JEE MAIN QUESTION PAPER -19.04.2014

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JEE MAIN QUESTION PAPER -19.04.2014

  1. 1. English : 1 Set : 10 Hindi : 1 Set : 10 PART A — PHYSICS 1. Match List - I (Event) with List - II (Order of the time interval for happening of the event) and select the correct option from the options given below the lists. (a) Rotation period of earth (i) 105 s (b) Revolution period of earth (ii) 107 s (c) Period of a light wave (iii) 10215 s (d) Period of a sound wave (iv) 1023 s List - I List - II (1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) (2) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii) (3) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) (4) (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv) Öæ» A — ÖæñçÌ·¤ çߙææÙ 1. 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 (a) §ÐûÄÍ œ‰Ë ìËÏøËá¾ œ‰ËÁ (i) 105 s (b) §ÐûÄÍ œ‰Ë §Ì¿Uœâ‰¼øË œ‰ËÁ (ii) 107 s (c) •œ‰ §âœ‰ËÅË ±¿™U  œ‰Ë œ‰ËÁ (iii) 10215 s (d) •œ‰ çÄ̾ ±¿™U  œ‰Ë œ‰ËÁ (iv) 1023 s ÇϤÍ- I ÇϤÍ- II (1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) (2) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii) (3) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) (4) (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
  2. 2. English : 2 Set : 10 Hindi : 2 Set : 10 2. A bullet looses th 1 n       of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be : (1) 2 n 2n 12 (2) 2 2n n 12 (3) Infinite (4) n 3. A heavy box is to be dragged along a rough 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 3 5 , the ratio F A F B is : (1) 3 (2) 5 3 (3) 3 2 (4) 2 3 2. °· ÕéÜðÅU°·¤ÌÌð âð»éÁÚUÙð ×ð´ ¥ÂÙð ßð» ·ð¤       1 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) 2 n 2n 12 (2) 2 2n n 12 (3) ¥Ù‹Ì (4) n 3. °·¤ 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¡·¤ 3 5 ãñ´, ÌÕ ¥ÙéÂæÌ F A F B ãñ´ : (1) 3 (2) 5 3 (3) 3 2 (4) 2 3
  3. 3. English : 3 Set : 10 Hindi : 3 Set : 10 4. Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration ‘a’ perpendicular to the axis of the cylinder. What is Ffriction at point P ? It is assumed that the cylinder does not slip. (1) Mg (2) Ma (3) Ma 2 (4) Ma 3 4. °·¤ 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 (2) Ma (3) Ma 2 (4) Ma 3
  4. 4. English : 4 Set : 10 Hindi : 4 Set : 10 5. 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 makes angle f with the horizontal. Then : (1) sin f5cos u (2) sin f5 1 2 cos u (3) sin f5 2 3 cos u (4) sin f5 3 4 cos u 5. °·¤ 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 (2) sin f5 1 2 cos u (3) sin f5 2 3 cos u (4) sin f5 3 4 cos u
  5. 5. English : 5 Set : 10 Hindi : 5 Set : 10 6. A ball of mass 160 g is thrown up at an 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) (1) 1.73 kg m2/s (2) 3.0 kg m2/s (3) 3.46 kg m2/s (4) 6.0 kg m2/s 7. The gravitational field in a region is given by g r 5 ˆ5N/kg i 1 ˆ12 N/kg j . The change in the gravitational potential energy of a particle of mass 2 kg when it is taken from the origin to a point (7 m,23 m) is : (1) 71 J (2) 13 58 J (3) 271 J (4) 1 J 6. 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 (2) 3.0 kg m2/s (3) 3.46 kg m2/s (4) 6.0 kg m2/s 7. °·¤ ÿæð˜æ ×ð´ »éL¤ˆßæ·¤áü‡æ ÿæð˜æ §â Âý·¤æÚU çÎØæ ÁæÌæ ãñ´ g r 5 ˆ5N/kg i 1 ˆ12 N/kg j 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´ : (1) 71 J (2) 13 58 J (3) 271 J (4) 1 J
  6. 6. English : 6 Set : 10 Hindi : 6 Set : 10 8. The velocity of water in a river is 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 water51022 poise. (1) 1021 N/m2 (2) 1022 N/m2 (3) 1023 N/m2 (4) 1024 N/m2 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 at which water flows through the tube is (g510 ms22) (1) 7.5 cc/s (2) 8.0 cc/s (3) 10.0 cc/s (4) 12.5 cc/s 8. °·¤ 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 (1) 1021 N/m2 (2) 1022 N/m2 (3) 1023 N/m2 (4) 1024 N/m2 9. 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) (1) 7.5 cc/s (2) 8.0 cc/s (3) 10.0 cc/s (4) 12.5 cc/s
  7. 7. English : 7 Set : 10 Hindi : 7 Set : 10 10. A large number of liquid drops each of 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 big drop is (given surface tension of liquid T, density r) (1)       T 1 1 r R 2 r (2)       2T 1 1 r R 2 r (3)       4T 1 1 r R 2 r (4)       6T 1 1 r R 2 r 10. 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) (1)       T 1 1 r R 2 r (2)       2T 1 1 r R 2 r (3)       4T 1 1 r R 2 r (4)       6T 1 1 r R 2 r
  8. 8. English : 8 Set : 10 Hindi : 8 Set : 10 11. A black coloured solid sphere of radius R 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 aT3 per unit mass with the temperature T of the sphere, where a is a constant, then the time taken for the sphere to cool down to temperature 2T0 will be (s is Stefan Boltzmann constant) (1) ln       2 M 3 4 R a p (2) ln       2 M 16 4 R a p (3) ln       2 M 16 16 R a p (4) ln       2 M 3 16 R a p 12. A gas is compressed from a volume of 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 : (1) Increases by 250 J (2) Decreases by 250 J (3) Increases by 50 J (4) Decreases by 50 J 11. °·¤ »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´) (1) ln       2 M 3 4 R a p (2) ln       2 M 16 4 R a p (3) ln       2 M 16 16 R a p (4) ln       2 M 3 16 R a p 12. °·¤ »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) 250 J âð Õɸð»è (2) 250 J âð ƒæÅðU»è (3) 50 J âð Õɸð»è (4) 50 J âð ƒæÅðU»è
  9. 9. English : 9 Set : 10 Hindi : 9 Set : 10 13. A gas molecule of mass M at the surface 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 attained is much less than radius of the earth. (kB is Boltzmann constant) (1) 0 (2) B273 k 2 Mg (3) B546 k 3 Mg (4) B819 k 2 Mg 14. A body is in simple harmonic motion with 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 its amplitude. (1) 4 cm/s (2) 6 cm/s (3) 12 cm/s (4) 16 cm/s 13. 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´) (1) 0 (2) B273 k 2 Mg (3) B546 k 3 Mg (4) B819 k 2 Mg 14. °·¤ 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 (1) 4 cm/s (2) 6 cm/s (3) 12 cm/s (4) 16 cm/s
  10. 10. English : 10 Set : 10 Hindi : 10 Set : 10 15. The total length of a sonometer wire 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 frequency with which three parts can vibrate ? (1) 1100 Hz (2) 1000 Hz (3) 166 Hz (4) 100 Hz 16. The electric field in a region of space is given by, o oE E 2 Ei j → ∧ ∧ 5 1 where E05100 N/C. The flux of this field through a circular surface of radius 0.02 m parallel to the Y-Z plane is nearly : (1) 0.125 Nm2/C (2) 0.02 Nm2/C (3) 0.005 Nm2/C (4) 3.14 Nm2/C 15. 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´ (1) 1100 Hz (2) 1000 Hz (3) 166 Hz (4) 100 Hz 16. ×é€Ì ¥æ·¤æàæ ·ð¤ °·¤ ÿæð˜æ ×ð´ çßléÌ ÿæð˜æ çÎØæ ÁæÌæ ãñ´ o oE E 2 Ei j → ∧ ∧ 5 1 Áãæ¡ E05100 N/CÐ 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 (1) 0.125 Nm2/C (2) 0.02 Nm2/C (3) 0.005 Nm2/C (4) 3.14 Nm2/C
  11. 11. English : 11 Set : 10 Hindi : 11 Set : 10 17. The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from Î1 at one plate to Î2 at the other. The capacitance of capacitor is : (1) Î0(Î11Î2)A/d (2) Î0(Î21Î1)A/2d (3) Î0A/[d ln(Î2/Î1)] (4) Î0(Î22Î1)A/[d 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 will be : (1) 0.45 A (2) 0.90 A (3) 1.35 A (4) 1.80 A 17. °·¤ 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 (2) Î0(Î21Î1)A/2d (3) Î0A/[d ln(Î2/Î1)] (4) Î0(Î22Î1)A/[d ln(Î2/Î1)] 18. ÂýˆØð·¤ 100 W ·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 (1) 0.45 A (2) 0.90 A (3) 1.35 A (4) 1.80 A
  12. 12. English : 12 Set : 10 Hindi : 12 Set : 10 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 left arm of the frame is at x510 cm from the wire is : (1) 2 mV (2) 1 mV (3) 0.75 mV (4) 0.5 mV 19. 10 cm ÖéÁæ ·¤æ °·¤ ß»æü·¤æÚU Èðý¤× ¥æñÚU ÏæÚUæ 1 A âð ÂýßæçãÌ °·¤ ܐÕæ âèÏæ ÌæÚU ·¤æ»$Á ·ð¤ ÌÜ ×ð´ ÚU¹ð ãñ´Ð ÌæÚU ·ð¤ â×è âð, Èýð¤× Îæ¡Øè ¥æðÚU °·¤ çSÍÚU ¿æÜ 10 ms21 âð »çÌ ·¤ÚUÌæ ãñ´Ð (翘æ Îð¹ð´)Ð ÌæÚU âð ÁÕ Èýð¤× ·¤è Õæ¡Øè ÖéÁæ x510 cm ÂÚU ãñ´ ÌÕ ©â â×Ø ÂýðçÚUÌ çßléÌ ßæã·¤ ÕÜ ãñ´ Ñ (1) 2 mV (2) 1 mV (3) 0.75 mV (4) 0.5 mV
  13. 13. English : 13 Set : 10 Hindi : 13 Set : 10 20. An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, the magnetic field Bs inside the superconductor will be such that : (1) Bs52B (2) Bs50 (3) Bs5B (4) BsB but Bs ≠ 0 20. ¥çÌ¿æÜ·¤ ¥æÎàæü ¥Ùé¿éÕ·¤ ·¤æ °·¤ ©ÎæãÚU‡æ ãñÐ §â·¤æ ¥Íü ãñ ç·¤ ÁÕ ÌèßýÌæ B ·ð¤ °·¤ ¿éÕ·¤èØ ÿæð˜æ ×ð´ ¥çÌ¿æÜ·¤ ·¤æð ÚU¹æ ÁæÌæ ãñ´, ÌÕ ¥çÌ¿æÜ·¤ ·ð¤ ¥‹ÎÚU ¿éÕ·¤èØ ÿæð˜æ Bs §â Âý·¤æÚU ãæð»æ Ñ (1) Bs52B (2) Bs50 (3) Bs5B (4) BsB ÂÚ´UÌé Bs ≠ 0
  14. 14. English : 14 Set : 10 Hindi : 14 Set : 10 21. Figure shows a circular area of radius R where a uniform magnetic field B → is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r) ? (1) (2) 21. 翘æ ç˜æ’Øæ R ·ð¤ °·¤ ßëžæèØ ÿæð˜æÈ¤Ü ·¤æð ÎàææüÌæ ãñ Áãæ¡ °·¤ °·¤â×æÙ ¿éÕ·¤èØ ÿæð˜æ B → ·¤æ»$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? (1) (2)
  15. 15. English : 15 Set : 10 Hindi : 15 Set : 10 (3) (4) 22. If denote microwaves, X rays, infrared, 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 (2) M, R, V, X, U, G and I (3) G, X, U, V, I, M and R (4) I, M, R, U, V, X and G (3) (4) 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 (1) R, M, I, V, U, X ¥æñÚU G (2) M, R, V, X, U, G ¥æñÚU I (3) G, X, U, V, I, M ¥æñÚU R (4) I, M, R, U, V, X ¥æñÚU G
  16. 16. English : 16 Set : 10 Hindi : 16 Set : 10 23. A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is uiC and the Brewster’s angle of incidence is uiB, such that sinuiC/sinuiB5h51.28. The relative refractive index of the two media is : (1) 0.2 (2) 0.4 (3) 0.8 (4) 0.9 24. The diameter of the objective lens of microscope makes an angle b at the focus 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. (1) Increases with decreasing value of n (2) Increases with decreasing value of b (3) Increases with increasing value of n sin 2b (4) Increases with increasing value of 1 n sin 2b 23. °·¤ 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 (3) 0.8 (4) 0.9 24. °·¤ âêÿ×Îàæèü ·ð¤ ¥çÖÎëàØ·¤ 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) n ·¤æ ×æÙ ƒæÅUÙð âð Õɸð»è (2) b ·¤æ ×æÙ ƒæÅUÙð âð Õɸð»è (3) n sin 2b ·¤æ ×æÙ ÕɸÙð âð Õɸð»è (4) 1 n sin 2b ·¤æ ×æÙ ÕɸÙð âð Õɸð»è
  17. 17. English : 17 Set : 10 Hindi : 17 Set : 10 25. In a Young’s double slit experiment, the 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 slit diffraction pattern is : (1) 3 (2) 6 (3) 12 (4) 24 25. 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 (1) 3 (2) 6 (3) 12 (4) 24
  18. 18. English : 18 Set : 10 Hindi : 18 Set : 10 26. Match List - I (Experiment performed) with List - II (Phenomena discovered/ associated) and select the correct option from the options given below the lists : (a) Davisson and Germer Experiment (i) Wave nature of electrons (b) Millikan’s oil drop experiment (ii) Charge of an electron (c) Rutherford experiment (iii) Quantisation of energy levels (d) Franck - Hertz experiment (iv) Existence of nucleus List - I List - II (1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) (2) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) (3) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) (4) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) 26. 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 (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 (c) ¿U³¿U­‰ËÕ¬áU §â½ËÕ  (iii) ‰¦Ëá S±¿U œ‰Ë þÄËøªÍœ‰¿UøË (d) ­Ö♉œ‰ - ȪáU¦ §â½ËÕ  (iv) ¾ËÌ»œ‰ œ‰Ë ŠÌS±íÄ ÇÏ¤Í - I ÇÏ¤Í - II (1) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) (2) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) (3) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) (4) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
  19. 19. English : 19 Set : 10 Hindi : 19 Set : 10 27. A piece of wood from a recently cut tree 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 approximately : (1) 10439 years (2) 13094 years (3) 19039 years (4) 39049 years 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 27. °·¤ 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 (1) 10439 ßáü (2) 13094 ßáü (3) 19039 ßáü (4) 39049 ßáü 28. 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
  20. 20. English : 20 Set : 10 Hindi : 20 Set : 10 29. Long range radio transmission is possible when the radiowaves are reflected from the ionosphere. For this to happen the frequency of the radiowaves must be in the range : (1) 80 - 150 MHz (2) 8 - 25 MHz (3) 1 - 3 MHz (4) 150 - 500 kHz 29. 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 (1) 80 - 150 MHz (2) 8 - 25 MHz (3) 1 - 3 MHz (4) 150 - 500 kHz
  21. 21. English : 21 Set : 10 Hindi : 21 Set : 10 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 against the string length of the pendulum in the figure. What is the value of g at the place ? (1) 9.81 m/s2 (2) 9.87 m/s2 (3) 9.91 m/s2 (4) 10.0 m/s2 30. °·¤ 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 §â SÍæÙ ÂÚU g ·¤æ ×æÙ ãñ´Ð (1) 9.81 m/s2 (2) 9.87 m/s2 (3) 9.91 m/s2 (4) 10.0 m/s2
  22. 22. English : 22 Set : 10 Hindi : 22 Set : 10 PART B — CHEMISTRY 31. Ionization energy of gaseous Na atoms is 495.5 kJmol21. The lowest possible frequency of light that ionizes a sodium atom is (h56.626310234 Js, NA56.02231023 mol21) (1) 7.503104 s21 (2) 4.7631014 s21 (3) 3.1531015 s21 (4) 1.2431015 s21 32. Choose the correct statement with respect to the vapour pressure of a liquid among the following : (1) Increases linearly with increasing temperature (2) Increases non-linearly with increasing temperature (3) Decreases linearly with increasing temperature (4) Decreases non-linearly with increasing temperature Öæ» B — ÚUâæØÙ çߙææÙ 31. »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 (2) 4.7631014 s21 (3) 3.1531015 s21 (4) 1.2431015 s21 32. ç·¤âè Îýß ·ð¤ ßæc ÎæÕ ·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ ×ð´ âð âãè °·¤ ·¤ÍÙ ·¤æð ¿éçÙ° Ñ (1) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU ÕɸÌæ ãñÐ (2) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ Ù âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU ÕɸÌæ ãñÐ (3) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU ƒæÅUÌæ ãñÐ (4) ÕɸÌð ÌæÂ×æÙ ·ð¤ âæÍ Ù âèÏè ÚðU¹æ ·ð¤ ¥ÙéâæÚU ƒæÅUÌæ ãñÐ
  23. 23. English : 23 Set : 10 Hindi : 23 Set : 10 33. Which one of the following molecules is paramagnetic ? (1) N2 (2) NO (3) CO (4) O3 34. Zirconium phosphate [Zr3(PO4)4] 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 Ksp is correct ? (1) S5{Ksp/(6912)1/7} (2) S5{Ksp/144}1/7 (3) S5(Ksp/6912)1/7 (4) S5{Ksp/6912}7 33. çِ٠¥‡æé¥æð´ ×ð´ âð ·¤æñÙ ¥Ùé¿éÕ·¤èØ ãñ? (1) N2 (2) NO (3) CO (4) O3 34. 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} (2) S5{Ksp/144}1/7 (3) S5(Ksp/6912)1/7 (4) S5{Ksp/6912}7
  24. 24. English : 24 Set : 10 Hindi : 24 Set : 10 35. For the decomposition of the compound, represented as NH2COONH4(s)ì 2NH3(g)1CO2(g) the Kp52.931025 atm3. If the reaction is started with 1 mol of the compound, the total pressure at equilibrium would be : (1) 1.9431022 atm (2) 5.8231022 atm (3) 7.6631022 atm (4) 38.831022 atm 36. For the reaction, 3A12B ® C1D, the differential rate law can be written as : (1) [ ] [ ] [ ] [ ]n md A d C1 k A B 3 dt dt 5 5 (2) [ ] [ ] [ ] [ ]n md A d C k A B dt dt 2 5 5 (3) [ ] [ ] [ ] [ ]n md A d C1 k A B 3 dt dt 1 52 5 (4) [ ] [ ] [ ] [ ]n md A d C1 k A B 3 dt dt 2 5 5 35. NH2COONH4(s)ì 2NH3(g)1CO2(g) âð âêç¿Ì Øæñç»·¤ ·ð¤ çßØæðÁÙ ·ð¤ çÜØð Kp52.931025 atm3 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 (1) 1.9431022 atm (2) 5.8231022 atm (3) 7.6631022 atm (4) 38.831022 atm 36. ¥çÖç·ý¤Øæ 3A12B ® C1D ·ð¤ çÜØð ¥ß·¤Ü ÎÚU çÙØ× çܹæ Áæ â·¤Ìæ ãñ Ñ (1) [ ] [ ] [ ] [ ]n md A d C1 k A B 3 dt dt 5 5 (2) [ ] [ ] [ ] [ ]n md A d C k A B dt dt 2 5 5 (3) [ ] [ ] [ ] [ ]n md A d C1 k A B 3 dt dt 1 52 5 (4) [ ] [ ] [ ] [ ]n md A d C1 k A B 3 dt dt 2 5 5
  25. 25. English : 25 Set : 10 Hindi : 25 Set : 10 37. Sulphur dioxide and oxygen were allowed 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 mass of sulphur532 u) : (1) 7.09 (2) 14.1 (3) 10.0 (4) 28.2 38. The observed osmotic pressure for a 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 Hoff factor (i) will be respectively : (R50.082 L atm k2mol21) (1) 5 and 4.42 (2) 4 and 4.00 (3) 5 and 3.42 (4) 3 and 5.42 37. °·¤ 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 (1) 7.09 (2) 14.1 (3) 10.0 (4) 28.2 38. 258 C 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 (R50.082 L atm k2×æðÜ21) (1) 5 ¥æñÚU 4.42 (2) 4 ¥æñÚU 4.00 (3) 5 ¥æñÚU 3.42 (4) 3 ¥æñÚU 5.42
  26. 26. English : 26 Set : 10 Hindi : 26 Set : 10 39. The total number of octahedral void(s) per atom present in a cubic close packed structure is : (1) 2 (2) 4 (3) 1 (4) 3 40. For an ideal solution of two components A and B, which of the following is true ? (1) DHmixing 0 (zero) (2) DHmixing 0 (zero) (3) A2B interaction is stronger than A2A and B2B interactions (4) A2A, B2B and A2B interactions are identical 41. Consider the reaction : 4 2 2 3(aq) (aq) 2 ( ) (aq) 4(aq) (aq)H SO Sn H O Sn HSO 3Hl →1 1 2 1 1 1 1 1 Which of the following statements is correct ? (1) Sn41 is the oxidizing agent because it undergoes oxidation (2) Sn41is the reducing agent because it undergoes oxidation (3) H2SO3 is the reducing agent because it undergoes oxidation (4) H2SO3 is the reducing agent because it undergoes reduction 39. 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 (2) 4 (3) 1 (4) 3 40. Îæð ƒæÅU·¤æð´ A ¥æñÚU B ·ð¤ ¥æÎàæü çßÜØÙ ·ð¤ çÜØð çِÙæð´ ×ð´ âð ·¤æñÙ âãè ãæð»æ? (1) DHçןæ‡æ 0 (zero) (2) DHçןæ‡æ 0 (zero) (3) A2A ¥æñÚU B2B ·¤è ÂÚUSÂÚU ÂýÖæß âð A2B ·¤æ ÂÚUSÂÚU ÂýÖæß ¥çÏ·¤ ÂýÕÜ ãæð»æÐ (4) A2A, B2B ¥æñÚU A2B âÖè ÂÚUSÂÚU ÂýÖæß °·¤ â×æÙ ãñ´Ð 41. ¥çÖç·ý¤Øæ 4 2 2 2 ( )3 4 H SO Sn H O Sn HSO 3Hl →1 1 2 11 1 1 1(¦Áͽ) (¦Áͽ) (¦Áͽ) (¦Áͽ) (¦Áͽ) ·ð¤ âÕ‹Ï ×ð´ çِ٠·¤ÍÙæð´ ×ð´ âð ·¤æñÙ-âæ âãè ãñ? (1) Sn41 ¥æ€âè·¤æÚU·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ ãæðÌæ ãñÐ (2) Sn41¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ ãæðÌæ ãñÐ (3) H2SO3 ¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ©Â¿ØÙ ãæðÌæ ãñÐ (4) H2SO3 ¥Â¿æØ·¤ ãñ €Øæð´ç·¤ §â·¤æ ¥Â¿ØÙ ãæðÌæ ãñÐ
  27. 27. English : 27 Set : 10 Hindi : 27 Set : 10 42. Which one of the following has largest ionic radius ? (1) Li1 (2) 2 2O 2 (3) B31 (4) F2 43. An octahedral complex with molecular composition M.5NH3.Cl.SO4 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 : (1) Linkage isomerism (2) Ionisation isomerism (3) Coordinate isomerism (4) Geometrical isomerism 44. How many electrons are involved in the following redox reaction ? Cr2O7 221Fe211 2 2 4C O 2 ® Cr311Fe311CO2 (Unbalanced) (1) 3 (2) 4 (3) 6 (4) 5 42. çِÙæð´ ×ð´ âð ç·¤â·¤è ¥æØçÙ·¤ ç˜æ’Øæ ¥çÏ·¤Ì× ãñ? (1) Li1 (2) 2 2O 2 (3) B31 (4) F2 43. ¥‡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) çÜ´·ð¤Á (â´Øæð»è) â×-¥ßØßÌæ (2) ¥æØÙè â×-¥ßØßÌæ (3) â׋ßØè â×-¥ßØßÌæ (4) ’Øæç×çžæØ â×-¥ßØßÌæ 44. çِ٠¥Â¿ØÙ-©Â¿ØÙ ¥çÖç·ý¤Øæ ×ð´ ç·¤ÌÙð §Üð€ÅþUæÙ âãÖæ»è ãñ´? Cr2O7 221Fe211 2 2 4C O 2 ® Cr311Fe311CO2 (¥â´ÌéçÜÌ) (1) 3 (2) 4 (3) 6 (4) 5
  28. 28. English : 28 Set : 10 Hindi : 28 Set : 10 45. Amongst LiCl, RbCl, BeCl2 and MgCl2 the compounds with the greatest and the least ionic character, respectively are : (1) LiCl and RbCl (2) RbCl and BeCl2 (3) MgCl2 and BeCl2 (4) RbCl and MgCl2 46. Nickel(Z528) combines with a uninegative monodentate ligand to form a diamagnetic complex [NiL4]22. The hybridisation involved and the number of unpaired electrons present in the complex are respectively : (1) sp3, two (2) dsp2, zero (3) dsp2, one (4) sp3, zero 47. Which of these statements is not true ? (1) NO1 is not isoelectronic with O2 (2) 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. 45. 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 46. 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 (1) sp3, Îæð (2) dsp2, àæê‹Ø (3) dsp2, °·¤ (4) sp3, àæê‹Ø 47. §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
  29. 29. English : 29 Set : 10 Hindi : 29 Set : 10 48. Example of a three-dimensional silicate is : (1) Zeolites (2) Ultramarines (3) Feldspars (4) Beryls 49. Amongst the following, identify the species with an atom in 16 oxidation state : (1) [MnO4]2 (2) [Cr(CN)6]32 (3) Cr2O3 (4) CrO2Cl2 50. Which one of the following ores is known as Malachite : (1) Cu2O (2) Cu2S (3) CuFeS2 (4) Cu(OH)2.CuCO3 51. The major product formed when 1, 1, 12 trichloro - propane is treated with aqueous potassium hydroxide is : (1) Propyne (2) 1 - Propanol (3) 2 - Propanol (4) Propionic acid 48. ç˜æ-çß×èØ çâçÜ·ð¤ÅUæ𴠷𤠩ÎæãÚU‡æ ãñ´ Ñ (1) ç$ÁØæðÜæ§Åð´U (2) ¥ËÅþUæ×ñÚUèÙð´ (3) Èð¤ËÇUSÂæÚð´U (4) ÕðçÚUÜð´ 49. çِÙæð´ ×ð´ 16 ©Â¿ØÙ ¥ßSÍæ ·ð¤ ÂÚU×æ‡æé ßæÜð SÂèàæè$Á ·¤è Âã¿æÙ ·¤èçÁØðÐ (1) [MnO4]2 (2) [Cr(CN)6]32 (3) Cr2O3 (4) CrO2Cl2 50. çِ٠×ð´ âð ·¤æñÙ ×ñÜæ·¤æ§ÅU ¥ØS·¤ Ùæ× âð ÁæÙè ÁæÌè ãñ Ñ (1) Cu2O (2) Cu2S (3) CuFeS2 (4) Cu(OH)2.CuCO3 51. 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
  30. 30. English : 30 Set : 10 Hindi : 30 Set : 10 52. Which one of the following is an example of thermosetting polymers ? (1) Neoprene (2) Buna -N (3) Nylon 6, 6 (4) Bakelite 53. The correct IUPAC name of the following compound is : (1) 4 - methyl - 3 - ethylhexane (2) 3 - ethyl - 4 - methylhexane (3) 3, 4 - ethylmethylhexane (4) 4 - ethyl - 3 - methylhexane 54. Which one of the following substituents at para-position is most effective in stabilizing the phenoxide , ion ? (1) 2CH3 (2) 2OCH3 (3) 2COCH3 (4) 2CH2OH 52. §Ù ×ð´ âð ·¤æñÙ ÌæÂÎëɸ ÕãéÜ·¤ ãñ? (1) çÙØæðÂýèÙ (2) ÕêÙæ - N (3) Ùæ§ÜæÙ 6, 6 (4) Õñ·ð¤Üæ§ÅU 53. §â Øæñç»·¤ ·¤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 54. çِ٠ÂýçÌSÍæ·¤æð´ ×ð´ âð ·¤æñÙ Èñ¤Ùæ€âæ§ÇU ¥æØÙ , ·ð¤ ÂñÚUæ SÍæÙ ÂÚU ãæðÙð âð §âð ¥çÏ·¤Ì× SÍæØè ÕÙæÙð ×ð´ ÂýÖæßè ãæðÌæ ãñ? (1) 2CH3 (2) 2OCH3 (3) 2COCH3 (4) 2CH2OH
  31. 31. English : 31 Set : 10 Hindi : 31 Set : 10 55. The final product formed when Methyl amine is treated with NaNO2 and HCl is : (1) Diazomethane (2) Methylalcohol (3) Methylcyanide (4) Nitromethane 56. Which one of the following compounds will not be soluble in sodium bicarbonate ? (1) 2, 4, 6 - Trinitrophenol (2) Benzoic acid (3) o - Nitrophenol (4) Benzene sulphonic acid 57. Williamson synthesis of ether is an example of : (1) Nucleophilic addition (2) Electrophilic addition (3) Electrophilic substitution (4) Nucleophilic substitution 55. ×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) ÇU槰ð$Áæð×èÍðÙ (2) ×ðçÍÜ °ðË·¤æðãæÜ (3) ×ðçÍÜçâØæÙæ§ÇU (4) Ùæ§ÅþUæð×èÍðÙ 56. §Ù×ð´ âð ·¤æñÙ-âæ Øæñç»·¤ âæðçÇUØ× Õ槷¤æÕæðüÙðÅU ×ð´ Ùãè´ ƒæéÜð»æ? (1) 2, 4, 6 - ÅþUæ§üÙæ§ÅþUæðç$ȤÙæòÜ (2) Õñ‹$Áæ𧷤 °ðçâÇU (3) o - Ùæ§ÅþUæðç$ȤÙæòÜ (4) Õñ‹$ÁèÙ âË$ȤæçÙ·¤ °ðçâÇU 57. §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
  32. 32. English : 32 Set : 10 Hindi : 32 Set : 10 58. The reason for double helical structure of DNA is the operation of : (1) Electrostatic attractions (2) van der Waals forces (3) Dipole - Dipole interactions (4) Hydrogen bonding 59. Among the following organic acids, the acid present in rancid butter is : (1) Pyruvic acid (2) Lactic acid (3) Butyric acid (4) Acetic acid 58. §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 59. 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
  33. 33. English : 33 Set : 10 Hindi : 33 Set : 10 60. In a set of reactions p - nitrotoluene yielded a product E The product E would be : (1) (2) (3) (4) 60. ¥çÖç·ý¤Øæ¥æ𴠷𤠧⠷ý¤× ×ð´ p - Ùæ§ÅþUæðÅUæËØé§üÙ âð ÂýæŒÌ ç·ý¤ØæÈ¤Ü E ãæð»æ Ñ (1) (2) (3) (4)
  34. 34. English : 34 Set : 10 Hindi : 34 Set : 10 PART C — MATHEMATICS 61. Let f : R®R be defined by f(x)5 1 1 x x 2 1 then f is : (1) both one - one and onto (2) one - one but not onto (3) onto but not one - one (4) neither one - one nor onto. 62. For all complex numbers z of the form 11ia, a e R, if z25x1iy, then : (1) y224x1250 (2) y214x2450 (3) y224x1450 (4) y214x1250 63. The equation 2 3 5x x1 1 5x23, where x is real, has : (1) no solution (2) exactly one solution (3) exactly two solutions (4) exactly four solutions. Öæ» C — »ç‡æÌ 61. ×æÙæ f : R®R , f(x)5 1 1 x x 2 1 mæÚUæ ÂçÚUÖæçáÌ ãñ, Ìæð f : (1) °·ñ¤·¤è ÌÍæ ¥æ‘ÀUæÎè ÎæðÙæð´ ãñ´Ð (2) °·ñ¤·¤è ãñ ÂÚ ¥æ‘ÀUæÎè Ùãè´ ãñÐ (3) ¥æ‘ÀUæÎè ãñ ÂÚU °·ñ¤·¤è Ùãè´ ãñÐ (4) Ù Ìæð °·ñ¤·¤è ãñ ¥æñÚU Ù ãè ¥æ‘ÀUæÎè ãñÐ 62. 11ia, a e R ·¤è Âý·¤æÚU ·¤è âÖè âç×Ÿæ ⴁØæ¥æð´ z ·ð¤ çÜØð, ØçÎ z25x1iy ãñ, Ìæð : (1) y224x1250 (2) y214x2450 (3) y224x1450 (4) y214x1250 63. â×è·¤ÚU‡æ 2 3 5x x1 1 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
  35. 35. English : 35 Set : 10 Hindi : 35 Set : 10 64. Let A and B be any two 333 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB2BA is : (1) skewsymmetric (2) symmetric (3) neither symmetric nor skewsymmetric (4) I or 2I, where I is an identity matrix. 65. If ( ) ( ) ( )( ) r 2 r 2r 1 3r 2 n n 1 a 2 1 1 n n 1 n 1 n 1 3n 4 2 2 2 2 D 5 2 2 2 2 1 , then the value of ∑ n 1 r r 1 2 D 5 : (1) depends only on a (2) depends only on n (3) depends both on a and n (4) is independent of both a and n. 64. ×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 AB2BA : (1) çßá× â×ç×Ì ãñ (2) â×ç×Ì ãñ (3) Ù Ìæð â×ç×Ì ãñ´ ¥æñÚU Ù ãè çßá× â×ç×Ì ãñ (4) I ¥Íßæ 2I ãñ´, Áãæ¡ I °·¤ ̈â×·¤ ¥æÃØêã ãñÐ 65. ØçÎ ( ) ( ) ( )( ) r 2 r 2r 1 3r 2 n n 1 a 2 1 1 n n 1 n 1 n 1 3n 4 2 2 2 2 D 5 2 2 2 2 1 ãñ´, Ìæð ∑ n 1 r r 1 2 D 5 ·¤æ ×æÙ : (1) ·ð¤ßÜ a ÂÚU çÙÖüÚU ãñ (2) ·ð¤ßÜ n ÂÚU çÙÖüÚU ãñ (3) a ÌÍæ n ÎæðÙæð´ ÂÚU çÙÖüÚU ãñ´ (4) a ÌÍæ n ÎæðÙæð´ âð SßÌ´˜æ ãñ´Ð
  36. 36. English : 36 Set : 10 Hindi : 36 Set : 10 66. Two women and some men participated 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 them- selves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval : (1) [8, 9] (2) [10, 12) (3) (11, 13] (4) (14, 17) 67. The coefficient of x1012 in the expansion of (11xn1x253)10, (where n £ 22 is any positive integer), is : (1) 1 (2) 10C4 (3) 4n (4) 253C4 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´Ùðð ÂýçÌØæð»èÌæ ×ð´ Öæ» çÜØæ, çِ٠¥´ÌÚUæÜ ×ð´ ãñ´ Ñ (1) [8, 9] (2) [10, 12) (3) (11, 13] (4) (14, 17) 67. (11xn1x253)10, (Áã¡æ n £ 22 ·¤æð§ü ÏÙ Âê‡ææZ·¤ ãñ´)·ð¤ ÂýâæÚU ×ð´ x1012 ·¤æ »é‡ææ´·¤ ãñ´ Ñ (1) 1 (2) 10C4 (3) 4n (4) 253C4
  37. 37. English : 37 Set : 10 Hindi : 37 Set : 10 68. The number of terms in an A.P. is even; the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by 10 1 2 , then the number of terms in the A.P. is : (1) 4 (2) 8 (3) 12 (4) 16 69. Let f(n) 5 n n      1 3 3 100 1 , where [n] denotes the greatest integer less than or equal to n. Then ( )f n∑ 56 n 15 is equal to : (1) 56 (2) 689 (3) 1287 (4) 1399 68. 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 ãñÐ ØçÎ ¥´çÌ× ÂÎ, ÂýÍ× ÂÎ âð 10 1 2 ¥çÏ·¤ ãñ, Ìæð â×æ´ÌÚU Ÿæðɸè ×ð´ ÂÎæð´ ·¤è ⴁØæ ãñ Ñ (1) 4 (2) 8 (3) 12 (4) 16 69. ×æÙæ f(n)5 n n      1 3 3 100 1 , Áãæ¡ [n] °·¤ ×ãžæ× Âê‡ææZ·¤, Áæð n âð ÀUæðÅUæ ¥Íßæ ÕÚUæÕÚU ãñ, Ìæð ( )f n∑ 56 n 15 ÕÚUæÕÚU ãñ Ñ (1) 56 (2) 689 (3) 1287 (4) 1399
  38. 38. English : 38 Set : 10 Hindi : 38 Set : 10 70. If the function ( )2 2 cos 1 , ( ) k , x x f x x x  ≠    1 2 p 5 p 2 5p is continuous at x5p, then k equals : (1) 0 (2) 1 2 (3) 2 (4) 1 4 71. Let f: R ® R be a function such that ?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. 70. ØçΠȤÜÙ ( )2 2 cos 1 , ( ) k , x x f x x x  ≠    1 2 p 5 p 2 5p x5p ÂÚU âÌÌ ãñ, Ìæð k ÕÚUæÕÚU ãñ : (1) 0 (2) 1 2 (3) 2 (4) 1 4 71. ×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
  39. 39. English : 39 Set : 10 Hindi : 39 Set : 10 72. If non-zero real numbers b and c are such that min f(x) max g(x), where f(x)5x212bx12c2 and g(x)52x222cx1b2 (x e R) ; then c b lies in the interval : (1) 1 0, 2       (2)     1 1 , 2 2 (3) 1 , 2 2       (4) ( )2,∞ 73. If the volume of a spherical ball is 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, is : (1) 1 6 (2) 1 9 (3) 1 36 (4) 1 24 72. 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´, Ìæð c b çÁâ ¥´ÌÚUæÜ ×ð´ ãñ, ßã ãñ : (1) 1 0, 2       (2)     1 1 , 2 2 (3) 1 , 2 2       (4) ( )2 ,∞ 73. 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 : (1) 1 6 (2) 1 9 (3) 1 36 (4) 1 24
  40. 40. English : 40 Set : 10 Hindi : 40 Set : 10 74. If m is a non - zero number and ( ) 5 1 4 1 32 2 d ( ) c 1 m m m m x x x f x x x ∫ 2 2 1 5 1 1 1 , then f(x) is : (1) ( ) 5 22 2 1 m m m x m x x1 1 (2) ( ) 4 22 2 1 m m m x m x x1 1 (3) ( ) ( ) 5 4 22 2 1 m m m m m x x x x 1 1 1 (4) ( ) ( ) 5 4 22 2 1 m m m m x x m x x 2 1 1 74. ØçÎ m °·¤ àæê‹ØðÌÚU ⴁØæ ãñ ÌÍæ ( ) 5 1 4 1 32 2 d ( ) c 1 m m m m x x x f x x x ∫ 2 2 1 5 1 1 1 ãñ, Ìæð f(x) ãñ : (1) ( ) 5 22 2 1 m m m x m x x1 1 (2) ( ) 4 22 2 1 m m m x m x x1 1 (3) ( ) ( ) 5 4 22 2 1 m m m m m x x x x 1 1 1 (4) ( ) ( ) 5 4 22 2 1 m m m m x x m x x 2 1 1
  41. 41. English : 41 Set : 10 Hindi : 41 Set : 10 75. Let function F be defined as t 1 e ( ) dt , 0 t x F x x ∫5 then the value of the integral x ∫ t 1 e dt t a1 , where a 0, is : (1) ea[F(x)2F(11a)] (2) e2a[F(x1a)2F(a)] (3) ea[F(x1a)2F(11a)] (4) e2a[F(x1a)2F(11a)] 76. The area of the region above the x-axis bounded by the curve y5tan x, 0 £ x £ 2 p and the tangent to the curve at x5 4 p is : (1) 1 1 log 2 2 2       2 (2) 1 1 log 2 2 2       1 (3) ( ) 1 1 log 2 2 2 (4) ( ) 1 1 log 2 2 1 75. ×æÙæ ȤÜÙ F, t 1 e ( ) dt , 0 t x F x x ∫5 mæÚUæ ÂçÚUÖæçáÌ ãñ, Ìæð â×æ·¤Ü x ∫ t 1 e dt t a1 , Áãæ¡ a 0 ãñ, ·¤æ ×æÙ ãñ : (1) ea[F(x)2F(11a)] (2) e2a[F(x1a)2F(a)] (3) ea[F(x1a)2F(11a)] (4) e2a[F(x1a)2F(11a)] 76. ß·ý¤ y5tan x, 0 £ x £ 2 p ÌÍæ ß·ý ÂÚU x5 4 p ÂÚU ¹è´¿è »§ü SÂàæü ÚðU¹æ mæÚUæ çƒæÚðU ÿæð˜æ, Áæð x ¥ÿæ â𠪤ÂÚU ãñ, ·¤æ ÿæð˜æÈ¤Ü ãñ : (1) 1 1 log 2 2 2       2 (2) 1 1 log 2 2 2       1 (3) ( ) 1 1 log 2 2 2 (4) ( ) 1 1 log 2 2 1
  42. 42. English : 42 Set : 10 Hindi : 42 Set : 10 77. If y x d d 1y tan x5sin 2x and y(0)51, then y(p) is equal to : (1) 1 (2) 21 (3) 25 (4) 5 78. The circumcentre of a triangle lies at the 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 lies on the line : (1) y22ax50 (2) y2(a211)x50 (3) y1x50 (4) (a21)2x2(a11)2y50 77. ØçÎ y x d d 1y tan x5sin 2x ÌÍæ y(0)51 ãñ Ìæð y(p) ÕÚUæÕÚU ãñ : (1) 1 (2) 21 (3) 25 (4) 5 78. °·¤ 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 (1) y22ax50 (2) y2(a211)x50 (3) y1x50 (4) (a21)2x2(a11)2y50
  43. 43. English : 43 Set : 10 Hindi : 43 Set : 10 79. If a line L is perpendicular to the line 5x2y51, and the area of the triangle formed by the line L and the coordinate axes is 5, then the distance of line L from the line x15y50 is : (1) 7 5 (2) 5 13 (3) 7 13 (4) 5 7 80. The equation of the circle described on the chord 3x1y1550 of the circle x21y2516 as diameter is : (1) x21y213x1y21150 (2) x21y213x1y1150 (3) x21y213x1y2250 (4) x21y213x1y22250 79. 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 : (1) 7 5 (2) 5 13 (3) 7 13 (4) 5 7 80. ßëžæ x21y2516 ·¤è °·¤ Áèßæ 3x1y1550 ·¤æð ÃØæâ ×æÙ·¤Ú ¹è´¿ð »° ßëžæ ·¤æ â×è·¤ÚU‡æ ãñ : (1) x21y213x1y21150 (2) x21y213x1y1150 (3) x21y213x1y2250 (4) x21y213x1y22250
  44. 44. English : 44 Set : 10 Hindi : 44 Set : 10 81. A chord is drawn through the focus of the parabola y256x such that its distance from the vertex of this parabola is 5 2 , then its slope can be : (1) 5 2 (2) 3 2 (3) 2 5 (4) 2 3 82. The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola 22 1 4 5 yx 2 5 ,meets x - axis and y - axis at A and B respectively. Then (OA)22(OB)2, where O is the origin, equals : (1) 20 9 2 (2) 16 9 (3) 4 (4) 4 3 2 81. ÂÚUßÜØ y256x ·¤è ÙæçÖ âð ãæð·¤ÚU ÁæÌè °·¤ Áèßæ ¹è´¿è »§ü ãñ çÁâ·¤è ÂÚUßÜØ ·ð¤ àæèáü âð ÎêÚUè 5 2 ãñ, Ìæð §â·¤è ÉUæÜ ãæð â·¤Ìè ãñ : (1) 5 2 (2) 3 2 (3) 2 5 (4) 2 3 82. ¥çÌÂÚUßÜØ 22 1 4 5 yx 2 5 ·ð¤ ÙæçÖÜ´Õ ·ð¤ °·¤ çâÚðU (Áæð ÂýÍ× ¿ÌéÍæZàæ ×ð´ ãñ) ÂÚU ¹è´¿è »§ü SÂàæü ÚðU¹æ x-¥ÿæ ÌÍæ y-¥ÿæ ·¤æð ·ý ×àæ çՋÎé¥æð´ A ÌÍæ B ÂÚU ç×ÜÌè ãñ´, Ìæð (OA)22(OB)2, Áãæ¡ O ×êÜ çÕ´Îé ãñ, ÕÚUæÕÚU ãñ : (1) 20 9 2 (2) 16 9 (3) 4 (4) 4 3 2
  45. 45. English : 45 Set : 10 Hindi : 45 Set : 10 83. Equation of the line of the shortest distance between the lines yx z 1 1 1 5 5 2 and yx z11 0 2 1 12 5 5 2 is : (1) yx z 1 1 2 5 5 2 2 (2) yx z11 1 1 2 12 5 5 2 2 (3) yx z11 1 1 1 12 5 5 2 (4) yx z 2 1 2 5 5 2 84. If the angle between the line 2(x11)5y5z14 and the plane 2x2y1 l z1450 is 6 p , then the value of l is : (1) 135 7 (2) 45 11 (3) 45 7 (4) 135 11 83. ÚðU¹æ¥æð´ yx z 1 1 1 5 5 2 ÌÍæ yx z11 0 2 1 12 5 5 2 ·ð¤ Õè¿ ‹ØêÙÌ× ÎêÚUè ßæÜè ÚðU¹æ ·¤æ â×è·¤ÚU‡æ ãñ : (1) yx z 1 1 2 5 5 2 2 (2) yx z11 1 1 2 12 5 5 2 2 (3) yx z11 1 1 1 12 5 5 2 (4) yx z 2 1 2 5 5 2 84. ØçÎ ÚðU¹æ 2(x11)5y5z14 ÌÍæ â×ÌÜ 2x2y1 l z1450 ·ð¤ Õè¿ ·¤æ ·¤æð‡æ 6 p ãñ, Ìæð l ·¤æ ×æÙ ãñ : (1) 135 7 (2) 45 11 (3) 45 7 (4) 135 11
  46. 46. English : 46 Set : 10 Hindi : 46 Set : 10 85. If x i j kˆˆ ˆ3 65 2 2 r , y i j kˆˆ ˆ4 35 1 2 r and z i j kˆˆ ˆ3 4 125 2 2 r , then the magnitude of the projection of x y3 r r on z r is : (1) 12 (2) 15 (3) 14 (4) 13 86. Let A and E be any two events with 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 false (4) Statement - 1 is false, Statement - 2 is true. 85. ØçÎ x i j kˆˆ ˆ3 65 2 2 r , y i j kˆˆ ˆ4 35 1 2 r ÌÍæ z i j kˆˆ ˆ3 4 125 2 2 r ãñ´ Ìæð x y3 r r ·ð¤ z r ÂÚU Âýÿæð ·¤æ ÂçÚU×æ‡æ ãñ : (1) 12 (2) 15 (3) 14 (4) 13 86. ×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 (4) ·¤ÍÙ-1 ¥âˆØ ãñ, ·¤ÍÙ-2 âˆØ ãñÐ
  47. 47. English : 47 Set : 10 Hindi : 47 Set : 10 87. Let x , M and s 2 be respectively the mean, mode and variance of n observations x1, x2, ..., xn and di52xi2a, i51, 2, ..., n, where a is any number. Statement I : Variance of d1, d2, ..., dn is s2. Statement II : Mean and mode of d1, d2, ..., dn are 2 x 2a and 2M2a, respectively (1) Statement I and Statement II are 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. The function f x x x( ) sin 4 cos 25 1 , is a periodic function with period : (1) 2p (2) p (3) 2 p (4) 4 p 87. ×æÙæ n Âýðÿæ‡ææð´ x1, x2, ..., xn·ð¤ ×æŠØ ÕãéÜ·¤ ÌÍæ ÂýâÚU‡æ ·ý¤×àæÑ x , M ÌÍæ s 2 ÌÍæ di52xi2a, i51, 2, ..., n ãñ´, Áãæ¡ a ·¤æð§ü ⴁØæ ãñ´Ð ·¤ÍÙ I : d1, d2, ..., dn ·¤æ ÂýâÚU‡æ s2 ãñ´ ·¤ÍÙ II : d1, d2, ..., dn ·ð¤ ×æŠØ ÌÍæ ÕãéÜ·¤ ·ý¤×æàæÑ 2 x 2a ÌÍæ 2M2a 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 88. ȤÜÙ f x x x( ) sin 4 cos 25 1 °·¤ ¥æßçÌü ȤÜÙ ãñ çÁâ·¤æ ¥æßÌü ·¤æÜ ãñ : (1) 2p (2) p (3) 2 p (4) 4 p
  48. 48. English : 48 Set : 10 Hindi : 48 Set : 10 89. The principal value of 1 43 tan cot 4       2 p is : (1) 3 4 p 2 (2) 3 4 p (3) 4 p 2 (4) 4 p 90. The contrapositive of the statement “if I am not feeling well, then I will go to the 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. - o 0 o - 89. 1 43 tan cot 4       2 p ·¤æ ×éØ×æÙ ãñ : (1) 3 4 p 2 (2) 3 4 p (3) 4 p 2 (4) 4 p 90. ·¤ÍÙ ÒÒØçÎ ×ñ´ ¥SßSÍ ã¡ê, Ìæð ×ñ´ ÇUæ€ÅUÚU ·ð¤ Âæâ Á檡¤»æÓÓ ·¤æ ÂýçÌÏÙæˆ×·¤ ãñ (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 (4) ØçÎ ×ñ´ UÇUæ€ÅUÚU ·ð¤ Âæâ Á檡¤»æ, Ìæð ×ñ´ SßSÍ Ùãè´ ã¡êÐ - o 0 o -

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