JEE Main 2014 Question Paper 19 Apr

PART A — PHYSICS Öæ» A — ÖæñçÌ·¤ çߙææÙ
1. Match List - I (Event) with List - II (Order 1. âê¿è-I(ƒæÅUÙæ) ·¤æð âê¿è-II (©â ƒæÅUÙæ ·ð¤ ãæðÙð ×´ð
of the time interval for happening of the Ü»ð â×Ø ¥‹ÌÚUæÜ ·¤è ·¤æðçÅU) âð âé×ðçÜÌ ·¤èçÁ°ð
event) and select the correct option from ¥æñÚU âêç¿Øæ´ð ·ð¤ ÕæÎ çÎØð »Øð çß·¤ËÂæ´ð ×ð´ âð âãè
the options given below the lists. çß·¤Ë ¿éçÙØðÐ
List - I List - II ÇϤÍ- I ÇϤÍ- II
Rotation period §ÐûÄÍ œ‰Ë ìËÏøËá¾
(a) (i) 10 5 s (a) (i) 105 s
of earth
œ‰ËÁ
Revolution §ÐûÄÍ œ‰Ë §Ì¿Uœâ‰¼øË
(b) (ii) 10 7 s (b) (ii) 107 s
period of earth
œ‰ËÁ
Period of a light •œ‰ §âœ‰ËÅË ±¿™U
(c) (iii) 10 215 s (c) (iii) 10215 s
wave
œ‰Ë œ‰ËÁ
Period of a •œ‰ çÄ̾ ±¿™U œ‰Ë
(d) (iv) 10 23 s (d) (iv) 1023 s
sound wave
œ‰ËÁ

(1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) (1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(2) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii) (2) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
(3) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) (3) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
(4) (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv) (4) (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)

English : 1 Set : 10 Hindi : 1 Set : 10

th
1 1
2. A bullet looses   of its velocity passing 2.
n
°· ÕéÜðÅU °·¤ ́Ìð âð »éÁÚUÙð ×ð´ ¥ÂÙð ßð» ·ð¤  n  ßæ¡
through one plank. The number of such ·¤è ãæçÙ ·¤ÚUÌè ãñ´Ð ÕéÜðÅU ·¤æð Âê‡æü çߟææ× ¥ßSÍæ ×´ð
planks that are required to stop the bullet ÜæÙð ·ð¤ çÜ°ð ç·¤ÌÙð §âè Âý·¤æÚU ·ð¤ ́Ìæð´ ·¤è
can be : ¥æßàØ·¤Ìæ ãæð»è Ñ
n2 n2
(1) (1)
2n21 2n21

2n 2 2n 2
(2) (2)
n21 n21
(3) Infinite (3) ¥Ù‹Ì
(4) n (4) n
3. A heavy box is to be dragged along a rough 3. °·¤ ¹éÚUÎéÚðU ÿæñçÌÁ Ȥàæü ÂÚU °·¤ ÖæÚUè Հâð ·¤æð ¹è´¿æ
horizontal floor. To do so, person A pushes ÁæÌæ ãñÐ °ðâæ ·¤ÚUÙð ·ð¤ çÜØð, ÃØç€Ì A ·¤æð ÿæñçÌÁ âð
it at an angle 308 from the horizontal and 308 ·¤æð‡æ ÂÚU π·¤æ Ü»æÙæ ÂǸÌæ ãñ ¥æñÚU ‹ØêÙÌ× ÕÜ
requires a minimum force FA, while person FA ·¤è ¥æßàØ·¤Ìæ ãæðÌè ãñ´ ÁÕ ç·¤ ÃØç€Ì B ·¤æð
B pulls the box at an angle 608 from the ÿæñçÌÁ âð 608 ·¤æð‡æ ÂÚU ¹è´¿Ùæ ãæðÌæ ãñ ¥æñÚU ‹ØêÙÌ×
horizontal and needs minimum force FB. ÕÜ FB ·¤è ¥æßàØ·¤Ìæ ãæðÌè ãñ´Ð ØçΠȤàæü °ß´ Հâð
F
If the coefficient of friction between the box 3 A
·ð¤ Õè¿ ƒæáü‡æ »é‡ææ¡·¤ ãñ´, ÌÕ ¥ÙéÂæÌ F ãñ´ :
5 B
F
3 A
and the floor is , the ratio F is :
5 B

(1) 3 (1) 3
5 5
(2) (2)
3 3

3 3
(3) (3)
2 2

2 2
(4) (4)
3 3
English : 2 Set : 10 Hindi : 2 Set : 10

4. Consider a cylinder of mass M resting on 4. °·¤ ¹éÚUÎéÚðU ÿæñçÌÁ ·¤æÜèÙ ÂÚU çߟææ× ¥ßSÍæ ×ð´
a rough horizontal rug that is pulled out ÎýÃØ×æÙ M ·ð¤ °·¤ ÕðÜÙ ÂÚU çß¿æÚU ·¤èçÁ°ðÐ ÕðÜÙ
from under it with acceleration ‘a’ ·¤è ¥ÿæ ·ð¤ ܐÕßÌ ˆßÚU‡æ ‘a’ âð ·¤æÜèÙ ·¤æð ¹è´¿
perpendicular to the axis of the cylinder. çÜØæ ÁæÌæ ãñ´Ð çՋÎé P ÂÚU Fƒæáü‡æ €Øæ ãñ´? Øã ×æÙ Üð´
What is Ffriction at point P ? It is assumed ç·¤ ÕðÜÙ çȤâÜÌæ Ùãè´ ãñ´Ð
that the cylinder does not slip.

(1) Mg (1) Mg
(2) Ma (2) Ma
Ma Ma
(3) (3)
2 2
Ma Ma
(4) (4)
3 3

English : 3 Set : 10 Hindi : 3 Set : 10

5. 5.

A particle is released on a vertical smooth °·¤ ª¤ŠßæüÏÚU ç¿·¤Ùð ¥hüßëžæèØ ÂÍ ·ð¤ çՋÎé X âð
semicircular track from point X so that OX °·¤ ·¤‡æ ·¤æð §â Âý·¤æÚU ÀUæðǸæ ÁæÌæ ãñ´ ç·¤ OX ª¤ŠßæüÏÚU
makes angle u from the vertical (see figure). âð ·¤æð‡æ u ÕÙæÌæ ãñ´ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ »Øæ ãñ´Ð
The normal reaction of the track on the ·¤‡æ ·ð¤ ª¤ÂÚU ÂÍ ·¤è ¥çÖÜÕ ÂýçÌç·ý¤Øæ çՋÎé Y
particle vanishes at point Y where OY ÂÚU â×æ# ãæð ÁæÌè ãñ´ Áãæ¡ OY ÿæñçÌÁ âð ·¤æð‡æ f
makes angle f with the horizontal. Then : ÕÙæÌæ ãñÐ ÌÕ Ñ
(1) sin f5cos u (1) sin f5cos u
1 1
(2) sin f5 cos u (2) sin f5 cos u
2 2
2 2
(3) sin f5 cos u (3) sin f5 cos u
3 3
3 3
(4) sin f5 cos u (4) sin f5 cos u
4 4

English : 4 Set : 10 Hindi : 4 Set : 10

6. A ball of mass 160 g is thrown up at an 6. ÿæñçÌÁ âð 608 ·ð¤ ·¤æð‡æ ÂÚU 10 ms21 ·¤è ¿æÜ âð
angle of 608 to the horizontal at a speed of 160 g ÎýÃØ×æÙ ·¤è °·¤ »ð´Î ª¤ÂÚU ·¤è ¥æðÚU Èð´¤·¤è
10 ms21. The angular momentum of the ÁæÌè ãñ´Ð ÂÍ ·ð¤ ©“æÌ× çՋÎé ÂÚU ©â çՋÎé ·ð¤ âæÂðÿæ,
ball at the highest point of the trajectory Áãæ¡ âð »ð´Î Èð´¤·¤è »§ü ãñ´, »ð´Î ·¤æ ·¤æð‡æèØ â´ßð» ֻܻ
with respect to the point from which the ãñ (g510 ms22)
ball is thrown is nearly (g510 ms22)
(1) 1.73 kg m2/s (1) 1.73 kg m2/s
(2) 3.0 kg m2/s (2) 3.0 kg m2/s
(3) 3.46 kg m2/s (3) 3.46 kg m2/s
(4) 6.0 kg m2/s (4) 6.0 kg m2/s

7. The gravitational field in a region is 7. °·¤ ÿæð˜æ ×ð´ »éL¤ˆßæ·¤áü‡æ ÿæð˜æ §â Âý·¤æÚU çÎØæ ÁæÌæ ãñ´
r r
given by g 5 5N/kg iˆ 1 12 N/kg ˆj . The g 5 5N/kg iˆ 1 12 N/kg ˆj ÎýÃØ×æÙ 2 kg ·ð¤
change in the gravitational potential °·¤ ·¤‡æ ·¤æð ×êÜ çՋÎé âð çՋÎé (7 m,23 m) Üð
energy of a particle of mass 2 kg when it is ÁæÙð ×ð´ »éL¤ˆßèØ çSÍçÌÁ ª¤Áæü ×ð´ ÂçÚUßÌüÙ ãñ´ :
taken from the origin to a point
(7 m,23 m) is :
(1) 71 J (1) 71 J

(2) 13 58 J (2) 13 58 J
(3) 271 J (3) 271 J
(4) 1J (4) 1J

English : 5 Set : 10 Hindi : 5 Set : 10

8. The velocity of water in a river is 8. °·¤ ÙÎè ×ð´ âÌã ·ð¤ â×è ÂæÙè ·¤æ ßð» 18 km/hr
18 km/hr near the surface. If the river is ãñ´Ð ØçÎ ÙÎè 5 m »ãÚUè ãñ, ÌÕ ÂæÙè ·¤è ÿæñçÌÁ ÂÚUÌæð´
5 m deep , find the shearing stress between ·ð¤ Õè¿ ¥ÂL¤Â‡æ ÂýçÌÕÜ ·¤è »‡æÙæ ·¤èçÁ°ðÐ ÂæÙè
the horizontal layers of water. The ·¤æ àØæÙÌæ »é‡ææ¡·¤ 51022 ÂæØÁÐ
co-efficient of viscosity of water510 22
poise.
(1) 1021 N/m2 (1) 1021 N/m2
(2) 1022 N/m2 (2) 1022 N/m2
(3) 1023 N/m2 (3) 1023 N/m2
(4) 1024 N/m2 (4) 1024 N/m2

9. 9.

In the diagram shown, the difference in ÎàææüØð »Øð 翘æ ×ð´, Îæð ÙçÜØæ´ð ·ð¤ ×ðÙæð×èÅUÚU ×ð´ ¥‹ÌÚU
the two tubes of the manometer is 5 cm, 5 cm ãñ´Ð A °ß´ B ÙçÜØæ𴠷𤠥ÙéÂýSÍ ·¤æÅU ·ý¤×àæÑ
the cross section of the tube at A and B is 6 mm2 °ß´ 10 mm2 ãñ´Ð ÙÜè ×ð´ ÂýßæçãÌ ÂæÙè ·¤è
6 mm2 and 10 mm2 respectively. The rate ÎÚU ãñ´ (g510 ms22)
at which water flows through the tube is
(g510 ms22)
(1) 7.5 cc/s (1) 7.5 cc/s
(2) 8.0 cc/s (2) 8.0 cc/s
(3) 10.0 cc/s (3) 10.0 cc/s
(4) 12.5 cc/s (4) 12.5 cc/s

English : 6 Set : 10 Hindi : 6 Set : 10

10. A large number of liquid drops each of 10. ÂýˆØð·¤ ç˜æ’Øæ r ·¤è ¥ˆØçÏ·¤ ⴁØæ ×ð´ Îýß ·¤è Õê¡Îð´
radius r coalesce to from a single drop of ç×Ü·¤ÚU ç˜æ’Øæ R ·¤è °·¤ Õê¡Î ÕÙæÌè ãñ´Ð Âýç·ý¤Øæ ×ð´
radius R. The energy released in the çÙ·¤Üè ª¤Áæü, ÕǸè Õê¡Î ·¤è »çÌÁ ª¤Áæü ×ð´ ÂçÚUßçÌüÌ
process is converted into kinetic energy of ãæð ÁæÌè ãñ´Ð ÕǸè Õê¡Î ·¤è ¿æÜ ã´ñ (çÎØæ ãñ´ Îýß ·¤æ
the big drop so formed. The speed of the ÂëcÆU ÌÙæß T,ƒæÙˆß r)
big drop is (given surface tension of liquid
T, density r)

T1 1 T1 1
(1)  2  (1)  2 
rr R rr R

2T  1 1 2T  1 1
(2)  2  (2)  2 
r r R r r R

4T  1 1 4T  1 1
(3)  2  (3)  2 
r r R r r R

6T  1 1 6T  1 1
(4)  2  (4)  2 
r r R r r R

English : 7 Set : 10 Hindi : 7 Set : 10

11. A black coloured solid sphere of radius R 11. °·¤ »éãæ, çÁâ×ð´ çÙßæüÌ ãñ´, ·ð¤ ¥‹ÎÚU ÎýÃØ×æÙ M °ß´
and mass M is inside a cavity with vacuum ç˜æ’Øæ R ·ð¤ °·¤ ·¤æÜð Ú´U» ·ð¤ ÆUæðâ »æðÜð ·¤æð ÚU¹æ »Øæ
inside. The walls of the cavity are ãñ´Ð »éãæ ·¤è ÎèßæÚUæð´ ·¤æ ÌæÂ×æÙ T0 ÂÚ ¥ÙéÚUçÿæÌ ç·¤Øæ
maintained at temperature T0. The initial »Øæ ãñ´Ð »æðÜð ·¤æ ÂýæÚUçÖ·¤ ÌæÂ×æÙ 3T0 ãñ´Ð ØçÎ »æðÜð
temperature of the sphere is 3T0. If the ·ð¤ ÂÎæÍü ·¤è çßçàæcÅU ª¤c×æ ÂýçÌ §·¤æ§ü ÎýÃØ×æÙ »æðÜð
specific heat of the material of the sphere ·ð¤ ÌæÂ×æÙ T âð aT3 ·ðð U ¥ÙéâæÚU ÂçÚUßçÌüÌ ãæðÌè ãñ´,
varies as aT 3 per unit mass with the Áãæ¡ a °·¤ çSÍÚUæ¡·¤ ãñ´, ÌÕ »æðÜð ·ð¤ ÌæÂ×æÙ ·¤æð 2T0
temperature T of the sphere, where a is a Ì·¤ ÆU´ÇUæ ãæðÙð ×ð´ â×Ø Ü»ð»æ (s SÅUèȤ٠ÕæðËÅUÁ×æÙ
constant, then the time taken for the sphere çSÍÚUæ¡·¤ ãñ´)
to cool down to temperature 2T0 will be
(s is Stefan Boltzmann constant)

Ma 3 Ma 3
(1) 2
ln   (1) 2
ln  
4 pR  4 pR 

Ma  16  Ma  16 
(2) 2
ln   (2) 2
ln  
4 pR    4 pR   

Ma  16  Ma  16 
(3) 2
ln   (3) 2
ln  
16 pR    16 pR   

Ma 3 Ma 3
(4) ln   (4) ln  
16 pR 2  16 pR 2 
12. A gas is compressed from a volume of 12. °·¤ »ñâ 100 N/m2 ·ð¤ çSÍÚU ÎæÕ ÂÚU ¥æØÌÙ
2 m3 to a volume of 1 m3 at a constant 2 m3 âð 1 m3 ×ð´ â´ÂèçÇUÌ ·¤è ÁæÌè ãñ´Ð çȤÚU §âð
pressure of 100 N/m2. Then it is heated at çSÍÚU ¥æØÌÙ ÂÚU 150 J ·¤è ª¤Áæü âð »×ü ç·¤Øæ ÁæÌæ
constant volume by supplying 150 J of ãñ´Ð ÂçÚU‡ææ×SßL¤Â »ñâ ·¤è ¥æ‹ÌçÚU·¤ ª¤Áæü Ñ
energy. As a result, the internal energy of
the gas : U
(1) Increases by 250 J (1) 250 J âð Õɸð»è
(2) Decreases by 250 J (2) 250 J âð ƒæÅðU»è
(3) Increases by 50 J (3) 50 J âð Õɸð»è
(4) Decreases by 50 J (4) 50 J âð ƒæÅðU»è

English : 8 Set : 10 Hindi : 8 Set : 10

13. A gas molecule of mass M at the surface 13. Âë‰ßè ·ð¤ ÂëcÆU ÂÚU ÎýÃØ×æÙ M ·ð¤ °·¤ »ñâ ¥‡æé ·¤è
of the Earth has kinetic energy equivalent »çÌÁ ª¤Áæü 08C ·ð¤ â×ÌéËØ ãñ´Ð ØçÎ Øã çÕÙæ ç·¤âè
to 08C. If it were to go up straight without ¥æñÚU ¥‡æé âð ÅU·¤ÚUæØð âèÏ𠪤ÂÚU ·¤è ¥æðÚU ÁæÌæ ãñ´, ÌÕ
colliding with any other molecules, how Øã 緤⠪¡¤¿æ§ü Ì·¤ Áæ°ð»æ?(Øã ×æÙ Üð´ Øã ª¡¤¿æ§ü
high it would rise ? Assume that the height Âë‰ßè ·¤è ç˜æ’Øæ âð ÕãéÌ ·¤× ãñ) (kB ÕæðËÅUÁ×æÙ
attained is much less than radius of the çSÍÚUæ¡·¤ ãñ´)
earth. (kB is Boltzmann constant)
(1) 0 (1) 0

273 k B 273 k B
(2) 2 Mg (2) 2 Mg

546 k B 546 k B
(3) 3 Mg (3) 3 Mg

819 k B 819 k B
(4) 2 Mg (4) 2 Mg

14. A body is in simple harmonic motion with 14. °·¤ ßSÌé ¥æßÌü·¤æÜ ¥æÏð âñç·¤‡ÇU (T50.5 s)
time period half second (T50.5 s) and ¥æñÚ ¥æØæ× °·¤ âð´ÅUè×èÅUÚU (A51 cm) âðU âÚUÜ
amplitude one cm (A51 cm). Find the ¥æßÌü »çÌ ·¤ÚU ÚUãè ãñ´Ð ÁÕ Øã ¥ÂÙè âæØæßSÍæ
average velocity in the interval in which it çSÍçÌ âð ¥ÂÙð ¥æÏð ¥æØæ× Ì·¤ Âãé¡¿Ìè ãñ´, ©â
moves from equilibrium position to half of ¥‹ÌÚUæÜ ×ð´ ¥æñâÌ ßð» ·¤è »‡æÙæ ·¤èçÁ°ðÐ
its amplitude.
(1) 4 cm/s (1) 4 cm/s
(2) 6 cm/s (2) 6 cm/s
(3) 12 cm/s (3) 12 cm/s
(4) 16 cm/s (4) 16 cm/s

English : 9 Set : 10 Hindi : 9 Set : 10

15. The total length of a sonometer wire 15. SÍæØè çâÚUæ´ð ·ð¤ Õè¿ °·¤ âæðÙæð×æÂè ÌæÚU ·¤è ·é¤Ü
between fixed ends is 110 cm. Two bridges ܐÕæ§ü 110 cm ãñ´Ð §â·¤è ܐÕæ§ü ·¤æð ¥ÙéÂæÌ
are placed to divide the length of wire in 6 : 3 : 2 ×ð´ çßÖæçÁÌ ·¤ÚUÙð ·ð¤ çÜØð Îæð âðÌé ÚU¹ð »Øð
ratio 6 : 3 : 2. The tension in the wire is ãñ´Ð ÌæÚU ×ð´ ÌÙæß 400 N ãñ´ ¥æñÚU ÂýçÌ §·¤æ§ü ܐÕæ§ü,
400 N and the mass per unit length is ÎýÃØ×æÙ 0.01 kg/m ãñ´Ð ß㠋ØêÙÌ× ©ÖØçÙcÆU
0.01 kg/m. What is the minimum common ¥æßëçžæ, çÁââð ç·¤ ÌèÙæð´ Öæ» ·¤ÂÙ ·¤ÚU â·ð´¤»ð´, ãñ´
frequency with which three parts can
vibrate ?
(1) 1100 Hz (1) 1100 Hz
(2) 1000 Hz (2) 1000 Hz
(3) 166 Hz (3) 166 Hz
(4) 100 Hz (4) 100 Hz

16. The electric field in a region of space is 16. ×é€Ì ¥æ·¤æàæ ·ð¤ °·¤ ÿæð˜æ ×ð´ çßléÌ ÿæð˜æ çÎØæ ÁæÌæ ãñ´
→ ∧ ∧ → ∧ ∧
given by, E 5 Eo i 1 2 Eo j where E 5 Eo i 1 2 Eo j Áãæ¡ E 0 5100 N/C Ð
E05100 N/C. The flux of this field through Y-Z ÌÜ ·ð¤ â×æ‹ÌÚU 0.02 m ç˜æ’Øæ ·ð¤ ßëžæèØ ÂëcÆU
a circular surface of radius 0.02 m parallel âð »éÁÚUÙð ÂÚU §â çßléÌ ÿæð˜æ ·¤æ Ü€â ֻܻ ãñ´ Ñ
to the Y-Z plane is nearly :
(1) 0.125 Nm2/C (1) 0.125 Nm2/C
(2) 0.02 Nm2/C (2) 0.02 Nm2/C
(3) 0.005 Nm2/C (3) 0.005 Nm2/C
(4) 3.14 Nm2/C (4) 3.14 Nm2/C

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

17. The gap between the plates of a parallel 17. °·¤ â×æ‹ÌÚU ŒÜðÅU â´ÏæçÚU˜æ ·¤è ÂýˆØð·¤ ŒÜðÅU ·¤æ ÿæð˜æȤÜ
plate capacitor of area A and distance A ãñ´ ¥æñÚU ŒÜðÅUæð´ ·ð¤ Õè¿ ÎêÚUè d ãñ´Ð ŒÜðÅUæð´ ·ð¤ Õè¿
between plates d, is filled with a dielectric SÍæÙ ·¤æð °·¤ ÂÚUæßñléÌ âð ÖÚUæ »Øæ ãñ çÁâ·¤è
whose permittivity varies linearly from Î1 çßléÌàæèÜÌæ °·¤ ŒÜðÅU ÂÚU Î1 âð ÎêâÚUè ŒÜðÅU ÂÚU Î2
at one plate to Î 2 at the other. The Ì·¤ ÚðUç¹·¤ M¤Â ×ð´ ÂçÚUßçÌüÌ ãæðÌè ãñÐ â´ÏæçÚU˜æ ·¤è
capacitance of capacitor is : ÏæçÚUÌæ ãñ´ Ñ
(1) Î0(Î11Î2)A/d (1) Î0(Î11Î2)A/d

(2) Î0(Î21Î1)A/2d (2) Î0(Î21Î1)A/2d

(3) Î0A/[d ln(Î2/Î1)] (3) Î0A/[d ln(Î2/Î1)]

(4) Î0(Î22Î1)A/[d ln(Î2/Î1)] (4) Î0(Î22Î1)A/[d ln(Î2/Î1)]

18. 18.

Four bulbs B1, B2, B3 and B4 of 100 W each ÂýˆØð·¤ 100 W ·ð¤ ¿æÚU ÕËÕ B1, B2, B3 °ß´ B4
are connected to 220 V main as shown in 220 V ×ð‹â âð ÁæðǸð »Øð ãñ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ
the figure. The reading in an ideal ammeter »Øæ ãñ´Ð °·¤ ¥æÎàæü ÏæÚUæ×æÂè ×ð´ ×æÂÙ ãæð»æ Ñ
will be :
(1) 0.45 A (1) 0.45 A
(2) 0.90 A (2) 0.90 A
(3) 1.35 A (3) 1.35 A
(4) 1.80 A (4) 1.80 A

English : 11 Set : 10 Hindi : 11 Set : 10

19. 19.

A square frame of side 10 cm and a long 10 cm ÖéÁæ ·¤æ °·¤ ß»æü·¤æÚU Èðý¤× ¥æñÚU ÏæÚUæ 1 A âð
straight wire carrying current 1 A are in ÂýßæçãÌ °·¤ ܐÕæ âèÏæ ÌæÚU ·¤æ»$Á ·ð¤ ÌÜ ×ð´ ÚU¹ð
the plane of the paper. Starting from close ãñ´Ð ÌæÚU ·ð¤ â×è âð, Èýð¤× Îæ¡Øè ¥æðÚU °·¤ çSÍÚU ¿æÜ
to the wire, the frame moves towards the 10 ms21 âð »çÌ ·¤ÚUÌæ ãñ´Ð (翘æ Îð¹ð´)Ð ÌæÚU âð
right with a constant speed of 10 ms21 (see ÁÕ Èýð¤× ·¤è Õæ¡Øè ÖéÁæ x510 cm ÂÚU ãñ´ ÌÕ ©â
figure). The e.m.f induced at the time the â×Ø ÂýðçÚUÌ çßléÌ ßæã·¤ ÕÜ ãñ´ Ñ
left arm of the frame is at x510 cm from
the wire is :
(1) 2 mV (1) 2 mV
(2) 1 mV (2) 1 mV
(3) 0.75 mV (3) 0.75 mV
(4) 0.5 mV (4) 0.5 mV

English : 12 Set : 10 Hindi : 12 Set : 10

20. An example of a perfect diamagnet is a 20. ¥çÌ¿æÜ·¤ ¥æÎàæü ¥Ùé¿éÕ·¤ ·¤æ °·¤ ©ÎæãÚU‡æ ãñÐ
superconductor. This implies that when a §â·¤æ ¥Íü ãñ ç·¤ ÁÕ ÌèßýÌæ B ·ð¤ °·¤ ¿éÕ·¤èØ ÿæð˜æ
superconductor is put in a magnetic field ×ð´ ¥çÌ¿æÜ·¤ ·¤æð ÚU¹æ ÁæÌæ ãñ´, ÌÕ ¥çÌ¿æÜ·¤ ·ð¤
of intensity B, the magnetic field Bs inside ¥‹ÎÚU ¿éÕ·¤èØ ÿæð˜æ Bs §â Âý·¤æÚU ãæð»æ Ñ
the superconductor will be such that :
(1) Bs52B (1) Bs52B
(2) Bs50 (2) Bs50
(3) Bs5B (3) Bs5B
(4) Bs<B but Bs ≠ 0 (4) Bs<B ÂÚ´UÌé Bs ≠ 0

English : 13 Set : 10 Hindi : 13 Set : 10

21. 21.

Figure shows a circular area of radius R 翘æ ç˜æ’Øæ R ·ð¤ °·¤ ßëžæèØ ÿæð˜æÈ¤Ü ·¤æð ÎàææüÌæ ãñ
→ →
where a uniform magnetic field B is going Áãæ¡ °·¤ °·¤â×æÙ ¿éÕ·¤èØ ÿæð˜æ B ·¤æ»$Á ·ð¤ ÌÜ
into the plane of paper and increasing in ×ð´ ãñ´ ¥æñÚU §â·¤è çSÍÚU ÎÚU âð ÂçÚU×æ‡æ ×ð´ ßëçh ãæð ÚUãè
magnitude at a constant rate. In that case, ãñ´Ð §â ¥ßSÍæ ×ð´, âæ´·ð¤çÌ·¤ M¤Â âð ¹è´¿æ »Øæ,
which of the following graphs, drawn ·¤æñÙ-âæ »ýæȤ ÂýðçÚUÌ çßléÌ ÿæð˜æ E(r) ·ð¤ ÂçÚUßÌüÙ ·¤æð
schematically, correctly shows the âãè Îàææü°ð»æ?
variation of the induced electric field
E(r) ?

(1) (1)

(2) (2)

English : 14 Set : 10 Hindi : 14 Set : 10

(3) (3)

(4) (4)

22. If denote microwaves, X rays, infrared, 22. ØçÎ çßléÌ ¿éÕ·¤èØ SÂð€ÅþU× ·ð¤ Öæ» âêÿ× ÌÚ´U»ð´, X
gamma rays, ultra-violet, radio waves and ç·¤ÚU‡æð´, ¥ßÚU€Ì, »æ×æ ç·¤ÚU‡æð´, ÂÚUæÕñ´»Ùè, ÚðUçÇUØæð ÌÚ´U»ð´
visible parts of the electromagnetic ¥æñÚU ÎëàØ Âý·¤æàæ ·ý¤×àæÑ M, X, I, G, U, R ¥æñÚU V
spectrum by M, X, I, G, U, R and V, the âð ç¿ç‹ãÌ ç·¤Øð ÁæØð, ÌÕ ÌÚ´U»ÎñƒØü ·ð¤ ©žæÚUæðžæÚU ·ý¤×
following is the arrangement in ascending ×ð´ çߋØæâ çِÙçÜç¹Ì ãæð»æ Ñ
order of wavelength :
(1) R, M, I, V, U, X and G (1) R, M, I, V, U, X ¥æñÚU G
(2) M, R, V, X, U, G and I (2) M, R, V, X, U, G ¥æñÚU I
(3) G, X, U, V, I, M and R (3) G, X, U, V, I, M ¥æñÚU R
(4) I, M, R, U, V, X and G (4) I, M, R, U, V, X ¥æñÚU G

English : 15 Set : 10 Hindi : 15 Set : 10

23. A ray of light is incident from a denser to
a rarer medium. The critical angle for total 23. °·¤ âƒæÙ âð çßÚUÜ ×æŠØ× ×ð´ Âý·¤æàæ ·¤è ç·¤ÚU‡æ
internal reflection is uiC and the Brewster’s ¥æÂçÌÌ ãñ´Ð Âê‡æü ¥æ‹ÌçÚU·¤ ÂÚUæßÌüÙ ·ð¤ çÜØð ·ý¤æç‹Ì·¤
angle of incidence is u iB , such that ·¤æð‡æ uiC ãñ ¥æñÚU ¥æÂÌÙ ·¤æ ÕýêSÅUÚU ·¤æð‡æ uiB §â
sinu iC /sinu iB 5h51.28. The relative Âý·¤æÚU ãñ´ ç·¤ sinuiC/sinuiB5h51.28Ð ÎæðÙæð´
refractive index of the two media is : ×æŠØ×æ´ð ·¤æ ¥æÂðçÿæ·¤ ¥ÂßÌüÙæ¡·¤ ãñ´ Ñ
(1) 0.2
(2) 0.4 (1) 0.2
(3) 0.8 (2) 0.4
(4) 0.9 (3) 0.8
(4) 0.9
24. The diameter of the objective lens of
microscope makes an angle b at the focus 24. °·¤ âê ÿ ×Îàæèü ·ð ¤ ¥çÖÎë à Ø·¤ Üð ‹ â ·¤æ ÃØæâ
of the microscope. Further, the medium âêÿ×Îàæèü ·ð¤ Ȥæð·¤â ÂÚU ·¤æð‡æ b ÕÙæÌæ ãñ ; ßSÌé °ß´
between the object and the lens is an oil of Üð‹â ·ð¤ Õè¿ ·¤æ ×æŠØ× ¥ÂßÌüÙæ¡·¤ n ·¤æ °·¤ ÌðÜ
refractive index n. Then the resolving ãñ´Ð ÌÕ âêÿ×Îàæèü ·¤è çßÖðÎÙ ÿæ×Ìæ Ñ
power of the microscope.
(1) Increases with decreasing value of n
(2) Increases with decreasing value of b (1) n ·¤æ ×æÙ ƒæÅUÙð âð Õɸð»è
(3) Increases with increasing value of (2) b ·¤æ ×æÙ ƒæÅUÙð âð Õɸð»è
n sin 2b (3) n sin 2b ·¤æ ×æÙ ÕɸÙð âð Õɸð»è
(4) Increases with increasing value of
1
1 (4)
n sin 2b
·¤æ ×æÙ ÕɸÙð âð Õɸð»è
n sin 2b

English : 16 Set : 10 Hindi : 16 Set : 10

25. In a Young’s double slit experiment, the 25. Ø´» ·ð¤ çmçÀUÎý ÂýØæð» ×ð´, Îæð âßüâ×M¤Âè çSÜÅUæð´ ·ð¤
distance between the two identical slits is Õè¿ ÎêÚUè çSÜÅU ¿æñǸæ§ü ·¤è 6.1 »éÙæ ãñ´Ð ÌÕ °·¤Ü
6.1 times larger than the slit width. Then çSÜÅU çßßÌüÙ ç¿˜æ ·ð¤ ·ð¤‹ÎýèØ ×ãžæ× ·ð¤ ¥‹ÎÚU
the number of intensity maxima observed ÃØçÌ·¤ÚU‡æ ç¿˜æ ·¤è ¥çÏ·¤Ì× ÌèßýÌæ¥æð´ ·¤è ⴁØæ
within the central maximum of the single ãñ´ Ñ
slit diffraction pattern is :
(1) 3 (1) 3
(2) 6 (2) 6
(3) 12 (3) 12
(4) 24 (4) 24

English : 17 Set : 10 Hindi : 17 Set : 10

26. Match List - I (Experiment performed) 26. âê¿è-I (ç·¤Øæ »Øæ ÂýØæð») ·¤æð âê¿è-II (çâhæ‹Ì
with List - II (Phenomena discovered/ ¹æðÁæ »Øæ ãñ/âÕçhÌ ãñ´) âð âé×ðçÜÌ ·¤èçÁ°ð ¥æñÚ
associated) and select the correct option âêç¿Øæð´ ·ð¤ Ùè¿ð çÎØð »Øð çß·¤ËÂæ´ð âð âãè çß·¤ËÂ
from the options given below the lists : ¿éçÙ°ð Ñ
List - I List - II ÇÏ¤Í - I ÇÏ¤Í - II
Davisson
Wave nature of ¬ÕUÄÍǾ ŠËÖ¿U ¦¼á¿U ŒÁÕþªãU˾Ëՙ œ‰Ë ±¿™U
(a) and Germer (i) (a) (i)
electrons §â½ËÕ §âœ‰Ë¿U
Experiment

Millikan’s oil
Charge of an ̼ÌÁœ‰Ë¾ œ‰Ë ³âÄ ŒÁÕþªãU˾ œ‰Ë
(b) drop (ii) (b) (ii)
electron œÕ‰ Ì ¿U¾Õ œ‰Ë §â½ËÕ ŠËÄÕÅË
experiment

Rutherford Quantisation of ‰¦Ëá S±¿U œ‰Ë
(c) (iii) (c) ¿U³¿U­‰ËÕ¬áU §â½ËÕ (iii)
experiment energy levels þÄËøªÍœ‰¿UøË
Franck -
Existence of ­Ö♉œ‰ - ȪáU¦ ¾ËÌ»œ‰ œ‰Ë
(d) Hertz (iv) (d) (iv)
nucleus §â½ËÕ ŠÌS±íÄ
experiment

(1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) (1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
(2) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) (2) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
(3) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) (3) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
(4) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) (4) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

English : 18 Set : 10 Hindi : 18 Set : 10

27. A piece of wood from a recently cut tree 27. °·¤ ÌæÁð ·¤æÅðU »Øð ÂðǸ ·¤è Ü·¤Ç¸è ·ð¤ ÅéU·¤Ç¸ð âð ÂýçÌ
shows 20 decays per minute. A wooden ç×ÙÅU 20 ÿæØ ãæðÌð ãñ´Ð ©âè ¥æ·¤æÚU ·¤æ Ü·¤Ç¸è ·¤æ
piece of same size placed in a museum ÅéU·¤Ç¸æ °·¤ ØêçÁØ× âð ÂýæŒÌ ãæðÌæ ãñ´ (Áæð ç·¤ Ü·¤Ç¸è
(obtained from a tree cut many years back) ·¤§ü ßáü ÂéÚUæÙè ·¤ÅUè ãé§ü ãñ) Áæð ç·¤ ÂýçÌ ç×ÙÅU 2 ÿæØ
shows 2 decays per minute. If half life of ÎàææüÌæ ãñ ; ØçÎ C14 ·¤è ¥Ïü ¥æØé 5730 ßáü ãñ´, ÌÕ
C14 is 5730 years, then age of the wooden ØêçÁØ× âð ÂýæŒÌ Ü·¤Ç¸è ·ð¤ ÅéU·¤Ç¸ð ·¤è ¥æØé ãñ´
piece placed in the museum is ֻܻ Ñ
approximately :
(1) 10439 years (1) 10439 ßáü
(2) 13094 years (2) 13094 ßáü
(3) 19039 years (3) 19039 ßáü
(4) 39049 years (4) 39049 ßáü

28. 28.

Given : A and B are input terminals. çÎØæ ãñ´ Ñ A °ß´ B çÙßðàæ ÅUç×üÙÜ ãñ´Ð
Logic 1 5 > 5 V ÜæçÁ·¤ 1 5 > 5 V
Logic 0 5 < 1 V ÜæçÁ·¤ 0 5 < 1 V
Which logic gate operation, the following çِÙçÜç¹Ì ÂçÚUÂÍ ·¤æñÙ-âð ÜæçÁ·¤ »ðÅU ·¤æ ·¤æØü
circuit does ? ·¤ÚU ÚUãæ ãñ´?
(1) AND Gate (1) AND »ðÅU
(2) OR Gate (2) OR »ðÅU
(3) XOR Gate (3) XOR »ðÅU
(4) NOR Gate (4) NOR »ðÅU

English : 19 Set : 10 Hindi : 19 Set : 10

29. Long range radio transmission is possible 29. ܐÕè ÚðU‹Á ×ð´ ÚðUçÇUØæð Âýðá‡æ âÖß ãñ´ ÁÕ ¥æØÙæðSȤèØÚU
when the radiowaves are reflected from âð ÚðUçÇUØæð ÌÚ´U»ð´ ÂÚUæßçÌüÌ ãæðÌè ãñ´Ð §â·ð¤ âÖß ãæðÙð
the ionosphere. For this to happen the ·ð¤ çÜØð ÚðUçÇUØæð ÌÚ´U»æð´ ·¤è ¥æßëçžæ §â ÚðU‹Á ×ð´ ¥ßàØ
frequency of the radiowaves must be in the ãæðÙè ¿æçã°ð Ñ
range :
(1) 80 - 150 MHz (1) 80 - 150 MHz
(2) 8 - 25 MHz (2) 8 - 25 MHz
(3) 1 - 3 MHz (3) 1 - 3 MHz
(4) 150 - 500 kHz (4) 150 - 500 kHz

English : 20 Set : 10 Hindi : 20 Set : 10

30. 30.

In an experiment for determining the °·¤ âÚUÜ ÜæðÜ·¤ ·¤è âãæØÌæ âð °·¤ SÍæÙ ÂÚU
gravitational acceleration g of a place with »éL¤ˆßèØ ˆßÚU‡æ g ·ð¤ ×æÂÙ ·ð¤ ÂýØæð» ×ð´, ÙæÂð »Øð
the help of a simple pendulum, the ¥æßÌü ·¤æÜ ·ð¤ ß»ü ·¤æ ÂçÚUßÌüÙ ÜæðÜ·¤ ·¤è ÇUæðÚUè ·¤è
measured time period square is plotted ܐÕæ§ü ·ð¤ âæÍ ç¿˜æ ×ð´ ÎàææüØæ »Øæ ãñ Ñ
against the string length of the pendulum
in the figure.
What is the value of g at the place ? §â SÍæÙ ÂÚU g ·¤æ ×æÙ ãñ´Ð
(1) 9.81 m/s2 (1) 9.81 m/s2
(2) 9.87 m/s2 (2) 9.87 m/s2
(3) 9.91 m/s2 (3) 9.91 m/s2
(4) 10.0 m/s2 (4) 10.0 m/s2

English : 21 Set : 10 Hindi : 21 Set : 10

PART B — CHEMISTRY Öæ» B — ÚUâæØÙ çߙææÙ
31. Ionization energy of gaseous Na atoms is 31. »ñâèØ âæðçÇUØ× ÂÚU×æ‡æé¥æð´ ·¤è ¥æØÙÙ ª¤Áæü ·¤æ ×æÙ
495.5 kJmol 21 . The lowest possible 495.5 kJ ×æðÜ21 ãñÐ âæðçÇUØ× ÂÚU×æ‡æé ·¤æ ¥æØÙÙ
frequency of light that ionizes a sodium ·¤ÚUÙð ·ð¤ çÜØð Âý·¤æàæ ·¤è âÖß ‹ØêÙÌ× ¥æßëçÌ
atom is (h56.626310234 Js, (frequency) €Øæ ãæð»è? (h56.626310234 Js,
NA56.02231023 mol21) NA56.02231023 ×æðÜ21)
(1) 7.503104 s21 (1) 7.503104 s21
(2) 4.7631014 s21 (2) 4.7631014 s21
(3) 3.1531015 s21 (3) 3.1531015 s21
(4) 1.2431015 s21 (4) 1.2431015 s21

32. Choose the correct statement with respect 32. ç·¤âè Îýß ·ð¤ ßæc ÎæÕ ·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ ×ð´
to the vapour pressure of a liquid among âð âãè °·¤ ·¤ÍÙ ·¤æð ¿éçÙ° Ñ
the following :
(1) Increases linearly with increasing (1) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
temperature ÕɸÌæ ãñÐ
(2) Increases non-linearly with (2) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ Ù âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
increasing temperature ÕɸÌæ ãñÐ
(3) Decreases linearly with increasing (3) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
temperature ƒæÅUÌæ ãñÐ
(4) Decreases non-linearly with (4) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ Ù âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU
increasing temperature ƒæÅUÌæ ãñÐ

English : 22 Set : 10 Hindi : 22 Set : 10

33. Which one of the following molecules is 33. çِ٠¥‡æé¥æð´ ×ð´ âð ·¤æñÙ ¥Ùé¿éÕ·¤èØ ãñ?
paramagnetic ?
(1) N2 (1) N2
(2) NO (2) NO
(3) CO (3) CO
(4) O3 (4) O3
34. Zirconium phosphate [Zr 3 (PO 4 ) 4 ] 34. çÁÚU·¤æðçÙØ× $ȤæS$Èð¤ÅU [Zr3(PO4)4] çßØæðçÁÌ ãæð·¤ÚU
dissociates into three zirconium cations of 14 ¥æßðàæ ÂýçÌ ·ð¤ÅUæØÙ ·ð¤ ÌèÙ çÁÚU·¤æðçÙØ× ·ð¤ÅUæØÙ
charge 14 and four phosphate anions of ¥æñÚU 23 ¥æßðàæ ÂýçÌÑ °ÙæØÙ ·ð¤ ¿æÚU $ȤæS$Èð¤ÅU °ÙæØÙ
charge 23. If molar solubility of zirconium ÎðÌæ ãñÐ ØçÎ çÁÚU·¤æðçÙØ× $ȤæS$Èð¤ÅU ·¤è ×æðÜÚU çßÜðØÌæ
phosphate is denoted by S and its solubility ·¤æð S âð ¥æñÚU §â·ð¤ çßÜðØÌæ »é‡æÙÈ¤Ü ·¤æð Ksp âð
product by Ksp then which of the following âêç¿Ì ç·¤Øæ ÁæØð Ìæð çِ٠âÕ‹Ïæð´ âð ·¤æñÙ-âæ
relationship between S and K sp is S ¥æñÚU Ksp ·¤æ âÕ‹Ï âãè ×æÙæ ÁæØð»æ?
correct ?
(1) S5{Ksp/(6912)1/7} (1) S5{Ksp/(6912)1/7}
(2) S5{Ksp/144}1/7 (2) S5{Ksp/144}1/7
(3) S5(Ksp/6912)1/7 (3) S5(Ksp/6912)1/7
(4) S5{Ksp/6912}7 (4) S5{Ksp/6912}7

English : 23 Set : 10 Hindi : 23 Set : 10

35. For the decomposition of the compound, 35. NH2COONH4(s) ì 2NH3(g)1CO2(g)
represented as
NH2COONH4(s) ì 2NH3(g)1CO2(g) âð âêç¿Ì Øæñç»·¤ ·ð¤ çßØæðÁÙ ·ð¤ çÜØð
the Kp52.931025 atm3. Kp52.931025 atm3
If the reaction is started with 1 mol of the ãæðÌæ ãñÐ ØçÎ ¥çÖç·ý¤Øæ ·¤æð Øæñç»·¤ ·ð¤ 1 ×æðÜ âð
compound, the total pressure at ¥æÚUÖ ç·¤Øæ ÁæØð Ìæð âæØ ¥ßSÍæ ×ð´ â·¤Ü ÎæÕ
equilibrium would be : ·¤æ ×æÙ ãæð»æ Ñ
(1) 1.9431022 atm (1) 1.9431022 atm
(2) 5.8231022 atm (2) 5.8231022 atm
(3) 7.6631022 atm (3) 7.6631022 atm
(4) 38.831022 atm (4) 38.831022 atm

36. For the reaction, 36. ¥çÖç·ý¤Øæ
3A12B ® C1D, 3A12B ® C1D
the differential rate law can be written ·ð¤ çÜØð ¥ß·¤Ü ÎÚU çÙØ× çܹæ Áæ â·¤Ìæ ãñ Ñ
as :

1 d [A ] d [C ] 1 d [A ] d [C]
5 k [A ] [ B ] 5 k [A ] [ B ]
n m n m
(1) 5 (1) 5
3 dt dt 3 dt dt

d [A ] d [C ] d [A ] d [C ]
5 k [A ] [ B ] 5 k [A ] [ B ]
n m n m
(2) 2 5 (2) 2 5
dt dt dt dt

1 d [A ] d [C ] 1 d [A ] d [C]
5 k [A ] [ B ] 5 k [A ] [ B ]
n m n m
(3) 1 52 (3) 1 52
3 dt dt 3 dt dt

1 d [A ] d [C ] 1 d [A ] d [C]
5 k [A ] [ B ] 5 k [A ] [ B ]
n m n m
(4) 2 5 (4) 2 5
3 dt dt 3 dt dt

English : 24 Set : 10 Hindi : 24 Set : 10

37. Sulphur dioxide and oxygen were allowed 37. °·¤ âÚ´UÏý ÂÚUÎð âð âË$ȤÚU ÇU槥æ€âæ§ÇU ¥æñÚU ¥æ€âèÁÙ
to diffuse through a porous partition. ·¤æð çßâçÚUÌ ãæðÙð çÎØæ »Øæ ãñÐ §â âÚ´UÏý ÂÚUÎð âð
20 dm3 of SO2 diffuses through the porous 20 dm3 SO2 ·ð¤ çßâçÚUÌ ãæðÙð ·¤æ â×Ø 60 âñ·¤‹ÇU
partition in 60 seconds. The volume of O2 ãæðÌæ ãñÐ °ðâè ãè ¥ßSÍæ ×ð´ çßâçÚUÌ ãæðÙð ßæÜè O2
in dm3 which diffuses under the similar ·¤æ ¥æØÌÙ dm3 ×ð´ 30 âñ·¤‹ÇU ·ð¤ çÜØð ãæð»æ (âË$ȤÚU
condition in 30 seconds will be (atomic ·ð¤ ÂÚU×æ‡æé ·¤æ ÎýÃØ×æÙ532 ×æ˜æ·¤) Ñ
mass of sulphur532 u) :
(1) 7.09 (1) 7.09
(2) 14.1 (2) 14.1
(3) 10.0 (3) 10.0
(4) 28.2 (4) 28.2

38. The observed osmotic pressure for a 38. 258 C ÂÚU Fe(NH4)2(SO4)2 ·ð¤ 0.10 M çßÜØÙ
0.10 M solution of Fe(NH4)2(SO4)2 at 258C ·¤æ ¥æâ×æçÅU·¤ (ÂÚUæâÚU‡æ) ÎæÕ 10.8 atm Îð¹æ
is 10.8 atm. The expected and »ØæÐ ßæ´ÅU ãæȤ »é‡æ·¤ ·ð¤ ¥æàææ ¥ÙéâæÚU ¥æñÚU ÂýæØæðç»·¤
experimental (observed) values of Van’t (×æçÂÌ) ×æÙ ·ý¤×æÙéâæÚU ãæð´»ð Ñ
Hoff factor (i) will be respectively :
(R50.082 L atm k2mol21) (R50.082 L atm k2×æðÜ21)
(1) 5 and 4.42 (1) 5 ¥æñÚU 4.42
(2) 4 and 4.00 (2) 4 ¥æñÚU 4.00
(3) 5 and 3.42 (3) 5 ¥æñÚU 3.42
(4) 3 and 5.42 (4) 3 ¥æñÚU 5.42

English : 25 Set : 10 Hindi : 25 Set : 10

39. The total number of octahedral void(s) per 39. ƒæÙæ·¤æÚU âéâ´·é¤çÜÌ (çÙçÕǸ) â´ÚU¿Ùæ ×ð´ ©ÂçSÍÌ
atom present in a cubic close packed ÂýçÌ ÂÚU×æ‡æé ¥cÅUȤܷ¤èØ çÚUç€ÌØæð´ ·¤è â·¤Ü â´Øæ
structure is : ãæð»è Ñ
(1) 2 (1) 2
(2) 4 (2) 4
(3) 1 (3) 1
(4) 3 (4) 3

40. For an ideal solution of two components 40. Îæð ƒæÅU·¤æð´ A ¥æñÚU B ·ð¤ ¥æÎàæü çßÜØÙ ·ð¤ çÜØð çِÙæð´
A and B, which of the following is true ? ×ð´ âð ·¤æñÙ âãè ãæð»æ?
(1) DHmixing < 0 (zero) (1) DHçןæ‡æ < 0 (zero)
(2) DHmixing > 0 (zero) (2) DHçןæ‡æ > 0 (zero)
(3) A2B interaction is stronger than (3) A2A ¥æñ Ú U B2B ·¤è ÂÚU S ÂÚU Âý Ö æß âð
A2A and B2B interactions A2B ·¤æ ÂÚUSÂÚU ÂýÖæß ¥çÏ·¤ ÂýÕÜ ãæð»æÐ
(4) A2A, B2B and A2B interactions (4) A2A, B2B ¥æñÚU A2B âÖè ÂÚUSÂÚU ÂýÖæß
are identical °·¤ â×æÙ ãñ´Ð
41. Consider the reaction : 41. ¥çÖç·ý¤Øæ
41 21
41
H 2 SO 3(aq)1Sn (aq)1H 2 O (l ) → Sn (aq)
21
1HSO24(aq)13H1(aq) H 2 SO 3(¦Áͽ)1Sn(¦Áͽ)1H 2 O(l ) → Sn(¦Áͽ)1HSO24(¦Áͽ)13H1
(¦Áͽ)

Which of the following statements is ·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ ×ð´ âð ·¤æñÙ-âæ âãè ãñ?
correct ?
(1) Sn41 is the oxidizing agent because (1) Sn41 ¥æ€âè·¤æÚU·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ
it undergoes oxidation ãæðÌæ ãñÐ
(2) Sn41is the reducing agent because (2) Sn41¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ
it undergoes oxidation ãæðÌæ ãñÐ
(3) H2SO3 is the reducing agent because (3) H2SO3 ¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ
it undergoes oxidation ãæðÌæ ãñÐ
(4) H2SO3 is the reducing agent because (4) H2SO3 ¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ¥Â¿ØÙ
it undergoes reduction ãæðÌæ ãñÐ

English : 26 Set : 10 Hindi : 26 Set : 10

42. Which one of the following has largest 42. çِÙæð´ ×ð´ âð ç·¤â·¤è ¥æØçÙ·¤ ç˜æ’Øæ ¥çÏ·¤Ì× ãñ?
ionic radius ?
(1) Li1 (1) Li1
22 22
(2) O2 (2) O2
(3) B31 (3) B31
(4) F2 (4) F2

43. An octahedral complex with molecular 43. ¥‡æé â´ÚU¿Ùæ M.5 NH3.Cl.SO4 ßæÜð ¥cÅU Ȥܷ¤èØ
composition M.5NH 3 .Cl.SO 4 has two â´·¤ÚU ·ð¤ Îæð â×æßØÌè A ¥æñÚU B ãñ´Ð A ·¤æ çßÜØÙ
isomers, A and B. The solution of A gives AgNO3 ·ð¤ çßÜØÙ ·ð¤ âæÍ â$Èð¤Î ¥ßÿæð ÎðÌæ ãñ
a white precipitate with AgNO3 solution ¥æñÚU B ·¤æ çßÜØÙ BaCl2 ·ð¤ çßÜØÙ ·ð¤ âæÍ â$Èð¤Î
and the solution of B gives white ¥ßÿæð ÎðÌæ ãñÐ §â â´·¤ÚU mæÚUæ ÂýÎçàæüÌ â×-¥ßØßÌæ
precipitate with BaCl2 solution. The type ·¤æ Âý·¤æÚU ãæð»æ Ñ
of isomerism exhibited by the complex is :
(1) Linkage isomerism (1) çÜ´·ð¤Á (â´Øæð»è) â×-¥ßØßÌæ
(2) Ionisation isomerism (2) ¥æØÙè â×-¥ßØßÌæ
(3) Coordinate isomerism (3) â׋ßØè â×-¥ßØßÌæ
(4) Geometrical isomerism (4) ’Øæç×çžæØ â×-¥ßØßÌæ

44. How many electrons are involved in the 44. çِ٠¥Â¿ØÙ-©Â¿ØÙ ¥çÖç·ý¤Øæ ×ð´ ç·¤ÌÙð §Üð€ÅþUæÙ
following redox reaction ? âãÖæ»è ãñ´?
Cr2O7221Fe211 C 2 O 242 Cr2O7221Fe211 C 2 O 242

® Cr311Fe311CO2 (Unbalanced) ® Cr311Fe311CO2 (¥â´ÌéçÜÌ)

(1) 3 (1) 3
(2) 4 (2) 4
(3) 6 (3) 6
(4) 5 (4) 5

English : 27 Set : 10 Hindi : 27 Set : 10

45. Amongst LiCl, RbCl, BeCl2 and MgCl2 the 45. LiCl, RbCl, BeCl2 ¥æñÚU MgCl2 ×ð´ âð ¥çÏ·¤Ì×
compounds with the greatest and the least ¥æñÚU ‹ØêÙÌ× ¥æØÙè çßàæðáÌæ ÚU¹Ùð ßæÜð Øæñç»·¤
ionic character, respectively are : ·ý¤×æÙéâæÚU ãñ´ Ñ
(1) LiCl and RbCl (1) LiCl ¥æñÚU RbCl
(2) RbCl and BeCl2 (2) RbCl ¥æñÚU BeCl2
(3) MgCl2 and BeCl2 (3) MgCl2 ¥æñÚU BeCl2
(4) RbCl and MgCl2 (4) RbCl ¥æñÚU MgCl2

46. Nickel(Z528) combines with a 46. çÙ·¤Ü (Z528) °·¤ «¤‡æè °·¤ ΋̷¤ çÜ»ñ´ÇU âð
uninegative monodentate ligand to form Øæð» ·¤ÚU °·¤ ÂýçÌ¿éÕ·¤èØ â´·¤ÚU [NiL4]22, ÕÙæÌæ
a diamagnetic complex [NiL 4 ] 22 . The ãñÐ §â â´·¤ÚU âð âÕç‹ÏÌ â´·¤ÚU‡æ Âý·¤æÚU ¥æñÚU
hybridisation involved and the number of ¥Øé»ç×Ì §Üñ€ÅþUæÙæð´ ·¤è ⴁØæ ·ý¤×æÙéâæÚU ãñ´ Ñ
unpaired electrons present in the complex
are respectively :
(1) sp3, two (1) sp3, Îæð
(2) dsp2, zero (2) dsp2, àæê‹Ø
(3) dsp2, one (3) dsp2, °·¤
(4) sp3, zero (4) sp3, àæê‹Ø

47. Which of these statements is not true ? 47. §Ù ·¤ÍÙæð´ ×ð´ âð ·¤æñÙ-âæ ·¤ÍÙ âˆØ Ùãè´ ãñ?
(1) NO1 is not isoelectronic with O2 (1) NO1 ÌÍæ O2 âקÜð€ÅþUæÙè Ùãè´ ãñ´Ð
(2) B is always covalent in its (2) ÕæðÚUæÙ ¥ÂÙð Øæñç»·¤æð´ ×ð´ âÎñß âãâ´ØæðÁè ãæðÌæ
compounds ãñÐ
(3) In aqueous solution, the Tl1 ion is (3) ÁÜèØ çßÜØÙ ×ð´, Tl (III) ·¤è ¥Âðÿææ Tl1
much more stable than Tl (III) ¥æØÙ ¥ˆØæçÏ·¤ SÍæØè ãæðÌæ ãñÐ
(4) LiAlH4 is a versatile reducing agent (4) LiAlH4 ·¤æÕüçÙ·¤ â´àÜðá‡ææð´ ×ð´ ÂýØæð» ãæðÙð
in organic synthesis. ßæÜæ °·¤ Õãé×é¹è ¥Â¿æØ·¤ ãñÐ

English : 28 Set : 10 Hindi : 28 Set : 10

48. Example of a three-dimensional silicate 48. ç˜æ-çß×èØ çâçÜ·ð¤ÅUæ𴠷𤠩ÎæãÚU‡æ ãñ´ Ñ
is :
(1) Zeolites (1) ç$ÁØæðÜæ§Åð´U
(2) Ultramarines (2) ¥ËÅþUæ×ñÚUèÙð´
(3) Feldspars (3) Èð¤ËÇUSÂæÚð´U
(4) Beryls (4) ÕðçÚUÜð´
49. Amongst the following, identify the 49. çِÙæð´ ×ð´ 16 ©Â¿ØÙ ¥ßSÍæ ·ð¤ ÂÚU×æ‡æé ßæÜð
species with an atom in 16 oxidation SÂèàæè$Á ·¤è Âã¿æÙ ·¤èçÁØðÐ
state :
(1) [MnO4]2 (1) [MnO4]2
(2) [Cr(CN)6]32 (2) [Cr(CN)6]32
(3) Cr2O 3 (3) Cr2O3
(4) CrO2Cl2 (4) CrO2Cl2

50. Which one of the following ores is known 50. çِ٠×ð´ âð ·¤æñÙ ×ñÜæ·¤æ§ÅU ¥ØS·¤ Ùæ× âð ÁæÙè
as Malachite : ÁæÌè ãñ Ñ
(1) Cu 2O (1) Cu 2O
(2) Cu 2S (2) Cu2S
(3) CuFeS2 (3) CuFeS2
(4) Cu(OH)2.CuCO3 (4) Cu(OH)2.CuCO3

51. The major product formed when 1, 1, 12 51. ÁÕ 1, 1, 12 ÅþU槀ÜæðÚUæðÂýæðÂðÙ ·¤è ÁÜèØ ÂæðÅñUçàæØ×
trichloro - propane is treated with aqueous ãæÇþUæ€âæ§ÇU âð ç·ý¤Øæ ·¤è ÁæÌè ãñ Ìæð ÂýæŒÌ ãé§ü Õɸè
potassium hydroxide is : ×æ˜ææ ·¤æ ç·ý¤Øæ È¤Ü ãæðÌæ ãñ Ñ
(1) Propyne (1) ÂýæðÂæ§Ù
(2) 1 - Propanol (2) 1 - ÂýæðÂðÙæòÜ
(3) 2 - Propanol (3) 2 - ÂýæðÂðÙæòÜ
(4) Propionic acid (4) ÂýæðçÂØæçÙ·¤ °ðçâÇU

English : 29 Set : 10 Hindi : 29 Set : 10

52. Which one of the following is an example 52. §Ù ×ð´ âð ·¤æñÙ ÌæÂÎëɸ ÕãéÜ·¤ ãñ?
of thermosetting polymers ?
(1) Neoprene (1) çÙØæðÂýèÙ
(2) Buna -N (2) ÕêÙæ - N
(3) Nylon 6, 6 (3) Ùæ§ÜæÙ 6, 6
(4) Bakelite (4) Õñ·ð¤Üæ§ÅU

53. The correct IUPAC name of the following 53. §â Øæñç»·¤
compound

is : ·¤æ âãè IUPAC Ùæ× ãñ Ñ
(1) 4 - methyl - 3 - ethylhexane (1) 4 - ×ðçÍÜ - 3 - °çÍÜãñ€âðÙ
(2) 3 - ethyl - 4 - methylhexane (2) 3 - °çÍÜ - 4 - ×ðçÍÜãñ€âðÙ
(3) 3, 4 - ethylmethylhexane (3) 3, 4 - °çÍÜ×ðçÍÜãñ€âðÙ
(4) 4 - ethyl - 3 - methylhexane (4) 4 - °çÍÜ - 3 - ×ðçÍÜãñ€âðÙ
54. Which one of the following substituents at 54. çِ٠ÂýçÌSÍæ·¤æð´ ×ð´ âð ·¤æñÙ Èñ¤Ùæ€âæ§ÇU ¥æØÙ
para-position is most effective in
, ·ð ¤ Âñ Ú U æ SÍæÙ ÂÚU ãæð Ù ð âð §âð
stabilizing the phenoxide ,
¥çÏ·¤Ì× SÍæØè ÕÙæÙð ×ð´ ÂýÖæßè ãæðÌæ ãñ?
ion ?
(1) 2CH3 (1) 2CH3
(2) 2OCH3 (2) 2OCH3
(3) 2COCH3 (3) 2COCH3
(4) 2CH2OH (4) 2CH2OH

English : 30 Set : 10 Hindi : 30 Set : 10

55. The final product formed when Methyl 55. ×ðçÍÜ °×èÙ ·¤è NaNO2 ¥æñÚU HCl ·ð¤ âæÍ ç·ý¤Øæ
amine is treated with NaNO2 and HCl ·¤ÚUÙð ÂÚU ©ÂÜŽÏ ¥ç‹Ì× ¥çÖç·ý¤Øæ È¤Ü ãæðÌæ ãñ Ñ
is :
(1) Diazomethane (1) ÇU槰ð$Áæð×èÍðÙ
(2) Methylalcohol (2) ×ðçÍÜ °ðË·¤æðãæÜ
(3) Methylcyanide (3) ×ðçÍÜçâØæÙæ§ÇU
(4) Nitromethane (4) Ùæ§ÅþUæð×èÍðÙ

56. Which one of the following compounds 56. §Ù×ð´ âð ·¤æñÙ-âæ Øæñç»·¤ âæðçÇUØ× Õ槷¤æÕæðüÙðÅU ×ð´
will not be soluble in sodium Ùãè´ ƒæéÜð»æ?
bicarbonate ?
(1) 2, 4, 6 - Trinitrophenol (1) 2, 4, 6 - ÅþUæ§üÙæ§ÅþUæðç$ȤÙæòÜ
(2) Benzoic acid (2) Õñ‹$Áæ𧷤 °ðçâÇU
(3) o - Nitrophenol (3) o - Ùæ§ÅþUæðç$ȤÙæòÜ
(4) Benzene sulphonic acid (4) Õñ‹$ÁèÙ âË$ȤæçÙ·¤ °ðçâÇU

57. Williamson synthesis of ether is an example 57. §üÍÚU ·¤æ çßçÜØ×âÙ â´àÜðá‡æ §Ù×ð´ âð 緤⠷¤æ
of : ©ÎæãÚU‡æ ãñ?
(1) Nucleophilic addition (1) ‹Øêç€ÜØæðç$ȤçÜ·¤ â´·¤ÜÙ
(2) Electrophilic addition (2) §Üñ€ÅþUæðç$ȤçÜ·¤ â´·¤ÜÙ
(3) Electrophilic substitution (3) §Üñ€ÅþUæðç$ȤçÜ·¤ ÂýçÌSÍæÂÙ
(4) Nucleophilic substitution (4) ‹Øêç€ÜØæðç$ȤçÜ·¤ ÂýçÌSÍæÂÙ

English : 31 Set : 10 Hindi : 31 Set : 10

58. The reason for double helical structure of 58. §Ù×ð´ âð ·¤æñÙ-âè ç·ý¤Øæ DNA ·¤è ÎæðãÚUè ·é¤‡ÇUÜèÎæÚU
DNA is the operation of : â´ÚU¿Ùæ ·¤æ ·¤æÚU‡æ ãæðÌè ãñ?
(1) Electrostatic attractions (1) çSÍÚUßñléÌ ¥æ·¤áü‡æ
(2) van der Waals forces (2) ßæÙÇUÚU ßæÜ ·ð¤ ÕÜ
(3) Dipole - Dipole interactions (3) çmÏýéß - çmÏýéß ÂÚUSÂÚU ç·ý¤Øæ
(4) Hydrogen bonding (4) ãæ§ÇþUæðÁÙ ¥æՋÏÙ
59. Among the following organic acids, the 59. Îé»ü‹Ïè ׀¹Ù ×ð´ ÂæØæ ÁæÙð ßæÜæ °ðçâÇU çِ٠°ðçâÇUæð´
acid present in rancid butter is : ×ð´ âð ·¤æñÙ-âæ ãæðÌæ ãñ?
(1) Pyruvic acid (1) Âæ§L¤çß·¤ °ðçâÇU
(2) Lactic acid (2) Üñç€ÅU·¤ °ðçâÇU
(3) Butyric acid (3) ŽØéÅUèçÚU·¤ °ðçâÇU
(4) Acetic acid (4) °âèçÅU·¤ °ðçâÇU

English : 32 Set : 10 Hindi : 32 Set : 10

60. In a set of reactions p - nitrotoluene yielded 60. ¥çÖç·ý¤Øæ¥æ𴠷𤠧⠷ý¤× ×ð´
a product E

The product E would be : p - Ùæ§ÅþUæðÅUæËØé§üÙ âð ÂýæŒÌ ç·ý¤ØæÈ¤Ü E ãæð»æ Ñ

(1) (1)

(2) (2)

(3) (3)

(4) (4)

English : 33 Set : 10 Hindi : 33 Set : 10

PART C — MATHEMATICS Öæ» C — »ç‡æÌ
x 21 x 21
61. Let f : R®R be defined by f(x)5
x 11
61. ×æÙæ f : R®R , f(x)5 x 1 1 mæÚUæ ÂçÚUÖæçáÌ ãñ,
then f is : Ìæð f :
(1) both one - one and onto (1) °·ñ¤·¤è ÌÍæ ¥æ‘ÀUæÎè ÎæðÙæð´ ãñ´Ð
(2) one - one but not onto (2) °·ñ¤·¤è ãñ ÂÚ ¥æ‘ÀUæÎè Ùãè´ ãñÐ
(3) onto but not one - one (3) ¥æ‘ÀUæÎè ãñ ÂÚU °·ñ¤·¤è Ùãè´ ãñÐ
(4) neither one - one nor onto. (4) Ù Ìæð °·ñ¤·¤è ãñ ¥æñÚU Ù ãè ¥æ‘ÀUæÎè ãñÐ

62. For all complex numbers z of the form 62. 11ia, a e R ·¤è Âý·¤æÚU ·¤è âÖè âç×Ÿæ ⴁØæ¥æð´
11ia, a e R, if z25x1iy, then : z ·ð¤ çÜØð, ØçÎ z25x1iy ãñ, Ìæð :
(1) y 2 24x1250 (1) y 224x1250
(2) y 2 14x2450 (2) y 214x2450
(3) y 2 24x1450 (3) y 224x1450
(4) y 2 14x1250 (4) y 214x1250

63. The equation 3x 21x15 5x23, where x 63. â×è·¤ÚU‡æ 3x 21x15 5x23, Áãæ¡ x ßæSÌçß·¤
is real, has : ãñ, ·¤æ / ·ð¤ :
(1) no solution (1) ·¤æð§ü ãÜ Ùãè´ ãñ´Ð
(2) exactly one solution (2) ÆUè·¤ °·¤ ãÜ ãñÐ
(3) exactly two solutions (3) ÆUè·¤ Îæð ãÜ ãñ´Ð
(4) exactly four solutions. (4) ÆUè·¤ ¿æÚU ãÜ ãñ´Ð

English : 34 Set : 10 Hindi : 34 Set : 10

64. Let A and B be any two 333 matrices. If 64. ×æÙæ A ÌÍæ B ·¤æð§ü Îæð 333 ·ð¤ ¥æÃØêã ãñ´Ð ØçÎ A
A is symmetric and B is skewsymmetric, â×ç×Ì ãñ ÌÍæ B çßá× â×ç×Ì ãñ, Ìæð ¥æÃØêã
then the matrix AB2BA is : AB2BA :
(1) skewsymmetric (1) çßá× â×ç×Ì ãñ
(2) symmetric (2) â×ç×Ì ãñ
(3) neither symmetric nor (3) Ù Ìæð â×ç×Ì ãñ´ ¥æñÚU Ù ãè çßá× â×ç×Ì ãñ
skewsymmetric
(4) I or 2I, where I is an identity matrix. (4) I ¥Íßæ 2I ãñ´, Áãæ¡ I °·¤ ̈â×·¤ ¥æÃØêã
65. If ãñÐ
65. ØçÎ
r 2r 2 1 3r 2 2
n r 2r 2 1 3r 2 2
Dr 5 n2 1 a
2 n
1 1 Dr 5 n2 1 a
n ( n 2 1) ( n 2 1 )2 ( n 2 1 )( 3n 1 4 ) , 2
2 2 1 1
n ( n 2 1) ( n 2 1 )2 ( n 2 1 )( 3n 1 4 )
2 2
n2 1
then the value of ∑ Dr : n2 1
r5 1
ãñ´, Ìæð ∑ Dr ·¤æ ×æÙ :
(1) depends only on a r5 1

(2) depends only on n (1) ·ð¤ßÜ a ÂÚU çÙÖüÚU ãñ
(3) depends both on a and n (2) ·ð¤ßÜ n ÂÚU çÙÖüÚU ãñ
(4) is independent of both a and n. (3) a ÌÍæ n ÎæðÙæð´ ÂÚU çÙÖüÚU ãñ´
(4) a ÌÍæ n ÎæðÙæð´ âð SßÌ´˜æ ãñ´Ð

English : 35 Set : 10 Hindi : 35 Set : 10

66. Two women and some men participated 66. àæÌÚ´UÁ ·¤è °·¤ ÂýçÌØæðç»Ìæ ×ð´ Îæð ×çãÜæ¥æð´ ÌÍæ ·é¤ÀU
in a chess tournament in which every ÂéL¤áæð´ Ùð Öæ» çÜØæ çÁâ×ð´ ÂýˆØð·¤ ÂýçÌØæð»è Ùð àæðá
participant played two games with each ÂýˆØð·¤ ÂýçÌØæð»è âð Îæð ÕæçÚUØæ´ ¹ðÜèÐ ØçÎ ÂéL¤áæð´ Ùð
of the other participants. If the number of ¥æÂâ ×ð´ çÁÌÙè ÕæçÚUØæ´ ¹ðÜè ©Ù·¤è ⴁØæ ÂéL¤áæð´
games that the men played between them- mæÚUæ ×çãÜæ¥æð´ ·ð¤ âæÍ ¹ðÜè ÕæçÚUØæð´ ·¤è ⴁØæ âð 66
selves exceeds the number of games that ¥çÏ·¤ ãñ´, Ìæð ÂéL¤áæð´ ·¤è ⴁØæ, çÁ‹ãæð´Ùð ÂýçÌØæð»èÌæ ×ð´
the men played with the women by 66, Öæ» çÜØæ, çِ٠¥´ÌÚUæÜ ×ð´ ãñ´ Ñ
then the number of men who participated
in the tournament lies in the interval :
(1) [8, 9] (1) [8, 9]
(2) [10, 12) (2) [10, 12)
(3) (11, 13] (3) (11, 13]
(4) (14, 17) (4) (14, 17)

67. The coefficient of x1012 in the expansion of 67. (11xn1x253)10, (Áã¡æ n £ 22 ·¤æð§ü ÏÙ Âê‡ææZ·¤
(11x n 1x 253 ) 10 , (where n £ 22 is any ãñ´)·ð¤ ÂýâæÚU ×ð´ x1012 ·¤æ »é‡ææ´·¤ ãñ´ Ñ
positive integer), is :
(1) 1 (1) 1
(2) 10C (2) 10C
4 4
(3) 4n (3) 4n
(4) 253C (4) 253C
4 4

English : 36 Set : 10 Hindi : 36 Set : 10

68. The number of terms in an A.P. is even; 68. ç·¤âè â×æ´ÌÚU Ÿæðɸè ×ð´ ÂÎæð´ ·¤è ⴁØæ â× ãñÐ §â·ð¤
the sum of the odd terms in it is 24 and çßá× ÂÎæð´ ·¤æ Øæð» 24 ãñ ÌÍæ â× ÂÎæð´ ·¤æ Øæð» 30
that the even terms is 30. If the last term 1
ãñÐ ØçÎ ¥´çÌ× ÂÎ, ÂýÍ× ÂÎ âð 10 2 ¥çÏ·¤ ãñ, Ìæð
1
exceeds the first term by 10 , then the
2 â×æ´ÌÚU Ÿæðɸè ×ð´ ÂÎæð´ ·¤è ⴁØæ ãñ Ñ
number of terms in the A.P. is :
(1) 4 (1) 4
(2) 8 (2) 8
(3) 12 (3) 12
(4) 16 (4) 16

1 3n  1 3n 
69. Let f(n) 5  1
3 100 
n , where [n] denotes 69. ×æÙæ f(n)5  3 1 100  n , Áãæ¡ [n] °·¤ ×ãžæ×
the greatest integer less than or equal to n. Âê ‡ ææZ · ¤, Áæð n âð ÀU æ ð Å U æ ¥Íßæ ÕÚU æ ÕÚU ãñ , Ìæð
56 56
Then ∑ f ( n ) is equal to : ∑ f ( n) ÕÚUæÕÚU ãñ Ñ
n5 1 n5 1
(1) 56 (1) 56
(2) 689 (2) 689
(3) 1287 (3) 1287
(4) 1399 (4) 1399

English : 37 Set : 10 Hindi : 37 Set : 10

70. If the function
 2 1 cos x2 1
 , x ≠p
f (x ) 5  ( p 2 x )
2
 2 1 cos x2 1
 , x ≠p 70. ØçΠȤÜÙ k
f (x ) 5  ( p 2 x )
2
 , x5p
k , x5p


is continuous at x5p, then k equals : x5p ÂÚU âÌÌ ãñ, Ìæð k ÕÚUæÕÚU ãñ :
(1) 0 (1) 0
1 1
(2) (2)
2 2
(3) 2 (3) 2
1 1
(4) (4)
4 4
71. Let f: R ® R be a function such that 71. ×æÙæ f: R ® R °·¤ °ðâæ ȤÜÙ ãñ ç·¤ âÖè x e R ·ð¤
?f(x)? £ x2, for all x e R. Then, at x50, f is : çÜ° ?f(x)? £ x2 ãñ, Ìæð x50 ÂÚU f :
(1) continuous but not differentiable (1) âÌÌ ãñ ÂÚU ¥ß·¤ÜÙèØ Ùãè´ ãñ
(2) continuous as well as differentiable (2) âÌÌ ÌÍæ ¥ß·¤ÜÙèØ ÎæðÙæð´ ãñ´
(3) neither continuous nor differentiable (3) Ù Ìæð âÌÌ ãñ ¥æñÚU Ù ãè ¥ß·¤ÜÙèØ ãñ
(4) differentiable but not continuous. (4) ¥ß·¤ÜÙèØ ãñ ÂÚU âÌÌ Ùãè´ ãñÐ

English : 38 Set : 10 Hindi : 38 Set : 10

72. If non-zero real numbers b and c are such 72. ØçÎ àæê‹ØðÌÚU ßæSÌçß·¤ ⴁØæ°¡ b ÌÍæ c °ðâè ãñ´ ç·¤
that min f(x) > max g(x), where min f(x) > max g(x), Áãæ¡ f(x)5x212bx12c2
ÌÍæ g(x)52x222cx1b2 (x e R) ãñ´,
f(x)5x212bx12c2 and

g(x)52x222cx1b2 (x e R) ;

c c
then
b
lies in the interval : Ìæð b çÁâ ¥´ÌÚUæÜ ×ð´ ãñ, ßã ãñ :

 1  1
(1)  0,  (1)  0, 
 2  2

1 1  1 1 
(2) 2 , 2  (2) 2 , 2 
   

 1   1 
(3)  2 , 2 (3)  2 , 2
   

(4) ( 2 ,∞ ) (4) ( 2 ,∞ )

73. If the volume of a spherical ball is 73. ØçÎ °·¤ »æðÜæ·¤æÚU »ð´Î ·¤æ ¥æØÌÙ 4p ƒæÙ âð×è/âñ.
increasing at the rate of 4p cc/sec, then ·¤è ÎÚU âð Õɸ ÚUãæ ãñ, Ìæð ÁÕ ¥æØÌÙ 288p ƒæÙ âð×è
the rate of increase of its radius ãñ, Ìæð ç˜æ’Øæ çÁâ ÎÚU (âð×è/âñ. ×ð´) âð Õɸ ÚUãè ãñ, ßã
(in cm/sec), when the volume is 288p cc, ãñ :
is :
1 1
(1) (1)
6 6
1 1
(2) (2)
9 9
1 1
(3) (3)
36 36
1 1
(4) (4)
24 24
English : 39 Set : 10 Hindi : 39 Set : 10

74. If m is a non - zero number and 74. ØçÎ m °·¤ àæê ‹ Øð Ì ÚU â´  Øæ ãñ ÌÍæ
x 5m21 1 2 x 4 m21 x 5m21 12 x 4 m21
∫ d x5 f ( x )1c , ∫ d x5 f ( x )1c
( ) ( )
3 3
x 2 m 1 x m 11 x 2 m 1 x m 11

then f(x) is : ãñ, Ìæð f(x) ãñ :
x 5m x 5m
(1) (1)
( ) ( )
2 2
2m x 2m 1 x m 1 1 2m x 2m 1 x m 1 1

x 4m x 4m
(2) (2)
( ) ( )
2 2
2m x 2m 1 x m 1 1 2m x 2m 1 x m 1 1

(
2 m x 5m 1 x 4m) (
2 m x 5m 1 x 4m)
(3) (3)
( x2m 1 xm 1 1) ( x2m 1 xm 1 1)
2 2

( x 5m 2 x 4 m ) ( x 5m 2 x 4 m )
(4) (4)
2 m ( x 2 m 1 x m 1 1) 2 m ( x 2 m 1 x m 1 1)
2 2

English : 40 Set : 10 Hindi : 40 Set : 10

t
×æÙæ ȤÜÙ F , F( x ) 5 ∫ e dt , x > 0 mæÚUæ
x

75. Let function F be defined as 75.
1 t

etx
x et
F( x ) 5 ∫ dt , x > 0 then the value of ÂçÚUÖæçáÌ ãñ, Ìæð â×æ·¤Ü ∫1 dt , Áãæ¡
1 t t1 a

x et
the integral ∫1 t 1 a dt , where a > 0 ãñ, ·¤æ ×æÙ ãñ :

a > 0, is :
(1) ea[F(x)2F(11a)] (1) ea[F(x)2F(11a)]
(2) e2a[F(x1a)2F(a)] (2) e2a[F(x1a)2F(a)]
(3) ea[F(x1a)2F(11a)] (3) ea[F(x1a)2F(11a)]
(4) e2a[F(x1a)2F(11a)] (4) e2a[F(x1a)2F(11a)]
p p
76. The area of the region above the x-axis 76. ß·ý¤ y5tan x, 0 £ x £ 2 ÌÍæ ß·ý ÂÚU x5 4
p
bounded by the curve y5tan x, 0 £ x £
2
ÂÚU ¹è´¿è »§ü SÂàæü ÚðU¹æ mæÚUæ çƒæÚðU ÿæð˜æ, Áæð x ¥ÿæ âð
p
and the tangent to the curve at x5
4
is : ª¤ÂÚU ãñ, ·¤æ ÿæð˜æÈ¤Ü ãñ :

1 1 1 1
(1)  log 2 2  (1)  log 2 2 
2 2 2 2

1 1 1 1
(2)  log 2 1  (2)  log 2 1 
2 2 2 2

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

English : 41 Set : 10 Hindi : 41 Set : 10

dy dy
77. If 1y tan x5sin 2x and y(0)51, then 77. ØçÎ 1y tan x5sin 2x ÌÍæ y(0)51 ãñ Ìæð
dx dx
y(p) is equal to : y(p) ÕÚUæÕÚU ãñ :
(1) 1 (1) 1
(2) 21 (2) 21
(3) 25 (3) 25
(4) 5 (4) 5

78. The circumcentre of a triangle lies at the 78. °·¤ ç˜æÖéÁ ·¤æ ÂçÚU·ð´¤Îý ×êÜ çՋÎé ÂÚU ãñ ÌÍæ ©â·¤æ
origin and its centroid is the mid point of ·ð¤‹Îý·¤, çՋÎé¥æð´ (a211, a211) ÌÍæ (2a, 22a),
the line segment joining the points a ¹ 0 ·¤æð ç×ÜæÙð ßæÜð ÚðU¹æ¹´ÇU ·¤æ ×ŠØ çÕ´Îé ãñ, Ìæð
(a211, a211) and (2a, 22a), a ¹ 0. Then ç·¤âè a ·¤ð çÜ° §â ç˜æÖéÁ ·¤æ Ü´Õ ·ð¤‹Îý çÁâ ÚðU¹æ
for any a, the orthocentre of this triangle ÂÚU çSÍÌ ãñ, ßã ãñ Ñ
lies on the line :
(1) y22ax50 (1) y22ax50
(2) y2(a211)x50 (2) y2(a 211)x50
(3) y1x50 (3) y1x50
(4) (a21)2x2(a11) 2y50 (4) (a21) 2x2(a11) 2y50

English : 42 Set : 10 Hindi : 42 Set : 10

79. If a line L is perpendicular to the line 79. ØçÎ °·¤ ÚðU¹æ L, ÚðU¹æ 5x2y51 ÂÚU Ü´ÕßÌ ãñ ÌÍæ
5x2y51, and the area of the triangle ÚðU¹æ L ÌÍæ çÙÎðüàææ´·¤ ¥ÿææð́ mæÚUæ ÕÙè ç˜æÖéÁ ·¤æ ÿæð˜æȤÜ
formed by the line L and the coordinate 5 ãñ, Ìæð ÚðU¹æ L ·¤è ÚðU¹æ x15y50 âð ÎêÚUè ãñ :
axes is 5, then the distance of line L from
the line x15y50 is :
7 7
(1) (1)
5 5

5 5
(2) (2)
13 13

7 7
(3) (3)
13 13

5 5
(4) (4)
7 7

80. The equation of the circle described on the 80. ßëžæ x21y2516 ·¤è °·¤ Áèßæ 3x1y1550
chord 3x1y1550 of the circle ·¤æð ÃØæâ ×æÙ·¤Ú ¹è´¿ð »° ßëžæ ·¤æ â×è·¤ÚU‡æ ãñ :
x21y2516 as diameter is :
(1) x 21y 213x1y21150 (1) x 21y 213x1y21150
(2) x 21y 213x1y1150 (2) x 2 1y 2 13x1y1150
(3) x 21y 213x1y2250 (3) x 2 1y 2 13x1y2250
(4) x 21y 213x1y22250 (4) x 21y 213x1y22250

English : 43 Set : 10 Hindi : 43 Set : 10

81. A chord is drawn through the focus of the 81. ÂÚUßÜØ y256x ·¤è ÙæçÖ âð ãæð·¤ÚU ÁæÌè °·¤ Áèßæ
parabola y256x such that its distance from 5
¹è´¿è »§ü ãñ çÁâ·¤è ÂÚUßÜØ ·ð¤ àæèáü âð ÎêÚUè ãñ,
5 2
the vertex of this parabola is , then its
2 Ìæð §â·¤è ÉUæÜ ãæð â·¤Ìè ãñ :
slope can be :

5 5
(1) (1)
2 2

3 3
(2) (2)
2 2
2 2
(3) (3)
5 5

2 2
(4) (4)
3 3

x2 y2
82. The tangent at an extremity (in the first 82. ¥çÌÂÚUßÜØ 2 5 1 ·ð¤ ÙæçÖÜ´Õ ·ð¤ °·¤
4 5
quadrant) of latus rectum of the hyperbola çâÚðU (Áæð ÂýÍ× ¿ÌéÍæZàæ ×ð´ ãñ) ÂÚU ¹è´¿è »§ü SÂàæü
x2 y2
4
2
5
5 1 ,meets x - axis and y - axis ÚðU¹æ x-¥ÿæ ÌÍæ y-¥ÿæ ·¤æð ·ý ×àæ çՋÎé¥æð´ A ÌÍæ B
at A and B respectively. Then ÂÚU ç×ÜÌè ãñ´, Ìæð (OA)22(OB)2, Áãæ¡ O ×êÜ çÕ´Îé
(OA) 2 2(OB) 2 , where O is the origin, ãñ, ÕÚUæÕÚU ãñ :
equals : 20
(1) 2
20 9
(1) 2
9 16
(2)
16 9
(2)
9 (3) 4
(3) 4 4
(4) 2
4 3
(4) 2
3

English : 44 Set : 10 Hindi : 44 Set : 10

x y z
83. Equation of the line of the shortest distance 83. Úð U ¹æ¥æð ´ 5 5 ÌÍæ
1 21 1
x y z x21 y11 z
between the lines
1
5
21
5
1
and 5 5 ·ð¤ Õè¿ ‹ØêÙÌ× ÎêÚUè
0 22 1
x21 y11 z
0
5
22
5 is :
1
ßæÜè ÚðU¹æ ·¤æ â×è·¤ÚU‡æ ãñ :

x y z x y z
(1) 5 5 (1) 5 5
1 21 22 1 21 22

x21 y11 z x21 y11 z
(2) 5 5 (2) 5 5
1 21 22 1 21 22

x21 y11 z x21 y11 z
(3) 5 5 (3) 5 5
1 21 1 1 21 1

x y z x y z
(4) 5 5 (4) 5 5
22 1 2 22 1 2
84. If the angle between the line 84. ØçÎ Úð U ¹æ 2(x11)5y5z14 ÌÍæ â×ÌÜ
2(x11)5y5z14 and the plane p
2x2y1 l z1450 ·ð¤ Õè¿ ·¤æ ·¤æð‡æ ãñ, Ìæð
p 6
2x2y1 l z1450 is , then the value l ·¤æ ×æÙ ãñ :
6
of l is :
135 135
(1) (1)
7 7

45 45
(2) (2)
11 11

45 45
(3) (3)
7 7

135 135
(4) (4)
11 11

English : 45 Set : 10 Hindi : 45 Set : 10

r r r
85. If x 5 3iˆ 2 6 ˆj 2 k̂ , y 5 iˆ 1 4 ˆj 2 3k̂ 85. ØçÎ xr 5 3iˆ 2 6 ˆj 2 k̂ , y 5 iˆ 1 4 ˆj 2 3k̂
r r r r
and z 5 3iˆ 2 4 ˆj 2 12k̂ ,
then the ÌÍæ z 5 3iˆ 2 4 ˆj 2 12k̂ ãñ´ Ìæð x 3y ·ð¤ zr ÂÚU
r r r
magnitude of the projection of x 3y on z Âýÿæð ·¤æ ÂçÚU×æ‡æ ãñ :
is :
(1) 12 (1) 12
(2) 15 (2) 15
(3) 14 (3) 14
(4) 13 (4) 13

86. Let A and E be any two events with 86. ×æÙæ A ÌÍæ E ·¤æð§ü Îæð °ðâè ƒæÅUÙæ°¡ ãñ çÁÙ·¤è
positive probabilities : ÂýæçØ·¤Ìæ°¡ ÏÙæˆ×·¤ ãñ´ Ñ
Statement - 1 : P(E/A) ³ P(A/E)P(E) ·¤ÍÙ-1 : P(E/A) ³ P(A/E)P(E)
Statement - 2 : P(A/E) ³ P(AÇE). ·¤ÍÙ-2 : P(A/E) ³ P(AÇE).
(1) Both the statements are true (1) ÎæðÙæð´ ·¤ÍÙ âˆØ ãñ´
(2) Both the statements are false (2) ÎæðÙæð´ ·¤ÍÙ ¥âˆØ ãñ´
(3) Statement - 1 is true, Statement - 2 is (3) ·¤ÍÙ-1 âˆØ ãñ, ·¤ÍÙ-2 ¥âˆØ ãñ
false
(4) Statement - 1 is false, Statement - 2 (4) ·¤ÍÙ-1 ¥âˆØ ãñ, ·¤ÍÙ-2 âˆØ ãñÐ
is true.

English : 46 Set : 10 Hindi : 46 Set : 10

87. Let x , M and s 2 be respectively the mean, 87. ×æÙæ n Âýðÿæ‡ææð´ x1, x2, ..., xn·ð¤ ×æŠØ ÕãéÜ·¤ ÌÍæ
mode and variance of n observations ÂýâÚU‡æ ·ý¤×àæÑ x , M ÌÍæ s 2 ÌÍæ di52xi2a,
x1, x2, ..., xn and di52xi2a, i51, 2, ..., n, i51, 2, ..., n ãñ´, Áãæ¡ a ·¤æð§ü ⴁØæ ãñ´Ð
where a is any number.
Statement I : Variance of d1, d2, ..., dn is ·¤ÍÙ I : d1, d2, ..., dn ·¤æ ÂýâÚU‡æ s2 ãñ´
s2.

Statement II : Mean and mode of ·¤ÍÙ II : d1, d2, ..., dn ·ð¤ ×æŠØ ÌÍæ ÕãéÜ·¤
d 1 , d 2 , ..., d n are 2 x 2a and 2M2a, ·ý¤×æàæÑ 2 x 2a ÌÍæ 2M2a ãñ
respectively
(1) Statement I and Statement II are (1) ·¤ÍÙ I ÌÍæ ·¤ÍÙ II ÎæðÙæð´ ¥âˆØ ãñ´Ð
both false
(2) Statement I and Statement II are (2) ·¤ÍÙ I ÌÍæ ·¤ÍÙ II ÎæðÙæð´ âˆØ ãñ´Ð
both true
(3) Statement I is true and Statement II (3) ·¤ÍÙ I âˆØ ãñ ÌÍæ ·¤ÍÙ II ¥âˆØ ãñÐ
is false
(4) Statement I is false and Statement II (4) ·¤ÍÙ I ¥âˆØ ãñ ÌÍæ ·¤ÍÙ II âˆØ ãñÐ
is true

88. The function f ( x )5 sin 4x 1 cos 2 x , is a 88. ȤÜÙ f ( x )5 sin 4x 1 cos 2x °·¤ ¥æßçÌü
periodic function with period : ȤÜÙ ãñ çÁâ·¤æ ¥æßÌü ·¤æÜ ãñ :
(1) 2p (1) 2p
(2) p (2) p
p p
(3) (3)
2 2
p p
(4) (4)
4 4

English : 47 Set : 10 Hindi : 47 Set : 10

21  43p   43p 
89. The principal value of tan  cot  is : 89. tan21  cot  ·¤æ ×éØ×æÙ ãñ :
 4   4 

3p 3p
(1) 2 (1) 2
4 4
3p 3p
(2) (2)
4 4
p p
(3) 2 (3) 2
4 4
p p
(4) (4)
4 4
90. The contrapositive of the statement “if I 90. ·¤ÍÙ ÒÒØçÎ ×ñ´ ¥SßSÍ ã¡ê, Ìæð ×ñ´ ÇUæ€ÅUÚU ·ð¤ Âæâ
am not feeling well, then I will go to the Á檡¤»æÓÓ ·¤æ ÂýçÌÏÙæˆ×·¤ ãñ
doctor” is :
(1) If I am feeling well, then I will not (1) ØçÎ ×ñ´ SßSÍ ã¡ê, Ìæð ÇUæ€ÅUÚU ·ð¤ Âæâ Ùãè´ Á檡¤»æ
go to the doctor
(2) If I will go to the doctor, then I am (2) ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Á檡¤»æ, Ìæð ×ñ´ SßSÍ ã¡ê
feeling well
(3) If I will not go to the doctor, then I
(3) ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Ùãè´ Á檡¤»æ, Ìæð ×ñ´
am feeling well
SßSÍ ã¡ê
(4) If I will go to the doctor, then I am
(4) ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Á檡¤»æ, Ìæð ×ñ´ SßSÍ
not feeling well.
Ùãè´ ã¡êÐ

-o0o-
-o0o-

English : 48 Set : 10 Hindi : 48 Set : 10