18 19

PART A — PHYSICS 1.

Match List - I (Event) with List - II (Order 1. of the time interval for happening of the event) and select the correct option from the options given below the lists.

List - I

Öæ» A — ÖæñçÌ·¤ çߙææÙ âê¿è-I(ƒæÅUÙæ) ·¤æð âê¿è-II (©â ƒæÅUÙæ ·ð¤ ãæðÙð ×´ð Ü»ð â×Ø ¥‹ÌÚUæÜ ·¤è ·¤æðçÅU) âð âé×ðçÜÌ ·¤èçÁ°ð ¥æñÚU âêç¿Øæ´ð ·ð¤ ÕæÎ çÎØð »Øð çß·¤ËÂæ´ð ×ð´ âð âãè çß·¤Ë ¿éçÙØðÐ

List - II

(a)

Rotation period (i) 10 5 s of earth

(a)

(b)

Revolution period of earth

(b)

(c)

Period of a light (iii) 10 215 s wave

(c)

(d)

Period of a sound wave

(d)

(ii) 10 7 s

(iv) 10 23 s

ÇϤÍ- I §ÐûÄÍ œ‰Ë ìËÏøËá¾ œ‰ËÁ §ÐûÄÍ œ‰Ë §Ì¿Uœâ‰¼øË œ‰ËÁ •œ‰ §âœ‰ËÅË ±¿™U  œ‰Ë œ‰ËÁ •œ‰ çÄ̾ ±¿™U  œ‰Ë œ‰ËÁ

ÇϤÍ- II (i) 105 s (ii) 107 s (iii) 10215 s (iv) 1023 s

(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

2.

1 A bullet looses   of its velocity passing 2. n

through one plank. The number of such planks that are required to stop the bullet can be :

3.

1

°· ÕéÜðÅU °·¤ ́Ìð âð »éÁÚUÙð ×ð´ ¥ÂÙð ßð» ·ð¤  n  ßæ¡ ·¤è ãæçÙ ·¤ÚUÌè ãñ´Ð ÕéÜðÅU ·¤æð Âê‡æü çߟææ× ¥ßSÍæ ×´ð ÜæÙð ·ð¤ çÜ°ð ç·¤ÌÙð §âè Âý·¤æÚU ·ð¤ ́Ìæð´ ·¤è ¥æßàØ·¤Ìæ ãæð»è Ñ

(1)

n2 2n21

(1)

n2 2n21

(2)

2n 2 n21

(2)

2n 2 n21

(3)

Infinite

(3)

¥Ù‹Ì

(4)

n

(4)

n

A heavy box is to be dragged along a rough 3. horizontal floor. To do so, person A pushes it at an angle 308 from the horizontal and requires a minimum force FA, while person

B pulls the box at an angle 608 from the

horizontal and needs minimum force FB. If the coefficient of friction between the box and the floor is

°·¤ ¹éÚUÎéÚðU ÿæñçÌÁ Ȥàæü ÂÚU °·¤ ÖæÚUè Հâð ·¤æð ¹è´¿æ ÁæÌæ ãñÐ °ðâæ ·¤ÚUÙð ·ð¤ çÜØð, ÃØç€Ì A ·¤æð ÿæñçÌÁ âð 308 ·¤æð‡æ ÂÚU π·¤æ Ü»æÙæ ÂǸÌæ ãñ ¥æñÚU ‹ØêÙÌ× ÕÜ FA ·¤è ¥æßàØ·¤Ìæ ãæðÌè ãñ´ ÁÕ ç·¤ ÃØç€Ì B ·¤æð ÿæñçÌÁ âð 608 ·¤æð‡æ ÂÚU ¹è´¿Ùæ ãæðÌæ ãñ ¥æñÚU ‹ØêÙÌ× ÕÜ FB ·¤è ¥æßàØ·¤Ìæ ãæðÌè ãñ´Ð ØçΠȤàæü °ß´ Հâð ·ð¤ Õè¿ ƒæáü‡æ »é‡ææ¡·¤

F A 3 , the ratio F is : 5 B

(1)

3

(1)

3

(2)

5 3

(2)

5 3

(3)

3 2

(3)

3 2

(4)

2 3

(4)

2 3

English : 2

Set : 10

Hindi : 2

3 5

ãñ´, ÌÕ ¥ÙéÂæÌ

F A F B

ãñ´ :

Set : 10

4.

What is Ffriction at point P ? It is assumed

°·¤ ¹éÚUÎéÚðU ÿæñçÌÁ ·¤æÜèÙ ÂÚU çߟææ× ¥ßSÍæ ×ð´ ÎýÃØ×æÙ M ·ð¤ °·¤ ÕðÜÙ ÂÚU çß¿æÚU ·¤èçÁ°ðÐ ÕðÜÙ ·¤è ¥ÿæ ·ð¤ ܐÕßÌ ˆßÚU‡æ ‘a’ âð ·¤æÜèÙ ·¤æð ¹è´¿ çÜØæ ÁæÌæ ãñ´Ð çՋÎé P ÂÚU Fƒæáü‡æ €Øæ ãñ´? Øã ×æÙ Üð´ ç·¤ ÕðÜÙ çȤâÜÌæ Ùãè´ ãñ´Ð

(1)

Mg

(1)

Mg

(2)

Ma

(2)

Ma

(3)

Ma 2

(3)

Ma 2

(4)

Ma 3

(4)

Ma 3

Consider a cylinder of mass M resting on 4. a rough horizontal rug that is pulled out from under it with acceleration ‘a’ perpendicular to the axis of the cylinder. that the cylinder does not slip.

English : 3

Set : 10

Hindi : 3

Set : 10

5.

5.

makes angle f with the horizontal. Then :

°·¤ ª¤ŠßæüÏÚU ç¿·¤Ùð ¥hüßëžæèØ ÂÍ ·ð¤ çՋÎé X âð °·¤ ·¤‡æ ·¤æð §â Âý·¤æÚU ÀUæðǸæ ÁæÌæ ãñ´ ç·¤ OX ª¤ŠßæüÏÚU âð ·¤æð‡æ u ÕÙæÌæ ãñ´ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ »Øæ ãñ´Ð ·¤‡æ ·ð¤ ª¤ÂÚU ÂÍ ·¤è ¥çÖÜÕ ÂýçÌç·ý¤Øæ çՋÎé Y ÂÚU â×æ# ãæð ÁæÌè ãñ´ Áãæ¡ OY ÿæñçÌÁ âð ·¤æð‡æ f ÕÙæÌæ ãñÐ ÌÕ Ñ

(1)

sin f5cos u

(1)

sin f5cos u

(2)

sin f5

1 cos u 2

(2)

sin f5

1 cos u 2

(3)

sin f5

2 cos u 3

(3)

sin f5

2 cos u 3

(4)

sin f5

3 cos u 4

(4)

sin f5

3 cos u 4

A particle is released on a vertical smooth semicircular track from point X so that OX makes angle u from the vertical (see figure). The normal reaction of the track on the particle vanishes at point Y where OY

English : 4

Set : 10

Hindi : 4

Set : 10

6.

A ball of mass 160 g is thrown up at an 6. angle of 608 to the horizontal at a speed of 10 ms21. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly (g510 ms22)

7.

ÿæñçÌÁ âð 608 ·ð¤ ·¤æð‡æ ÂÚU 10 ms21 ·¤è ¿æÜ âð 160 g ÎýÃØ×æÙ ·¤è °·¤ »ð´Î ª¤ÂÚU ·¤è ¥æðÚU Èð´¤·¤è ÁæÌè ãñ´Ð ÂÍ ·ð¤ ©“æÌ× çՋÎé ÂÚU ©â çՋÎé ·ð¤ âæÂðÿæ, Áãæ¡ âð »ð´Î Èð´¤·¤è »§ü ãñ´, »ð´Î ·¤æ ·¤æð‡æèØ â´ßð» ֻܻ ãñ (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

The gravitational field in a region is 7. r given by g 5 5N/kg iˆ 1 12 N/kg ˆj . The change in the gravitational potential energy of a particle of mass 2 kg when it is

°·¤ ÿæð˜æ ×ð´ »éL¤ˆßæ·¤áü‡æ ÿæð˜æ §â Âý·¤æÚU çÎØæ ÁæÌæ ãñ´ r g 5 5N/kg iˆ 1 12 N/kg ˆj ÎýÃØ×æÙ 2 kg ·ð¤ °·¤ ·¤‡æ ·¤æð ×êÜ çՋÎé âð çՋÎé (7 m,23 m) Üð 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. 18 km/hr near the surface. If the river is 5 m deep , find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water510 22

°·¤ ÙÎè ×ð´ âÌã ·ð¤ â×è ÂæÙè ·¤æ ßð» 18 km/hr ãñ´Ð ØçÎ ÙÎè 5 m »ãÚUè ãñ, ÌÕ ÂæÙè ·¤è ÿæñçÌÁ ÂÚUÌæð´ ·ð¤ Õè¿ ¥ÂL¤Â‡æ ÂýçÌÕÜ ·¤è »‡æÙæ ·¤èçÁ°ðÐ ÂæÙè ·¤æ àØæÙÌæ »é‡ææ¡·¤ 51022 ÂæØÁÐ

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 the two tubes of the manometer is 5 cm, the cross section of the tube at A and B is 6 mm2 and 10 mm2 respectively. The rate

ÎàææüØð »Øð 翘æ ×ð´, Îæð ÙçÜØæ´ð ·ð¤ ×ðÙæð×èÅUÚU ×ð´ ¥‹ÌÚU 5 cm ãñ´Ð A °ß´ B ÙçÜØæ𴠷𤠥ÙéÂýSÍ ·¤æÅU ·ý¤×àæÑ 6 mm2 °ß´ 10 mm2 ãñ´Ð ÙÜè ×ð´ ÂýßæçãÌ ÂæÙè ·¤è 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. radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the

ÂýˆØð·¤ ç˜æ’Øæ r ·¤è ¥ˆØçÏ·¤ ⴁØæ ×ð´ Îýß ·¤è Õê¡Îð´ ç×Ü·¤ÚU ç˜æ’Øæ R ·¤è °·¤ Õê¡Î ÕÙæÌè ãñ´Ð Âýç·ý¤Øæ ×ð´ çÙ·¤Üè ª¤Áæü, ÕǸè Õê¡Î ·¤è »çÌÁ ª¤Áæü ×ð´ ÂçÚUßçÌüÌ ãæð ÁæÌè ãñ´Ð ÕǸè Õê¡Î ·¤è ¿æÜ ã´ñ (çÎØæ ãñ´ Îýß ·¤æ ÂëcÆU ÌÙæß T,ƒæÙˆß r)

big drop is (given surface tension of liquid T, density r) (1)

T1 1  2  R rr

(1)

T1 1  2  R rr

(2)

2T  1 1  2  r r R

(2)

2T  1 1  2  r r R

(3)

4T  1 1  2  r r R

(3)

4T  1 1  2  r r R

(4)

6T  1 1  2  r r R

(4)

6T  1 1  2  r r R

English : 7

Set : 10

Hindi : 7

Set : 10

11.

A black coloured solid sphere of radius R 11. and mass M is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature T0. The initial temperature of the sphere is 3T0. If the specific heat of the material of the sphere

varies as aT 3 per unit mass with the temperature T of the sphere, where a is a constant, then the time taken for the sphere

°·¤ »éãæ, çÁâ×ð´ çÙßæüÌ ãñ´, ·ð¤ ¥‹ÎÚU ÎýÃØ×æÙ M °ß´ ç˜æ’Øæ R ·ð¤ °·¤ ·¤æÜð Ú´U» ·ð¤ ÆUæðâ »æðÜð ·¤æð ÚU¹æ »Øæ ãñ´Ð »éãæ ·¤è ÎèßæÚUæð´ ·¤æ ÌæÂ×æÙ T0 ÂÚ ¥ÙéÚUçÿæÌ ç·¤Øæ »Øæ ãñ´Ð »æðÜð ·¤æ ÂýæÚUçÖ·¤ ÌæÂ×æÙ 3T0 ãñ´Ð ØçÎ »æðÜð ·ð¤ ÂÎæÍü ·¤è çßçàæcÅU ª¤c×æ ÂýçÌ §·¤æ§ü ÎýÃØ×æÙ »æðÜð ·ð¤ ÌæÂ×æÙ T âð aT3 ·ðð U ¥ÙéâæÚU ÂçÚUßçÌüÌ ãæðÌè ãñ´, Áãæ¡ a °·¤ çSÍÚUæ¡·¤ ãñ´, ÌÕ »æðÜð ·ð¤ ÌæÂ×æÙ ·¤æð 2T0 Ì·¤ ÆU´ÇUæ ãæðÙð ×ð´ â×Ø Ü»ð»æ (s SÅUèȤ٠ÕæðËÅUÁ×æÙ çSÍÚUæ¡·¤ ãñ´)

to cool down to temperature 2T0 will be (s is Stefan Boltzmann constant)

12.

(1)

Ma 3 ln   2 4 pR 

(1)

Ma 3 ln   2 4 pR 

(2)

Ma  16  ln   2 4 pR   

(2)

Ma  16  ln   2 4 pR   

(3)

Ma  16  ln   2 16 pR   

(3)

Ma  16  ln   2 16 pR   

(4)

Ma 3 ln   16 pR 2 

(4)

Ma 3 ln   16 pR 2 

A gas is compressed from a volume of 12. 2 m3 to a volume of 1 m3 at a constant pressure of 100 N/m2. Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas :

°·¤ »ñâ 100 N/m2 ·ð¤ çSÍÚU ÎæÕ ÂÚU ¥æØÌÙ 2 m3 âð 1 m3 ×ð´ â´ÂèçÇUÌ ·¤è ÁæÌè ãñ´Ð çȤÚU §âð çSÍÚU ¥æØÌÙ ÂÚU 150 J ·¤è ª¤Áæü âð »×ü ç·¤Øæ ÁæÌæ ãñ´Ð ÂçÚU‡ææ×SßL¤Â »ñâ ·¤è ¥æ‹ÌçÚU·¤ ª¤Áæü Ñ U

(1)

Increases by 250 J

(1)

(2)

Decreases by 250 J

(2)

(3)

Increases by 50 J

(3)

(4)

Decreases by 50 J

(4)

English : 8

Set : 10

âð Õɸð»è 250 J âð ƒæÅðU»è 50 J âð Õɸð»è 50 J âð ƒæÅðU»è 250 J

Hindi : 8

Set : 10

13.

attained is much less than radius of the

Âë‰ßè ·ð¤ ÂëcÆU ÂÚU ÎýÃØ×æÙ M ·ð¤ °·¤ »ñâ ¥‡æé ·¤è »çÌÁ ª¤Áæü 08C ·ð¤ â×ÌéËØ ãñ´Ð ØçÎ Øã çÕÙæ ç·¤âè ¥æñÚU ¥‡æé âð ÅU·¤ÚUæØð âèÏ𠪤ÂÚU ·¤è ¥æðÚU ÁæÌæ ãñ´, ÌÕ Øã 緤⠪¡¤¿æ§ü Ì·¤ Áæ°ð»æ?(Øã ×æÙ Üð´ Øã ª¡¤¿æ§ü Âë‰ßè ·¤è ç˜æ’Øæ âð ÕãéÌ ·¤× ãñ) (kB ÕæðËÅUÁ×æÙ çSÍÚUæ¡·¤ ãñ´)

earth. (kB is Boltzmann constant) (1) 0

(1)

0

A gas molecule of mass M at the surface 13. of the Earth has kinetic energy equivalent to 08C. If it were to go up straight without colliding with any other molecules, how high it would rise ? Assume that the height

14.

(2)

273 k B 2 Mg

(2)

273 k B 2 Mg

(3)

546 k B 3 Mg

(3)

546 k B 3 Mg

(4)

819 k B 2 Mg

(4)

819 k B 2 Mg

A body is in simple harmonic motion with 14. time period half second (T50.5 s) and amplitude one cm (A51 cm). Find the average velocity in the interval in which it moves from equilibrium position to half of

°·¤ ßSÌé ¥æßÌü·¤æÜ ¥æÏð âñç·¤‡ÇU (T50.5 s) ¥æñÚ ¥æØæ× °·¤ âð´ÅUè×èÅUÚU (A51 cm) âðU âÚUÜ ¥æßÌü »çÌ ·¤ÚU ÚUãè ãñ´Ð ÁÕ Øã ¥ÂÙè âæØæßSÍæ çSÍçÌ âð ¥ÂÙð ¥æÏð ¥æØæ× Ì·¤ Âãé¡¿Ìè ãñ´, ©â ¥‹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. between fixed ends is 110 cm. Two bridges are placed to divide the length of wire in ratio 6 : 3 : 2. The tension in the wire is 400 N and the mass per unit length is 0.01 kg/m. What is the minimum common

SÍæØè çâÚUæ´ð ·ð¤ Õè¿ °·¤ âæðÙæð×æÂè ÌæÚU ·¤è ·é¤Ü ܐÕæ§ü 110 cm ãñ´Ð §â·¤è ܐÕæ§ü ·¤æð ¥ÙéÂæÌ 6 : 3 : 2 ×ð´ çßÖæçÁÌ ·¤ÚUÙð ·ð¤ çÜØð Îæð âðÌé ÚU¹ð »Øð ãñ´Ð ÌæÚU ×ð´ ÌÙæß 400 N ãñ´ ¥æñÚU ÂýçÌ §·¤æ§ü ܐÕæ§ü, ÎýÃØ×æÙ 0.01 kg/m ãñ´Ð ß㠋ØêÙÌ× ©ÖØçÙcÆU ¥æßëçžæ, çÁââð ç·¤ ÌèÙæð´ Öæ» ·¤ÂÙ ·¤ÚU â·ð´¤»ð´, ãñ´

frequency with which three parts can vibrate ?

16.

(1)

1100 Hz

(1)

1100 Hz

(2)

1000 Hz

(2)

1000 Hz

(3)

166 Hz

(3)

166 Hz

(4)

100 Hz

(4)

100 Hz

The electric field in a region of space is 16. given

by,

→

∧

∧

E 5 Eo i 1 2 Eo j

where

E05100 N/C. The flux of this field through a circular surface of radius 0.02 m parallel

×é€Ì ¥æ·¤æàæ ·ð¤ °·¤ ÿæð˜æ ×ð´ çßléÌ ÿæð˜æ çÎØæ ÁæÌæ ãñ´ →

∧

∧

E 5 Eo i 1 2 Eo j

Áãæ¡

E 0 5100 N/C Ð

Y-Z ÌÜ

·ð¤ â×æ‹ÌÚU 0.02 m ç˜æ’Øæ ·ð¤ ßëžæèØ ÂëcÆU 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.

at one plate to Î 2 at the other. The capacitance of capacitor is :

°·¤ â×æ‹ÌÚU ŒÜðÅU â´ÏæçÚU˜æ ·¤è ÂýˆØð·¤ ŒÜðÅU ·¤æ ÿæð˜æÈ¤Ü A ãñ´ ¥æñÚU ŒÜðÅUæð´ ·ð¤ Õè¿ ÎêÚUè d ãñ´Ð ŒÜðÅUæð´ ·ð¤ Õè¿ SÍæÙ ·¤æð °·¤ ÂÚUæßñléÌ âð ÖÚUæ »Øæ ãñ çÁâ·¤è çßléÌàæèÜÌæ °·¤ ŒÜðÅU ÂÚU Î1 âð ÎêâÚUè ŒÜðÅU ÂÚU Î2 Ì·¤ ÚðUç¹·¤ M¤Â ×ð´ ÂçÚUßçÌüÌ ãæðÌè ãñÐ â´ÏæçÚU˜æ ·¤è 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

(3)

Î0A/[d

(4)

Î0(Î22Î1)A/[d

(4)

Î0(Î22Î1)A/[d

ÂýˆØð·¤

100 W

The gap between the plates of a parallel 17. plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from Î1

ln(Î2/Î1)] ln(Î2/Î1)]

18.

ln(Î2/Î1)] ln(Î2/Î1)]

18.

Four bulbs B1, B2, B3 and B4 of 100 W each

are connected to 220 V main as shown in

the figure. The reading in an ideal ammeter

·ð¤ ¿æÚU ÕËÕ B1, B2, B3 °ß´ B4 220 V ×ð‹â âð ÁæðǸð »Øð ãñ Áñâæ ç·¤ 翘æ ×ð´ ÎàææüØæ »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 straight wire carrying current 1 A are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of 10 ms21 (see figure). The e.m.f induced at the time the

10 cm ÖéÁæ

·¤æ °·¤ ß»æü·¤æÚU Èðý¤× ¥æñÚU ÏæÚUæ 1 A âð ÂýßæçãÌ °·¤ ܐÕæ âèÏæ ÌæÚU ·¤æ»$Á ·ð¤ ÌÜ ×ð´ ÚU¹ð ãñ´Ð ÌæÚU ·ð¤ â×è âð, Èýð¤× Îæ¡Øè ¥æðÚU °·¤ çSÍÚU ¿æÜ 10 ms21 âð »çÌ ·¤ÚUÌæ ãñ´Ð (翘æ Îð¹ð´)Ð ÌæÚU âð ÁÕ Èýð¤× ·¤è Õæ¡Øè ÖéÁæ x510 cm ÂÚU ãñ´ ÌÕ ©â 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.

of intensity B, the magnetic field Bs inside

¥çÌ¿æÜ·¤ ¥æÎàæü ¥Ùé¿éÕ·¤ ·¤æ °·¤ ©ÎæãÚU‡æ ãñÐ §â·¤æ ¥Íü ãñ ç·¤ ÁÕ ÌèßýÌæ B ·ð¤ °·¤ ¿éÕ·¤èØ ÿæð˜æ ×ð´ ¥çÌ¿æÜ·¤ ·¤æð ÚU¹æ ÁæÌæ ãñ´, ÌÕ ¥çÌ¿æÜ·¤ ·ð¤ ¥‹ÎÚU ¿éÕ·¤èØ ÿæð˜æ Bs §â Âý·¤æÚU ãæð»æ Ñ

(1)

Bs52B

(1)

Bs52B

(2)

Bs50

(2)

Bs50

(3)

Bs5B

(3)

Bs5B

(4)

Bs
(4)

An example of a perfect diamagnet is a 20. superconductor. This implies that when a superconductor is put in a magnetic field the superconductor will be such that :

English : 13

Set : 10

Bs
Hindi : 13

Set : 10

21.

21.

Figure shows a circular area of radius R →

where a uniform magnetic field B is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the

翘æ ç˜æ’Øæ R ·ð¤ °·¤ ßëžæèØ ÿæð˜æÈ¤Ü ·¤æð ÎàææüÌæ ãñ → Áãæ¡ °·¤ °·¤â×æÙ ¿éÕ·¤èØ ÿæð˜æ B ·¤æ»$Á ·ð¤ ÌÜ ×ð´ ãñ´ ¥æñÚU §â·¤è çSÍÚU ÎÚU âð ÂçÚU×æ‡æ ×ð´ ßëçh ãæð ÚUãè ãñ´Ð §â ¥ßSÍæ ×ð´, âæ´·ð¤çÌ·¤ M¤Â âð ¹è´¿æ »Øæ, ·¤æñÙ-âæ »ýæȤ ÂýðçÚUÌ çßléÌ ÿæð˜æ E(r) ·ð¤ ÂçÚUßÌüÙ ·¤æð âãè Îàææü°ð»æ?

variation of the induced electric field E(r) ?

(1)

(1)

(2)

(2)

English : 14

Set : 10

Hindi : 14

Set : 10

22.

(3)

(3)

(4)

(4)

If denote microwaves, X rays, infrared, 22.

ØçÎ çßléÌ ¿éÕ·¤èØ SÂð€ÅþU× ·ð¤ Öæ» âêÿ× ÌÚ´U»ð´, X ç·¤ÚU‡æð´, ¥ßÚU€Ì, »æ×æ ç·¤ÚU‡æð´, ÂÚUæÕñ´»Ùè, ÚðUçÇUØæð ÌÚ´U»ð´ ¥æñÚU ÎëàØ Âý·¤æàæ ·ý¤×àæÑ M, X, I, G, U, R ¥æñÚU V âð ç¿ç‹ãÌ ç·¤Øð ÁæØð, ÌÕ ÌÚ´U»ÎñƒØü ·ð¤ ©žæÚUæðžæÚU ·ý¤× ×ð´ çߋØæâ çِÙçÜç¹Ì ãæð»æ Ñ

gamma rays, ultra-violet, radio waves and visible parts of the electromagnetic spectrum by M, X, I, G, U, R and V, the following is the arrangement in ascending order of wavelength : (1)

R, M, I, V, U, X and G

(1)

(2)

M, R, V, X, U, G and I

(2)

(3)

G, X, U, V, I, M and R

(3)

(4)

I, M, R, U, V, X and G

(4)

English : 15

Set : 10

¥æñÚU G M, R, V, X, U, G ¥æñÚU I G, X, U, V, I, M ¥æñÚU R I, M, R, U, V, X ¥æñÚU G R, M, I, V, U, X

Hindi : 15

Set : 10

23.

A ray of light is incident from a denser to a rarer medium. The critical angle for total 23. internal reflection is uiC and the Brewster’s angle of incidence is u iB , such that sinu iC /sinu iB 5h51.28. The relative refractive index of the two media is :

24.

°·¤ âƒæÙ âð çßÚUÜ ×æŠØ× ×ð´ Âý·¤æàæ ·¤è ç·¤ÚU‡æ ¥æÂçÌÌ ãñ´Ð Âê‡æü ¥æ‹ÌçÚU·¤ ÂÚUæßÌüÙ ·ð¤ çÜØð ·ý¤æç‹Ì·¤ ·¤æð‡æ uiC ãñ ¥æñÚU ¥æÂÌÙ ·¤æ ÕýêSÅUÚU ·¤æð‡æ uiB §â Âý·¤æÚU ãñ´ ç·¤ sinuiC/sinuiB5h51.28Ð ÎæðÙæð´ ×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

The diameter of the objective lens of microscope makes an angle b at the focus 24. of the microscope. Further, the medium between the object and the lens is an oil of refractive index n. Then the resolving power of the microscope.

°·¤ âê ÿ ×Îàæèü ·ð ¤ ¥çÖÎë à Ø·¤ Üð ‹ â ·¤æ ÃØæâ âêÿ×Îàæèü ·ð¤ Ȥæð·¤â ÂÚU ·¤æð‡æ b ÕÙæÌæ ãñ ; ßSÌé °ß´ Üð‹â ·ð¤ Õè¿ ·¤æ ×æŠØ× ¥ÂßÌüÙæ¡·¤ n ·¤æ °·¤ ÌðÜ ãñ´Ð ÌÕ âêÿ×Îàæèü ·¤è çßÖðÎÙ ÿæ×Ìæ Ñ

(1)

Increases with decreasing value of n

(2)

Increases with decreasing value of b

(1)

(3)

Increases with increasing value of

(2)

n sin 2b

(3)

(4)

n ·¤æ

×æÙ ƒæÅUÙð âð Õɸð»è b ·¤æ ×æÙ ƒæÅUÙð âð Õɸð»è n sin 2b ·¤æ ×æÙ ÕɸÙð âð Õɸð»è

Increases with increasing value of 1 n sin 2b

English : 16

(4)

Set : 10

Hindi : 16

1 n sin 2b

·¤æ ×æÙ ÕɸÙð âð Õɸð»è

Set : 10

25.

In a Young’s double slit experiment, the 25. distance between the two identical slits is 6.1 times larger than the slit width. Then the number of intensity maxima observed within the central maximum of the single

Ø´» ·ð¤ çmçÀUÎý ÂýØæð» ×ð´, Îæð âßüâ×M¤Âè çSÜÅUæð´ ·ð¤ Õè¿ ÎêÚUè çSÜÅU ¿æñǸæ§ü ·¤è 6.1 »éÙæ ãñ´Ð ÌÕ °·¤Ü çSÜÅU çßßÌüÙ ç¿˜æ ·ð¤ ·ð¤‹ÎýèØ ×ãžæ× ·ð¤ ¥‹ÎÚU ÃØçÌ·¤ÚU‡æ ç¿˜æ ·¤è ¥çÏ·¤Ì× ÌèßýÌæ¥æð´ ·¤è ⴁØæ 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. with List - II (Phenomena discovered/ associated) and select the correct option from the options given below the lists :

List - I Davisson (a) and Germer Experiment

âê¿è-I (ç·¤Øæ »Øæ ÂýØæð») ·¤æð âê¿è-II (çâhæ‹Ì ¹æðÁæ »Øæ ãñ/âÕçhÌ ãñ´) âð âé×ðçÜÌ ·¤èçÁ°ð ¥æñÚ âêç¿Øæð´ ·ð¤ Ùè¿ð çÎØð »Øð çß·¤ËÂæ´ð âð âãè çß·¤Ë ¿éçÙ°ð Ñ

ÇÏ¤Í - I

List - II (i)

Wave nature of electrons

Millikan’s oil Charge of an (b) drop (ii) electron experiment

ÇÏ¤Í - II

(a)

¬ÕUÄÍǾ ŠËÖ¿U ¦¼á¿U §â½ËÕ 

(i)

ŒÁÕþªãU˾Ëՙ œ‰Ë ±¿™U  §âœ‰Ë¿U

(b)

̼ÌÁœ‰Ë¾ œ‰Ë ³âÄ œÕ‰ Ì ¿U¾Õ œ‰Ë §â½ËÕ 

(ii)

ŒÁÕþªãU˾ œ‰Ë ŠËÄÕÅË

Rutherford experiment

(iii)

Quantisation of energy levels

(c)

¿U³¿U­‰ËÕ¬áU §â½ËÕ 

(iii)

‰¦Ëá S±¿U œ‰Ë þÄËøªÍœ‰¿UøË

Franck (d) Hertz experiment

(iv)

Existence of nucleus

(d)

­Ö♉œ‰ - ȪáU¦ §â½ËÕ 

(iv)

¾ËÌ»œ‰ œ‰Ë ŠÌS±íÄ

(c)

(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. shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of C14 is 5730 years, then age of the wooden piece

placed

in

the

museum

is

°·¤ ÌæÁð ·¤æÅðU »Øð ÂðǸ ·¤è Ü·¤Ç¸è ·ð¤ ÅéU·¤Ç¸ð âð ÂýçÌ ç×ÙÅU 20 ÿæØ ãæðÌð ãñ´Ð ©âè ¥æ·¤æÚU ·¤æ Ü·¤Ç¸è ·¤æ ÅéU·¤Ç¸æ °·¤ ØêçÁØ× âð ÂýæŒÌ ãæðÌæ ãñ´ (Áæð ç·¤ Ü·¤Ç¸è ·¤§ü ßáü ÂéÚUæÙè ·¤ÅUè ãé§ü ãñ) Áæð ç·¤ ÂýçÌ ç×ÙÅU 2 ÿæØ ÎàææüÌæ ãñ ; ØçÎ C14 ·¤è ¥Ïü ¥æØé 5730 ßáü ãñ´, ÌÕ ØêçÁØ× âð ÂýæŒÌ Ü·¤Ç¸è ·ð¤ ÅéU·¤Ç¸ð ·¤è ¥æØé ãñ´ ֻܻ Ñ

approximately : (1)

10439 years

(1)

10439

(2)

13094 years

(2)

13094

(3)

19039 years

(3)

19039

(4)

39049 years

(4)

39049

ßáü ßáü ßáü ßáü

28.

28.

Given : A and B are input terminals. Logic 1 5 > 5 V Logic 0 5 < 1 V Which logic gate operation, the following circuit does ? (1)

AND Gate

(2)

OR Gate

(3)

XOR Gate

(4)

NOR Gate

English : 19

Set : 10

çÎØæ ãñ´ Ñ A °ß´ B çÙßðàæ ÅUç×üÙÜ ãñ´Ð ÜæçÁ·¤ 1 5 > 5 V ÜæçÁ·¤ 0 5 < 1 V çِÙçÜç¹Ì ÂçÚUÂÍ ·¤æñÙ-âð ÜæçÁ·¤ »ðÅU ·¤æ ·¤æØü ·¤ÚU ÚUãæ ãñ´? (1) AND »ðÅU (2) OR »ðÅU (3) XOR »ðÅU (4) NOR »ðÅU Hindi : 19

Set : 10

29.

Long range radio transmission is possible 29. when the radiowaves are reflected from the ionosphere. For this to happen the frequency of the radiowaves must be in the

ܐÕè ÚðU‹Á ×ð´ ÚðUçÇUØæð Âýðá‡æ âÖß ãñ´ ÁÕ ¥æØÙæðSȤèØÚU âð ÚðUçÇUØæð ÌÚ´U»ð´ ÂÚUæßçÌüÌ ãæðÌè ãñ´Ð §â·ð¤ âÖß ãæðÙð ·ð¤ çÜØð ÚðUçÇUØæð ÌÚ´U»æð´ ·¤è ¥æßëçžæ §â ÚðU‹Á ×ð´ ¥ßàØ 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 gravitational acceleration g of a place with the help of a simple pendulum, the measured time period square is plotted

°·¤ âÚUÜ ÜæðÜ·¤ ·¤è âãæØÌæ âð °·¤ SÍæÙ ÂÚU »éL¤ˆßèØ ˆßÚU‡æ g ·ð¤ ×æÂÙ ·ð¤ ÂýØæð» ×ð´, ÙæÂð »Øð ¥æßÌü ·¤æÜ ·ð¤ ß»ü ·¤æ ÂçÚUßÌüÙ ÜæðÜ·¤ ·¤è ÇUæðÚUè ·¤è 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 31.

Ionization energy of gaseous Na atoms is 31. 495.5 kJmol 21 . The lowest possible frequency of light that ionizes a sodium atom is (h56.626310234 Js, NA56.02231023 mol21)

32.

Öæ» B — ÚUâæØÙ çߙææÙ »ñâèØ âæðçÇUØ× ÂÚU×æ‡æé¥æð´ ·¤è ¥æØÙÙ ª¤Áæü ·¤æ ×æÙ 495.5 kJ ×æðÜ21 ãñÐ âæðçÇUØ× ÂÚU×æ‡æé ·¤æ ¥æØÙÙ ·¤ÚUÙð ·ð¤ çÜØð Âý·¤æàæ ·¤è âÖß ‹ØêÙÌ× ¥æßëçÌ (frequency) €Øæ ãæð»è? (h56.626310234 Js, 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

Choose the correct statement with respect 32. to the vapour pressure of a liquid among

ç·¤âè Îýß ·ð¤ ßæc ÎæÕ ·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ ×ð´ âð âãè °·¤ ·¤ÍÙ ·¤æð ¿éçÙ° Ñ

the following : (1)

Increases linearly with increasing

(1)

temperature (2)

Increases

non-linearly

with

(2)

Decreases linearly with increasing

(3)

increasing temperature (3)

temperature (4)

Decreases

non-linearly

with

increasing temperature

English : 22

Set : 10

(4)

ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU ÕɸÌæ ãñÐ ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ Ù âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU ÕɸÌæ ãñÐ ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU ƒæÅUÌæ ãñÐ ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ Ù âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU ƒæÅUÌæ ãñÐ

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 ?

34.

(1)

N2

(1)

N2

(2)

NO

(2)

NO

(3)

CO

(3)

CO

(4)

O3

(4)

O3

Zirconium

phosphate

[Zr 3 (PO 4 ) 4 ] 34.

dissociates into three zirconium cations of

charge 14 and four phosphate anions of charge 23. If molar solubility of zirconium phosphate is denoted by S and its solubility product by Ksp then which of the following

relationship between S and K sp correct ?

is

çÁÚU·¤æðçÙØ× $ȤæS$Èð¤ÅU [Zr3(PO4)4] çßØæðçÁÌ ãæð·¤ÚU 14 ¥æßðàæ ÂýçÌ ·ð¤ÅUæØÙ ·ð¤ ÌèÙ çÁÚU·¤æðçÙØ× ·ð¤ÅUæØÙ ¥æñÚU 23 ¥æßðàæ ÂýçÌÑ °ÙæØÙ ·ð¤ ¿æÚU $ȤæS$Èð¤ÅU °ÙæØÙ ÎðÌæ ãñÐ ØçÎ çÁÚU·¤æðçÙØ× $ȤæS$Èð¤ÅU ·¤è ×æðÜÚU çßÜðØÌæ ·¤æð S âð ¥æñÚU §â·ð¤ çßÜðØÌæ »é‡æÙÈ¤Ü ·¤æð Ksp âð âêç¿Ì ç·¤Øæ ÁæØð Ìæð çِ٠âÕ‹Ïæð´ âð ·¤æñÙ-âæ S ¥æñÚU Ksp ·¤æ âÕ‹Ï âãè ×æÙæ ÁæØð»æ?

(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. represented as NH2COONH4(s) ì 2NH3(g)1CO2(g)

âð âêç¿Ì Øæñç»·¤ ·ð¤ çßØæðÁÙ ·ð¤ çÜØð

the Kp52.931025 atm3. If the reaction is started with 1 mol of the

Kp52.931025 atm3

compound,

the

total

pressure

ãæðÌæ ãñÐ ØçÎ ¥çÖç·ý¤Øæ ·¤æð Øæñç»·¤ ·ð¤ 1 ×æðÜ âð ¥æÚUÖ ç·¤Øæ ÁæØð Ìæð âæØ ¥ßSÍæ ×ð´ â·¤Ü ÎæÕ ·¤æ ×æÙ ãæð»æ Ñ

at

equilibrium would be :

36.

NH2COONH4(s) ì 2NH3(g)1CO2(g)

(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

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

(1)

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

(2)

2

d [A ] d [C ] n m 5 5 k [A ] [ B ] dt dt

(2)

2

d [A ] d [C ] n m 5 5 k [A ] [ B ] dt dt

(3)

1

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

(3)

1

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

(4)

2

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

(4)

2

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

English : 24

Set : 10

Hindi : 24

Set : 10

37.

Sulphur dioxide and oxygen were allowed 37. to diffuse through a porous partition. 20 dm3 of SO2 diffuses through the porous

partition in 60 seconds. The volume of O2 in dm3 which diffuses under the similar condition in 30 seconds will be (atomic

°·¤ âÚ´UÏý ÂÚUÎð âð âË$ȤÚU ÇU槥æ€âæ§ÇU ¥æñÚU ¥æ€âèÁÙ ·¤æð çßâçÚUÌ ãæðÙð çÎØæ »Øæ ãñÐ §â âÚ´UÏý ÂÚUÎð âð 20 dm3 SO2 ·ð¤ çßâçÚUÌ ãæðÙð ·¤æ â×Ø 60 âñ·¤‹ÇU ãæðÌæ ãñÐ °ðâè ãè ¥ßSÍæ ×ð´ çßâçÚUÌ ãæðÙð ßæÜè O2 ·¤æ ¥æØÌÙ dm3 ×ð´ 30 âñ·¤‹ÇU ·ð¤ çÜØð ãæð»æ (âË$ȤÚU ·ð¤ ÂÚU×æ‡æé ·¤æ ÎýÃØ×æÙ532 ×æ˜æ·¤) Ñ

mass of sulphur532 u) :

38.

(1)

7.09

(1)

7.09

(2)

14.1

(2)

14.1

(3)

10.0

(3)

10.0

(4)

28.2

(4)

28.2

The observed osmotic pressure for a 38. 0.10 M solution of Fe(NH4)2(SO4)2 at 258C

is

10.8

atm.

The

expected

and

experimental (observed) values of Van’t

ÂÚU Fe(NH4)2(SO4)2 ·ð¤ 0.10 M çßÜØÙ ·¤æ ¥æâ×æçÅU·¤ (ÂÚUæâÚU‡æ) ÎæÕ 10.8 atm Îð¹æ »ØæÐ ßæ´ÅU ãæȤ »é‡æ·¤ ·ð¤ ¥æàææ ¥ÙéâæÚU ¥æñÚU ÂýæØæðç»·¤ (×æçÂÌ) ×æÙ ·ý¤×æÙéâæÚU ãæð´»ð Ñ

258 C

Hoff factor (i) will be respectively : (R50.082 L atm k2mol21)

(R50.082 L atm k2×æðÜ21)

(1)

5 and 4.42

(1)

(2)

4 and 4.00

(2)

(3)

5 and 3.42

(3)

(4)

3 and 5.42

(4)

English : 25

Set : 10

¥æñÚU 4.42 4 ¥æñÚU 4.00 5 ¥æñÚU 3.42 3 ¥æñÚU 5.42 5

Hindi : 25

Set : 10

39.

structure is :

ƒæÙæ·¤æÚU âéâ´·é¤çÜÌ (çÙçÕǸ) â´ÚU¿Ùæ ×ð´ ©ÂçSÍÌ ÂýçÌ ÂÚU×æ‡æé ¥cÅUȤܷ¤èØ çÚUç€ÌØæð´ ·¤è â·¤Ü â´Øæ ãæð»è Ñ

(1)

2

(1)

2

(2)

4

(2)

4

(3)

1

(3)

1

(4)

3

(4)

3

The total number of octahedral void(s) per 39. atom present in a cubic close packed

40.

A and B, which of the following is true ?

Îæð ƒæÅU·¤æð´ A ¥æñÚU B ·ð¤ ¥æÎàæü çßÜØÙ ·ð¤ çÜØð çِÙæð´ ×ð´ âð ·¤æñÙ âãè ãæð»æ?

(1)

DHmixing < 0 (zero)

(1)

(2)

DHmixing > 0 (zero)

(2)

(3)

A2B interaction is stronger than

(3)

For an ideal solution of two components 40.

A2A and B2B interactions (4)

A2A, B2B and A2B interactions are identical

41.

Consider the reaction :

41.

41 21 H 2 SO 3(aq)1Sn (aq) 1H 2 O (l ) → Sn (aq) 1HSO24(aq)13H1(aq)

Which of the following statements is

¥æñ Ú U B2B ·¤è ÂÚU S ÂÚU Âý Ö æß âð A2B ·¤æ ÂÚUSÂÚU ÂýÖæß ¥çÏ·¤ ÂýÕÜ ãæð»æÐ (4) A2A, B2B ¥æñÚU A2B âÖè ÂÚUSÂÚU ÂýÖæß °·¤ â×æÙ ãñ´Ð ¥çÖç·ý¤Øæ

Sn41 is the oxidizing agent because

·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ ×ð´ âð ·¤æñÙ-âæ âãè ãñ? (1)

it undergoes oxidation (2)

Sn41is the reducing agent because

(2)

it undergoes oxidation (3)

H2SO3 is the reducing agent because

(3)

H2SO3 is the reducing agent because

(4)

it undergoes oxidation (4)

it undergoes reduction English : 26

Set : 10

A2A

41 21 H 2 SO 3(¦Áͽ)1Sn(¦Áͽ) 1H 2 O(l ) → Sn(¦Áͽ) 1HSO24(¦Áͽ)13H1 (¦Áͽ)

correct ? (1)

DHçןæ‡æ < 0 (zero) DHçןæ‡æ > 0 (zero)

Sn41 ¥æ€âè·¤æÚU·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ

ãæðÌæ ãñÐ Sn41¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ ãæðÌæ ãñÐ H2SO3 ¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ ãæðÌæ ãñÐ H2SO3 ¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ¥Â¿ØÙ ãæðÌæ ãñÐ

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 ?

43.

(1)

Li1

(1)

Li1

(2)

O2

(2)

O2

(3)

B31

(3)

B31

(4)

F2

(4)

F2

22

An octahedral complex with molecular 43. composition M.5NH 3 .Cl.SO 4 has two isomers, A and B. The solution of A gives a white precipitate with AgNO3 solution

and the solution of B gives white precipitate with BaCl2 solution. The type of isomerism exhibited by the complex is :

44.

22

¥‡æé â´ÚU¿Ùæ M.5 NH3.Cl.SO4 ßæÜð ¥cÅU Ȥܷ¤èØ â´·¤ÚU ·ð¤ Îæð â×æßØÌè A ¥æñÚU B ãñ´Ð A ·¤æ çßÜØÙ AgNO3 ·ð¤ çßÜØÙ ·ð¤ âæÍ â$Èð¤Î ¥ßÿæð ÎðÌæ ãñ ¥æñÚU B ·¤æ çßÜØÙ BaCl2 ·ð¤ çßÜØÙ ·ð¤ âæÍ â$Èð¤Î ¥ßÿæð ÎðÌæ ãñÐ §â â´·¤ÚU mæÚUæ ÂýÎçàæüÌ â×-¥ßØßÌæ ·¤æ Âý·¤æÚU ãæð»æ Ñ

(1)

Linkage isomerism

(1)

(2)

Ionisation isomerism

(2)

(3)

Coordinate isomerism

(3)

(4)

Geometrical isomerism

(4)

çÜ´·ð¤Á (â´Øæð»è) â×-¥ßØßÌæ ¥æØÙè â×-¥ßØßÌæ â׋ßØè â×-¥ßØßÌæ ’Øæç×çžæØ â×-¥ßØßÌæ

following redox reaction ?

çِ٠¥Â¿ØÙ-©Â¿ØÙ ¥çÖç·ý¤Øæ ×ð´ ç·¤ÌÙð §Üð€ÅþUæÙ âãÖæ»è ãñ´?

Cr2O7221Fe211 C 2 O 242

Cr2O7221Fe211 C 2 O 242

How many electrons are involved in the 44.

®

Cr311Fe311CO2 (Unbalanced)

®

(1)

3

(1)

3

(2)

4

(2)

4

(3)

6

(3)

6

(4)

5

(4)

5

English : 27

Set : 10

Hindi : 27

Cr311Fe311CO2

(¥â´ÌéçÜÌ)

Set : 10

45.

Amongst LiCl, RbCl, BeCl2 and MgCl2 the 45. compounds with the greatest and the least ionic character, respectively are :

46.

(1)

LiCl and RbCl

(2) (3)

RbCl and BeCl2 MgCl2 and BeCl2

(4)

RbCl and MgCl2

Nickel(Z528)

combines

with

a 46.

uninegative monodentate ligand to form a diamagnetic complex [NiL 4 ] 22 . The hybridisation involved and the number of

LiCl, RbCl, BeCl2 ¥æñÚU MgCl2

×ð´ âð ¥çÏ·¤Ì× ¥æñÚU ‹ØêÙÌ× ¥æØÙè çßàæðáÌæ ÚU¹Ùð ßæÜð Øæñç»·¤ ·ý¤×æÙéâæÚU ãñ´ Ñ (1) LiCl ¥æñÚU RbCl (2) RbCl ¥æñÚU BeCl2 (3) MgCl2 ¥æñÚU BeCl2 (4) RbCl ¥æñÚU MgCl2 çÙ·¤Ü (Z528) °·¤ «¤‡æè °·¤ ΋̷¤ çÜ»ñ´ÇU âð Øæð» ·¤ÚU °·¤ ÂýçÌ¿éÕ·¤èØ â´·¤ÚU [NiL4]22, ÕÙæÌæ ãñÐ §â â´·¤ÚU âð âÕç‹ÏÌ â´·¤ÚU‡æ Âý·¤æÚU ¥æñÚU ¥Øé»ç×Ì §Üñ€ÅþUæÙæð´ ·¤è ⴁØæ ·ý¤×æÙéâæÚU ãñ´ Ñ

unpaired electrons present in the complex are respectively :

47.

(1)

sp3, two

(1)

sp3, Îæð

(2)

dsp2, zero

(2)

dsp2,

(3)

dsp2, one

(3)

(4)

sp3, zero

(4)

Which of these statements is not true ? (1) (2)

NO1 is not isoelectronic with O2 B is always covalent in its compounds

(3)

In aqueous solution, the Tl1 ion is much more stable than Tl (III)

(4)

LiAlH4 is a versatile reducing agent

in organic synthesis.

English : 28

Set : 10

47.

àæê‹Ø dsp2, °·¤ sp3, àæê‹Ø

§Ù ·¤ÍÙæð´ ×ð´ âð ·¤æñÙ-âæ ·¤ÍÙ âˆØ Ùãè´ ãñ? (1) NO1 ÌÍæ O2 âקÜð€ÅþUæÙè Ùãè´ ãñ´Ð (2) ÕæðÚUæÙ ¥ÂÙð Øæñç»·¤æð´ ×ð´ âÎñß âãâ´ØæðÁè ãæðÌæ ãñÐ (3) ÁÜèØ çßÜØÙ ×ð´, Tl (III) ·¤è ¥Âðÿææ Tl1 ¥æØÙ ¥ˆØæçÏ·¤ SÍæØè ãæðÌæ ãñÐ (4) LiAlH4 ·¤æÕüçÙ·¤ â´àÜðá‡ææð´ ×ð´ ÂýØæð» ãæðÙð ßæÜæ °·¤ Õãé×é¹è ¥Â¿æØ·¤ ãñÐ

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 :

49.

(1)

Zeolites

(2)

Ultramarines

(3)

Feldspars

(4)

Beryls

ç$ÁØæðÜæ§Åð´U (2) ¥ËÅþUæ×ñÚUèÙð´ (3) Èð¤ËÇUSÂæÚð´U (4) ÕðçÚUÜð´ çِÙæð´ ×ð´ 16 ©Â¿ØÙ ¥ßSÍæ ·ð¤ ÂÚU×æ‡æé ßæÜð SÂèàæè$Á ·¤è Âã¿æÙ ·¤èçÁØðÐ (1)

Amongst the following, identify the 49. species with an atom in 16 oxidation state :

50.

51.

(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

as Malachite :

çِ٠×ð´ âð ·¤æñÙ ×ñÜæ·¤æ§ÅU ¥ØS·¤ Ùæ× âð ÁæÙè 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

Which one of the following ores is known 50.

The major product formed when 1, 1, 12 51. trichloro - propane is treated with aqueous potassium hydroxide is : (1)

Propyne

(2)

1 - Propanol

(3)

2 - Propanol

(4)

Propionic acid

English : 29

Set : 10

ÁÕ 1, 1, 12 ÅþU槀ÜæðÚUæðÂýæðÂðÙ ·¤è ÁÜèØ ÂæðÅñUçàæØ× ãæÇþUæ€âæ§ÇU âð ç·ý¤Øæ ·¤è ÁæÌè ãñ Ìæð ÂýæŒÌ ãé§ü Õɸè ×æ˜ææ ·¤æ ç·ý¤Øæ È¤Ü ãæðÌæ ãñ Ñ (1) ÂýæðÂæ§Ù (2) 1 - ÂýæðÂðÙæòÜ (3) 2 - ÂýæðÂðÙæòÜ (4) ÂýæðçÂØæçÙ·¤ °ðçâÇU

Hindi : 29

Set : 10

52.

Which one of the following is an example 52.

§Ù ×ð´ âð ·¤æñÙ ÌæÂÎëɸ ÕãéÜ·¤ ãñ?

of thermosetting polymers ?

53.

(1)

Neoprene

(1)

(2)

Buna -N

(2)

(3)

Nylon 6, 6

(3)

(4)

Bakelite

(4)

The correct IUPAC name of the following 53.

çÙØæðÂýèÙ ÕêÙæ - N Ùæ§ÜæÙ 6, 6 Õñ·ð¤Üæ§ÅU

§â Øæñç»·¤

compound

is :

54.

(1)

4 - methyl - 3 - ethylhexane

(2)

3 - ethyl - 4 - methylhexane

(3)

3, 4 - ethylmethylhexane

(4)

4 - ethyl - 3 - methylhexane

Which one of the following substituents at 54.

·¤æ âãè IUPAC Ùæ× ãñ Ñ (1) 4 - ×ðçÍÜ - 3 - °çÍÜãñ€âðÙ (2) 3 - °çÍÜ - 4 - ×ðçÍÜãñ€âðÙ (3) 3, 4 - °çÍÜ×ðçÍÜãñ€âðÙ (4) 4 - °çÍÜ - 3 - ×ðçÍÜãñ€âðÙ çِ٠ÂýçÌSÍæ·¤æð´ ×ð´ âð ·¤æñÙ Èñ¤Ùæ€âæ§ÇU ¥æØÙ

para-position is most effective in , stabilizing the phenoxide

,

·ð ¤ Âñ Ú U æ SÍæÙ ÂÚU ãæð Ù ð âð §âð

¥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.

amine is treated with NaNO2 and HCl

×ðçÍÜ °×èÙ ·¤è NaNO2 ¥æñÚU HCl ·ð¤ âæÍ ç·ý¤Øæ ·¤ÚUÙð ÂÚU ©ÂÜŽÏ ¥ç‹Ì× ¥çÖç·ý¤Øæ È¤Ü ãæðÌæ ãñ Ñ

(1)

Diazomethane

(1)

(2)

Methylalcohol

(2)

(3)

Methylcyanide

(3)

(4)

Nitromethane

(4)

The final product formed when Methyl 55. is :

56.

Which one of the following compounds 56. will

not

be

soluble

in

sodium

ÇU槰ð$Áæð×èÍðÙ ×ðçÍÜ °ðË·¤æðãæÜ ×ðçÍÜçâØæÙæ§ÇU Ùæ§ÅþUæð×èÍðÙ

§Ù×ð´ âð ·¤æñÙ-âæ Øæñç»·¤ âæðçÇUØ× Õ槷¤æÕæðüÙðÅU ×ð´ Ùãè´ ƒæéÜð»æ?

bicarbonate ?

57.

(1)

2, 4, 6 - Trinitrophenol

(1)

(2)

Benzoic acid

(2)

(3)

o - Nitrophenol

(3)

(4)

Benzene sulphonic acid

(4)

Williamson synthesis of ether is an example 57. of : (1)

Nucleophilic addition

(2)

Electrophilic addition

(3)

Electrophilic substitution

(4)

Nucleophilic substitution

English : 31

Set : 10

ÅþUæ§üÙæ§ÅþUæðç$ȤÙæòÜ Õñ‹$Áæ𧷤 °ðçâÇU o - Ùæ§ÅþUæðç$ȤÙæòÜ Õñ‹$ÁèÙ âË$ȤæçÙ·¤ °ðçâÇU 2, 4, 6 -

§üÍÚU ·¤æ çßçÜØ×âÙ â´àÜðá‡æ §Ù×ð´ âð 緤⠷¤æ ©ÎæãÚU‡æ ãñ? (1) ‹Øêç€ÜØæðç$ȤçÜ·¤ â´·¤ÜÙ (2) §Üñ€ÅþUæðç$ȤçÜ·¤ â´·¤ÜÙ (3) §Üñ€ÅþUæðç$ȤçÜ·¤ ÂýçÌSÍæÂÙ (4) ‹Øêç€ÜØæðç$ȤçÜ·¤ ÂýçÌSÍæÂÙ

Hindi : 31

Set : 10

58.

The reason for double helical structure of 58. DNA is the operation of :

59.

(1)

Electrostatic attractions

(2)

van der Waals forces

(3)

Dipole - Dipole interactions

(4)

Hydrogen bonding

Among the following organic acids, the 59. acid present in rancid butter is : (1)

Pyruvic acid

(2)

Lactic acid

(3)

Butyric acid

(4)

Acetic acid

English : 32

Set : 10

§Ù×ð´ âð ·¤æñÙ-âè ç·ý¤Øæ DNA ·¤è ÎæðãÚUè ·é¤‡ÇUÜèÎæÚU â´ÚU¿Ùæ ·¤æ ·¤æÚU‡æ ãæðÌè ãñ? (1) çSÍÚUßñléÌ ¥æ·¤áü‡æ (2) ßæÙÇUÚU ßæÜ ·ð¤ ÕÜ (3) çmÏýéß - çmÏýéß ÂÚUSÂÚU ç·ý¤Øæ (4) ãæ§ÇþUæðÁÙ ¥æՋÏÙ Îé»ü‹Ïè ׀¹Ù ×ð´ ÂæØæ ÁæÙð ßæÜæ °ðçâÇU çِ٠°ðçâÇUæð´ ×ð´ âð ·¤æñÙ-âæ ãæðÌæ ãñ? (1) Âæ§L¤çß·¤ °ðçâÇU (2) Üñç€ÅU·¤ °ðçâÇU (3) ŽØéÅUèçÚU·¤ °ðçâÇU (4) °âèçÅU·¤ °ðçâÇU

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

(1)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

English : 33

Set : 10

Hindi : 33

âð ÂýæŒÌ ç·ý¤ØæÈ¤Ü E ãæð»æ Ñ

Set : 10

Öæ» C — »ç‡æÌ

PART C — MATHEMATICS 61.

62.

Let f : R®R be defined by f(x)5

×æÙæ f : R®R , f(x)5

then f is :

Ìæð

(1)

both one - one and onto

(1)

(2)

one - one but not onto

(2)

(3)

onto but not one - one

(3)

(4)

neither one - one nor onto.

(4)

For all complex numbers z of the form 62. 11ia, a e R, if

63.

x 21 61. x 11

z25x1iy,

then :

°·ñ¤·¤è ÌÍæ ¥æ‘ÀUæÎè ÎæðÙæð´ ãñ´Ð °·ñ¤·¤è ãñ ÂÚ ¥æ‘ÀUæÎè Ùãè´ ãñÐ ¥æ‘ÀUæÎè ãñ ÂÚU °·ñ¤·¤è Ùãè´ ãñÐ Ù Ìæð °·ñ¤·¤è ãñ ¥æñÚU Ù ãè ¥æ‘ÀUæÎè ãñÐ

11ia, a e R ·¤è z ·ð¤

çÜØð, ØçÎ

Âý·¤æÚU ·¤è âÖè âç×Ÿæ ⴁØæ¥æð´ ãñ, Ìæð :

z25x1iy

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

3x 21x15 5x23, where x 63.

is real, has : (1)

no solution

(2)

exactly one solution

(3)

exactly two solutions

(4)

exactly four solutions.

English : 34

Set : 10

mæÚUæ ÂçÚUÖæçáÌ ãñ,

f :

(1)

The equation

x 21 x 11

â×è·¤ÚU‡æ 3x 21x15 5x23, Áãæ¡ x ßæSÌçß·¤ ãñ, ·¤æ / ·ð¤ : (1) ·¤æð§ü ãÜ Ùãè´ ãñ´Ð (2) ÆUè·¤ °·¤ ãÜ ãñÐ (3) ÆUè·¤ Îæð ãÜ ãñ´Ð (4) ÆUè·¤ ¿æÚU ãÜ ãñ´Ð

Hindi : 34

Set : 10

64.

A is symmetric and B is skewsymmetric,

×æÙæ A ÌÍæ B ·¤æð§ü Îæð 333 ·ð¤ ¥æÃØêã ãñ´Ð ØçÎ A â×ç×Ì ãñ ÌÍæ B çßá× â×ç×Ì ãñ, Ìæð ¥æÃØêã

then the matrix AB2BA is :

AB2BA :

(1)

skewsymmetric

(1)

(2)

symmetric

(2)

(3)

neither

Let A and B be any two 333 matrices. If 64.

symmetric

nor

(3)

I or 2I, where I is an identity matrix.

(4)

çßá× â×ç×Ì ãñ â×ç×Ì ãñ Ù Ìæð â×ç×Ì ãñ´ ¥æñÚU Ù ãè çßá× â×ç×Ì ãñ

skewsymmetric (4) 65. If 65.

Dr 5

r n 2

1 n ( n 2 1) 2

2r 2 1

3r 2 2

n2 1

a

( n 2 1 )2

then the value of

n2 1

∑

r5 1

1 ( n 2 1 )( 3n 1 4 ) , 2

Dr :

ØçÎ

Dr 5

ãñ´, Ìæð

depends only on a

(2)

depends only on n

(1)

(3)

depends both on a and n

(2)

(4)

is independent of both a and n.

(3) (4)

Set : 10

2r 2 1

3r 2 2

n2 1

a

( n 2 1 )2

1 ( n 2 1 )( 3n 1 4 ) 2

r n 2

1 n ( n 2 1) 2

(1)

English : 35

¥Íßæ 2I ãñ´, Áãæ¡ I °·¤ ̈â×·¤ ¥æÃØêã ãñÐ I

n2 1

∑

r5 1

Dr

·¤æ ×æÙ :

·ð¤ßÜ a ÂÚU çÙÖüÚU ãñ ·ð¤ßÜ n ÂÚU çÙÖüÚU ãñ a ÌÍæ n ÎæðÙæð´ ÂÚU çÙÖüÚU ãñ´ a ÌÍæ n ÎæðÙæð´ âð SßÌ´˜æ ãñ´Ð

Hindi : 35

Set : 10

66.

Two women and some men participated 66. in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66,

àæÌÚ´UÁ ·¤è °·¤ ÂýçÌØæðç»Ìæ ×ð´ Îæð ×çãÜæ¥æð´ ÌÍæ ·é¤ÀU ÂéL¤áæð´ Ùð Öæ» çÜØæ çÁâ×ð´ ÂýˆØð·¤ ÂýçÌØæð»è Ùð àæðá ÂýˆØð·¤ ÂýçÌØæð»è âð Îæð ÕæçÚUØæ´ ¹ðÜèÐ ØçÎ ÂéL¤áæð´ Ùð ¥æÂâ ×ð´ çÁÌÙè ÕæçÚUØæ´ ¹ðÜè ©Ù·¤è ⴁØæ ÂéL¤áæð´ mæÚUæ ×çãÜæ¥æð´ ·ð¤ âæÍ ¹ðÜè ÕæçÚUØæð´ ·¤è ⴁØæ âð 66 ¥çÏ·¤ ãñ´, Ìæð ÂéL¤áæð´ ·¤è ⴁØæ, çÁ‹ãæð´Ùð ÂýçÌØæð»èÌæ ×ð´ Öæ» çÜØæ, çِ٠¥´ÌÚUæÜ ×ð´ ãñ´ Ñ

then the number of men who participated in the tournament lies in the interval :

67.

(1)

[8, 9]

(1)

[8, 9]

(2)

[10, 12)

(2)

[10, 12)

(3)

(11, 13]

(3)

(11, 13]

(4)

(14, 17)

(4)

(14, 17)

The coefficient of x1012 in the expansion of 67. (11x n 1x 253 ) 10 ,

(where n £ 22 is any

(11xn1x253)10,

ãñ´)·ð¤ ÂýâæÚU ×ð´

(Áã¡æ n £ 22 ·¤æð§ü ÏÙ Âê‡ææZ·¤ »é‡ææ´·¤ ãñ´ Ñ

x1012 ·¤æ

positive integer), is : (1)

1

(2)

10C

(3)

4n

(4)

253C

English : 36

4

4

Set : 10

(1)

1

(2)

10C

(3)

4n

(4)

253C

Hindi : 36

4

4

Set : 10

68.

The number of terms in an A.P. is even; 68. the sum of the odd terms in it is 24 and that the even terms is 30. If the last term

1

ãñÐ ØçÎ ¥´çÌ× ÂÎ, ÂýÍ× ÂÎ âð 10 2 ¥çÏ·¤ ãñ, Ìæð

1 , then the 2 number of terms in the A.P. is :

exceeds the first term by 10

69.

ç·¤âè â×æ´ÌÚU Ÿæðɸè ×ð´ ÂÎæð´ ·¤è ⴁØæ â× ãñÐ §â·ð¤ çßá× ÂÎæð´ ·¤æ Øæð» 24 ãñ ÌÍæ â× ÂÎæð´ ·¤æ Øæð» 30 â×æ´ÌÚU Ÿæðɸè ×ð´ ÂÎæð´ ·¤è ⴁØæ ãñ Ñ

(1)

4

(1)

4

(2)

8

(2)

8

(3)

12

(3)

12

(4)

16

(4)

16

3n  1 n , where [n] denotes 69. Let f(n) 5  1 100  3

×æÙæ f(n)5  3 1 100  n , Áãæ¡

1

the greatest integer less than or equal to n.

Âê ‡ ææZ · ¤, Áæð

Then

56 ∑ f ( n ) is equal to : n5 1

56 ∑ f ( n) n5 1

(1)

56

(1)

56

(2)

689

(2)

689

(3)

1287

(3)

1287

(4)

1399

(4)

1399

English : 37

Set : 10

Hindi : 37

n

3n 

[n]

°·¤ ×ãžæ×

âð ÀU æ ð Å U æ ¥Íßæ ÕÚU æ ÕÚU ãñ , Ìæð

ÕÚUæÕÚU ãñ Ñ

Set : 10

70.

If the function

 2 1 cos x2 1 , x ≠p  2 f (x ) 5  ( p 2 x ) k , x5p 

71.

70.

ØçΠȤÜÙ

is continuous at x5p, then k equals :

x5p ÂÚU

(1)

0

(1)

0

(2)

1 2

(2)

1 2

(3)

2

(3)

2

(4)

1 4

(4)

1 4

Let f: R ® R be a function such that 71. ?f(x)? £

x2,

for all x e R. Then, at x50, f is :

(1)

continuous but not differentiable

(2)

continuous as well as differentiable

(3)

neither continuous nor differentiable

(4)

differentiable but not continuous.

English : 38

Set : 10

 2 1 cos x2 1 , x ≠p  2 f (x ) 5  ( p 2 x ) k , x5p 

âÌÌ ãñ, Ìæð k ÕÚUæÕÚU ãñ :

×æÙæ f: R ® R °·¤ °ðâæ ȤÜÙ ãñ ç·¤ âÖè x e R ·ð¤ çÜ° ?f(x)? £ x2 ãñ, Ìæð x50 ÂÚU f : (1) âÌÌ ãñ ÂÚU ¥ß·¤ÜÙèØ Ùãè´ ãñ (2) âÌÌ ÌÍæ ¥ß·¤ÜÙèØ ÎæðÙæð´ ãñ´ (3) Ù Ìæð âÌÌ ãñ ¥æñÚU Ù ãè ¥ß·¤ÜÙèØ ãñ (4) ¥ß·¤ÜÙèØ ãñ ÂÚU âÌÌ Ùãè´ ãñÐ

Hindi : 38

Set : 10

72.

If non-zero real numbers b and c are such 72. that min f(x) > max g(x), where f(x)5x212bx12c2 and

ØçÎ àæê‹ØðÌÚU ßæSÌçß·¤ ⴁØæ°¡ b ÌÍæ c °ðâè ãñ´ ç·¤ min f(x) > max g(x), Áãæ¡ f(x)5x212bx12c2 ÌÍæ g(x)52x222cx1b2 (x e R) ãñ´,

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

73.

then

c lies in the interval : b

Ìæð

(1)

 1  0,   2

(1)

 1  0,   2

(2)

1 1  2 , 2   

(2)

1 1  2 , 2   

(3)

 1   2 , 2  

(3)

 1   2 , 2  

(4)

(

(4)

(

2 ,∞

)

If the volume of a spherical ball is 73. increasing at the rate of 4p cc/sec, then the rate of increase of its radius (in cm/sec), when the volume is 288p cc,

c b

çÁâ ¥´ÌÚUæÜ ×ð´ ãñ, ßã ãñ :

2 ,∞

)

ØçÎ °·¤ »æðÜæ·¤æÚU »ð´Î ·¤æ ¥æØÌÙ 4p ƒæÙ âð×è/âñ. ·¤è ÎÚU âð Õɸ ÚUãæ ãñ, Ìæð ÁÕ ¥æØÌÙ 288p ƒæÙ âð×è ãñ, Ìæð ç˜æ’Øæ çÁâ ÎÚU (âð×è/âñ. ×ð´) âð Õɸ ÚUãè ãñ, ßã ãñ :

is : (1)

1 6

(1)

1 6

(2)

1 9

(2)

1 9

(3)

1 36

(3)

1 36

(4)

1 24

(4)

1 24

English : 39

Set : 10

Hindi : 39

Set : 10

74.

If m is a non - zero number and 74.

∫

x 5m21 1 2 x 4 m21

(

)

x 2 m 1 x m 11

3

∫

d x5 f ( x )1c ,

(2)

(

x 5m

)

2m x 2m 1 x m 1 1

(

x 4m

)

2m x 2m 1 x m 1 1

(

(3)

(4)

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

2 m x 5m 1 x 4m

English : 40

(

)

Set : 10

3

d x5 f ( x )1c

f(x) ãñ :

(

x 5m

)

2

)

2

2m x 2m 1 x m 1 1

(2)

2

°·¤ àæê ‹ Øð Ì ÚU â´  Øæ ãñ ÌÍæ

x 2 m 1 x m 11

(1)

2

) 2 ( x2m 1 xm 1 1)

m

x 5m21 12 x 4 m21

ãñ, Ìæð

then f(x) is : (1)

ØçÎ

(

x 4m

2m x 2m 1 x m 1 1

(

(3)

) 2 ( x2m 1 xm 1 1)

(4)

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

Hindi : 40

2 m x 5m 1 x 4m

Set : 10

75.

Let

function

F( x ) 5

the

F

be

defined

as 75.

et ∫1 t dt , x > 0 then the value of x

integral

et ∫1 t 1 a dt , x

et dt , x > 0 1 t

×æÙæ ȤÜÙ F , F( x ) 5 ∫

x

x

et

ÂçÚUÖæçáÌ ãñ, Ìæð â×æ·¤Ü ∫1 t1 a a > 0 ãñ,

where

dt

mæÚUæ , Áãæ¡

·¤æ ×æÙ ãñ :

a > 0, is :

76.

(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)]

The area of the region above the x-axis 76. bounded by the curve y5tan x, 0 £ x £ and the tangent to the curve at x5

p 2

p is : 4

ß·ý¤ y5tan x, 0 £ x £

x5

p 4

ª¤ÂÚU ãñ, ·¤æ ÿæð˜æÈ¤Ü ãñ :

1 1  log 2 2  2 2

(1)

1 1  log 2 2  2 2

(2)

1 1  log 2 1  2 2

(2)

1 1  log 2 1  2 2

(3)

1 ( 1 2 log 2 ) 2

(3)

1 ( 1 2 log 2 ) 2

(4)

1 ( 1 1 log 2 ) 2

(4)

1 ( 1 1 log 2 ) 2

Set : 10

ÌÍæ ß·ý ÂÚU

ÂÚU ¹è´¿è »§ü SÂàæü ÚðU¹æ mæÚUæ çƒæÚðU ÿæð˜æ, Áæð x ¥ÿæ âð

(1)

English : 41

p 2

Hindi : 41

Set : 10

77.

78.

dy 1y tan x5sin 2x and y(0)51, then 77. dx y(p) is equal to :

If

dy 1y tan x5sin 2x dx y(p) ÕÚUæÕÚU ãñ :

ØçÎ

(1)

1

(1)

1

(2)

21

(2)

21

(3)

25

(3)

25

(4)

5

(4)

5

The circumcentre of a triangle lies at the 78. origin and its centroid is the mid point of the line segment joining the points (a211, a211) and (2a, 22a), a ¹ 0. Then for any a, the orthocentre of this triangle

ÌÍæ y(0)51 ãñ Ìæð

°·¤ ç˜æÖéÁ ·¤æ ÂçÚU·ð´¤Îý ×êÜ çՋÎé ÂÚU ãñ ÌÍæ ©â·¤æ ·ð¤‹Îý·¤, çՋÎé¥æð´ (a211, a211) ÌÍæ (2a, 22a), a ¹ 0 ·¤æð ç×ÜæÙð ßæÜð ÚðU¹æ¹´ÇU ·¤æ ×ŠØ çÕ´Îé ãñ, Ìæð ç·¤âè a ·¤ð çÜ° §â ç˜æÖéÁ ·¤æ Ü´Õ ·ð¤‹Îý çÁâ ÚðU¹æ 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

English : 42

(4)

Set : 10

(a21) 2x2(a11) 2y50

Hindi : 42

Set : 10

79.

If a line L is perpendicular to the line 79. 5x2y51, and the area of the triangle formed by the line L and the coordinate

ØçÎ °·¤ ÚðU¹æ L, ÚðU¹æ 5x2y51 ÂÚU Ü´ÕßÌ ãñ ÌÍæ ÚðU¹æ L ÌÍæ çÙÎðüàææ´·¤ ¥ÿææð´ mæÚUæ ÕÙè ç˜æÖéÁ ·¤æ ÿæð˜æÈ¤Ü 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 :

80.

(1)

7 5

(1)

7 5

(2)

5 13

(2)

5 13

(3)

7 13

(3)

7 13

(4)

5 7

(4)

5 7

The equation of the circle described on the 80. chord

3x1y1550

x21y2516

of

the

circle

ßëžæ x21y2516 ·¤è °·¤ Áèßæ 3x1y1550 ·¤æð ÃØæâ ×æÙ·¤Ú ¹è´¿ð »° ßëžæ ·¤æ â×è·¤ÚU‡æ ãñ :

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. parabola y256x such that its distance from

ÂÚUßÜØ y256x ·¤è ÙæçÖ âð ãæð·¤ÚU ÁæÌè °·¤ Áèßæ ¹è´¿è »§ü ãñ çÁâ·¤è ÂÚUßÜØ ·ð¤ àæèáü âð ÎêÚUè

5 , then its the vertex of this parabola is 2

5 2

ãñ,

Ìæð §â·¤è ÉUæÜ ãæð â·¤Ìè ãñ :

slope can be :

82.

(1)

5 2

(1)

5 2

(2)

3 2

(2)

3 2

(3)

2 5

(3)

2 5

(4)

2 3

(4)

2 3

y2 x2 2 5 1 ·ð¤ 4 5

The tangent at an extremity (in the first 82.

¥çÌÂÚUßÜØ

quadrant) of latus rectum of the hyperbola

çâÚðU (Áæð ÂýÍ× ¿ÌéÍæZàæ ×ð´ ãñ) ÂÚU ¹è´¿è »§ü SÂàæü

y2 x2 2 5 1 ,meets x - axis and y - axis 4 5

ÚðU¹æ x-¥ÿæ ÌÍæ y-¥ÿæ ·¤æð ·ý ×àæ çՋÎé¥æð´ A ÌÍæ B

at A and B

respectively. Then

(OA) 2 2(OB) 2 , where O is the origin, equals : (1)

2

(2)

16 9

(3)

4

(4)

2

English : 44

20 9

4 3

Set : 10

ÙæçÖÜ´Õ ·ð¤ °·¤

ÂÚU ç×ÜÌè ãñ´, Ìæð (OA)22(OB)2, Áãæ¡ O ×êÜ çÕ´Îé ãñ, ÕÚUæÕÚU ãñ : (1)

2

(2)

16 9

(3)

4

(4)

2

Hindi : 44

20 9

4 3

Set : 10

83.

Equation of the line of the shortest distance 83. between the lines

y x z 5 5 and 1 21 1

y11 x21 z 5 5 22 0 1

y11 x21 z 5 5 is : 0 22 1

84.

y x z 5 5 1 21 1

Úð U ¹æ¥æð ´

·ð¤ Õè¿ ‹ØêÙÌ× ÎêÚUè

ßæÜè ÚðU¹æ ·¤æ â×è·¤ÚU‡æ ãñ :

(1)

y x z 5 5 1 21 22

(1)

y x z 5 5 1 21 22

(2)

y11 x21 z 5 5 21 22 1

(2)

y11 x21 z 5 5 21 22 1

(3)

y11 x21 z 5 5 21 1 1

(3)

y11 x21 z 5 5 1 21 1

(4)

y x z 5 5 22 1 2

(4)

y x z 5 5 22 1 2

If

the

angle

2(x11)5y5z14

between and

the the

line 84. plane

p 2x2y1 l z1450 is , then the value 6 of l is :

ØçÎ Úð U ¹æ l ·¤æ

×æÙ ãñ :

135 7

(1)

135 7

(2)

45 11

(2)

45 11

(3)

45 7

(3)

45 7

(4)

135 11

(4)

135 11

Set : 10

2(x11)5y5z14

2x2y1 l z1450

(1)

English : 45

ÌÍæ

Hindi : 45

ÌÍæ â×ÌÜ

·ð¤ Õè¿ ·¤æ ·¤æð‡æ

p ãñ, 6

Ìæð

Set : 10

85.

r r If x 5 3iˆ 2 6 ˆj 2 kˆ , y 5 iˆ 1 4 ˆj 2 3kˆ 85. and

r z 5 3iˆ 2 4 ˆj 2 12kˆ ,

ØçÎ ÌÍæ

then the r r r magnitude of the projection of x 3y on z

r r x 5 3iˆ 2 6 ˆj 2 kˆ , y 5 iˆ 1 4 ˆj 2 3kˆ r r r r z 5 3iˆ 2 4 ˆj 2 12kˆ ãñ´ Ìæð x 3y ·ð¤ z ÂÚU

Âýÿæð ·¤æ ÂçÚU×æ‡æ ãñ :

is :

86.

(1)

12

(1)

12

(2)

15

(2)

15

(3)

14

(3)

14

(4)

13

(4)

13

Let A and E be any two events with 86. positive probabilities : Statement - 1 : P(E/A) ³ P(A/E)P(E) Statement - 2 : P(A/E) ³ P(AÇE). (1)

Both the statements are true

(2)

Both the statements are false

(3)

Statement - 1 is true, Statement - 2 is

×æÙæ A ÌÍæ E ·¤æð§ü Îæð °ðâè ƒæÅUÙæ°¡ ãñ çÁÙ·¤è ÂýæçØ·¤Ìæ°¡ ÏÙæˆ×·¤ ãñ´ Ñ ·¤ÍÙ-1 : P(E/A) ³ P(A/E)P(E) ·¤ÍÙ-2 : P(A/E) ³ P(AÇE). (1) ÎæðÙæð´ ·¤ÍÙ âˆØ ãñ´ (2) ÎæðÙæð´ ·¤ÍÙ ¥âˆØ ãñ´ (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. mode and variance of n observations

×æÙæ n Âýðÿæ‡ææð´ ÂýâÚU‡æ ·ý¤×àæÑ

x1, x2, ..., xn·ð¤ ×æŠØ ÕãéÜ·¤ ÌÍæ x , M ÌÍæ s 2 ÌÍæ di52xi2a,

x1, x2, ..., xn and di52xi2a, i51, 2, ..., n, where a is any number.

i51, 2, ..., n ãñ´,

Statement I : Variance of d1, d2, ..., dn is s2.

·¤ÍÙ I : d1, d2, ..., dn ·¤æ ÂýâÚU‡æ

Statement II : Mean and mode of

·¤ÍÙ II : d1, d2, ..., dn ·ð¤ ×æŠØ ÌÍæ ÕãéÜ·¤ ·ý¤×æàæÑ 2 x 2a ÌÍæ 2M2a ãñ

d 1 , d 2 , ..., d n are 2 x 2a and 2M2a, respectively (1)

Statement I and Statement II are

Áãæ¡ a ·¤æð§ü ⴁØæ ãñ´Ð

s2 ãñ´

(1)

·¤ÍÙ I ÌÍæ ·¤ÍÙ II ÎæðÙæð´ ¥âˆØ ãñ´Ð

(2)

·¤ÍÙ I ÌÍæ ·¤ÍÙ II ÎæðÙæð´ âˆØ ãñ´Ð

(3)

·¤ÍÙ I âˆØ ãñ ÌÍæ ·¤ÍÙ II ¥âˆØ ãñÐ

(4)

·¤ÍÙ I ¥âˆØ ãñ ÌÍæ ·¤ÍÙ II âˆØ ãñÐ

both false (2)

Statement I and Statement II are both true

(3)

Statement I is true and Statement II is false

(4)

Statement I is false and Statement II is true

88.

periodic function with period :

ȤÜÙ f ( x )5 sin 4x 1 cos 2x °·¤ ¥æßçÌü ȤÜÙ ãñ çÁâ·¤æ ¥æßÌü ·¤æÜ ãñ :

(1)

2p

(1)

2p

(2)

p

(2)

p

(3)

p 2

(3)

p 2

(4)

p 4

(4)

p 4

The function f ( x )5 sin 4x 1 cos 2 x , is a 88.

English : 47

Set : 10

Hindi : 47

Set : 10

89.

90.

43p  21   is : 89. The principal value of tan  cot 4   3p 4

(1)

2

(2)

3p 4

(3)

2

(4)

p 4

p 4

The contrapositive of the statement “if I 90. am not feeling well, then I will go to the

43p   tan21  cot  4  

·¤æ ×éØ×æÙ ãñ :

3p 4

(1)

2

(2)

3p 4

(3)

2

(4)

p 4

p 4

·¤ÍÙ ÒÒØçÎ ×ñ´ ¥SßSÍ ã¡ê, Ìæð ×ñ´ ÇUæ€ÅUÚU ·ð¤ Âæâ Á檡¤»æÓÓ ·¤æ ÂýçÌÏÙæˆ×·¤ ãñ

doctor” is : (1)

If I am feeling well, then I will not go to the doctor

(2)

If I will go to the doctor, then I am feeling well

(3)

If I will not go to the doctor, then I am feeling well

(4)

If I will go to the doctor, then I am not feeling well.

(1)

ØçÎ ×ñ´ SßSÍ ã¡ê, Ìæð ÇUæ€ÅUÚU ·ð¤ Âæâ Ùãè´ Á檡¤»æ

(2)

ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Á檡¤»æ, Ìæð ×ñ´ SßSÍ ã¡ê

(3)

ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Ùãè´ Á檡¤»æ, Ìæð ×ñ´ SßSÍ ã¡ê ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Á檡¤»æ, Ìæð ×ñ´ SßSÍ Ùãè´ ã¡êÐ

(4)

-o0o-

English : 48

-o0o-

Set : 10

Hindi : 48

Set : 10