JEE Main 2014 Question Paper 12 Apr

PART A — PHYSICS Öæ» A — ÖæñçÌ·¤ çߙææÙ
1. From the following combinations of 1. ÖæñçÌ·¤ çSÍÚUæ´·¤æð´ ·ð¤ çِÙçÜç¹Ì â´ØæðÁÙ âð (¥ÂÙð
physical constants (expressed through âæÏæÚU‡æ ÂýØæð» ×ð´ çÜØð »Øð 翋ãæð´ mæÚUæ ÂýÎçàæüÌ),
their usual symbols) the only combination, ·ð¤ßÜ ßã â´ØæðÁÙ, Áæð ç·¤ §·¤æ§Øæð´ ·ð¤ çßçÖóæ çÙ·¤æØæð´
that would have the same value in different ×ð´ °·¤ ãè ×æÙ ÚU¹Ìæ ãñ, ãñ Ñ
systems of units, is :
ch ch
(1) 2 peo2 (1) 2 peo2

e2 e2
(2) (me5 mass of electron) (2) (me5§Üð€ÅþUæòÙ ·¤æ ÎýÃØ×æÙ)
2peo Gm e 2 2peo Gm e 2

mo e o G mo eo G
(3) 2 2 (3) 2
c he c h e2

2 p mo eo h 2 p mo eo h
(4) 2 (4) 2
ce G ce G

2. A person climbs up a stalled escalator 2. °·¤ ÃØç€ˆæ °·¤ SÍæçÂÌ °S·¤ÜðÅUÚU ·¤è ÎêÚUè 60 s ×ð´
in 60 s . If standing on the same but ¿É¸Ìæ ãñÐ ØçÎ ©â ÂÚU ¹Ç¸ð ãæð·¤ÚU ÂÚU‹Ìé çSÍÚU ßð» âð
escalator running with constant velocity °S·¤ÜðÅUÚU ·ð¤ ¿ÜÙð ÂÚU ßã 40 s ÜðÌæ ãñÐ ÃØ瀈æ
he takes 40 s. How much time is taken by »çÌàæèÜ °S·¤ÜðÅUÚU ÂÚU ¿Ü·¤ÚU §âè ÎêÚUè ·¤æð ÌØ
the person to walk up the moving ·¤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. m, 2m °ß´ 3m ·ð¤ ÌèÙ ÎýÃØ×æÙ x-y ÌÜ ×ð´ ¿æÜ
in x-y plane with speed 3u, 2u, and u ·ý¤×àæÑ 3u, 2u, °ß´ u âð »çÌàæèÜ ãñ, Áñâæ ç·¤ 翘æ
respectively as shown in figure. The three ×ð´ ÎàææüØæ »Øæ ãñÐ ÌèÙæð´ ÎýÃØ×æÙ °·¤ ãè çՋÎé ÂÚU
masses collide at the same point at P and ⴃæ^ ·¤ÚUÌð ãñ´ ¥æñÚU °·¤ âæÍ ç¿Â·¤ ÁæÌð ãñ´Ð ÂçÚU‡ææ×è
stick together. The velocity of resulting ÎýÃØ×æÙ ·¤æ ßð» ãæð»æ Ñ
mass will be :

(1) (
u ∧ ∧
i 1 3j )
(1)
u ∧
i1( ∧
3j ) 12
12
(2) (
u ∧
i 2 3j
∧
)
(2)
u ∧
i2( ∧
3j ) 12
12
(3) (
u ∧
2i 1 3j
∧
)
(3)
u ∧
(
2i 1 3j
∧
) 12
12
(4) (
u ∧
2i 2 3j
∧
)
(4)
u ∧
12
(
2i 2 3j
∧
) 12

4. °·¤ ×ð$Á ÂÚU çߟææ× ¥ßSÍæ ×ð´ çSÍÌ 0.8 kg Ü·¤Ç¸è
4. A 4 g bullet is fired horizontally with a ·ð¤ ŽÜæ·¤ ·¤æð 300 m/s ·¤è ¿æÜ âð °·¤ 4 g ·¤è
speed of 300 m/s into 0.8 kg block of wood »æðÜè ÿæñçÌÁ Îæ»Ìè ãñÐ ØçÎ ×ð$Á °ß´ ŽÜæ·¤ ·ð¤ Õè¿
at rest on a table. If the coefficient of ƒæáü‡æ »é‡ææ´·¤ 0.3 ãñ, ÌÕ ŽÜæ·¤ ֻܻ ç·¤ÌÙè ÎêÚU
friction between the block and the table is 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. çÕÙæ ÌæçÙÌ ÜÕæ§ü l ·¤è °·¤ ·¤×æÙè âð °·¤
mass m with one end fixed to a rigid ÎýÃØ×æÙ m §â Âý·¤æÚU ãñ ç·¤ §â·¤æ °·¤ çâÚUæ °·¤ Îëɸ
support. Assuming spring to be made of a ¥æÏæÚU ÂÚU Õ¡Ïæ ãñÐ Øã ×æÙÌð ãéØð ç·¤ ·¤×æÙè °·¤
uniform wire, the kinetic energy possessed °·¤â×æÙ ÌæÚU âð ÕÙè ãñ, §â×ð´ »çÌÁ ª¤Áæü ãæð»è ØçÎ
by it if its free end is pulled with uniform §â·¤æ Sß̋˜æ çâÚUæ °·¤â×æÙ ßð» v âð ¹è´¿æ Áæ° Ñ
velocity v is :
1 1
(1) m v2 (1) m v2
2 2
(2) mv 2 (2) mv 2
1 1
(3) m v2 (3) m v2
3 3
1 1
(4) m v2 (4) m v2
6 6

6. A particle is moving in a circular path of 6. °·¤ ·¤‡æ ç˜æ’Øæ a ·ð¤ °·¤ ßëžæèØ ÂÍ ÂÚU °·¤ çSÍÚU
radius a, with a constant velocity v as ßð» v âð »çÌàæèÜ ãñ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ »Øæ ãñÐ
shown in the figure. The center of circle is ßëžæ ·¤æ ·ð¤‹Îý ‘C’ âð ç¿ç‹ãÌ ç·¤Øæ »Øæ ãñÐ ×êÜ çՋÎé
marked by ‘C’. The angular momentum O âð ·¤æð‡æèØ â´ßð» §â Âý·¤æÚU çܹæ Áæ â·¤Ìæ ãñ Ñ
from the origin O can be written as :

(1) va(11cos 2u)
(1) va(11cos 2u) (2) va(11cos u)
(2) va(11cos u) (3) va cos 2u
(3) va cos 2u (4) va
(4) va

English : 3 Set : 06 Hindi : 3 Set : 06

7. 7.

Two hypothetical planets of masses m1 and ÎýÃØ×æÙ m1 °ß´ m2 ·ð¤ Îæð ÂçÚU·¤çËÂÌ ©Â»ýã çߟææ×
m 2 are at rest when they are infinite ¥ßSÍæ ×ð´ ãñ´ ÁÕ ßð °·¤ ÎêâÚðU â𠥋æ‹Ì ÎêÚUè ÂÚU ãñ´Ð
distance apart. Because of the gravitational »éL¤ˆßæ·¤áü‡æ ÕÜ ·ð¤ ·¤æÚU‡æ ©Ù·ð¤ ·ð¤‹Îýæð´ ·¤æð ç×ÜæÙð
force they move towards each other along ßæÜè ÚðU¹æ ÂÚU °·¤ ÎêâÚðU ·¤è ¥æðÚU »çÌ ·¤ÚUÙæ ÂýæÚUÖ
the line joining their centres. What is their ·¤ÚUÌð ãñ´Ð ÁÕ ©‹æ·ð¤ Õè¿ ÎêÚUè ‘d’ ãñ, ÌÕ ©Ù·¤è ¿æÜ
speed when their separation is ‘d’ ? €Øæ ãñ?
(Speed of m1 is v1 and that of m2 is v2) ( m1 ·¤è ¿æÜ v1 °ß´ m2 ·¤è ¿æÜ v2 ãñ )
(1) v 15v 2 (1) v 15v 2

2G 2G
(2) v1 5 m 2 (2) v1 5 m 2
d(m 11m 2 ) d(m 11m 2 )

2G 2G
v2 5 m 1 v2 5 m 1
d(m 11m 2 ) d(m 11m 2 )

2G 2G
(3) v1 5 m 1 (3) v1 5 m 1
d(m 11m 2 ) d(m 11m 2 )

2G 2G
v2 5 m 2 v2 5 m 2
d(m 11m 2 ) d(m 11m 2 )

2G 2G
(4) v1 5 m 2 (4) v1 5 m 2
m1 m1

2G 2G
v2 5 m 1 v2 5 m 1
m2 m2

English : 4 Set : 06 Hindi : 4 Set : 06

8. Steel ruptures when a shear of 8. SÅUèÜ È¤ÅU ÁæÌæ ãñ ÁÕ ©â ÂÚU 3.53108 Nm22
3.5310 8 N m 22 is applied. The force ·¤æ ¥ÂM¤Â‡æ Ü»æØæ ÁæÌæ ãñÐ 0.3 cm ×æðÅUè SÅUèÜ
needed to punch a 1 cm diameter hole in àæèÅU ×ð´ 1 cm ÃØæâ ·¤æ çÀUÎý ·¤ÚUÙð ×ð´ Ü»æØð ÁæÙð
a steel sheet 0.3 cm thick is nearly : ßæÜæ ÕÜ Ü»Ö» ãñ Ñ
(1) 1.43104 N (1) 1.43104 N
(2) 2.73104 N (2) 2.73104 N
(3) 3.33104 N (3) 3.33104 N
(4) 1.13104 N (4) 1.13104 N
9. A cylindrical vessel of cross-section A 9. ¥ÙéÂýSÍ ·¤æÅU A ßæÜð °·¤ ÕðÜÙæ·¤æÚU ÕÌüÙ ×ð´ ÂæÙè
contains water to a height h. There is a ª¡¤¿æ§ü h Ì·¤ ÖÚUæ ãñÐ §â·¤è ÌÜè ×ð´ ç˜æ’Øæ ‘a’ ·¤æ
hole in the bottom of radius ‘a’. The time °·¤ çÀUÎý ãñÐ ßã â×Ø, çÁâ×ð´ Øã ÕÌüÙ çÚU€ˆæ ãæð
in which it will be emptied is : Áæ°»æ, ãñ Ñ
2A h 2A h
(1) 2 g (1) 2 g
pa pa

2A h 2A h
(2) (2)
pa 2 g pa 2 g

2 2A h 2 2A h
(3) 2 g (3) 2 g
pa pa

A h A h
(4) 2 g (4) 2 g
2 pa 2 pa

English : 5 Set : 06 Hindi : 5 Set : 06

10. Two soap bubbles coalesce to form a single 10. Îæð âæÕéÙ ·ð¤ ÕéÜÕéÜð ç×Ü·¤ÚU °·¤ ÕéÜÕéÜæ ÕÙæÌð ãñ´Ð
bubble. If V is the subsequent change in ØçÎ §Ù×ð´ çSÍÌ ßæØé ·ð¤ ¥æØÌÙ ×ð´ ÂÚUßÌèü ÂçÚUßÌüÙ
volume of contained air and S the change V ãñ ¥æñÚU âÂê‡æü ÂëcÆ ÿæð˜æÈ¤Ü ×ð´ ÂçÚUßÌüÙ S ãñ,
in total surface area, T is the surface T ÂëcÆU ÌÙæß ãñ ¥æñÚU P ßæØé×´ÇUÜ ÎæÕ ãñ, ÌÕ
tension and P atmospheric pressure, which çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ-âæ âÕ‹Ï âãè ãñ?
of the following relation is correct ?
(1) 4PV13ST50 (1) 4PV13ST50
(2) 3PV14ST50 (2) 3PV14ST50
(3) 2PV13ST50 (3) 2PV13ST50
(4) 3PV12ST50 (4) 3PV12ST50

11. Hot water cools from 608C to 508C in the 11. »×ü ÂæÙè 608C âð 508C ÂãÜð 10 ç×ÙÅU ×ð´ Æ´UÇUæ ãæðÌæ
first 10 minutes and to 428C in the next ãñ ¥æñÚU 428C Ì·¤ ÎêâÚðU 10 ç×ÙÅU ×ð´ Æ´UÇUæ ãæðÌæ ãñÐ
10 minutes. The temperature of the ßæÌæßÚU‡æ ·¤æ ÌæÂ×æÙ ãñ Ñ
surroundings is :
(1) 258C (1) 258C
(2) 108C (2) 108C
(3) 158C (3) 158C
(4) 208C (4) 208C
12. A Carnot engine absorbs 1000 J of heat 12. °·¤ ·¤æÙæðü §´ÁÙ °·¤ ·é´¤ÇU âð 1278C ÂÚU 1000 J
energy from a reservoir at 1278C and rejects ª¤c×èØ ª¤Áæü ¥ßàææðçáÌ ·¤ÚUÌæ ãñ ¥æñÚU ÂýˆØð·¤ ¿·ý¤
600 J of heat energy during each cycle. The ×ð´ 600 J ª¤c×èØ ª¤Áæü ¥Sßè·¤æÚU ·¤ÚU ÎðÌæ ãñÐ §´ÁÙ
efficiency of engine and temperature of ·¤è ÎÿæÌæ ¥æñÚU çâ´·¤ ·¤æ ÌæÂ×æÙ ãæð»æ Ñ
sink will be :
(1) 20% and 2438C (1) 20% °ß´ 2438C
(2) 40% and 2338C (2) 40% °ß´ 2338C
(3) 50% and 2208C (3) 50% °ß´ 2208C
(4) 70% and 2108C (4) 70% °ß´ 2108C

English : 6 Set : 06 Hindi : 6 Set : 06

13. At room temperature a diatomic gas is 13. ·¤×ÚðU ·ð¤ ÌæÂ×æÙ ÂÚU °·¤ çmÂÚU×æ‡æé·¤ »ñâ ·¤è
found to have an r.m.s. speed of ß»ü-×æŠØ-×êÜ ¿æÜ 1930 ms21 ÂæØè ÁæÌè ãñÐ
1930 ms21. The gas is : »ñâ ãñ Ñ
(1) H2 (1) H2
(2) Cl2 (2) Cl2
(3) O2 (3) O2
(4) F2 (4) F2

14. Which of the following expressions 14. çِÙçÜç¹Ì ÃØ´Á·¤æð´ ×ð´ âð ·¤æñÙ âæ °·¤ âÚUÜ ÚðU¹æ
corresponds to simple harmonic motion ÂÚU âÚUÜ ¥æßÌü »çÌ ·ð¤ â´»Ì ãñ, Áãæ¡ x çßSÍæÂÙ ãñ
along a straight line, where x is the ¥æñÚU a, b, c ÏÙæˆ×·¤ çSÍÚUæ´·¤ ãñ ?
displacement and a, b, c are positive
constants ?
(1) a1bx2cx 2 (1) a1bx2cx 2
(2) bx2 (2) bx2
(3) a2bx1cx 2 (3) a2bx1cx 2
(4) 2bx (4) 2bx

15. A source of sound A emitting waves of 15. ¥æßëçžæ 1800 Hz ·¤è Ì´ÚU»ð´ ©ˆâçÁüÌ ·¤ÚU ÚUãæ ŠßçÙ
frequency 1800 Hz is falling towards dæðÌ A °·¤ âè×æ‹Ì ßð» v âð ÏÚUÌè ·¤è ¥æðÚU ç»ÚU ÚUãæ
ground with a terminal speed v. The ãñÐ dæðÌ ·ð¤ ÆUè·¤ Ùè¿ð ÏÚUÌè ÂÚU °·¤ Âýðÿæ·¤ B
observer B on the ground directly beneath ¥æßëçžæ 2150 Hz ·¤è ÌÚ´U»ð´ ÂýæŒˆæ ·¤ÚUÌæ ãñÐ dæðÌ A,
the source receives waves of frequency ÏÚUÌè âð ÂÚUæßçÌüÌ Ü»Ö» §â ¥æßëçžæ ·¤è ÌÚ´U»ð´ Âý挈æ
2150 Hz. The source A receives waves, ·¤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. °·¤ »æðÜèØ â×ç×Ìè ¥æßðàæ çßÌÚU‡æ ¥æßðàæ ƒæوß
distribution is characterised by a charge ·¤æ çِÙçÜç¹Ì çß¿ÚU‡æ ÚU¹Ìæ ãñ Ñ
density having the following variation :  r
r(r)5ro  1 2  r < R ·ð¤ çÜ°
 r  R
r(r)5ro  1 2  for r < R
 R r(r)50 r / R ·ð¤ çÜ°
r(r)50 for r / R Áãæ¡ r ¥æßðàæ çßÌÚU‡æ ·ð¤ ·ð¤‹Îý âð ÎêÚUè ãñ´ ¥æñÚU ro °·¤
Where r is the distance from the centre of çSÍÚUæ´·¤ ãñÐ °·¤ ¥‹ÌÑ çՋÎé (r < R) ÂÚU çßléÌ ÿæð˜æ
the charge distribution and ro is a constant. ãñ Ñ
The electric field at an internal point
(r < R) is :
ro  r r2 
ro  r r2  (1)  2 
(1)  2  4e o  3 4R 
4eo  3 4R 
ro  r r2 
ro  r r2  (2)  2 
(2)  2  eo  3 4R 
eo  3 4R 
ro  r r2 
ro  r r2  (3)  2 
(3)  2  3eo  3 4R 
3e o  3 4R 
ro  r r2 
ro  r r2  (4)  2 
(4)  2  12 eo  3 4R 
12 eo  3 4R 

English : 8 Set : 06 Hindi : 8 Set : 06

17. The space between the plates of a parallel 17. °·¤ â×æ‹ÌÚU Âç^·¤æ â´ÏæçÚU˜æ ·¤è Âç^·¤æ¥æð´ ·ð¤ Õè¿
plate capacitor is filled with a ‘dielectric’ ·¤æ SÍæÙ °·¤ ÂÚæßñléÌ âð ÖÚUæ ÁæÌæ ãñ çÁâ·¤æ ÂÚUæßñléÌ
whose ‘dielectric constant’ varies with çSÍÚUæ´·¤ ÎêÚUè ·ð¤ âæÍ çِ٠âÕ‹Ï ¥ÙéâæÚU ÂçÚUßçÌüÌ
distance as per the relation : ãæðÌæ ãñ Ñ
K(x)5Ko1lx (l5 a constant) K(x)5Ko1lx (l5°·¤ çSÍÚUæ´·¤)
The capacitance C, of this capacitor, would â´ÏæçÚU˜æ ·¤è ÏæçÚUÌæ C, §â·¤è çÙßæüÌ ÏæçÚUÌæ, Co ·ð¤
be related to its ‘vacuum’ capacitance Co âæÍ çِ٠âÕ‹Ï ¥ÙéâæÚU âÕç‹ÏÌ ãæð»è Ñ
as per the relation :
ld ld
(1) C5 Co (1) C5 Co
l n (1 1 K o ld) l n (1 1 K o ld)
l l
(2) C5 Co (2) C5 Co
d. l n (1 1 K o ld) d. l n (1 1 K o ld)

ld ld
(3) C5 Co (3) C5 Co
l n (1 1 ld/K o ) l n (1 1 ld/K o )
l l
(4) C5 Co (4) C5 Co
d. l n (1 1 K o /ld) d. l n (1 1 K o /ld)

English : 9 Set : 06 Hindi : 9 Set : 06

18. The circuit shown here has two batteries 18. ÎàææüØð »Øð ÂçÚUÂÍ ×ð´ 8.0 V °ß´ 16.0 V ·¤è Îæð
of 8.0 V and 16.0 V and three resistors ÕñÅUçÚUØæ¡ ¥æñÚU 3 V, 9 V °ß´ 9 V ·ð¤ ÌèÙ ÂýçÌÚUæðÏ ÌÍæ
3 V, 9 V and 9 V and a capacitor 5.0 mF. 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?
steady state ?
(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
19. A positive charge ‘q’ of mass ‘m’ is moving 19. ÎýÃØ×æÙ ‘m’ ·¤æ °·¤ ÏÙæˆ×·¤ ¥æßðàæ ‘q’, 1x ¥ÿæ
along the 1x axis. We wish to apply a ÂÚU »çÌàæèÜ ãñÐ ã× °·¤ °·¤â×æÙ ¿éÕ·¤èØ ÿæð˜æ B
uniform magnetic field B for time Dt so that â×Ø Dt ·ð¤ çÜ° Ü»æÙæ ¿æãÌð ãñ´ çÁââð ç·¤ ¥æßðàæ
the charge reverses its direction crossing ·¤è çÎàææ d ÎêÚUè ÂÚU y - ¥ÿæ ·¤æð ·¤æÅUÌð ãé° ÂýçÌÜæðç×Ì
the y axis at a distance d. Then : ãæð Áæ°, ÌÕ Ñ
mv pd mv pd
(1) 5 DQGDW5 (1) 5  •Ä™  D W5
qd v qd v

mv pd mv pd
(2) 5 DQG D W5 (2) 5  •Ä™  D W5
2 qd 2v 2 qd 2v

2 mv pd 2 mv pd
(3) 5 DQG D W5 (3) 5  •Ä™  D W5
qd 2v qd 2v

2 mv pd 2 mv pd
(4) 5 DQG D W5 (4) 5  •Ä™  D W5
qd v qd v

English : 10 Set : 06 Hindi : 10 Set : 06

20. Consider two thin identical conducting 20. Îæð ÂÌÜð âßü â×M¤Âè ¿æÜ·¤èØ ÌæÚU ÕãéÌ ÂÌÜð ÚUæðÏè
wires covered with very thin insulating ÂÎæÍü âð ɸ·ð¤ ãé° ãñ´Ð °·¤ ÌæÚU ·¤æð ×æðǸ·¤ÚU °·¤ ÜêÂ
material. One of the wires is bent into a ÕÙæØæ ÁæÌæ ãñ Áæð ç·¤ ¥ÂÙð ·ð¤‹Îý ÂÚU ¿éÕ·¤èØ ÿæð˜æ
loop and produces magnetic field B1, at its B1 ©ˆÂóæ ·¤ÚUÌæ ãñ ÁÕ §â×ð´ ÏæÚUæ I ÂýßæçãÌ ãæðÌè ãñÐ
centre when a current I passes through it. ÎêâÚðU ÌæÚU ·¤æð ÌèÙ âßüâ×M¤Âè ÜêÂæð´ ×ð´ ×æðǸ·¤ÚU ¥æñÚU
The second wire is bent into a coil with °·¤ âæÍ ÚU¹·¤ÚU ·é¤‡ÇUÜè ÕÙæÌð ãñ´ Áæð ç·¤ ÜêÂæð´ ·ð¤
three identical loops adjacent to each other ·ð¤‹Îý ÂÚU ¿éÕ·¤èØ ÿæð˜æ B2 ©ˆÂóæ ·¤ÚUÌæ ãñ ÁÕ §â×ð´
and produces magnetic field B 2 at the ÏæÚUæ I/3 ÂýßæçãÌ ãæðÌè ãñÐ ¥ÙéÂæÌ B1 : B2 ãñ Ñ
centre of the loops when current I/3 passes (1) 1:1
through it. The ratio B1 : B2 is : (2) 1:3
(1) 1:1 (3) 1:9
(2) 1:3 (4) 9:1
(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
21. A sinusoidal voltage V(t)5100 sin (500t) ·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. °·¤ ÜðÂ âÖè çÎàææ¥æð´ ×ð´ °·¤â×æÙ M¤Â âð °·¤ß‡æèü
uniformly in all directions. The lamp is 3% ãÚUæ Âý·¤æàæ ©ˆâçÁüÌ ·¤ÚU ÚUãæ ãñÐ ÜðÂ ·¤è çßléÌ
efficient in converting electrical power to àæç€ˆæ ·¤æð çßléÌ ¿éÕ·¤èØ ÌÚ´U»æð´ ×ð´ ÂçÚUßÌüÙ ·¤ÚUÙð
electromagnetic waves and consumes ·¤è ÎÿæÌæ 3% ãñ ¥æñÚU 100 W àæç€ˆæ ·¤è ¹ÂÌ ·¤ÚUÌæ
100 W of power. The amplitude of the ãñÐ ÜðÂ âð 5 m ÎêÚUè ÂÚU çßléÌ ¿éÕ·¤èØ çßç·¤ÚU‡æ
electric field associated with the 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. °·¤ ¥ßÌÜ Üð‹â ·ð¤ ÂÎæÍü ·¤æ ¥ÂßÌüÙæ´·¤ m ãñÐ
concave lens is m. It is immersed in a §âð ¥ÂßÌüÙæ´·¤ m1 ·ð¤ ×æŠØ× ×ð´ ÇéUÕæðØæ ÁæÌæ ãñÐ
medium of refractive index m1. A parallel Âý·¤æàæ ·¤è °·¤ â×æ‹ÌÚU Âé´Á Üð‹â ÂÚU ¥æÂçÌÌ ãñÐ
beam of light is incident on the lens. The ÁÕ m1 > m ãñ´, ÌÕ çÙ»üÌ ç·¤ÚU‡ææð´ ·¤æ ÂÍ ãñ Ñ
path of the emergent rays when m1 > m is :

(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. °·¤ dæðÌ ’S’ âð çÙ·¤Ü ÚUãè Îæð ç·¤ÚU‡ææ𴠷𤠥ŠØæÚUæð‡æ
to superimposition of two rays coming out âð ‘P’ ÂÚU °·¤ ÃØçÌ·¤ÚU‡æ 翘æ ÂæØæ ÁæÌæ ãñ, Áñâæ ç·¤
from a source ‘S’ as shown in the figure. 翘æ ×ð´ ÎàææüØæ »Øæ ãñÐ ‘l’ ·¤æ ßã ×æÙ, çÁâ·ð¤ çÜ°
The value of ‘l’ for which maxima is ‘P’ ÂÚU Âý挈æ 翘æ ×ð´ ×ãžæ× ÌèßýÌæ ãñ, ãñ Ñ
obtained at ‘P’ is : (R °·¤ Âê‡æüÌØæ ÂÚUæßÌèü ÂëcÆU ãñ )
(R is perfect reflecting surface) :

2 nl
(1) l5
2 nl 321
(1) l5
321 (2n21)l
(2) l5
(2n21)l 2 ( 3 2 1)
(2) l5
2 ( 3 2 1)
(2n21)l 3
(3) l5
(2n21)l 3 4 ( 22 3 )
(3) l5
4 ( 22 3 )
(2n21)l
(4) l5
(2n21)l 3 21
(4) l5
3 21
25. °·¤Ü çSÜÅU çßßÌüÙ ç¿˜æ ·ð¤ ÂýØæð» ×ð´, ÜæÜ Âý·¤æàæ
25. In an experiment of single slit diffraction ·¤æ ÂýÍ× ‹ØêÙÌ× °·¤ ÎêâÚUè ÌÚ´U»ÎñŠØü ·ð¤ ÂýÍ× ×ãžæ×
pattern, first minimum for red light â´ÂæÌè ãñÐ ØçÎ ÜæÜ Âý·¤æàæ ·¤è ÌÚ´U»ÎñŠØü 6600 Å
coincides with first maximum of some 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. Îæð ÌÚ´U»ÎñŠØæðZ 4972Å °ß´ 6216 Å ßæÜð Âý·¤æàæ ·¤è
4972 Å and 6216 Å with a total intensity °·¤ Âé´Á ·¤è ·é¤Ü ÌèßýÌæ 3.631023 Wm22 ãñ Áæð
of 3.631023 Wm22 equally distributed ç·¤ ÎæðÙæð´ ÌÚ´U»ÎñŠØæðZ ×ð´ °·¤ â×æÙ çßÌçÚUÌ ãñÐ 2.3 eV
among the two wavelengths. The beam ·¤æØü È ¤ÜÙ ßæÜð °·¤ âæȤ ÏæÌé ·ð ¤ Âë c ÆU ·ð ¤
falls normally on an area of 1 cm2 of a clean 1 cm2 ÿæð˜æÈ¤Ü ÂÚU Øã Âé´Á ¥çÖܐÕßÌ÷ ¥æÂçÌÌ
metallic surface of work function 2.3 eV. ãñ´Ð Øã ×æÙ Üð´ ç·¤ ÂÚUæßÌüÙ mæÚUæ ç·¤âè Öè Âý·¤æàæ ·¤æ
Assume that there is no loss of light by Oæâ Ùãè´ ãæðÌæ ãñ ¥æñÚU ÂýˆØð·¤ ÿæç×Ì È¤æðÅUæÙ °·¤ §Üð€ÅþUæÙò
reflection and that each capable photon ©ˆâçÁüÌ ·¤ÚUÌæ ãñÐ 2s ×ð´ ©ˆâçÁüÌ È¤æðÅUæð §Üð€ÅþUæòÙæð´
ejects one electron. The number of photo ·¤è ⴁØæ ãñ ֻܻ Ñ
electrons liberated in 2s is
approximately :
(1) 6310 11 (1) 6310 11
(2) 9310 11 (2) 9310 11
(3) 11310 11 (3) 11310 11
(4) 15310 11 (4) 15310 11

27. A piece of bone of an animal from a ruin 27. °·¤ ¹‡ÇUãÚU âð ÂýæŒˆæ °·¤ Âàæé ·¤è ãaè ·ð¤ ÅéU·¤Ç¸ð ·¤è
is found to have 14 C activity of 14C âç·ý¤ØÌæ §â·ð¤ ·¤æÕüÙ ¥´àæ ·¤è ÂýçÌ »ýæ× ÂýçÌ

12 disintegrations per minute per gm of ç×ÙÅU 12 ç߃æÅUÙ ãñÐ °·¤ ç’æ‹Îæ Âàæé ·¤è 14C âç·ý¤ØÌæ
its carbon content. The 14C activity of a 16 ç߃æÅUÙ ÂýçÌ ç×ÙÅU ÂýçÌ »ýæ× ãñ Рֻܻ ç·¤ÌÙð
living animal is 16 disintegrations per ßáü ÂãÜð Âàæé ·¤è ×ëˆØé ãé§ü? (çÎØæ ãñ 14C ·¤è ¥hü
minute per gm. How long ago nearly did ¥æØé t1/255760 ßáü)
the animal die ? (Given half life of
14C is t
1/255760 years)
(1) 1672 years (1) 1672 ßáü
(2) 2391 years (2) 2391 ßáü
(3) 3291 years (3) 3291 ßáü
(4) 4453 years (4) 4453 ßáü

English : 15 Set : 06 Hindi : 15 Set : 06

28. For LED’s to emit light in visible region of 28. LED’s çßléÌ ¿éÕ·¤èØ Âý·¤æàæ ·ð¤ ÎëàØ ÿæð˜æ ×ð´
electromagnetic light, it should have Âý·¤æàæ ©ˆâçÁüÌ ·¤ÚðU, §â·ð¤ çÜØð §Ù·¤è Õñ‹Ç ¥‹ÌÚUæÜ
energy band gap in the range of : §â ÚðU‹Á ×ð´ ãæðÙè ¿æçãØð Ñ
(1) 0.1 eV to 0.4 eV (1) 0.1 eV âð 0.4 eV
(2) 0.5 eV to 0.8 eV (2) 0.5 eV âð 0.8 eV
(3) 0.9 eV to 1.6 eV (3) 0.9 eV âð 1.6 eV
(4) 1.7 eV to 3.0 eV (4) 1.7 eV âð 3.0 eV
29. For sky wave propagation, the radio 29. ¥æ·¤æàæ ÌÚ´U» â´¿ÚU‡æ ·ð¤ çÜ°, ÚðUçÇUØæð ÌÚ´U»ð´ §â ¥æßëçžæ
waves must have a frequency range in ÚðU‹Á ·ð¤ Õè¿ ãæðÙè ¿æçã° Ñ
between :
(1) 1 MHz to 2 MHz (1) 1 MHz âð 2 MHz
(2) 5 MHz to 25 MHz (2) 5 MHz âð 25 MHz
(3) 35 MHz to 40 MHz (3) 35 MHz âð 40 MHz
(4) 45 MHz to 50 MHz (4) 45 MHz âð 50 MHz

30. In the experiment of calibration of 30. °·¤ ßæðËÅU×æÂè ·ð¤ ¥´àæàææðÏÙ ·ð¤ ÂýØæð» ×ð´, 1.1 ßæðËÅU
voltmeter, a standard cell of e.m.f. 1.1 volt çßléÌßæã·¤ ÕÜ ·ð¤ °·¤ ×æÙ·¤ âñÜ ·ð¤ â´ÌéçÜÌ
is balanced against 440 cm of 440 cm ·¤æ çßÖß×æÂè ÌæÚU ÂæØæ ÁæÌæ ãñÐ °·¤
potentiometer wire. The potential ÂýçÌÚUæðÏ ·ð¤ çâÚUæð´ ÂÚU çßÖßæ‹ÌÚU ÌæÚU ·ð¤ 220 cm ·ð¤
difference across the ends of resistance is â´ÌéçÜÌ ÂæØæ ÁæÌæ ãñÐ ßæðËÅU×æÂè ·¤æ â´»Ì ÂÆUÙ
found to balance against 220 cm of the 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) 20.15 ßæðËÅU
(2) 0.15 volt (2) 0.15 ßæðËÅU
(3) 0.5 volt (3) 0.5 ßæðËÅU
(4) 20.05 volt (4) 20.05 ßæðËÅU

English : 16 Set : 06 Hindi : 16 Set : 06

PART B — CHEMISTRY Öæ» B — ÚUâæØÙ çߙææÙ
31. If m and e are the mass and charge of the 31. ØçÎ ãæ§ÇþæðÁÙ ÂÚU×æ‡æé ·ð¤ ç˜æ’Øæ r ·¤è ¥æÚUçÕÅU ×ð´
revolving electron in the orbit of radius r ƒæê×Ùð ßæÜð §Üñ€ÅþUæòÙ ·¤æ ÎýÃØ×æÙ m ¥æñÚU ¥æßðàæ e ãæð´
for hydrogen atom, the total energy of the Ìæð, ƒæê×Ùð ßæÜð §Üñ€ÅþUæòÙ ·¤è â·¤Ü ª¤Áæü ãæð»è Ñ
revolving electron will be :

1 e2 1 e2
(1) (1)
2 r 2 r

e2 e2
(2) 2 (2) 2
r r

me 2 me 2
(3) (3)
r r

1 e2 1 e2
(4) 2 (4) 2
2 r 2 r

32. The de-Broglie wavelength of a particle of 32. ÎýÃØ×æÙ 6.63 g ·ð¤ ·¤‡æ ·¤æ ¥æßð» 100 ms21 âð
mass 6.63 g moving with a velocity of »çÌ×æÙ ãæðÙð ÂÚU Îè-Õýæ‚Üè ÌÚ´U»ÎñŠØü ãæð»è Ñ
100 ms21 is :
(1) 10233 m (1) 10233 m
(2) 10235 m (2) 10235 m
(3) 10231 m (3) 10231 m
(4) 10225 m (4) 10225 m

33. What happens when an inert gas is added 33. âæØ ÚU¹Ùð ßæÜð ¥æØÌÙ ·¤æð ¥ÂçÚUßçÌüÌ ÚU¹Ùð ßæÜè
to an equilibrium keeping volume çSÍçÌ ×ð´ °·¤ ¥ç·ý¤Ø »ñâ ÇæÜÙð ÂÚU €Øæ ãæð»æ?
unchanged ? (1) ¥çÏ·¤ ç·ý¤Øæ È¤Ü Âý挈æ ãæð»æÐ
(1) More product will form (2) ·¤× ç·ý¤Øæ È¤Ü Âý挈æ ãæð»æÐ
(2) Less product will form (3) ¥çÏ·¤ ¥çÖç·ý¤Øæ ãæð»èÐ
(3) More reactant will form (4) âæØ ¥ÂçÚUßçÌüÌ ÚUãð»æÐ
(4) Equilibrium will remain unchanged

English : 17 Set : 06 Hindi : 17 Set : 06

34. The amount of BaSO4 formed upon mixing 34. ÁÕ Ba5137, Cl535.5, S532, H51 ¥æñÚU
100 mL of 20.8% BaCl 2 solution with O516 ×æÙæ ÁæØð Ìæð 20.8% BaCl2 çßÜØÙ ·ð¤
50 mL of 9.8% H2SO4 solution will be : 100 mL ·¤æð 9.8%, H 2 SO 4 ·ð ¤ çßÜØÙ ·ð ¤
(Ba5137, Cl535.5, S532, H51 and 50 mL ×ð´ ç×ÜæÙð ÂÚU ç·¤ÌÙæ BaSO4 ÕÙð»æ?
O516)
(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
35. The rate coefficient (k) for a particular 35. 1008C ÂÚU °·¤ çßàæðá ¥çÖç·ý¤Øæ ·¤æ ÎÚU çÙØÌæ´·¤ (k)
reactions is 1.331024 M21 s21 at 1008C, 1.331024 M21 s21 ãñ ¥æñÚU 1508C ÂÚU §â·¤æ
and 1.331023 M21 s21 at 1508C. What ×æÙ 1.331023 M21 s21 ãñÐ §â ¥çÖç·ý¤Øæ ·ð¤
is the energy of activation (EA) (in kJ) for çÜØð °ð€ÅUèßðàæÙ ª¤Áæü (EA) kJ ×ð´ ç·¤ÌÙè ãæð»è?
this reaction ? (R5molar gas (R5×æðÜÚU »ñâ çÙØÌæ´·¤ 58.314 JK21 ×æðÜ 21)
constant58.314 JK21 mol21)
(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. ·¤æÂÚU âË$Èð¤ÅUU ·ð¤ ÁÜèØ çßÜØÙ ·ð¤ §Üñ€ÅþUæòÜðçââ ×ð´
deposit 6.35 g of copper at the cathode ·ñ¤ÍæðÇ ÂÚU 6.35 »ýæ× ·¤æÂÚU ·ð¤ Á×æ¥æð´ ·ð¤ çÜØð
during the electrolysis of an aqueous ç·¤ÌÙð §Üñ€ÅþUæòÙæð´ ·¤è ¥æßàØ·¤Ìæ ãæð»è? (·¤æÂÚU ·¤æ
solution of copper sulphate ? (Atomic mass ÂÚU×æ‡æé ÎýÃØ×æÙ 5 63.5 ×æ˜æ·¤, NA5 °ðßæð»æÎýæð
of copper 5 63.5 u, N A 5Avogadro’s çÙØÌæ´·¤)
constant) :
NA NA
(1) (1)
20 20
NA NA
(2) (2)
10 10
NA NA
(3) (3)
5 5
NA NA
(4) (4)
2 2

37. The entropy (S o ) of the following 37. çِ٠ÂÎæÍæðZ ·ð¤ °ð‹ÅþUæÂè ×æÙ ãñ (So) ãñ´ Ñ
substances are : CH4 (g) 186.2 J K21 ×æðÜ21
CH4 (g) 186.2 J K21 mol21 O 2 (g) 205.0 J K21 ×æðÜ21
O2 (g) 205.0 J K21 mol21 CO 2 (g) 213.6 J K21 ×æðÜ21
CO 2 (g) 213.6 J K21 mol21 H2O (l) 69.9 J K21 ×æðÜ21
H2O (l) 69.9 J K21 mol21 ¥çÖç·ý¤Øæ
The entropy change (DSo) for the reaction CH 4 (g)12O 2 (g) ® CO 2 (g)12H 2 O(l)
CH4(g)12O2(g) ® CO2(g)12H2O(l) is : ·ð¤ çÜØð °ð‹ÅþUæÂè ÂçÚUßÌüÙ (DSo) ·¤æ ×æÙ ãæð»æ Ñ
(1) 2312.5 J K21 mol21 (1) 2312.5 J K21 ×æðÜ21
(2) 2242.8 J K21 mol21 (2) 2242.8 J K21 ×æðÜ21
(3) 2108.1 J K21 mol21 (3) 2108.1 J K21 ×æðÜ21
(4) 237.6 J K21 mol21 (4) 237.6 J K21 ×æðÜ21

English : 19 Set : 06 Hindi : 19 Set : 06

38. The conjugate base of hydrazoic acid is : 38. ãæ§ÇþUæð$Áæ𧷤 °ðçâÇU ·¤æ â´Øé‚×è ÿææÚU ãñ Ñ
(1) N23 (1) N23
(2) N2
3 (2) N2
3

(3) N2
2 (3) N2
2

(4) HN2
3 (4) HN2
3

39. In a monoclinic unit cell, the relation of 39. °·¤ ×æðÙæðç€ÜçÙ·¤ °·¤·¤ âñÜ ×ð´ Âÿææ𴠷𤠷¤æðÙæ çՋÎé¥æð´
sides and angles are respectively : âð âÕ‹Ï ·ý¤×æÙéâæÚU ãæðÌð ã´ñ Ñ
(1) a5b ¹ c and a5b5g5908 (1) a5b ¹ c ¥æñÚU a5b5g5908
(2) a ¹ b ¹ c and a5b5g5908 (2) a ¹ b ¹ c ¥æñÚU a5b5g5908
(3) a ¹ b ¹ c and b5g5908 ¹ a (3) a ¹ b ¹ c ¥æñÚU b5g5908 ¹ a
(4) a ¹ b ¹ c and a ¹ b ¹ g ¹ 908 (4) a ¹ b ¹ c ¥æñÚU a ¹ b ¹ g ¹ 908

40. The standard enthalpy of formation 40. ×èÍðÙ, CH4, ÕÙÙð ·¤è ×æÙ·¤ °ð‹ÍñËÂè (DfHo298)
(D f H o 298 ) for methane, CH 4 is 274.9 kJ ×æðÜ21 ãæðÌè ãñÐ §ââð C2H ¥æՋÏ
274.9 kJ mol21. In order to calculate the ·¤è ׊Ø×æÙ ª¤Áæü ·¤æ ¥æ·¤ÜÙ ·¤ÚUÙð ·ð¤ çÜØð çِÙæð´
average energy given out in the formation 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) H2 ¥‡æé ·¤è çßØæðÁÙ ª¤ÁæüÐ
hydrogen molecule, H2.
(2) the first four ionisation energies of (2) ·¤æÕüÙ ·¤è ÂãÜè ¿æÚU ¥æØÙÙ ª¤Áæü°¡Ð
carbon.
(3) the dissociation energy of H2 and (3) H2 ·¤è çßØæðÁÙ ª¤Áæü ¥æñÚU ·¤æÕüÙ (»ýð$Ȥæ§Å)U
enthalpy of sublimation of carbon ·¤è ª¤ŠßüÂæÌÙ ª¤ÁæüÐ
(graphite).
(4) the first four ionisation energies of (4) ·¤æÕüÙ ·¤è ÂýÍ× ¿æÚU ¥æØÙÙ ª¤Áæü°¡ ¥æñÚ
carbon and electron affinity of ãæ§ÇþUæðÁÙ ·¤è §Üñ€ÅþUæò٠ՋÏéÌæÐ
hydrogen.

English : 20 Set : 06 Hindi : 20 Set : 06

41. Which of the following xenon-OXO 41. $ÁèÙæÙ ÜæðÚUæ§ÇUæð´ ·ð¤ ÁÜèØ ¥ÂƒæÅUÙ âð çِ٠$ÁèÙæÙ-
compounds may not be obtained by ¥æ€âæð-Øæñç»·¤æð´ ×ð´ âð 緤ⷤæð Âý挈æ Ùãè´ ç·¤Øæ Áæ
hydrolysis of xenon fluorides ? â·¤Ìæ ãñ?
(1) Xe O2F2 (1) Xe O2F2
(2) Xe O F4 (2) Xe O F4
(3) Xe O3 (3) Xe O3
(4) Xe O4 (4) Xe O4
42. Excited hydrogen atom emits light in the 42. 2.47310 15 Hz ÂÚU ÂÚU æ Õñ ´ » Ùè ÿæð ˜ æ ×ð ´ ©žæð ç ÁÌ
ultraviolet region at 2.4731015 Hz. With ãæ§ÇþUæðÁÙ ÂÚU×æ‡æé Âý·¤æàæ ©ˆâçÁüÌ ·¤ÚUÌæ ãñÐ §â
this frequency, the energy of a single ¥æßëçžæ ·ð¤ âæÍ °·¤ ¥·ð¤Üð ȤæðÅUæòÙ ·¤è ª¤Áæü ãæð»è Ñ
photon is : (h56.63310234 Js)
(h56.63310234 Js)
(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

43. Which one of the following exhibits the 43. çِÙæð´ ×ð´ âð ·¤æñÙ °·¤ ¥çÏ·¤Ì× â´Øæ ×ð´ ¥æò€âè·¤ÚU‡æ
largest number of oxidation states ? ¥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)

English : 21 Set : 06 Hindi : 21 Set : 06

44. Copper becomes green when exposed to 44. ܐÕð â×Ø Ì·¤ »èÜè ßæØé ·ð¤ âÂ·ü¤ ×ð´ ÚUãÙð ÂÚU
moist air for a long period. This is due to : ·¤æÂÚU ãÚUæ ãæð ÁæÌæ ãñÐ §â·¤æ ·¤æÚU‡æ ãæðÌæ ãñ Ñ
(1) the formation of a layer of cupric (1) ·¤æÂÚU ÌÜ ÂÚU €ØêçÂý·¤ ¥æò€âæ§ÇU ·¤æ ÂÚUÌ
oxide on the surface of copper. ÕÙÙæÐ
(2) the formation of a layer of basic (2) ·¤æÂÚU ÌÜ ÂÚU ·¤æÂÚU ·ð¤ ÿææÚUèØ ·¤æÕæðüÙðÅU ·¤æ
carbonate of copper on the surface ÂÚUÌ ÕÙÙæÐ
of copper.
(3) the formation of a layer of cupric (3) ·¤æÂÚU ÌÜ ÂÚU €ØêçÂý·¤ ãæ§ÇþU¥æò€âæ§ÇU ·¤æ ÂÚUÌ
hydroxide on the surface of copper. ÕÙÙæÐ
(4) the formation of basic copper (4) ÏæÌé ÌÜ ÂÚU ÿææÚUèØ ·¤æÂÚU âË$Èð¤ÅU ·¤æ ÂÚUÌ
sulphate layer on the surface of the ÕÙÙæÐ
metal.

45. Among the following species the one 45. çِ٠ÂÎæÍæðZ ×ð´ âð ·¤æñÙ °·¤ çÜ»ñ‹ÇU M¤Â ×ð´ ¥çÏ·¤Ì×
which causes the highest CFSE, Do as a CFSE, Do ·¤æ ·¤æÚU‡æ ÕÙÌæ ãñ?
ligand is :
(1) CN2 (1) CN2
(2) NH3 (2) NH3
(3) F2 (3) F2
(4) CO (4) CO
46. Similarity in chemical properties of the 46. ¥æßÌü âæÚU‡æè ·ð¤ ç·¤âè »ýé ×ð´ Ìˆß ·ð¤ ÂÚU×æ‡æé¥æð´ ·ð¤
atoms of elements in a group of the ÚUæâæØçÙ·¤ »é‡ææð´ ×ð´ ¥çÏ·¤Ì× â×æÙÌæ ·ð¤ ·¤æÚU‡æ ãæðÌð
Periodic table is most closely related to : ãñ´ Ñ
(1) atomic numbers (1) ÂÚU×æ‡æé·¤ ِÕÚU
(2) atomic masses (2) ÂÚU×æ‡æé·¤ ÎýÃØ×æÙ
(3) number of principal energy levels (3) ÕǸð (Principal) ª¤Áæü SÌÚUæð´ ·¤è ⴁØæ
(4) number of valence electrons (4) ßñÜð‹âè §Üñ€ÅþUæòÙæð´ ·¤è ⴁØæ

English : 22 Set : 06 Hindi : 22 Set : 06

47. Which of the following arrangements 47. çِ٠ÃØßSÍæ¥æð ´ ×ð ´ âð ·¤æñ Ù çÎØð »Øð ÂÎæÍæð Z
represents the increasing order (smallest O22, S22, N32, P32 ·¤è ¥æØçÙ·¤ ç˜æ’Øæ¥æð´ ·ð¤
to largest) of ionic radii of the given species ÕɸÌð ·ý¤× (‹ØêÙÌ× âð ßëãžæ×) ·¤æð ÂýSÌéÌ ·¤ÚUÌè ãñ?
O22, S22, N32, P32 ?
(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

48. Global warming is due to increase of : 48. â´âæçÚU·¤ ©žææÂÙ ·¤æ ·¤æÚU‡æ ãæðÌæ ãñ ßæØéׇÇUÜ ×ð´
ÕɸÙæ Ñ
(1) methane and nitrous oxide in (1) ×èÍðÙ ¥æñÚU Ùæ§ÅþUâ ¥æò€âæ§ÇU ·¤æÐ
atmosphere
(2) methane and CO2 in atmosphere (2) ×èÍðÙ ¥æñÚU CO2 ·¤æÐ
(3) methane and O3 in atmosphere (3) ×èÍðÙ ¥æñÚU O3 ·¤æÐ
(4) methane and CO in atmosphere (4) ×èÍðÙ ¥æñÚU CO ·¤æÐ

49. Hydrogen peroxide acts both as an 49. ãæ§ÇþUæðÁÙ ÂÚU¥æò€âæ§ÇU ¥Â¿æØ·¤ ÌÍæ ©Â¿æØ·¤ ÎæðÙæð´
oxidising and as a reducing agent Âý·¤æÚU âð ÃØßãæÚU ·¤ÚUÌæ ãñ ¥æñÚU Øã çÙÖüÚU ·¤ÚUÌæ ãñ
depending upon the nature of the reacting ¥çæç·ý¤Øæ ·¤ÚUÙð ßæÜð SÂèàæè$Á ·ð¤ SßæÖæß ÂÚUÐ çِÙ
species. In which of the following cases ×ð́ âð ç·¤â·ð¤ âæÍ H2O2 ¥ÜèØ ×æŠØ× ×ð́ ¥Â¿æØ·¤
H 2 O 2 acts as a reducing agent in acid ·ð¤ M¤Â ×ð´ ç·ý¤Øæ ·¤ÚUÌæ ãñ?
medium ?
(1) MnO42 (1) MnO42
22 22
(2) Cr2 O 7 (2) Cr2 O 7
22 22
(3) SO 3 (3) SO 3
(4) KI (4) KI

English : 23 Set : 06 Hindi : 23 Set : 06

50. Which one of the following complexes will 50. çِ٠·¤æòŒÜð€âæð´ (â´·¤ÚUæð´) ×ð´ âð ·¤æñÙ ÎëàØ Âý·¤æàæ ·¤æð
most likely absorb visible light ? ¥ßàææðçáÌ ·¤ÚUÙð ·¤è âßæüçÏ·¤ â´ÖæßÙæ ÚU¹Ìæ ãñ?
(At nos. Sc521, Ti522, V523, Zn530) ( ÂÚU × æ‡æé ·ý ¤ ×æ´ · ¤ Sc521, Ti522, V523,
(1) [Sc(H2O)6]31 Zn530)
(2) [Ti (NH3)6]41 (1) [Sc(H2O)6]31
(3) [V(NH3)6]31 (2) [Ti (NH3)6]41
(4) [Zn(NH3)6]21 (3) [V(NH3)6]31
(4) [Zn(NH3)6]21

51. on mercuration-
51. ×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. ç߀ÅUÚU ×ðØÚU ·ð¤ ÂÚUèÿæ‡æ ç·ý¤Øæ ×ð´ 18, 28 ¥æñÚU 38 ·ð¤
(1) Red, colourless, blue °ðË·¤æðãæÜæð´ mæÚUæ çÎØæ Ú´U» ·ý¤×æÙéâæÚU ãæðÌæ ãñ Ñ
(2) Red, blue, colourless (1) ÜæÜ, Ú´U»ãèÙ, ÙèÜæ
(3) Colourless, red, blue (2) ÜæÜ, ÙèÜæ, Ú´U»ãèÙ
(4) Red, blue, violet (3) Ú´U»ãèÙ, ÜæÜ, ÙèÜæ
(4) ÜæÜ, ÙèÜæ, Áæ×Ùè

English : 24 Set : 06 Hindi : 24 Set : 06

53. Conversion of benzene diazonium chloride 53. Õñ‹$ÁèÙ ÇUæØæ$ÁæðçÙØ× €ÜæðÚUæ§ÇU ·¤æ €ÜæðÚUæð Õñ‹$ÁèÙ ×ð´
to chloro benzene is an example of which ÕÎÜÙæ §Ù×ð´ âð 緤⠥çÖç·ý¤Øæ ·¤æ ©ÎæãÚU‡æ ãæðÌæ
of the following reactions ? ãñ?
(1) Claisen (1) €Üð$ÁÙ
(2) Friedel-craft (2) Èý¤èÇUÜ-·ý¤æ$$ÅU
(3) Sandmeyer (3) âñ´ÇU×æØÚU
(4) Wurtz (4) ßéÅ÷üU $Á
54. In the presence of peroxide, HCl and HI 54. ÂÚU¥æò€âæ§ÇU ·¤è ©ÂçSÍçÌ ×ð´ °ðË·¤èÙæð´ ·¤æð HCl ¥æñÚU
do not give anti-Markownikoff’s addition 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 ¥æñ Ú U HI ·ð ¤ âÕ‹Ï ×ð ´ °·¤ ¿ÚU ‡ æ
HCl and HI ª¤c×æàææðáè ãñÐ
(2) Both HCl and HI are strong acids (2) HCl ¥æñÚU HI ÎæðÙæð´, ÂýÕÜ ¥Ü ãñ´Ð
(3) HCl is oxidizing and the HI is (3) HCl ©Â¿æØ·¤ ¥æñÚU HI ¥Â¿æØ·¤ ãñÐ
reducing
(4) All the steps are exothermic in HCl (4) HCl ¥æñÚU HI ·ð¤ âÕ‹Ïæð´ ×ð´ âÖè ¿ÚU‡æ
and HI ª¤c×æÂýÎ ãñ´Ð

55. The major product obtained in the photo 55. 2- ×ðçÍ܎ØéÅðUÙ ·ð¤ Âý·¤æàæ mæÚUæ ©ˆÂýðçÚUÌ Õýæð×èÙðàæÙ ×ð´
catalysed bromination of 2-methylbutane ÕǸæ ç·ý¤ØæÈ¤Ü ãæðÌæ ãñ Ñ
is :
(1) 1-bromo-2-methylbutane (1) 1-Õýæð×æð-2-×ðçÍ܎ØéÅðUÙ
(2) 1-bromo-3-methylbutane (2) 1-Õýæð×æð-3-×ðçÍ܎ØéÅðUÙ
(3) 2-bromo-3-methylbutane (3) 2-Õýæð×æð-3-×ðçÍËæŽØéÅðUÙ
(4) 2-bromo-2-methylbutane (4) 2-Õýæð×æð-2-×ðçÍ܎ØéÅðUÙ

English : 25 Set : 06 Hindi : 25 Set : 06

56. Which of the following molecules has two 56. çِ٠¥‡æé¥æð´ ×ð´ âð 緤⠥‡æé ×ð´ Îæð çâ‚×æ (s) ¥æñÚU Îæð
sigma(s) and two pi(p) bonds ? Âæ§ü (p) ¥æÕ‹Ï ãæðÌð ãñ´?
(1) C 2H 4 (1) C2H 4
(2) N2F2 (2) N2F2
(3) C2H2Cl2 (3) C2H2Cl2
(4) HCN (4) HCN

57. Which one of the following acids does not 57. çِ٠¥Üæð´ ×ð´ âð ·¤æñÙ Âý·¤æàæèØ â×æßØßÌæ Ùãè´
exhibit optical isomerism ? çιæÌæ?
(1) Lactic acid (1) Üñç€ÅU·¤ °ðçâÇU
(2) Tartaric acid (2) ÅUæÚUÅñUçÚU·¤ °çâÇU
(3) Maleic acid (3) ×ñÜè·¤ °çâÇU
(4) a-amino acids (4) a- °×æØÙæð´ °ðçâÇU
58. Aminoglycosides are usually used as : 58. ¥×æØÙæð‚Ü槷¤æðâæ§ÇUæð´ ·¤æð ÂýæØÑ çِ٠緤â Âý·¤æÚU
ÂýØæð» ç·¤Øæ ÁæÌæ ãñ?
(1) antibiotic (1) °ð‹ÅUè ÕæØæðçÅU·¤ M¤Â ×ð´ (ÂýçÌ Áñçß·¤)
(2) analgesic (2) °ðÙÜÁñçâ·¤ M¤Â ×ð´ (ÂèǸæ Ùæàæ·¤)
(3) hypnotic (3) çãÂÙæçÅU·¤ M¤Â ×ð´ (çÙÎýæ ÂýÎ)
(4) antifertility (4) °ð‹ÅUè ȤÚUçÅUçÜÅUè M¤Â ×ð´ (°ð‹ÅUè çÙáð¿·¤)

59. Which of the following will not show 59. §Ù×ð´ âð ·¤æñÙ ØêÅUæÚUæðÅðUàæÙ Ùãè´ çιæØð»æ?
mutarotation ?
(1) Maltose (1) ×æËÅUæð$Á
(2) Lactose (2) Üñ€ÅUæð$Á
(3) Glucose (3) ‚Üê·¤æð$Á
(4) Sucrose (4) âê·ý¤æð$Á

English : 26 Set : 06 Hindi : 26 Set : 06

60. Phthalic acid reacts with resorcinol in the 60. âæ‹Îý H 2SO4 ·¤è ©ÂçSÍçÌ ×ð ´ Íñ ç Ü·¤ °ð ç âÇU
presence of concentrated H2SO4 to give : çÚU$ÁæÚUâèÙæÜ âð ¥çÖç·ý¤Øæ ·¤ÚU ÎðÌæ ãñ Ñ
(1) Phenolphthalein (1) çȤÙæËȤÍðÜèÙ
(2) Alizarin (2) °ðçÜ$ÁðÚUèÙ
(3) Coumarin (3) ·é¤×ýèÙ
(4) Fluorescein (4) $ÜæðÚðUâèÙ

English : 27 Set : 06 Hindi : 27 Set : 06

PART C — MATHEMATICS Öæ» C — »ç‡æÌ
61. A relation on the set A5{x : ?x? < 3, xeZ}, 61. â×é“æØ A5{x : ?x? < 3, xeZ}, Áãæ¡ Z Âê‡ææZ·¤æð´ ·¤æ
where Z is the set of integers is defined by â×é “ æØ ãñ , ÂÚU °·¤ â´ Õ ´ Ï R,
R5{(x, y) : y 5? x ? , x ≠2 1 }. Then the R5{(x, y) : y5?x?, x ≠2 1 } mæÚUæ ÂçÚUÖæçáÌ ãñÐ
number of elements in the power set of R Ìæð R ·ð¤ ƒææÌ â×é“æØ ×ð´ ¥ßØßæð´ ·¤è ⴁØæ ãñ Ñ
is :
(1) 32 (1) 32
(2) 16 (2) 16
(3) 8 (3) 8
(4) 64 (4) 64

62. Let z ¹ 2i be any complex number such 62. ×æÙæ z ¹ 2i ·¤æð§ü °ðâè âç×Ÿæ ⴁØæ ãñ ç·¤
z2 i z2 i
that
z1 i
is a purely imaginary number.
z1 i
°·¤ àæé h ·¤æËÂçÙ·¤ â´  Øæ ãñ , Ìæð
1 1
Then z1
z
is : z1
z
ãñ Ñ
(1) 0 (1) 0
(2) any non-zero real number other (2) 1 ·ð¤ ¥çÌçÚU€ˆæ ·¤æð§ü àæê‹ØðžæÚU ßæSÌçß·¤ ⴁØæÐ
than 1.
(3) any non-zero real number. (3) ·¤æð§ü àæê‹ØðžæÚU ßæSÌçß·¤ ⴁØæÐ
(4) a purely imaginary number. (4) °·¤ àæéh ·¤æËÂçÙ·¤ ⴁØæÐ

63. The sum of the roots of the equation, 63. â×è·¤ÚU ‡ æ x21?2x23?2450, ·ð ¤ ×ê Ü æð ´ ·¤æ
x21?2x23?2450, is : Øæð»È¤Ü ãñ Ñ
(1) 2 (1) 2
(2) 22 (2) 22
(3) 2 (3) 2
(4) 2 2 (4) 2 2

English : 28 Set : 06 Hindi : 28 Set : 06

64. If 64. ØçÎ
a2 b2 c2 a2 b2 c2 a2 b2 c2 a2 b2 c2
( a1l )2 ( b1l )2 )2
( c1l 5k l a b c , l ≠ 0, ( a1l )2 ( b1l )2 )2
( c1l 5k l a b c , l ≠ 0,
( a2l )2 ( b2l )2 ( c2l )2 1 1 1 ( a2l )2 ( b2l )2 ( c2l )2 1 1 1

then k is equal to : ãñ, Ìæð k ÕÚUæÕÚU ãñ Ñ
(1) 4labc (1) 4labc
(2) 24labc (2) 24labc
(3) 4l2 (3) 4l2
(4) 24l2 (4) 24l2

y  y 
1 2 x 1 2 x
65. If A 5   and B 5  x  be such 65. ØçÎ A 5   
 ÌÍæ B 5  x  °ðâð ãñ´ ç·¤
 3 21 2    3 21 2
 1     1 

6  6 
that AB 5   , then : AB 5   , ãñ, Ìæð Ñ
8  8 
(1) y52x (1) y52x
(2) y522x (2) y522x
(3) y5x (3) y5x
(4) y52x (4) y52x

66. 8 - digit numbers are formed using the 66. ¥´·¤æð´ 1, 1, 2, 2, 2, 3, 4, 4 ·ð¤ ÂýØæð» âð, ¥æÆU ¥´·¤èØ
digits 1, 1, 2, 2, 2, 3, 4, 4. The number of ⴁØæ°¡ ÕÙæ§ü »§ü ãñд °ðâè ⴁØæ¥æð´ ·¤è ⴁØæ çÁÙ×ð´
such numbers in which the odd digits do 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

55
 x x  55
67. If  2 1  is expanded in the ascending 67. ØçÎ  2 1  ·¤æ x ·¤è ¥æÚUæðãè ƒææÌæð´ ×ð´ ÂýâæÚU
 3  3
powers of x and the coefficients of powers ·¤ÚUÙð ÂÚU, ÂýâæÚU ×ð´ Îæð ·ý¤ç×·¤ ÂÎæð´ ×ð´ x ·¤è ƒææÌð´ â×æÙ
of x in two consecutive terms of the ãñ´, Ìæð Øã ÂÎ ã´ñ Ñ
expansion are equal, then these terms
are :
(1) 7th and 8th (1) 7 ßæ¡ ÌÍæ 8 ßæ¡
(2) 8th and 9th (2) 8 ßæ¡ ÌÍæ 9 ßæ¡
(3) 28th and 29th (3) 28 ßæ¡ ÌÍæ 29 ßæ¡
(4) 27th and 28th (4) 27 ßæ¡ ÌÍæ 28 ßæ¡

68. 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 ÌÍæ 1 ·¤æ â×æ‹ÌÚU ×æŠØ M ãñÐ ØçÎ
1 1 a b
arithmetic mean of 1 and . If : G is
a b M 1
: G 5 4 : 5 ãñ, Ìæð a : b ãæð â·¤Ìð ãñ´ Ñ
4 : 5, then a : b can be : M
(1) 1:4 (1) 1 : 4
(2) 1:2 (2) 1:2
(3) 2:3 (3) 2:3
(4) 3:4 (4) 3:4
69. The least positive integer n such that 69. ÏÙ Âê‡ææZ·¤ n ·¤æ ß㠋ØêÙÌ× ×æÙ çÁâ·ð¤ çÜØð
2 2 2 1 2 2 2 1
12 2 2 2........ 2 n21 < , is : 12 2 2 2........ 2 n21 < , ãñ, ãñ Ñ
3 3 3 100 3 3 3 100
(1) 4 (1) 4
(2) 5 (2) 5
(3) 6 (3) 6
(4) 7 (4) 7

English : 30 Set : 06 Hindi : 30 Set : 06

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

English : 31 Set : 06 Hindi : 31 Set : 06

72. Let f and g be two differentiable functions 72. ×æÙæ R ÂÚU f ÌÍæ g Îæð °ðâð ¥ß·¤ÜÙèØ È¤ÜÙ ãñ ç·¤
on R such that f 9(x) > 0 and g9(x) < 0, for âÖè x e R ·ð¤ çÜ° f 9(x) > 0 ÌÍæ g9(x) < 0 ãñ, Ìæð
all x e R. Then for all x : 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))

5 73. ØçÎ âÖè x e R ·ð¤ çÜ°
If 11x41x55 ∑ ai ( 1 1 x ) , for all x in R,
i
73. 5
11x41x55 ∑ ai ( 1 1 x )
i
i50 ãñ, Ìæð a2 ãñ Ñ
then a2 is : i50
(1) 24 (1) 24
(2) 6 (2) 6
(3) 28 (3) 28
(4) 10 (4) 10

sin 2 x cos2 x sin 2 x cos 2 x
74. The integral ∫( 2
d x is 74. â×æ·¤Ü ∫ d x ÕÚUæÕÚU ãñ Ñ
sin x 1 cos x )
3 3 ( sin 3 x 1 cos3 x )2
equal to :
1 1
(1) 1c (1) 1c
( 1 1 cot x )
3 ( 1 1 cot 3 x )
1 1
(2) 2 1c (2) 2 1c
3 ( 1 1 tan 3 x ) 3 ( 1 1 tan 3 x )

sin 3 x sin 3 x
(3) 1c (3) 1c
( 1 1 cos3 x ) ( 1 1 cos3 x )
cos 3 x cos 3 x
(4) 2 1c (4) 2 1c
3 ( 1 1 sin 3 x ) 3 ( 1 1 sin 3 x )

English : 32 Set : 06 Hindi : 32 Set : 06

75. If [ ] denotes the greatest integer function, 75. ØçÎ [ ] °·¤ ×ãžæ× Âê ‡ ææZ · ¤èØ È¤ÜÙ ãñ , Ìæð
p p
then the integral ∫ [ cos x ] d x is equal to :
0
â×æ·¤Ü ∫ 0 [ cos x ] d x ÕÚUæÕÚU ãñ Ñ
p p
(1) (1)
2 2
(2) 0 (2) 0
(3) 21 (3) 21
p p
(4) 2 (4) 2
2 2

76. If for a continuous function f(x), 76. ØçÎ °·¤ âÌÌ È¤ÜÙ f(x) ·ð¤ çÜ°, âÖè
t t /2p ·ð¤ çÜ°
2 2
∫ ( f ( x ) 1 x)d x 5 p 2 t , for all t
2 2
2p
∫ ( f ( x ) 1 x)d x 5 p 2 t ãñ , Ìæð
2p
 p
t/2p, then f 2  is equal to :
 3  p
f 2  ÕÚUæÕÚU ãñ Ñ
 3
(1) p
(1) p p
(2)
p 2
(2)
2 p
(3)
p 3
(3)
3 p
(4)
p 6
(4)
6

English : 33 Set : 06 Hindi : 33 Set : 06

77. The general solution of the differential 77. ¥ß·¤Ü â×è·¤ÚU‡æ
dy dy
equation, sin 2x  2

tan x 2 y 5 0 , sin 2x  2

tan x 2 y 5 0 ·¤æ ÃØæ·¤
 dx   dx 
is : ãÜ ãñ Ñ
(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
78. If a line intercepted between the coordinate 78. çÙÎðüàææ´·¤ ¥ÿææð´ ·ð¤ Õè¿ ¥´Ìѹ´çÇUÌ °·¤ ÚðU¹æ, °·¤
axes is trisected at a point A(4, 3), which çÕ´Îé A(4, 3) Áæð x- ¥ÿæ ·ð¤ Âæâ ãñ, ÂÚU Sæ×ç˜æÖæçÁÌ
is nearer to x-axis, then its equation is : ãæðÌè ãñ, Ìæð ©â·¤æ â×è·¤ÚU‡æ ãñ Ñ
(1) 4x23y57 (1) 4x23y57
(2) 3x12y518 (2) 3x12y518
(3) 3x18y536 (3) 3x18y536
(4) x13y513 (4) x13y513

79. If the three distinct lines x12ay1a50, 79. ØçÎ ÌèÙ çßçÖóæ Úð U ¹æ°¡ x12ay1a50,
x13by1b50 and x14ay1a50 are x13by1b50 ÌÍæ x14ay1a50 â´»æ×è ã´ñ,
concurrent, then the point (a, b) lies on a : Ìæð çÕ´Îé (a, b) °·¤ Ñ
(1) circle (1) ßëžæ ÂÚU çSÍÌ ãñ
(2) hyperbola (2) ¥çÌ ÂÚUßÜØ ÂÚU çSÍÌ ãñ
(3) straight line (3) âÚUÜ ÚðU¹æ ÂÚU çSÍÌ ãñ
(4) parabola (4) ÂÚUßÜØ ÂÚU çSÍÌ ãñ

English : 34 Set : 06 Hindi : 34 Set : 06

80. For the two circles x 2 1y 2 516 and 80. Îæð ßëžææð´ x21y2516 ÌÍæ x21y222y50, ·ð¤
x21y222y50, there is/are : çÜ° ãñ/ã´ñ Ñ
(1) one pair of common tangents (1) ©ÖØçÙcÆU SÂàæü ÚðU¹æ¥æð´ ·¤æ °·¤ Øé‚×Ð
(2) two pairs of common tangents (2) ©ÖØçÙcÆU SÂàæü ÚðU¹æ¥æð´ ·ð¤ Îæð Øé‚×Ð
(3) three common tangents (3) ÌèÙ ©ÖØçÙcÆU SÂàæü ÚðU¹æ°´Ð
(4) no common tangent (4) ·¤æð§ü ©ÖØçÙcÆU SÂàæü ÚðU¹æ Ùãè´Ð

81. Two tangents are drawn from a point 81. °·¤ çÕ´Îé (22, 21) âð °·¤ ß·ý¤ y254x ÂÚU Îæð
(22, 21) to the curve, y254x. If a is the SÂàæü ÚðU¹æ°¡ ¹è´¿è »§ü ãñ, ØçÎ ©Ù·ð¤ Õè¿ ·¤æ ·¤æð‡æ a
angle between them, then ?tan a? is equal ãñ, Ìæð ?tan a? ÕÚUæÕÚU ãñ Ñ
to :
1 1
(1) (1)
3 3
1 1
(2) (2)
3 3
(3) 3 (3) 3
(4) 3 (4) 3
82. The minimum area of a triangle formed
x2 y2
by any tangent to the ellipse 82. Îèƒæüßëžæ 1 5 1 ÂÚU ¹è´¿è »§ü ç·¤âè SÂàæü
16 81
x2 y2 ÚðU¹æ ÌÍæ çÙÎðüàææ´·¤ ¥ÿææð´ mæÚUæ ÕÙè ç˜æÖéÁ ·¤æ ‹ØêÙÌ×
1 5 1 and the co-ordinate axes
16 81 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. â×ÌÜæð´ x5ay1b ÌÍæ z5cy1d ·¤è Âýç̑ÀðUÎè
intersection of the planes x5ay1b and ÚðU¹æ ·¤æ â×ç×Ì M¤Â ãñ Ñ
z5cy1d is :
x2b y 21 z2d x2b y 21 z2d
(1) 5 5 (1) 5 5
a 1 c a 1 c
x 2 b2 a y 21 z 2 d2 c x 2 b2 a y 21 z 2 d2 c
(2) 5 5 (2) 5 5
a 1 c a 1 c
x2a y 20 z2c x2a y 20 z2c
(3) 5 5 (3) 5 5
b 1 d b 1 d
x 2 b2 a y 21 z 2 d2 c x 2 b2 a y 21 z 2 d2 c
(4) 5 5 (4) 5 5
b 0 d b 0 d

84. If the distance between planes, 84. ØçÎ â×ÌÜæð ´ 4x22y24z1150 ÌÍæ
4x22y24z1150 and 4x22y24z1d50 ·ð¤ Õè¿ ·¤è ÎêÚUè 7, Ìæð d ãñ Ñ
4x22y24z1d50 is 7, then d is :
(1) 41 or 242 (1) 41 ¥Íßæ 242
(2) 42 or 243 (2) 42 ¥Íßæ 243
(3) 241 or 43 (3) 241 ¥Íßæ 43
(4) 242 or 44 (4) 242 ¥Íßæ 44
∧ ∧ ∧ ∧ ∧ ∧
85. If x , y and z are three unit vectors in 85. ØçÎ ç˜æ-çß×èØ ¥æ·¤æàæ ×ð´ x , y ÌÍæ z ÌèÙ ×æ˜æ·¤
three-dimensional space, then the ∧ ∧ ∧ ∧ ∧ ∧
âçÎàæ ãñ´, Ìæð ?x 1 y?2 1 ?y 1 z?2 1 ?z 1 x?2
minimum value of
∧ ∧ ∧ ∧ ∧ ∧ ·¤æ ‹ØêÙÌ× ×æÙ ãñ Ñ
?x 1 y?2 1 ?y 1 z?2 1 ?z 1 x?2 is :
3 3
(1) (1)
2 2
(2) 3 (2) 3
(3) 3 3 (3) 3 3
(4) 6 (4) 6

English : 36 Set : 06 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 X ÌÍæ
deviation about X of n observations X ·ð¤ âæÂðÿæ ©Ù·¤æ ×æŠØ çß¿ÜÙ M.D. ãñÐ ØçÎ
xi, i51, 2, ....., n. If each of the observations ÂýˆØð·¤ Âýðÿæ‡æ ×ð´ 5 Õɸæ çÎØæ Áæ° Ìæð ÙØæ ×æŠØ ÌÍæ
is increased by 5, then the new mean and ‹æØð ×æŠØ ·ð¤ âæÂðÿæ ©Ù·¤æ ×æŠØ çß¿ÜÙ ·ý¤×àæÑ ãñ Ñ
the mean deviation about the new mean,
respectively, are :
(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

87. A number x is chosen at random from the 87. â×é“æØ {1, 2, 3, 4, ....., 100} ×ð´ âð °·¤ ⴁØæ x
set {1, 2, 3, 4, ....., 100}. Define the ØæÎë‘ÀUØæ ¿éÙè »§üÐ ƒæÅUÙæ A ·¤æð ÂçÚUÖæçáÌ ·¤èçÁ° Ñ
event : A5 the chosen number x satisfies A5 ¿éÙè »§ü ⴁØæ x

( x 2 10) ( x 2 50) ( x 2 10) ( x 2 50)
/0 / 0 ·¤æð â´ÌécÅ ·¤ÚUÌè ãñÐ
( x 2 30) ( x 2 30)

Then P(A) is : Ìæð P(A) ãñ Ñ
(1) 0.71 (1) 0.71
(2) 0.70 (2) 0.70
(3) 0.51 (3) 0.51
(4) 0.20 (4) 0.20

English : 37 Set : 06 Hindi : 37 Set : 06

88. Statement I : The equation 88. ·¤ÍÙ I : â×è·¤ÚU‡æ
(sin 21 x) 3 1(cos 21 x) 3 2ap 3 50 has a (sin21x)31(cos21x)32ap350 ·¤æ âÖè

solution for all a/ 1 . a/
1
·ð¤ çÜ° °·¤ ãÜ ãñÐ
32 32
Statement II : For any x e R, ·¤ÍÙ II : ç·¤âè x e R ·ð¤ çÜ°
p p
sin21x1cos21x5
2
and sin21x1cos21x5
2
ÌÍæ

 21 p 2 9p2  21 p 2 9p2
0 [  sin x2  [ . 0 [  sin x2  [ .
 4 16  4 16
(1) Both statements I and II are true. (1) ·¤ÍÙ I ÌÍæ II ÎæðÙæð´ âˆØ ãñ´Ð
(2) Both statements I and II are false. (2) ·¤ÍÙ I ÌÍæ II ÎæðÙæð´ ¥âˆØ ãñ´Ð
(3) Statement I is true and (3) ·¤ÍÙ I âˆØ ãñ ÌÍæ ·¤ÍÙ II ¥âˆØ ãñÐ
statement II is false.
(4) Statement I is false and (4) ·¤ÍÙ I ¥SæˆØ ãñ, ÌÍæ ·¤ÍÙ II âˆØ ãñÐ
statement II is true.

1 cos u 1 1 cos u 1
89. If f (u) 5 2sin u 1 2cos u and 89. ØçÎ f (u) 5 2sin u 1 2cos u ãñ,
21 sin u 1 21 sin u 1

A and B are respectively the maximum and ÌÍæ A ÌÍæ B ·ý¤×àæÑ f (u) ·ð¤ ¥çÏ·¤Ì× ÌÍæ
the minimum values of f (u), then ‹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 , 2 2 2 ) (2) (4, 22 2 )

(4) ( 21 2 , 21 ) (3) ( 21 2 , 2 2 2 )
(4) ( 21 2 , 21 )

English : 38 Set : 06 Hindi : 38 Set : 06

90. Let p, q, r denote arbitrary statements. Then 90. ×æÙæ p, q, r Sßð ‘ ÀU ·¤ÍÙ Îàææü Ì ð ãñ ´ Ð ·¤ÍÙ
the logically equivalent of the 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- -o0o-

English : 39 Set : 06 Hindi : 39 Set : 06