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# JEE MAIN QUESTION PAPER - 09.04.2014

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JEE MAIN QUESTION PAPER

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### JEE MAIN QUESTION PAPER - 09.04.2014

1. 1. English : 1 Set : 01 Hindi : 1 Set : 01 PART A  PHYSICS 1. An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be : (1) 1.7% (2) 2.7% (3) 4.4% (4) 2.27% 2. The position of a projectile launched from the origin at t50 is given by r (40 50 ) mi j → ∧ ∧ 5 1 at t52s. If the projectile was launched at an angle u from the horizontal, then u is (take g510 ms22). (1) tan21 2 3 (2) tan21 3 2 (3) tan21 7 4 (4) tan21 4 5 Öæ» A  ÖæñçÌ·¤ çßææÙ 1. ÜÕæ§ü L ·ð¤ °·¤ âÚUÜ ÜæðÜ·¤ ·¤æ ÂýØæð» ·¤ÚU »éL¤ßèØ ßÚUæ g ·¤æ ×æÙ çÙ·¤æÜÙð ·¤æ °·¤ ÂýØæð» ç·¤Øæ ÁæÌæ ãñÐ §â ÂýØæð» ×ð´ 100 ÎæðÜÙæð´ ·¤æ â×Ø 1 âð·´¤ÇUU ¥ËÂÌ×æ¡·¤ ßæÜè æÇ¸Uè âð ×æÂæ ÁæÌæ ãñ ¥æñÚ ×æÙ 90.0 âð·´¤ÇU ãñÐ ÜÕæ§ü L 1 mm ¥ËÂÌ×æ¡·¤ ßæÜð ×èÅUÚU Âñ×æÙð âð ×æÂè ÁæÌè ãñ ¥æñÚU §â·¤æ ×æÙ 20.0 cm ãñÐ g ·ð¤ ×æÙ ·ð¤ çÙÏüæÚUæ ×ð´ æéçÅU ãæð»è Ñ (1) 1.7% (2) 2.7% (3) 4.4% (4) 2.27% 2. ×êÜ çÕÎé âð t50 ÂÚU ÂýÿæðçÂÌ °·¤ ÂýÿæðÂ ·¤è çSÍçÌ t52s ÂÚU r (40 50 ) mi j → ∧ ∧ 5 1 âð Îè ÁæÌè ãñÐ ØçÎ ÂýÿæðÂ ÿæñçÌÁ âð u ·¤æðæ ÂÚU ÂýÿæðçÂÌ ç·¤Øæ »Øæ Íæ, ÌÕ u ãñ (g510 ms22 Üð´). (1) tan21 2 3 (2) tan21 3 2 (3) tan21 7 4 (4) tan21 4 5
2. 2. English : 2 Set : 01 Hindi : 2 Set : 01 3. Water is flowing at a speed of 1.5 ms21 through a horizontal tube of cross-sectional area 1022 m2 and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water5103 kgm23). (1) 15 N (2) 22.5 N (3) 33.7 N (4) 45 N 4. A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be : (1) 30 N (2) 25 N (3) 27 N (4) 48 N 3. 1022 m2 ·ð¤ ¥ÙéÂýSÍ ·¤æÅU ßæÜè ÿæñçÌÁ ÙÜè âð 1.5 ms21 ·¤è »çÌ âð ÂæÙè ÂýßæçãÌ ãæð ÚUãæ ãñ ¥æñÚU ¥æÂ ¥ÂÙè ãÍðÜè âð Õãæß ·¤æð ÚUæð·¤Ùð ·¤æ ÂýØæâ ·¤ÚU ÚUãð ãñ´Ð Øã ×æÙÌð ãéØð ç·¤ ÂæÙè ãÍðÜè âð ÅU·¤ÚUæÌð ãè L¤·¤ ÁæÌæ ãñ, ¥æÂ·¤æð ¥ÂÙè ãÍðÜè âð ·¤× âð ·¤× §ÌÙæ ÕÜ Ü»æÙæ ÂÇ¸ð»æÐ (ÂæÙè ·¤æ æÙß5103 kgm23). (1) 15 N (2) 22.5 N (3) 33.7 N (4) 45 N 4. ÎýÃØ×æÙ 4 kg ·ð¤ °·¤ Üæ·¤ A ·¤æð °·¤ ÎêâÚðU ÎýÃØ×æÙ 5 kg ·ð¤ °·¤ Üæ·¤ B ·ð¤ ª¤ÂÚU ÚU¹æ ãñ ¥æñÚU Üæ·¤ B °·¤ ç¿·¤Ùè ÿæñçÌÁ ×ðÁ ÂÚU çßææ× ¥ßSÍæ ×ð´ ÚU¹æ ãñÐ ØçÎ Üæ·¤ A ÂÚU ßã ØêÙÌ× ÕÜ, çÁââð ç·¤ ÎæðÙæ´ð Üæ·¤ °·¤ âæÍ »çÌàæèÜ ãæð´, 12 N ãñ ÌÕ Üæ·¤ B ÂÚU Ü»æØæ »Øæ ¥çÏ·¤Ì× ÕÜ, çÁââð ç·¤ ÎæðÙæ´ð Üæ·¤ »çÌàæèÜ ãæð´, ãæð»æ Ñ (1) 30 N (2) 25 N (3) 27 N (4) 48 N
3. 3. English : 3 Set : 01 Hindi : 3 Set : 01 5. Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad/s, and amplitude 1.6 cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g510 ms22). (1) 20 N (2) 10 N (3) 60 N (4) 40 N 5. ÎýÃØ×æÙ 1 kg °ß´ 4 kg ·¤è Îæð ßSÌé°ð´ °·¤ ª¤ßæüÏÚU ·¤×æÙè mæÚUæ ç¿æ ·ð¤ ¥ÙéâæÚU ÁæðÇ¸Uè »Øè ãñ´Ð ¥ËÂÌÚU ÎýÃØ×æÙ ·¤æðæèØ ¥æßëçæ 25 rad/s °ß´ ¥æØæ× 1.6 cm ·¤è âÚUÜ ¥æßÌü »çÌ ·¤ÚU ÚUãæ ãñ ÁÕç·¤ ÕëãæÚU ÎýÃØ×æÙ çSÍÚU ÚUãÌæ ãñÐ çÙ·¤æØ mæÚUæ È¤àæü ÂÚU Ü»æØæ »Øæ ¥çÏ·¤Ì× ÕÜ ãñ (g510 ms22 Üð´). (1) 20 N (2) 10 N (3) 60 N (4) 40 N
4. 4. English : 4 Set : 01 Hindi : 4 Set : 01 6. A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively. (See Figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio c s sin sin u u is : (1) 8 7 (2) 15 14 (3) 8 7 (4) 15 14 6. ÎýÃØ×æÙ Mc ·ð¤ °·¤ ÕðÜÙ °ß´ ÎýÃØ×æÙ Ms ·ð¤ °·¤ »æðÜð ·¤æð ·ý¤×àæÑ Îæð ¥æÙÌ ÌÜæð´ ·ð¤ çÕÎé¥æð´ A °ß´ B ÂÚU ÚU¹æ »Øæ ãñÐ (ç¿æ Îð¹ð´) Ð ØçÎ ßð çÕÙæ çÈ¤âÜð ¥æÙÌ ÌÜ ÂÚU §â Âý·¤æÚU ÜéÉ¸·¤Ìð ãñ´ ç·¤ ©Ù·ð¤ ßÚUæ °·¤ â×æÙ ãñ, ÌÕ ¥ÙéÂæÌ c s sin sin u u ãñ : (1) 8 7 (2) 15 14 (3) 8 7 (4) 15 14
5. 5. English : 5 Set : 01 Hindi : 5 Set : 01 7. Indias Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the semi-major axis of Earths orbit is ae51.531011 m, that of Mars orbit am52.2831011 m, taken Keplers laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to : (1) 500 days (2) 320 days (3) 260 days (4) 220 days 7. ÖæÚUÌ ·¤æ ×´»ÜØæÙ ×´»Ü »ýã ·ð¤ çÜØð âêØü ·ð¤ ¿æÚUæð´ ¥æðÚU SÍæÙæÌÚUæ ·¤ÿæ EOM ×ð´ ÂýÿæðçÂÌ ç·¤Øæ »ØæÐ §âÙð Âëßè ·¤æð E ÂÚU ÀUæðÇ¸æ ¥æñÚU ×´»Ü »ýã âð Øã M ÂÚU ç×ÜÌæ ãñÐ ØçÎ Âëßè ·¤è ¥hü-Îèæü ¥ÿæ ae51.531011 m ãñ ¥æñÚU ×´»Ü »ýã ·¤è ¥hü-Îèæü ¥ÿæ am52.2831011 m ãñ, ÌÕ ·ð¤ÂÜÚU ·ð¤ çÙØ× ·ð¤ ¥ÙéâæÚU Âëßè âð ×´»Ü»ýã Ì·¤ ×´»ÜØæÙ ·ð¤ Âãé¡¿Ùð ·¤æ â×Ø Ü»Ö» ãæð»æ Ñ (1) 500 çÎÙ (2) 320 çÎÙ (3) 260 çÎÙ (4) 220 çÎÙ
6. 6. English : 6 Set : 01 Hindi : 6 Set : 01 8. In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is : (1) Youngs modulii < shear modulii < bulk modulii. (2) Bulk modulii < shear modulii < Youngs modulii. (3) Shear modulii < Youngs modulii < bulk modulii. (4) Bulk modulii < Youngs modulii < shear modulii. 9. The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 551.601, ln 250.693). (1) 231 s (2) 208 s (3) 161 s (4) 142 s 8. °ËØéç×çÙØ× °ß´ Ìæ¡Õð Áñâð ÂÎæÍæðü´ ·ð¤ çÜØð çßçÖÙ ÂýØæSÍÌæ »éææ¡·¤æð´ ·ð¤ ÂçÚU×ææ ·¤æ âãè ·ý¤× ãñ Ñ (1) Ø´» ÂýØæSÍÌæ »éææ¡·¤ < ¥ÂM¤Âæ ÂýØæSÍÌæ »éææ¡·¤ < ¥æØÌÙ ÂýØæSÍÌæ »éææ¡·¤. (2) ¥æØÌÙ ÂýØæSÍÌæ »éææ¡·¤ < ¥ÂM¤Âæ ÂýØæSÍÌæ »éææ¡·¤ < Ø´» ÂýØæSÍÌæ »éææ¡·¤. (3) ¥ÂM¤Âæ ÂýØæSÍÌæ »éææ¡·¤ < Ø´» ÂýØæSÍÌæ »éææ¡·¤ < ¥æØÌÙ ÂýØæSÍÌæ »éææ¡·¤. (4) ¥æØÌÙ ÂýØæSÍÌæ »éææ¡·¤ < Ø´» ÂýØæSÍÌæ »éææ¡·¤ < ¥ÂM¤Âæ ÂýØæSÍÌæ »éææ¡·¤. 9. ßæØé ×ð´ ÎæðÜÙ ·¤ÚU ÚUãð °·¤ ÌÙé »æðÜèØ ÕæÕ ßæÜð âÚUÜ ÜæðÜ·¤ ·¤æ ¥æØæ× 40 âð·´¤ÇU ×ð´ 10 cm âð 8 cm Ì·¤ æÅU ÁæÌæ ãñ Ð Øã ×æÙ Üð´ ç·¤ SÅUæð·¤ ·¤æ çÙØ× âãè ãñ ¥æñÚU ßæØé ·¤æ ·¤æÕüÙ ÇUæ§ü¥æòâæ§Ç âð àØæÙÌæ »éææ´·¤ ·¤æ ¥ÙéÂæÌ 1.3 ãñ, ÌÕ ·¤æÕüÙ ÇUæ§ü ¥æòâæ§ÇU ×ð´ §â ÜæðÜ·¤ ·ð¤ ¥æØæ× ·¤æð 10 cm âð 5 cm Ì·¤ æÅUÙð ×ð´ Ü»æ â×Ø Ü»Ö» ãæð»æ (ln 551.601, ln 250.693). (1) 231 s (2) 208 s (3) 161 s (4) 142 s
7. 7. English : 7 Set : 01 Hindi : 7 Set : 01 10. A capillary tube is immersed vertically in water and the height of the water column is x. When this arrangement is taken into a mine of depth d, the height of the water column is y. If R is the radius of earth, the ratio x y is : (1) d 1 R      2 (2) 2d 1 R      2 (3) R d R d      2 1 (4) R d R d      1 2 11. Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 278C to 778C ? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible). (1) 8 min 20 s (2) 6 min 2 s (3) 7 min (4) 14 min 10. °·¤ ·ð¤àæÙçÜ·¤æ ·¤æð ª¤ßæüÏÚU ÂæÙè ×ð´ ÇéUÕæðØæ ÁæÌæ ãñ ¥æñÚU ÌÕ ÂæÙè ·ð¤ SÌÖ ·¤è ª¡¤¿æ§ü x ãæð ÁæÌè ãñÐ ÁÕ §â çßØæâ ·¤æð °·¤ »ãÚUæ§ü d ßæÜè °·¤ ¹æÙ ×ð´ Üð ÁæØæ ÁæÌæ ãñ, ÌÕ ÂæÙè ·ð¤ SÌÖ ·¤è ª¡¤¿æ§ü y ãñÐ ØçÎ Âëßè ·¤è çæØæ R ãñ, ÌÕ ¥ÙéÂæÌ x y ãñ Ñ (1) d 1 R      2 (2) 2d 1 R      2 (3) R d R d      2 1 (4) R d R d      1 2 11. °·¤ ÕÎ Âææ ×ð´ 2 L ¥æØÌÙ ÂæÙè ·¤æð 1 kW ·¤è ·é¤ÇUÜè âð »×ü ç·¤Øæ ÁæÌæ ãñÐ ÁÕ ÂæÙè »×ü ãæð ÚUãæ ãñ, ÌÕ Âææ 160 J/s ·¤è ÎÚU âð ª¤Áæü ·¤æ ÿæØ ·¤ÚU ÚUãæ ãñÐ ç·¤ÌÙð â×Ø ×ð´ ÂæÙè ·¤æ ÌæÂ×æÙ 278C âð 778C Âãé¡¿ð»æ? (ÂæÙè ·¤è çßçàæcÅU ª¤c×æ 4.2 kJ/kg ãñ ¥æñÚU Âææ ·¤è çßçàæcÅU ª¤c×æ Ù»Ø ãñ) (1) 8 ç×ÙÅU 20 âð·´¤ÇU (2) 6 ç×ÙÅU 2 âð·´¤ÇUU (3) 7 ç×ÙÅU (4) 14 ç×ÙÅU
8. 8. English : 8 Set : 01 Hindi : 8 Set : 01 12. The equation of state for a gas is given by PV5nRT1aV, where n is the number of moles and a is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are To and Po respectively. The work done by the gas when its temperature doubles isobarically will be : (1) o o o P T R P 2a (2) o o o P T R P 1a (3) Po To R ln 2 (4) Po To R 13. Modern vacuum pumps can evacuate a vesseldowntoapressureof4.0310215 atm. at room temperature (300 K). Taking R58.3 JK21 mole21, 1 atm5105 Pa and NAvogadro5631023 mole21, the mean distance between molecules of gas in an evacuated vessel will be of the order of : (1) 0.2 mm (2) 0.2 mm (3) 0.2 cm (4) 0.2 nm 12. °·¤ »ñâ ·¤è ¥ßSÍæ ·¤æ â×è·¤ÚUæ PV5nRT1aV âð çÎØæ ÁæÌæ ãñ, Áãæ¡ n ×æðÜ ·¤è â´Øæ ãñ ¥æñÚU a °·¤ ÏÙæ×·¤ çSÍÚUæ¡·¤ ãñÐ °·¤ ÕðÜÙ ×ð´ ÚU¹ð »ñâ ·ð¤ °·¤ ×æðÜ ·¤æ ÂýæÚUçÖ·¤ ÌæÂ×æÙ °ß´ ÎæÕ ·ý¤×àæÑ To °ß´ Po ãñÐ ÁÕ §â·¤æ ÌæÂ×æÙ â×ÎæÕ ÂÚU Îæð»éÙæ ãæð Áæ°ð»æ, ÌÕ »ñâ mæÚUæ ç·¤Øæ »Øæ ·¤æØü ãæð»æ Ñ (1) o o o P T R P 2a (2) o o o P T R P 1a (3) Po To R ln 2 (4) Po To R 13. ¥æÏéçÙ·¤ çÙßæüÌ ÂÂ ·¤×ÚðU ·ð¤ ÌæÂ×æÙ (300 K) ÂÚU 4.0310215 °ÅUU×æSÈ¤èØÚU ÎæÕ Ì·¤ °·¤ ÕÌüÙ ·¤æð çÙßæüçÌÌ ·¤ÚU â·¤Ìæ ãñÐ R58.3 JK21 ×æðÜ21, 1 °ÅU×æSÈ¤èØÚU5105 ÂæS·¤Ü ¥æñÚU °ßæð»ðÇþUæð â´Øæ 5631023 ×æðÜ21 ÜðÌð ãéØð °·¤ çÙßæüçÌÌ ÕÌüÙ ×ð´ »ñâ ·ð¤ ¥æé¥æ´ð ·ð¤ Õè¿ ×æØ ÎêÚUè ·¤æ ×æÙ Ü»Ö» §ÌÙæ ãæð»æ Ñ (1) 0.2 mm (2) 0.2 mm (3) 0.2 cm (4) 0.2 nm
9. 9. English : 9 Set : 01 Hindi : 9 Set : 01 14. A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by ; x5a1 cos vt and y5a2 cos 2vt traces a curve given by : (1) (2) (3) (4) 14. °·¤ ·¤æ, çÁâ ÂÚU °·¤ âæÍ Îæð ÜÕßÌ÷ âÚUÜ ¥æßÌü »çÌØæ¡ x5a1 cos vt ¥æñÚU y5a2 cos 2vt Ü» ÚUãè ãñ´, §â ß·ý¤ ·¤æð ÎàææüØð»æ Ñ (1) (2) (3) (4)
10. 10. English : 10 Set : 01 Hindi : 10 Set : 01 15. A transverse wave is represented by : y5 10 p sin 2 2 t T x      p p 2 l For what value of the wavelength the wave velocity is twice the maximum particle velocity ? (1) 40 cm (2) 20 cm (3) 10 cm (4) 60 cm 16. The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about 150 N/C, directed inward towards the center of the Earth. This gives the total net surface charge carried by the Earth to be : [Given eo58.85310212 C2/N-m2, RE56.373106 m] (1) 1670 kC (2) 2670 kC (3) 2680 kC (4) 1680 kC 15. °·¤ ¥ÙéÂýSÍ ÌÚ´U» §ââð ÎàææüØè ÁæÌè ãñ Ñ y5 10 p sin 2 2 t T x      p p 2 l ÌÚ´U»ÎñØü ·ð¤ ç·¤â ×æÙ ·ð¤ çÜ°ð ÌÚ´U» ßð» ·¤æ ×æÙ ¥çÏ·¤Ì× ·¤æ ßð» ·¤æ Îæð»éÙæ ãæð»æ? (1) 40 cm (2) 20 cm (3) 10 cm (4) 60 cm 16. Âëßè ·ð¤ ÂëcÆU âð ÁÚUæ ª¤ÂÚU ßæÌæßÚUæ ×ð´ âæÏæÚUæÌØæ ©ÂçSÍÌ ¥æñâÌ çßléÌ ÿæðæ ·¤æ ÂçÚU×ææ 150 N/C ·ð¤ Ü»Ö» ãñ çÁâ·¤è çÎàææ Âëßè ·ð¤ ·ð¤Îý ·¤è ¥æðÚU ¥ÌÚU×é¹è ãñÐ Øã Âëßè mæÚUæ ßæã·¤ ÂçÚUææ×è ÂëcÆU ¥æßðàæ Îð»æ Ñ [çÎØæ ãñ eo58.85310212 C2/N-m2, RE56.373106 m] (1) 1670 kC (2) 2670 kC (3) 2680 kC (4) 1680 kC
11. 11. English : 11 Set : 01 Hindi : 11 Set : 01 17. Three capacitances, each of 3 mF, are provided. These cannot be combined to provide the resultant capacitance of : (1) 1 mF (2) 2 mF (3) 4.5 mF (4) 6 mF 18. A d.c. main supply of e.m.f. 220 V is connected across a storage battery of e.m.f. 200 V through a resistance of 1 V. The battery terminals are connected to an external resistance R. The minimum value of R, so that a current passes through the battery to charge it is : (1) 7 V (2) 9 V (3) 11 V (4) Zero 17. ÂýØð·¤ 3 mF ·ð¤ ÌèÙ â´ÏæçÚUæ çÎØð »Øð ãñ´Ð §Ù·¤æ ç·¤âè Öè Âý·¤æÚU ·¤æ â´ØæðÁÙ çÙÙ ×ð´ âð ·¤æñÙ âæ ÂçÚUææ×è ÏæçÚUÌæ Ùãè´ Îð»æ? (1) 1 mF (2) 2 mF (3) 4.5 mF (4) 6 mF 18. çßléÌ ßæã·¤ ÕÜ 220 V ·¤è °·¤ çÎcÅU ÏæÚUæ ×éØ âÜæ§ü ·¤æð °·¤ 1 V ·¤ð¤ ÂýçÌÚUæðÏ mæÚUæ çßléÌ ßæã·¤ ÕÜ 200 V ·¤è °·¤ â´ÖæçÚUÌ ÕñÅUÚè âð ÁæðÇ¸æ ÁæÌæ ãñÐ ÕñÅUÚUè ·ð¤ ÅUç×üÙÜ ·¤æð °·¤ Õæ±Ø ÂýçÌÚUæðÏ R âð ÁæðÇ¸æ ÁæÌæ ãñÐ R ·¤æ ØêÙÌ× ×æÙ, çÁââð ç·¤ ÕñÅUÚUè ×ð´ ÏæÚUæ ÂýßæçãÌ ãæð·¤ÚU ©âð ¥æßðçàæÌ ·¤ÚðU, ãñ Ñ (1) 7 V (2) 9 V (3) 11 V (4) àæêØ
12. 12. English : 12 Set : 01 Hindi : 12 Set : 01 19. The mid points of two small magnetic dipoles of length d in end-on positions, are separated by a distance x, (x >> d). The force between them is proportional to x2n where n is : (1) 1 (2) 2 (3) 3 (4) 4 20. The magnetic field of earth at the equator is approximately 431025 T. The radius of earth is 6.43106 m. Then the dipole moment of the earth will be nearly of the order of : (1) 1023 A m2 (2) 1020 A m2 (3) 1016 A m2 (4) 1010 A m2 19. ¥ÿæèØ çSÍçÌ ×ð´ ÜÕæ§ü d ·ð¤ Îæð ÌÙé ¿éÕ·¤èØ çmÏéýßæ´ð ·ð¤ ×Ø çÕÎé¥æð´ ·¤æð x ÎêÚUè ÂÚU ÚU¹æ »Øæ ãñ (x >>d)Ð ÎæðÙæð´ ·ð¤ Õè¿ ÕÜ x2n ·¤ð¤ â×æÙéÂæÌè ãñ, Áãæ¡ n ãñ : (1) 1 (2) 2 (3) 3 (4) 4 20. Öê×Ø ÚðU¹æ ÂÚU Âëßè ·ð¤ ¿éÕ·¤èØ ÿæðæ ·¤æ ×æÙ Ü»Ö» 431025 T ãñÐ Âëßè ·¤è çæØæ 6.43106 m ãñÐ ÌÕ Âëßè ·¤æ çmÏýéß ¥ææêæü Ü»Ö» §â ·¤æðçÅU ·¤æ ãæð»æ Ñ (1) 1023 A m2 (2) 1020 A m2 (3) 1016 A m2 (4) 1010 A m2
13. 13. English : 13 Set : 01 Hindi : 13 Set : 01 21. When the rms voltages VL, VC and VR are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio VL : VC : VR51 : 2 : 3. If the rms voltage of the AC source is 100 V, then VR is close to : (1) 50 V (2) 70 V (3) 90 V (4) 100 V 21. °·¤ ÂýØæßÌèü ÏæÚUæ ææðÌ âð ÁéÇ¸ð æðæè LCR ÂçÚUÂÍ ×ð´ ÂýðÚU·¤ß L â´ÏæçÚUÌ C ¥æñÚU ÂýçÌÚUæðÏ·¤ R ÂÚU ×æÂð »Øð ß»ü-×æØ-×êÜ ßæðËÅUÌæ°ð´ ·ý¤×àæÑ VL, VC °ß´ VR ãñ´, ÌÕ Øã ÂæØæ ÁæÌæ ãñ ç·¤ VL : VC : VR51 : 2 : 3 Ð ØçÎ ÂýØæßÌèü ÏæÚUæ oýæðÌ ·¤è ß»ü-×æØ-×êÜ ßæðËÅUÌæ 100 V ãñ´, ÌÕ VR ·¤æ ×æÙ Ü»Ö» ãñ Ñ (1) 50 V (2) 70 V (3) 90 V (4) 100 V
14. 14. English : 14 Set : 01 Hindi : 14 Set : 01 22. Match List I (Wavelength range of electromagnetic spectrum) with List II. (Method of production of these waves) and select the correct option from the options given below the lists. (a) 700 nm to 1 mm (i) Vibration of atoms and molecules. (b) 1 nm to 400 nm (ii) Inner shell electrons in atoms moving from one energy level to a lower level. (c) < 1023 nm (iii) Radioactive decay of the nucleus. (d) 1 mm to 0.1 m (iv) Magnetron valve. List I List II (1) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) (2) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) (3) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i) (4) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) 22. âê¿è I (çßléÌ ¿éÕ·¤èØ SÂðÅþU× ·¤è ÌÚ´U»ÎñØü ÚðUÁ) ·¤æð âê¿è II (§Ù ÌÚ´U»æð´ ·ð¤ çÙ×æüæ ·¤è çßçÏ) âð âé×ðçÜÌ ·¤èçÁ°ð ¥æñÚU âê¿è ·ð¤ Ùè¿ð çÎØð »Øð çß·¤ËÂæ´ð ×ð´ âð âãè çß·¤ËÂ ¿éçÙ°Ð (a) 700 nm ÇÕ 1 mm (i) øËÎËÕ Ä §¿U¼ËøËÎËÕ Õ §¾ ÇÕ (b) 1 nm ÇÕ 400 nm (ii) §¿U¼ËøËÎËÕ Õ Ëü±Ì¿U ÅËÖÁ ÁÕþªãUË¾ËÕ Í  ¦Ëá S±¿U ÇÕ Ì¾¤ÁÕ S±¿U Í  Ì± ÇÕ (c) < 1023 nm (iii) ¾ËÌ» Õ ¿ÕUÌ¬U½ËÕ ÇÌâ½ äË½ ÇÕ (d) 1 mm ÇÕ 0.1 m (iv) ¼Öó¾ÕªãUË¾ ÄË°Ä ÇÕ ÇÏ¤Í I ÇÏ¤Í II (1) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) (2) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) (3) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i) (4) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
15. 15. English : 15 Set : 01 Hindi : 15 Set : 01 23. A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is 4 3 , and the divers eyes are 15 cm below the surface of water. Then the radius of the circle is : (1) 15333 5 cm (2) 1533 7 cm (3) 15 7 cm 3 3 (4) 15 3 cm 7 3 23. °·¤ »æðÌæ¹æðÚU ÂæÙè ·ð¤ ¥ÎÚU âð ÕæãÚU ·¤è ÎéçÙØæ ·¤æð °·¤ ßëæèØ ÿæñçÌÁ ×ð´ çÙçãÌ Îð¹Ìæ ãñÐ ÂæÙè ·¤æ ¥ÂßÌüÙæ¡·¤ 4 3 ãñ ¥æñÚU »æðÌæ¹æðÚU ·¤è ¥æ¡¹ ÂæÙè ·ð¤ ÂëcÆU âð 15 cm Ùè¿ð ãñ´Ð ÌÕ ßëæ ·¤è çæØæ ãñ Ñ (1) 15333 5 cm (2) 1533 7 cm (3) 15 7 cm 3 3 (4) 15 3 cm 7 3
16. 16. English : 16 Set : 01 Hindi : 16 Set : 01 24. Using monochromatic light of wavelength l, an experimentalist sets up the Youngs double slit experiment in three ways as shown. If she observes that y5b9, the wavelength of light used is : 24. ÌÚ´U»ÎñØü l ·ð¤ °·¤ßæèü Âý·¤æàæ ·ð¤ ÂýØæð» âð °·¤ ßñææçÙ·¤ Ø´» ·ð¤ çmçÀUÎý ÂýØæð» ·¤æð ÎàææüØð »Øð ÌèÙ Âý·¤æÚU âð ÃØßçSÍÌ ·¤ÚUÌè ãñÐ ØçÎ ßã ÂæÌè ãñ ç·¤ y5b9, ÌÕ ÂýØæð» ç·¤Øð »Øð Âý·¤æàæ ·¤è ÌÚ´U»ÎñØü ãñ Ñ
17. 17. English : 17 Set : 01 Hindi : 17 Set : 01 (1) 520 nm (2) 540 nm (3) 560 nm (4) 580 nm 25. The focal lengths of objective lens and eye lens of a Gallelian Telescope are respectively 30 cm and 3.0 cm. Telescope produces virtual, erect image of an object situated far away from it at least distance of distinct vision from the eye lens. In this condition, the Magnifying Power of the Gallelian Telescope should be : (1) 111.2 (2) 211.2 (3) 28.8 (4) 18.8 26. For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship ? (1) an electron (2) a proton (3) an a-particle (4) a dust particle (1) 520 nm (2) 540 nm (3) 560 nm (4) 580 nm 25. °·¤ »ñçÜçÜØÙ ÎêÚUÎàæèü ·ð¤ ¥çÖÎëàØ·¤ °ß´ Ùðçæ·¤æ Üðâ ·¤è \$È¤æð·¤â ÜÕæ§Øæ¡ ·ý¤×àæÑ 30 cm °ß´ 3.0 cm ãñÐ ÎêÚUÎàæèü Ùðçæ·¤æ Üðâ âð âéSÂcÅU ÎàæüÙ ·¤è ØêÙÌ× ÎêÚUè ÂÚU °·¤ ¥ØÌ ÎêÚU ·¤è ßSÌé ·¤æ ¥æÖæâè, âèÏæ ÂýçÌçÕÕ ÕÙæÌæ ãñÐ §â çSÍçÌ ×ð´, »ñçÜçÜØÙ ÎêÚUÎàæèü ·¤è ¥æßÏüÙ ÿæ×Ìæ ãæð»è Ñ (1) 111.2 (2) 211.2 (3) 28.8 (4) 18.8 26. çÙÙçÜç¹Ì ·¤ææð´ ×ð´ âð ç·¤â ·¤æ ·ð¤ çÜØð ÇUè-ÕýæÜè âÕÏ ·¤æ ÂýæØæðç»·¤ âØæÂÙ ¥ØçÏ·¤ ×éçà·¤Ü ãæð»æ? (1) °·¤ §ÜðÅþUæÙ\$ (2) °·¤ ÂýæðÅUæòÙ (3) °·¤ a-·¤æ (4) °·¤ ÏêÜ ·¤æ ·¤æ
18. 18. English : 18 Set : 01 Hindi : 18 Set : 01 27. If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove the electron from the first excited state of Li11 is : (1) 122.4 eV (2) 30.6 eV (3) 13.6 eV (4) 3.4 eV 28. Identify the gate and match A, B, Y in bracket to check. (1) AND (A51, B51, Y51) (2) OR (A51, B51, Y50) (3) NOT (A51, B51, Y51) (4) XOR (A50, B50, Y50) 29. A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight (LOS) mode ? (1) 55.4 km (2) 45.5 km (3) 54.5 km (4) 455 km 27. ØçÎ ãæ§ÇþUæðÁÙ ÂÚU×ææé ×ð´ §ÜðÅþUæÙ ·¤è ÕÏÙ ª¤Áæü 13.6 eV ãñ, ÌÕ Li11 ·¤è ÂýÍ× ©æðçÁÌ ¥ßSÍæ âð §ÜðÅþUæÙ ÕæãÚU çÙ·¤æÜÙð ×ð´ ¥æßàØ·¤ ª¤Áæü ãñ Ñ (1) 122.4 eV (2) 30.6 eV (3) 13.6 eV (4) 3.4 eV 28. »ðÅU ·¤æð Âã¿æçÙ°ð ¥æñÚU ·¤æðcÅU·¤ ×ð´ A, B, Y ·ð¤ ×æÙ âð âé×ðçÜÌ ·¤ÚU Áæ¡¿ ·¤èçÁ°ðÐ (1) AND (A51, B51, Y51) (2) OR (A51, B51, Y50) (3) NOT (A51, B51, Y51) (4) XOR (A50, B50, Y50) 29. °·¤ ×èÙæÚU ·ð¤ àæèáü ÂÚU Âýðáæ °çÅUÙæ ·¤è ª¡¤¿æ§ü 32 m ãñ ¥æñÚU ¥çÖ»ýæãè °çÅUÙæ ·¤è ª¡¤¿æ§ü 50 m ãñÐ ÎëçcÅUÚðU¹èØ (LOS) ×æðÇU ×ð´ â´ÌæðáÂýÎ â´¿ÚUæ ·ð¤ çÜ° ÎæðÙæ´ð °çÅUÙæ ·ð¤ Õè¿ ¥çÏ·¤Ì× ÎêÚUè Øæ ãñ? (1) 55.4 km (2) 45.5 km (3) 54.5 km (4) 455 km
19. 19. English : 19 Set : 01 Hindi : 19 Set : 01 30. An n-p-n transistor has three leads A, B and C. Connecting B and C by moist fingers, A to the positive lead of an ammeter, and C to the negative lead of the ammeter, one finds large deflection. Then, A, B and C refer respectively to : (1) Emitter, base and collector (2) Base, emitter and collector (3) Base, collector and emitter (4) Collector, emitter and base. 30. °·¤ n-p-n ÅþUæçÁSÅUÚU ×ð´ ÌèÙ ¿æÜ·¤ ÌæÚU A, B °ß´ C ãñ´Ð »èÜè ¥´»éçÜØæð´ âð B °ß´ C ·¤æð ÁæðÇ¸Ùð ÂÚU, °·¤ ÏæÚUæ×æÂè ·¤æð ÏÙæ×·¤ ¿æÜ·¤ ÌæÚU ·¤æð A âð ÁæðÇ¸Ùð ÂÚU ¥æñÚU ÏæÚUæ×æÂè ·¤è «¤ææ×·¤ ¿æÜ·¤ ÌæÚU ·¤æð C âð ÁæðÇ¸Ùð ÂÚU °·¤ Âýðÿæ·¤ ¥ØçÏ·¤ çßÿæðÂ ÂæÌæ ãñÐ ÌÕ A, B °ß´ C ·¤æ â´ÎÖü ·ý¤×àæÑ §Ùâð ãñ Ñ (1) ©âÁü·¤, ¥æÏæÚU °ß´ â´»ýæãè (2) ¥æÏæÚU, ©âÁü·¤ °ß´ â´»ýæãè (3) ¥æÏæÚU, â´»ýæãè °ß´ ©âÁü·¤ (4) â´»ýæãè, ©âÁü·¤ °ß´ ¥æÏæÚU
20. 20. English : 20 Set : 01 Hindi : 20 Set : 01 PART B  CHEMISTRY 31. In a face centered cubic lattice atoms A are at the corner points and atoms B at the face centered points. If atom B is missing from one of the face centered points, the formula of the ionic compound is : (1) AB2 (2) A5B2 (3) A2B3 (4) A2B5 32. Van der Waals equation for a gas is stated as, 2 nRT n p a V nb V      5 2 2 . This equation reduces to the perfect gas equation, nRT p V 5 when , (1) temperature is sufficiently high and pressure is low. (2) temperature is sufficiently low and pressure is high. (3) both temperature and pressure are very high. (4) both temperature and pressure are very low. Öæ» B  ÚUâæØÙ çßææÙ 31. °·¤ È¤Ü·¤ ·ð¤çÎýÌ æÙæ·¤æÚU ÁæÜ·¤ ×ð´ A ·ð¤¤ ÂÚU×ææé ·¤æðÙæð´ ·ð¤ çÕÎé¥æð´ ÂÚU ãñ´ ¥æñÚU B ·ð¤ ÂÚU×ææé È¤Ü·¤ ·ð¤Îýæð´ ÂÚU ãñ´Ð ØçÎ B ÂÚU×ææé °·¤ È¤Ü·¤ ·ð¤Îý ÂÚU Ù ãæð Ìæð ¥æØçÙ·¤ Øæñç»·¤ ·¤æ âêæ ãæð»æ Ñ (1) AB2 (2) A5B2 (3) A2B3 (4) A2B5 32. °·¤ »ñâ ·ð¤ çÜØð ßæÇUÚU ßæÜ â×è·¤ÚUæ 2 nRT n p a V nb V      5 2 2 . ãæðÌæ ãñÐ Øã â×è·¤ÚUæ ¥æÎàæü »ñâ â×è·¤ÚUæ ·¤æ M¤Â, nRT p V 5 ÏæÚUæ ·¤ÚU Üð»æ ÁÕ Ñ (1) ÌæÂ ÂØæüÌ ©¿ ãæð»æ ¥æñÚU ÎæÕ ØêÙ ãæð»æÐ (2) ÌæÂ ÂØæüÌ ØêÙ ãæð»æ ¥æñÚU ÎæÕ ©¿ ãæð»æÐ (3) ÌæÂ ¥æñÚU ÎæÕ ÎæðÙæð´ ÕãéÌ ©¿ ãæð´»ðÐ (4) ÌæÂ ¥æñÚU ÎæÕ ÎæðÙæð´ ÕãéÌ ØêÙ ãæð´»ððÐ
21. 21. English : 21 Set : 01 Hindi : 21 Set : 01 33. The standard electrode potentials ( )M /M o E 1 of four metals A, B, C and D are 21.2 V , 0.6 V, 0.85 V and 20.76 V, respectively. The sequence of deposition of metals on applying potential is : (1) A, C, B, D (2) B, D, C, A (3) C, B, D, A (4) D, A, B, C 34. At a certain temperature, only 50% HI is dissociated into H2 and I2 at equilibrium. The equilibrium constant is : (1) 1.0 (2) 3.0 (3) 0.5 (4) 0.25 35. Dissolving 120 g of a compound of (mol. wt. 60) in 1000 g of water gave a solution of density 1.12 g/mL. The molarity of the solution is : (1) 1.00 M (2) 2.00 M (3) 2.50 M (4) 4.00 M 33. ¿æÚU ÏæÌé¥æð´ A, B, C ¥æñÚU D ·ð¤ SÅñUÇUÇüU (×æÙ·¤) §ÜñÅþUæðÇU çßÖß ( )M /M o E 1 ·ý×æÙéâæÚU 21.2 V, 0.6 V, 0.85 V ¥æñÚU 20.76 V ãñ´Ð çßÖß Üæ»ê ·¤ÚUÙð ÂÚU ÏæÌé Á×Ùð ·¤æ ·ý¤× ãæð»æ Ñ (1) A, C, B, D (2) B, D, C, A (3) C, B, D, A (4) D, A, B, C 34. °·¤ ÌæÂ çßàæðá âæØÂÚU ·ð¤ßÜ 50% HI, H2 ¥æñÚU I2 ×ð´ çßÖæçÁÌ ãæðÌæ ãñÐ âæØ çSÍÚUæ´·¤ ·¤æ ×æÙ ãæð»æ Ñ (1) 1.0 (2) 3.0 (3) 0.5 (4) 0.25 35. °·¤ Øæñç»·¤ (¥æéÖæÚU 60) ·¤è 120 »ýæ× ×æææ ·¤æð 1000 »ýæ× ÁÜ ×ð´ ææðÜÙð ÂÚU ÂýæÌ ãé° çßÜØÙ ·¤æ æÙß 1.12 »ýæ× ÂýçÌ ç×çÜ çÜÅUÚU ãñÐ çßÜØÙ ·¤è ×æðÜñçÚUÅUè ãæð»è Ñ (1) 1.00 M (2) 2.00 M (3) 2.50 M (4) 4.00 M
22. 22. English : 22 Set : 01 Hindi : 22 Set : 01 36. The half-life period of a first order reaction is 15 minutes. The amount of substance left after one hour will be : (1) 1 4 of the original amount (2) 1 8 of the original amount (3) 1 16 of the original amount (4) 1 32 of the original amount 37. A current of 10.0 A flows for 2.00 h through an electrolytic cell containing a molten salt of metal X. This results in the decomposition of 0.250 mol of metal X at the cathode. The oxidation state of X in the molten salt is : (F596,500 C) (1) 11 (2) 21 (3) 31 (4) 41 36. °·¤ ÂýÍ× ·¤æðçÅU ·¤è ¥çÖç·ý¤Øæ ·¤æ ¥Ïü-¥æØé ·¤æÜ 15 ç×ÙÅU ãñÐ °·¤ æÅUæ Âà¿æÌ÷ ÂÎæÍü ·¤è àæðá ÚUãè ×æææ ãæð»è Ñ (1) ÂýæÚUçÖ·¤ ×æææ ·¤æ 1 4 Öæ» (2) ÂýæÚUçÖ·¤ ×æææ ·¤æ 1 8 Öæ» (3) ÂýæÚUçÖ·¤ ×æææ ·¤æ 1 16 Öæ» (4) ÂýæÚUçÖ·¤ ×æææ ·¤æ 1 32 Öæ» 37. ÏæÌé X ·ð¤ çÂæÜð ãé° Üßæ ÏæÚU·¤ §ÜñÅþUæðçÜçÅU·¤ âñÜ ×ð´ âð 2.00 æÅðU ·ð¤ çÜØð 10.0 A ·¤è çßléÌ ÏæÚUæ ¿ÜæÙð ÂÚU 0.250 ×æðÜ X ÏæÌé ·¤æ Á×æß ãé¥æÐ çÂæÜð ãé° Üßæ ×ð´ ÏæÌé X ·¤è ¥æâè·ë¤Ì ¥ßSÍæ ãæð»è Ñ (ÁÕç·¤ F596,500 C) (1) 11 (2) 21 (3) 31 (4) 41
23. 23. English : 23 Set : 01 Hindi : 23 Set : 01 38. The energy of an electron in first Bohr orbit of H - atom is 213.6 eV. The energy value of electron in the excited state of Li21 is : (1) 227.2 eV (2) 30.6 eV (3) 230.6 eV (4) 27.2 eV 39. The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at 300 K is : (Atomic masses : He54 u, O516 u) (1) 300 K (2) 600 K (3) 1200 K (4) 2400 K 40. The standard enthalpy of formation of NH3 is 246.0 kJ/mol. If the enthalpy of formation of H2 from its atoms is 2436 kJ/mol and that of N2 is 2712 kJ/mol, the average bond enthalpy of N2H bond in NH3 is : (1) 21102 kJ/mol (2) 2964 kJ/mol (3) 1352 kJ/mol (4) 11056 kJ/mol 38. H-ÂÚU×ææé ·ð¤ ÂýÍ× ÕæðãÚU ¥æçÕüÅU ×ð´ §ÜñÅþUæÙ ·¤è ª¤Áæü 213.6 eV ãñÐ Li 21 ·¤è ©æðçÁÌ ¥ßSÍæ ×ð´ §ÜñÅþUæÙ ·¤æ ª¤Áæü ×æÙ ãæð»æ Ñ (1) 227.2 eV (2) 30.6 eV (3) 230.6 eV (4) 27.2 eV 39. ÌæÂ, çÁâ ÂÚU ¥æòâèÁÙ ¥æé¥æð´ ·¤è ß»ü ×æØ×êÜ SÂèÇU ·¤æ ×æÙ ßãè ãæðÌæ ãñ Áæð ãèçÜØ× ÂÚU×ææé¥æð´ ·¤æ 300 K ÂÚU ãæðÌæ ãñ, (ÂÚU×ææé ÎýÃØ×æÙ Ñ He54 ×ææ·¤, O516 ×ææ·¤) ãæð»æ Ñ (1) 300 K (2) 600 K (3) 1200 K (4) 2400 K 40. NH3 ÕÙÙð ·¤è ×æÙ·¤ ª¤Áæü 246.0 kJ/×æðÜ ãñÐ ØçÎ ¥ÂÙð ÂÚU×ææé¥æð´ âð H2 ÕÙÙð ·¤è ª¤Áæü 2436 kJ/×æðÜ ¥æñÚU N2 ·¤è 2712 kJ/×æðÜ ãæð Ìæð N2H ·¤è NH3 ×ð´ ¥æñâÌ Õæ¡ÇU ª¤Áæü ãæð»è Ñ (1) 21102 kJ/×æðÜ (2) 2964 kJ/×æðÜ (3) 1352 kJ/×æðÜ (4) 11056 kJ/×æðÜ
24. 24. English : 24 Set : 01 Hindi : 24 Set : 01 41. The amount of oxygen in 3.6 moles of water is : (1) 115.2 g (2) 57.6 g (3) 28.8 g (4) 18.4 g 42. The gas evolved on heating CaF2 and SiO2 with concentrated H2SO4, on hydrolysis gives a white gelatinous precipitate. The precipitate is : (1) hydrofluosilicic acid (2) silica gel (3) silicic acid (4) calciumfluorosilicate 43. Chloro compound of Vanadium has only spin magnetic moment of 1.73 BM. This Vanadium chloride has the formula : (at. no. of V523) (1) VCl2 (2) VCl4 (3) VCl3 (4) VCl5 41. 3.6 ×æðÜ ÁÜ ×ð´ ¥æòâèÁÙ ·¤è ×æææ ãæðÌè ãñ Ñ (1) 115.2 »ýæ× (2) 57.6 »ýæ× (3) 28.8 »ýæ× (4) 18.4 »ýæ× 42. CaF2 ¥æñÚU SiO2 ·¤æð âæÎý H2SO4 ·ð¤ âæÍ »ÚU× ·¤ÚUÙð âð ÂýæÌ ãé§ü »ñâ ãæ§ÇþUæÜðçââ ÂÚU °·¤ â\$Èð¤Î ÁñÜ Áñâæ ¥ßÿæðÂ ÎðÌè ãñÐ Øã ¥ßÿæðÂ ãæð»æ Ñ (1) ãæ§ÇþUæðÜæðçâçÜçâ·¤ °ðçâÇU (2) çâçÜ·¤æ ÁñÜ (3) çâçÜçâ·¤ °ðçâÇ (4) ·ñ¤çËàæØ×ÜæðÚUæðçâçÜ·ð¤ÅU 43. ßñÙðçÇUØ× ·¤æ °·¤ ÜæðÚUæð Øæñç»·¤ 1.73 BM ·¤æ ·ð¤ßÜ çSÂÙ ×ñÙðçÅU·¤ ×æð×ñÅU ÚU¹Ìæ ãñ (V ·¤æ ÂÚU×ææê ·ý¤×æ´·¤523) §â ßñÙðçÇUØ× ÜæðÚUæ§ÇU ·¤æ âêæ ãæðÌæ ãñ Ñ (1) VCl2 (2) VCl4 (3) VCl3 (4) VCl5
25. 25. English : 25 Set : 01 Hindi : 25 Set : 01 44. An octahedral complex of Co31 is diamagnetic. The hybridisation involved in the formation of the complex is : (1) sp3d2 (2) dsp2 (3) d2sp3 (4) dsp3d 45. Which of the following is not formed when H2S reacts with acidic K2Cr2O7 solution ? (1) CrSO4 (2) Cr2(SO4) 3 (3) K2SO4 (4) S 46. Which of the following has unpaired electron(s) ? (1) N2 (2) 2O2 (3) 2 2N 1 (4) 2 2O 2 44. Co31 ·¤æ °·¤ ¥cÅÈ¤Ëæ·¤èØ â´·¤ÚU ÂýçÌ¿éÕ·¤èØ ãæðÌæ ãñÐ §â â´·¤ÚU ·ð¤ ÕÙÙð âð âÕçÏÌ â´·¤ÚUæ ãæð»æ Ñ (1) sp3d2 (2) dsp2 (3) d2sp3 (4) dsp3d 45. ¥ÜèØ K2Cr2O7 ææðÜ ·¤è H2S ·ð¤ âæÍ ¥çÖç·ý¤Øæ ãæðÙð ÂÚU çÙÙæð´ ×ð´ âð ·¤æñÙ Ùãè´ ÕÙÌæ? (1) CrSO4 (2) Cr2(SO4) 3 (3) K2SO4 (4) S 46. §Ù ×ð´ âð ç·¤â ×ð´ ¥Øéç×Ì §ÜñÅþUæÙ ãæðÌæ ãñ Øæ ãæðÌð ãñ´ ? (1) N2 (2) 2O2 (3) 2 2N 1 (4) 2 2O 2
26. 26. English : 26 Set : 01 Hindi : 26 Set : 01 47. In the following sets of reactants which two sets best exhibit the amphoteric character of Al2O3 . xH2O ? Set 1 : Al2O3 . xH2O (s) and OH 2 (aq) Set 2 : Al2O3 . xH2O (s) and H2O (l) Set 3 : Al2O3 . xH2O (s) and H 1 (aq) Set 4 : Al2O3 . xH2O (s) and NH3 (aq) (1) 1 and 2 (2) 1 and 3 (3) 2 and 4 (4) 3 and 4 48. The number and type of bonds in 2 2C 2 ion in CaC2 are : (1) One s bond and one p2bond (2) One s bond and two p2bonds (3) Two s bonds and two p2bonds (4) Two s bonds and one p2bond 49. The form of iron obtained from blast furnace is : (1) Steel (2) Cast Iron (3) Pig Iron (4) Wrought Iron 47. ç·ý¤Øæ ·¤æÚU·¤æð´ ·ð¤ çÙÙ âðÅUæð´ ×ð´ âð ç·¤â Îæð ×ð´ Al2O3 . xH2O ·¤æ ©ÖØ Ï×èü ÃØßãæÚU Îð¹æ ÁæÌæ ãñ? Set 1 : Al2O3 . xH2O (s) ¥æñÚU OH 2 (ÁÜèØ) Set 2 : Al2O3 . xH2O (s) ¥æñÚU H2O (Îýß) Set 3 : Al2O3 . xH2O (s) ¥æñÚU H 1 (ÁÜèØ) Set 4 : Al2O3 . xH2O (s) ¥æñÚU NH3 (ÁÜèØ) (1) 1 ¥æñÚU 2 (2) 1 ¥æñÚU 3 (3) 2 ¥æñÚU 4 (4) 3 ¥æñÚU 4 48. CaC2 ·ð 2 2C 2 ¥æØÙ ×ð´ ¥æÕÏæð´ ·¤è â´Øæ °ß´ Âý·¤æÚU çÙÙ ·¤æñÙâè ãñ? (1) °·¤ s ¥æÕÏ ¥æñÚU °·¤ p2¥æÕÏ (2) °·¤ s ¥æÕÏ ¥æñÚU Îæð p2¥æÕÏ (3) Îæð s ¥æÕÏ ¥æñÚU Îæð p2¥æÕÏ (4) Îæð s ¥æÕÏ ¥æñÚU °·¤ p2¥æÕÏ 49. Ûææð´·¤æ Ö^è âð ÂýæÌ ãé° Üæðãð ·¤æ M¤Â ·¤ãÜæÌæ ãñ Ñ (1) §SÂæÌ (Steel) (2) ÉUÜßæ¡ Üæðãæ (Cast Iron) (3) ·¤¿æ Üæðãæ (Pig Iron) (4) çÂÅUßæ´ Üæðãæ (Wrought Iron)
27. 27. English : 27 Set : 01 Hindi : 27 Set : 01 50. The correct statement about the magnetic properties of [Fe(CN)6]32 and [FeF6]32 is : (Z526). (1) both are paramagnetic. (2) both are diamagnetic. (3) [Fe(CN)6]32 is diamagnetic, [FeF6]32 is paramagnetic. (4) [Fe(CN)6]32 is paramagnetic, [FeF6]32 is diamagnetic. 51. Which one of the following reactions will not result in the formation of carbon- carbon bond ? (1) Reimer-Tieman reaction (2) Friedel Crafts acylation (3) Wurtz reaction (4) Cannizzaro reaction 52. In the hydroboration - oxidation reaction of propene with diborane, H2O2 and NaOH, the organic compound formed is : (1) CH3CH2OH (2) CH3CHOHCH3 (3) CH3CH2CH2OH (4) (CH3) 3 COH 50. [Fe(CN)6]32 ¥æñÚU [FeF6]32 ·ð¤ ¿éÕ·¤èØ »éææð´ ·¤æ ØÍæÍü çßßÚUæ ãñ Ñ (Z526). (1) ÎæðÙæ´ð ¥Ùé¿éÕ·¤èØ ãñ´Ð (2) ÎæðÙæð´ ÂýçÌ ¿éÕ·¤èØ ãñ´Ð (3) [Fe(CN)6]32 ÂýçÌ¿éÕ·¤èØ ¥æñÚU [FeF6]32¥Ùé¿éÕ·¤èØ ãñÐ (4) [Fe (CN)6]32¥Ùé¿éÕ·¤èØ ¥æñÚU [FeF6]32 ÂýçÌ¿éÕ·¤èØ ãñÐ 51. §Ù ¥çÖç·ý¤Øæ¥æð´ ×ð´ âð ç·¤â ×ð´ ·¤æÕüÙ - ·¤æÕüÙ ¥æÕÏ Ùãè´ ÂýæÌ ãæð»æ? (1) ÚUæð×ÚU - ÅUè×Ù ¥çÖç·ý¤ØæÐ (2) Èý¤èÇUÜ ·ý¤æÈ¤ÅU °ðâèÜðàæÙÐ (3) ßéÅüU\$Á ¥çÖç·ý¤ØæÐ (4) ·ñ¤Ùè\$ÁñÚUæð ¥çÖç·ý¤ØæÐ 52. ÂýæðÂèÙ ·ð¤ ÇUæ§ÕæðÚðUÙ, H2O2 ¥æñÚU NaOH ·ð¤ âæÍ ãæ§ÇþUæðÕæðÚðUàæÙ-¥æòâè·¤ÚUæ ¥çÖç·ý¤Øæ ×ð´ ÕÙæ ·¤æÕüçÙ·¤ Øæñç»·¤ ãñ Ñ (1) CH3CH2OH (2) CH3CHOHCH3 (3) CH3CH2CH2OH (4) (CH3) 3 COH
28. 28. English : 28 Set : 01 Hindi : 28 Set : 01 53. The major product of the reaction 2 2 4NaNO /H SO → is : (1) (2) (3) (4) 54. For the compounds CH3Cl, CH3Br, CH3I and CH3F, the correct order of increasing C-halogen bond length is : (1) CH3F < CH3Cl < CH3Br < CH3I (2) CH3F < CH3Br < CH3Cl < CH3I (3) CH3F < CH3I < CH3Br < CH3Cl (4) CH3Cl < CH3Br < CH3F < CH3I 53. ¥çÖç·ý¤Øæ 2 2 4NaNO /H SO → ·¤æ ×éØ ç·ý¤Øæ È¤Ü ãñ Ñ (1) (2) (3) (4) 54. Øæñç»·¤æð´ CH3Cl,CH3Br,CH3I ¥æñÚU CH3F ×ð´ ·¤æÕüÙ-ãñÜæðÁÙ Õæ¡ÇU ·¤è ÕÉ¸Ìè ÜÕæ§ü ·¤æ ÆUè·¤ ·ý¤× ãñ Ñ (1) CH3F < CH3Cl < CH3Br < CH3I (2) CH3F < CH3Br < CH3Cl < CH3I (3) CH3F < CH3I < CH3Br < CH3Cl (4) CH3Cl < CH3Br < CH3F < CH3I
29. 29. English : 29 Set : 01 Hindi : 29 Set : 01 55. Allyl phenyl ether can be prepared by heating : (1) C6H5Br1CH25CH2CH22ONa (2) CH25CH2CH22Br1C6H5ONa (3) C6H52CH5CH2Br1CH32ONa (4) CH25CH2Br1C6H52CH22ONa 56. In a nucleophilic substitution reaction : R2Br1Cl2 DMF → R_Cl1Br2, which one of the following undergoes complete inversion of configuration ? (1) C6H5CHC6H5Br (2) C6H5CH2Br (3) C6H5CH CH3Br (4) C6H5CCH3C6H5Br 57. In which of the following pairs A is more stable than B ? A B (1) (2) (3) (4) Ph3C • , (CH3) 3 C • 55. °Üæ§Ü çÈ¤Ùæ§Ü §üÍÚU §ãð´ »ÚU× ·¤ÚU ÕÙæØæ Áæ â·¤Ìæ ãñ Ñ (1) C6H5Br1CH25CH2CH22ONa (2) CH25CH2CH22Br1C6H5ONa (3) C6H52CH5CH2Br1CH32ONa (4) CH25CH2Br1C6H52CH22ONa 56. ØêçÜØâ SÙðãè ¥ÎÜ ÕÎÜ ¥çÖç·ý¤Øæ Ñ R2Br1Cl2 DMF → R_Cl1Br2, ×ð´ çÙÙ ÂÎæÍæðZ âð ·¤æñÙ ÃØßSÍæ ·¤æ â´ÂêUæü ÕÎÜ ·¤ÚU ÜðÌæ ãñ ? (1) C6H5CHC6H5Br (2) C6H5CH2Br (3) C6H5CH CH3Br (4) C6H5CCH3C6H5Br 57. çÙÙ Øé×æð´ ×ð´ âð ç·¤â×ð´ A, ¥çÏ·¤ SÍæ§ü ãñ B âð ? A B (1) (2) (3) (4) Ph3C • , (CH3) 3 C •
30. 30. English : 30 Set : 01 Hindi : 30 Set : 01 58. Structure of some important polymers are given. Which one represents Buna-S ? (1) (2) (3) (4) 59. Which is the major product formed when acetone is heated with iodine and potassium hydroxide ? (1) Iodoacetone (2) Acetic acid (3) Iodoform (4) Acetophenone 60. Which one of the following class of compounds is obtained by polymerization of acetylene ? (1) Poly-yne (2) Poly-ene (3) Poly-ester (4) Poly-amide 58. ·é¤ÀU Âýçâh ÕãéÜ·¤æð´ ·¤è â´ÚU¿Ùæ°´ Ùè¿ð Îè »§ü ãñ §Ù×ð´ âð ·¤æñÙ ÕêÙæ-S ·¤è âê¿·¤ ãñ? (1) (2) (3) (4) 59. ·¤æñÙ âè ÕÇ¸è ×æææ ×ð´ ç·ý Øæ È¤Ü ÂýæÌ ãæðÌæ ãñ ÁÕ °ðâèÅUæðÙ ·¤æð ¥æØæðÇUèÙ ¥æñÚU ÂæðÅñUçàæØ× ãæ§ÇþUæâæ§ÇU ·ð¤ âæÍ »ÚU× ç·¤Øæ ÁæÌæ ãñ? (1) ¥æØæðÇUæð°ðâèÅUæðÙ (2) °âèçÅU·¤ °ðçâÇU (3) ¥æØæðÇUæð\$È¤æ×ü (4) °ðâèÅUæð çÈ¤ÙæðÙ 60. °çâçÅUÜèÙ ·ð¤ ÕãéÜ·¤è·¤ÚUæ âð ·¤æñÙâæ çÙÙ Âý·¤æÚU ·¤æ Øæñç»·¤ ÂýæÌ ãæðÌæ ãñ? (1) ÂæòÜè-¥æ§Ù (2) ÂæòÜè-§üÙ (3) ÂæòÜè-°ðSÅUÚU (4) ÂæòÜè-°×æ§ÇU
31. 31. English : 31 Set : 01 Hindi : 31 Set : 01 PART C  MATHEMATICS 61. Let P be the relation defined on the set of all real numbers such that P5{(a, b) : sec2 a2tan2 b51}. Then P is : (1) reflexive and symmetric but not transitive. (2) reflexive and transitive but not symmetric. (3) symmetric and transitive but not reflexive. (4) an equivalence relation. 62. Let w(Im w ¹ 0) be a complex number. Then the set of all complex numbers z satisfying the equation w2 wz5k (12z), for some real number k, is : (1) {z : ?z?51} (2) {z : z5 z } (3) {z : z ¹ 1} (4) {z : ?z?51, z ¹ 1} 63. If equations ax21bx1c50, (a, b, c Î R, a ¹ 0) and 2x213x1450 have a common root, then a : b : c equals : (1) 1 : 2 : 3 (2) 2 : 3 : 4 (3) 4 : 3 : 2 (4) 3 : 2 : 1 Öæ» C  »çæÌ 61. ×æÙ P âÖè ßæSÌçß·¤ â´Øæ¥æð´ ÂÚU ÂçÚUÖæçáÌ °·¤ °ðâæ â´Õ´Ï ãñ ç·¤ P5{(a, b) : sec2 a2tan2 b51} ãñ, Ìæð P Ñ (1) SßÌéËØ ÌÍæ â×ç×Ì ãñ ÂÚUÌé â´·ý¤æ×·¤ Ùãè´ ãñÐ (2) SßÌéËØ ÌÍæ â´·ý¤æ×·¤ ãñ ÂÚUÌé â×ç×Ì Ùãè´ ãñÐ (3) â×ç×Ì ÌÍæ â´·ý¤æ×·¤ ãñ ÂÚUÌé SßÌéËØ Ùãè´ ãñÐ (4) °·¤ ÌéËØÌæ â´Õ´Ï ãñÐ 62. ×æÙæ w(Im w ¹ 0) °·¤ âç×æ â´Øæ ãñ, Ìæð âÖè âç×æ â´Øæ¥æð´ z ·¤æ â×éæØ, Áæð ç·¤âè ßæSÌçß·¤ â´Øæ k ·ð¤ çÜ°, â×è·¤ÚUæ w2 wz5k (12z) ·¤æð â´ÌécÅU ·¤ÚUÌæ ãñ, ãñ Ñ (1) {z : ?z?51} (2) {z : z5 z } (3) {z : z ¹ 1} (4) {z : ?z?51, z ¹ 1} 63. ØçÎ â×è·¤ÚUææð´ ax21bx1c50, (a, b, c Î R, a ¹ 0) ÌÍæ 2x213x1450 ·¤æ °·¤ ×êÜ ©ÖØçÙcÅU ãñ, Ìæð a : b : c ÕÚUæÕÚU ãñ Ñ (1) 1 : 2 : 3 (2) 2 : 3 : 4 (3) 4 : 3 : 2 (4) 3 : 2 : 1
32. 32. English : 32 Set : 01 Hindi : 32 Set : 01 64. If 1 a and 1 b are the roots of the equation, ax21bx1150 (a ¹ 0, a, b Î R), then the equation, x(x1b3)1(a323abx)50 has roots : (1) 3 2a and 3 2b (2) a 1 2b and 1 2a b (3) a b and a b (4) 3 2 2 a and 3 2 2 b 65. If a, b, c are non - zero real numbers and if the system of equations (a21)x5y1z, (b21)y5z1x, (c21)z5x1y, has a non-trivial solution, then ab1bc1ca equals : (1) a1b1c (2) abc (3) 1 (4) 21 64. ØçÎ 1 a ÌÍæ 1 b â×è·¤ÚUæ ax21bx1150 (a ¹ 0, a, b Î R) ·ð¤ ×êÜ ãñ, Ìæð â×è·¤ÚUæ x(x1b3)1(a323abx)50 ·ð¤ ×êÜ ã´ñ Ñ (1) 3 2a ÌÍæ 3 2b (2) a 1 2b ÌÍæ 1 2a b (3) a b ÌÍæ a b (4) 3 2 2 a ÌÍæ 3 2 2 b 65. ØçÎ a, b, c àæêØðÌÚU ßæSÌçß·¤ â´Øæ°¡ ãñ´ ÌÍæ ØçÎ â×è·¤ÚUæ çÙ·¤æØ (a21)x5y1z, (b21)y5z1x, (c21)z5x1y, ·¤æ °·¤ ¥ÌéÀU ãÜ ãñ, Ìæð ab1bc1ca ÕÚUæÕÚU ãñ Ñ (1) a1b1c (2) abc (3) 1 (4) 21
33. 33. English : 33 Set : 01 Hindi : 33 Set : 01 66. If B is a 333 matrix such that B250, then det. [(I1B)50250B] is equal to : (1) 1 (2) 2 (3) 3 (4) 50 67. The number of terms in the expansion of (11x)101 (11x22x)100 in powers of x is : (1) 302 (2) 301 (3) 202 (4) 101 68. The sum of the digits in the units place of all the 4-digit numbers formed by using the numbers 3, 4, 5 and 6, without repetition, is : (1) 432 (2) 108 (3) 36 (4) 18 66. ØçÎ B °·¤ °ðâæ 333 ¥æÃØêã ãñ ç·¤ B250 ãñ, Ìæð det. [(I1B)50250B] ÕÚUæÕÚU ãñ Ñ (1) 1 (2) 2 (3) 3 (4) 50 67. (11x)101 (11x22x)100 ·ð¤ x ·¤è ææÌæð´ ×ð´ ÂýâæÚU ×ð´ ÂÎæð´ ·¤è â´Øæ ãñ Ñ (1) 302 (2) 301 (3) 202 (4) 101 68. â´Øæ¥æð´ 3, 4, 5 ÌÍæ 6 ·ð¤ ÂýØæð» âð, çÕÙæ ·¤æð§ü â´Øæ ÎæðãÚUæ°, ÕÙÙð ßæÜè âÖè ¿æÚU ¥´·¤æð´ ·¤è â´Øæ¥æð´ ·ð¤ §·¤æ§ü ·ð¤ SÍæÙ ÂÚU ¥æÙð ßæÜð ¥´·¤æð´ ·¤æ Øæð» ãñ Ñ (1) 432 (2) 108 (3) 36 (4) 18
34. 34. English : 34 Set : 01 Hindi : 34 Set : 01 69. Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4th term is : (1) 8 (2) 16 (3) 20 (4) 24 70. If the sum 2 2 2 2 2 2 3 5 7 1 1 2 1 2 3 .......1 1 1 1 1 1 1 upto 20 terms is equal to k 21 , then k is equal to : (1) 120 (2) 180 (3) 240 (4) 60 71. If f(x) is continuous and ( )9 2 2 9f ,5 then 20 1 cos 3 lim x x f x→      2 is equal to : (1) 9/2 (2) 2/9 (3) 0 (4) 8/9 69. Îè »§ü °·¤ â×æ´ÌÚU æðÉ¸è ·ð¤ âÖè ÂÎ ÏÙÂêææZ·¤ ãñ´Ð §â·ð¤ ÂýÍ× Ùæñ ÂÎæð´ ·¤æ Øæð» 200 âð ¥çÏ·¤ ÌÍæ 220 âð ·¤× ãñÐ ØçÎ §â·¤æ ÎêâÚUæ ÂÎ 12 ãñ, Ìæð §â·¤æ ¿æñÍæ ÂÎ ãñ Ñ (1) 8 (2) 16 (3) 20 (4) 24 70. ØçÎ 2 2 2 2 2 2 3 5 7 1 1 2 1 2 3 .......1 1 1 1 1 1 1 ·ð¤20 ÂÎæð´ Ì·¤ ·¤æ Øæð» k 21 ·ð¤ ÕÚUæÕÚU ãñ, Ìæð k ÕÚUæÕÚU ãñ Ñ (1) 120 (2) 180 (3) 240 (4) 60 71. ØçÎ f(x) âÌÌ ãñ ÌÍæ ( )9 2 2 9f 5 ãñ, Ìæð 20 1 cos 3 lim x x f x→      2 ÕÚUæÕÚU ãñ Ñ (1) 9/2 (2) 2/9 (3) 0 (4) 8/9
35. 35. English : 35 Set : 01 Hindi : 35 Set : 01 72. If y5enx, then 2 2 2 2 d d d d y x x y             is equal to : (1) n enx (2) n e2nx (3) 1 (4) 2n e2nx 73. If the Rolles theorem holds for the function f(x)52x31ax21bx in the interval [21, 1] for the point c5 1 2 , then the value of 2a1b is : (1) 1 (2) 21 (3) 2 (4) 22 74. If 3 4 ( ) 1 5 5 x x f x            5 1 2 , x Î R, then the equation f(x)50 has : (1) no solution (2) one solution (3) two solutions (4) more than two solutions 72. ØçÎ y5enx ãñ, Ìæð 2 2 2 2 d d d d y x x y             ÕÚUæÕÚU ãñ Ñ (1) n enx (2) n e2nx (3) 1 (4) 2n e2nx 73. ØçÎ È¤ÜÙ f(x)52x31ax21bx ·ð¤¤ çÜ° ¥´ÌÚUæÜ [21, 1] ×ð´ çÕ´Îé c5 1 2 ÂÚU ÚUæðÜð ·¤æ Âý×ðØ Üæ»ê ãñ, Ìæð 2a1b ·¤æ ×æÙ ãñ Ñ (1) 1 (2) 21 (3) 2 (4) 22 74. ØçÎ 3 4 ( ) 1 5 5 x x f x            5 1 2 , x Î R ãñ, Ìæð â×è·¤ÚUæ f(x)50 ·¤æ/·ð¤ Ñ (1) ·¤æð§ü ãÜ Ùãè´ ãñÐ (2) °·¤ ãÜ ãñÐ (3) Îæð ãÜ ãñ´Ð (4) Îæð âð ¥çÏ·¤ ãÜ ãñ´Ð
36. 36. English : 36 Set : 01 Hindi : 36 Set : 01 75. 8 8 2 2 sin cos d (1 2 sin cos ) x x x x x ∫ 2 2 is equal to : (1) 1 2 sin 2x1c (2) 1 2 2 sin 2x1c (3) 1 2 2 sin x1c (4) 2sin2 x1c 76. The integral 1 2 0 2 (1 2 ) d 1 4 ln x x x ∫ 1 1 , equals : (1) 4 p ln 2 (2) 8 p ln 2 (3) 16 p ln 2 (4) 32 p ln 2 77. Let A5{(x, y) : y2 [ 4x, y22x/24}. The area (in square units) of the region A is : (1) 8 (2) 9 (3) 10 (4) 11 75. 8 8 2 2 sin cos d (1 2 sin cos ) x x x x x ∫ 2 2 ÕÚUæÕÚU ãñ Ñ (1) 1 2 sin 2x1c (2) 1 2 2 sin 2x1c (3) 1 2 2 sin x1c (4) 2sin2 x1c 76. â×æ·¤Ü 1 2 0 2 (1 2 ) d 1 4 ln x x x ∫ 1 1 , ÕÚUæÕÚU ãñ Ñ (1) 4 p ln 2 (2) 8 p ln 2 (3) 16 p ln 2 (4) 32 p ln 2 77. ×æÙæ A5{(x, y) : y2 [ 4x, y22x/24} ãñÐ ÿæðæ A ·¤æ ÿæðæÈ¤Ü (ß»ü §·¤æ§üØæð´ ×ð´) ãñ Ñ (1) 8 (2) 9 (3) 10 (4) 11
37. 37. English : 37 Set : 01 Hindi : 37 Set : 01 78. If the differential equation representing the family of all circles touching x-axis at the origin is (x22y2) d d y x 5g(x) y, then g(x) equals : (1) 1 2 x (2) 2x2 (3) 2x (4) 1 2 x2 79. Let a and b be any two numbers satisfying 2 2 1 1 1 4a b 1 5 . Then, the foot of perpendicular from the origin on the variable line, 1 a b yx 1 5 , lies on : (1) a hyperbola with each semi-axis5 2 . (2) a hyperbola with each semi-axis52. (3) a circle of radius52 (4) a circle of radius5 2 78. ØçÎ ©Ù âÖè ßëææð´ ·ð¤ ·é¤Ü, Áæð x-¥ÿæ ·¤æð ×êÜ çÕ´Îé ÂÚU SÂàæü ·¤ÚUÌð ãñ´, ·¤æ ¥ß·¤Ü â×è·¤ÚUæ (x22y2) d d y x 5g(x) y, ãñ, Ìæð g(x) ÕÚUæÕÚU ãñ Ñ (1) 1 2 x (2) 2x2 (3) 2x (4) 1 2 x2 79. ×æÙ a ¥æñÚU b, 2 2 1 1 1 4a b 1 5 ·¤æð â´ÌécÅU ·¤ÚUÙð ßæÜè Îæð â´Øæ°¡ ãñ´, Ìæð ¿ÚUÚðU¹æ, 1 a b yx 1 5 ×êÜ çÕ´Îé âð ÇUæÜð »° Ü´Õ ·¤æ ÂæÎ, çSÍÌ ãñ Ñ (1) °·¤ ¥çÌÂÚUßÜØ ÂÚU, çÁâ·¤æ ÂýØð·¤ ¥Ïü ¥ÿæ5 2 ãñÐ (2) °·¤ ¥çÌÚUÂÚUßÜØ ÂÚU, çÁâ·¤æ ÂýØð·¤ ¥Ïü ¥ÿæ52 ãñÐ (3) °·¤ ßëæ ÂÚU, çÁâ·¤è çæØæ52 ãñÐ (4) °·¤ ßëæ ÂÚU, çÁâ·¤è çæØæ5 2 ãñÐ
38. 38. English : 38 Set : 01 Hindi : 38 Set : 01 80. Given three points P, Q, R with P(5, 3) and R lies on the x-axis. If equation of RQ is x22y52 and PQ is parallel to the x-axis, then the centroid of DPQR lies on the line : (1) 2x1y2950 (2) x22y1150 (3) 5x22y50 (4) 2x25y50 81. If the point (1, 4) lies inside the circle x21y226x210y1p50 and the circle does not touch or intersect the coordinate axes, then the set of all possible values of p is the interval : (1) (0, 25) (2) (25, 39) (3) (9, 25) (4) (25, 29) 82. If OB is the semi-minor axis of an ellipse, F1 and F2 are its foci and the angle between F1B and F2B is a right angle, then the square of the eccentricity of the ellipse is : (1) 1 2 (2) 1 2 (3) 1 2 2 (4) 1 4 80. ÌèÙ çÎ° »° çÕ´Îé¥æð´ P, Q, R ×ð´ P(5, 3) ãñ ÌÍæ R, x-¥ÿæ ÂÚU çSÍÌ ãñÐ ØçÎ RQ ·¤æ â×è·¤ÚUæ x22y52 ãñ ÌÍæ PQ, x-¥ÿæ ·ð¤ â×æ´ÌÚU ãñ, Ìæð DPQR ·¤æ ·ð´¤Îý·¤ çÁâ ÚðU¹æ ÂÚU çSÍÌ ãñ, ßã ãñ Ñ (1) 2x1y2950 (2) x22y1150 (3) 5x22y50 (4) 2x25y50 81. ØçÎ çÕ´Îé (1, 4) ßëæ x21y226x210y1p50 ·ð¤ ¥ÌÑ Öæ» ×ð´ çSÍÌ ãñ ÌÍæ ßëæ, çÙÎðüàææ´·¤ ¥ÿææð´ ·¤æð Ù Ìæð SÂàæü ·¤ÚUÌæ ãñ, ¥æñÚU Ù ãè ·¤æÅUÌæ ãññ, Ìæð p ·ð¤ âÖè â´Öß ×æÙæð´ ·¤æ â×é¿Ø çÙÙ ¥Ì´ÚUæÜ ãñ Ñ (1) (0, 25) (2) (25, 39) (3) (9, 25) (4) (25, 29) 82. ØçÎ OB, °·¤ Îèæüßëæ ·¤æ ¥Ïü Üæé¥ÿæ ãñ, F1 ÌÍæ F2 ©â·¤è ÙæçÖØæ¡ ãñ´ ÌÍæ F1B ÌÍæ F2B ·ð¤ Õè¿ ·¤æ ·¤æðæ °·¤ â×·¤æðæ ãñ, Ìæð Îèæüßëæ ·¤è ©·ð´¤ÎýÌæ ·¤æ ß»ü ãñ Ñ (1) 1 2 (2) 1 2 (3) 1 2 2 (4) 1 4
39. 39. English : 39 Set : 01 Hindi : 39 Set : 01 83. Equation of the plane which passes through the point of intersection of lines 1 2 3 3 1 2 x y z2 2 2 5 5 and 3 1 2 1 2 3 x y z2 2 2 5 5 and has the largest distance from the origin is : (1) 7x12y14z554 (2) 3x14y15z549 (3) 4x13y15z550 (4) 5x14y13z557 84. A line in the 3-dimensional space makes an angle 0 < 2      p u u [ with both the x and y axes. Then the set of all values of u is the interval : (1) 0 4 ,      p (2) 6 3 ,      p p (3) 4 2 ,      p p (4) 3 2 ,      p p 83. ©â â×ÌÜ ·¤æ â×è·¤ÚUæ, Áæð ÚðU¹æ¥æð´ 1 2 3 3 1 2 x y z2 2 2 5 5 ÌÍæ 3 1 2 1 2 3 x y z2 2 2 5 5 ·ð¤ ÂýçÌÀðUÎÙ çÕ´Îé âð ãæð ·¤ÚU ÁæÌæ ãñ, ÌÍæ ×êÜçÕ´Îé âð ¥çÏ·¤Ì× ÎêÚUè ÂÚU ãñ, ãñ Ñ (1) 7x12y14z554 (2) 3x14y15z549 (3) 4x13y15z550 (4) 5x14y13z557 84. çæçß×èØ ¥æ·¤æàæ (space) ×ð´ °·¤ ÚðU¹æ x ÌÍæ y, ÎæðÙæ´ð ¥ÿææð´ ·ð¤ âæÍ ·¤æðæ 0 < 2      p u u [ ÕÙæÌè ãñ, Ìæð u ·ð¤ âÖè ×æÙæð´ ·¤æ â×é¿Ø çÙÙ ¥´ÌÚUæÜ ãñ Ñ (1) 0 4 ,      p (2) 6 3 ,      p p (3) 4 2 ,      p p (4) 3 2 ,      p p
40. 40. English : 40 Set : 01 Hindi : 40 Set : 01 85. If a 2, b 3 →→ ? ?5 ? ?5 and 2 a b 5 →→ ? 2 ?5 , then 2 a b →→ ? 1 ? equals : (1) 17 (2) 7 (3) 5 (4) 1 86. In a set of 2n distinct observations, each of the observation below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3. Then the mean of the new set of observations : (1) increases by 1. (2) decreases by 1. (3) decreases by 2. (4) increases by 2. 87. If A and B are two events such that P(AÈB)5P(AÇB), then the incorrect statement amongst the following statements is : (1) A and B are equally likely (2) P(AÇB9)50 (3) P(A9ÇB)50 (4) P(A)1P(B)51 85. ØçÎ a 2, b 3 →→ ? ?5 ? ?5 ÌÍæ 2 a b 5 →→ ? 2 ?5 ãñ, Ìæð 2 a b →→ ? 1 ? ÕÚUæÕÚU ãñ Ñ (1) 17 (2) 7 (3) 5 (4) 1 86. 2n çßçÖóæ Âýðÿæææð´ ·ð¤ â×é¿Ø ×ð´, ©Ù âÖè Âýðÿæææð´, Áæð âÖè Âýðÿæææð´ ·ð¤ ×æØ·¤ âð ·¤× ãñ´, ÂýØð·¤ ·¤æð 5 âð ÕÉ¸æ çÎØæ »Øæ ÌÍæ àæðá âÖè Âðýÿæææð´ ×´ð ÂýØð·¤ ·¤æð 3 âð ·¤× ·¤ÚU çÎØæ »Øæ, Ìæð Âýðÿæææð´ ·ð¤ Ù° â×é¿Ø ·¤æ ×æØ Ñ (1) 1 âð ÕÉ¸ ÁæÌæ ãñÐ (2) 1 âð æÅU ÁæÌæ ãñÐ (3) 2 âð æÅU ÁæÌæ ãñÐ (4) 2 âð ÕÉ¸ ÁæÌæ ãñÐ 87. A ÌÍæB Îæð °ðâè æÅUÙæ°¡ ãñ´ ç·¤ P(AÈB)5P(AÇB) ãñ, Ìæð çÙÙ ·¤ÍÙæð´ ×ð´ âð ·¤æñÙ âæ ·¤ÍÙ »ÜÌ ãñ ? (1) A ÌÍæ B â×â´ÖæçßÌ ã´ñ (2) P(AÇB9)50 (3) P(A9ÇB)50 (4) P(A)1P(B)51
41. 41. English : 41 Set : 01 Hindi : 41 Set : 01 88. The number of values of a in [0, 2p] for which 2 sin3 a27 sin2 a17 sin a52, is : (1) 6 (2) 4 (3) 3 (4) 1 89. If cosec p q p q 1 u5 2 (p¹q¹0), then cot 4 2      p u 1 is equal to : (1) p q (2) q p (3) pq (4) pq 90. The contrapositive of the statement I go to school if it does not rain is : (1) If it rains, I do not go to school. (2) If I do not go to school, it rains. (3) If it rains, I go to school. (4) If I go to school, it rains. - o 0 o - 88. [0, 2p] ×ð´ a ·ð¤ ©Ù ×æÙæð´ ·¤è â´Øæ, çÁÙ·ð¤ çÜ° 2 sin3 a27 sin2 a17 sin a52 ãñ, ãñ Ñ (1) 6 (2) 4 (3) 3 (4) 1 89. ØçÎ cosec p q p q 1 u5 2 (p¹q¹0) ãñ, Ìæð cot 4 2      p u 1 ÕÚUæÕÚU ãñ Ñ (1) p q (2) q p (3) pq (4) pq 90. ·¤ÍÙ ÒÒ×ñ´ S·ê¤Ü ÁæÌæ ã¡ê ØçÎ ßáæü Ùãè´ ãæðÌèÓÓ ·¤æ ÂýçÌÏÙæ×·¤ (Contrapositive) ·¤ÍÙ ãñ Ñ (1) ØçÎ ßáæü ãæðÌè ãñ, ×ñ´ S·ê¤Ü Ùãè´ ÁæÌæÐ (2) ØçÎ ×ñ´ S·ê¤Ü Ùãè´ ÁæÌæ, ßáæü ãæðÌè ãñÐ (3) ØçÎ ßáæü ãæðÌè ãñ, ×ñ´ S·ê¤Ü ÁæÌæ ã¡êÐ (4) ØçÎ ×ñ´ S·ê¤Ü ÁæÌæ ã¡ê, ßáæü ãæðÌè ãñÐ - o 0 o -