3. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãF/Page 3
4. The metal that cannot be obtained by
electrolysis of an aqueous solution of its
salts is :
(1) Ca
(2) Cu
(3) Cr
(4) Ag
5. On heating an aliphatic primary amine
with chloroform and ethanolic potassium
hydroxide, the organic compound formed
is :
(1) an alkanediol
(2) an alkyl cyanide
(3) an alkyl isocyanide
(4) an alkanol
6. For the reaction SO2(g)1
1
2
O2(g) ìSO3(g),
if KP5KC(RT)x where the symbols have
usual meaning then the value of x is :
(assuming ideality)
(1)
1
2
2
(2)
1
2
(3) 1
(4) 21
4. ÏæÌé Áæð ¥ÂÙð Ü߇ææð´ ·ð¤ ÁÜèØ çßÜØÙæð´ ·ð¤
§Üñ€ÅþUæÜðçââ (çßléÌ ¥ÂƒæÅUÙ) âð ÂýæŒÌ Ùãè´ ãæð
â·¤Ìè ãæðÌè ãñ Ñ
(1) Ca
(2) Cu
(3) Cr
(4) Ag
5. °ðçÜÈñ¤çÅU·¤ ÂýæØ×ÚUè °×èÙ ·¤æð €ÜæðÚUæðȤæ×ü ¥æñÚU
°ÍæÙæðçÜ·¤ ÂæðÅñUçàæØ× ãæ§ÇþUæ€âæ§ÇU ·ð¤ âæÍ »ÚU× ·¤ÚUÙð
ÂÚU ÕÙæ ¥æÚU»ñçÙ·¤ Øæñç»·¤ ãæðÌæ ãñ Ñ
(1) °·¤ °ðË·ð¤ÙÇUæØæðÜ
(2) °·¤ °ðçË·¤Ü çâØæÙæ§ÇU
(3) °·¤ °ðçË·¤Ü ¥æ§âæðçâØæÙæ§ÇU
(4) °·¤ °ðË·¤æÙæðÜ
6. ¥çÖç·ý¤Øæ, SO2(g)1
1
2
O2(g) ì SO3(g) ·ð¤ çÜ°
KP5KC(RT)x ãæð»æ ÁÕ·¤è âÕ âê¿·¤ ¥ÿæÚU âæ×æ‹Ø
¥Íü ÚU¹Ìð ãñ´ Ìæð ¥æÎàæüÚUM¤ÂÌæ ×æÙÌð ãé° x ·¤æ ×æÙ
ãæð»æ Ñ
(1)
1
2
2
(2)
1
2
(3) 1
(4) 21
4. F/Page 4 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
7. Given below are the half - cell reactions :
Mn2112e2® Mn ; Eo521.18 V
2(Mn311e2® Mn21) ; Eo511.51 V
The Eo for 3Mn21® Mn12Mn31 will be :
(1) 22.69 V ; the reaction will occur
(2) 20.33 V ; the reaction will not occur
(3) 20.33 V ; the reaction will occur
(4) 22.69 V ; the reaction will not occur
8. If Z is a compressibility factor,
van der Waals equation at low pressure
can be written as :
(1) Z512
a
VRT
(2) Z512
Pb
RT
(3) Z511
Pb
RT
(4) Z511
RT
Pb
9. In the reaction,
4 5LiAlH PCl Alc. KOH
3CH COOH A B C££££“ £££“ £££££“ ,
the product C is :
(1) Acetylene
(2) Ethylene
(3) Acetyl chloride
(4) Acetaldehyde
7. Ùè¿ð ·é¤ÀU ¥hü âðÜ ¥çÖç·ý¤Øæ°´ Îè »§ü ãñ´ Ñ
Mn2112e2® Mn ; Eo521.18 V
2(Mn311e2® Mn21) ; Eo511.51 V
3Mn21® Mn12Mn31 ·ð¤ çÜØð Eo ãæð»æ Ñ
(1) 22.69 V ; ¥çÖç·ý¤Øæ ãæð»èÐ
(2) 20.33 V ; ¥çÖç·ý¤Øæ Ùãè´ ãæð»èÐ
(3) 20.33 V ; ¥çÖç·ý¤Øæ ãæð»èÐ
(4) 22.69 V ; ¥çÖç·ý¤Øæ Ùãè´ ãæð»èÐ
8. ØçÎ Z â´ÂèǸ٠»é‡æ·¤ ãæð Ìæð ·¤× ÎæÕ ÂÚU ßæ´ÇUÚßæËâ
â×è·¤ÚU‡æ ·¤æð çܹæ Áæ â·¤Ìæ ãñ Ñ
(1) Z512
a
VRT
(2) Z512
Pb
RT
(3) Z511
Pb
RT
(4) Z511
RT
Pb
9. ¥çÖç·ý¤Øæ âðÅ,
4 5LiAlH PCl Alc. KOH
3CH COOH A B C££££“ £££“ £££££“
×ð´ ç·ý¤Øæ È¤Ü C ãæðÌæ ãñ Ñ
(1) °çâçÅUÜèÙ
(2) §Íæ§üÜèÙ
(3) °çâÅUæ§Ü €ÜæðÚUæ§ÇU
(4) °ðçâÅU°ðçËÇUãæ§ÇU
6. F/Page 6 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
14. For which of the following molecule
significant m¹0 ?
(a) (b)
(c) (d)
(1) (a) and (b)
(2) Only (c)
(3) (c) and (d)
(4) Only (a)
15. CsCl crystallises in body centred cubic
lattice. If ‘a’ is its edge length then which
of the following expressions is correct ?
(1) Cs Cl
3a
r r
2
1 21 5
(2) Cs Cl
3
r r a
2
1 21 5
(3) Cs Cl
r r 3a1 21 5
(4) Cs Cl
r r 3a1 21 5
16. Which one is classified as a condensation
polymer ?
(1) Neoprene
(2) Teflon
(3) Acrylonitrile
(4) Dacron
14. çÙÙ ×ð´ âð 緤⠥‡æé ·ð¤ çÜØð ÕãéÌ âè×æ Ì·¤ m¹0
ãæð»æ?
(a) (b)
(c) (d)
(1) (a) ¥æñÚU (b)
(2) ·ð¤ßÜ (c)
(3) (c) ¥æñÚU (d)
(4) ·ð¤ßÜ (a)
15. CsCl ·¤æØ ·ð¤ç‹ÎýÌ ƒæÙæ·¤ÚU ÁæÜ·¤ ×ð´ ç·ý¤SÅUçÜÌ
ãæðÌæ ãñÐ ØçÎ ç·¤ÙæÚðU ·¤è ÜÕæ§ü ‘a’ ãæð Ìæð çÙÙ âê˜ææð´
×ð´ âð ·¤æñÙ-âæ ÆUè·¤ ãæð»æ?
(1) Cs Cl
3a
r r
2
1 21 5
(2) Cs Cl
3
r r a
2
1 21 5
(3) Cs Cl
r r 3a1 21 5
(4) Cs Cl
r r 3a1 21 5
16. §Ù×ð´ âð 緤ⷤæð ·¤‹ÇñU‹âðàæÙ ÕãéÜ·¤ ×æÙæ ÁæØð»æ?
(1) çÙØæðçÂýÙ
(2) ÅñU$ȤÜæÙ
(3) °ðç·ý¤ÜæðÙæ§ÅþUæ§Ü
(4) ÇñU·¤ÚUæÙ
13. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãF/Page 13
31.
2
20
sin ( cos )
x
x
lim
x
p
“
is equal to :
(1) p
(2)
2
p
(3) 1
(4) 2p
32. Let the population of rabbits surviving at
a time t be governed by the differential
equation
dp(t) 1
p(t)
dt 2
5 2200.
If p(0)5100, then p(t) equals :
(1) 4002300 e2t/2
(2) 4002300 et/2
(3) 3002200 e2t/2
(4) 6002500 et/2
33. The statement ~(p « ~q) is :
(1) a fallacy
(2) equivalent to p « q
(3) equivalent to ~p « q
(4) a tautology
31.
2
20
sin ( cos )
x
x
lim
x
p
“
·¤æ ×æÙ ãñ Ñ
(1) p
(2)
2
p
(3) 1
(4) 2p
32. ×æÙæ ç·¤âè â×Ø t ÂÚU ÁèçßÌ ¹ÚU»æðàææð´ ·¤è ÁÙâ´Øæ
¥ß·¤Ü â×è·¤ÚU‡æ
dp(t) 1
p(t)
dt 2
5 2200 mæÚUæ
çÙØ´ç˜æÌ ãñ´Ð
ØçÎ p(0)5100 ãñ, Ìæð p(t) ÕÚUæÕÚU ãñ Ñ
(1) 4002300 e2t/2
(2) 4002300 et/2
(3) 3002200 e2t/2
(4) 6002500 et/2
33. ·¤ÍÙ ~(p « ~q) ãñ Ñ
(1) °·¤ ãðˆßæÖæâ (fallacy)
(2) p « q ·ð¤ ÌéËØ
(3) ~p « q ·ð¤ ÌéËØ
(4) °·¤ ÂéÙL¤ç€Ì (tautology)
PART B — MATHEMATICS Öæ» B — »ç‡æÌ
14. F/Page 14 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
34. Let a and b be the roots of equation
px21qx1r50, p¹0. If p, q, r are in A.P.
and
1 1
41 5
a b
, then the value of ?a2b?
is :
(1)
2 13
9
(2)
61
9
(3)
2 17
9
(4)
34
9
35. Let PS be the median of the triangle with
vertices P(2, 2), Q(6,21) and R(7, 3). The
equation of the line passing through
(1, 21) and parallel to PS is :
(1) 2x29y21150
(2) 4x27y21150
(3) 2x19y1750
(4) 4x17y1350
36. The area of the region described by
A5{(x, y) : x21y2 [ 1 and y2 [ 12x} is :
(1)
2
2 3
p
1
(2)
4
2 3
p
1
(3)
4
2 3
p
2
(4)
2
2 3
p
2
34. ×æÙæ a ÌÍæ b â×è·¤ÚU‡æ px21qx1r50, p¹0 ·ð¤
×êÜ ãñ´Ð ØçÎ p, q, r â×æ´ÌÚU Ÿæðɸè ×ð´ ãñ´ ÌÍæ
1 1
41 5
a b
ãñ, Ìæð ?a2b? ·¤æ ×æÙ ãñ Ñ
(1)
2 13
9
(2)
61
9
(3)
2 17
9
(4)
34
9
35. ×æÙæ PS °·¤ ç˜æÖéÁ ·¤è ×æçŠØ·¤æ ãñ çÁâ·ð¤ àæèáü
P(2, 2), Q(6,21) ÌÍæ R(7, 3) ãñ´Ð (1, 21) âð
ãæð·¤ÚU ÁæÙð ßæÜè ÚðU¹æ, Áæð PS ·ð¤ â×æ´ÌÚU ãñ, ·¤æ
â×è·¤ÚU‡æ ãñ Ñ
(1) 2x29y21150
(2) 4x27y21150
(3) 2x19y1750
(4) 4x17y1350
36. A5{(x, y) : x21y2 [ 1 ÌÍæ y2 [ 12x} ·ð¤
mæÚUæ ÂýΞæ ÿæð˜æ ·¤æ ÿæð˜æÈ¤Ü ãñ Ñ
(1)
2
2 3
p
1
(2)
4
2 3
p
1
(3)
4
2 3
p
2
(4)
2
2 3
p
2
15. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãF/Page 15
37. If A is an 333 non - singular matrix such
that AA95A9A and B5A21 A9, then BB9
equals :
(1) (B21)9
(2) I1B
(3) I
(4) B21
38. The image of the line
31 4
3 1 5
yx z22 2
5 5
2
in the plane
2x2y1z1350 is the line :
(1)
53 2
3 1 5
yx z12 2
5 5
2 2
(2)
53 2
3 1 5
yx z21 2
5 5
2
(3)
53 2
3 1 5
yx z21 1
5 5
2 2
(4)
53 2
3 1 5
yx z12 2
5 5
2
39. If x521 and x52 are extreme points of
f(x)5a log ?x?1bx21x then :
(1) a52, b5
1
2
(2) a526, b5
1
2
(3) a526, b52
1
2
(4) a52, b52
1
2
37. ØçÎ A °·¤ °ðâæ 333 ÃØ鈷ý¤×‡æèØ ¥æÃØêã ãñ ç·¤
AA95A9A ÌÍæ B5A21 A9 ãñ, Ìæð BB9 ÕÚUæÕÚU
ãñ Ñ
(1) (B21)9
(2) I1B
(3) I
(4) B21
38. â×ÌÜ 2x2y1z1350 ×ð´ ÚðU¹æ
31 4
3 1 5
yx z22 2
5 5
2
·ð¤ ÂýçÌçÕ´Õ ßæÜè
ÚðU¹æ ãñ Ñ
(1)
53 2
3 1 5
yx z12 2
5 5
2 2
(2)
53 2
3 1 5
yx z21 2
5 5
2
(3)
53 2
3 1 5
yx z21 1
5 5
2 2
(4)
53 2
3 1 5
yx z12 2
5 5
2
39. ØçÎ x521 ÌÍæ x52,
f(x)5a log ?x?1bx21x ·ð¤ ¿ÚU×çÕ´Îé ãñ´, Ìæð Ñ
(1) a52, b5
1
2
(2) a526, b5
1
2
(3) a526, b52
1
2
(4) a52, b52
1
2
17. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãF/Page 17
42. If the coefficients of x3 and x4 in the
expansion of (11ax1bx2) (122x)18 in
powers of x are both zero, then (a, b) is
equal to :
(1)
272
16
3
,
Ë ÛÜÌ ÜÌ ÜÌÍ Ý
(2)
251
16
3
,
Ë ÛÜÌ ÜÌ ÜÌÍ Ý
(3)
251
14
3
,
Ë ÛÜÌ ÜÌ ÜÌÍ Ý
(4)
272
14
3
,
Ë ÛÜÌ ÜÌ ÜÌÍ Ý
43. If z is a complex number such that ?z?/2,
then the minimum value of
1
z
2
1 :
(1) is strictly greater than
3
2
but less
than
5
2
(2) is equal to
5
2
(3) lies in the interval (1, 2)
(4) is strictly greater than
5
2
42. ØçÎ (11ax1bx2) (122x)18 ·ð¤ x ·¤è ƒææÌæð´ ×ð´
ÂýâæÚU ×ð´ x3 ÌÍæ x4, ÎæðÙæ𴠷𤠻é‡ææ´·¤ àæê‹Ø ãñ´, Ìæð (a, b)
ÕÚUæÕÚU ãñ Ñ
(1)
272
16
3
,
Ë ÛÜÌ ÜÌ ÜÌÍ Ý
(2)
251
16
3
,
Ë ÛÜÌ ÜÌ ÜÌÍ Ý
(3)
251
14
3
,
Ë ÛÜÌ ÜÌ ÜÌÍ Ý
(4)
272
14
3
,
Ë ÛÜÌ ÜÌ ÜÌÍ Ý
43. ØçÎ z °·¤ °ðâè âçןæ â´Øæ ãñ ç·¤ ?z?/2 ãñ, Ìæð
1
z
2
1 ·¤æ ‹ØêÙÌ× ×æÙ Ñ
(1)
3
2
âð çÙÚ´UÌÚU ÕǸæ ãñ ÂÚU‹Ìé
5
2
âð ·¤× ãñÐ
(2)
5
2
·ð¤ ÕÚUæÕÚU ãñÐ
(3) ¥´ÌÚUæÜ (1, 2) ×ð´ çSÍÌ ãñÐ
(4)
5
2
âð çÙÚ´UÌÚU ÕǸæ ãñÐ
18. F/Page 18 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
44. The integral
1
1
1 e d
x
xx x
x
Ë ÛÜÌ ÜÌ ÜÌÍ Ý×
1
1 2 is
equal to :
(1) 2x
1
e c
x
x
1
1
(2) (x21)
1
e c
x
x
1
1
(3) x
1
e c
x
x
1
1
(4) (x11)
1
e c
x
x
1
1
45. The slope of the line touching both the
parabolas y254x and x25232y is :
(1)
2
3
(2)
1
2
(3)
3
2
(4)
1
8
44. â×æ·¤Ü
1
1
1 e d
x
xx x
x
Ë ÛÜÌ ÜÌ ÜÌÍ Ý×
1
1 2 ÕÚUæÕÚU ãñ Ñ
(1) 2x
1
e c
x
x
1
1
(2) (x21)
1
e c
x
x
1
1
(3) x
1
e c
x
x
1
1
(4) (x11)
1
e c
x
x
1
1
45. ÂÚUßÜØæð´ y254x ÌÍæ x25232y ÎæðÙæð´ ·¤æð SÂàæü
·¤ÚUÙð ßæÜè ÚðU¹æ ·¤è Âý߇æÌæ ãñ Ñ
(1)
2
3
(2)
1
2
(3)
3
2
(4)
1
8
20. F/Page 20 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
49. Let A and B be two events such that
( )
1
P A B
6
5 , ( )
1
P A B
4
¬ 5 and
( )
1
P A
4
5 , where A stands for the
complement of the event A. Then the
events A and B are :
(1) independent and equally likely.
(2) mutually exclusive and independent.
(3) equally likely but not independent.
(4) independent but not equally likely.
50. The locus of the foot of perpendicular
drawn from the centre of the ellipse
x213y256 on any tangent to it is :
(1) (x21y2)256x222y2
(2) (x22y2)256x212y2
(3) (x22y2)256x222y2
(4) (x21y2)256x212y2
51. If f and g are differentiable functions in
[0, 1] satisfying f (0)525g(1), g(0)50 and
f (1)56, then for some ce]0, 1[ :
(1) f 9(c)52g9(c)
(2) 2f 9(c)5g9(c)
(3) 2f 9(c)53g9(c)
(4) f 9(c)5g9(c)
49. ×æÙæ A ÌÍæ B Îæð °ðâè ƒæÅUÙæ°¡ ãñ´ ç·¤
( )
1
P A B
6
5 , ( )
1
P A B
4
¬ 5 ÌÍæ
( )
1
P A
4
5 ãñ ÁÕç·¤ A ƒæÅUÙæ A ·ð¤ ÂêÚU·¤ ·¤æð
ÎàææüÌæ ãñÐ Ìæð ƒæÅUÙæ°¡ A ÌÍæ B Ñ
(1) SßÌ´˜æ ãñ´ ÌÍæ â×âÖæßè ãñ´Ð
(2) ÂÚUSÂÚU ¥ÂßÁèü ÌÍæ SßÌ´˜æ ãñ´Ð
(3) â×âÖæßè ãñ´ ÂÚU‹Ìé SßÌ´˜æ Ùãè´ ãñ´Ð
(4) SßÌ´˜æ ãñ´ ÂÚU‹Ìé â×âÖæßè Ùãè´ ãñ´Ð
50. Îèƒæüßëžæ x213y256 ·ð¤ ·ð´¤Îý âð §â·¤è ç·¤âè SÂàæü
ÚðU¹æ ÂÚU ¹è´¿ð »° Ü´Õ ·ð¤ ÂæÎ ·¤æ çÕ´Îé ÂÍ ãñ Ñ
(1) (x21y2)256x222y2
(2) (x22y2)256x212y2
(3) (x22y2)256x222y2
(4) (x21y2)256x212y2
51. ØçÎ f ÌÍæ g, [0, 1] ×𴠥߷¤ÜÙèØ È¤ÜÙ ãñ´ Áæð
f (0)525g(1), g(0)50 ¥æñÚU f (1)56 ·¤æð â´ÌécÅU
·¤ÚUÌð ãñ´, Ìæð ç·¤âè ce]0, 1[ ·ð¤ çÜ° Ñ
(1) f 9(c)52g9(c)
(2) 2f 9(c)5g9(c)
(3) 2f 9(c)53g9(c)
(4) f 9(c)5g9(c)
21. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãF/Page 21
52. Three positive numbers form an increasing
G.P. If the middle term in this G.P. is
doubled, the new numbers are in A.P.
Then the common ratio of the G.P. is :
(1) 2 31
(2) 2 31
(3) 3 21
(4) 2 32
53. If g is the inverse of a function f and
f 9 (x)5 5
1
1 x1
, then g9 (x) is equal to :
(1) 11{g(x)}5
(2) 11x5
(3) 5x4
(4)
{ }5
1
1 ( )g x1
54. Let a, b, c and d be non-zero numbers. If
the point of intersection of the lines
4ax12ay1c50 and 5bx12by1d50 lies
in the fourth quadrant and is equidistant
from the two axes then :
(1) 3bc12ad50
(2) 2bc23ad50
(3) 2bc13ad50
(4) 3bc22ad50
52. ÌèÙ ÏÙæˆ×·¤ â´Øæ°´ ÕɸÌè »é‡ææðžæÚU Ÿæðɸè ×ð´ ãñ´Ð ØçÎ
§â »é‡ææðžæÚU ŸæðÉ¸è ·¤è Õè¿ ßæÜè â´Øæ Îé»éÙè ·¤ÚU Îè
Áæ°, Ìæð Ù§ü ÕÙè â´Øæ°´ â×æ´ÌÚU Ÿæðɸè ×ð´ ãæð ÁæÌè ãñ´Ð
»é‡ææðžæÚU ŸæðÉ¸è ·¤æ âæßü¥ÙéÂæÌ ãñ Ñ
(1) 2 31
(2) 2 31
(3) 3 21
(4) 2 32
53. ØçÎ g ȤÜÙ f ·¤æ ÃØ鈷ý¤× ãñ ÌÍæ f9 (x)5 5
1
1 x1
ãñ, Ìæð g9 (x) ÕÚUæÕÚU ãñ Ñ
(1) 11{g(x)}5
(2) 11x5
(3) 5x4
(4)
{ }5
1
1 ( )g x1
54. ×æÙæ a, b, c ÌÍæ d àæê‹ØðÌÚU â´Øæ°¡ ãñ´Ð ØçÎ ÚðU¹æ¥æð´
4ax12ay1c50 ÌÍæ 5bx12by1d50 ·¤æ
ÂýçÌ‘ÀðUÎ çÕ´Îé ¿æñÍð ¿ÌéÍæZàæ ×ð´ ãñ ÌÍæ ÎæðÙæð´ ¥ÿææð´ âð
â×ÎêÚUSÍ ãñ, Ìæð Ñ
(1) 3bc12ad50
(2) 2bc23ad50
(3) 2bc13ad50
(4) 3bc22ad50
22. F/Page 22 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
55. If a, b¹0, and f (n)5an1bn and
3 1 (1) 1 (2)
1 (1) 1 (2) 1 (3)
1 (2) 1 (3) 1 (4)
f f
f f f
f f f
1 1
1 1 1
1 1 1
5K(12a)2 (12b)2 (a2b)2, then K is
equal to :
(1) 21
(2) ab
(3)
1
ab
(4) 1
56. The integral
2
0
1 4 sin 4 sin d
2 2
x x
x×
p
1 2 equals :
(1) 4 3 4
3
p
2 2
(2) p24
(3)
2
4 4 3
3
p
2 2
(4) 4 3 42
57. If (10)912(11)1 (10)813(11)2 (10)71...
110 (11)95k (10)9, then k is equal to :
(1) 110
(2)
121
10
(3)
441
100
(4) 100
55. ØçÎ a, b¹0, f (n)5an1bn ÌÍæ
3 1 (1) 1 (2)
1 (1) 1 (2) 1 (3)
1 (2) 1 (3) 1 (4)
f f
f f f
f f f
1 1
1 1 1
1 1 1
5K(12a)2 (12b)2 (a2b)2 ãñ, Ìæð K ÕÚUæÕÚU
ãñ Ñ
(1) 21
(2) ab
(3)
1
ab
(4) 1
56. â×æ·¤Ü
2
0
1 4 sin 4 sin d
2 2
x x
x×
p
1 2 ÕÚUæÕÚU ãñ Ñ
(1) 4 3 4
3
p
2 2
(2) p24
(3)
2
4 4 3
3
p
2 2
(4) 4 3 42
57. ØçÎ (10)912(11)1 (10)813(11)2 (10)71...
110 (11)95k (10)9 ãñ, Ìæð k ÕÚUæÕÚU ãñ Ñ
(1) 110
(2)
121
10
(3)
441
100
(4) 100
23. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãF/Page 23
58. The angle between the lines whose
direction cosines satisfy the equations
l1m1n50 and l25m21n2 is :
(1)
2
p
(2)
3
p
(3)
4
p
(4)
6
p
59. The variance of first 50 even natural
numbers is :
(1)
437
4
(2)
833
4
(3) 833
(4) 437
60. If X5{4n23n21 : n e N} and
Y5{9(n21) : n e N}, where N is the set of
natural numbers, then XÈY is equal to :
(1) Y
(2) N
(3) Y2X
(4) X
58. Îæð ÚðU¹æ°¡, çÁÙ·ð¤ çη÷¤-·¤æð’Øæ, â×è·¤ÚU‡ææð´
l1m1n50 ÌÍæ l25m21n2 ·¤æð â´ÌécÅU ·¤ÚUÌð ãñ´,
·ð¤ Õè¿ ·¤æ ·¤æð‡æ ãñ Ñ
(1)
2
p
(2)
3
p
(3)
4
p
(4)
6
p
59. ÂãÜè 50 â× Âýæ·ë¤Ì â´Øæ¥æð´ ·¤æ ÂýâÚU‡æ ãñ Ñ
(1)
437
4
(2)
833
4
(3) 833
(4) 437
60. ØçÎ X5{4n23n21 : n e N} ÌÍæ
Y5{9(n21) : n e N} ãñ´, Áãæ¡ N, Âýæ·ë¤Ì â´Øæ¥æð´
·¤æ â×é“æØ ãñ, Ìæð XÈY ÕÚUæÕÚU ãñ Ñ
(1) Y
(2) N
(3) Y2X
(4) X
24. F/Page 24 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
61. The pressure that has to be applied to the
ends of a steel wire of length 10 cm to keep
its length constant when its temperature
is raised by 1008C is :
(For steel Young’s modulus is
231011 N m22 and coefficient of thermal
expansion is 1.131025 K21)
(1) 2.23109 Pa
(2) 2.23107 Pa
(3) 2.23106 Pa
(4) 2.23108 Pa
62. In the circuit shown here, the point ‘C’ is
kept connected to point ‘A’ till the current
flowing through the circuit becomes
constant. Afterward, suddenly, point ‘C’
is disconnected from point ‘A’ and
connected to point ‘B’ at time t50. Ratio
of the voltage across resistance and the
inductor at t5L/R will be equal to :
(1) 1
(2) 21
(3)
1 e
e
2
(4)
e
1 e2
61. 10 cm ÜÕæ§ü ·ð¤ °·¤ SÅUèÜ ·ð¤ ÌæÚU ·ð¤ çâÚUæð ÂÚU ÁÕ
ÌæÂ×æÙ ×ð´ ßëçh 1008C ·¤è ÁæÌè ãñ´ ÌÕ §â·¤è ÜÕæ§ü
çSÍÚU ÚU¹Ùð ·ð¤ çÜØð çâÚUæð ÂÚU Ü»æØæ »Øæ ÎæÕ ãñ Ñ
(SÅUèÜ ·¤æ Ø´» ÂýˆØæSÍÌæ »é‡ææ´·¤ 231011 N m22
¥æñÚU ÚðUç¹·¤ ÂýâæÚU »é‡ææ´·¤ 1.131025 K21 ãñ´)
(1) 2.23109 ÂæS·¤Ü
(2) 2.23107 ÂæS·¤Ü
(3) 2.23106 ÂæS·¤Ü
(4) 2.23108 ÂæS·¤Ü
62. Øãæ¡ ÎàææüØð »Øð ÂçÚUÂÍ ×ð´, çÕ‹Îé ‘C’ ·¤æð çÕ‹Îé ‘A’ âð
ÌÕ Ì·¤ ÁæðǸð ÚU¹æ ÁæÌæ ãñ ÁÕ Ì·¤ ç·¤ ÂçÚUÂÍ ×ð´
ÂýßæçãÌ ÏæÚUæ çSÍÚU Ù ãæð Áæ°Ð ̈Âà¿æÌ÷, ¥¿æÙ·¤,
çÕ‹Îé ‘C’ ·¤æð çÕ‹Îé ‘A’ âð ãÅUæ·¤ÚU çÕ‹Îé ‘B’ âð t50
â×Ø ÂÚU ÁæðǸ çÎØæ ÁæÌæ ãñÐ t5L/R ÂÚU ÂýçÌÚUæðÏ
ÂÚU ßæðËÅUÌæ ·¤æ ÂýðÚU·¤ˆß ÂÚU ßæðËÅUÌæ âð ¥ÙéÂæÌ ãæð»æ Ñ
(1) 1
(2) 21
(3)
1 e
e
2
(4)
e
1 e2
PART C — PHYSICS Öæ» C — ÖæñçÌ·¤ çß™ææÙ
27. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãF/Page 27
67. A green light is incident from the water to
the air - water interface at the critical
angle(u). Select the correct statement.
(1) The spectrum of visible light whose
frequency is less than that of green
light will come out to the air
medium.
(2) The spectrum of visible light whose
frequency is more than that of green
light will come out to the air
medium.
(3) The entire spectrum of visible light
will come out of the water at various
angles to the normal.
(4) The entire spectrum of visible light
will come out of the water at an
angle of 908 to the normal.
68. A block of mass m is placed on a surface
with a vertical cross section given by
y5
3
6
x
. If the coefficient of friction is 0.5,
the maximum height above the ground at
which the block can be placed without
slipping is :
(1)
2
m
3
(2)
1
m
3
(3)
1
m
2
(4)
1
m
6
67. °·¤ ãÚðU Ú´U» ·¤æ Âý·¤æàæ ÂæÙè âð ßæØé-ÁÜ ¥‹ÌÚUæÂëcÆU
ÂÚU ·ý¤æç‹Ì·¤ ·¤æð‡æ(u) âð ¥æÂçÌÌ ãñÐ âãè ·¤ÍÙ
¿éçÙØðÐ
(1) ÎëàØ Âý·¤æàæ ·¤æ ßã SÂð€ÅþU×, çÁâ·¤è ÌÚ´U»ÎñƒØü
ãÚðU Âý·¤æàæ âð ·¤× ãñ, ÂæÙè âð ßæØé ·ð¤ ×æŠØ×
×ð´ ÕæãÚU çÙ·¤Üð»æÐ
(2) ÎëàØ Âý·¤æàæ ·¤æ ßã SÂð€ÅþU×, çÁâ·¤è ÌÚ´U»ÎñƒØü
ãÚðU Âý·¤æàæ âð ¥çÏ·¤ ãñ, ÂæÙè âð ßæØé ·ð¤ ×æŠØ×
×ð´ ÕæãÚU çÙ·¤Üð»æÐ
(3) ÎëàØ Âý·¤æàæ ·¤æ âÂê‡æü SÂð€ÅþU× ÂæÙè âð
¥çÖÜÕ âð çßçÖóæ ·¤æð‡ææð´ ÂÚU ÕæãÚU çÙ·¤Üð»æÐ
(4) ¥çÖÜÕ âð 908 ·¤æð‡æ ÂÚU ÂæÙè âð ÎëàØ Âý·¤æàæ
·¤æ âÂê‡æü SÂð€ÅþU× ÕæãÚU çÙ·¤Üð»æÐ
68. °·¤ ÂëcÆU ÂÚU °·¤ ÎýÃØ×æÙ m ·¤æ ŽÜæò·¤ ÚU¹æ ãñÐ
ÂëcÆU ·¤è ª¤ŠßæüÏÚU ¥ÙéÂýSÍ ·¤æÅU y5
3
6
x
âð Îè ÁæÌè
ãñÐ ØçÎ ƒæáü‡æ »é‡ææ´·¤ 0.5 ãñ, ÌÕ ÏÚUÌè â𠪤ÂÚU ßã
¥çÏ·¤Ì× ª¡¤¿æ§ü, çÁâ ÂÚU çÕÙæ çȤâÜð ŽÜæò·¤ ÚU¹æ
Áæ â·¤Ìæ ãñ´, ãñ Ñ
(1)
2
m
3
(2)
1
m
3
(3)
1
m
2
(4)
1
m
6
28. F/Page 28 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
69. The coercivity of a small magnet where the
ferromagnet gets demagnetized is
33103 A m21. The current required to be
passed in a solenoid of length 10 cm and
number of turns 100, so that the magnet
gets demagnetized when inside the
solenoid, is :
(1) 60 mA
(2) 3 A
(3) 6 A
(4) 30 mA
70. A conductor lies along the z-axis
at 21.5 [ z < 1.5 m and carries
a fixed current of 10.0 A in az
¾
2
direction (see figure). For a field
B
“
53.031024 e20.2x ay
¾
T, find the
power required to move the conductor at
constant speed to x52.0 m, y50 m in
531023 s. Assume parallel motion along
the x-axis.
(1) 2.97 W
(2) 14.85 W
(3) 29.7 W
(4) 1.57 W
69. °·¤ ÀUæðÅðU ¿éÕ·¤ ·¤è çÙ»ýæçãÌæ, Áãæ¡ Üæðã¿éÕ·¤
¥¿éÕ·¤èØ ãæð ÁæÌæ ãñ, 33103 A m21 ãñÐ ¿·ý¤æð´
·¤è â´Øæ100 °ß´ ÜÕæ§ü10 cm ·¤è °·¤ ÂçÚUÙæçÜ·¤æ
âð ÂýßæçãÌ ¥æßàØ·¤ ÏæÚUæ ·¤æ ×æÙ, çÁââð ç·¤ ¿éÕ·¤
ÂçÚUÙæçÜ·¤æ ·ð¤ ¥‹ÎÚU ãæðÙð ÂÚU ¥¿éÕ·¤èØ ãæð ÁæØð,
ãñ Ñ
(1) 60 mA
(2) 3 A
(3) 6 A
(4) 30 mA
70. °·¤ âé¿æÜ·¤ z-¥ÿæ ·ð¤ âæÍ 21.5 [ z < 1.5 m
ÂÚU ÚU¹æ ãñ ¥æñÚU §â×ð´ az
¾
2 çÎàææ ×ð´ çSÍÚU ÏæÚUæ
10.0 A ÂýßæçãÌ ãæð ÚUãè ãñÐ (翘æ Îð¹ð´)Ð ÿæð˜æ
B
“
53.031024 e20.2x ay
¾
T ·ð¤ çÜØð,
âé¿æÜ·¤ ·¤æð çSÍÚU ¿æÜ âð x52.0 m, y50 m
Ì·¤ 531023 s ×ð´ »çÌ ·¤ÚUæÙð ·ð¤ çÜØð ¥æßàØ·¤
àæç€Ì ·¤è »‡æÙæ ·¤èçÁ°Ð x-¥ÿæ ÂÚU â×æ‹ÌÚU »çÌ
×æÙ Üð´Ð
(1) 2.97 W
(2) 14.85 W
(3) 29.7 W
(4) 1.57 W
30. F/Page 30 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
74. Match List - I (Electromagnetic wave type)
with List - II (Its association/application)
and select the correct option from the
choices given below the lists :
(a)
Infrared
waves
(i)
To treat muscular
strain
(b) Radio waves (ii) For broadcasting
(c) X - rays (iii)
To detect fracture
of bones
(d)
Ultraviolet
rays
(iv)
Absorbed by the
ozone layer of the
atmosphere
List - I List - II
(a) (b) (c) (d)
(1) (i) (ii) (iv) (iii)
(2) (iii) (ii) (i) (iv)
(3) (i) (ii) (iii) (iv)
(4) (iv) (iii) (ii) (i)
75. The current voltage relation of diode is
given by I5(e1000V/T21) mA, where the
applied voltage V is in volts and the
temperature T is in degree Kelvin. If a
student makes an error measuring
60.01 V while measuring the current of
5 mA at 300 K, what will be the error in
the value of current in mA ?
(1) 0.02 mA
(2) 0.5 mA
(3) 0.05 mA
(4) 0.2 mA
74. âê¿è - I (çßléÌ ¿éÕ·¤èØ ÌÚ´U» Âý·¤æÚU) ·¤æð
âê¿è - II (§Ùâð âÕçhÌ/¥ÙéÂýØæðç»Ì) âð âé×ðçÜÌ
·¤èçÁØð ¥æñÚU âêç¿Øæð´ ·ð¤ Ùè¿ð çÎØð »Øð çß·¤ËÂæð´ ×ð´ âð
âãè çß·¤Ë ¿éçÙØðÑ
(a) ŠÄ¿Uþ± ±¿™U Õ (i)
¼Ë†Ç§ÕÌÅ˽ËÕ™ œ‰Í ÌĜЉ̱
œÕ‰ ŒÁ˦ œÕ‰ ÌÁ½Õ
(b) ¿ÕU̬U½ËÕ ±¿™U Õ (ii) §âÇË¿UøË œÕ‰ ÌÁ½Õ
(c) •þÇ-Ìœ‰¿UøËÕ™ (iii)
ÈÌa½ËÕ™ œÕ‰ ŠÌS²»™ œ‰Í
§È¤Ë¾ œÕ‰ ÌÁ½Õ
(d)
§¿U˺֙ ¾Í
Ìœ‰¿UøËÕ™
(iv)
Ä˱ËÄ¿UøË œ‰Í ŠËÕ$¦ËÕ¾
§¿U± mË¿UË ŠÄÅËËÕÆøË
ÇÏ¤Í - I ÇÏ¤Í - II
(a) (b) (c) (d)
(1) (i) (ii) (iv) (iii)
(2) (iii) (ii) (i) (iv)
(3) (i) (ii) (iii) (iv)
(4) (iv) (iii) (ii) (i)
75. °·¤ ÇUæØæðÇU ·¤è ÏæÚUæ-ßæðËÅUÌæ âÕ‹Ï
I5(e1000V/T21) mA âð Îè ÁæÌè ãñ´, Áãæ¡ V Ü»æ§ü
»§ü ßæðËÅUÌæ ßæðËÅU ×ð´ ãñ ¥æñÚU ÌæÂ×æÙ T çÇU»ýè ·ñ¤çËßÙ
×ð´ ãñÐ ØçÎ °·¤ çßlæÍèü 300 K ÂÚU 5 mA ÏæÚUæ
ÙæÂÌð ãéØð ×æÂÙ ×ð´ 60.01 V ·¤è ˜æéçÅU ·¤ÚUÌæ ãñ, ÌÕ
ÏæÚUæ ·ð¤ ×æÙ ×ð´ mA ×ð´ ˜æéçÅU €Øæ ãæð»è?
(1) 0.02 mA
(2) 0.5 mA
(3) 0.05 mA
(4) 0.2 mA
31. SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãF/Page 31
76. One mole of diatomic ideal gas undergoes
a cyclic process ABC as shown in figure.
The process BC is adiabatic. The
temperatures at A, B and C are 400 K,
800 K and 600 K respectively. Choose the
correct statement :
(1) The change in internal energy in the
process CA is 700 R.
(2) The change in internal energy in the
process AB is 2350 R.
(3) The change in internal energy in the
process BC is 2500 R.
(4) The change in internal energy in
whole cyclic process is 250 R.
77. A pipe of length 85 cm is closed from one
end. Find the number of possible natural
oscillations of air column in the pipe whose
frequencies lie below 1250 Hz. The
velocity of sound in air is 340 m/s.
(1) 8
(2) 6
(3) 4
(4) 12
76. çmÂÚU×æ‡æé·¤ ¥æÎàæü »ñâ ·¤æ °·¤ ×æðÜ ¿·ý¤èØ Âýç·ý¤Øæ
ABC âð »éÁÚUÌæ ãñ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ »Øæ ãñÐ
Âýç·ý¤Øæ BC L¤hæðc× ãñÐ A, B °ß´ C ·ð¤ ÌæÂ×æÙ
·ý¤×àæÑ 400 K, 800 K °ß´ 600 K ãñ´Ð âãè ·¤ÍÙ
¿éçÙØð Ñ
(1) Âýç·ý¤Øæ CA ×ð´ ¥æ‹ÌçÚU·¤ ª¤Áæü ×ð´ ÂçÚUßÌüÙ
700 R ãñÐ
(2) Âýç·ý¤Øæ AB ×ð´ ¥æ‹ÌçÚU·¤ ª¤Áæü ×ð´ ÂçÚUßÌüÙ
2350 R ãñÐ
(3) Âýç·ý¤Øæ BC ×ð´ ¥æ‹ÌçÚU·¤ ª¤Áæü ×ð´ ÂçÚUßÌüÙ
2500 R ãñÐ
(4) âÂê‡æü ¿·ý¤èØ Âýç·ý¤Øæ ×ð´ ¥æ‹ÌçÚU·¤ ª¤Áæü ×ð´
ÂçÚUßÌüÙ 250 R ãñÐ
77. ÜÕæ§ü 85 cm ·ð¤ °·¤ Âæ§Â ·ð¤ °·¤ çâÚðU ·¤æð Õ‹Î
·¤ÚU çÎØæ ÁæÌæ ãñÐ Âæ§Â ×ð´ ßæØé SÌÖ ·ð¤ âÖß
Âýæ·ë¤çÌ·¤ ÎæðÜÙæð ·¤è ßã â´Øæ çÙ·¤æçÜ°ð çÁÙ·¤è
¥æßëçžæ 1250 Hz âð ·¤× ãñÐ ßæØé ×ð´ ŠßçÙ ·¤æ ßð»
340 m/s ãñÐ
(1) 8
(2) 6
(3) 4
(4) 12
32. F/Page 32 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
78. In a large building, there are 15 bulbs of
40 W, 5 bulbs of 100 W, 5 fans of 80 W
and 1 heater of 1 kW. The voltage of the
electric mains is 220 V. The minimum
capacity of the main fuse of the building
will be :
(1) 10 A
(2) 12 A
(3) 14 A
(4) 8 A
79. Four particles, each of mass M and
equidistant from each other, move along
a circle of radius R under the action of their
mutual gravitational attraction. The speed
of each particle is :
(1)
GM
2 2
R
(2) ( )GM
1 2 2
R
1
(3) ( )1 GM
1 2 2
2 R
1
(4)
GM
R
78. °·¤ ÕëãÌ ÖßÙ ×ð´, 40 W ·ð¤ 15 ÕËÕ, 100 W ·ð¤
5 ÕËÕ, 80 W ·ð¤ 5 ´¹ð °ß´ 1 kW ·¤æ 1 ãèÅUÚU ãñ´Ð
çÕÁÜè ·ð¤ ×ð‹â ·¤è ßæðËÅUÌæ 220 V ãñ´Ð ÖßÙ ·ð¤
×éØ Øê$Á ·¤è ‹ØêÙÌ× ÿæ×Ìæ ãæð»è Ñ
(1) 10 A
(2) 12 A
(3) 14 A
(4) 8 A
79. ÂýˆØð·¤ ÎýÃØ×æÙ M ·ð¤ ¿æÚU ·¤‡æ Áæð ç·¤ °·¤ ÎêâÚðU âð
â×æÙ ÎêÚUè ÂÚU ãñ´, °·¤ ÎêâÚðU ·ð¤ ¥‹Øæð‹Ø »éL¤ˆßæ·¤áü‡æ
ÂýÖæß ×ð´ ç˜æ’Øæ R ·ð¤ °·¤ ßëžæ ÂÚU »çÌàæèÜ ãñ´Ð ÂýˆØð·¤
·¤‡æ ·¤è ¿æÜ ãñ Ñ
(1)
GM
2 2
R
(2) ( )GM
1 2 2
R
1
(3) ( )1 GM
1 2 2
2 R
1
(4)
GM
R
36. F/Page 36 SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
86. A mass ‘m’ is supported by a massless
string wound around a uniform hollow
cylinder of mass m and radius R. If the
string does not slip on the cylinder, with
what acceleration will the mass fall on
release ?
(1)
g
2
(2)
5g
6
(3) g
(4)
2g
3
87. During the propagation of electromagnetic
waves in a medium :
(1) Electric energy density is half of the
magnetic energy density.
(2) Electric energy density is equal to the
magnetic energy density.
(3) Both electric and magnetic energy
densities are zero.
(4) Electric energy density is double of
the magnetic energy density.
86. ç˜æ’Øæ R °ß´ ÎýÃØ×æÙ m ·ð¤ °·¤ °·¤â×æÙ ¹æð¹Üð
ÕðÜÙ ·ð¤ ¿æÚUæð´ ÌÚUȤ °·¤ ÎýÃØ×æÙçßãèÙ ÇUæðÚUè âð °·¤
ÎýÃØ×æÙ ‘m’ ¥ßÜ´çÕÌ ãñ´Ð ØçÎ ÇUæðÚUè ÕðÜÙ ÂÚU
çȤâÜÌè Ùãè´ ãñ, ÌÕ ÀUæðǸð ÁæÙð ÂÚU ÎýÃØ×æÙ ç·¤â
ˆßÚU‡æ âð ç»ÚðU»æ?
(1)
g
2
(2)
5g
6
(3) g
(4)
2g
3
87. °·¤ ×æŠØ× ×ð´ çßléÌ ¿éÕ·¤èØ ÌÚ´U»æð´ ·ð¤ â´¿ÚU‡æ ·ð¤
ÎæñÚUæÙ Ñ
(1) çßléÌèØ ª¤Áæü ƒæÙˆß ¿éÕ·¤èØ ª¤Áæü ƒæÙˆß
·¤æ ¥æÏæ ãñÐ
(2) çßléÌèØ ª¤Áæü ƒæÙˆß ¿éÕ·¤èØ ª¤Áæü ƒæÙˆß
·ð¤ ÕÚUæÕÚU ãñÐ
(3) ÎæðÙæð´ çßléÌèØ °ß´ ¿éÕ·¤èØ ª¤Áæü ƒæÙˆß àæê‹Ø
ãñÐ
(4) çßléÌèØ ª¤Áæü ƒæÙˆß ¿éÕ·¤èØ ª¤Áæü ƒæÙˆß
·¤æ Îæð»éÙæ ãñÐ
38. 90. When a rubber-band is stretched by a
distance x, it exerts a restoring force of
magnitude F5ax1bx2 where a and b are
constants. The work done in stretching
the unstretched rubber-band by L is :
(1)
1
2
(aL21bL3)
(2)
2 3
aL bL
2 3
1
(3)
2 3
1 aL bL
2 2 3
Ë ÛÜÌ ÜÌ ÜÌ ÜÜÌÍ Ý
1
(4) aL21bL3
- o 0 o -
F/Page 38
SPACE FOR ROUGH WORK / ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
90. ÁÕ °·¤ ÚUÕǸ ·ð¤ ÀUËÜð ·¤æð x ÎêÚUè Ì·¤ ÌæçÙÌ ç·¤Øæ
ÁæÌæ ãñ; ÌÕ ÂçÚU×æ‡æ F5ax1bx2 ·¤æ °·¤ ÂýˆØÙØÙ
ÕÜ Ü»Ìæ ãñ Áãæ¡ a °ß´ b çSÍÚUæ´·¤ ãñ´Ð çÕÙæ ÌæçÙÌ
ÚUÕǸ ·ð¤ ÀUËÜð ·¤æð L âð ÌæçÙÌ ·¤ÚUÙð ×ð´ ç·¤Øæ »Øæ
·¤æØü ãñ Ñ
(1)
1
2
(aL21bL3)
(2)
2 3
aL bL
2 3
1
(3)
2 3
1 aL bL
2 2 3
Ë ÛÜÌ ÜÌ ÜÌ ÜÜÌÍ Ý
1
(4) aL21bL3
- o 0 o -
