JEE MAIN QUESTION PAPER

1. English : 1 Set : 06 Hindi : 1 Set : 06
PART A — PHYSICS
1. From the following combinations of
physical constants (expressed through
their usual symbols) the only combination,
that would have the same value in different
systems of units, is :
(1) 2
o
c
2
h
pe
(2)
2
2
o e
e
2 Gmpe
(me5 mass of electron)
(3)
o o
2 2
G
c eh
m e
(4)
o o
2
2
Gce
hp m e
2. A person climbs up a stalled escalator
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
escalator ?
(1) 37 s
(2) 27 s
(3) 24 s
(4) 45 s
Öæ» A — ÖæñçÌ·¤ çß™ææÙ
1. ÖæñçÌ·¤ çSÍÚUæ´·¤æð´ ·ð¤ çِÙçÜç¹Ì â´ØæðÁÙ âð (¥ÂÙð
âæÏæÚU‡æ ÂýØæð» ×ð´ çÜØð »Øð ç¿‹ãæð´ mæÚUæ ÂýÎçàæüÌ),
·ð¤ßÜ ßã â´ØæðÁÙ, Áæð ç·¤ §·¤æ§Øæð´ ·ð¤ çßçÖóæ çÙ·¤æØæð´
×ð´ °·¤ ãè ×æÙ ÚU¹Ìæ ãñ, ãñ Ñ
(1) 2
o
c
2
h
pe
(2)
2
2
o e
e
2 Gmpe
(me5§Üð€ÅþUæòÙ ·¤æ ÎýÃØ×æÙ)
(3)
o o
2 2
G
c eh
m e
(4)
o o
2
2
Gce
hp m e
2. °·¤ 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?
(1) 37 s
(2) 27 s
(3) 24 s
(4) 45 s

2. English : 2 Set : 06 Hindi : 2 Set : 06
3. Three masses m, 2m and 3m are moving
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
mass will be :
(1) ( )u
3
12
i j
∧ ∧
1
(2) ( )u
3
12
i j
∧ ∧
2
(3) ( )u
3
12
i j
∧ ∧
2 1
(4) ( )u
3
12
i j
∧ ∧
2 2
4. 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
0.3, how far will the block slide
approximately ?
(1) 0.19 m
(2) 0.379 m
(3) 0.569 m
(4) 0.758 m
3. m, 2m °ß´ 3m ·ð¤ 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 çÕ‹Îé ÂÚU
â´ƒæ^ ·¤ÚUÌð ãñ´ ¥æñÚU °·¤ âæÍ ç¿Â·¤ ÁæÌð ãñ´Ð ÂçÚU‡ææ×è
ÎýÃØ×æÙ ·¤æ ßð» ãæð»æ Ñ
(1) ( )u
3
12
i j
∧ ∧
1
(2) ( )u
3
12
i j
∧ ∧
2
(3) ( )u
3
12
i j
∧ ∧
2 1
(4) ( )u
3
12
i j
∧ ∧
2 2
4. °·¤ ×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?
(1) 0.19 m
(2) 0.379 m
(3) 0.569 m
(4) 0.758 m

3. English : 3 Set : 06 Hindi : 3 Set : 06
5. A spring of unstretched length l has a
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
velocity v is :
(1)
21
m
2
v
(2) mv2
(3)
21
m
3
v
(4)
21
m
6
v
6. A particle is moving in a circular path of
radius a, with a constant velocity v as
shown in the figure. The center of circle is
marked by ‘C’. The angular momentum
from the origin O can be written as :
(1) va(11cos 2u)
(2) va(11cos u)
(3) va cos 2u
(4) va
5. 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 SßÌ‹˜æ çâÚUæ °·¤â×æÙ ßð» v âð ¹è´¿æ Áæ° Ñ
(1)
21
m
2
v
(2) mv2
(3)
21
m
3
v
(4)
21
m
6
v
6. °·¤ ·¤‡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 çÕ‹Îé
O âð ·¤æð‡æèØ â´ßð» §â Âý·¤æÚU çܹæ Áæ â·¤Ìæ ãñ Ñ
(1) va(11cos 2u)
(2) va(11cos u)
(3) va cos 2u
(4) va

4. English : 4 Set : 06 Hindi : 4 Set : 06
7.
Two hypothetical planets of masses m1 and
m2 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) v15v2
(2) 1 2
1 2
2G
m
d(m m )
v 5
1
2 1
1 2
2G
m
d(m m )
v 5
1
(3) 1 1
1 2
2G
m
d(m m )
v 5
1
2 2
1 2
2G
m
d(m m )
v 5
1
(4) 1 2
1
2G
m
m
v 5
2 1
2
2G
m
m
v 5
7.
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) v15v2
(2) 1 2
1 2
2G
m
d(m m )
v 5
1
2 1
1 2
2G
m
d(m m )
v 5
1
(3) 1 1
1 2
2G
m
d(m m )
v 5
1
2 2
1 2
2G
m
d(m m )
v 5
1
(4) 1 2
1
2G
m
m
v 5
2 1
2
2G
m
m
v 5

5. English : 5 Set : 06 Hindi : 5 Set : 06
8. Steel ruptures when a shear of
3.53108 N m22 is applied. The force
needed to punch a 1 cm diameter hole in
a steel sheet 0.3 cm thick is nearly :
(1) 1.43104 N
(2) 2.73104 N
(3) 3.33104 N
(4) 1.13104 N
9. A cylindrical vessel of cross-section A
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
2A h
gap
(2) 2
2A h
gap
(3) 2
2 2A h
gap
(4) 2
A h
g2 ap
8. 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) 2.73104 N
(3) 3.33104 N
(4) 1.13104 N
9. ¥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
(1) 2
2A h
gap
(2) 2
2A h
gap
(3) 2
2 2A h
gap
(4) 2
A h
g2 ap

6. English : 6 Set : 06 Hindi : 6 Set : 06
10. Two soap bubbles coalesce to form a single
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
of the following relation is correct ?
(1) 4PV13ST50
(2) 3PV14ST50
(3) 2PV13ST50
(4) 3PV12ST50
11. Hot water cools from 608C to 508C in the
first 10 minutes and to 428C in the next
10 minutes. The temperature of the
surroundings is :
(1) 258C
(2) 108C
(3) 158C
(4) 208C
12. A Carnot engine absorbs 1000 J of heat
energy from a reservoir at 1278C and rejects
600 J of heat energy during each cycle. The
efficiency of engine and temperature of
sink will be :
(1) 20% and 2438C
(2) 40% and 2338C
(3) 50% and 2208C
(4) 70% and 2108C
10. 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?
(1) 4PV13ST50
(2) 3PV14ST50
(3) 2PV13ST50
(4) 3PV12ST50
11. »×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
(1) 258C
(2) 108C
(3) 158C
(4) 208C
12. °·¤ ·¤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
(1) 20% °ß´ 2438C
(2) 40% °ß´ 2338C
(3) 50% °ß´ 2208C
(4) 70% °ß´ 2108C

7. English : 7 Set : 06 Hindi : 7 Set : 06
13. At room temperature a diatomic gas is
found to have an r.m.s. speed of
1930 ms21. The gas is :
(1) H2
(2) Cl2
(3) O2
(4) F2
14. Which of the following expressions
corresponds to simple harmonic motion
along a straight line, where x is the
displacement and a, b, c are positive
constants ?
(1) a1bx2cx2
(2) bx2
(3) a2bx1cx2
(4) 2bx
15. A source of sound A emitting waves of
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,
reflected from ground, of frequency
nearly : (Speed of sound 5343 m/s)
(1) 2150 Hz
(2) 2500 Hz
(3) 1800 Hz
(4) 2400 Hz
13. ·¤×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
(2) Cl2
(3) O2
(4) F2
14. 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 ?
(1) a1bx2cx2
(2) bx2
(3) a2bx1cx2
(4) 2bx
15. ¥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)
(1) 2150 Hz
(2) 2500 Hz
(3) 1800 Hz
(4) 2400 Hz

8. English : 8 Set : 06 Hindi : 8 Set : 06
16. A spherically symmetric charge
distribution is characterised by a charge
density having the following variation :
r(r)5ro
r
1
R
 
 
 
2 for r < R
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 :
(1)
2
o
o
r r
4 3 4R
 
 
 
r
2
e
(2)
2
o
o
r r
3 4R
 
 
 
r
2
e
(3)
2
o
o
r r
3 3 4R
 
 
 
r
2
e
(4)
2
o
o
r r
12 3 4R
 
 
 
r
2
e
16. °·¤ »æðÜèØ â×ç×Ìè ¥æßðàæ çßÌÚU‡æ ¥æßðàæ ƒæÙˆß
·¤æ çِÙçÜç¹Ì çß¿ÚU‡æ ÚU¹Ìæ ãñ Ñ
r(r)5ro
r
1
R
 
 
 
2 r < R ·ð¤ çÜ°
r(r)50 r / R ·ð¤ çÜ°
Áãæ¡ r ¥æßðàæ çßÌÚU‡æ ·ð¤ ·ð¤‹Îý âð ÎêÚUè ãñ´ ¥æñÚU ro °·¤
çSÍÚUæ´·¤ ãñÐ °·¤ ¥‹ÌÑ çÕ‹Îé (r < R) ÂÚU çßléÌ ÿæð˜æ
ãñ Ñ
(1)
2
o
o
r r
4 3 4R
 
 
 
r
2
e
(2)
2
o
o
r r
3 4R
 
 
 
r
2
e
(3)
2
o
o
r r
3 3 4R
 
 
 
r
2
e
(4)
2
o
o
r r
12 3 4R
 
 
 
r
2
e

9. English : 9 Set : 06 Hindi : 9 Set : 06
17. The space between the plates of a parallel
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 :
(1) o
o
d
C C
(1 K d)ln
l
5
1 l
(2) o
o
C C
d. (1 K d)ln
l
5
1 l
(3) o
o
d
C C
(1 d/K )ln
l
5
1 l
(4) o
o
C C
d. (1 K / d)ln
l
5
1 l
17. °·¤ 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) o
o
d
C C
(1 K d)ln
l
5
1 l
(2) o
o
C C
d. (1 K d)ln
l
5
1 l
(3) o
o
d
C C
(1 d/K )ln
l
5
1 l
(4) o
o
C C
d. (1 K / d)ln
l
5
1 l

10. English : 10 Set : 06 Hindi : 10 Set : 06
18. The circuit shown here has two batteries
of 8.0 V and 16.0 V and three resistors
3 V, 9 V and 9 V and a capacitor 5.0 mF.
How much is the current I in the circuit in
steady state ?
(1) 1.6 A
(2) 0.67 A
(3) 2.5 A
(4) 0.25 A
19. A positive charge ‘q’ of mass ‘m’ is moving
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 :
(1)
m d
DQG W
qd
v
v
p
5 D 5
(2)
m d
DQG W
2 qd 2
v
v
p
5 D 5
(3)
2 m d
DQG W
qd 2
v
v
p
5 D 5
(4)
2 m d
DQG W
qd
v
v
p
5 D 5
18. 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
SÍæØè ¥ßSÍæ ×ð´ ÂçÚUÂÍ ×ð´ ÏæÚUæ I ·¤æ ×æÙ €Øæ ãñ?
(1) 1.6 A
(2) 0.67 A
(3) 2.5 A
(4) 0.25 A
19. 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)
m d
W
qd
v
v
p
5 D 5•Ä™
(2)
m d
W
2 qd 2
v
v
p
5 D 5•Ä™
(3)
2 m d
W
qd 2
v
v
p
5 D 5•Ä™
(4)
2 m d
W
qd
v
v
p
5 D 5•Ä™

11. English : 11 Set : 06 Hindi : 11 Set : 06
20. Consider two thin identical conducting
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 B2 at the
centre of the loops when current I/3 passes
through it. The ratio B1 : B2 is :
(1) 1 : 1
(2) 1 : 3
(3) 1 : 9
(4) 9 : 1
21. A sinusoidal voltage V(t)5100 sin (500t)
is applied across a pure inductance of
L50.02 H. The current through the coil
is :
(1) 10 cos (500t)
(2) 210 cos (500t)
(3) 10 sin (500t)
(4) 210 sin (500t)
20. 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
(2) 1 : 3
(3) 1 : 9
(4) 9 : 1
21. °·¤ ’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
(1) 10 cos (500t)
(2) 210 cos (500t)
(3) 10 sin (500t)
(4) 210 sin (500t)

12. English : 12 Set : 06 Hindi : 12 Set : 06
22. A lamp emits monochromatic green light
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
electromagnetic radiation at a distance of
5 m from the lamp will be nearly :
(1) 1.34 V/m
(2) 2.68 V/m
(3) 4.02 V/m
(4) 5.36 V/m
22. °·¤ 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
(1) 1.34 V/m
(2) 2.68 V/m
(3) 4.02 V/m
(4) 5.36 V/m

13. English : 13 Set : 06 Hindi : 13 Set : 06
23. The refractive index of the material of a
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 :
(1)
(2)
(3)
(4)
23. °·¤ ¥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)
(2)
(3)
(4)

14. English : 14 Set : 06 Hindi : 14 Set : 06
24. Interference pattern is observed at ‘P’ due
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 :
(R is perfect reflecting surface) :
(1)
2 n
3 1
l
l
5
2
(2)
(2n 1)
2 ( 3 1)
l
2 l
5
2
(3)
(2n 1) 3
4 ( 2 3)
l
2 l
5
2
(4)
(2n 1)
3 1
l
2 l
5
2
25. In an experiment of single slit diffraction
pattern, first minimum for red light
coincides with first maximum of some
other wavelength. If wavelength of red
light is 6600 Å , then wavelength of first
maximum will be :
(1) 3300 Å
(2) 4400 Å
(3) 5500 Å
(4) 6600 Å
24. °·¤ 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 )
(1)
2 n
3 1
l
l
5
2
(2)
(2n 1)
2 ( 3 1)
l
2 l
5
2
(3)
(2n 1) 3
4 ( 2 3)
l
2 l
5
2
(4)
(2n 1)
3 1
l
2 l
5
2
25. °·¤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
(1) 3300 Å
(2) 4400 Å
(3) 5500 Å
(4) 6600 Å

15. English : 15 Set : 06 Hindi : 15 Set : 06
26. A beam of light has two wavelengths
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 is
approximately :
(1) 631011
(2) 931011
(3) 1131011
(4) 1531011
27. A piece of bone of an animal from a ruin
is found to have 14C 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
14C is t1/255760 years)
(1) 1672 years
(2) 2391 years
(3) 3291 years
(4) 4453 years
26. 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
·¤æØüȤÜÙ ßæÜð °·¤ âæȤ ÏæÌé ·ð¤ ÂëcÆU ·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€ÅþUæòÙ
©ˆâçÁüÌ ·¤ÚUÌæ ãñÐ 2s ×ð´ ©ˆâçÁüÌ È¤æðÅUæð §Üð€ÅþUæòÙæð´
·¤è ⴁØæ ãñ ֻܻ Ñ
(1) 631011
(2) 931011
(3) 1131011
(4) 1531011
27. °·¤ 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)
(1) 1672 ßáü
(2) 2391 ßáü
(3) 3291 ßáü
(4) 4453 ßáü

16. English : 16 Set : 06 Hindi : 16 Set : 06
28. For LED’s to emit light in visible region of
electromagnetic light, it should have
energy band gap in the range of :
(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
29. For sky wave propagation, the radio
waves must have a frequency range in
between :
(1) 1 MHz to 2 MHz
(2) 5 MHz to 25 MHz
(3) 35 MHz to 40 MHz
(4) 45 MHz to 50 MHz
30. In the experiment of calibration of
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
wire. The corresponding reading of
voltmeter is 0.5 volt. The error in the
reading of voltmeter will be :
(1) 20.15 volt
(2) 0.15 volt
(3) 0.5 volt
(4) 20.05 volt
28. LED’s 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
29. ¥æ·¤æàæ ÌÚ´U» â´¿ÚU‡æ ·ð¤ çÜ°, ÚðUçÇUØæð ÌÚ´U»ð´ §â ¥æßëçžæ
ÚðU‹Á ·ð¤ Õè¿ ãæðÙè ¿æçã° Ñ
(1) 1 MHz âð 2 MHz
(2) 5 MHz âð 25 MHz
(3) 35 MHz âð 40 MHz
(4) 45 MHz âð 50 MHz
30. °·¤ 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 ×ð´ ˜æéçÅU ãæð»è Ñ
(1) 20.15 ßæðËÅU
(2) 0.15 ßæðËÅU
(3) 0.5 ßæðËÅU
(4) 20.05 ßæðËÅU

17. English : 17 Set : 06 Hindi : 17 Set : 06
PART B — CHEMISTRY
31. If m and e are the mass and charge of the
revolving electron in the orbit of radius r
for hydrogen atom, the total energy of the
revolving electron will be :
(1)
2
1 e
2 r
(2)
2
e
r
2
(3)
2
me
r
(4)
2
1 e
2 r
2
32. The de-Broglie wavelength of a particle of
mass 6.63 g moving with a velocity of
100 ms21 is :
(1) 10233 m
(2) 10235 m
(3) 10231 m
(4) 10225 m
33. What happens when an inert gas is added
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
Öæ» B — ÚUâæØÙ çß™ææÙ
31. 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
(1)
2
1 e
2 r
(2)
2
e
r
2
(3)
2
me
r
(4)
2
1 e
2 r
2
32. 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
(2) 10235 m
(3) 10231 m
(4) 10225 m
33. 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

18. English : 18 Set : 06 Hindi : 18 Set : 06
34. The amount of BaSO4 formed upon mixing
100 mL of 20.8% BaCl2 solution with
50 mL of 9.8% H2SO4 solution will be :
(Ba5137, Cl535.5, S532, H51 and
O516)
(1) 23.3 g
(2) 11.65 g
(3) 30.6 g
(4) 33.2 g
35. The rate coefficient (k) for a particular
reactions is 1.331024 M21 s21 at 1008C,
and 1.331023 M21 s21 at 1508C. What
is the energy of activation (EA) (in kJ) for
this reaction ? (R5molar gas
constant58.314 JK21 mol21)
(1) 16
(2) 60
(3) 99
(4) 132
34. ÁÕ Ba5137, Cl535.5, S532, H51 ¥æñÚU
O516 ×æÙæ ÁæØð Ìæð 20.8% BaCl2 çßÜØÙ ·ð¤
100 mL ·¤æð 9.8%, H2SO4 ·ð¤ çßÜØÙ ·ð¤
50 mL ×ð´ ç×ÜæÙð ÂÚU ç·¤ÌÙæ BaSO4 ÕÙð»æ?
(1) 23.3 g
(2) 11.65 g
(3) 30.6 g
(4) 33.2 g
35. 1008C 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)
(1) 16
(2) 60
(3) 99
(4) 132

19. English : 19 Set : 06 Hindi : 19 Set : 06
36. How many electrons would be required to
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, NA5Avogadro’s
constant) :
(1)
AN
20
(2)
AN
10
(3)
AN
5
(4)
AN
2
37. The entropy (So) of the following
substances are :
CH4 (g) 186.2 J K21 mol21
O2 (g) 205.0 J K21 mol21
CO2 (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) 2242.8 J K21 mol21
(3) 2108.1 J K21 mol21
(4) 237.6 J K21 mol21
36. ·¤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)
AN
20
(2)
AN
10
(3)
AN
5
(4)
AN
2
37. çِ٠ÂÎæÍæðZ ·ð¤ °ð‹ÅþUæÂè ×æÙ ãñ (So) ãñ´ Ñ
CH4 (g) 186.2 J K21 ×æðÜ21
O2 (g) 205.0 J K21 ×æðÜ21
CO2 (g) 213.6 J K21 ×æðÜ21
H2O (l) 69.9 J K21 ×æðÜ21
¥çÖç·ý¤Øæ
CH4(g)12O2(g) ® CO2(g)12H2O(l)
·ð¤ çÜØð °ð‹ÅþUæÂè ÂçÚUßÌüÙ (DSo) ·¤æ ×æÙ ãæð»æ Ñ
(1) 2312.5 J K21 ×æðÜ21
(2) 2242.8 J K21 ×æðÜ21
(3) 2108.1 J K21 ×æðÜ21
(4) 237.6 J K21 ×æðÜ21

20. English : 20 Set : 06 Hindi : 20 Set : 06
38. The conjugate base of hydrazoic acid is :
(1) N23
(2) 3N2
(3) 2N2
(4) 3HN2
39. In a monoclinic unit cell, the relation of
sides and angles are respectively :
(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
40. The standard enthalpy of formation
(DfHo
298) for methane, CH4 is
274.9 kJ mol21. In order to calculate the
average energy given out in the formation
of a C2H bond from this it is necessary to
know which one of the following ?
(1) the dissociation energy of the
hydrogen molecule, H2.
(2) the first four ionisation energies of
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
hydrogen.
38. ãæ§ÇþUæð$Áæ𧷤 °ðçâÇU ·¤æ â´Øé‚×è ÿææÚU ãñ Ñ
(1) N23
(2) 3N2
(3) 2N2
(4) 3HN2
39. °·¤ ×æðÙæðç€ÜçÙ·¤ °·¤·¤ âñÜ ×ð´ Âÿææ𴠷𤠷¤æðÙæ çÕ‹Îé¥æð´
âð âÕ‹Ï ·ý¤×æÙéâæÚU ãæðÌð ã´ñ Ñ
(1) a5b ¹ c ¥æñÚU a5b5g5908
(2) a ¹ b ¹ c ¥æñÚU a5b5g5908
(3) a ¹ b ¹ c ¥æñÚU b5g5908 ¹ a
(4) a ¹ b ¹ c ¥æñÚU a ¹ b ¹ g ¹ 908
40. ×èÍðÙ, CH4, ÕÙÙð ·¤è ×æÙ·¤ °ð‹ÍñËÂè (DfHo
298)
274.9 kJ ×æðÜ21 ãæðÌè ãñÐ §ââð C2H ¥æÕ‹Ï
·¤è ׊Ø×æÙ ª¤Áæü ·¤æ ¥æ·¤ÜÙ ·¤ÚUÙð ·ð¤ çÜØð çِÙæð´
âð 緤⠰·¤ ·¤æð ÁæÙÙæ ¥æßàØ·¤ ãæð»æ?
(1) H2 ¥‡æé ·¤è çßØæðÁÙ ª¤ÁæüÐ
(2) ·¤æÕüÙ ·¤è ÂãÜè ¿æÚU ¥æØÙÙ ª¤Áæü°¡Ð
(3) H2 ·¤è çßØæðÁÙ ª¤Áæü ¥æñÚU ·¤æÕüÙ (»ýð$Ȥæ§Å)U
·¤è ª¤ŠßüÂæÌÙ ª¤ÁæüÐ
(4) ·¤æÕüÙ ·¤è ÂýÍ× ¿æÚU ¥æØÙÙ ª¤Áæü°¡ ¥æñÚ
ãæ§ÇþUæðÁÙ ·¤è §Üñ€ÅþUæòÙ Õ‹ÏéÌæÐ

21. English : 21 Set : 06 Hindi : 21 Set : 06
41. Which of the following xenon-OXO
compounds may not be obtained by
hydrolysis of xenon fluorides ?
(1) Xe O2F2
(2) Xe O F4
(3) Xe O3
(4) Xe O4
42. Excited hydrogen atom emits light in the
ultraviolet region at 2.4731015 Hz. With
this frequency, the energy of a single
photon is :
(h56.63310234 Js)
(1) 8.041310240 J
(2) 2.680310219 J
(3) 1.640310218 J
(4) 6.111310217 J
43. Which one of the following exhibits the
largest number of oxidation states ?
(1) Ti (22)
(2) V(23)
(3) Cr (24)
(4) Mn (25)
41. $ÁèÙæÙ ÜæðÚUæ§ÇUæð´ ·ð¤ ÁÜèØ ¥ÂƒæÅUÙ âð çِ٠$ÁèÙæÙ-
¥æ€âæð-Øæñç»·¤æð´ ×ð´ âð 緤ⷤæð Âý挈æ Ùãè´ ç·¤Øæ Áæ
â·¤Ìæ ãñ?
(1) Xe O2F2
(2) Xe O F4
(3) Xe O3
(4) Xe O4
42. 2.4731015 Hz 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
(h56.63310234 Js)
(1) 8.041310240 J
(2) 2.680310219 J
(3) 1.640310218 J
(4) 6.111310217 J
43. çِÙæð´ ×ð´ âð ·¤æñÙ °·¤ ¥çÏ·¤Ì× â´Øæ ×ð´ ¥æò€âè·¤ÚU‡æ
¥ßSÍæ°¡ çιæÌæ ãñ?
(1) Ti (22)
(2) V(23)
(3) Cr (24)
(4) Mn (25)

22. English : 22 Set : 06 Hindi : 22 Set : 06
44. Copper becomes green when exposed to
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
of copper.
(3) the formation of a layer of cupric
hydroxide on the surface of copper.
(4) the formation of basic copper
sulphate layer on the surface of the
metal.
45. Among the following species the one
which causes the highest CFSE, Do as a
ligand is :
(1) CN2
(2) NH3
(3) F2
(4) CO
46. Similarity in chemical properties of the
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
44. 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
(3) ·¤æÂÚU ÌÜ ÂÚU €ØêçÂý·¤ ãæ§ÇþU¥æò€âæ§ÇU ·¤æ ÂÚUÌ
ÕÙÙæÐ
(4) ÏæÌé ÌÜ ÂÚU ÿææÚUèØ ·¤æÂÚU âË$Èð¤ÅU ·¤æ ÂÚUÌ
ÕÙÙæÐ
45. çِ٠ÂÎæÍæðZ ×ð´ âð ·¤æñÙ °·¤ çÜ»ñ‹ÇU M¤Â ×ð´ ¥çÏ·¤Ì×
CFSE, Do ·¤æ ·¤æÚU‡æ ÕÙÌæ ãñ?
(1) CN2
(2) NH3
(3) F2
(4) CO
46. ¥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

23. English : 23 Set : 06 Hindi : 23 Set : 06
47. çِ٠ÃØßSÍæ¥æð´ ×ð´ âð ·¤æñÙ çÎØð »Øð ÂÎæÍæðZ
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
(2) O22< P32< N32 < S22
(3) N32 < O22< P32 < S22
(4) N32< S22< O22 < P32
48. â´âæçÚU·¤ ©žææÂÙ ·¤æ ·¤æÚU‡æ ãæðÌæ ãñ ßæØéׇÇUÜ ×ð´
ÕɸÙæ Ñ
(1) ×èÍðÙ ¥æñÚU Ùæ§ÅþUâ ¥æò€âæ§ÇU ·¤æÐ
(2) ×èÍðÙ ¥æñÚU CO2 ·¤æÐ
(3) ×èÍðÙ ¥æñÚU O3 ·¤æÐ
(4) ×èÍðÙ ¥æñÚU CO ·¤æÐ
49. 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
×ð´ âð ç·¤â·ð¤ âæÍ H2O2 ¥ÜèØ ×æŠØ× ×𴠥¿æØ·¤
·ð¤ M¤Â ×ð´ ç·ý¤Øæ ·¤ÚUÌæ ãñ?
(1) MnO4
2
(2)
2
2 7
Cr O
2
(3)
2
3
SO
2
(4) KI
47. Which of the following arrangements
represents the increasing order (smallest
to largest) of ionic radii of the given species
O22, S22, N32, P32 ?
(1) O22< N32< S22 < P32
(2) O22< P32< N32 < S22
(3) N32 < O22< P32 < S22
(4) N32< S22< O22 < P32
48. Global warming is due to increase of :
(1) methane and nitrous oxide in
atmosphere
(2) methane and CO2 in atmosphere
(3) methane and O3 in atmosphere
(4) methane and CO in atmosphere
49. Hydrogen peroxide acts both as an
oxidising and as a reducing agent
depending upon the nature of the reacting
species. In which of the following cases
H2O2 acts as a reducing agent in acid
medium ?
(1) MnO4
2
(2)
2
2 7
Cr O
2
(3)
2
3
SO
2
(4) KI

24. English : 24 Set : 06 Hindi : 24 Set : 06
50. Which one of the following complexes will
most likely absorb visible light ?
(At nos. Sc521, Ti522, V523, Zn530)
(1) [Sc(H2O)6]31
(2) [Ti (NH3)6]41
(3) [V(NH3)6]31
(4) [Zn(NH3)6]21
51. on mercuration-
demercuration produces the major
product :
(1)
(2)
(3)
(4)
52. In the Victor-Meyer’s test, the colour given
by 18, 28 and 38 alcohols are respectively :
(1) Red, colourless, blue
(2) Red, blue, colourless
(3) Colourless, red, blue
(4) Red, blue, violet
50. 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,
Zn530)
(1) [Sc(H2O)6]31
(2) [Ti (NH3)6]41
(3) [V(NH3)6]31
(4) [Zn(NH3)6]21
51. ×ÚU€ØêÚðUàæÙ-¥×ÚU€ØêÚðUàæÙ ÂÚ
Uâð Âý挈æ ×éØ ç·ý¤ØæȤÜ
ãæðÌæ ãñ Ñ
(1)
(2)
(3)
(4)
52. ç߀ÅUÚU ×ðØÚU ·ð¤ ÂÚUèÿæ‡æ ç·ý¤Øæ ×ð´ 18, 28 ¥æñÚU 38 ·ð¤
°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

25. English : 25 Set : 06 Hindi : 25 Set : 06
53. Conversion of benzene diazonium chloride
to chloro benzene is an example of which
of the following reactions ?
(1) Claisen
(2) Friedel-craft
(3) Sandmeyer
(4) Wurtz
54. In the presence of peroxide, HCl and HI
do not give anti-Markownikoff’s addition
to alkenes because :
(1) One of the steps is endothermic in
HCl and HI
(2) Both HCl and HI are strong acids
(3) HCl is oxidizing and the HI is
reducing
(4) All the steps are exothermic in HCl
and HI
55. The major product obtained in the photo
catalysed bromination of 2-methylbutane
is :
(1) 1-bromo-2-methylbutane
(2) 1-bromo-3-methylbutane
(3) 2-bromo-3-methylbutane
(4) 2-bromo-2-methylbutane
53. 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÷üUU$Á
54. ÂÚU¥æò€âæ§ÇU ·¤è ©ÂçSÍçÌ ×ð´ °ðË·¤èÙæð´ ·¤æð HCl ¥æñÚU
HI °ð‹ÅUè×æÚU·¤æðÙè·¤æȤ Øæð» Ùãè´ ÎðÌð €Øæð´ ç·¤ Ñ
(1) HCl ¥æñÚU HI ·ð¤ âÕ‹Ï ×ð´ °·¤ ¿ÚU‡æ
ª¤c×æàææðáè ãñÐ
(2) HCl ¥æñÚU HI ÎæðÙæð´, ÂýÕÜ ¥Ü ãñ´Ð
(3) HCl ©Â¿æØ·¤ ¥æñÚU HI ¥Â¿æØ·¤ ãñÐ
(4) HCl ¥æñÚU HI ·ð¤ âÕ‹Ïæð´ ×ð´ âÖè ¿ÚU‡æ
ª¤c×æÂýÎ ãñ´Ð
55. 2- ×ðçÍÜŽØéÅðUÙ ·ð¤ Âý·¤æàæ mæÚUæ ©ˆÂýðçÚUÌ Õýæð×èÙðàæÙ ×ð´
ÕǸæ ç·ý¤ØæÈ¤Ü ãæðÌæ ãñ Ñ
(1) 1-Õýæð×æð-2-×ðçÍÜŽØéÅðUÙ
(2) 1-Õýæð×æð-3-×ðçÍÜŽØéÅðUÙ
(3) 2-Õýæð×æð-3-×ðçÍËæŽØéÅðUÙ
(4) 2-Õýæð×æð-2-×ðçÍÜŽØéÅðUÙ

26. English : 26 Set : 06 Hindi : 26 Set : 06
56. Which of the following molecules has two
sigma(s) and two pi(p) bonds ?
(1) C2H4
(2) N2F2
(3) C2H2Cl2
(4) HCN
57. Which one of the following acids does not
exhibit optical isomerism ?
(1) Lactic acid
(2) Tartaric acid
(3) Maleic acid
(4) a-amino acids
58. Aminoglycosides are usually used as :
(1) antibiotic
(2) analgesic
(3) hypnotic
(4) antifertility
59. Which of the following will not show
mutarotation ?
(1) Maltose
(2) Lactose
(3) Glucose
(4) Sucrose
56. çِ٠¥‡æé¥æð´ ×ð´ âð 緤⠥‡æé ×ð´ Îæð çâ‚×æ (s) ¥æñÚU Îæð
Âæ§ü (p) ¥æÕ‹Ï ãæðÌð ãñ´?
(1) C2H4
(2) N2F2
(3) C2H2Cl2
(4) HCN
57. 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
58. ¥×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¿·¤)
59. §Ù×ð´ âð ·¤æñÙ ØêÅUæÚUæðÅðUàæÙ Ùãè´ çιæØð»æ?
(1) ×æËÅUæð$Á
(2) Üñ€ÅUæð$Á
(3) ‚Üê·¤æð$Á
(4) âê·ý¤æð$Á

27. English : 27 Set : 06 Hindi : 27 Set : 06
60. Phthalic acid reacts with resorcinol in the
presence of concentrated H2SO4 to give :
(1) Phenolphthalein
(2) Alizarin
(3) Coumarin
(4) Fluorescein
60. âæ‹Îý H2SO4 ·¤è ©ÂçSÍçÌ ×ð´ ÍñçÜ·¤ °ðçâÇU
çÚU$ÁæÚUâèÙæÜ âð ¥çÖç·ý¤Øæ ·¤ÚU ÎðÌæ ãñ Ñ
(1) çȤÙæËȤÍðÜèÙ
(2) °ðçÜ$ÁðÚUèÙ
(3) ·é¤×ýèÙ
(4) $$ÜæðÚðUâèÙ

28. English : 28 Set : 06 Hindi : 28 Set : 06
PART C — MATHEMATICS
61. A relation on the set A5{x : ?x? < 3, xeZ},
where Z is the set of integers is defined by
R5{(x, y) : y5?x?, 1x ≠2 }. Then the
number of elements in the power set of R
is :
(1) 32
(2) 16
(3) 8
(4) 64
62. Let z ¹ 2i be any complex number such
that
z i
z i
2
1
is a purely imaginary number.
Then z1
1
z
is :
(1) 0
(2) any non-zero real number other
than 1.
(3) any non-zero real number.
(4) a purely imaginary number.
63. The sum of the roots of the equation,
x21?2x23?2450, is :
(1) 2
(2) 22
(3) 2
(4) 22
Öæ» C — »ç‡æÌ
61. 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?, 1x ≠2 } mæÚUæ ÂçÚUÖæçáÌ ãñÐ
Ìæð R ·ð¤ ƒææÌ â×é“æØ ×ð´ ¥ßØßæð´ ·¤è ⴁØæ ãñ Ñ
(1) 32
(2) 16
(3) 8
(4) 64
62. ×æÙæ z ¹ 2i ·¤æð§ü °ðâè âç×Ÿæ ⴁØæ ãñ ç·¤
z i
z i
2
1
°·¤ àæéh ·¤æËÂçÙ·¤ ⴁØæ ãñ, Ìæð
z1
1
z
ãñ Ñ
(1) 0
(2) 1 ·ð¤ ¥çÌçÚU€ˆæ ·¤æð§ü àæê‹ØðžæÚU ßæSÌçß·¤ ⴁØæÐ
(3) ·¤æð§ü àæê‹ØðžæÚU ßæSÌçß·¤ ⴁØæÐ
(4) °·¤ àæéh ·¤æËÂçÙ·¤ ⴁØæÐ
63. â×è·¤ÚU‡æ x21?2x23?2450, ·ð¤ ×êÜæð´ ·¤æ
Øæð»È¤Ü ãñ Ñ
(1) 2
(2) 22
(3) 2
(4) 22

29. English : 29 Set : 06 Hindi : 29 Set : 06
64. If
( ) ( ) ( )
( ) ( ) ( )
2 2 2 2 2 2
22 2
22 2
a b c a b c
a b c k a b c , 0,
1 1 1a b c
≠1l 1l 1l 5 l l
2l 2l 2l
then k is equal to :
(1) 4labc
(2) 24labc
(3) 4l2
(4) 24l2
65. If
1 2
A
3 1 2
x 
 
 
5
2
and B
1
y
x
 
 
 
  
5 be such
that
6
AB
8
 
 
 
5 , then :
(1) y52x
(2) y522x
(3) y5x
(4) y52x
66. 8 - digit numbers are formed using the
digits 1, 1, 2, 2, 2, 3, 4, 4. The number of
such numbers in which the odd digits do
not occupy odd places, is :
(1) 160
(2) 120
(3) 60
(4) 48
64. ØçÎ
( ) ( ) ( )
( ) ( ) ( )
2 2 2 2 2 2
22 2
22 2
a b c a b c
a b c k a b c , 0,
1 1 1a b c
≠1l 1l 1l 5 l l
2l 2l 2l
ãñ, Ìæð k ÕÚUæÕÚU ãñ Ñ
(1) 4labc
(2) 24labc
(3) 4l2
(4) 24l2
65. ØçÎ
1 2
A
3 1 2
x 
 
 
5
2
ÌÍæ B
1
y
x
 
 
 
  
5 °ðâð ãñ´ ç·¤
6
AB
8
 
 
 
5 , ãñ, Ìæð Ñ
(1) y52x
(2) y522x
(3) y5x
(4) y52x
66. ¥´·¤æð´ 1, 1, 2, 2, 2, 3, 4, 4 ·ð¤ ÂýØæð» âð, ¥æÆU ¥´·¤èØ
ⴁØæ°¡ ÕÙæ§ü »§ü ãñ´Ð °ðâè ⴁØæ¥æð´ ·¤è ⴁØæ çÁÙ×ð´
çßá× ¥´·¤ çßá× SÍæÙæð´ ÂÚU Ù ¥æØð´, ãñ Ñ
(1) 160
(2) 120
(3) 60
(4) 48

30. English : 30 Set : 06 Hindi : 30 Set : 06
67. If
55
2
3
x 
 
 
1 is expanded in the ascending
powers of x and the coefficients of powers
of x in two consecutive terms of the
expansion are equal, then these terms
are :
(1) 7th and 8th
(2) 8th and 9th
(3) 28th and 29th
(4) 27th and 28th
68. Let G be the geometric mean of two
positive numbers a and b, and M be the
arithmetic mean of 1
a
and
1
b
. If
1
: G
M
is
4 : 5, then a : b can be :
(1) 1 : 4
(2) 1 : 2
(3) 2 : 3
(4) 3 : 4
69. The least positive integer n such that
2 n 1
2 2 2 1
1
3 1003 3
........ ,<2
2 2 2 2 is :
(1) 4
(2) 5
(3) 6
(4) 7
67. ØçÎ
55
2
3
x 
 
 
1 ·¤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
(1) 7 ßæ¡ ÌÍæ 8 ßæ¡
(2) 8 ßæ¡ ÌÍæ 9 ßæ¡
(3) 28 ßæ¡ ÌÍæ 29 ßæ¡
(4) 27 ßæ¡ ÌÍæ 28 ßæ¡
68. ×æÙæ Îæð Ï٠ⴁØæ¥æð´ a ÌÍæ b ·¤æ »é‡ææðžæÚU ×æŠØ G ãñ
ÌÍæ 1
a
ÌÍæ 1
b
·¤æ â×æ‹ÌÚU ×æŠØ M ãñÐ ØçÎ
1
: G
M
5 4 : 5 ãñ, Ìæð a : b ãæð â·¤Ìð ãñ´ Ñ
(1) 1 : 4
(2) 1 : 2
(3) 2 : 3
(4) 3 : 4
69. ÏÙ Âê‡ææZ·¤ n ·¤æ ßã ‹ØêÙÌ× ×æÙ çÁâ·ð¤ çÜØð
2 n 1
2 2 2 1
1
3 1003 3
........ ,<2
2 2 2 2 ãñ, ãñ Ñ
(1) 4
(2) 5
(3) 6
(4) 7

31. English : 31 Set : 06 Hindi : 31 Set : 06
70. Let f, g : R®R be two functions defined by
f (x)
1
sin 0
, and ( ) ( )
0 , 0
x , x
g x x f xx
x
  
≠   


5 5
5
Statement I : f is a continuous function at
x50.
Statement II : g is a differentiable function
at x50.
(1) Both statements I and II are false.
(2) Both statements I and II are true.
(3) Statement I is true, statement II is
false.
(4) Statement I is false, statement II is
true.
71. If f(x)5x22x15,
1
>
2
x , and g(x) is its
inverse function, then g9(7) equals :
(1)
1
3
2
(2)
1
13
(3)
1
3
(4)
1
13
2
70. ×æÙæ f, g : R®R Îæð ȤÜÙ ãñ´ Áæð
f (x)
1
sin 0
, ( ) ( )
0 , 0
x , x
g x x f xx
x
  
≠   


5 5
5
±²Ë
mæÚUæ ÂçÚUÖæçáÌ ãñ´ Ñ
·¤ÍÙ I : x50 ÂÚU f °·¤ âÌÌ È¤ÜÙ ãñÐ
·¤ÍÙ II : x50 ÂÚU g °·¤ ¥ß·¤ÜèØ È¤ÜÙ ãñÐ
(1) ·¤ÍÙ I ÌÍæ II ÎæðÙæð´ ¥âˆØ ãñ´Ð
(2) ·¤ÍÙ I ÌÍæ II ÎæðÙæð´ âˆØ ãñ´Ð
(3) ·¤ÍÙ I âˆØ ãñ, ·¤ÍÙ II ¥âˆØ ãñÐ
(4) ·¤ÍÙ I ¥âˆØ ãñ, ·¤ÍÙ II âˆØ ãñÐ
71. ØçÎ f(x)5x22x15,
1
>
2
x ,ÌÍæ g(x) §â·¤æ
ÃØ鈷ý¤× ȤÜÙ ãñ, Ìæð g9(7) ÕÚUæÕÚU ãñ Ñ
(1)
1
3
2
(2)
1
13
(3)
1
3
(4)
1
13
2

32. English : 32 Set : 06 Hindi : 32 Set : 06
72. Let f and g be two differentiable functions
on R such that f 9(x) > 0 and g9(x) < 0, for
all x e R. Then for all x :
(1) f(g(x)) > f (g(x21))
(2) f(g(x)) > f (g(x11))
(3) g(f(x)) > g (f(x21))
(4) g(f(x)) < g (f(x11))
73. If 11x41x55 ( )
5
i
i
i 0
a 1 x∑
5
1 , for all x in R,
then a2 is :
(1) 24
(2) 6
(3) 28
(4) 10
74. The integral
( )
2 2
23 3
sin cos
d
sin cos
x x
x
x x
∫
1
is
equal to :
(1) ( )3
1
c
1 cot x
1
1
(2) ( )3
1
c
3 1 tan x
2 1
1
(3)
( )
3
3
sin
c
1 cos
x
x
1
1
(4)
( )
3
3
cos
c
3 1 sin
x
x
2 1
1
72. ×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))
(2) f(g(x)) > f(g(x11))
(3) g(f(x)) > g(f(x21))
(4) g(f(x)) < g(f(x11))
73. ØçÎ âÖè x e R ·ð¤ çÜ°
11x41x55 ( )
5
i
i
i 0
a 1 x∑
5
1 ãñ, Ìæð a2 ãñ Ñ
(1) 24
(2) 6
(3) 28
(4) 10
74. â×æ·¤Ü
( )
2 2
23 3
sin cos
d
sin cos
x x
x
x x
∫
1
ÕÚUæÕÚU ãñ Ñ
(1) ( )3
1
c
1 cot x
1
1
(2) ( )3
1
c
3 1 tan x
2 1
1
(3)
( )
3
3
sin
c
1 cos
x
x
1
1
(4)
( )
3
3
cos
c
3 1 sin
x
x
2 1
1

33. English : 33 Set : 06 Hindi : 33 Set : 06
75. If [ ] denotes the greatest integer function,
then the integral [ ]
0
cos dx x∫
p
is equal to :
(1)
2
p
(2) 0
(3) 21
(4)
2
p
2
76. If for a continuous function f(x),
( )
t
2 2
( ) d t ,f x x x∫
2p
1 5 p 2 for all
t/2p, then
3
f
 
 
 
p
2 is equal to :
(1) p
(2)
2
p
(3)
3
p
(4)
6
p
75. ØçÎ [ ] °·¤ ×ãžæ× Âê‡ææZ·¤èØ È¤ÜÙ ãñ, Ìæð
â×æ·¤Ü [ ]
0
cos dx x∫
p
ÕÚUæÕÚU ãñ Ñ
(1)
2
p
(2) 0
(3) 21
(4)
2
p
2
76. ØçÎ °·¤ âÌÌ È¤ÜÙ f(x) ·ð¤ çÜ°, âÖè
t /2p ·ð¤ çÜ°
( )
t
2 2
( ) d tf x x x∫
2p
1 5 p 2 ãñ, Ìæð
3
f
 
 
 
p
2 ÕÚUæÕÚU ãñ Ñ
(1) p
(2)
2
p
(3)
3
p
(4)
6
p

34. English : 34 Set : 06 Hindi : 34 Set : 06
77. The general solution of the differential
equation, sin 2x
d
tan 0
d
y
x y
x
 
 
 
2 2 5 ,
is :
(1) y tan x 5x1c
(2) y cot x 5tan x1c
(3) y tan x 5cot x1c
(4) y cot x 5x1c
78. If a line intercepted between the coordinate
axes is trisected at a point A(4, 3), which
is nearer to x-axis, then its equation is :
(1) 4x23y57
(2) 3x12y518
(3) 3x18y536
(4) x13y513
79. If the three distinct lines x12ay1a50,
x13by1b50 and x14ay1a50 are
concurrent, then the point (a, b) lies on a :
(1) circle
(2) hyperbola
(3) straight line
(4) parabola
77. ¥ß·¤Ü â×è·¤ÚU‡æ
sin 2x
d
tan 0
d
y
x y
x
 
 
 
2 2 5 ·¤æ ÃØæ·¤
ãÜ ãñ Ñ
(1) y tan x 5x1c
(2) y cot x 5tan x1c
(3) y tan x 5cot x1c
(4) y cot x 5x1c
78. 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
(3) 3x18y536
(4) x13y513
79. ØçÎ ÌèÙ çßçÖóæ ÚðU¹æ°¡ 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

35. English : 35 Set : 06 Hindi : 35 Set : 06
80. For the two circles x21y2516 and
x21y222y50, there is/are :
(1) one pair of common tangents
(2) two pairs of common tangents
(3) three common tangents
(4) no common tangent
81. Two tangents are drawn from a point
(22, 21) to the curve, y254x. If a is the
angle between them, then ?tan a? is equal
to :
(1)
1
3
(2)
1
3
(3) 3
(4) 3
82. The minimum area of a triangle formed
by any tangent to the ellipse
22
1
16 81
yx
1 5 and the co-ordinate axes
is :
(1) 12
(2) 18
(3) 26
(4) 36
80. 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
81. °·¤ 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
(1)
1
3
(2)
1
3
(3) 3
(4) 3
82. Îèƒæüßëžæ
22
1
16 81
yx
1 5 ÂÚU ¹è´¿è »§ü ç·¤âè SÂàæü
ÚðU¹æ ÌÍæ çÙÎðüàææ´·¤ ¥ÿææð´ mæÚUæ ÕÙè ç˜æÖéÁ ·¤æ ‹ØêÙÌ×
ÿæð˜æÈ¤Ü ãñ Ñ
(1) 12
(2) 18
(3) 26
(4) 36

36. English : 36 Set : 06 Hindi : 36 Set : 06
83. A symmetrical form of the line of
intersection of the planes x5ay1b and
z5cy1d is :
(1)
1b d
a 1 c
yx z22 2
5 5
(2)
1b a d c
a 1 c
yx z22 2 2 2
5 5
(3)
0a c
b 1 d
yx z22 2
5 5
(4)
1b a d c
b 0 d
yx z22 2 2 2
5 5
84. If the distance between planes,
4x22y24z1150 and
4x22y24z1d50 is 7, then d is :
(1) 41 or 242
(2) 42 or 243
(3) 241 or 43
(4) 242 or 44
85. If x
∧
, y
∧
and z
∧
are three unit vectors in
three-dimensional space, then the
minimum value of
2 2 2
x y y z z x
∧ ∧ ∧ ∧ ∧ ∧
? 1 ? 1 ? 1 ? 1 ? 1 ? is :
(1)
3
2
(2) 3
(3) 3 3
(4) 6
83. â×ÌÜæð´ x5ay1b ÌÍæ z5cy1d ·¤è ÂýçÌ‘ÀðUÎè
ÚðU¹æ ·¤æ â×ç×Ì M¤Â ãñ Ñ
(1)
1b d
a 1 c
yx z22 2
5 5
(2)
1b a d c
a 1 c
yx z22 2 2 2
5 5
(3)
0a c
b 1 d
yx z22 2
5 5
(4)
1b a d c
b 0 d
yx z22 2 2 2
5 5
84. ØçÎ â×ÌÜæð´ 4x22y24z1150 ÌÍæ
4x22y24z1d50 ·ð¤ Õè¿ ·¤è ÎêÚUè 7, Ìæð d ãñ Ñ
(1) 41 ¥Íßæ 242
(2) 42 ¥Íßæ 243
(3) 241 ¥Íßæ 43
(4) 242 ¥Íßæ 44
85. ØçÎ ç˜æ-çß×èØ ¥æ·¤æàæ ×ð´ x
∧
, y
∧
ÌÍæ z
∧
ÌèÙ ×æ˜æ·¤
âçÎàæ ãñ´, Ìæð 2 2 2
x y y z z x
∧ ∧ ∧ ∧ ∧ ∧
? 1 ? 1 ? 1 ? 1 ? 1 ?
·¤æ ‹ØêÙÌ× ×æÙ ãñ Ñ
(1)
3
2
(2) 3
(3) 3 3
(4) 6

37. English : 37 Set : 06 Hindi : 37 Set : 06
86. Let X and M.D. be the mean and the mean
deviation about X of n observations
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 :
(1) X , M.D.
(2) X 15, M.D.
(3) X , M.D.15
(4) X 15, M.D.15
87. A number x is chosen at random from the
set {1, 2, 3, 4, ....., 100}. Define the
event : A5 the chosen number x satisfies
( 10) ( 50)
0
( 30)
x x
x
2 2
/
2
Then P(A) is :
(1) 0.71
(2) 0.70
(3) 0.51
(4) 0.20
86. ×æÙæ n Âýðÿæ‡ææð´ xi, i51, 2, ....., n ·¤æ ×æŠØ X ÌÍæ
X ·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
(1) X , M.D.
(2) X 15, M.D.
(3) X , M.D.15
(4) X 15, M.D.15
87. 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
( 10) ( 50)
0
( 30)
x x
x
2 2
/
2 ·¤æð â´ÌécÅ ·¤ÚUÌè ãñÐ
Ìæð P(A) ãñ Ñ
(1) 0.71
(2) 0.70
(3) 0.51
(4) 0.20

38. English : 38 Set : 06 Hindi : 38 Set : 06
88. Statement I : The equation
(sin21x)31(cos21x)32ap350 has a
solution for all a/ 1
32
.
Statement II : For any x e R,
sin21x1cos21x5
2
p
and
0 [
2
1
sin
4
x
 
 
 
2 p
2 [
2
9
16
p
.
(1) Both statements I and II are true.
(2) Both statements I and II are false.
(3) Statement I is true and
statement II is false.
(4) Statement I is false and
statement II is true.
89. If
1 cos 1
( ) sin 1 cos and
1 sin 1
f
u
u 5 2 u 2 u
2 u
A and B are respectively the maximum and
the minimum values of f (u), then
(A, B) is equal to :
(1) (3, 21)
(2) (4, 2 22 )
(3) ( )2 2 2 2,1 2
(4) ( )2 2 1,1 2
88. ·¤ÍÙ I : â×è·¤ÚU‡æ
(sin21x)31(cos21x)32ap350 ·¤æ âÖè
a/
1
32
·ð¤ çÜ° °·¤ ãÜ ãñÐ
·¤ÍÙ II : ç·¤âè x e R ·ð¤ çÜ°
sin21x1cos21x5
2
p
ÌÍæ
0 [
2
1
sin
4
x
 
 
 
2 p
2 [
2
9
16
p
.
(1) ·¤ÍÙ I ÌÍæ II ÎæðÙæð´ âˆØ ãñ´Ð
(2) ·¤ÍÙ I ÌÍæ II ÎæðÙæð´ ¥âˆØ ãñ´Ð
(3) ·¤ÍÙ I âˆØ ãñ ÌÍæ ·¤ÍÙ II ¥âˆØ ãñÐ
(4) ·¤ÍÙ I ¥SæˆØ ãñ, ÌÍæ ·¤ÍÙ II âˆØ ãñÐ
89. ØçÎ
1 cos 1
( ) sin 1 cos
1 sin 1
f
u
u 5 2 u 2 u
2 u
ãñ,
ÌÍæ A ÌÍæ B ·ý¤×àæÑ f (u) ·ð¤ ¥çÏ·¤Ì× ÌÍæ
‹ØêÙÌ× ×æÙ ãñ´, Ìæð (A, B) ÕÚUæÕÚU ãñ Ñ
(1) (3, 21)
(2) (4, 2 22 )
(3) ( )2 2 2 2,1 2
(4) ( )2 2 1,1 2

39. English : 39 Set : 06 Hindi : 39 Set : 06
90. Let p, q, r denote arbitrary statements. Then
the logically equivalent of the
statement p Þ (q Ú r) is :
(1) (p Ú q) Þ r
(2) (p Þ q) Ú (p Þ r)
(3) (p Þ ~q) Ù (p Þ r)
(4) (p Þ q) Ù (p Þ ~r)
- o 0 o -
90. ×æÙæ p, q, r Sßð‘ÀU ·¤ÍÙ ÎàææüÌð ãñ´Ð ·¤ÍÙ
p Þ (q Ú r) ·¤æ Ìæç·ü¤·¤ â×ÌéËØ ãñ Ñ
(1) (p Ú q) Þ r
(2) (p Þ q) Ú (p Þ r)
(3) (p Þ ~q) Ù (p Þ r)
(4) (p Þ q) Ù (p Þ ~r)
- o 0 o -