡æé Âý·¤æàæ ©ˆâçÁüÌ ·¤ÚUÌæ ãñÐ §â
¥æßëçžæ ·ð¤ âæÍ °·¤ ¥·ð¤Üð ȤæðÅUæòÙ ·¤è ª¤Áæü ãæð»è Ñ
2.47310 15 Hz
(h56.63310234 Js)
photon is :
(h56.63310234 Js)
43.
(1)
8.041310 240 J
(1)
8.041310240 J
(2)
2.680310 219 J
(2)
2.680310219 J
(3)
1.640310 218 J
(3)
1.640310218 J
(4)
6.111310 217 J
(4)
6.111310217 J
largest number of oxidation states ?
çِÙæð´ ×ð´ âð ·¤æñÙ °·¤ ¥çÏ·¤Ì× â´Øæ ×ð´ ¥æò€âè·¤ÚU‡æ
¥ßSÍæ°¡ çιæÌæ ãñ?
(1)
Ti (22)
(1)
Ti (22)
(2)
V(23)
(2)
V(23)
(3)
Cr (24)
(3)
Cr (24)
(4)
Mn (25)
(4)
Mn (25)
Which one of the following exhibits the 43.
English : 21
Set : 06
Hindi : 21
Set : 06
44.
Copper becomes green when exposed to 44.
moist air for a long period. This is due to :
(1)
the formation of a layer of cupric
oxide on the surface of copper.
(2)
the formation of a layer of basic
carbonate of copper on the surface
ܐÕð â×Ø Ì·¤ »èÜè ßæØé ·ð¤ âÂ·ü¤ ×ð´ ÚUãÙð ÂÚU
·¤æÂÚU ãÚUæ ãæð ÁæÌæ ãñÐ §â·¤æ ·¤æÚU‡æ ãæðÌæ ãñ Ñ
(1) ·¤æÂÚU ÌÜ ÂÚU €ØêçÂý·¤ ¥æò€âæ§ÇU ·¤æ ÂÚUÌ
ÕÙÙæÐ
(2) ·¤æÂÚU ÌÜ ÂÚU ·¤æÂÚU ·ð¤ ÿææÚUèØ ·¤æÕæðüÙðÅU ·¤æ
ÂÚUÌ ÕÙÙæÐ
of copper.
(3)
the formation of a layer of cupric
(3)
hydroxide on the surface of copper.
(4)
the formation of basic copper
(4)
sulphate layer on the surface of the
·¤æÂÚU ÌÜ ÂÚU €ØêçÂý·¤ ãæ§ÇþU¥æò€âæ§ÇU ·¤æ ÂÚUÌ
ÕÙÙæÐ
ÏæÌé ÌÜ ÂÚU ÿææÚUèØ ·¤æÂÚU âË$Èð¤ÅU ·¤æ ÂÚUÌ
ÕÙÙæÐ
metal.
45.
Among the following species the one 45.
which causes the highest CFSE, Do as a
çِ٠ÂÎæÍæðZ ×ð´ âð ·¤æñÙ °·¤ çÜ»ñ‹ÇU M¤Â ×ð´ ¥çÏ·¤Ì×
CFSE, Do ·¤æ ·¤æÚU‡æ ÕÙÌæ ãñ?
ligand is :
(1)
CN2
(1)
CN2
(2)
NH3
(2)
F2
(3)
NH3
CO
(4)
(3)
(4)
46.
Similarity in chemical properties of the 46.
atoms of elements in a group of the
Periodic table is most closely related to :
(1)
atomic numbers
(2)
atomic masses
(3)
number of principal energy levels
(4)
number of valence electrons
English : 22
Set : 06
F2
CO
¥æßÌü âæÚU‡æè ·ð¤ ç·¤âè »ýé ×ð´ Ìˆß ·ð¤ ÂÚU×æ‡æé¥æð´ ·ð¤
ÚUæâæØçÙ·¤ »é‡ææð´ ×ð´ ¥çÏ·¤Ì× â×æÙÌæ ·ð¤ ·¤æÚU‡æ ãæðÌð
ãñ´ Ñ
(1) ÂÚU×æ‡æé·¤ ِÕÚU
(2) ÂÚU×æ‡æé·¤ ÎýÃØ×æÙ
(3) ÕǸð (Principal) ª¤Áæü SÌÚUæð´ ·¤è ⴁØæ
(4) ßñÜð‹âè §Üñ€ÅþUæòÙæð´ ·¤è ⴁØæ
Hindi : 22
Set : 06
47.
Which of the following arrangements 47.
represents the increasing order (smallest
to largest) of ionic radii of the given species
O22, S22, N32, P32 ?
48.
çِ٠ÃØßSÍæ¥æð ´ ×ð ´ âð ·¤æñ Ù çÎØð »Øð ÂÎæÍæð Z
O22, S22, N32, P32 ·¤è ¥æØçÙ·¤ ç˜æ’Øæ¥æð´ ·ð¤
ÕɸÌð ·ý¤× (‹ØêÙÌ× âð ßëãžæ×) ·¤æð ÂýSÌéÌ ·¤ÚUÌè ãñ?
(1)
O22< N32< S22 < P32
(1)
O22< N32< S22 < P32
(2)
O22< P32< N32 < S22
(2)
O22< P32< N32 < S22
(3)
N32 < O22< P32 < S22
(3)
N32 < O22< P32 < S22
(4)
N32< S22< O22 < P32
(4)
N32< S22< O22 < P32
Global warming is due to increase of :
(1)
48.
methane and nitrous oxide in
â´âæçÚU·¤ ©žææÂÙ ·¤æ ·¤æÚU‡æ ãæðÌæ ãñ ßæØéׇÇUÜ ×ð´
ÕɸÙæ Ñ
(1) ×èÍðÙ ¥æñÚU Ùæ§ÅþUâ ¥æò€âæ§ÇU ·¤æÐ
atmosphere
(2)
(3)
(4)
49.
methane and CO2 in atmosphere
methane and O3 in atmosphere
(2)
(3)
methane and CO in atmosphere
(4)
Hydrogen peroxide acts both as an 49.
oxidising and as a reducing agent
depending upon the nature of the reacting
species. In which of the following cases
H 2 O 2 acts as a reducing agent in acid
×èÍðÙ ¥æñÚU CO2 ·¤æÐ
×èÍðÙ ¥æñÚU O3 ·¤æÐ
×èÍðÙ ¥æñÚU CO ·¤æÐ
ãæ§ÇþUæðÁÙ ÂÚU¥æò€âæ§ÇU ¥Â¿æØ·¤ ÌÍæ ©Â¿æØ·¤ ÎæðÙæð´
Âý·¤æÚU âð ÃØßãæÚU ·¤ÚUÌæ ãñ ¥æñÚU Øã çÙÖüÚU ·¤ÚUÌæ ãñ
¥çæç·ý¤Øæ ·¤ÚUÙð ßæÜð SÂèàæè$Á ·ð¤ SßæÖæß ÂÚUÐ çِÙ
×ð́ âð ç·¤â·ð¤ âæÍ H2O2 ¥ÜèØ ×æŠØ× ×ð́ ¥Â¿æØ·¤
·ð¤ M¤Â ×ð´ ç·ý¤Øæ ·¤ÚUÌæ ãñ?
medium ?
(1)
MnO42
(1)
MnO42
(2)
Cr2 O 7
(2)
Cr2 O 7
(3)
SO 3
(3)
SO 3
(4)
KI
(4)
KI
22
22
English : 23
Set : 06
22
22
Hindi : 23
Set : 06
50.
Which one of the following complexes will 50.
most likely absorb visible light ?
(At nos. Sc521, Ti522, V523, Zn530)
(1)
(2)
(3)
(4)
[Sc(H2O)6]31
Zn530)
]41
[Ti (NH3)6
[V(NH3)6]31
(1)
(2)
[Zn(NH3)6]21
51.
çِ٠·¤æòŒÜð€âæð´ (â´·¤ÚUæð´) ×ð´ âð ·¤æñÙ ÎëàØ Âý·¤æàæ ·¤æð
¥ßàææðçáÌ ·¤ÚUÙð ·¤è âßæüçÏ·¤ â´ÖæßÙæ ÚU¹Ìæ ãñ?
( ÂÚU × æ‡æé ·ý ¤ ×æ´ · ¤ Sc521, Ti522, V523,
(3)
(4)
on mercuration-
51.
[Sc(H2O)6]31
[Ti (NH3)6]41
[V(NH3)6]31
[Zn(NH3)6]21
×ÚU€ØêÚðUàæÙ-¥×ÚU€ØêÚðUàæÙ ÂÚ
demercuration produces the major
U âð Âý挈æ ×éØ ç·ý¤ØæȤÜ
product :
ãæðÌæ ãñ Ñ
(1)
(1)
(2)
(2)
(3)
(3)
(4)
(4)
52.
In the Victor-Meyer’s test, the colour given
by 18, 28 and 38 alcohols are respectively : 52.
(1)
Red, colourless, blue
(2)
Red, blue, colourless
(3)
Colourless, red, blue
(4)
Red, blue, violet
English : 24
Set : 06
ç߀ÅUÚU ×ðØÚU ·ð¤ ÂÚUèÿæ‡æ ç·ý¤Øæ ×ð´ 18, 28 ¥æñÚU
°ðË·¤æðãæÜæð´ mæÚUæ çÎØæ Ú´U» ·ý¤×æÙéâæÚU ãæðÌæ ãñ Ñ
(1) ÜæÜ, Ú´U»ãèÙ, ÙèÜæ
(2) ÜæÜ, ÙèÜæ, Ú´U»ãèÙ
(3) Ú´U»ãèÙ, ÜæÜ, ÙèÜæ
(4) ÜæÜ, ÙèÜæ, Áæ×Ùè
Hindi : 24
38
·ð¤
Set : 06
53.
Conversion of benzene diazonium chloride 53.
to chloro benzene is an example of which
of the following reactions ?
54.
(1)
Claisen
(2)
Friedel-craft
(3)
Sandmeyer
(4)
Wurtz
In the presence of peroxide, HCl and HI 54.
do not give anti-Markownikoff’s addition
Õñ‹$ÁèÙ ÇUæØæ$ÁæðçÙØ× €ÜæðÚUæ§ÇU ·¤æ €ÜæðÚUæð Õñ‹$ÁèÙ ×ð´
ÕÎÜÙæ §Ù×ð´ âð 緤⠥çÖç·ý¤Øæ ·¤æ ©ÎæãÚU‡æ ãæðÌæ
ãñ?
(1) €Üð$ÁÙ
(2) Èý¤èÇUÜ-·ý¤æ$$ÅU
(3) âñ´ÇU×æØÚU
(4) ßéÅ÷üU $Á
ÂÚU¥æò€âæ§ÇU ·¤è ©ÂçSÍçÌ ×ð´ °ðË·¤èÙæð´ ·¤æð HCl ¥æñÚU
HI °ð‹ÅUè×æÚU·¤æðÙè·¤æȤ Øæð» Ùãè´ ÎðÌð €Øæð´ ç·¤ Ñ
to alkenes because :
(1)
One of the steps is endothermic in
(1)
HCl and HI
(2)
Both HCl and HI are strong acids
(2)
(3)
HCl is oxidizing and the HI is
(3)
reducing
(4)
All the steps are exothermic in HCl
(4)
and HI
55.
The major product obtained in the photo 55.
catalysed bromination of 2-methylbutane
·ð¤ Âý·¤æàæ mæÚUæ ©ˆÂýðçÚUÌ Õýæð×èÙðàæÙ ×ð´
ÕǸæ ç·ý¤ØæÈ¤Ü ãæðÌæ ãñ Ñ
(1)
1-bromo-2-methylbutane
(1)
(2)
1-bromo-3-methylbutane
(2)
(3)
2-bromo-3-methylbutane
(3)
(4)
2-bromo-2-methylbutane
(4)
Set : 06
¥æñÚU HI ·ð¤ âÕ‹Ïæð´ ×ð´ âÖè ¿ÚU‡æ
ª¤c×æÂýÎ ãñ´Ð
HCl
2- ×ðçÍ܎ØéÅðUÙ
is :
English : 25
¥æñ Ú U HI ·ð ¤ âÕ‹Ï ×ð ´ °·¤ ¿ÚU ‡ æ
ª¤c×æàææðáè ãñÐ
HCl ¥æñÚU HI ÎæðÙæð´, ÂýÕÜ ¥Ü ãñ´Ð
HCl ©Â¿æØ·¤ ¥æñÚU HI ¥Â¿æØ·¤ ãñÐ
HCl
1-Õýæð×æð-2-×ðçÍ܎ØéÅðUÙ
1-Õýæð×æð-3-×ðçÍ܎ØéÅðUÙ
2-Õýæð×æð-3-×ðçÍËæŽØéÅðUÙ
2-Õýæð×æð-2-×ðçÍ܎ØéÅðUÙ
Hindi : 25
Set : 06
56.
sigma(s) and two pi(p) bonds ?
çِ٠¥‡æé¥æð´ ×ð´ âð 緤⠥‡æé ×ð´ Îæð çâ‚×æ (s) ¥æñÚU Îæð
Âæ§ü (p) ¥æÕ‹Ï ãæðÌð ãñ´?
(1)
C 2H 4
(1)
C2H2Cl2
(3)
Which of the following molecules has two 56.
(2)
(3)
(4)
57.
N2F2
(2)
HCN
(4)
Which one of the following acids does not 57.
exhibit optical isomerism ?
58.
59.
(1)
Lactic acid
(2)
Tartaric acid
(3)
Maleic acid
(4)
a-amino acids
Aminoglycosides are usually used as :
(1)
antibiotic
(2)
analgesic
(3)
hypnotic
(4)
antifertility
58.
Which of the following will not show 59.
C2H2Cl2
HCN
§Ù×ð´ âð ·¤æñÙ ØêÅUæÚUæðÅðUàæÙ Ùãè´ çιæØð»æ?
(1)
Maltose
(1)
(2)
Lactose
(2)
(3)
Glucose
(3)
(4)
Sucrose
(4)
Set : 06
N2F2
çِ٠¥Üæð´ ×ð´ âð ·¤æñÙ Âý·¤æàæèØ â×æßØßÌæ Ùãè´
çιæÌæ?
(1) Üñç€ÅU·¤ °ðçâÇU
(2) ÅUæÚUÅñUçÚU·¤ °çâÇU
(3) ×ñÜè·¤ °çâÇU
(4) a- °×æØÙæð´ °ðçâÇU
¥×æØÙæð‚Ü槷¤æðâæ§ÇUæð´ ·¤æð ÂýæØÑ çِ٠緤â Âý·¤æÚU
ÂýØæð» ç·¤Øæ ÁæÌæ ãñ?
(1) °ð‹ÅUè ÕæØæðçÅU·¤ M¤Â ×ð´ (ÂýçÌ Áñçß·¤)
(2) °ðÙÜÁñçâ·¤ M¤Â ×ð´ (ÂèǸæ Ùæàæ·¤)
(3) çãÂÙæçÅU·¤ M¤Â ×ð´ (çÙÎýæ ÂýÎ)
(4) °ð‹ÅUè ȤÚUçÅUçÜÅUè M¤Â ×ð´ (°ð‹ÅUè çÙáð¿·¤)
mutarotation ?
English : 26
C2H 4
×æËÅUæð$Á
Üñ€ÅUæð$Á
‚Üê·¤æð$Á
âê·ý¤æð$Á
Hindi : 26
Set : 06
60.
Phthalic acid reacts with resorcinol in the 60.
presence of concentrated H2SO4 to give :
(1)
Phenolphthalein
(2)
Alizarin
(3)
Coumarin
(4)
Fluorescein
English : 27
Set : 06
âæ‹Îý H 2SO4 ·¤è ©ÂçSÍçÌ ×ð ´ Íñ ç Ü·¤ °ð ç âÇU
çÚU$ÁæÚUâèÙæÜ âð ¥çÖç·ý¤Øæ ·¤ÚU ÎðÌæ ãñ Ñ
(1) çȤÙæËȤÍðÜèÙ
(2) °ðçÜ$ÁðÚUèÙ
(3) ·é¤×ýèÙ
(4) $ÜæðÚðUâèÙ
Hindi : 27
Set : 06
Öæ» C — »ç‡æÌ
PART C — MATHEMATICS
61.
A relation on the set A5{x : ?x? < 3, xeZ}, 61.
where Z is the set of integers is defined by
R5{(x, y) : y 5? x ? , x ≠2 1 }. Then the
number of elements in the power set of R
â×é“æØ A5{x : ?x? < 3, xeZ}, Áãæ¡ Z Âê‡ææZ·¤æð´ ·¤æ
â×é “ æØ ãñ , ÂÚU °·¤ â´ Õ ´ Ï R,
R5{(x, y) : y5?x?, x ≠2 1 } mæÚUæ ÂçÚUÖæçáÌ ãñÐ
Ìæð R ·ð¤ ƒææÌ â×é“æØ ×ð´ ¥ßØßæð´ ·¤è ⴁØæ ãñ Ñ
is :
62.
(1)
32
(1)
32
(2)
16
(2)
16
(3)
8
(3)
8
(4)
64
(4)
64
×æÙæ
z ¹ 2i
Let z ¹ 2i be any complex number such 62.
that
z2 i
is a purely imaginary number.
z1 i
Then z1
z2 i
z1 i
1
is :
z
z1
°·¤ àæé h ·¤æËÂçÙ·¤ â´  Øæ ãñ , Ìæð
1
z
ãñ Ñ
(1)
0
(1)
(2)
any non-zero real number other
(2)
1 ·ð¤ ¥çÌçÚU€ˆæ ·¤æð§ü àæê‹ØðžæÚU ßæSÌçß·¤ ⴁØæÐ
·¤æð§ü àæê‹ØðžæÚU ßæSÌçß·¤ ⴁØæÐ
°·¤ àæéh ·¤æËÂçÙ·¤ ⴁØæÐ
than 1.
63.
·¤æð§ü °ðâè âç×Ÿæ ⴁØæ ãñ ç·¤
(3)
any non-zero real number.
(3)
(4)
a purely imaginary number.
(4)
0
x21?2x23?2450, is :
â×è·¤ÚU ‡ æ x21?2x23?2450, ·ð ¤ ×ê Ü æð ´ ·¤æ
Øæð»È¤Ü ãñ Ñ
(1)
2
(1)
2
(2)
22
(2)
22
(3)
(4)
2
(3)
(4)
2
The sum of the roots of the equation, 63.
2 2
English : 28
Set : 06
2 2
Hindi : 28
Set : 06
64.
64.
If
a2
65.
66.
b2
( a1l
)2
( a2l
)2
c2
( b1l
)2
( b2l
)2
a2
a2
b2
( c1l 5k l a
b
c , l ≠ 0,
1
1
1
)2
( c2l
)2
ØçÎ
c2
b2
( a1l
)2
( a2l
)2
c2
( b1l
)2
( b2l
)2
ãñ, Ìæð k ÕÚUæÕÚU ãñ Ñ
(1)
4labc
(1)
4labc
(2)
24labc
(2)
24labc
(3)
4l2
(3)
4l2
(4)
24l2
(4)
24l2
y 
x
1 2
If A 5 
and
B 5  x  be such 65.

 
 3 21 2 
 1 
ØçÎ
6 
that AB 5   , then :
8 
6 
AB 5   , ãñ,
8 
(1)
y52x
(1)
y52x
(2)
y522x
(2)
y522x
(3)
y5x
(3)
y5x
(4)
y52x
(4)
y52x
digits 1, 1, 2, 2, 2, 3, 4, 4. The number of
such numbers in which the odd digits do
b2
( c1l 5k l a
b
c , l ≠ 0,
1
1
1
( c2l
then k is equal to :
8 - digit numbers are formed using the 66.
a2
)2
)2
x
1 2
A5 

 3 21 2 
ÌÍæ
c2
y 
B 5  x  °ðâð
 
 1 
ãñ´ ç·¤
Ìæð Ñ
¥´·¤æð´ 1, 1, 2, 2, 2, 3, 4, 4 ·ð¤ ÂýØæð» âð, ¥æÆU ¥´·¤èØ
ⴁØæ°¡ ÕÙæ§ü »§ü ãñд °ðâè ⴁØæ¥æð´ ·¤è ⴁØæ çÁÙ×ð´
çßá× ¥´·¤ çßá× SÍæÙæð´ ÂÚU Ù ¥æØð,´ ãñ Ñ
not occupy odd places, is :
(1)
160
(1)
160
(2)
120
(2)
120
(3)
60
(3)
60
(4)
48
(4)
48
English : 29
Set : 06
Hindi : 29
Set : 06
67.
x 55

If  2 1  is expanded in the ascending 67.
3

ØçÎ
x  55

21 
3

·¤æ x ·¤è ¥æÚUæðãè ƒææÌæð´ ×ð´ ÂýâæÚU
·¤ÚUÙð ÂÚU, ÂýâæÚU ×ð´ Îæð ·ý¤ç×·¤ ÂÎæð´ ×ð´ x ·¤è ƒææÌð´ â×æÙ
ãñ´, Ìæð Øã ÂÎ ã´ñ Ñ
powers of x and the coefficients of powers
of x in two consecutive terms of the
expansion are equal, then these terms
are :
68.
(1)
7th and 8th
(1)
(2)
8th
(2)
and
9th
(3)
28th
29th
(3)
(4)
27th and 28th
(4)
and
ÌÍæ 8 ßæ¡
8 ßæ¡ ÌÍæ 9 ßæ¡
28 ßæ¡ ÌÍæ 29 ßæ¡
27 ßæ¡ ÌÍæ 28 ßæ¡
Let G be the geometric mean of two 68.
×æÙæ Îæð Ï٠ⴁØæ¥æð´ a ÌÍæ b ·¤æ »é‡ææðžæÚU ×æŠØ G ãñ
positive numbers a and b, and M be the
ÌÍæ
1
1
arithmetic mean of 1 and . If
: G is
b
M
a
4 : 5, then a : b can be :
69.
7 ßæ¡
1 ÌÍæ 1
b
a
·¤æ â×æ‹ÌÚU ×æŠØ
(1)
1:4
1
: G 5 4 : 5 ãñ,
M
(1) 1 : 4
(2)
1:2
(2)
1:2
(3)
2:3
(3)
2:3
(4)
3:4
(4)
3:4
The least positive integer n such that 69.
12
2
2
2
1
2 2 2........ 2 n21 <
, is :
3
100
3
3
ÏÙ Âê‡ææZ·¤
12
4
(1)
4
(2)
5
(2)
5
(3)
6
(3)
6
(4)
7
(4)
7
Set : 06
Hindi : 30
ãñÐ ØçÎ
Ìæð a : b ãæð â·¤Ìð ãñ´ Ñ
·¤æ ß㠋ØêÙÌ× ×æÙ çÁâ·ð¤ çÜØð
2
2
2
1
2 2 2........ 2 n21 <
,
3
100
3
3
(1)
English : 30
n
M
ãñ, ãñ Ñ
Set : 06
70.
Let f, g : R®R be two functions defined by 70.

(2)
Both statements I and II are true.
(3)
Statement I is true, statement II is
 1
x sin   , x ≠ 0
 x
, ±²Ë g ( x ) 5 x f ( x )
0
, x50

mæÚUæ ÂçÚUÖæçáÌ ãñ´ Ñ
·¤ÍÙ I : x50 ÂÚU f °·¤ âÌÌ È¤ÜÙ ãñÐ
·¤ÍÙ II : x50 ÂÚU g °·¤ ¥ß·¤ÜèØ È¤ÜÙ ãñÐ
71.
1
, and g(x) is its
2
inverse function, then g9(7) equals :
If f(x)5x22x15, x >
(1)
1
2
3
(2)
1
13
(3)
1
3
(4)
1
2
13
English : 31
Set : 06
(4)
·¤ÍÙ I ¥âˆØ ãñ, ·¤ÍÙ
(2)
Statement I is false, statement II is
true.
(3)
·¤ÍÙ I ÌÍæ II ÎæðÙæð´ ¥âˆØ ãñ´Ð
·¤ÍÙ I ÌÍæ II ÎæðÙæð´ âˆØ ãñ´Ð
·¤ÍÙ I âˆØ ãñ, ·¤ÍÙ II ¥âˆØ ãñÐ
(1)
false.
(4)
ȤÜÙ ãñ´ Áæð
f (x)5
Statement I : f is a continuous function at
x50.
Statement II : g is a differentiable function
at x50.
Both statements I and II are false.
f, g : R®R Îæð

 1
x sin   , x ≠ 0
 x
, and g ( x ) 5 x f ( x )
0
, x50

f (x)5
(1)
×æÙæ
71.
ØçÎ
f(x)5x22x15, x >
II âˆØ
ãñÐ
1
, ÌÍæ g(x)
2
§â·¤æ
ÃØ鈷ý¤× ȤÜÙ ãñ, Ìæð g9(7) ÕÚUæÕÚU ãñ Ñ
1
3
(1)
2
(2)
1
13
(3)
1
3
(4)
2
Hindi : 31
1
13
Set : 06
72.
all x e R. Then for all x :
×æÙæ R ÂÚU f ÌÍæ g Îæð °ðâð ¥ß·¤ÜÙèØ È¤ÜÙ ãñ ç·¤
âÖè x e R ·ð¤ çÜ° f 9(x) > 0 ÌÍæ g9(x) < 0 ãñ, Ìæð
âÖè x ·ð¤ çÜ° Ñ
(1)
f(g(x)) > f (g(x21))
(1)
f(g(x)) > f(g(x21))
(2)
f(g(x)) > f (g(x11))
(2)
f(g(x)) > f(g(x11))
(3)
g(f(x)) > g (f(x21))
(3)
g(f(x)) > g(f(x21))
(4)
g(f(x)) < g (f(x11))
(4)
g(f(x)) < g(f(x11))
Let f and g be two differentiable functions 72.
on R such that f 9(x) > 0 and g9(x) < 0, for
73.
5
i
If 11x41x55 ∑ ai ( 1 1 x ) , for all x in R,
73.
i50
x e R ·ð¤
çÜ°
5
∑ ai ( 1 1 x )i ãñ, Ìæð a2 ãñ Ñ
11x41x55
then a2 is :
74.
ØçÎ âÖè
i50
(1)
24
(1)
24
(2)
6
(2)
6
(3)
28
(3)
28
(4)
10
(4)
10
∫(
The integral
sin 2 x cos2 x
3
sin x 1 cos
3
x)
d x is 74.
2
â×æ·¤Ü ∫
sin 2 x cos 2 x
( sin 3 x 1 cos3 x )2
dx
ÕÚUæÕÚU ãñ Ñ
equal to :
1
(1)
( 1 1 cot x )
(2)
2
3
1
3 ( 1 1 tan 3 x )
sin 3 x
(3)
( 1 1 cos3 x )
(4)
2
English : 32
1c
cos 3 x
1c
1c
3 ( 1 1 sin 3 x )
1c
Set : 06
1
(1)
( 1 1 cot 3 x )
(2)
2
1
3 ( 1 1 tan 3 x )
sin 3 x
(3)
( 1 1 cos3 x )
(4)
2
Hindi : 32
1c
cos 3 x
1c
1c
3 ( 1 1 sin 3 x )
1c
Set : 06
75.
If [ ] denotes the greatest integer function, 75.
then the integral
(2)
p
2
0
(3)
21
(4)
2
(1)
76.
p
p
2
2
2
∫ ( f ( x ) 1 x)d x 5 p 2 t ,
for
all
 p
t/2p, then f 2  is equal to :
 3
(1)
p
(2)
p
2
(3)
(4)
p
3
p
6
English : 33
Set : 06
°·¤ ×ãžæ× Âê ‡ ææZ · ¤èØ È¤ÜÙ ãñ , Ìæð
(2)
p
2
0
(3)
21
(4)
2
(1)
t
[ ]
p
â×æ·¤Ü ∫ 0 [ cos x ] d x ÕÚUæÕÚU ãñ Ñ
∫ 0 [ cos x ] d x is equal to :
If for a continuous function f(x), 76.
2p
ØçÎ
p
2
ØçÎ °·¤ âÌÌ È¤ÜÙ
t /2p ·ð¤ çÜ°
f(x)
·ð¤ çÜ°, âÖè
t
2
2
∫ ( f ( x ) 1 x)d x 5 p 2 t
2p
 p
f 2 
 3
(1)
p
(2)
p
2
(3)
p
3
(4)
p
6
Hindi : 33
ãñ ,
Ìæð
ÕÚUæÕÚU ãñ Ñ
Set : 06
77.
The general solution of the differential 77.
¥ß·¤Ü â×è·¤ÚU‡æ
dy
equation, sin 2x 
2
 dx
dy
sin 2x 
2
 dx

tan x 2 y 5 0 ,

(1)
y tan x 5x1c
(1)
y tan x 5x1c
(2)
y cot x 5tan x1c
(2)
y cot x 5tan x1c
(3)
y tan x 5cot x1c
(3)
y tan x 5cot x1c
(4)
y cot x 5x1c
(4)
y cot x 5x1c
(1)
4x23y57
If a line intercepted between the coordinate 78.
axes is trisected at a point A(4, 3), which
is nearer to x-axis, then its equation is :
79.
·¤æ ÃØæ·¤
ãÜ ãñ Ñ
is :
78.

tan x 2 y 5 0

çÙÎðüàææ´·¤ ¥ÿææð´ ·ð¤ Õè¿ ¥´Ìѹ´çÇUÌ °·¤ ÚðU¹æ, °·¤
çÕ´Îé A(4, 3) Áæð x- ¥ÿæ ·ð¤ Âæâ ãñ, ÂÚU Sæ×ç˜æÖæçÁÌ
ãæðÌè ãñ, Ìæð ©â·¤æ â×è·¤ÚU‡æ ãñ Ñ
(1)
4x23y57
(2)
3x12y518
(2)
3x12y518
(3)
3x18y536
(3)
3x18y536
(4)
x13y513
(4)
x13y513
If the three distinct lines x12ay1a50, 79.
x13by1b50 and x14ay1a50 are
concurrent, then the point (a, b) lies on a :
(1)
circle
(2)
hyperbola
(3)
straight line
(4)
parabola
English : 34
Set : 06
ØçÎ ÌèÙ çßçÖóæ Úð U ¹æ°¡ x12ay1a50,
x13by1b50 ÌÍæ x14ay1a50 â´»æ×è ã´ñ,
Ìæð çÕ´Îé (a, b) °·¤ Ñ
(1) ßëžæ ÂÚU çSÍÌ ãñ
(2) ¥çÌ ÂÚUßÜØ ÂÚU çSÍÌ ãñ
(3) âÚUÜ ÚðU¹æ ÂÚU çSÍÌ ãñ
(4) ÂÚUßÜØ ÂÚU çSÍÌ ãñ
Hindi : 34
Set : 06
80.
For the two circles x 2 1y 2 516 and 80.
x21y222y50, there is/are :
81.
(1)
one pair of common tangents
(2)
two pairs of common tangents
(3)
three common tangents
(4)
no common tangent
Two tangents are drawn from a point 81.
(22, 21) to the curve, y254x. If a is the
angle between them, then ?tan a? is equal
Îæð ßëžææð´ x21y2516 ÌÍæ x21y222y50, ·ð¤
çÜ° ãñ/ã´ñ Ñ
(1) ©ÖØçÙcÆU SÂàæü ÚðU¹æ¥æð´ ·¤æ °·¤ Øé‚×Ð
(2) ©ÖØçÙcÆU SÂàæü ÚðU¹æ¥æð´ ·ð¤ Îæð Øé‚×Ð
(3) ÌèÙ ©ÖØçÙcÆU SÂàæü ÚðU¹æ°´Ð
(4) ·¤æð§ü ©ÖØçÙcÆU SÂàæü ÚðU¹æ Ùãè´Ð
°·¤ çÕ´Îé (22, 21) âð °·¤ ß·ý¤ y254x ÂÚU Îæð
SÂàæü ÚðU¹æ°¡ ¹è´¿è »§ü ãñ, ØçÎ ©Ù·ð¤ Õè¿ ·¤æ ·¤æð‡æ a
ãñ, Ìæð ?tan a? ÕÚUæÕÚU ãñ Ñ
to :
(1)
1
3
(1)
(2)
1
3
(2)
1
3
(3)
3
(3)
3
(4)
82.
1
3
3
(4)
The minimum area of a triangle formed
by
any
tangent
to
the
ellipse 82.
y2
x2
1
5 1 and the co-ordinate axes
16
81
3
Îèƒæüßëžæ
y2
x2
1
51
16
81
ÂÚU ¹è´¿è »§ü ç·¤âè SÂàæü
ÚðU¹æ ÌÍæ çÙÎðüàææ´·¤ ¥ÿææð´ mæÚUæ ÕÙè ç˜æÖéÁ ·¤æ ‹ØêÙÌ×
ÿæð˜æÈ¤Ü ãñ Ñ
is :
(1)
12
(1)
12
(2)
18
(2)
18
(3)
26
(3)
26
(4)
36
(4)
36
English : 35
Set : 06
Hindi : 35
Set : 06
83.
A symmetrical form of the line of 83.
intersection of the planes x5ay1b and
â×ÌÜæð´ x5ay1b ÌÍæ
ÚðU¹æ ·¤æ â×ç×Ì M¤Â ãñ Ñ
z5cy1d ·¤è
Âýç̑ÀðUÎè
z5cy1d is :
84.
(1)
y 21
x2b
z2d
5
5
a
1
c
(1)
y 21
x2b
z2d
5
5
a
1
c
(2)
y 21
x 2 b2 a
z 2 d2 c
5
5
a
1
c
(2)
y 21
x 2 b2 a
z 2 d2 c
5
5
a
1
c
(3)
y 20
x2a
z2c
5
5
b
1
d
(3)
y 20
x2a
z2c
5
5
b
1
d
(4)
y 21
x 2 b2 a
z 2 d2 c
5
5
b
0
d
(4)
y 21
x 2 b2 a
z 2 d2 c
5
5
b
0
d
ØçÎ
â×ÌÜæð ´
If
the
distance
between
planes, 84.
4x22y24z1150
and
ÌÍæ
4x22y24z1d50 ·ð¤ Õè¿ ·¤è ÎêÚUè 7, Ìæð d ãñ Ñ
4x22y24z1d50 is 7, then d is :
85.
(1)
41 or 242
(1)
(2)
42 or 243
(2)
(3)
241 or 43
(3)
(4)
242 or 44
(4)
∧
∧
∧
4x22y24z1150
¥Íßæ 242
42 ¥Íßæ 243
241 ¥Íßæ 43
242 ¥Íßæ 44
41
If x , y and z are three unit vectors in 85.
ØçÎ ç˜æ-çß×èØ ¥æ·¤æàæ ×ð´
three-dimensional space, then the
âçÎàæ ãñ´, Ìæð
minimum value of
∧
∧
∧
∧
∧
∧
?x 1 y?2 1 ?y 1 z?2 1 ?z 1 x?2 is :
(1)
(2)
(3)
(4)
3
2
3
(2)
(3)
(4)
6
English : 36
Set : 06
∧
ÌÍæ
∧
z
ÌèÙ ×æ˜æ·¤
∧
∧
∧
∧
∧
∧
?x 1 y?2 1 ?y 1 z?2 1 ?z 1 x?2
·¤æ ‹ØêÙÌ× ×æÙ ãñ Ñ
(1)
3 3
∧
x, y
3
2
3
3 3
6
Hindi : 36
Set : 06
86.
Let X and M.D. be the mean and the mean 86.
×æÙæ n Âýðÿæ‡ææð´ xi, i51, 2, ....., n ·¤æ ×æŠØ
deviation about X of n observations
·ð¤ âæÂðÿæ ©Ù·¤æ ×æŠØ çß¿ÜÙ M.D. ãñÐ ØçÎ
ÂýˆØð·¤ Âýðÿæ‡æ ×ð´ 5 Õɸæ çÎØæ Áæ° Ìæð ÙØæ ×æŠØ ÌÍæ
‹æØð ×æŠØ ·ð¤ âæÂðÿæ ©Ù·¤æ ×æŠØ çß¿ÜÙ ·ý¤×àæÑ ãñ Ñ
X
ÌÍæ
X
xi, i51, 2, ....., n. If each of the observations
is increased by 5, then the new mean and
the mean deviation about the new mean,
respectively, are :
87.
(1)
X , M.D.
(1)
X , M.D.
(2)
X 15, M.D.
(2)
X 15, M.D.
(3)
X , M.D.15
(3)
X , M.D.15
(4)
X 15, M.D.15
(4)
X 15, M.D.15
event : A5 the chosen number x satisfies
â×é“æØ {1, 2, 3, 4, ....., 100} ×ð´ âð °·¤ ⴁØæ x
ØæÎë‘ÀUØæ ¿éÙè »§üÐ ƒæÅUÙæ A ·¤æð ÂçÚUÖæçáÌ ·¤èçÁ° Ñ
A5 ¿éÙè »§ü ⴁØæ x
( x 2 10) ( x 2 50)
/0
( x 2 30)
( x 2 10) ( x 2 50)
/0
( x 2 30)
A number x is chosen at random from the 87.
set {1, 2, 3, 4, ....., 100}. Define the
Ìæð P(A) ãñ Ñ
Then P(A) is :
(1)
0.71
(2)
0.70
(3)
0.51
(4)
0.20
English : 37
·¤æð â´ÌécÅ ·¤ÚUÌè ãñÐ
Set : 06
(1)
0.71
(2)
0.70
(3)
0.51
(4)
0.20
Hindi : 37
Set : 06
88.
Statement
I
:
The
equation 88.
(sin 21 x) 3 1(cos 21 x) 3 2ap 3 50 has a
I:
â×è·¤ÚU‡æ
(sin21x)31(cos21x)32ap350
solution for all a/ 1 .
32
Statement II : For any x e R,
sin21x1cos21x5
·¤ÍÙ
1
·ð¤
32
·¤ÍÙ II :
a/
p
and
2
çÜ° °·¤ ãÜ ãñÐ
ç·¤âè
·ð¤ çÜ°
xeR
sin21x1cos21x5
p
2
ÌÍæ
p 2 9p2
 21
0 [  sin x2  [
.

4
16
p 2 9p2
 21
0 [  sin x2  [
.

4
16
(1)
Both statements I and II are true.
(1)
(2)
Both statements I and II are false.
(2)
(3)
Statement
I
is
true
and
(3)
·¤ÍÙ I ÌÍæ II ÎæðÙæð´ âˆØ ãñ´Ð
·¤ÍÙ I ÌÍæ II ÎæðÙæð´ ¥âˆØ ãñ´Ð
·¤ÍÙ I âˆØ ãñ ÌÍæ ·¤ÍÙ II ¥âˆØ ãñÐ
false
and
(4)
·¤ÍÙ I ¥SæˆØ ãñ, ÌÍæ ·¤ÍÙ II âˆØ ãñÐ
statement II is false.
(4)
Statement
I
is
·¤æ âÖè
statement II is true.
1
89.
cos u
1
1
2cos u and
If f (u) 5 2sin u 1
21
sin u
1
A and B are respectively the maximum and
the minimum values of f (u), then
89.
ØçÎ
cos u
1
2cos u
f (u) 5 2sin u 1
21
sin u
1
ãñ,
ÌÍæ A ÌÍæ B ·ý¤×àæÑ f (u) ·ð¤ ¥çÏ·¤Ì× ÌÍæ
‹ØêÙÌ× ×æÙ ãñ´, Ìæð (A, B) ÕÚUæÕÚU ãñ Ñ
(A, B) is equal to :
(1)
(3, 21)
(2)
(4, 22 2 )
(1)
(3, 21)
(3)
( 21
2, 22 2)
(2)
(4, 22 2 )
(4)
( 21
2 , 21 )
(3)
( 21
2, 22 2)
(4)
( 21
2 , 21 )
English : 38
Set : 06
Hindi : 38
Set : 06
90.
Let p, q, r denote arbitrary statements. Then 90.
the
logically
equivalent
of
the
×æÙæ
p, q, r
Sßð ‘ ÀU ·¤ÍÙ Îàææü Ì ð ãñ ´ Ð ·¤ÍÙ
p Þ (q Ú r) ·¤æ Ìæç·ü¤·¤ â×ÌéËØ ãñ Ñ
statement p Þ (q Ú r) is :
(1)
(p Ú q) Þ r
(1)
(p Ú q) Þ r
(2)
(p Þ q) Ú (p Þ r)
(2)
(p Þ q) Ú (p Þ r)
(3)
(p Þ ~q) Ù (p Þ r)
(3)
(p Þ ~q) Ù (p Þ r)
(4)
(p Þ q) Ù (p Þ ~r)
(4)
(p Þ q) Ù (p Þ ~r)
-o0o-
English : 39
-o0o-
Set : 06
Hindi : 39
Set : 06