IIT-JEE Mains 2015 Online Previous Question Paper Day 2
1. Page 1 PHYSICS : English & Hindi 01
1. If electronic charge e, electron mass m,
speed of light in vacuum c and Planck’s
constant h are taken as fundamental
quantities, the permeability of vacuum m0
can be expressed in units of :
(1) 2
hc
me
(2) 2
h
me
(3) 2
h
ce
(4)
2
2
mc
he
2. A vector A
→
is rotated by a small angle Du
radians (Du<<1) to get a new vector B
→
.
In that case B A
→ →
2 is :
(1) 0
(2)
2
A 1
2
→
Du
2
(3) A
→
Du
(4) B A
→ →
Du 2
1. ØçÎ §Üð€ÅþUæòÙ-¥æßðàæ e, §Üð€ÅþUæòÙ-ÎýÃØ×æÙ m, çÙßæüÌ÷
×ð´ Âý·¤æàæ ·ð¤ ßð» c ÌÍæ ŒÜæ¡·¤ çSÍÚUæ´·¤ h, ·¤æð ×êÜ
ÚUæçàæØæ¡ ×æÙ çÜØæ ÁæØ Ìæð, çÙßæüÌ÷ ·¤è ¿éÕ·¤àæèÜÌæ
m0 ·¤æ ×æ˜æ·¤ ãæð»æ Ñ
(1) 2
hc
me
(2) 2
h
me
(3) 2
h
ce
(4)
2
2
mc
he
2. ç·¤âè âçÎàæ A
→
·¤æð Du ÚðUçÇUØÙ (Du<<1) ƒæé×æ ÎðÙð
ÂÚU °·¤ ÙØæ âçÎàæ B
→
ÂýæŒÌ ãæðÌæ ãñÐ §â ¥ßSÍæ ×ð´
B A
→ →
2 ãæð»æ Ñ
(1) àæê‹Ø
(2)
2
A 1
2
→
Du
2
(3) A
→
Du
(4) B A
→ →
Du 2
2. Page 2 PHYSICS : English & Hindi 01
3. A large number (n) of identical beads, each
of mass m and radius r are strung on a
thin smooth rigid horizontal rod of length
L (L>>r) and are at rest at random
positions. The rod is mounted between
two rigid supports (see figure). If one of
the beads is now given a speed v, the
average force experienced by each support
after a long time is (assume all collisions
are elastic) :
(1)
2
m
L nr
v
2
(2)
2
m
L 2nr
v
2
(3)
2
m
2(L nr)
v
2
(4) zero
4. A particle is moving in a circle of radius r
under the action of a force F5ar2 which
is directed towards centre of the circle.
Total mechanical energy (kinetic
energy1potential energy) of the particle
is (take potential energy50 for r50) :
(1) ar3
(2)
31
r
2
a
(3)
34
r
3
a
(4)
35
r
6
a
3. °·¤ ÂÌÜè ç¿·¤Ùè ÿæñçÌÁ ÀUǸ ÂÚU ·¤§ü (n) âßüâ×
×ç‡æ·¤æØð´ (ÕèÇU) çÂÚUæð§ü »§ü ãñ´ Áæð ÀUǸ ÂÚU ¥çÙØç×Ì
ÌÍæ çßÚUæ× ¥ßSÍæ ×ð´ ãñ´Ð ÂýˆØð·¤ ÕèÇU ·¤æ ÎýÃØ×æÙ
m ÌÍæ ç˜æ’Øæ r ãñ ¥æñÚU ÀUǸ ·¤è Ü´Õæ§ü L ãñ (L>>r)Ð
Øã ÀUǸ Îæð ÅðU·¤æð´ (¥æÏæÚUæð´) ÂÚU, ¥æÚðU¹ ×ð´ ÎàææüØð »Øð
¥ÙéâæÚU çÅU·¤è ãñÐ ØçÎ °·¤ ÕèÇU ·¤æð v ßð» ÂýÎæÙ
ç·¤Øæ ÁæØ Ìæð, °·¤ ÜÕð â×Ø ·ð¤ Âà¿æÌ÷ ÂýˆØð·¤
ÅðU·¤ (¥æÏæÚU) ÂÚU Ü»Ùð ßæÜð ¥æñâÌ ÕÜ ·¤æ ×æÙ
ãæð»æ (ØçÎ âÖè ÅU€·¤Úð´U ÂýˆØæSÍ ãñ´) Ñ
(1)
2
m
L nr
v
2
(2)
2
m
L 2nr
v
2
(3)
2
m
2(L nr)
v
2
(4) àæê‹Ø
4. ç·¤âè ÕÜ F5ar2 ·ð¤ ·¤æÚU‡æ, °·¤ ·¤‡æ r ç˜æ’Øæ ·ð¤
ßëžæ ×ð´ »çÌ ·¤ÚUÌæ ãñÐ ÕÜ ·¤è çÎàææ ßëžæ ·ð¤ ·ð¤‹Îý ·¤è
¥æðÚU ãñÐ ØçÎ, r50 ·ð¤ çÜØð çSÍçÌÁ ª¤Áæü ·¤æð àæê‹Ø
×æÙæ ÁæØ Ìæð, §â ·¤‡æ ·¤è ·é¤Ü Øæ´ç˜æ·¤ ª¤Áæü (»çÌÁ
ª¤Áæü1çSÍçÌÁ ª¤Áæü) ãæð»è Ñ
(1) ar3
(2)
31
r
2
a
(3)
34
r
3
a
(4)
35
r
6
a
3. Page 3 PHYSICS : English & Hindi 01
5. A uniform thin rod AB of length L has
linear mass density m(x)5
b
a
L
x
1 , where
x is measured from A. If the CM of the
rod lies at a distance of
7
L
12
from A,
then a and b are related as :
(1) a5b
(2) a52b
(3) 2a5b
(4) 3a52b
6. A particle of mass 2 kg is on a smooth
horizontal table and moves in a circular
path of radius 0.6 m. The height of the
table from the ground is 0.8 m. If the
angular speed of the particle is 12 rad s21,
the magnitude of its angular momentum
about a point on the ground right under
the centre of the circle is :
(1) 8.64 kg m2s21
(2) 11.52 kg m2s21
(3) 14.4 kg m2s21
(4) 20.16 kg m2s21
5. L ÜÕæ§ü ÌÍæ °·¤â×æÙ ÂÌÜè ÀUǸ AB, ·¤æ ÚñUç¹·¤
ÎýÃØ×æÙ ƒæÙˆß m(x)5
b
a
L
x
1 ãñ, Áãæ¡ x ·¤æð ÀUǸ
·ð¤ çâÚðUA âð ×æÂæ ÁæÌæ ãñÐ ØçÎ §â ÀUǸ ·¤æ ÎýÃØ×æÙ-
·ð¤‹Îý ÀUǸ ·ð¤ çâÚðU A âð
7
L
12
ÎêÚUè ÂÚU ãñ Ìæð,
a ÌÍæ b ·ð¤ Õè¿ â´Õ´Ï ãæð»æ Ñ
(1) a5b
(2) a52b
(3) 2a5b
(4) 3a52b
6. 2 kg ÎýÃØ×æÙ ·¤æ °·¤ ·¤‡æ, ç·¤âè ç¿·¤Ùð ÿæñçÌÁ
×ðÁ ÂÚU çSÍÌ ãñ ÌÍæ 0.6 m ç˜æ’Øæ ·ð¤ ßëžææ·¤æÚU ÂÍ
ÂÚU »çÌ ·¤ÚU ÚUãæ ãñÐ Öê-ÌÜ âð ×ðÁ ·¤è ª¡¤¿æ§ü 0.8 m
ãñÐ ØçÎ ·¤‡æ ·¤è ·¤æð‡æèØ ¿æÜ 12 rad s21 ãæð Ìæð,
ßëžæ ·ð¤ ·ð¤‹Îý ·ð¤ ÆUè·¤ Ùè¿ð Öê-ÌÜ ÂÚU ç·¤âè çÕ‹Îé ·ð¤
ÂçÚUÌÑ, §â ·¤‡æ ·¤æ ·¤æð‡æèØ â´ßð» ·¤æ ÂçÚU×æ‡æ ãæð»æ Ñ
(1) 8.64 kg m2s21
(2) 11.52 kg m2s21
(3) 14.4 kg m2s21
(4) 20.16 kg m2s21
8. Page 8 PHYSICS : English & Hindi 01
14. A wire, of length L(520 cm), is bent into
a semi-circular arc. If the two equal halves,
of the arc, were each to be uniformly
charged with charges 6Q, [|Q|5103 e0
Coulomb where e0 is the permittivity (in
SI units) of free space] the net electric field
at the centre O of the semi-circular arc
would be :
(1) (503103 N/C) j
∧
(2) (253103 N/C) i
∧
(3) (253103 N/C) j
∧
(4) (503103 N/C) i
∧
15. An electric field
( ) 1
E 25 i 30 j NC
→ ∧ ∧
25 1 exists in a
region of space. If the potential at the
origin is taken to be zero then the potential
at x52 m, y52 m is :
(1) 2130 J
(2) 2120 J
(3) 2140 J
(4) 2110 J
14. L(520 cm) ÜÕæ§ü ·ð¤ °·¤ ÌæÚU ·¤æð °·¤ ¥Ïü ßëžææ·¤æÚU
¿æ ·ð¤ M¤Â ×ð´ ×æðǸ çÎØæ »Øæ ãñÐ ØçÎ §â ¿æ ·ð¤ Îæð
â×æÙ Öæ»æð´ ·¤æð 6Q ¥æßðàæ âð °·¤â×æÙ ¥æßðçàæÌ
·¤ÚU çÎØæ ÁæØ [|Q|5103 e0 ·ê¤Üæò× Áãæ¡ e0 (SI
×æ˜æ·¤ ×ð´) ×é€Ì ¥æ·¤æàæ ·¤è çßléÌàæèÜÌæ
(ÂÚUæßñléÌæ´·¤) ãñ ], Ìæð, ¥Ïüßëžææ·¤æÚU ¿æ ·ð¤ ·ð¤‹Îý O
ÂÚU ÙðÅU çßléÌ ÿæð˜æ ãæð»æ Ñ
(1) (503103 N/C) j
∧
(2) (253103 N/C) i
∧
(3) (253103 N/C) j
∧
(4) (503103 N/C) i
∧
15. ç·¤âè SÍæÙ ÂÚU °·¤ çßléÌ ÿæð˜æ,
( ) 1
E 25 i 30 j NC
→ ∧ ∧
25 1 , çßl×æÙ ãñÐ ØçÎ
×êÜçÕ‹Îé ÂÚU çßÖß ·¤æ ×æÙ àæê‹Ø ×æÙæ ÁæØ Ìæð,
x52 m, y52 m ÂÚU çßÖß ãæð»æ Ñ
(1) 2130 J
(2) 2120 J
(3) 2140 J
(4) 2110 J
10. Page 10 PHYSICS : English & Hindi 01
18. The value of the resistor, RS, needed in the
dc voltage regulator circuit shown here,
equals :
(1) (Vi2VL)/n IL
(2) (Vi1VL)/n IL
(3) (Vi2VL)/(n11) IL
(4) (Vi1VL)/(n11) IL
18. Øãæ¡ ÎàææüØð »Øð ÇUè.âè. (dc) ßæðËÅUÌæ çÙØ´˜æ·¤ ÂçÚUÂÍ
×ð´, ¥æßàØ·¤ ÂýçÌÚUæðÏ RS ·¤æ ×æÙ ãæð»æ Ñ
(1) (Vi2VL)/n IL
(2) (Vi1VL)/n IL
(3) (Vi2VL)/(n11) IL
(4) (Vi1VL)/(n11) IL
11. Page 11 PHYSICS : English & Hindi 01
19. Îæð ÜÕð, âèÏð, â×æ‹ÌÚU ÌæÚUæð´ ·ð¤ Õè¿ ·¤è ÎêÚUè d ãñÐ
§Ùâð I1 ÌÍæ I2 ÏæÚUæØð´ ÂýßæçãÌ ãæð ÚUãè ãñ´ (çÁÙ·ð¤ ×æÙ
â×æØæðçÁÌ ç·¤Øð Áæ â·¤Ìð ãñ´) ØçÎ §Ù ÌæÚUæð´ ·ð¤ Õè¿
ÂýçÌ·¤áü‡æ ãæðÙð ÂÚU §Ù·ð¤ Õè¿ ÕÜ ‘F’ ·¤æð ÒÏÙæˆ×·¤Ó
ÌÍæ §Ù ·ð¤ Õè¿ ¥æ·¤áü‡æ ãæðÙð ÂÚU ÕÜ F ·¤æ𠫤‡ææˆ×·¤
×æÙæ ÁæØ Ìæð, I1 ÌÍæ I2 ·ð¤ »é‡æÙÈ¤Ü (I1I2) ÂÚU ‘F’
·ð¤ çÙÖüÚU ãæðÙð ·¤æð ·¤æñÙ âæ »ýæȤ ÆUè·¤ (âãè) ÎàææüÌæ
ãñ?
(1)
(2)
(3)
(4)
19. Two long straight parallel wires, carrying
(adjustable) currents I1 and I2, are kept at
a distance d apart. If the force ‘F’ between
the two wires is taken as ‘positive’ when
the wires repel each other and ‘negative’
when the wires attract each other, the
graph showing the dependence of ‘F’, on
the product I1I2, would be :
(1)
(2)
(3)
(4)
16. Page 16 PHYSICS : English & Hindi 01
29. ¥æÚðU¹ ×ð´ 2V ·¤è °·¤ ÕñÅUÚUè A ß B ·ð¤ Õè¿ ÁéǸè ãñÐ
ØçÎ ÂãÜè Îàææ ×ð´ ÕñÅUÚUè ·¤æ ÏÙæˆ×·¤ ÅUç×üÙÜ A âð
ÌÍæ ÎêâÚUè Îàææ ×ð´ ÏÙæˆ×·¤ ÅUç×üÙÜ B âð ÁéǸæ ãæð Ìæð,
§Ù ÎæðÙæð´ Îàææ¥æð´ ×ð´ ÕñÅUÚUè mæÚUæ ÂýΞæ çßléÌ ÏæÚUæ ·¤æ
×æÙ ·ý¤×àæÑ ãæð»æ Ñ
(1) 0.2 A ÌÍæ 0.1 A
(2) 0.4 A ÌÍæ 0.2 A
(3) 0.1 A ÌÍæ 0.2 A
(4) 0.2 A ÌÍæ 0.4 A
30. ç·¤âè ÂýçÌÚUæðÏ ·ð¤ çâÚUæð´ ·ð¤ Õè¿ AC (°.âè.) ßæðËÅUÌæ
·¤æð ×æÂæ Áæ â·¤Ìæ ãñ Ñ
(1) ÂæðÅðUç‹àæØæð×èÅUÚU (çßÖß×æÂè) mæÚUæ
(2) ¿Ü ·é´¤ÇUÜè ÏæÚUæ×æÂè (»ñËßðÙæð×èÅUÚU) mæÚUæ
(3) ¿Ü-¿éÕ·¤ »ñËßðÙæð×èÅUÚU mæÚUæ
(4) ÌŒÌ ÌæÚU ßæðËÅU×èÅUÚU mæÚUæ
29. A 2V battery is connected across AB as
shown in the figure. The value of the
current supplied by the battery when in
one case battery’s positive terminal is
connected to A and in other case when
positive terminal of battery is connected
to B will respectively be :
(1) 0.2 A and 0.1 A
(2) 0.4 A and 0.2 A
(3) 0.1 A and 0.2 A
(4) 0.2 A and 0.4 A
30. The AC voltage across a resistance can be
measured using a :
(1) potentiometer
(2) moving coil galvanometer
(3) moving magnet galvanometer
(4) hot wire voltmeter
19. Page 3 CHEMISTRY : English & Hindi 01
9. A12B ® C, the rate equation for this
reaction is given as
Rate5k[A][B].
If the concentration of A is kept the same
but that of B is doubled what will happen
to the rate itself ?
(1) halved
(2) the same
(3) doubled
(4) quadrupled
10. Under ambient conditions, which among
the following surfactants will form micelles
in aqueous solution at lowest molar
concentration ?
(1)
(2) CH32(CH2)132 3OSO2
Na1
(3)
(4)
11. Choose the incorrect formula out of the
four compounds for an element X below :
(1) X2Cl3
(2) X2O3
(3) X2(SO4)3
(4) XPO4
12. Calamine is an ore of :
(1) Aluminium
(2) Copper
(3) Iron
(4) Zinc
9. ¥çÖç·ý¤Øæ A12B ® C ·¤æ ÎÚU â×è·¤ÚU‡æ ãñ
ÎÚU5k[A][B].
A ·¤è âæ´ÎýÌæ çSÍÚU ÚU¹Ìð ãé° B ·¤è âæ´ÎýÌæ Îé»éÙè ·¤ÚUÙð
ÂÚU ßð» ·¤æ ×æÙ €Øæ ãæð»æ?
(1) ¥æÏæ ÚUã Áæ°»æ
(2) â×æÙ ÚUãð»æ
(3) Îé»éÙæ ãæð Áæ°»æ
(4) ¿æÚU »éÙæ ãæð Áæ°»æ
10. ÂçÚUßðàæ çSÍçÌ ÂÚU, ·¤æñÙ-ÂëcÆU â´ç·ý¤Ø·¤ ÁÜèØ çßÜØÙ
×ð´ âÕâð ·¤× ×æðÜèØ âæ´Îý‡æ ×ð´ ç×âðÜ ÕÙæ°»æ?
(1)
(2) CH32(CH2)132 3OSO2
Na1
(3)
(4)
11. Ìˆß X ·ð¤ ¿æÚU Øæñç»·¤æð´ ·ð¤ âê˜ææð´ ×ð´ âð »ÜÌ âê˜æ
¿éçÙ° Ñ
(1) X2Cl3
(2) X2O3
(3) X2(SO4)3
(4) XPO4
12. ·ñ¤Üæç×Ù çÁâ·¤æ ¥ØS·¤ ãñ, ßã ãñ Ñ
(1) °ðÜéç×çÙØ×
(2) ·¤æòÂÚU
(3) ¥æØÚUÙ
(4) çÁ´·¤
20. Page 4 CHEMISTRY : English & Hindi 01
13. Which physical property of dihydrogen is
wrong ?
(1) Colourless gas
(2) Odourless gas
(3) Tasteless gas
(4) Non-inflammable gas
14. Which of the alkaline earth metal halides
given below is essentially covalent in
nature ?
(1) MgCl2
(2) BeCl2
(3) SrCl2
(4) CaCl2
15. Which of the following compounds has a
P2P bond ?
(1) H4P2O5
(2) H4P2O6
(3) H4P2O7
(4) (HPO3)3
16. Chlorine water on standing loses its colour
and forms :
(1) HCl only
(2) HOCl and HOCl2
(3) HCl and HOCl
(4) HCl and HClO2
17. Which of the following statements is
false ?
(1)
2
4CrO
2
is tetrahedral in shape
(2) 2
72Cr O
2
has a Cr2O2Cr bond
(3) Na2Cr2O7 is a primary standard in
volumetry
(4) Na2Cr2O7 is less soluble than
K2Cr2O7
13. ÇUæ§ãæ§ÇþUæðÁÙ ·ð¤ â´ÎÖü ×ð´ ·¤æñÙ-âæ ÖæñçÌ·¤ »é‡æ »ÜÌ
ãñ?
(1) ߇æüãèÙ »ñâ
(2) »´ÏãèÙ »ñâ
(3) SßæÎãèÙ »ñâ
(4) ¥’ßÜÙàæèÜ »ñâ
14. çÙÙçÜç¹Ì ÿææÚUèØ ×ëÎæ ÏæÌé ·ð¤ ãñÜæ§ÇUæð´ ×ð´ âð 緤ⷤæ
SßÖæß ßæSÌß ×ð´ âãâ´ØæðÁ·¤ ãñ?
(1) MgCl2
(2) BeCl2
(3) SrCl2
(4) CaCl2
15. çΰ »° Øæñç»·¤æð´ ×ð´ âð P2P Õ´Ï·¤ ç·¤â ×ð´ ãñ?
(1) H4P2O5
(2) H4P2O6
(3) H4P2O7
(4) (HPO3)3
16. €ÜæðÚUèÙ ÁÜ ·é¤ÀU â×Ø ·ð¤ Âà¿æÌ÷ ¥ÂÙæ Ú´U» ¹æð ÎðÌæ
ãñ ¥æñÚU ÕÙæÌæ ãñ Ñ
(1) ·ð¤ßÜ HCl
(2) HOCl ¥æñÚU HOCl2
(3) HCl ¥æñÚU HOCl
(4) HCl ¥æñÚU HClO2
17. çÙÙ ·¤ÍÙæð´ ×ð´ âð »ÜÌ ·¤ÍÙ ¿éçÙØð?
(1)
2
4CrO
2
¿ÌécȤܷ¤èØ ¥æ·¤æÚU ·¤æ ãñÐ
(2) 2
72Cr O
2
×ð´ °·¤ Cr2O2Cr ¥æÕ´Ï ãñÐ
(3) ¥æØÌÙè çßàÜðá‡æ ×ð´ Na2Cr2O7 °·¤
ÂýæÍç×·¤ ×æÙ·¤ ãñÐ
(4) Na2Cr2O7 ·¤è çßÜØÌæ K2Cr2O7 âð ·¤×
ãñÐ
22. Page 6 CHEMISTRY : English & Hindi 01
22. Which of the following pairs of
compounds are positional isomers ?
(1) CH32CH22CH22CH22CHO
and
(2) and
(3) and
(4) and
23. The number of structural isomers for C6H14
is :
(1) 3
(2) 4
(3) 5
(4) 6
22. çÙÙçÜç¹Ì ×ð´ âð ·¤æñÙ-âð Øæñç»·¤ Øé‚× â×êã
â×æßØßè ãñ´?
(1) CH32CH22CH22CH22CHO ¥æñÚU
(2) ¥æñÚU
(3) ¥æñÚU
(4) ¥æñÚU
23. C6H14 ·¤è â´ÚU¿Ùæˆ×·¤ â×æßØçßØæð´ ·¤è â´Øæ ãñ Ñ
(1) 3
(2) 4
(3) 5
(4) 6
24. Page 8 CHEMISTRY : English & Hindi 01
26. Which compound exhibits maximum
dipole moment among the following ?
(1)
(2)
(3)
(4)
27. Which one of the following structures
represents the neoprene polymer ?
(1)
(2)
(3)
(4)
26. çÙÙçÜç¹Ì ×ð´ âð ·¤æñÙ-âæ Øæñç»·¤ âßæüçÏ·¤ çmÏýéß
¥æƒæê‡æü ÎàææüÌæ ãñ?
(1)
(2)
(3)
(4)
27. ÕãéÜ·¤ çÙØæðÂýèÙ ·¤è â´ÚU¿Ùæ çÙÙçÜç¹Ì â´ÚU¿Ùæ¥æð´
×ð´ âð ·¤æñÙ-âè ãñ?
(1)
(2)
(3)
(4)
25. Page 9 CHEMISTRY : English & Hindi 01
28. ¥æðÁSßè ÃØæØæ× ·ð¤ ȤÜSßM¤Â, ×æ´âÂðçàæØæð´ ×ð´ ç·¤â
Øæñç»·¤ ·¤æ â´¿ØÙ ãæðÌæ ãñ?
(1) ‚Üê·¤æð$Á
(2) ‚Üñ·¤æð$ÁÙ
(3) L-Üñç€ÅU·¤ ¥Ü
(4) ÂñM¤çß·¤ ¥Ü
29. 緤⠷ë¤ç˜æ× ×ÏéÚU·¤ ×ð´ €ÜæðÚUèÙ ãñ?
(1) °ðSÂæÅðüU×
(2) âñ·¤ÚUèÙ
(3) âê·ý¤æÜæðâ
(4) °ðçÜÅðU×
30. °·¤ »éÜæÕè Ü߇æ, »ÚU× ·¤ÚUÙð ÂÚU ÙèÜæ ãæð ÁæÌæ ãñÐ
Ü߇æ ×ð´ ç·¤â ÏÙæØÙ ·ð¤ ãæðÙð ·¤è âßæüçÏ·¤ â´ÖæßÙæ
ãñ?
(1) Cu21
(2) Fe21
(3) Zn21
(4) Co21
- o 0 o -
28. Accumulation of which of the following
molecules in the muscles occurs as a result
of vigorous exercise ?
(1) Glucose
(2) Glycogen
(3) L-lactic acid
(4) Pyruvic acid
29. Which artificial sweetener contains
chlorine ?
(1) Aspartame
(2) Saccharin
(3) Sucralose
(4) Alitame
30. A pink coloured salt turns blue on heating.
The presence of which cation is most
likely ?
(1) Cu21
(2) Fe21
(3) Zn21
(4) Co21
- o 0 o -
26. Page 1 MATHEMATICS : English & Hindi 01
1. Let A5{x1, x2, ..., x7} and B5{y1, y2, y3}
be two sets containing seven and three
distinct elements respectively. Then the
total number of functions f : A ® B that
are onto, if there exist exactly three
elements x in A such that f(x)5y2, is equal
to :
(1) 14 . 7C2
(2) 16 . 7C3
(3) 12 . 7C2
(4) 14 . 7C3
2. If z is a non-real complex number, then
the minimum value of
5
5
Im
(Im )
z
z
is :
(1) 21
(2) 22
(3) 24
(4) 25
3. If the two roots of the equation,
(a21)(x41x211)1(a11)(x21x11)250
are real and distinct, then the set of all
values of ‘a’ is :
(1)
1
, 0
2
2
(2) (2:, 22) È (2, :)
(3)
1 1
, 0 0,
2 2
∪
2
(4)
1
0,
2
4. If A is a 333 matrix such that ?5. adjA?55,
then ?A? is equal to :
(1)
1
5
6
(2) 65
(3) 61
(4)
1
25
6
1. ×æÙæ A5{x1, x2, ..., x7} ÌÍæ B5{y1, y2, y3}
°ðâð Îæð â×é“æØ ãñ´ çÁÙ×ð´ ·ý¤×àæÑ âæÌ ÌÍæ ÌèÙ çßçÖóæ
¥ßØß ãñ´ ; Ìæð °ðâð ȤÜÙæð´ f : A ® B ·¤è ·é¤Ü
â´Øæ, Áæð ç·¤ ¥æ‘ÀUæη¤ ãñ´, ØçÎ A ×ð´ °ðâð ÆUè·¤ ÌèÙ
x ¥ßØß ãñ´ çÁÙ·ð¤ çÜ° f(x)5y2 ãñ, ãñ Ñ
(1) 14 . 7C2
(2) 16 . 7C3
(3) 12 . 7C2
(4) 14 . 7C3
2. ØçÎ z °·¤ ¥ßæSÌçß·¤ âçןæ â´Øæ ãñ, Ìæð
5
5
Im
(Im )
z
z
·¤æ ‹ØêÙÌ× ×æÙ ãñ Ñ
(1) 21
(2) 22
(3) 24
(4) 25
3. ØçÎ â×è·¤ÚU‡æ
(a21)(x41x211)1(a11)(x21x11)250
·ð¤ Îæð ×êÜ ßæSÌçß·¤ ÌÍæ çßçÖóæ ãñ´, Ìæð ‘a’ ·ð¤ âÖè
×æÙæð´ ·¤æ â×êã ãñ Ñ
(1)
1
, 0
2
2
(2) (2:, 22) È (2, :)
(3)
1 1
, 0 0,
2 2
∪
2
(4)
1
0,
2
4. ØçÎ A °·¤ °ðâæ 333 ¥æÃØêã ãñ ç·¤ ?5. adjA?55
ãñ, Ìæð ?A? ÕÚUæÕÚU ãñ Ñ
(1)
1
5
6
(2) 65
(3) 61
(4)
1
25
6
27. Page 2 MATHEMATICS : English & Hindi 01
5. If
2
2
2
1 2
a 122 3 1 3 3 3
2 3 2 1 2 1
x x x x
xx x x x
x x x x
1 1 2
5 21 2 2
1 1 2 2
,
then ‘a’ is equal to :
(1) 12
(2) 24
(3) 212
(4) 224
6. If in a regular polygon the number of
diagonals is 54, then the number of sides
of this polygon is :
(1) 10
(2) 12
(3) 9
(4) 6
7. The term independent of x in the binomial
expansion of
8
5 21 1
1 3 2x x
x x
2 1 2 is :
(1) 400
(2) 496
(3) 2400
(4) 2496
8. The sum of the 3rd and the 4th terms of a
G.P. is 60 and the product of its first three
terms is 1000. If the first term of this G.P.
is positive, then its 7th term is :
(1) 7290
(2) 320
(3) 640
(4) 2430
5. ØçÎ
2
2
2
1 2
a 122 3 1 3 3 3
2 3 2 1 2 1
x x x x
xx x x x
x x x x
1 1 2
5 21 2 2
1 1 2 2
ãñ, Ìæð ‘a’ ÕÚUæÕÚU ãñ Ñ
(1) 12
(2) 24
(3) 212
(4) 224
6. ØçÎ °·¤ çÙØç×Ì ÕãéÖéÁ ·ð¤ çß·¤‡ææðZ ·¤è â´Øæ 54
ãñ, Ìæð ÕãéÖéÁ ·ð¤ ÖéÁæ¥æð´ ·¤è â´Øæ ãñ Ñ
(1) 10
(2) 12
(3) 9
(4) 6
7.
8
5 21 1
1 3 2x x
x x
2 1 2 ·ð¤ çmÂÎ ÂýâæÚU
×ð´ x âð SßÌ´˜æ ÂÎ ãñ Ñ
(1) 400
(2) 496
(3) 2400
(4) 2496
8. °·¤ »é‡ææðžæÚU Ÿæðɸè (G.P.) ·ð¤ ÌèâÚðU ÌÍæ ¿æñÍð ÂÎæð´ ·¤æ
Øæð» 60 ãñ ÌÍæ §â·ð¤ ÂýÍ× ÌèÙ ÂÎæð´ ·¤æ »é‡æÙȤÜ
1000 ãñÐ ØçÎ §â »é‡ææðžæÚU ŸæðÉ¸è ·¤æ ÂýÍ× ÂÎ ÏÙæˆ×·¤
ãñ, Ìæð §â·¤æ âæÌßæ´ ÂÎ ãñ Ñ
(1) 7290
(2) 320
(3) 640
(4) 2430
28. Page 3 MATHEMATICS : English & Hindi 01
9. If
5
n 1
1 k
n(n 1)(n 2)(n 3) 35
S 5
1 1 1
, then k is
equal to :
(1)
55
336
(2)
17
105
(3)
1
6
(4)
19
112
10. Let k be a non-zero real number. If
2
(e 1)
, 0
( ) sin log 1
k 4
12 , 0
x
x
x x
f x
x
≠
2
5 1
5
is a continuous function, then the value of
k is :
(1) 1
(2) 2
(3) 3
(4) 4
11. The equation of a normal to the curve,
sin sin
3
y x y
p
5 1 at x50, is :
(1) 2 3 0x y1 5
(2) 2 3 0y x2 5
(3) 2 3 0y x1 5
(4) 2 3 0x y2 5
9. ØçÎ
5
n 1
1 k
n(n 1)(n 2)(n 3) 35
S 5
1 1 1
ãñ, Ìæð k
ÕÚUæÕÚU ãñ Ñ
(1)
55
336
(2)
17
105
(3)
1
6
(4)
19
112
10. ×æÙæ k °·¤ àæê‹ØðÌÚU ßæSÌçß·¤ â´Øæ ãñÐ ØçÎ
2
(e 1)
, 0
( ) sin log 1
k 4
12 , 0
x
x
x x
f x
x
≠
2
5 1
5
°·¤ â´ÌÌ È¤ÜÙ ãñ, Ìæð k ·¤æ ×æÙ ãñ Ñ
(1) 1
(2) 2
(3) 3
(4) 4
11. x50 ÂÚU ß·ý¤ sin sin
3
y x y
p
5 1 ·ð¤
¥çÖÜ´Õ ·¤æ â×è·¤ÚU‡æ ãñ Ñ
(1) 2 3 0x y1 5
(2) 2 3 0y x2 5
(3) 2 3 0y x1 5
(4) 2 3 0x y2 5
30. Page 5 MATHEMATICS : English & Hindi 01
15. ×æÙæ f : R ® R °·¤ °ðâæ ȤÜÙ ãñ, ç·¤ âÖè x e R
·ð¤ çÜ°, f (22x)5f (21x) ÌÍæ f (42x)5
f (41x) ãñ ¥æñÚU
2
0
( ) d 5f x x∫ 5 ãñ, Ìæð
50
10
( ) df x x∫
·¤æ ×æÙ ãñ Ñ
(1) 80
(2) 100
(3) 125
(4) 200
16. ×æÙæ f : (21, 1) ® R °·¤ â´ÌÌ È¤ÜÙ ãñÐ ØçÎ
sin
0
3
(t) dt
2
x
f x∫ 5 ãñ, Ìæð
3
2
f
ÕÚUæÕÚU ãñ Ñ
(1)
3
2
(2) 3
(3)
3
2
(4)
1
2
17. x5f(y) ¥ß·¤Ü â×è·¤ÚU‡æ
ydx2(x12y2)dy50 ·¤æ ãÜ ãñÐ
ØçÎ f(21)51 ãñ, Ìæð f(1) ÕÚUæÕÚU ãñ Ñ
(1) 4
(2) 3
(3) 2
(4) 1
15. Let f : R ® R be a function such that
f (22x)5f (21x) and f (42x)5f (41x),
for all x e R and
2
0
( ) d 5f x x∫ 5 . Then the
value of
50
10
( ) df x x∫ is :
(1) 80
(2) 100
(3) 125
(4) 200
16. Let f : (21, 1) ® R be a continuous
function. If
sin
0
3
(t) dt
2
x
f x∫ 5 , then
3
2
f
is equal to :
(1)
3
2
(2) 3
(3)
3
2
(4)
1
2
17. The solution of the differential equation
ydx2(x12y2)dy50 is x5f(y).
If f(21)51, then f(1) is equal to :
(1) 4
(2) 3
(3) 2
(4) 1
31. Page 6 MATHEMATICS : English & Hindi 01
18. A straight line L through the point (3, 22)
is inclined at an angle of 608 to the line
3 1x y1 5 . If L also intersects the
x-axis, then the equation of L is :
(1) 3 2 3 3 0y x1 1 2 5
(2) 3 2 3 3 0y x2 1 1 5
(3) 3 3 2 3 0y x2 1 1 5
(4) 3 3 2 3 0y x1 2 1 5
19. If the incentre of an equilateral triangle is
(1, 1) and the equation of its one side is
3x14y1350, then the equation of the
circumcircle of this triangle is :
(1) x21y222x22y2250
(2) x21y222x22y21450
(3) x21y222x22y1250
(4) x21y222x22y2750
20. If a circle passing through the point
(21, 0) touches y-axis at (0, 2), then the
length of the chord of the circle along the
x-axis is :
(1)
3
2
(2)
5
2
(3) 3
(4) 5
18. çÕ´Îé (3, 22) âð ãæð·¤ÚU ÁæÙð ßæÜè °·¤ âÚUÜ ÚðU¹æ L,
ÚUð¹æ 3 1x y1 5 ·ð¤ âæÍ 608 ·¤æ ·¤æð‡æ ÕÙæÌè
ãñÐ ØçÎ L, x-¥ÿæ ·¤æð Öè ·¤æÅUÌè ãñ, Ìæð L ·¤æ
â×è·¤ÚU‡æ ãñ Ñ
(1) 3 2 3 3 0y x1 1 2 5
(2) 3 2 3 3 0y x2 1 1 5
(3) 3 3 2 3 0y x2 1 1 5
(4) 3 3 2 3 0y x1 2 1 5
19. ØçÎ °·¤ â×Õæãé ç˜æÖéÁ ·¤æ ¥´ÌÑ·ð´¤Îý (1, 1) ãñ ÌÍæ
§â·¤è °·¤ ÖéÁæ ·¤æ â×è·¤ÚU‡æ 3x14y1350 ãñ,
Ìæð §â ç˜æÖéÁ ·ð¤ ÂçÚUßëžæ ·¤æ â×è·¤ÚU‡æ ãñ Ñ
(1) x21y222x22y2250
(2) x21y222x22y21450
(3) x21y222x22y1250
(4) x21y222x22y2750
20. ØçÎ çÕ´Îé (21, 0) âð ãæð·¤ÚU ÁæÙð ßæÜæ °·¤ ßëžæ
y-¥ÿæ ·¤æð (0, 2) ÂÚU SÂàæü ·¤ÚUÌæ ãñ, Ìæð x-¥ÿæ ·¤è
çÎàææ ×ð´ ßëžæ ·¤è Áèßæ ·¤è Ü´Õæ§ü ãñ Ñ
(1)
3
2
(2)
5
2
(3) 3
(4) 5
33. Page 8 MATHEMATICS : English & Hindi 01
25. In a parallelogram ABCD, 5a,
5b and 5c, then has the
value :
(1) ( )2 2 21
a b c
2
2 1
(2) ( )2 2 21
a b c
4
1 2
(3) ( )2 2 21
b c a
3
1 2
(4) ( )2 2 21
a b c
2
1 1
26. If the lengths of the sides of a triangle are
decided by the three throws of a single fair
die, then the probability that the triangle
is of maximum area given that it is an
isosceles triangle, is :
(1)
1
26
(2)
1
27
(3)
1
21
(4)
1
15
27. If the mean and the variance of a binomial
variate X are 2 and 1 respectively, then the
probability that X takes a value greater
than or equal to one is :
(1)
1
16
(2)
9
16
(3)
3
4
(4)
15
16
25. °·¤ â×æ´ÌÚU ¿ÌéÖéüÁ ABCD ×ð´, 5a, 5b
ÌÍæ 5c ãñ, Ìæð ·¤æ ×æÙ ãñ Ñ
(1) ( )2 2 21
a b c
2
2 1
(2) ( )2 2 21
a b c
4
1 2
(3) ( )2 2 21
b c a
3
1 2
(4) ( )2 2 21
a b c
2
1 1
26. °·¤ ¥ÙçÖÙÌ Âæâð ·¤æð ÌèÙ ÕæÚU Èð´¤·¤ ·¤ÚU °·¤ ç˜æÖéÁ
·¤è ÖéÁæ¥æð´ ·¤è Ü´Õæ§Øæ¡ çÙÏæüçÚUÌ ·¤è ÁæÌè ãñ, Ìæð
ç˜æÖéÁ ·ð¤ ¥çÏ·¤Ì× ÿæð˜æÈ¤Ü ·ð¤ ãæðÙð ·¤è ÂýæçØ·¤Ìæ,
ÁÕ ç·¤ çÎØæ ãñ ç·¤ ç˜æÖéÁ â×çmÕæãé ãñ, ãñ Ñ
(1)
1
26
(2)
1
27
(3)
1
21
(4)
1
15
27. ØçÎ °·¤ çmÂÎ ¿ÚU X ·ð¤ ×æŠØ ÌÍæ ÂýâÚU‡æ ·ý¤×àæÑ 2
ÌÍæ 1 ãñ´, Ìæð X ·¤æ ×æÙ 1 Øæ §ââð ¥çÏ·¤ ãæðÙð ·¤è
ÂýæçØ·¤Ìæ ãñ Ñ
(1)
1
16
(2)
9
16
(3)
3
4
(4)
15
16
35. Page 10 MATHEMATICS : English & Hindi 01
30. Consider the following statements :
P : Suman is brilliant.
Q : Suman is rich.
R : Suman is honest.
The negation of the statement,
“Suman is brilliant and dishonest if and
only if Suman is rich” can be equivalently
expressed as :
(1) ~ Q « ~ P Ù R
(2) ~ Q « ~ P Ú R
(3) ~ Q « P Ú ~ R
(4) ~ Q « P Ù ~ R
- o 0 o -
30. çÙÙ ·¤ÍÙæð´ ÂÚU çß¿æÚU ·¤èçÁ° Ñ
P : âé×Ù ÂýçÌÖæàææÜè ãñÐ
Q : âé×Ù ¥×èÚU ãñÐ
R : âé×Ù §ü×æÙÎæÚU ãñÐ
·¤ÍÙ ÒÒâé×Ù ÂýçÌÖæàææÜè ÌÍæ Õð§ü×æÙ ãñ ØçÎ ¥æñÚU
·ð¤ßÜ ØçÎ âé×Ù ¥×èÚU ãñÓÓ ·¤æ çÙáðÏ çÙÙ Âý·¤æÚU âð
ÃØ€Ì ç·¤Øæ Áæ â·¤Ìæ ãñ Ñ
(1) ~ Q « ~ P Ù R
(2) ~ Q « ~ P Ú R
(3) ~ Q « P Ú ~ R
(4) ~ Q « P Ù ~ R
- o 0 o -