JEE Main 2015 Question Paper 10 Apr B.Tech with Answer Key

JEE Main 2015
Question Paper & Answers

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JEE Main Question Paper 10 Apr 2015

Page 1 PHYSICS : English & Hindi 09
1. x and y displacements of a particle are 1. ØçÎ ç·¤âè ·¤‡æ ·ð¤ x ÌÍæ y çßSÍæÂÙæð´ ·¤æð ·ý¤×àæÑ,
given as x(t)5a sinvt and y(t)5a sin2vt.
x(t)5a sinvt ÌÍæ y(t)5a sin2vt, âð çÙM¤çÂÌ
Its trajectory will look like :
ç·¤Øæ ÁæÌæ ãñ Ìæð, §â·¤æ Âýÿæð - ÂÍ, çِÙæ´ç·¤Ì ×ð´ âð
ç·¤â·ð¤ Áñâæ çιæ§ü Îð»æ?

(1)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

Page 2 PHYSICS : English & Hindi 09
2. If a body moving in a circular path 2. ØçÎ ßëžææ·¤æÚU ÂÍ ×ð´ »çÌ ·¤ÚUÌð ãé° ç·¤âè ç´ÇU (ßSÌé)
maintains constant speed of 10 ms21, then
·¤è ¿æÜ 10 ms21 ãñ ¥æñÚU Øã ¥¿ÚU ÕÙè ÚUãÌè ãñ Ìæð,
which of the following correctly describes
relation between acceleration and çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙâæ ¥æÜð¹, ˆßÚU‡æ ÌÍæ ç˜æ’Øæ ·ð¤
radius ? Õè¿ âÕ‹Ï ·¤æ ÆUè·¤ (âãè) 翘æ‡æ ·¤ÚUÌæ ãñ?

(1) (1)

(2) (2)

(3) (3)

(4) (4)

Page 3 PHYSICS : English & Hindi 09
3. A block of mass m510 kg rests on a 3. ç·¤âè ŽÜæò·¤ (»éÅU·ð¤) ·¤æ ÎýÃØ×æÙ m510 kg ãñÐ
horizontal table. The coefficient of friction
Øã °·¤ ÿæñçÌÁ ×ðÁ ÂÚU ÚU¹æ ãñÐ §Ù ÎæðÙæð´ ·ð¤ Õè¿
between the block and the table is 0.05.
When hit by a bullet of mass 50 g moving ƒæáü‡æ »é‡ææ´·¤50.05 ãñÐ §â ŽÜæò·¤ ÂÚU 50 g ÎýÃØ×æÙ
with speed v, that gets embedded in it, the ·¤è °·¤ »æðÜè v ¿æÜ âð ÅU·¤ÚUæÌè ¥æñÚU §â×ð´ Ï´â
block moves and comes to stop after ÁæÌè ãñÐ §ââð Ø㠎Üæò·¤, ×ðÁ ÂÚU 2 m çßSÍæçÂÌ
moving a distance of 2 m on the table.
ãæð·¤ÚU L¤·¤ ÁæÌæ ãñÐ
If a freely falling object were to acquire
ØçÎ, H ª¡¤¿æ§ü âð ×é€Ì M¤Â âð ç»ÚUæÙð ·ð¤ Âà¿æÌ÷ ·¤æð§ü
speed after being dropped from height
v
10 ßSÌé v
¿æÜ ÂýæŒÌ ·¤ÚU ÜðÌè ãñ Ìæð, ª¤Áæü-ÿæØ ·¤æð
H, then neglecting energy losses and 10
taking g510 ms22, the value of H is close Ù»‡Ø ×æÙÌð ãé°, H ·¤æ âç‹Ù·¤ÅU ×æÙ ãæð»æ Ñ
to : (g510 ms22)
(1) 0.2 km (1) 0.2 km
(2) 0.3 km (2) 0.3 km
(3) 0.4 km (3) 0.4 km
(4) 0.5 km (4) 0.5 km

4. A block of mass m50.1 kg is connected to 4. ç·¤âè ŽÜæò·¤ ·¤æ ÎýÃØ×æÙ m50.1 kg ãñÐ Øã °·¤
a spring of unknown spring constant k. It
is compressed to a distance x from its °ðâè ·¤×æÙè (çSÂý»´ ) âð ÁéÇæ¸ ãñ çÁâ·¤æ ·¤×æÙè çSÍÚUæ·´ ¤
equilibrium position and released from rest. k ãñÐ §â·¤æð §â·¤è âæØæßSÍæ âð x ÎêÚUè Ì·¤ ÎÕæ·¤ÚU
çßÚUæ×æßSÍæ âð ÀUæðǸ çÎØæ ÁæÌæ ãñÐ âæØæßSÍæ âð
After approaching half the distance  
x
2  x  ÎêÚUè ÂÚU ¥æÙð ÂÚU Øã °·¤ ¥‹Ø ŽÜæò·¤ âð ÅU·¤ÚUæÌæ
from equilibrium position, it hits another
 
2
block and comes to rest momentarily, while
ãñ ¥æñÚU ÿæç‡æ·¤ M¤Â âð L¤·¤ ÁæÌæ ãñ, ÁÕç·¤, ÎêâÚUæ
the other block moves with a velocity
3 ms 21. The total initial energy of the ŽÜæò·¤ 3 ms21 ·ð¤ ßð» âð »çÌ ·¤ÚUÙð Ü»Ìæ ãñÐ Ìæð,
spring is : ·¤×æÙè ·¤è ·é¤Ü ÂýæÚ´UçÖ·¤ ª¤Áæü ãñ Ñ
(1) 1.5 J (1) 1.5 J
(2) 0.6 J (2) 0.6 J
(3) 0.3 J (3) 0.3 J
(4) 0.8 J (4) 0.8 J

5. A uniform solid cylindrical roller of mass 5. ‘m’ ÎýÃØ×æÙ ·ð¤ ç·¤âè °·¤â×æÙ ÆUæðâ çâç܋ÇUÚU ·ð¤
‘m’ is being pulled on a horizontal surface
with force F parallel to the surface and
·ð¤‹Îý ÂÚU °·¤ ÕÜ F ܻ淤ÚU, ©âð ç·¤âè â×ÌÜ
applied at its centre. If the acceleration of âÌã ÂÚU, ©â·ð¤ â×æ‹ÌÚU ¹è´¿æ Áæ ÚUãæ ãñÐ ØçÎ Øã
the cylinder is ‘a’ and it is rolling without çâç܋ÇUÚU Õ»ñÚU (çÕÙæ) çȤâÜð ‘a’ ˆßÚU‡æ âð Üéɸ·¤
slipping then the value of ‘F’ is : ÚUãæ ãñ Ìæð, ‘F’ ·¤æ ×æÙ ãæð»æ Ñ
(1) ma
(1) ma
(2) 2 ma
(2) 2 ma

(3)
3
(3)
ma 3
2 ma
2

(4)
5
(4)
ma 5
3 ma
3

Page 4 PHYSICS : English & Hindi 09
6. Consider a thin uniform square sheet made 6. °·¤ ÂÌÜè, °·¤â×æÙ, ß»æü·¤æÚU, ¿æÎÚU (àæèÅU) ç·¤âè
of a rigid material. If its side is ‘a’, mass m
Îëɸ ÂÎæÍü ·¤è ÕÙè ãñÐ ØçÎ §â·¤è °·¤ ÖéÁæ ‘a’,
and moment of inertia I about one of its
diagonals, then : ÎýÃØ×æÙ m ÌÍæ ç·¤âè °·¤ çß·¤‡æü ·ð¤ ÂçÚUÌÑ, §â·¤æ
ÁǸˆß ¥æƒæê‡æü I ãñ Ìæð Ñ
(1)
ma 2
I>
(1)
12 ma 2
I>
12
(2)
ma 2 ma 2
<I<
(2)
24 12 ma 2 ma 2
<I<
24 12
(3)
ma 2
I5
(3)
12 ma 2
I5
12
(4)
ma 2
I5
(4)
24 ma 2
I5
24
7. A very long (length L) cylindrical galaxy
is made of uniformly distributed mass and 7. °·¤ ÕãéÌ ÜÕè »ñÜð€âè (×´Îæç·¤Ùè) (ܐÕæ§ü L)
has radius R (R<<L). A star outside the
galaxy is orbiting the galaxy in a plane
°·¤â×æÙ çßÌçÚUÌ ÎýÃØ ·¤è ÕÙè ãñ, §â·¤è ç˜æ’Øæ
perpendicular to the galaxy and passing R (R<<L) ãñÐ §â »ñÜð€âè ·ð¤ ÕæãÚ °·¤ ÌæÚUæ,
through its centre. If the time period of star »ñÜð€âè ·¤è ÂçÚU·ý¤×æ ·¤ÚU ÚUãæ ãñÐ §â·¤è ÂçÚU·ý¤×æ ·¤æ
is T and its distance from the galaxy’s axis â×ÌÜ »ñÜð€âè ·ð¤ â×ÌÜ ·ð¤ ܐÕßÌ÷ ãñ ÌÍæ §â·ð¤
is r, then :
·ð¤‹Îý âð ãæð·¤ÚU »é$ÁÚUÌæ ãñÐ ØçÎ, ÌæÚðU ·¤è »ñÜð€âè ·¤è
(1) T2 ; r3
¥ÿæ âð ÎêÚUè r ãñ ¥æñÚU ÌæÚðU ·¤æ ¥æßÌü ·¤æÜ T ãñ Ìæð ÑU
(2) T ; r2
(1) T2 ; r3
(3) T;r
(2) T ; r2
(4) T; r (3) T;r
(4)
If it takes 5 minutes to fill a 15 litre bucket
T; r
8.

from a water tap of diameter cm then
2

ÂæÙè ·ð¤ ÙÜ ·¤è °·¤ ÅUæð´ÅUè ·¤æ ÃØæâ cm ãñÐ
p 2
8.
the Reynolds number for the flow is p
(density of water510 3 kg/m 3 and §ââð 15 çÜÅUÚU ·¤è °·¤ ÕæËÅUè ·¤æð ÖÚUÙð ×ð´ 5 ç×ÙÅU
viscosity of water51023 Pa.s) close to :
·¤æ â×Ø Ü»Ìæ ãñ Ð (ØçÎ, ÁÜ ·¤æ
(1) 5500 ƒæوß5103 kg/m3 ÌÍæ ÁÜ ·¤è àØæÙÌæ51023
(2) 11,000 Pa.s ãñ) Ìæð, §â Âýßæã ·ð¤ çÜØð ÚðUÙËÇ÷Uâ ⴁØæ
(3) 550 ãæð»è Ñ
(4) 1100 (1) 5500
(2) 11,000
(3) 550
(4) 1100

Page 5 PHYSICS : English & Hindi 09
9. If two glass plates have water between 9. ØçÎ ·¤æ¡¿ ·¤è Îæð ŒÜðÅUæð´ ·ð¤ Õè¿ ×ð´ ÁÜ ·¤è °·¤
them and are separated by very small
ÂÌÜè ÂÚUÌ ãæð (¥æÚðU¹ Îðç¹Øð) Ìæð ©Ù ŒÜðÅUæð´ ·¤æð
distance (see figure), it is very difficult to
pull them apart. It is because the water in ¹è´¿·¤ÚU ¥Ü» ·¤ÚUÙæ ÕãéÌ ·¤çÆUÙ ãæðÌæ ãñÐ
between forms cylindrical surface on the
side that gives rise to lower pressure in the
water in comparison to atmosphere. If the
radius of the cylindrical surface is R and §â·¤æ ·¤æÚU‡æ Øã ãñ ç·¤, ÁÜ, ç·¤ÙæÚUæð´ ÂÚU çâçÜ´ÇUÚUè
surface tension of water is T then the
pressure in water between the plates is (ÕðÜÙæ·¤æÚU) âÌãð´ ÕÙæ ÎðÌæ ãñ çÁââð ßæØé×´ÇUÜ ·¤è
lower by : ÌéÜÙæ ×ð´ ßãæ¡ ÎæÕ ·¤× ãæð ÁæÌæ ãñÐ ØçÎ §â çâçÜ´ÇUÚUè
âÌã (ÂëcÆU) ·¤è ç˜æ’Øæ R ãñ ÌÍæ ÁÜ ·¤æ ÂëcÆU ÌÙæß
T ãñ Ìæð, Îæð ŒÜðÅUæð´ ·ð¤ Õè¿ ÁÜ ×ð´ ÎæÕ ç·¤ÌÙæ ·¤×
ãæð»æ?
(1)
T

(1)
4R T
4R
(2)
T

(2)
2R T
2R
(3)
4T

(3)
R 4T
R
(4)
2T

(4)
R 2T
R

Page 6 PHYSICS : English & Hindi 09
10. An ideal gas goes through a reversible 10. °·¤ ¥æÎàæü »ñ⠷𤠩ˆ·ý¤×‡æèØ ¿·ý¤ a®b®c®d ,
cycle a®b®c®d has the V - T diagram ·ð¤ çÜØð V - T ¥æÚðU¹ Øãæ¡ ÎàææüØæ »Øæ ãñÐ Âý·ý¤×
shown below. Process d®a and b®c are d®a ÌÍæ b®c L¤Î÷Ïæðc× ãñ´Ð
adiabatic.

The corresponding P - V diagram for the
Ìæð, §â Âý·ý¤× ·ð¤ çÜØð, â´»Ì P - V ¥æÚðU¹ ãæð»æ
process is (all figures are schematic and (âÖè ¥æÚðU¹ ÃØßSÍæ ¥æÚðU¹ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤ ¥ÙéâæÚU
not drawn to scale) : Ùãè´ ãñ´) Ñ

(1) (1)

(2) (2)

(3) (3)

(4) (4)

Page 7 PHYSICS : English & Hindi 09
11. In an ideal gas at temperature T, the 11. ç·¤âè ¥æÎàæü »ñâ ×ð´, ç·¤âè ¥‡æé mæÚUæ »ñâ ·ð¤ ՋÎ
average force that a molecule applies on
Âæ˜æ ·¤è ÎèßæÚUæð´ ÂÚU Ü»æØæ »Øæ ¥æñâÌ ÕÜ, »ñâ ·ð¤
the walls of a closed container depends on
T as T . A good estimate for q is :
q Ìæ T ÂÚU, Tq ·ð¤ ¥ÙéâæÚU çÙÖüÚU ·¤ÚUÌæ ãñÐ Ìæð, q ·¤æ
(1) 2 âç‹Ù·¤ÅU ×æÙ ãñ Ñ
(2) 1 (1) 2
(2) 1
(3)
1

(3)
2 1
2
(4)
1

(4)
4 1
4
12. A simple harmonic oscillator of angular
frequency 2 rad s21 is acted upon by an 12. ç·¤âè âÚUÜ ¥æßÌü ÎæðçÜ˜æ ·¤è ·¤æð‡æèØ ¥æßëçžæ
external force F5sint N. If the oscillator
2 rad s21 ãñÐ §â ÂÚU °·¤ Õæs ÕÜ, F5sint
is at rest in its equilibrium position at t50,
its position at later times is proportional ‹ØêÅUÙ (N) Ü»Ìæ ãñÐ ØçÎ â×Ø t50 ÂÚU, Øã Îæðçܘæ,
to : ¥ÂÙè âæØæßSÍæ ×ð´ çßÚUæ× çSÍçÌ ×ð´ ãñ Ìæð, §â·ð¤
Âà¿æÌ÷ ·ð¤ ç·¤âè â×Ø ×ð´, §â·¤è çSÍçÌ çِÙæ´ç·¤Ì
(1) ×ð´ ç·¤â·ð¤ â×æÙéÂæÌè ãæð»è?
1
sint 1 sin 2t
2

(2) (1)
1
sint 1
1
cos 2t sint 1 sin 2t
2 2

(3) (2)
1
cost 2
1
sin 2t sint 1 cos 2t
2 2

(4) (3)
1
sint 2
1
sin 2t cost 2 sin 2t
2 2

(4)
1
A bat moving at 10 ms21 towards a wall
sint 2 sin 2t
13.
sends a sound signal of 8000 Hz towards
2

it. On reflection it hears a sound of
frequency f. The value of f in Hz is close to 13. 10 ms21 ·¤è ¿æÜ âð ç·¤âè ÎèßæÚU ·¤è ¥æðÚU ÁæÌæ
(speed of sound5320 ms21) ãé¥æ °·¤ ¿×»æÎǸ, ÎèßæÚU ·¤è ¥æðÚU 8000 Hz ·¤æ
(1) 8258 ŠßçÙ â´·ð¤Ì (çâ‚ÙÜ) ÂýðçáÌ ·¤ÚUÌæ (ÖðÁÌæ) ãñÐ
(2) 8516 ÎèßæÚU âð ÂÚUæßÌüÙ ·ð¤ Âà¿æÌ÷ ß㠑f ’ ¥æßëçžæ ·¤è
(3) 8000 ŠßçÙ, âéÙÌæ ãñÐ ØçÎ, ŠßçÙ ·¤è ¿æÜ 320 ms21 ãñ
(4) 8424 Ìæð, Hz ×ð´ f ·¤æ âç‹Ù·¤ÅU ×æÙ ãæð»æ Ñ
(1) 8258
(2) 8516
(3) 8000
(4) 8424

Page 8 PHYSICS : English & Hindi 09
14. A thin disc of radius b52a has a concentric 14. °·¤ ÂÌÜè çÇUS·¤ (¿ç·ý¤·¤æ) ·¤è ç˜æ’Øæ ‘b’ ãñÐ §â×ð´
hole of radius ‘a’ in it (see figure). It carries
ÕÙð °·¤ â´·ð¤‹Îýè çÀUÎý (ÀðUÎ) ·¤è ç˜æ’Øæ ‘a’ ãñÐ
uniform surface charge ‘s’ on it. If the
electric field on its axis at height ‘h’ (h<<a) (b52a) Ð çÇS·¤ ÂÚU °·¤â×æÙ ÂëcÆU ¥æßðàæ s ãñÐ
from its centre is given as ‘Ch’ then value ØçÎ §â·¤è ¥ÿæ ÂÚU ÌÍæ §â·ð¤ ·ð¤‹Îý âð ‘h’ ª¡¤¿æ§ü
of ‘C’ is : ÂÚU, (h<<a), çßléÌ ÿæð˜æ ‘Ch’ ãæð Ìæð, ‘C’ ·¤æ ×æÙ
ãñ Ñ

(1)
s
ae 0
(1)
s
s
ae 0
(2) 2ae0
s
(2) 2ae0
(3)
s
4ae0
(3)
s
4ae0
(4)
s
8ae0
(4)
s
8ae0

Page 9 PHYSICS : English & Hindi 09
15. Shown in the figure are two point charges 15. Øãæ¡ ¥æÚðU¹ ×ð´, ç·¤âè »æðÜæ·¤æÚU ·¤æðàæ (àæñÜ) ·ð¤ ·¤æðÅUÚU
1Q and 2Q inside the cavity of a
·ð¤ ÖèÌÚU Îæð çՋÎé-¥æßðàæ 1Q ÌÍæ 2Q ÎàææüØð »Øð
spherical shell. The charges are kept near
the surface of the cavity on opposite sides ãñ´Ð Øð ¥æßðàæ ·¤æðÅUÚU ·¤è âÌã ·ð¤ çÙ·¤Å U§â Âý·¤æÚU
of the centre of the shell. If s1 is the surface ÚU¹ð »Øð ãñ´ ç·¤, °·¤ ¥æßðàæ ·¤æðàæ ·ð¤ ·ð¤‹Îý ·¤è °·¤
charge on the inner surface and Q1 net ¥æðÚU ãñ ¥æñÚU ÎêâÚUæ ·ð¤‹Îý ·ð¤ çßÂÚUèÌ ÎêâÚUè ¥æðÚUÐ ØçÎ,
charge on it and s2 the surface charge on
the outer surface and Q2 net charge on it
ÖèÌÚUè ÌÍæ ÕæãÚUè âÌãæð´ (ÂëcÆUæð´) ÂÚU, ÂëcÆU ¥æßðàæ
then : ·ý¤×àæÑ s1 ÌÍæ s2 ¥æñÚU ÙðÅU ¥æßðàæ ·ý¤×àæÑ Q1 ÌÍæ
Q2 ãæð Ìæð Ñ

(1) s1 ¹ 0, Q1 ¹ 0
s2 ¹ 0, Q2 ¹ 0 (1) s1 ¹ 0, Q1 ¹ 0

(2) s1 ¹ 0, Q1 5 0 s2 ¹ 0, Q2 ¹ 0

s2 ¹ 0, Q2 5 0 (2) s1 ¹ 0, Q1 5 0

(3) s1 ¹ 0, Q1 5 0 s2 ¹ 0, Q2 5 0

s2 5 0, Q2 5 0 (3) s1 ¹ 0, Q1 5 0
(4) s1 5 0, Q1 5 0 s2 5 0, Q2 5 0
s2 5 0, Q2 5 0 (4) s1 5 0, Q1 5 0
s2 5 0, Q2 5 0
16. If the capacitance of a nanocapacitor is
measured in terms of a unit ‘u’ made by 16. ØçÎ ç·¤âè ÙñÙæð â´ÏæçÚU˜æ ·¤è ÏæçÚUÌæ, °·¤ °ðâð ×æ˜æ·¤
combining the electronic charge ‘e’, Bohr
radius ‘a0’, Planck’s constant ‘h’ and speed ‘u’ ×ð´ ×æÂè ÁæØ, Áæð §Üð€ÅþUæòÙ ¥æßðàæ ‘e’ , ÕæðÚU-ç˜æ’Øæ
of light ‘c’ then : ‘a0’, ŒÜæ´·¤ çSÍÚUæ´·¤ ‘h’ ÌÍæ Âý·¤æàæ ·¤è ¿æÜ ‘c’ ·ð¤
â´ØæðÁÙ âð ÕÙæ ãñ Ìæð Ñ
(1)
e2 c
u5
(1)
e2 c
u5
ha0
ha0

(2)
e2 h
u5
(2)
ca0 e2 h
u5
ca0

(3)
e 2 a0
u5
(3)
hc e 2 a0
u5
hc
(4)
hc
u5 2
(4)
e a0 hc
u5 2
e a0

Page 10 PHYSICS : English & Hindi 09
17. Suppose the drift velocity vd in a material 17. ØçÎ, ç·¤âè ÂÎæÍü ×ð´ ¥Âßæã ßð», vd ·¤æ ×æÙ, Ü»æØð
varied with the applied electric field E as
»Øð çßléÌ ÿæð˜æ E ÂÚU §â Âý·¤æÚU çÙÖüÚU ·¤ÚUÌæ ãñ, ç·¤
vd ; E . Then V - I graph for a wire
vd ; E Ð Ìæð çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙ-âæ »ýæȤ
made of such a material is best given by :
(¥æÜð¹), §â ÂÎæÍü âð ÕÙð ÌæÚU ·ð¤ çÜØð, âç‹Ù·¤ÅU
V - I »ýæȤ ãæð»æ?

(1)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

Page 11 PHYSICS : English & Hindi 09
18. A 10V battery with internal resistance 18. °·¤ ßæðËÅU×èÅUÚU âð â×æ‹ÌÚU ·ý¤× ×ð´, Îæð ÕñÅUçÚUØæ¡, ÁæðǸè
1V and a 15V battery with internal
»§ü ãñ´Ð ÂãÜè, 10V ÌÍæ 1V ¥æ‹ÌçÚU·¤ ÂýçÌÚUæðÏ ·¤è
resistance 0.6V are connected in parallel
to a voltmeter (see figure). The reading in ¥æñÚU ÎêâÚUè, 15V ÌÍæ 0.6V ¥æ‹ÌçÚU·¤ ÂýçÌÚUæðÏ ·¤è
the voltmeter will be close to : (¥æÚðU¹ Îðç¹Øð) Ìæð, ßæðËÅU×èÅUÚU ·ð¤ ÂÆUÙ (ÚUèçÇ´U»)
·¤æ âç‹Ù·¤ÅU ×æÙ ãæð»æ Ñ

(1) 11.9 V
(2) 12.5 V (1) 11.9 V
(3) 13.1 V (2) 12.5 V
(4) 24.5 V (3) 13.1 V
(4) 24.5 V

19. A proton (mass m) accelerated by a
potential difference V flies through a 19. çßÖßæ‹ÌÚ ‘V’ mæÚUæ ˆßçÚUÌ, °·¤ ÂýæðÅUæòÙ (ÎýÃØ×æÙ m),
uniform transverse magnetic field B. The ç·¤âè ¥ÙéÂýSÍ °·¤â×æÙ ¿éÕ·¤èØ ÿæð˜æ B âð ãæð·¤ÚU
field occupies a region of space by width
‘d’. If ‘a’ be the angle of deviation of proton
Ìèßý ¿æÜ âð »é$ÁÚUÌæ ãñÐ Øã ¿éÕ·¤èØ ÿæð˜æ ‘d’ ¿æñǸæ§ü
from initial direction of motion (see Ì·¤ çßSÌçÚUÌ ãñÐ ØçÎ, Øã ÂýæðÅUæòÙ, ¿éÕ·¤èØ ÿæðð˜æ ·ð¤
figure), the value of sin a will be : ·¤æÚU‡æ ¥ÂÙè »çÌ ·¤è ÂýæÚ´UçÖ·¤ çÎàææ âð ‘a’ ·¤æð‡æ âð
çß¿çÜÌ ãæð ÁæÌæ ãñ (¥æÚð U ¹ Îð ç ¹Øð ) Ìæð ,
sin a ·¤æ ×æÙ ãæð»æ Ñ

(1)
B qd
2 mV

(1)
B qd
(2)
B q
2 mV
d 2mV

(2)
B q
(3)
q d 2mV
Bd
2mV

(3)
q
Bd
(4)
Bd 2mV
qV
2m
(4)
Bd
qV
2m

Page 12 PHYSICS : English & Hindi 09
20. A 25 cm long solenoid has radius 2 cm 20. ç·¤âè ÂçÚUÙæçÜ·¤æ ·¤è ܐÕæ§ü 25 cm ÌÍæ ç˜æ’Øæ
and 500 total number of turns. It carries a
2 cm ãñ ¥æñÚU §â×ð´ ÌæÚU ·ð¤ ·é¤Ü 500 Èð¤ÚðU ÜÂðÅðU »Øð
current of 15 A. If it is equivalent to a
magnet of the same size and magnetization ãñ´Ð §ââð 15 A ·¤è ÏæÚUæ ÂýßæçãÌ ãæð ÚUãè ãñÐ Øã

M (magnetic moment/volume), then ?M?
ÂçÚUÙæçÜ·¤æ, §âè âæ§Á ÌÍæ ¿éÕ·¤Ù M (¿éÕ·¤èØ
→ → →

is :
¥æƒæê‡æü/¥æØÌÙ), ·ð¤ ÌéËØ ãñ Ìæð , ?M? ãñ Ñ
→

(1) 3p Am21
(1) 3p Am21
(2) 30000 Am21
(2) 30000 Am21
(3) 300 Am21
(3) 300 Am21
(4) 30000p Am21
(4) 30000p Am21

21. When current in a coil changes from 5 A
to 2 A in 0.1 s, an average voltage of 50 V 21. ç·¤âè ·é´¤ÇUÜè âð ÂýßæçãÌ çßléÌ ÏæÚUæ ·¤æ ×æÙ, 0.1 s
is produced. The self - inductance of the ×ð´, 5 A âð 2 A ãæð ÁæÌæ ãñ çÁââð, 50 V ·¤è ¥æñâÌ
coil is :
ßæðËÅUÌæ ©ˆÂ‹Ù ãæðÌè ãñÐ Ìæð, §â ·é´¤ÇUÜè ·¤æ SßÂýðÚU·¤ˆß
(1) 0.67 H
ãñ Ñ
(2) 1.67 H
(1) 0.67 H
(3) 3H
(2) 1.67 H
(4) 6H
(3) 3H
(4) 6H

Page 13 PHYSICS : English & Hindi 09
22. In the circuits (a) and (b) switches S1 and 22. Îæð ÂçÚUÂÍæð´ (a) ÌÍæ (b) ×ð´ çSß¿ S1 ÌÍæ S2, t50
S2 are closed at t50 and are kept closed
ÂÚU ՋΠ緤Øð ÁæÌð ãñ´ ¥æñÚU ÂØæüŒÌ ܐÕð â×Ø Ì·¤
for a long time. The variation of currents
in the two circuits for t ³ 0 are roughly
ՋΠÚU¹ð ÁæÌð ãñ´, Ìæð t ³ 0 ·ð¤ çÜØð, Îæð ÂçÚUÂÍæð´ ×ð´
shown by (figures are schematic and not çßléÌ ÏæÚUæ¥æð´ ·ð¤ çß¿ÜÙ (ÂçÚUßÌüÙ) ·¤æð, ·¤æñÙâæ
drawn to scale) : »ý æ Ȥ çÙ·¤ÅU Ì × Îàææü Ì æ ãñ ? (¥æÚð U ¹ ·ð ¤ ßÜ
ÃØßSÍæˆ×·¤ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤ ¥ÙéâæÚU Ùãè´ ãñ´)

(1)
(1)

(2)
(2)

(3)
(3)

(4)
(4)

Page 14 PHYSICS : English & Hindi 09
23. An electromagnetic wave travelling in the 23. x-çÎàææ ×ð´ ¿ÜÌè ãé§ü ç·¤âè çßléÌ ¿éÕ·¤èØ ÌÚ´U» ·¤è
x-direction has frequency of 231014 Hz
¥æßëçžæ 231014 Hz ãñ ÌÍæ §â·¤æ çßléÌ ÿæð˜æ
and electric field amplitude of 27 Vm21.
From the options given below, which one 27 Vm21 ãñÐ Ìæð, çÎØð »Øð çِÙæ´ç·¤Ì çß·¤ËÂæð´ ×ð´
describes the magnetic field for this âð ·¤æñÙ âæ çß·¤ËÂ, §â ÌÚ´U» ·ð¤ ¿éÕ·¤èØ ÿæð˜æ ·¤æð
wave ? Âý·¤ÅU ·¤ÚUÌæ ãñ?
(1) (1)
→ ∧
B ( x , t)5(331028 T) j →
B ( x , t)5(331028 T) j
∧

sin  2 p(1.531028 x2231014 t) sin  2 p(1.531028 x2231014 t)
   
(2) (2)
→ ∧
B ( x , t)5(931028 T) k →
B ( x , t)5(931028 T) k
∧

sin  2 p(1.531026 x2231014 t) sin  2 p(1.531026 x2231014 t)
   
(3) (3)
→ ∧
B ( x , t)5(931028 T) i →
B ( x , t)5(931028 T) i
∧

sin  2 p(1.531028 x2231014 t) sin  2 p(1.531028 x2231014 t)
   
(4) (4)
→ ∧
B ( x , t)5(931028 T) j →
B ( x , t)5(931028 T) j
∧

sin 1.531026 x2231014 t  sin 1.531026 x2231014 t 
   

You are asked to design a shaving mirror
¥æ·¤æð °·¤ àæðçß´» ÎÂü‡æ ÕÙæÙð ·¤æð ·¤ãæ ÁæÌæ ãñÐ
24.
assuming that a person keeps it 10 cm from
24.
his face and views the magnified image of ØçÎ ·¤æð§ü ÃØç€Ì §â ÎÂü‡æ ·¤æð ¥ÂÙð ¿ðãÚðU âð 10 cm
the face at the closest comfortable distance ÎêÚU ÚU¹Ìæ ãñ ¥æñÚU ¿ðãÚðU ·ð¤ ¥æßçÏüÌ ÂýçÌçÕÕ ·¤æð,
of 25 cm. The radius of curvature of the âéçßÏæÁÙ·¤-ÎàæüÙ ·¤è çÙ·¤ÅUÌ× ÎêÚUè, 25 cm ÂÚU
mirror would then be :
Îð¹Ìæ ãñ Ìæð, ÎÂü‡æ ·¤è ß·ý¤Ìæ ç˜æ’Øæ ãæð»è Ñ
(1) 30 cm
(1) 30 cm
(2) 24 cm
(2) 24 cm
(3) 60 cm
(3) 60 cm
(4) 224 cm
(4) 224 cm

Page 15 PHYSICS : English & Hindi 09
25. A parallel beam of electrons travelling in 25. x-çÎàææ ×ð´ »çÌ ·¤ÚUÌæ ãé¥æ °·¤ â×æ‹ÌÚU §Üð€ÅþUæòÙ Âé´Á
x-direction falls on a slit of width d (see
d ¿æñÇæ¸ §ü ·¤è çÛæÚUè ÂÚU ¥æÂçÌÌ ãæðÌæ ãñ (¥æÚðU¹ Îðç¹Øð)Ð
figure). If after passing the slit, an electron
acquires momentum py in the y-direction ØçÎ §â çÛæÚUè âð çÙ·¤ÜÙð ·ð¤ Âà¿æÌ÷ §Üð€ÅþUæòÙ,
then for a majority of electrons passing y-çÎàææ ×ð´, py â´ßð» ÂýæŒÌ ·¤ÚU ÜðÌð ãñ´ Ìæð, çSÜÅU âð
through the slit (h is Planck’s constant) : »éÁÚUÙð ßæÜð ¥çÏ·¤æ´àæ §Üð€ÅþUæòÙæð´ ·ð¤ çÜØð (ØçÎ h
ŒÜæ´·¤ çÙØÌæ´·¤ ãñ) Ñ

(1) ?py?d ; h
(2) ?py?d>h (1) ?py?d ; h
(3) ?py?d<h (2) ?py?d>h
(4) ?py?d>>h (3) ?py?d<h
(4) ?py?d>>h
26. A telescope has an objective lens of focal
length 150 cm and an eyepiece of focal
length 5 cm. If a 50 m tall tower at a 26. ç·¤âè ÎêÚUÎàæü·¤ ·ð¤ ¥çÖÎëàØ·¤ ÌÍæ Ùðç˜æ·¤æ ·¤è Ȥæð·¤â
distance of 1 km is observed through this ÎêçÚUØæ¡ ·ý¤×àæÑ 150 cm ÌÍæ 5 cm ãñ´Ð ØçÎ 1 km
telescope in normal setting, the angle ÎêÚU çSÍÌ ç·¤âè 50 m ª¡¤¿ð ÅUæßÚU (×èÙæÚU) ·¤æð, âæ×æ‹Ø
formed by the image of the tower is u, then
u is close to : çߋØæâ ×ð´, ÎêÚUÎàæü·¤ âð Îð¹Ùð ÂÚU, ÅUæßÚU ·ð¤ ÂýçÌçՐÕ
(1) 18 mæÚUæ ÕÙæØæ »Øæ ·¤æð‡æ, u ãæð Ìæð, u ·¤æ ×æÙ ãæð»æ
(2) 158
ֻܻ Ñ
(3) 308 (1) 18

(4) 608 (2) 158
(3) 308

27. de-Broglie wavelength of an electron (4) 608
accelerated by a voltage of 50 V is close to
(?e?51.6310 219 C, m e59.1310 231 kg,
27. 50 V ßæðËÅUÌæ mæÚUæ ˆßçÚUÌ §Üð€ÅþUæòÙ ·¤è Îð-Õýæò‚Üè
h56.6310234 Js) :
ÌÚ´U»ÎñƒØü ·¤æ çÙ·¤ÅUÌ× ×æÙ ãæð»æ Ñ
(1) 0.5 Å
(?e?51.6310 219 C, m e59.1310 231 kg,
(2) 1.2 Å h56.6310234 Js)
(3) 1.7 Å (1) 0.5 Å
(4) 2.4 Å (2) 1.2 Å
(3) 1.7 Å
(4) 2.4 Å

Page 16 PHYSICS : English & Hindi 09
28. If one were to apply Bohr model to a 28. ØçÎ ¿éÕ·¤èØ ÿæð˜æ ‘B’ ·ð¤ ÂýÖæß ×ð´, â×ÌÜ ×ð´ »çÌ
particle of mass ‘m’ and charge ‘q’ moving
·¤ÚUÌð ãé°, ‘m’ ÎýÃØ×æÙ ÌÍæ ‘q’ ¥æßðàæ ·ð¤ ·¤‡æ ÂÚU,
in a plane under the influence of a
magnetic field ‘B’, the energy of the ÕæðÚU ×æòÇUÜ Üæ»ê ç·¤Øæ (ÂýØæð» ×ð´ ÜæØæ) ÁæØ Ìæð,
charged particle in the nth level will be : ¥æßðçàæÌ ·¤‡æ ·¤è n ßè´ SÌÚU ×ð´ ª¤Áæü ãæð»è Ñ

(1) (1)
 hqB   hqB 
n  n 
 2 pm   2 pm 

(2) (2)
 hqB   hqB 
n  n 
 4 pm   4 pm 

(3) (3)
 hqB   hqB 
n  n 
 8 pm   8 pm 

(4) (4)
 hqB   hqB 
n  n 
 pm   pm 

29. In an unbiased n-p junction electrons 29. ç·¤âè ¥-ÕæØçâÌ n-p â´çÏ ×ð´ §Üð€ÅþUæòÙ n - ÿæð˜æ âð
diffuse from n - region to p - region
p - ÿæð˜æ ·¤æð çßâçÚUÌ ãæðÌð ãñ´ €Øæð´ç·¤ Ñ
because :
(1) holes in p - region attract them (1) p - ÿæð˜æ ×ð´ çÀUÎý (ãæðÜ) ©‹ã𴠥淤çáüÌ ·¤ÚUÌð
(2) electrons travel across the junction ãñд
due to potential difference (2) §Üð€ÅþUæòÙ çßÖßæ‹ÌÚU ·ð¤ ·¤æÚU‡æ â´çÏ ·ð¤ ÂæÚU
(3) electron concentration in n - region ¿Üð ÁæÌð ãñ´Ð
is more as compared to that in
p - region (3) n - ÿæð˜æ ×ð´ §Üð€ÅþUæòÙæð´ ·¤è âæ´ÎýÌæ p - ÿæð˜æ âð
(4) only electrons move from n to p ¥çÏ·¤ ãæðÌè ãñÐ
region and not the vice - versa
(4) §Üð€ÅþUæòÙ ·ð¤ßÜ n âð p ÿæð˜æ ·¤æð ÁæÌð ã´ñ §â·ð¤
çßÂÚèUÌ (p âð n ·¤æð ) Ùãè´Ð

Page 17 PHYSICS : English & Hindi 09
30. Diameter of a steel ball is measured using 30. SÅUèÜ ·¤è °·¤ »æðÜè ·¤æ ÃØæâ °·¤ °ðâð ßçÙüØÚU
a Vernier callipers which has divisions of
·ñ¤ÜèÂâü âð ÙæÂæ ÁæÌæ ãñ çÁâ·ð¤ ×éØ Âñ×æÙð ·¤æ °·¤
0.1 cm on its main scale (MS) and 10
divisions of its vernier scale (VS) match 9 Öæ» (MSD) 0.1 cm ãñ, ÌÍæ §â×ð´ ßçÙüØÚ Âñ×æÙðU
divisions on the main scale. Three such (VS) ·ð¤ 10 Öæ», ×éØ Âñ×æÙð ·ð¤ 9 Öæ»æð´ ·ð¤ ÕÚUæÕÚU
measurements for a ball are given as : ãñ´Ð »æðÜè ·ð¤ ÃØæâ ·ð¤ çÜØð ÌèÙ ÂæÆ÷UØæ´·¤ (ÚUèçÇU´»)
S.No. MS (cm) VS divisions
Øãæ¡ çÎØð »Øð ãñ´ Ñ

¼Î€½ §Ö¼Ë¾Õ Ä̾὿U §Ö¼Ë¾Õ œÕ‰
1. 0.5 8
2. 0.5 4 œâ‰¼Ë™œ‰
3. 0.5 6 œ‰Í ¼Ë§ cm »Ë
If the zero error is 20.03 cm, then mean
1. 0.5 8

corrected diameter is :
2. 0.5 4

(1) 0.56 cm
3. 0.5 6

(2) 0.59 cm ØçÎ ßçÙüØÚU ·ñ¤ÜèÂâü ·¤è àæê‹Ø ˜æéçÅU 20.03 cm, ãñ
(3) 0.53 cm Ìæð, ÃØæâ ·¤æ ×æŠØ â´àææðçÏÌ ×æÙ ãæð»æ Ñ
(4) 0.52 cm
(1) 0.56 cm
(2) 0.59 cm
-o0o-
(3) 0.53 cm
(4) 0.52 cm

-o0o-

Page 1 Chemistry : English & Hindi 09
1. A sample of a hydrate of barium chloride 1. 61 g ÕðçÚUØ× €ÜæðÚUæ§ÇU ·ð¤ ãæ§ÇþðUÅU ·ð¤ °·¤ Ù×êÙð ·¤æð
weighing 61 g was heated until all the
»ÚU× ·¤ÚU·ð¤ âé¹æØæ »ØæÐ âê¹ð Ù×êÙð ·¤æ ßÁÙ 52 g
water of hydration is removed. The dried
sample weighed 52 g. The formula of the ÍæÐ ãæ§ÇþðUÅU Üß‡æ ·¤æ âê˜æ ãñ Ñ (ÂÚU×æ‡æé ÎýÃØ×æÙ,
hydrated salt is : (atomic mass, Ba5137 amu, Cl535.5 amu)
Ba5137 amu, Cl535.5 amu) (1) BaCl2.H2O
(1) BaCl2.H2O (2) BaCl2.2H2O
(2) BaCl2.2H2O (3) BaCl2.3H2O
(3) BaCl2.3H2O (4) BaCl2.4H2O
(4) BaCl2.4H2O
2. çِ٠×ð´ âð ·¤æñÙ âè »ñâæ𴠷𤠥‡æé»çÌ·¤ çâhæ´Ì ·¤è
2. Which of the following is not an ¥ßÏæÚU‡ææ Ùãè´ ãñ?
assumption of the kinetic theory of gases ?
(1) A gas consists of many identical
(1) °·¤ »ñâ ÕãéÌ âæÚðU â×M¤Â ·¤‡ææð´ âð ÕÙÌè ãñ
particles which are in continual Áæð Ü»æÌæÚU »çÌ·¤ ¥ßSÍæ ×ð´ ÚUãÌð ãñ´Ð
motion. (2) »ñ⠷𤠷¤‡ææð´ ·¤æ ¥æØÌÙ Ù»‡Ø ãñÐ
(2) Gas particles have negligible volume.
(3) ©“æ ÎæÕ ÂÚU »ñâ ·¤‡ææð´ ·¤æ â´ÂèÇUÙ ·¤çÆUÙ ãñÐ
(3) At high pressure, gas particles are
difficult to compress. (4) »ñ⠷𤠷¤‡ææð´ ·ð¤ ×ŠØ â´ƒæ^ Âê‡æüÌÑ ÂýˆØæSÍ
(4) Collisions of gas particles are ãæðÌð ãñ´Ð
perfectly elastic.

3. ×éØ €ßæ´ÅU× â´Øæ n56 ·ð¤ çÜ° §Üð€ÅþUæòÙæð´ ·ð¤ ÖÚUÙð
3. If the principal quantum number n56, the
·¤æ âãè ·ý¤× ãñ Ñ
correct sequence of filling of electrons will
be : (1) ns®np®(n21)d®(n22)f
(1) ns®np®(n21)d®(n22)f (2) ns®(n22)f®(n21)d®np
(2) ns®(n22)f®(n21)d®np (3) ns®(n21)d®(n22)f®np
(3) ns®(n21)d®(n22)f®np (4) ns®(n22)f®np®(n21)d
(4) ns®(n22)f®np®(n21)d

Page 2 Chemistry : English & Hindi 09
4. After understanding the assertion and 4. ¥çÖ·¤ÍÙ ¥æñÚU Ì·ü¤ ·¤æð â×Ûæ·¤ÚU âãè çß·¤Ë ¿éçÙ°Ð
reason, choose the correct option.
¥çÖ·¤ÍÙ : ãæ§ÇþUæðÁÙ ·ð¤ ¥æÕ´Ïè ¥æç‡ß·¤ ·¤ÿæ·¤
Assertion : In the bonding molecular
orbital (MO) of H2, electron ×ð´ §Üð€ÅþUæòÙ ƒæÙˆß ÙæçÖ·¤æð´ ·ð¤ Õè¿
density is increased between Õɸæ ãé¥æ ãæðÌæ ãñÐ
the nuclei.
Ì·ü¤ : ¥æÕ´Ïè ¥æç‡ß·¤ ·¤ÿæ·¤ cA1cB ãñ
Reason : The bonding MO is cA1c B,
which shows destructive
Áæð â´ØæðÁè §Üð€ÅþUæòÙ ÌÚ´U»æð´ ·¤æ çßÙæàæè
interference of the combining ÃØçÌ·¤ÚU‡æ ÎàææüÌæ ãñÐ
electron waves. (1) ¥çÖ·¤ÍÙ ß Ì·ü¤ ÎæðÙæð´ âãè ãñ´ ¥æñÚU Ì·ü¤
(1) Assertion and reason are correct and ¥çÖ·¤ÍÙ ·¤æ âãè SÂcÅUè·¤ÚU‡æ ãñÐ
reason is the correct explanation for
the assertion. (2) ¥çÖ·¤ÍÙ ß Ì·ü¤ ÎæðÙæð´ âãè ãñ´ ×»ÚU Ì·ü¤
(2) Assertion and reason are correct, but ¥çÖ·¤ÍÙ ·¤æ âãè SÂcÅUè·¤ÚU‡æ Ùãè´ ãñÐ
reason is not the correct explanation
for the assertion.
(3) ¥çÖ·¤ÍÙ âãè ãñ ×»ÚU Ì·ü¤ »ÜÌ ãñÐ
(3) Assertion is correct, reason is (4) ¥çÖ·¤ÍÙ »ÜÌ ãñ ¥æñÚU Ì·ü¤ âãè ãñÐ
incorrect.
(4) Assertion is incorrect, reason is 5. ç×Íð Ù ÌÍæ §Íð Ù ·ð ¤ ·¤‡æè·¤ÚU ‡ æ ª¤c×æ ·ý ¤ ×àæÑ
correct.
360 kJ/mol ÌÍæ 620 kJ/mol ãñ´Ð C - C ¥æÕ´Ï
·¤æð ÌæðǸÙð ·¤è ÿæ×Ìæ ÚU¹Ùð ßæÜè Âý·¤æàæ ·¤è ÎèƒæüÌ×
5. The heat of atomization of methane and
ethane are 360 kJ/mol and 620 kJ/mol,
ÌÚ´U»ÎñŠØü ãæð»è (¥æßæð»æÎýæð ⴁØæ56.0231023,
respectively. The longest wavelength of h56.62310234 J s) :
light capable of breaking the C - C bond is (1) 1.493103 nm
(Avogadro number56.0231023, (2) 2.483103 nm
h56.62310234 J s) :
(3) 2.483104 nm
(1) 1.493103 nm
(4) 1.493104 nm
(2) 2.483103 nm
(3) 2.483104 nm
6. 208C ÂÚU °·¤ çßÜØÙ ×ð´ 1.5 ×æðÜ Õð‹ÁèÙ ¥æñÚU
(4) 1.493104 nm
3.5 ×æðÜ ÅUæðÜé§Ù ãñ´Ð ¥»ÚU §â Ìæ ÂÚU àæéh Õð‹ÁèÙ
¥æñÚU àæéh ÅUæðÜé§Ù ·ð¤ ßæc ÎæÕ ·ý¤×àæÑ 74.7 torr
6. A solution at 208C is composed of 1.5 mol
of benzene and 3.5 mol of toluene. If the ¥æñÚU 22.3 torr ãñ´, ÌÕ çßÜØÙ ·¤æ ·é¤Ü ßæc ÎæÕ
vapour pressure of pure benzene and pure ¥æñÚU Õð‹ÁèÙ ·¤æ ×æðÜ ¥´àæ §â·ð¤ âæØ ×ð´ ·ý¤×àæÑ ãñ´ Ñ
toluene at this temperature are 74.7 torr
(1) 35.0 torr ¥æñÚU 0.480
and 22.3 torr, respectively, then the total
vapour pressure of the solution and the (2) 38.0 torr ¥æñÚU 0.589
benzene mole fraction in equilibrium with
it will be, respectively : (3) 30.5 torr ¥æñÚU 0.389
(1) 35.0 torr and 0.480 (4) 35.8 torr ¥æñÚU 0.280
(2) 38.0 torr and 0.589
(3) 30.5 torr and 0.389
(4) 35.8 torr and 0.280

Page 3 Chemistry : English & Hindi 09
7. Gaseous N2O 4 dissociates into gaseous 7. »ñâèØ N2O4 »ñâèØ NO2 ×ð´ çِ٠¥çÖç·ý¤Øæ ·ð¤
NO2 according to the reaction
¥ÙéâæÚU çßØæðçÁÌ ãæðÌæ ãñ Ñ
N2O4(g) ì 2NO2(g)
N2O4(g) ì 2NO2(g)
At 300 K and 1 atm pressure, the degree
of dissociation of N2O4 is 0.2. If one mole 300 K ¥æñÚU 1 atm ÎæÕ ÂÚU N2O4 ·¤è çßØæðÁÙ
of N2O4 gas is contained in a vessel, then ×æ˜ææ 0.2 ãñÐ ¥»ÚU °·¤ ×æðÜ N2O4 »ñâ ·¤æð °·¤ Âæ˜æ
the density of the equilibrium mixture is : ×ð´ çÜØæ Áæ° ÌÕ âæØ çןæ‡æ ·¤æ ƒæÙˆß ãñ Ñ
(1) 1.56 g/L (1) 1.56 g/L
(2) 3.11 g/L (2) 3.11 g/L
(3) 4.56 g/L (3) 4.56 g/L
(4) 6.22 g/L (4) 6.22 g/L

8. A variable, opposite external potential
8. 1.1 V çßÖß ·ð¤ âðÜ
(Eext) is applied to the cell
Zn|Zn21 (1 M) ?? Cu21 (1 M) | Cu, of Zn|Zn21 (1 M) ?? Cu21 (1 M) | Cu, ×ð´ °·¤
potential 1.1 V. When Eext < 1.1 V and ÂçÚUßÌèü çßÂÚUèÌ Õæs çßÖß (Eext) Ü»æØæ »ØæÐ
Eext > 1.1 V, respectively electrons flow
from : ÁÕ Eext < 1.1 V ÌÍæ Eext > 1.1 V, ãæð ÌÕ
(1) anode to cathode and cathode to §Üð€ÅþUæòÙæð´ ·¤æ Âýßæã ãæð»æ Ñ
anode (1) °ÙæðÇU âð ·ñ¤ÍæðÇU ÌÍæ ·ñ¤ÍæðÇU âð °ÙæðÇU
(2) cathode to anode and anode to
cathode
(2) ·ñ¤ÍæðÇU âð °ÙæðÇU ÌÍæ °ÙæðÇU âð ·ñ¤ÍæðÇU
(3) cathode to anode in both cases (3) ÎæðÙæð´ çSÍçÌ ×ð´ ·ñ¤ÍæðÇU âð °ÙæðÇU
(4) anode to cathode in both cases (4) ÎæðÙæð´ çSÍçÌ ×ð´ °ÙæðÇU âð ·ñ¤ÍæðÇU

9. The reaction 9. çِ٠¥çÖç·ý¤Øæ °·¤ ÂýÍ× ·¤æðÅUè ÕÜ»çÌ·¤è ãñ Ñ
2N2O5(g) ® 4NO2(g)1O2(g) 2N2O5(g) ® 4NO2(g)1O2(g)
follows first order kinetics. The pressure
of a vessel containing only N 2 O 5 was 30 min ×ð´, °·¤ Âæ˜æ çÁâ×ð´ ·ð¤ßÜ N2O5 Íæ, ©â·¤æ
found to increase from 50 mm Hg to ÎæÕ 50 mm Hg âð 87.5 mm Hg Õɸ »ØæÐ
87.5 mm Hg in 30 min. The pressure 60 min ·ð¤ ÕæÎ Øã ÎæÕ ãæð»æ (×æÙ ÜèçÁ° ·¤è ÌæÂ
exerted by the gases after 60 min. will be çÙØÌ ãñ) :
(Assume temperature remains constant) :
(1) 106.25 mm Hg
(1) 106.25 mm Hg
(2) 116.25 mm Hg
(2) 116.25 mm Hg
(3) 125 mm Hg
(3) 125 mm Hg
(4) 150 mm Hg
(4) 150 mm Hg

Page 4 Chemistry : English & Hindi 09
10. The following statements relate to the 10. çِ٠·¤ÍÙ ÆUæðâ ÂëcÆU ÂÚU »ñâèØ ¥çÏàææðá‡æ ·ð¤ â´ÎÖü
adsorption of gases on a solid surface.
×ð´ ãñ´Ð §Ù×ð´ âð »ÜÌ ·¤ÍÙ ãñ Ñ
Identify the incorrect statement among
them : (1) ¥çÏàææðá‡æ ·¤è °‹ÍñËÂè «¤‡ææˆ×·¤ ãñÐ
(1) Enthalpy of adsorption is negative (2) ¥çÏàææðá‡æ ·¤è °‹ÅþUæòÂè «¤‡ææˆ×·¤ ãñÐ
(2) Entropy of adsorption is negative
(3) ¥çÏàææðá‡æ ÂÚU, ÂëcÆU ÂÚU ¥ßçàæcÅU ÕÜ ÕɸÌð
(3) On adsorption, the residual forces on
the surface are increased
ãñд
(4) On adsorption decrease in surface (4) ¥çÏàææðá‡æ ÂÚU, ÂëcÆU ª¤Áæü ·¤æ Oæâ ª¤c×æ ·ð¤
energy appears as heat M¤Â ×ð´ Âý·¤ÅU ãæðÌæ ãñÐ

11. In the long form of the periodic table, the 11. ¥æßÌü âæÚU‡æè ·ð¤ Îèƒæü SßM¤Â ×ð´, ¥»ÚU â´ØæðÁè ·¤æðàæ
valence shell electronic configuration of
5s2 5p4 corresponds to the element present §Üð€ÅþUæòÙ çߋØæâ 5s2 5p4 ãñ ÌÕ ßã Ìˆß ©ÂçSÍÌ
in : ãñ Ñ
(1) Group 16 and period 6 (1) ß»ü 16 ¥æñÚU ¥æßÌü 6 ×ð´
(2) Group 17 and period 5
(2) ß»ü 17 ¥æñÚU ¥æßÌü 5 ×ð´
(3) Group 16 and period 5
(3) ß»ü 16 ¥æñÚU ¥æßÌü 5 ×ð´
(4) Group 17 and period 6
(4) ß»ü 17 ¥æñÚU ¥æßÌü 6 ×ð´
12. In the isolation of metals, calcination
process usually results in : 12. ÏæÌé¥æð´ ·ð¤ çÙc·¤áü‡æ ×ð´, çÙSÌæÂÙ âð ¥·¤âÚU ÕÙÌð
(1) metal carbonate ãñ´ Ñ
(2) metal oxide
(1) ÏæÌé ·¤æÕæðüÙðÅU
(3) metal sulphide
(2) ÏæÌé ¥æò€âæ§ÇU
(4) metal hydroxide
(3) ÏæÌé âËȤæ§ÇU
13. Permanent hardness in water cannot be (4) ÏæÌé ãæ§ÇþUæò€âæ§ÇU
cured by :
(1) Boiling
13. ÁÜ ·¤è SÍæØè ·¤ÆUæðÚUÌæ ·¤æð §â Âýç·ý¤Øæ âð ÆUè·¤ Ùãè´
(2) Ion exchange method
ç·¤Øæ Áæ â·¤Ìæ ãñ Ñ
(3) Calgon’s method
(4) Treatment with washing soda
(1) ©ÕæÜÙæ
(2) ¥æØÙ çßçÙ×Ø çßçÏ
(3) ·ð¤Ü»æòÙ çßçÏ
(4) ÏæßÙ âæðÇUæ ·ð¤ ©Â¿æÚU âð

Page 5 Chemistry : English & Hindi 09
14. The correct order of thermal stability of 14. ãæ§ÇþUæò€âæ§ÇUæð´ ·¤æ ÌæÂèØ SÍæçØˆß ·¤æ âãè ·ý¤× ãñ Ñ
hydroxides is :
(1) Ba(OH)2 < Sr(OH) 2 < Ca(OH) 2 <
(1) Ba(OH)2 < Sr(OH) 2 < Ca(OH) 2 < Mg(OH)2
Mg(OH)2
(2) Ba(OH)2 < Ca(OH) 2 < Sr(OH) 2 <
(2) Ba(OH)2 < Ca(OH) 2 < Sr(OH) 2 < Mg(OH)2
Mg(OH)2
(3) Mg(OH)2 < Ca(OH) 2 < Sr(OH) 2 <
(3) Mg(OH)2 < Ca(OH) 2 < Sr(OH) 2 < Ba(OH)2
Ba(OH)2
(4) Mg(OH)2 < Sr(OH) 2 < Ca(OH) 2 <
(4) Mg(OH)2 < Sr(OH) 2 < Ca(OH) 2 < Ba(OH)2
Ba(OH)2

15. âÕâð ·¤× â´Øæ ·ð¤ ¥æ€âè¥Ü ÕÙæÌæ ãñ Ñ
15. The least number of oxyacids are formed
by : (1) Ùæ§ÅþUæðÁÙ
(1) Nitrogen (2) âËȤÚU
(2) Sulphur
(3) Üé¥æðÚUèÙ
(3) Fluorine
(4) Chlorine
(4) €ÜæðÚUèÙ

16. The geometry of XeOF4 by VSEPR theory 16. ßè.°â.§ü.Âè.¥æÚU. (VSEPR) çâhæ´Ì ·ð¤ ¥ÙéâæÚU,
is : XeOF4 ·¤è ’Øæç×çÌ ãñ Ñ
(1) trigonal bipyramidal (1) ç˜æ·¤æð‡æèØ çmçÂÚUæç×ÇUè
(2) square pyramidal
(2) ß»ü çÂÚUæç×ÇUè
(3) octahedral
(4) pentagonal planar (3) ¥cÅUȤܷ¤èØ
(4) ´¿·¤æð‡æèØ â×ÌÜèØ
17. An aqueous solution of a salt X turns blood
red on treatment with SCN2 and blue on
17. Ü߇æ X ·¤æ ÁÜèØ çßÜØÙ SCN2 ·ð¤ âæÍ ¹êÙè
treatment with K4[Fe(CN)6]. X also gives
a positive chromyl chloride test. The salt ÜæÜ Ú´U» ¥æñÚU K4[Fe(CN)6] ·ð¤ âæÍ ÙèÜæ Ú´U» ÎðÌæ
X is : ãñÐ X °·¤ â·¤æÚUæˆ×·¤ ·ý¤æðç×Ü €ÜæðÚUæ§ÇU ÂÚUèÿæ‡æ Öè
(1) CuCl2 ÎðÌæ ãñÐ Ü߇æ X ãñ Ñ
(2) FeCl3 (1) CuCl2
(3) Cu(NO3)2 (2) FeCl3
(4) Fe(NO3)3 (3) Cu(NO3)2
(4) Fe(NO3)3
18. Which molecule/ion among the following
cannot act as a ligand in complex
compounds ?
18. çِ٠×ð´ âð ·¤æñÙ âæ ¥‡æé/¥æØÙ â´·é¤Ü Øæñç»·¤æð´ ×ð´
(1) CO
çÜ»ñ‹ÇU Ùãè´ ãæð â·¤Ìæ ãñ?
(2) CN2 (1) CO

(3) CH4 (2) CN2

(4) Br2 (3) CH4
(4) Br2

Page 6 Chemistry : English & Hindi 09
19. The correct statement on the isomerism 19. çِ٠ⴷé¤Ü ¥æØÙæð´ âð âÕç‹ÏÌ â×æßØßÌæ ÂÚU
associated with the following complex
âãè ·¤ÍÙ ãñ´
ions,
(a) [Ni(H2O)5NH3]21,
(a) [Ni(H2O)5NH3]21,
(b) [Ni(H2O)4(NH3)2]21 and (b) [Ni(H2O)4(NH3)2]21 ¥æñÚU
(c) [Ni(H2O)3(NH3)3]21 is : (c) [Ni(H2O)3(NH3)3]21 :
(1) (a) and (b) show only geometrical (1) (a) ¥æñÚU (b) ·ð¤ßÜ ’Øæç×ÌèØ â×æßØßÌæ
isomerism ÎàææüÌð ãñ´Ð
(2) (a) and (b) show geometrical and
(2) (a) ¥æñÚU (b) ’Øæç×ÌèØ ¥æñÚU Ïýé߇æ â×æßØßÌæ
optical isomerism
(3) (b) and (c) show geometrical and
ÎàææüÌð ãñ´Ð
optical isomerism (3) (b) ¥æñÚU (c) ’Øæç×ÌèØ ¥æñÚU Ïýé߇æ â×æßØßÌæ
(4) (b) and (c) show only geometrical ÎàææüÌð ãñ´Ð
isomerism
(4) (b) ¥æñÚU (c) ·ð¤ßÜ ’Øæç×ÌèØ â×æßØßÌæ
ÎàææüÌð ãñ´Ð
20. Photochemical smog consists of excessive
amount of X, in addition to aldehydes,
ketones, peroxy acetyl nitrile (PAN), and 20. Âý·¤æàæ ÚUæâæØçÙ·¤ Ïê× ·¤æðãÚðU ×ð´ °ðçËÇUãæ§ÇU, ·¤èÅUæðÙ,
so forth. X is :
ÂðÚUæ€ð âè °çâÅUæ§Ü Ùæ§ÅþUæ§Ü (PAN) §ˆØæçÎ ·ð¤ ¥Üæßæ
(1) CH4 ¥çÏ·¤ ×æ˜ææ ×ð´ X Öè ãæðÌæ ãñ, X ãñ Ñ
(2) CO
(1) CH4
(3) CO 2
(2) CO
(4) O3
(3) CO 2
(4) O3
21. 1.4 g of an organic compound was digested
according to Kjeldahl’s method and the
ammonia evolved was absorbed in 60 mL 21. 1.4 g ·¤æÕüçÙ·¤ Øæñç»·¤ ·¤æð ·ñ¤ËÇUæÜ çßçÏ ·ð¤ ¥ÙéâæÚU
of M/10 H 2 SO 4 solution. The excess Âæç¿Ì ç·¤Øæ »Øæ ÌÍæ çÙ·¤Üð ¥×æðçÙØæ ·¤æð 60 mL,
sulphuric acid required 20 mL of M/10
M/10, H2SO4 çßÜØÙ ×ð´ ¥ßàææðçáÌ ç·¤Øæ »ØæÐ
NaOH solution for neutralization. The
percentage of nitrogen in the compound ¥çÌçÚU€Ì âˍØêçÚU·¤ ¥Ü ·¤æð ©ÎæâèÙ ·¤ÚUÙð ·ð¤
is : çÜ°, 20 mL, M/10, NaOH Ü»æÐ §â Øæñç»·¤
(1) 3 ×ð´ Ùæ§ÅþUæðÁÙ ·¤è ÂýçÌàæÌÌæ ãñ Ñ
(2) 5 (1) 3
(3) 10 (2) 5
(4) 24 (3) 10
(4) 24
22. The optically inactive compound from the
following is :
22. çِ٠×ð´ âð Ïýéß‡æ ¥ƒæê‡æü·¤ Øæñç»·¤ ãñ Ñ
(1) 2 - chloropropanal
(2) 2 - chloropentane (1) 2 - €ÜæðÚUæðÂýæðÂðÙÜ

(3) 2 - chlorobutane (2) 2 - €ÜæðÚUæðÂð‹ÅðUÙ
(4) 2 - chloro - 2 - methylbutane (3) 2 - €ÜæðÚUæðŽØêÅðUÙ
(4) 2 - €ÜæðÚUæð - 2 - ×ðçÍ܎ØêÅðUÙ

Page 7 Chemistry : English & Hindi 09

23.

23.

A is :
A ãñ Ñ
(1)
(1)
(2)
(2)
(3)
(3)

(4)
(4)

24. A compound A with molecular formula
C 10 H 13 Cl gives a white precipitate on
adding silver nitrate solution. A on 24. Øæñç»·¤ A çÁâ·¤æ ¥‡æéâê˜æ C10H13Cl ãñ, çâËßÚU
reacting with alcoholic KOH gives Ùæ§ÅþðUÅU çßÜØÙ ç×ÜæÙð ÂÚU àßðÌ ¥ßÿæð ÎðÌæ ãñÐ
compound B as the main product. B on A °ðË·¤æðãæòçÜ·¤ KOH ·ð¤ âæÍ ¥çÖç·ý¤Øæ ·¤ÚUÙð
ozonolysis gives C and D. C gives
Cannizaro reaction but not aldol ÂÚU ×é  Ø M¤Â âð Øæñ ç »·¤ B Îð Ì æ ãñ Ð B ·¤æ
condensation. D gives aldol condensation ¥æðÁæðÙ-¥ÂƒæÅUÙ ·¤ÚUÙð ÂÚU Øæñç»·¤ C ÌÍæ D ÂýæŒÌ
but not Cannizaro reaction. A is : ãæðÌð ãñ´Ð C ·ñ¤çÙÁæÚUæð ¥çÖç·ý¤Øæ ÎðÌæ ãñ, ÂÚU‹Ìé °ðËÇUæÜ
ⴃæÙÙ Ùãè´ ÎðÌæÐ D °ðËÇUæÜ â´ƒæÙÙ ÎðÌæ ãñ, ÂÚU‹Ìé
(1)
·ñ¤çÙÁæÚUæð ¥çÖç·ý¤Øæ Ùãè´ ÎðÌæÐ A ãñ Ñ

(1)
(2)

(3) C6H52CH22CH22CH22CH22Cl (2)

(3) C6H52CH22CH22CH22CH22Cl
(4)

(4)

Page 8 Chemistry : English & Hindi 09
25. In the presence of a small amount of 25. ȤæòSȤæðÚUâ ·¤è ·¤× ×æ˜ææ ·¤è ©ÂçSÍçÌ ×ð´ °ÜèÈð¤çÅU·¤
phosphorous, aliphatic carboxylic acids
·¤æÕæðüç€âçÜ·¤ ¥Ü €ÜæðÚUèÙ ¥æñÚU Õýæð×èÙ ·ð¤ âæÍ
react with chlorine or bromine to yield a
compound in which a - hydrogen has been ¥çÖç·ý¤Øæ ·¤ÚUÌð ãé° ¥ÂÙð a - ãæ§ÇþUæðÁÙ ·¤æð ãñÜæðÁÙ
replaced by halogen. This reaction is ×ð´ ÂçÚUßçÌüÌ ·¤ÚUÌð ãñ´Ð §â ¥çÖç·ý¤Øæ ·¤æ Ùæ× ãñ Ñ
known as :
(1) ßæðËȤ-ç·¤àÙÚU ¥çÖç·ý¤Øæ
(1) Wolff - Kischner reaction
(2) Etard reaction
(2) §üÅUæÇüU ¥çÖç·ý¤Øæ
(3) Hell - Volhard - Zelinsky reaction (3) ãðÜ-ȤæðÜæÇüU-ÁðçÜ´S·¤è ¥çÖç·ý¤Øæ
(4) Rosenmund reaction (4) ÚUæðÁðÙ×é´ÇU ¥çÖç·ý¤Øæ

26. Arrange the following amines in the order 26. çِ٠¥×èÙæð´ ·¤æð ÿææÚU·¤Ìæ ·ð¤ ÕɸÌð ·ý¤× ×ð´ ܻ槰Ð
of increasing basicity.

(1)
(1)

(2)
(2)

(3)
(3)

(4)
(4)

Page 9 Chemistry : English & Hindi 09
27. Match the polymers in column-A with 27. ·¤æòÜ×-A ×ð´ çΰ »° ÕãéÜ·¤æð´ ·¤æð ·¤æòÜ×-B ×ð´ ©Ù·ð¤
their main uses in column-B and choose
Âý×é¹ ©ÂØæð» ·ð¤ âæÍ âé×ðçÜÌ ·¤Úð´U ÌÍæ âãè çß·¤ËÂ
the correct answer :
¿éÙð´ Ñ
Column - A Column - B
(A) Polystyrene (i) Paints and œ‰Ë×Á¼ - A œ‰Ë×Á¼ - B
lacquers (A) §ËÁÍSªUˌ¿U; (i) §âÁÕ§ ŠËÖ¿U §âÁËäË
(B) Glyptal (ii) Rain coats
º¾Ë¾Õ ¼Õ™
(B) ÌóÁåªUÁ (ii) º¿UÇË̱½Ë† º¾Ë¾Õ ¼Õ™
(C) Polyvinyl (iii) Manufacture of

(C) §Ë×ÁÍÄˌ̾Á (iii) ̞ÁËÖ¾Õ º¾Ë¾Õ ¼Õ™
Chloride toys
(D) Bakelite (iv) Computer discs

(1) (A) - (ii), (B) - (i), (C) - (iii), (D) - (iv) þÁËÕ¿Uˌ¬U
(2) (A) - (iii), (B) - (i), (C) - (ii), (D) - (iv) (D) ºÖœÕ‰ÁˌªU (iv) œ™‰å½ÏªU¿U ̬USœ‰
(3) (A) - (ii), (B) - (iv), (C) - (iii), (D) - (i) º¾Ë¾Õ ¼Õ™
(4) (A) - (iii), (B) - (iv), (C) - (ii), (D) - (i)
(1) (A) - (ii), (B) - (i), (C) - (iii), (D) - (iv)
(2) (A) - (iii), (B) - (i), (C) - (ii), (D) - (iv)
28. Complete hydrolysis of starch gives : (3) (A) - (ii), (B) - (iv), (C) - (iii), (D) - (i)
(1) glucose and fructose in equimolar (4) (A) - (iii), (B) - (iv), (C) - (ii), (D) - (i)
amounts
(2) galactose and fructose in equimolar 28. SÅUæ¿ü ·ð¤ Âê‡æü ÁÜ ¥ÂƒæÅUÙ âð ç×ÜÌæ ãñ Ñ
amounts (1) ‚Üê·¤æðâ ¥æñÚU Èý餀ÅUæðâ ·¤è â××æðÜ ×æ˜ææ
(3) glucose only (2) »ñÜð€ÅUæðâ ¥æñÚU Èý餀ÅUæðâ ·¤è â××æðÜ ×æ˜ææ
(4) glucose and galactose in equimolar (3) ·ð¤ßÜ ‚Üê·¤æðâ
amounts
(4) ‚Üê·¤æðâ ¥æñÚU »ñÜð€ÅUæðâ ·¤è â××æðÜ ×æ˜ææ

29. is used as :
29. ·¤æ ÂýØæð» ç·¤â M¤Â ×ð´ ãæðÌæ ãñ?

(1) Insecticide (1) ·¤èÅUÙæàæ·¤
(2) Antihistamine (2) ÂýçÌçãSÅñUç×Ù
(3) Analgesic (3) ÂèǸæãæÚUè
(4) Antacid (4) ÂýçÌ¥Ü

30. The cation that will not be precipitated by 30. ßã ÏÙæØÙ Áæð ÌÙé HCl ·ð¤ ©ÂçSÍçÌ ×ð´ H2S âð
H2S in the presence of dil HCl is :
¥ßÿæðçÂÌ Ùãè´ ãæðÌæ ãñ, ßã ãñ Ñ
(1) Cu 21 (1) Cu 21
(2) Pb21 (2) Pb21
(3) As31 (3) As31
(4) Co21
(4) Co21
-oOo- -oOo-

Page 1 MATHEMATICS : English & Hindi 09
1. In a certain town, 25% of the families own 1. ç·¤âè àæãÚU ×ð´, 25% ÂçÚUßæÚUæð´ ·ð¤ Âæâ ȤæðÙ ãñ ÌÍæ
15% ·ð¤ Âæâ ·¤æÚU ãñ ; 65% ÂçÚUßæÚUæð´ ·ð¤ Âæâ Ù Ìæð
a phone and 15% own a car ; 65% families
own neither a phone nor a car and 2,000
families own both a car and a phone. ȤæðÙ ãñ ¥æñÚU Ù ãè ·¤æÚU ãñ, ÌÍæ 2,000 ÂçÚUßæÚUæð´ ·ð¤ Âæâ
Consider the following three statements : ȤæðÙ ÌÍæ ·¤æÚU ÎæðÙæð´ ãñ´Ð çِ٠ÌèÙ ·¤ÍÙæð´ ÂÚU çß¿æÚU
(a) 5% families own both a car and a ·¤èçÁ° Ñ
phone.
(a) 5% ÂçÚUßæÚUæð´ ·ð¤ Âæâ ·¤æÚU ÌÍæ ȤæðÙ ÎæðÙæð´ ãñ´Ð
(b) 35% families own either a car or a
phone. (b) 35% ÂçÚUßæÚUæð´ ·ð¤ Âæâ Øæ Ìæð ·¤æÚU ãñ Øæ ȤæðÙ
(c) 40,000 families live in the town. ãñÐ
Then, (c) àæãÚU ×ð´ 40,000 ÂçÚUßæÚU ÚUãÌð ãñ´Ð
(1) Only (a) and (b) are correct. Ìæð,
(2) Only (a) and (c) are correct.
(1) ·ð¤ßÜ (a) ÌÍæ (b) âãè ãñ´Ð
(3) Only (b) and (c) are correct.
(4) All (a), (b) and (c) are correct.
(2) ·ð¤ßÜ (a) ÌÍæ (c) âãè ãñ´Ð
(3) ·ð¤ßÜ (b) ÌÍæ (c) âãè ãñ´Ð
2. The largest value of r for which the region (4) (a), (b) ÌÍæ (c) âÖè âãè ãñ´Ð
represented by the set {v e C/?v242i?[r}
is contained in the region represented by
the set {z e C/?z21?[?z1i?}, is equal to : 2. r ·¤æ ßã ¥çÏ·¤Ì× ×æÙ çÁâ·ð¤ çÜ° â×é“æØ
{v e C/?v242i?[r} mæÚUæ çÙÏæüçÚUÌ ÿæð˜æ, â×é“æØ
(1)
{z e C/?z21?[?z1i?} mæÚU æ çÙÏæü ç ÚU Ì ÿæð ˜ æ ×ð ´
17

(2) 2 2 âç×çÜÌ ãñ, ãñ Ñ
(3) (1)
3
2 17
2
(2) 2 2
(4)
5
2
(3)
2 3
2
2
3. If 213i is one of the roots of the equation
(4) 5
2
2x329x21kx21350, k e R, then the real 2
root of this equation :
(1) does not exist.
3. ØçÎ 213i, â×è·¤ÚU‡æ 2x329x21kx21350,
k e R ·¤æ °·¤ ×êÜ ãñ, Ìæð §â â×è·¤ÚU‡æ ·¤æ ßæSÌçß·¤
(2) exists and is equal to .
1
2 ×êÜ Ñ
(3) exists and is equal to 2
1
. (1) çßl×æÙ Ùãè´ ãñÐ
2
(2) çßl×æÙ ãñ ÌÍæ ·ð¤ ÕÚUæÕÚU ãñÐ
1
(4) exists and is equal to 1.
2

(3) çßl×æÙ ãñ ÌÍæ 2 1 ·ð¤ ÕÚUæÕÚU ãñÐ
2
(4) çßl×æÙ ãñ ÌÍæ 1 ·ð¤ ÕÚUæÕÚU ãñÐ

Page 2 MATHEMATICS : English & Hindi 09
4. The least value of the product xyz for 4. »é‡æÙÈ¤Ü xyz ·¤æ ß㠋ØêÙÌ× ×êËØ çÁâ·ð¤ çÜ°
x 1 1 x 1 1
which the determinant 1 y 1 is âæÚUç‡æ·¤ 1 y 1 «¤‡æðÌÚU ãñ, ãñ Ñ
1 1 z 1 1 z
non-negative, is :
(1) 22 2
(1) 22 2
(2)
(2)
216 2
(3) 28
2 16 2
(3) 28
(4) 21
(4) 21

ØçÎ A 5   ãñ, Ìæð çِ٠×ð´ âð ·¤æñÙ-âæ °·¤
 0 21 
 0 21  5.
5. If A 5   , then which one of the 1 0 
·¤ÍÙ âãè Ùãè´ ãñ?
1 0 
following statements is not correct ?
(1) A42I5A21I
(1) A42I5A21I
(2) A32I5A(A2I)
(2) A32I5A(A2I)
(3) A21I5A(A22I)
(3) A21I5A(A22I)
(4) A31I5A(A32I)
(4) A31I5A(A32I)

6. The number of ways of selecting 15 teams 6. 15 ÂéL¤áæð´ ÌÍæ 15 ×çãÜæ¥æð´ ×ð´ âð °ðâè 15 ÅUè×ð´,
from 15 men and 15 women, such that çÁÙ×ð´ ÂýˆØð·¤ ×ð´ °·¤ ÂéL¤á ÌÍæ °·¤ ×çãÜæ ãæð, ¿éÙÙð
each team consists of a man and a woman, ·ð¤ ÌÚUè·¤æð´ ·¤è ⴁØæ ãñ Ñ
is :
(1) 1120
(1) 1120
(2) 1240
(2) 1240
(3) 1880
(3) 1880
(4) 1960
(4) 1960

7. Let the sum of the first three terms of an
7. ×æÙæ °·¤ â×æ´ÌÚU ŸæðÉ¸è ·ð¤ ÂýÍ× ÌèÙ ÂÎæð´ ·¤æ Øæð» 39
A.P. be 39 and the sum of its last four terms ãñ ÌÍæ §â·ð¤ ¥´çÌ× ¿æÚU ÂÎæð´ ·¤æ Øæð» 178 ãñÐ ØçÎ
be 178. If the first term of this A.P. is 10, §â â×æ´ÌÚU ŸæðÉ¸è ·¤æ ÂýÍ× ÂÎ 10 ãñ, Ìæð §â â×æ´ÌÚU
then the median of the A.P. is : ŸæðÉ¸è ·¤æ ×æŠØ·¤ ãñ Ñ
(1) 26.5
(1) 26.5
(2) 28
(2) 28
(3) 29.5
(3) 29.5
(4) 31
(4) 31

Page 3 MATHEMATICS : English & Hindi 09
8. If the coefficients of the three successive 8. ØçÎ (11x)n ·ð¤ çmÂÎ çßSÌæÚU ×ð´ ÌèÙ ·ý¤ç×·¤ ÂÎæð´
terms in the binomial expansion of (11x)n
·ð¤ »é‡ææ´·¤æð´ ×ð´ 1 : 7 : 42 ·¤æ ¥ÙéÂæÌ ãñ, Ìæð §Ù ×ð´ âð
are in the ratio 1 : 7 : 42, then the first of
these terms in the expansion is : çßSÌæÚU ×ð´ ÂãÜæ ÂÎ ãñ Ñ
(1) 6 th (1) ÀUÆUæ
(2) 7 th (2) âæÌßæ´
(3) 8 th
(3) ¥æÆUßæ´
(4) 9 th
(4) Ùæñßæ´

30
9. The value of ∑ (r 1 2)(r 2 3) is equal to :
∑ (r 1 2)(r 2 3) ·¤æ ×æÙ ÕÚUæÕÚU ãñ Ñ
30
r516 9.
r516
(1) 7785
(2) 7780 (1) 7785

(3) 7775 (2) 7780

(4) 7770 (3) 7775
(4) 7770

2
e x 2 cosx
10. is equal to :
e x 2 cosx
ÕÚUæÕÚU ãñ Ñ
2
lim
10.
x →0 2
sin x lim
x →0 sin 2 x
(1) 3
(1) 3
3
(2) 3
2 (2)
2
5
(3) 5
4 (3)
(4) 2
4
(4) 2

11. The distance, from the origin, of the
normal to the curve, x52 cost 1 2t sint, 11. ß·ý¤ x52 cost12t sint, y52 sint22t cost
ÂÚU t 5 p ÂÚU ¹è´¿ð »° ¥çÖÜ´Õ ·¤è ×êÜ çÕ´Îé âð
p
y 5 2 sint22t cost at t 5 , is :
4 4
(1) 4 ÎêÚUè ãñ Ñ
(2) 2 2 (1) 4
(3) 2 (2) 2 2

(4) 2 (3) 2

(4) 2

Page 4 MATHEMATICS : English & Hindi 09
12. If Rolle’s theorem holds for the function 12. ØçΠȤÜÙ f (x)52x31bx21cx, x e [21, 1]
f (x)52x 3 1bx 2 1cx, x e [21, 1], at the
·ð¤ çÜ° çÕ´Îé x 5 1 ÂÚU ÚUæðÜð ·¤æ Âý×ðØ Üæ»ê ãæðÌæ ãñ,
point x 5 , then 2b1c equals :
1
2
2
Ìæð 2b1c ÕÚUæÕÚU ãñ Ñ
(1) 1
(1) 1
(2) 21
(2) 21
(3) 2
(3) 2
(4) 23
(4) 23

13. Let the tangents drawn to the circle,
x21y2516 from the point P(0, h) meet the 13. ×æÙæ çÕ´Îé P(0, h) âð ßëžæ x21y2516 ÂÚU ¹è´¿è
x-axis at points A and B. If the area of »§ü SÂàæü ÚðU¹æ°¡ x-¥ÿæ ·¤æð çÕ´Îé¥æð´ A ÌÍæ B ÂÚU
DAPB is minimum, then h is equal to : ç×ÜÌè ãñ´Ð ØçÎ DAPB ·¤æ ÿæð˜æÈ¤Ü ‹ØêÙÌ× ãñ, Ìæð
(1) 4 3 h ÕÚUæÕÚU ãñ Ñ

(2) 3 3 (1) 4 3

(3) 3 2 (2) 3 3

(4) 4 2 (3) 3 2

(4) 4 2
dx
14. The integral ∫ 3 5 is equal
(x 1 1) 4 (x 2 2) 4
â×æ·¤Ü ∫ ÕÚUæÕÚU ãñ Ñ
dx
14.
to :
3 5
(x 1 1) 4 (x 2 2) 4

 x 11 4
1

(1)  1C  x 11 4
1

 x 22   1C
4
(1)
 x 22 
4

 x 22 4
1

(2)  1C  x 22 4
1

 x 11   1C
4
(2)
 x 11 
4

4  x 11 4
1

(3) 2   1C 4  x 11 4
1

3  x 22  (3) 2   1C
3  x 22 

4  x 22 4
1

(4) 2   1C 4  x 22 4
1

3  x 11  (4) 2   1C
3  x 11 

Page 5 MATHEMATICS : English & Hindi 09

x > 0 ·ð¤ çÜ° ×æÙæ f ( x ) 5 ∫ dt ãñ, Ìæð
x x
15. For x > 0, let f ( x ) 5 ∫ dt . Then 15.
log t log t
11t 11t
1 1

f ( x ) 1 f   is equal to : f ( x ) 1 f   ÕÚUæÕÚU ãñ Ñ
1 1
x x

1 1
(1) (log x )2 (1) (log x )2
4 4

1 1
(2) (log x )2 (2) (log x )2
2 2
(3) log x (3) log x
1 1
(4) log x 2 (4) log x 2
4 4

16. The area (in square units) of the region 16. ß·ý¤æð´ y12x250 ÌÍæ y13x251 mæÚUæ ÂçÚUÕh ÿæð˜æ
bounded by the curves y12x 2 50 and
·¤æ ÿæð˜æÈ¤Ü (ß»ü §·¤æ§Øæð´ ×ð´) ÕÚUæÕÚU ãñ Ñ
y13x251, is equal to :
3
3 (1)
(1) 5
5
3
3 (2)
(2) 4
4
1
1 (3)
(3) 3
3
4
4 (4)
(4) 3
3

17. If y(x) is the solution of the differential 17. ØçÎ y(x), ¥ß·¤Ü â×è·¤ÚU‡æ

5 x 2 14x29 , x ¹ 22 5 x 2 14x29 , x ¹ 22 ¥æñÚU
dy
equation ( x12) ( x12)
dy
dx
y(0)50, ·¤æ ãÜ ãñ, Ìæð y(24) ÕÚUæÕÚU ãñ Ñ
dx
and y(0)50, then y(24) is equal to :
(1) 0 (1) 0
(2) 1 (2) 1
(3) 21 (3) 21
(4) 2 (4) 2

Page 6 MATHEMATICS : English & Hindi 09

18. The points  0, 8  , (1, 3) and (82, 30) : 18. çÕ´Îé  0, 8  , (1, 3) ÌÍæ (82, 30) Ñ
 3  3
(1) form an obtuse angled triangle. (1) °·¤ ¥çÏ·¤·¤æð‡æ ç˜æÖéÁ ÕÙæÌð ãñ´Ð
(2) form an acute angled triangle.
(2) °·¤ ‹ØêÙ·¤æð‡æ ç˜æÖéÁ ÕÙæÌð ãñ´Ð
(3) form a right angled triangle.
(3) °·¤ â×·¤æð‡æ ç˜æÖéÁ ÕÙæÌð ãñ´Ð
(4) lie on a straight line.
(4) °·¤ âÚUÜ ÚðU¹æ ÂÚU çSÍÌ ãñ´Ð
19. Let L be the line passing through the point
P(1, 2) such that its intercepted segment 19. ×æÙæ L, çÕ´Îé P(1, 2) âð ãæð·¤ÚU ÁæÙð ßæÜè ßã ÚðU¹æ ãñ
between the co-ordinate axes is bisected
at P. If L1 is the line perpendicular to L
çÁâ·¤æ çÙÎðüàææ´·¤ ¥ÿææð´ ·ð¤ Õè¿ ·¤ÅUæ ÚðU¹æ¹‡ÇU P ÂÚU
and passing through the point (22, 1), â×çmÖæçÁÌ ãæðÌæ ãñÐ ×æÙæ L1 ßã ÚðU¹æ ãñ Áæð L ÂÚU
then the point of intersection of L and L1 Ü´ÕßÌ ãñ ÌÍæ çÕ´Îé (22, 1) âð ãæð·¤ÚU ÁæÌè ãñ, Ìæð
is : L ÌÍæ L1 ·¤æ Âýç̑ÀðUÎÙ çÕ´Îé ãñ Ñ
 4 12 
(1)  ,  4 12 
(1)

5 5   , 
5 5 
 11 29 
(2)  ,  11 29 
(2)

 20 10   , 
 20 10 
 3 17 
(3)  ,  3 17 
(3)

 10 5   , 
 10 5 
 3 23 
(4)  ,  3 23 
(4)

 5 10   , 
 5 10 

20. If y13x50 is the equation of a chord of
the circle, x 2 1y 2 230x50, then the 20. ØçÎ y13x50, ßëžæ x21y2230x50 ·¤è °·¤
equation of the circle with this chord as Áèßæ ·¤æ â×è·¤ÚU‡æ ãñ, Ìæð ©â ßëžæ, çÁâ·¤æ ÃØæâ,
diameter is : Øã Áèßæ ãñ, ·¤æ â×è·¤ÚU‡æ ãñ Ñ
(1) x 21y 2 13x19y50 (1) x 21y 2 13x19y50
(2) x 21y 2 23x19y50 (2) x 21y 2 23x19y50
(3) x 21y 2 23x29y50 (3) x 21y 2 23x29y50
(4) x 21y 2 13x29y50 (4) x 21y 2 13x29y50

Page 7 MATHEMATICS : English & Hindi 09
21. If the tangent to the conic, y265x 2 at 21. ØçÎ àææ´·¤ß y265x2 ·ð¤ çÕ´Îé (2, 10) ÂÚU ¹è´¿è
(2, 10) touches the circle,
»§ü SÂàæü Úð U ¹ æ ßë ž æ x21y218x22y5k ·¤æð
x21y218x22y5k (for some fixed k) at a
point (a, b) ; then (a, b) is : (ç·¤âè çÙçà¿Ì k ·ð¤ çÜ°) çÕ´Îé (a, b) ÂÚU SÂàæü
·¤ÚUÌè ãñ, Ìæð (a, b) ãñ Ñ
 6 10 
(1) 2 , 
 6 10 
(1)
 17 17 
,
2 
 17 17 
(2)  8 2 
2 , 
(2) 
 17 17  8 2 
2 , 
 17 17 
(3)
 4 1 
2 , 
(3)
 17 17   4 1 
2 , 
 17 17 
(4)
 7 6 
2 , 
(4)
 17 17   7 6 
2 , 
 17 17 

22. An ellipse passes through the foci of the
hyperbola, 9x 224y 2 536 and its major 22. °·¤ Îèƒæü ß ë ž æ, ¥çÌÂÚU ß ÜØ 9x224y2536 ·ð ¤
and minor axes lie along the transverse and
conjugate axes of the hyperbola
ÙæçÖ·ð´¤Îýæð´ âð ãæð·¤ÚU ÁæÌæ ãñ ÌÍæ §â·ð¤ Îèƒæü ÌÍæ ܃æé
respectively. If the product of eccentricities ¥ÿæ ·ý¤×àæÑ ¥çÌÂÚUßÜØ ·ð¤ ¥ÙéÂýSÍ ÌÍæ â´Øé‚×è
¥ÿææð́ ·ð¤ ¥ÙéçÎàæ ãñ́Ð ØçÎ §Ù Îæð àææ´·¤ßæð́ ·¤è ©ˆ·ð́¤ÎýÌæ¥æð́
of the two conics is, then which of the
1

·¤æ »é‡æÙÈ¤Ü ãñ, Ìæð çِ٠×ð´ âð ·¤æñÙ-âæ çÕ´Îé
2 1
following points does not lie on the 2
ellipse ? Îèƒæüßëžæ ÂÚU çSÍÌ Ùãè´ ãñ?
(1) ( 13 , 0 ) (1) ( 13 , 0 )
 39 
(2)  , 3  39 
 2  (2)  , 3
 2 
1 3
(3)  13 ,  1 3
2 2  (3)  13 , 
2 2 

 13 
(4)  , 6  13 
 2  (4)  , 6
 2 

23. If the points (1, 1, l) and (23, 0, 1) are
equidistant from the plane, 23. ØçÎ çÕ´ Î é (1, 1, l) ÌÍæ (23, 0, 1) â×ÌÜ
3x14y212z11350, then l satisfies the 3x14y212z11350 âð â×ÎêÚUSÍ ãñ´, Ìæð l, çِÙ
equation : â×è·¤ÚU‡æ ·¤æð â´ÌécÅU ·¤ÚUÌæ ãñ Ñ
(1) 3x 2 210x1750 (1) 3x 2 210x1750
(2) 3x 2 110x1750 (2) 3x 2 110x1750
(3) 3x 2 110x21350 (3) 3x 2 110x21350
(4) 3x 2 210x12150 (4) 3x 2 210x12150

Page 8 MATHEMATICS : English & Hindi 09
24. If the shortest distance between the lines
ØçÎ ÚðU¹æ¥æð´
x 21 y 11 z
24. 5 5 , (a ¹21)
x 21 y 11 z a 21
5 5 , (a ¹21) and 1
a 21 1 ÌÍæ x1y1z115052x2y1z13 ·ð¤ Õè¿
x1y1z115052x2y1z13 is , then ·¤è ‹ØêÙÌ× ÎêÚUè ãñ, Ìæð a ·¤æ °·¤ ×æÙ ãñ Ñ
1 1
3 3
a value of a is :
16
16 (1) 2
(1) 2 19
19
19
19 (2) 2
(2) 2 16
16
32
32 (3)
(3) 19
19
19
19 (4)
(4) 32
32

×æÙæ ÌÍæ b °ð â ð ×æ˜æ·¤ âçÎàæ ãñ ´ ç·¤
→ →
→ → 25.
25. Let a and b be two unit vectors such
a
5 3 ãñÐ ØçÎ
that 5 3 . If
→ → →
( → →
)
→ → →
c 5 a 12 b 13 a 3 b (→ →
) ãñ, Ìæð ÕÚUæÕÚU
c 5 a 1 2 b 1 3 a 3 b , then is
equal to :
ãñ Ñ
(1) 55 (1) 55

(2) 51 (2) 51

(3) 43 (3) 43

(4) 37 (4) 37

26. Let X be a set containing 10 elements and 26. ×æÙæ X °·¤ â×é“æØ ãñ çÁâ×ð´ 10 ¥ßØß ãñ´ ÌÍæ
P(X) be its power set. If A and B are picked P(X) §â·¤æ ƒææÌ â×é“æØ ãñÐ ØçÎ P(X) âð A ÌÍæ
up at random from P(X), with B ØæÎë‘ÀUØæ, ÂýçÌSÍæÂÙæ âçãÌ, çÜ° »° ãñ´, Ìæð
replacement, then the probability that A
and B have equal number of elements, is : A ÌÍæ B ×ð´ ÕÚUæÕÚU ¥ßØßæð´ ·ð¤ ãæðÙð ·¤è ÂýæçØ·¤Ìæ ãñ Ñ
20 20
(1)
C10
(1)
C10
2 10 2 10

( 2 10 2 1 ) ( 210 2 1 )
(2) (2)
2 20 2 20

( 2 10 2 1 ) ( 210 2 1 )
(3) (3)
2 10 2 10
20 20
(4)
C10
(4)
C10
2 20 2 20

Page 9 MATHEMATICS : English & Hindi 09
27. A factory is operating in two shifts, day 27. °·¤ Èñ¤€ÅþUè Îæð ÂæçÚUØæð´, çÎÙ ÌÍæ ÚUæÌ, ×ð´ ¿ÜÌè ãñ
and night, with 70 and 30 workers
çÁÙ×ð´ ·ý¤×àæÑ 70 ÌÍæ 30 ·¤æ×»æÚU ·¤æØü ·¤ÚUÌð ãñ´Ð
respectively. If per day mean wage of the
day shift workers is ` 54 and per day mean ØçÎ çÎÙ ·¤è ÂæÚUè ·ð¤ ·¤æ×»æÚUæð´ ·¤æ ×æŠØ ÂýçÌçÎÙ
wage of all the workers is ` 60, then per ßðÌÙ ` 54 ãñ ÌÍæ âÖè ·¤æ×»æÚUæð´ ·¤æ ×æŠØ ÂýçÌçÎÙ
day mean wage of the night shift workers ßðÌÙ ` 60 ãñ, Ìæð ÚUæÌ ×ð´ ·¤æØü ·¤ÚUÙð ßæÜð ·¤æ×»æÚUæð´ ·¤æ
(in `) is :
×æŠØ ÂýçÌçÎÙ ßðÌÙ (` ×ð´) ãñ Ñ
(1) 66
(1) 66
(2) 69
(2) 69
(3) 74
(3) 74
(4) 75
(4) 75

28. In a DABC, 5 2 1 3 and ÐC5608.
°·¤ ç˜æÖéÁ ABC ×ð´, a 5 2 1 3 ÌÍæ ÐC5608
a
b 28.
Then the ordered pair (ÐA, ÐB) is equal
b
to : ãñ, Ìæð ·ý¤ç×Ì Øé‚× (ÐA, ÐB) ÕÚUæÕÚU ãñ Ñ
(1) (158, 1058) (1) (158, 1058)
(2) (1058, 158) (2) (1058, 158)
(3) (458, 758) (3) (458, 758)
(4) (758, 458) (4) (758, 458)

29.
 2x 
If f ( x ) 5 2tan21 x 1 sin21   , x > 1, 29. ØçÎ f ( x ) 5 2tan21 x 1 sin21  2x 
2
,x>1
 1 1 x2   11x 
then f (5) is equal to : ãñ, Ìæð f (5) ÕÚUæÕÚU ãñ Ñ
p
(1)
p
2 (1)
2
(2) p (2) p
(3) 4 tan21(5) (3) 4 tan21(5)

tan21 
 65 
(4)  (4)
 65 
tan21  
 156   156 

30. The contrapositive of the statement 30. ·¤ÍÙ Ñ
“If it is raining, then I will not come”, is :
ÒÒØçÎ ßáæü ãæð ÚUãè ãñ, Ìæð ×ñ´ Ùãè´ ¥æª´¤»æÓÓ
(1) If I will come, then it is not raining.
(2) If I will not come, then it is raining. ·¤æ ÂýçÌÏÙæˆ×·¤ ·¤ÍÙ ãñ Ñ
(3) If I will not come, then it is not (1) ØçÎ ×ñ´ ¥æª´¤»æ, Ìæð ßáæü Ùãè´ ãæð ÚUãè ãñÐ
raining.
(2) ØçÎ ×ñ´ Ùãè´ ¥æª´¤»æ, Ìæð ßáæü ãæð ÚUãè ãñÐ
(4) If I will come, then it is raining.
(3) ØçÎ ×ñ´ Ùãè´ ¥æª´¤»æ, Ìæð ßáæü Ùãè´ ãæð ÚUãè ãñÐ
-o0o- (4) ØçÎ ×ñ´ ¥æª´¤»æ, Ìæð ßáæü ãæð ÚUãè ãñÐ

-o0o-

Answer Key
Question No. Answer Key Question No. Answer Key Question No. Answer Key
Q1 3 Q31 2 Q61 4
Q2 3 Q32 3 Q62 4
Q3 3 Q33 2 Q63 2
Q4 2 Q34 3 Q64 3
Q5 3 Q35 1 Q65 3
Q6 3 Q36 2 Q66 2
Q7 3 Q37 2 Q67 3
Q8 1 Q38 1 Q68 2
Q9 * Q39 1 Q69 2
Q10 1 Q40 3 Q70 2
Q11 3 Q41 4 Q71 3
Q12 4 Q42 2 Q72 2
Q13 2 Q43 1 Q73 4
Q14 3 Q44 3 Q74 3
Q15 3 Q45 3 Q75 2
Q16 3 Q46 2 Q76 4
Q17 3 Q47 2 Q77 1
Q18 3 Q48 3 Q78 4
Q19 3 Q49 4 Q79 1
Q20 2 Q50 4 Q80 2
Q21 2 Q51 3 Q81 2
Q22 1 Q52 4 Q82 3
Q23 2 Q53 2 Q83 1
Q24 3 Q54 1 Q84 3
Q25 3 Q55 3 Q85 1
Q26 4 Q56 4 Q86 4
Q27 3 Q57 2 Q87 3
Q28 2 Q58 3 Q88 2
Q29 3 Q59 3 Q89 2
Q30 2 Q60 4 Q90 1