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JEE MAIN QUESTION PAPER -12.04.2014

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JEE MAIN QUESTION PAPER -12.04.2014

1. 1. English : 1 Set : 06 Hindi : 1 Set : 06 PART A  PHYSICS 1. From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is : (1) 2 o c 2 h pe (2) 2 2 o e e 2 Gmpe (me5 mass of electron) (3) o o 2 2 G c eh m e (4) o o 2 2 Gce hp m e 2. A person climbs up a stalled escalator in 60 s . If standing on the same but escalator running with constant velocity he takes 40 s. How much time is taken by the person to walk up the moving escalator ? (1) 37 s (2) 27 s (3) 24 s (4) 45 s Öæ» A  ÖæñçÌ·¤ çßææÙ 1. ÖæñçÌ·¤ çSÍÚUæ´·¤æð´ ·ð¤ çÙÙçÜç¹Ì â´ØæðÁÙ âð (¥ÂÙð âæÏæÚUæ ÂýØæð» ×ð´ çÜØð »Øð ç¿ãæð´ mæÚUæ ÂýÎçàæüÌ), ·ð¤ßÜ ßã â´ØæðÁÙ, Áæð ç·¤ §·¤æ§Øæð´ ·ð¤ çßçÖóæ çÙ·¤æØæð´ ×ð´ °·¤ ãè ×æÙ ÚU¹Ìæ ãñ, ãñ Ñ (1) 2 o c 2 h pe (2) 2 2 o e e 2 Gmpe (me5§ÜðÅþUæòÙ ·¤æ ÎýÃØ×æÙ) (3) o o 2 2 G c eh m e (4) o o 2 2 Gce hp m e 2. °·¤ ÃØçæ °·¤ SÍæçÂÌ °S·¤ÜðÅUÚU ·¤è ÎêÚUè 60 s ×ð´ ¿É¸Ìæ ãñÐ ØçÎ ©â ÂÚU ¹Ç¸ð ãæð·¤ÚU ÂÚUÌé çSÍÚU ßð» âð °S·¤ÜðÅUÚU ·ð¤ ¿ÜÙð ÂÚU ßã 40 s ÜðÌæ ãñÐ ÃØçæ »çÌàæèÜ °S·¤ÜðÅUÚU ÂÚU ¿Ü·¤ÚU §âè ÎêÚUè ·¤æð ÌØ ·¤ÚUÙð ×ð´ ç·¤ÌÙæ â×Ø Üð»æ? (1) 37 s (2) 27 s (3) 24 s (4) 45 s
2. 2. English : 2 Set : 06 Hindi : 2 Set : 06 3. Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u, and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be : (1) ( )u 3 12 i j ∧ ∧ 1 (2) ( )u 3 12 i j ∧ ∧ 2 (3) ( )u 3 12 i j ∧ ∧ 2 1 (4) ( )u 3 12 i j ∧ ∧ 2 2 4. A 4 g bullet is fired horizontally with a speed of 300 m/s into 0.8 kg block of wood at rest on a table. If the coefficient of friction between the block and the table is 0.3, how far will the block slide approximately ? (1) 0.19 m (2) 0.379 m (3) 0.569 m (4) 0.758 m 3. m, 2m °ß´ 3m ·ð¤ ÌèÙ ÎýÃØ×æÙ x-y ÌÜ ×ð´ ¿æÜ ·ý¤×àæÑ 3u, 2u, °ß´ u âð »çÌàæèÜ ãñ, Áñâæ ç·¤ ç¿æ ×ð´ ÎàææüØæ »Øæ ãñÐ ÌèÙæð´ ÎýÃØ×æÙ °·¤ ãè çÕÎé ÂÚU â´æ^ ·¤ÚUÌð ãñ´ ¥æñÚU °·¤ âæÍ ç¿Â·¤ ÁæÌð ãñ´Ð ÂçÚUææ×è ÎýÃØ×æÙ ·¤æ ßð» ãæð»æ Ñ (1) ( )u 3 12 i j ∧ ∧ 1 (2) ( )u 3 12 i j ∧ ∧ 2 (3) ( )u 3 12 i j ∧ ∧ 2 1 (4) ( )u 3 12 i j ∧ ∧ 2 2 4. °·¤ ×ð\$Á ÂÚU çßææ× ¥ßSÍæ ×ð´ çSÍÌ 0.8 kg Ü·¤Ç¸è ·ð¤ Üæ·¤ ·¤æð 300 m/s ·¤è ¿æÜ âð °·¤ 4 g ·¤è »æðÜè ÿæñçÌÁ Îæ»Ìè ãñÐ ØçÎ ×ð\$Á °ß´ Üæ·¤ ·ð¤ Õè¿ æáüæ »éææ´·¤ 0.3 ãñ, ÌÕ Üæ·¤ Ü»Ö» ç·¤ÌÙè ÎêÚU çÈ¤âÜð»æ? (1) 0.19 m (2) 0.379 m (3) 0.569 m (4) 0.758 m
3. 3. English : 3 Set : 06 Hindi : 3 Set : 06 5. A spring of unstretched length l has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity v is : (1) 21 m 2 v (2) mv2 (3) 21 m 3 v (4) 21 m 6 v 6. A particle is moving in a circular path of radius a, with a constant velocity v as shown in the figure. The center of circle is marked by C. The angular momentum from the origin O can be written as : (1) va(11cos 2u) (2) va(11cos u) (3) va cos 2u (4) va 5. çÕÙæ ÌæçÙÌ ÜÕæ§ü l ·¤è °·¤ ·¤×æÙè âð °·¤ ÎýÃØ×æÙ m §â Âý·¤æÚU ãñ ç·¤ §â·¤æ °·¤ çâÚUæ °·¤ ÎëÉ¸ ¥æÏæÚU ÂÚU Õ¡Ïæ ãñÐ Øã ×æÙÌð ãéØð ç·¤ ·¤×æÙè °·¤ °·¤â×æÙ ÌæÚU âð ÕÙè ãñ, §â×ð´ »çÌÁ ª¤Áæü ãæð»è ØçÎ §â·¤æ SßÌæ çâÚUæ °·¤â×æÙ ßð» v âð ¹è´¿æ Áæ° Ñ (1) 21 m 2 v (2) mv2 (3) 21 m 3 v (4) 21 m 6 v 6. °·¤ ·¤æ çæØæ a ·ð¤ °·¤ ßëæèØ ÂÍ ÂÚU °·¤ çSÍÚU ßð» v âð »çÌàæèÜ ãñ Áñâæ ç·¤ ç¿æ ×ð´ ÎàææüØæ »Øæ ãñÐ ßëæ ·¤æ ·ð¤Îý C âð ç¿çãÌ ç·¤Øæ »Øæ ãñÐ ×êÜ çÕÎé O âð ·¤æðæèØ â´ßð» §â Âý·¤æÚU çÜ¹æ Áæ â·¤Ìæ ãñ Ñ (1) va(11cos 2u) (2) va(11cos u) (3) va cos 2u (4) va
4. 4. English : 4 Set : 06 Hindi : 4 Set : 06 7. Two hypothetical planets of masses m1 and m2 are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is d ? (Speed of m1 is v1 and that of m2 is v2) (1) v15v2 (2) 1 2 1 2 2G m d(m m ) v 5 1 2 1 1 2 2G m d(m m ) v 5 1 (3) 1 1 1 2 2G m d(m m ) v 5 1 2 2 1 2 2G m d(m m ) v 5 1 (4) 1 2 1 2G m m v 5 2 1 2 2G m m v 5 7. ÎýÃØ×æÙ m1 °ß´ m2 ·ð¤ Îæð ÂçÚU·¤çËÂÌ ©Â»ýã çßææ× ¥ßSÍæ ×ð´ ãñ´ ÁÕ ßð °·¤ ÎêâÚðU âð ¥æÌ ÎêÚUè ÂÚU ãñ´Ð »éL¤ßæ·¤áüæ ÕÜ ·ð¤ ·¤æÚUæ ©Ù·ð¤ ·ð¤Îýæð´ ·¤æð ç×ÜæÙð ßæÜè ÚðU¹æ ÂÚU °·¤ ÎêâÚðU ·¤è ¥æðÚU »çÌ ·¤ÚUÙæ ÂýæÚUÖ ·¤ÚUÌð ãñ´Ð ÁÕ ©æ·ð¤ Õè¿ ÎêÚUè d ãñ, ÌÕ ©Ù·¤è ¿æÜ Øæ ãñ? ( m1 ·¤è ¿æÜ v1 °ß´ m2 ·¤è ¿æÜ v2 ãñ ) (1) v15v2 (2) 1 2 1 2 2G m d(m m ) v 5 1 2 1 1 2 2G m d(m m ) v 5 1 (3) 1 1 1 2 2G m d(m m ) v 5 1 2 2 1 2 2G m d(m m ) v 5 1 (4) 1 2 1 2G m m v 5 2 1 2 2G m m v 5
5. 5. English : 5 Set : 06 Hindi : 5 Set : 06 8. Steel ruptures when a shear of 3.53108 N m22 is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly : (1) 1.43104 N (2) 2.73104 N (3) 3.33104 N (4) 1.13104 N 9. A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius a. The time in which it will be emptied is : (1) 2 2A h gap (2) 2 2A h gap (3) 2 2 2A h gap (4) 2 A h g2 ap 8. SÅUèÜ È¤ÅU ÁæÌæ ãñ ÁÕ ©â ÂÚU 3.53108 Nm22 ·¤æ ¥ÂM¤Âæ Ü»æØæ ÁæÌæ ãñÐ 0.3 cm ×æðÅUè SÅUèÜ àæèÅU ×ð´ 1 cm ÃØæâ ·¤æ çÀUÎý ·¤ÚUÙð ×ð´ Ü»æØð ÁæÙð ßæÜæ ÕÜ Ü»Ö» ãñ Ñ (1) 1.43104 N (2) 2.73104 N (3) 3.33104 N (4) 1.13104 N 9. ¥ÙéÂýSÍ ·¤æÅU A ßæÜð °·¤ ÕðÜÙæ·¤æÚU ÕÌüÙ ×ð´ ÂæÙè ª¡¤¿æ§ü h Ì·¤ ÖÚUæ ãñÐ §â·¤è ÌÜè ×ð´ çæØæ a ·¤æ °·¤ çÀUÎý ãñÐ ßã â×Ø, çÁâ×ð´ Øã ÕÌüÙ çÚUæ ãæð Áæ°»æ, ãñ Ñ (1) 2 2A h gap (2) 2 2A h gap (3) 2 2 2A h gap (4) 2 A h g2 ap
6. 6. English : 6 Set : 06 Hindi : 6 Set : 06 10. Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S the change in total surface area, T is the surface tension and P atmospheric pressure, which of the following relation is correct ? (1) 4PV13ST50 (2) 3PV14ST50 (3) 2PV13ST50 (4) 3PV12ST50 11. Hot water cools from 608C to 508C in the first 10 minutes and to 428C in the next 10 minutes. The temperature of the surroundings is : (1) 258C (2) 108C (3) 158C (4) 208C 12. A Carnot engine absorbs 1000 J of heat energy from a reservoir at 1278C and rejects 600 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be : (1) 20% and 2438C (2) 40% and 2338C (3) 50% and 2208C (4) 70% and 2108C 10. Îæð âæÕéÙ ·ð¤ ÕéÜÕéÜð ç×Ü·¤ÚU °·¤ ÕéÜÕéÜæ ÕÙæÌð ãñ´Ð ØçÎ §Ù×ð´ çSÍÌ ßæØé ·ð¤ ¥æØÌÙ ×ð´ ÂÚUßÌèü ÂçÚUßÌüÙ V ãñ ¥æñÚU âÂêæü ÂëcÆ ÿæðæÈ¤Ü ×ð´ ÂçÚUßÌüÙ S ãñ, T ÂëcÆU ÌÙæß ãñ ¥æñÚU P ßæØé×´ÇUÜ ÎæÕ ãñ, ÌÕ çÙÙçÜç¹Ì ×ð´ âð ·¤æñÙ-âæ âÕÏ âãè ãñ? (1) 4PV13ST50 (2) 3PV14ST50 (3) 2PV13ST50 (4) 3PV12ST50 11. »×ü ÂæÙè 608C âð 508C ÂãÜð 10 ç×ÙÅU ×ð´ Æ´UÇUæ ãæðÌæ ãñ ¥æñÚU 428C Ì·¤ ÎêâÚðU 10 ç×ÙÅU ×ð´ Æ´UÇUæ ãæðÌæ ãñÐ ßæÌæßÚUæ ·¤æ ÌæÂ×æÙ ãñ Ñ (1) 258C (2) 108C (3) 158C (4) 208C 12. °·¤ ·¤æÙæðü §´ÁÙ °·¤ ·é´¤ÇU âð 1278C ÂÚU 1000 J ª¤c×èØ ª¤Áæü ¥ßàææðçáÌ ·¤ÚUÌæ ãñ ¥æñÚU ÂýØð·¤ ¿·ý¤ ×ð´ 600 J ª¤c×èØ ª¤Áæü ¥Sßè·¤æÚU ·¤ÚU ÎðÌæ ãñÐ §´ÁÙ ·¤è ÎÿæÌæ ¥æñÚU çâ´·¤ ·¤æ ÌæÂ×æÙ ãæð»æ Ñ (1) 20% °ß´ 2438C (2) 40% °ß´ 2338C (3) 50% °ß´ 2208C (4) 70% °ß´ 2108C
7. 7. English : 7 Set : 06 Hindi : 7 Set : 06 13. At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 ms21. The gas is : (1) H2 (2) Cl2 (3) O2 (4) F2 14. Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants ? (1) a1bx2cx2 (2) bx2 (3) a2bx1cx2 (4) 2bx 15. A source of sound A emitting waves of frequency 1800 Hz is falling towards ground with a terminal speed v. The observer B on the ground directly beneath the source receives waves of frequency 2150 Hz. The source A receives waves, reflected from ground, of frequency nearly : (Speed of sound 5343 m/s) (1) 2150 Hz (2) 2500 Hz (3) 1800 Hz (4) 2400 Hz 13. ·¤×ÚðU ·ð¤ ÌæÂ×æÙ ÂÚU °·¤ çmÂÚU×ææé·¤ »ñâ ·¤è ß»ü-×æØ-×êÜ ¿æÜ 1930 ms21 ÂæØè ÁæÌè ãñÐ »ñâ ãñ Ñ (1) H2 (2) Cl2 (3) O2 (4) F2 14. çÙÙçÜç¹Ì ÃØ´Á·¤æð´ ×ð´ âð ·¤æñÙ âæ °·¤ âÚUÜ ÚðU¹æ ÂÚU âÚUÜ ¥æßÌü »çÌ ·ð¤ â´»Ì ãñ, Áãæ¡ x çßSÍæÂÙ ãñ ¥æñÚU a, b, c ÏÙæ×·¤ çSÍÚUæ´·¤ ãñ ? (1) a1bx2cx2 (2) bx2 (3) a2bx1cx2 (4) 2bx 15. ¥æßëçæ 1800 Hz ·¤è Ì´ÚU»ð´ ©âçÁüÌ ·¤ÚU ÚUãæ ßçÙ dæðÌ A °·¤ âè×æÌ ßð» v âð ÏÚUÌè ·¤è ¥æðÚU ç»ÚU ÚUãæ ãñÐ dæðÌ ·ð¤ ÆUè·¤ Ùè¿ð ÏÚUÌè ÂÚU °·¤ Âýðÿæ·¤ B ¥æßëçæ 2150 Hz ·¤è ÌÚ´U»ð´ Âýææ ·¤ÚUÌæ ãñÐ dæðÌ A, ÏÚUÌè âð ÂÚUæßçÌüÌ Ü»Ö» §â ¥æßëçæ ·¤è ÌÚ´U»ð´ Âýææ ·¤ÚðU»æ Ñ ( ßçÙ ·¤è ¿æÜ 5343 m/s) (1) 2150 Hz (2) 2500 Hz (3) 1800 Hz (4) 2400 Hz
8. 8. English : 8 Set : 06 Hindi : 8 Set : 06 16. A spherically symmetric charge distribution is characterised by a charge density having the following variation : r(r)5ro r 1 R       2 for r < R r(r)50 for r / R Where r is the distance from the centre of the charge distribution and ro is a constant. The electric field at an internal point (r < R) is : (1) 2 o o r r 4 3 4R       r 2 e (2) 2 o o r r 3 4R       r 2 e (3) 2 o o r r 3 3 4R       r 2 e (4) 2 o o r r 12 3 4R       r 2 e 16. °·¤ »æðÜèØ â×ç×Ìè ¥æßðàæ çßÌÚUæ ¥æßðàæ æÙß ·¤æ çÙÙçÜç¹Ì çß¿ÚUæ ÚU¹Ìæ ãñ Ñ r(r)5ro r 1 R       2 r < R ·ð¤ çÜ° r(r)50 r / R ·ð¤ çÜ° Áãæ¡ r ¥æßðàæ çßÌÚUæ ·ð¤ ·ð¤Îý âð ÎêÚUè ãñ´ ¥æñÚU ro °·¤ çSÍÚUæ´·¤ ãñÐ °·¤ ¥ÌÑ çÕÎé (r < R) ÂÚU çßléÌ ÿæðæ ãñ Ñ (1) 2 o o r r 4 3 4R       r 2 e (2) 2 o o r r 3 4R       r 2 e (3) 2 o o r r 3 3 4R       r 2 e (4) 2 o o r r 12 3 4R       r 2 e
9. 9. English : 9 Set : 06 Hindi : 9 Set : 06 17. The space between the plates of a parallel plate capacitor is filled with a dielectric whose dielectric constant varies with distance as per the relation : K(x)5Ko1lx (l5 a constant) The capacitance C, of this capacitor, would be related to its vacuum capacitance Co as per the relation : (1) o o d C C (1 K d)ln l 5 1 l (2) o o C C d. (1 K d)ln l 5 1 l (3) o o d C C (1 d/K )ln l 5 1 l (4) o o C C d. (1 K / d)ln l 5 1 l 17. °·¤ â×æÌÚU Âç^·¤æ â´ÏæçÚUæ ·¤è Âç^·¤æ¥æð´ ·ð¤ Õè¿ ·¤æ SÍæÙ °·¤ ÂÚæßñléÌ âð ÖÚUæ ÁæÌæ ãñ çÁâ·¤æ ÂÚUæßñléÌ çSÍÚUæ´·¤ ÎêÚUè ·ð¤ âæÍ çÙÙ âÕÏ ¥ÙéâæÚU ÂçÚUßçÌüÌ ãæðÌæ ãñ Ñ K(x)5Ko1lx (l5°·¤ çSÍÚUæ´·¤) â´ÏæçÚUæ ·¤è ÏæçÚUÌæ C, §â·¤è çÙßæüÌ ÏæçÚUÌæ, Co ·ð¤ âæÍ çÙÙ âÕÏ ¥ÙéâæÚU âÕçÏÌ ãæð»è Ñ (1) o o d C C (1 K d)ln l 5 1 l (2) o o C C d. (1 K d)ln l 5 1 l (3) o o d C C (1 d/K )ln l 5 1 l (4) o o C C d. (1 K / d)ln l 5 1 l
10. 10. English : 10 Set : 06 Hindi : 10 Set : 06 18. The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors 3 V, 9 V and 9 V and a capacitor 5.0 mF. How much is the current I in the circuit in steady state ? (1) 1.6 A (2) 0.67 A (3) 2.5 A (4) 0.25 A 19. A positive charge q of mass m is moving along the 1x axis. We wish to apply a uniform magnetic field B for time Dt so that the charge reverses its direction crossing the y axis at a distance d. Then : (1) m d DQG W qd v v p 5 D 5 (2) m d DQG W 2 qd 2 v v p 5 D 5 (3) 2 m d DQG W qd 2 v v p 5 D 5 (4) 2 m d DQG W qd v v p 5 D 5 18. ÎàææüØð »Øð ÂçÚUÂÍ ×ð´ 8.0 V °ß´ 16.0 V ·¤è Îæð ÕñÅUçÚUØæ¡ ¥æñÚU 3 V, 9 V °ß´ 9 V ·ð¤ ÌèÙ ÂýçÌÚUæðÏ ÌÍæ 5.0 mF ·¤æ °·¤ â´ÏæçÚUæ ãñÐ SÍæØè ¥ßSÍæ ×ð´ ÂçÚUÂÍ ×ð´ ÏæÚUæ I ·¤æ ×æÙ Øæ ãñ? (1) 1.6 A (2) 0.67 A (3) 2.5 A (4) 0.25 A 19. ÎýÃØ×æÙ m ·¤æ °·¤ ÏÙæ×·¤ ¥æßðàæ q, 1x ¥ÿæ ÂÚU »çÌàæèÜ ãñÐ ã× °·¤ °·¤â×æÙ ¿éÕ·¤èØ ÿæðæ B â×Ø Dt ·ð¤ çÜ° Ü»æÙæ ¿æãÌð ãñ´ çÁââð ç·¤ ¥æßðàæ ·¤è çÎàææ d ÎêÚUè ÂÚU y - ¥ÿæ ·¤æð ·¤æÅUÌð ãé° ÂýçÌÜæðç×Ì ãæð Áæ°, ÌÕ Ñ (1) m d W qd v v p 5 D 5Ä (2) m d W 2 qd 2 v v p 5 D 5Ä (3) 2 m d W qd 2 v v p 5 D 5Ä (4) 2 m d W qd v v p 5 D 5Ä
11. 11. English : 11 Set : 06 Hindi : 11 Set : 06 20. Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B1, at its centre when a current I passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field B2 at the centre of the loops when current I/3 passes through it. The ratio B1 : B2 is : (1) 1 : 1 (2) 1 : 3 (3) 1 : 9 (4) 9 : 1 21. A sinusoidal voltage V(t)5100 sin (500t) is applied across a pure inductance of L50.02 H. The current through the coil is : (1) 10 cos (500t) (2) 210 cos (500t) (3) 10 sin (500t) (4) 210 sin (500t) 20. Îæð ÂÌÜð âßü â×M¤Âè ¿æÜ·¤èØ ÌæÚU ÕãéÌ ÂÌÜð ÚUæðÏè ÂÎæÍü âð É¸·ð¤ ãé° ãñ´Ð °·¤ ÌæÚU ·¤æð ×æðÇ¸·¤ÚU °·¤ ÜêÂ ÕÙæØæ ÁæÌæ ãñ Áæð ç·¤ ¥ÂÙð ·ð¤Îý ÂÚU ¿éÕ·¤èØ ÿæðæ B1 ©Âóæ ·¤ÚUÌæ ãñ ÁÕ §â×ð´ ÏæÚUæ I ÂýßæçãÌ ãæðÌè ãñÐ ÎêâÚðU ÌæÚU ·¤æð ÌèÙ âßüâ×M¤Âè ÜêÂæð´ ×ð´ ×æðÇ¸·¤ÚU ¥æñÚU °·¤ âæÍ ÚU¹·¤ÚU ·é¤ÇUÜè ÕÙæÌð ãñ´ Áæð ç·¤ ÜêÂæð´ ·ð¤ ·ð¤Îý ÂÚU ¿éÕ·¤èØ ÿæðæ B2 ©Âóæ ·¤ÚUÌæ ãñ ÁÕ §â×ð´ ÏæÚUæ I/3 ÂýßæçãÌ ãæðÌè ãñÐ ¥ÙéÂæÌ B1 : B2 ãñ Ñ (1) 1 : 1 (2) 1 : 3 (3) 1 : 9 (4) 9 : 1 21. °·¤ ØæÃæ·ý¤èØ ßæðËÅUÌæ V(t)5100 sin (500t) °·¤ çßàæéh ÂýðÚU·¤ß L50.02 H ÂÚU Ü»æ§ü ÁæÌè ãñÐ ·é¤ÇUÜè âð ÂýßæçãÌ ÏæÚUæ ãñ Ñ (1) 10 cos (500t) (2) 210 cos (500t) (3) 10 sin (500t) (4) 210 sin (500t)
12. 12. English : 12 Set : 06 Hindi : 12 Set : 06 22. A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly : (1) 1.34 V/m (2) 2.68 V/m (3) 4.02 V/m (4) 5.36 V/m 22. °·¤ ÜðÂ âÖè çÎàææ¥æð´ ×ð´ °·¤â×æÙ M¤Â âð °·¤ßæèü ãÚUæ Âý·¤æàæ ©âçÁüÌ ·¤ÚU ÚUãæ ãñÐ ÜðÂ ·¤è çßléÌ àæçæ ·¤æð çßléÌ ¿éÕ·¤èØ ÌÚ´U»æð´ ×ð´ ÂçÚUßÌüÙ ·¤ÚUÙð ·¤è ÎÿæÌæ 3% ãñ ¥æñÚU 100 W àæçæ ·¤è ¹ÂÌ ·¤ÚUÌæ ãñÐ ÜðÂ âð 5 m ÎêÚUè ÂÚU çßléÌ ¿éÕ·¤èØ çßç·¤ÚUæ âð âÕçhÌ çßléÌ ÿæðæ ·¤æ ¥æØæ× Ü»Ö» ãæð»æ Ñ (1) 1.34 V/m (2) 2.68 V/m (3) 4.02 V/m (4) 5.36 V/m
13. 13. English : 13 Set : 06 Hindi : 13 Set : 06 23. The refractive index of the material of a concave lens is m. It is immersed in a medium of refractive index m1. A parallel beam of light is incident on the lens. The path of the emergent rays when m1 > m is : (1) (2) (3) (4) 23. °·¤ ¥ßÌÜ Üðâ ·ð¤ ÂÎæÍü ·¤æ ¥ÂßÌüÙæ´·¤ m ãñÐ §âð ¥ÂßÌüÙæ´·¤ m1 ·ð¤ ×æØ× ×ð´ ÇéUÕæðØæ ÁæÌæ ãñÐ Âý·¤æàæ ·¤è °·¤ â×æÌÚU Âé´Á Üðâ ÂÚU ¥æÂçÌÌ ãñÐ ÁÕ m1 > m ãñ´, ÌÕ çÙ»üÌ ç·¤ÚUææð´ ·¤æ ÂÍ ãñ Ñ (1) (2) (3) (4)
14. 14. English : 14 Set : 06 Hindi : 14 Set : 06 24. Interference pattern is observed at P due to superimposition of two rays coming out from a source S as shown in the figure. The value of l for which maxima is obtained at P is : (R is perfect reflecting surface) : (1) 2 n 3 1 l l 5 2 (2) (2n 1) 2 ( 3 1) l 2 l 5 2 (3) (2n 1) 3 4 ( 2 3) l 2 l 5 2 (4) (2n 1) 3 1 l 2 l 5 2 25. In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength. If wavelength of red light is 6600 Å , then wavelength of first maximum will be : (1) 3300 Å (2) 4400 Å (3) 5500 Å (4) 6600 Å 24. °·¤ dæðÌ S âð çÙ·¤Ü ÚUãè Îæð ç·¤ÚUææð´ ·ð¤ ¥ØæÚUæðÂæ âð P ÂÚU °·¤ ÃØçÌ·¤ÚUæ ç¿æ ÂæØæ ÁæÌæ ãñ, Áñâæ ç·¤ ç¿æ ×ð´ ÎàææüØæ »Øæ ãñÐ l ·¤æ ßã ×æÙ, çÁâ·ð¤ çÜ° P ÂÚU Âýææ ç¿æ ×ð´ ×ãæ× ÌèßýÌæ ãñ, ãñ Ñ (R °·¤ ÂêæüÌØæ ÂÚUæßÌèü ÂëcÆU ãñ ) (1) 2 n 3 1 l l 5 2 (2) (2n 1) 2 ( 3 1) l 2 l 5 2 (3) (2n 1) 3 4 ( 2 3) l 2 l 5 2 (4) (2n 1) 3 1 l 2 l 5 2 25. °·¤Ü çSÜÅU çßßÌüÙ ç¿æ ·ð¤ ÂýØæð» ×ð´, ÜæÜ Âý·¤æàæ ·¤æ ÂýÍ× ØêÙÌ× °·¤ ÎêâÚUè ÌÚ´U»ÎñØü ·ð¤ ÂýÍ× ×ãæ× â´ÂæÌè ãñÐ ØçÎ ÜæÜ Âý·¤æàæ ·¤è ÌÚ´U»ÎñØü 6600 Å ãñ, ÌÕ ÂýÍ× ×ãæ× ·ð¤ â´»Ì ÌÚ´U»ÎñØü ãæð»è Ñ (1) 3300 Å (2) 4400 Å (3) 5500 Å (4) 6600 Å
15. 15. English : 15 Set : 06 Hindi : 15 Set : 06 26. A beam of light has two wavelengths 4972 Å and 6216 Å with a total intensity of 3.631023 Wm22 equally distributed among the two wavelengths. The beam falls normally on an area of 1 cm2 of a clean metallic surface of work function 2.3 eV. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photo electrons liberated in 2s is approximately : (1) 631011 (2) 931011 (3) 1131011 (4) 1531011 27. A piece of bone of an animal from a ruin is found to have 14C activity of 12 disintegrations per minute per gm of its carbon content. The 14C activity of a living animal is 16 disintegrations per minute per gm. How long ago nearly did the animal die ? (Given half life of 14C is t1/255760 years) (1) 1672 years (2) 2391 years (3) 3291 years (4) 4453 years 26. Îæð ÌÚ´U»ÎñØæðZ 4972Å °ß´ 6216 Å ßæÜð Âý·¤æàæ ·¤è °·¤ Âé´Á ·¤è ·é¤Ü ÌèßýÌæ 3.631023 Wm22 ãñ Áæð ç·¤ ÎæðÙæð´ ÌÚ´U»ÎñØæðZ ×ð´ °·¤ â×æÙ çßÌçÚUÌ ãñÐ 2.3 eV ·¤æØüÈ¤ÜÙ ßæÜð °·¤ âæÈ¤ ÏæÌé ·ð¤ ÂëcÆU ·ð¤ 1 cm2 ÿæðæÈ¤Ü ÂÚU Øã Âé´Á ¥çÖÜÕßÌ÷ ¥æÂçÌÌ ãñ´Ð Øã ×æÙ Üð´ ç·¤ ÂÚUæßÌüÙ mæÚUæ ç·¤âè Öè Âý·¤æàæ ·¤æ Oæâ Ùãè´ ãæðÌæ ãñ ¥æñÚU ÂýØð·¤ ÿæç×Ì È¤æðÅUæÙ °·¤ §ÜðÅþUæòÙ ©âçÁüÌ ·¤ÚUÌæ ãñÐ 2s ×ð´ ©âçÁüÌ È¤æðÅUæð §ÜðÅþUæòÙæð´ ·¤è â´Øæ ãñ Ü»Ö» Ñ (1) 631011 (2) 931011 (3) 1131011 (4) 1531011 27. °·¤ ¹ÇUãÚU âð Âýææ °·¤ Âàæé ·¤è ãaè ·ð¤ ÅéU·¤Ç¸ð ·¤è 14C âç·ý¤ØÌæ §â·ð¤ ·¤æÕüÙ ¥´àæ ·¤è ÂýçÌ »ýæ× ÂýçÌ ç×ÙÅU 12 çßæÅUÙ ãñÐ °·¤ çæÎæ Âàæé ·¤è 14C âç·ý¤ØÌæ 16 çßæÅUÙ ÂýçÌ ç×ÙÅU ÂýçÌ »ýæ× ãñ Ð Ü»Ö» ç·¤ÌÙð ßáü ÂãÜð Âàæé ·¤è ×ëØé ãé§ü? (çÎØæ ãñ 14C ·¤è ¥hü ¥æØé t1/255760 ßáü) (1) 1672 ßáü (2) 2391 ßáü (3) 3291 ßáü (4) 4453 ßáü
16. 16. English : 16 Set : 06 Hindi : 16 Set : 06 28. For LEDs to emit light in visible region of electromagnetic light, it should have energy band gap in the range of : (1) 0.1 eV to 0.4 eV (2) 0.5 eV to 0.8 eV (3) 0.9 eV to 1.6 eV (4) 1.7 eV to 3.0 eV 29. For sky wave propagation, the radio waves must have a frequency range in between : (1) 1 MHz to 2 MHz (2) 5 MHz to 25 MHz (3) 35 MHz to 40 MHz (4) 45 MHz to 50 MHz 30. In the experiment of calibration of voltmeter, a standard cell of e.m.f. 1.1 volt is balanced against 440 cm of potentiometer wire. The potential difference across the ends of resistance is found to balance against 220 cm of the wire. The corresponding reading of voltmeter is 0.5 volt. The error in the reading of voltmeter will be : (1) 20.15 volt (2) 0.15 volt (3) 0.5 volt (4) 20.05 volt 28. LEDs çßléÌ ¿éÕ·¤èØ Âý·¤æàæ ·ð¤ ÎëàØ ÿæðæ ×ð´ Âý·¤æàæ ©âçÁüÌ ·¤ÚðU, §â·ð¤ çÜØð §Ù·¤è ÕñÇ ¥ÌÚUæÜ §â ÚðUÁ ×ð´ ãæðÙè ¿æçãØð Ñ (1) 0.1 eV âð 0.4 eV (2) 0.5 eV âð 0.8 eV (3) 0.9 eV âð 1.6 eV (4) 1.7 eV âð 3.0 eV 29. ¥æ·¤æàæ ÌÚ´U» â´¿ÚUæ ·ð¤ çÜ°, ÚðUçÇUØæð ÌÚ´U»ð´ §â ¥æßëçæ ÚðUÁ ·ð¤ Õè¿ ãæðÙè ¿æçã° Ñ (1) 1 MHz âð 2 MHz (2) 5 MHz âð 25 MHz (3) 35 MHz âð 40 MHz (4) 45 MHz âð 50 MHz 30. °·¤ ßæðËÅU×æÂè ·ð¤ ¥´àæàææðÏÙ ·ð¤ ÂýØæð» ×ð´, 1.1 ßæðËÅU çßléÌßæã·¤ ÕÜ ·ð¤ °·¤ ×æÙ·¤ âñÜ ·ð¤ â´ÌéçÜÌ 440 cm ·¤æ çßÖß×æÂè ÌæÚU ÂæØæ ÁæÌæ ãñÐ °·¤ ÂýçÌÚUæðÏ ·ð¤ çâÚUæð´ ÂÚU çßÖßæÌÚU ÌæÚU ·ð¤ 220 cm ·ð¤ â´ÌéçÜÌ ÂæØæ ÁæÌæ ãñÐ ßæðËÅU×æÂè ·¤æ â´»Ì ÂÆUÙ 0.5 ßæðËÅU ãñÐ ßæðËÅU×æÂè ·ð¤ ÂÆUÙ ×ð´ æéçÅU ãæð»è Ñ (1) 20.15 ßæðËÅU (2) 0.15 ßæðËÅU (3) 0.5 ßæðËÅU (4) 20.05 ßæðËÅU
17. 17. English : 17 Set : 06 Hindi : 17 Set : 06 PART B  CHEMISTRY 31. If m and e are the mass and charge of the revolving electron in the orbit of radius r for hydrogen atom, the total energy of the revolving electron will be : (1) 2 1 e 2 r (2) 2 e r 2 (3) 2 me r (4) 2 1 e 2 r 2 32. The de-Broglie wavelength of a particle of mass 6.63 g moving with a velocity of 100 ms21 is : (1) 10233 m (2) 10235 m (3) 10231 m (4) 10225 m 33. What happens when an inert gas is added to an equilibrium keeping volume unchanged ? (1) More product will form (2) Less product will form (3) More reactant will form (4) Equilibrium will remain unchanged Öæ» B  ÚUâæØÙ çßææÙ 31. ØçÎ ãæ§ÇþæðÁÙ ÂÚU×ææé ·ð¤ çæØæ r ·¤è ¥æÚUçÕÅU ×ð´ æê×Ùð ßæÜð §ÜñÅþUæòÙ ·¤æ ÎýÃØ×æÙ m ¥æñÚU ¥æßðàæ e ãæð´ Ìæð, æê×Ùð ßæÜð §ÜñÅþUæòÙ ·¤è â·¤Ü ª¤Áæü ãæð»è Ñ (1) 2 1 e 2 r (2) 2 e r 2 (3) 2 me r (4) 2 1 e 2 r 2 32. ÎýÃØ×æÙ 6.63 g ·ð¤ ·¤æ ·¤æ ¥æßð» 100 ms21 âð »çÌ×æÙ ãæðÙð ÂÚU Îè-ÕýæÜè ÌÚ´U»ÎñØü ãæð»è Ñ (1) 10233 m (2) 10235 m (3) 10231 m (4) 10225 m 33. âæØ ÚU¹Ùð ßæÜð ¥æØÌÙ ·¤æð ¥ÂçÚUßçÌüÌ ÚU¹Ùð ßæÜè çSÍçÌ ×ð´ °·¤ ¥ç·ý¤Ø »ñâ ÇæÜÙð ÂÚU Øæ ãæð»æ? (1) ¥çÏ·¤ ç·ý¤Øæ È¤Ü Âýææ ãæð»æÐ (2) ·¤× ç·ý¤Øæ È¤Ü Âýææ ãæð»æÐ (3) ¥çÏ·¤ ¥çÖç·ý¤Øæ ãæð»èÐ (4) âæØ ¥ÂçÚUßçÌüÌ ÚUãð»æÐ
18. 18. English : 18 Set : 06 Hindi : 18 Set : 06 34. The amount of BaSO4 formed upon mixing 100 mL of 20.8% BaCl2 solution with 50 mL of 9.8% H2SO4 solution will be : (Ba5137, Cl535.5, S532, H51 and O516) (1) 23.3 g (2) 11.65 g (3) 30.6 g (4) 33.2 g 35. The rate coefficient (k) for a particular reactions is 1.331024 M21 s21 at 1008C, and 1.331023 M21 s21 at 1508C. What is the energy of activation (EA) (in kJ) for this reaction ? (R5molar gas constant58.314 JK21 mol21) (1) 16 (2) 60 (3) 99 (4) 132 34. ÁÕ Ba5137, Cl535.5, S532, H51 ¥æñÚU O516 ×æÙæ ÁæØð Ìæð 20.8% BaCl2 çßÜØÙ ·ð¤ 100 mL ·¤æð 9.8%, H2SO4 ·ð¤ çßÜØÙ ·ð¤ 50 mL ×ð´ ç×ÜæÙð ÂÚU ç·¤ÌÙæ BaSO4 ÕÙð»æ? (1) 23.3 g (2) 11.65 g (3) 30.6 g (4) 33.2 g 35. 1008C ÂÚU °·¤ çßàæðá ¥çÖç·ý¤Øæ ·¤æ ÎÚU çÙØÌæ´·¤ (k) 1.331024 M21 s21 ãñ ¥æñÚU 1508C ÂÚU §â·¤æ ×æÙ 1.331023 M21 s21 ãñÐ §â ¥çÖç·ý¤Øæ ·ð¤ çÜØð °ðÅUèßðàæÙ ª¤Áæü (EA) kJ ×ð´ ç·¤ÌÙè ãæð»è? (R5×æðÜÚU »ñâ çÙØÌæ´·¤ 58.314 JK21 ×æðÜ 21) (1) 16 (2) 60 (3) 99 (4) 132
19. 19. English : 19 Set : 06 Hindi : 19 Set : 06 36. How many electrons would be required to deposit 6.35 g of copper at the cathode during the electrolysis of an aqueous solution of copper sulphate ? (Atomic mass of copper 5 63.5 u, NA5Avogadros constant) : (1) AN 20 (2) AN 10 (3) AN 5 (4) AN 2 37. The entropy (So) of the following substances are : CH4 (g) 186.2 J K21 mol21 O2 (g) 205.0 J K21 mol21 CO2 (g) 213.6 J K21 mol21 H2O (l) 69.9 J K21 mol21 The entropy change (DSo) for the reaction CH4(g)12O2(g) ® CO2(g)12H2O(l) is : (1) 2312.5 J K21 mol21 (2) 2242.8 J K21 mol21 (3) 2108.1 J K21 mol21 (4) 237.6 J K21 mol21 36. ·¤æÂÚU âË\$Èð¤ÅUU ·ð¤ ÁÜèØ çßÜØÙ ·ð¤ §ÜñÅþUæòÜðçââ ×ð´ ·ñ¤ÍæðÇ ÂÚU 6.35 »ýæ× ·¤æÂÚU ·ð¤ Á×æ¥æð´ ·ð¤ çÜØð ç·¤ÌÙð §ÜñÅþUæòÙæð´ ·¤è ¥æßàØ·¤Ìæ ãæð»è? (·¤æÂÚU ·¤æ ÂÚU×ææé ÎýÃØ×æÙ 5 63.5 ×ææ·¤, NA5 °ðßæð»æÎýæð çÙØÌæ´·¤) (1) AN 20 (2) AN 10 (3) AN 5 (4) AN 2 37. çÙÙ ÂÎæÍæðZ ·ð¤ °ðÅþUæÂè ×æÙ ãñ (So) ãñ´ Ñ CH4 (g) 186.2 J K21 ×æðÜ21 O2 (g) 205.0 J K21 ×æðÜ21 CO2 (g) 213.6 J K21 ×æðÜ21 H2O (l) 69.9 J K21 ×æðÜ21 ¥çÖç·ý¤Øæ CH4(g)12O2(g) ® CO2(g)12H2O(l) ·ð¤ çÜØð °ðÅþUæÂè ÂçÚUßÌüÙ (DSo) ·¤æ ×æÙ ãæð»æ Ñ (1) 2312.5 J K21 ×æðÜ21 (2) 2242.8 J K21 ×æðÜ21 (3) 2108.1 J K21 ×æðÜ21 (4) 237.6 J K21 ×æðÜ21
20. 20. English : 20 Set : 06 Hindi : 20 Set : 06 38. The conjugate base of hydrazoic acid is : (1) N23 (2) 3N2 (3) 2N2 (4) 3HN2 39. In a monoclinic unit cell, the relation of sides and angles are respectively : (1) a5b ¹ c and a5b5g5908 (2) a ¹ b ¹ c and a5b5g5908 (3) a ¹ b ¹ c and b5g5908 ¹ a (4) a ¹ b ¹ c and a ¹ b ¹ g ¹ 908 40. The standard enthalpy of formation (DfHo 298) for methane, CH4 is 274.9 kJ mol21. In order to calculate the average energy given out in the formation of a C2H bond from this it is necessary to know which one of the following ? (1) the dissociation energy of the hydrogen molecule, H2. (2) the first four ionisation energies of carbon. (3) the dissociation energy of H2 and enthalpy of sublimation of carbon (graphite). (4) the first four ionisation energies of carbon and electron affinity of hydrogen. 38. ãæ§ÇþUæð\$Áæð§·¤ °ðçâÇU ·¤æ â´Øé×è ÿææÚU ãñ Ñ (1) N23 (2) 3N2 (3) 2N2 (4) 3HN2 39. °·¤ ×æðÙæðçÜçÙ·¤ °·¤·¤ âñÜ ×ð´ Âÿææð´ ·ð¤ ·¤æðÙæ çÕÎé¥æð´ âð âÕÏ ·ý¤×æÙéâæÚU ãæðÌð ã´ñ Ñ (1) a5b ¹ c ¥æñÚU a5b5g5908 (2) a ¹ b ¹ c ¥æñÚU a5b5g5908 (3) a ¹ b ¹ c ¥æñÚU b5g5908 ¹ a (4) a ¹ b ¹ c ¥æñÚU a ¹ b ¹ g ¹ 908 40. ×èÍðÙ, CH4, ÕÙÙð ·¤è ×æÙ·¤ °ðÍñËÂè (DfHo 298) 274.9 kJ ×æðÜ21 ãæðÌè ãñÐ §ââð C2H ¥æÕÏ ·¤è ×Ø×æÙ ª¤Áæü ·¤æ ¥æ·¤ÜÙ ·¤ÚUÙð ·ð¤ çÜØð çÙÙæð´ âð ç·¤â °·¤ ·¤æð ÁæÙÙæ ¥æßàØ·¤ ãæð»æ? (1) H2 ¥æé ·¤è çßØæðÁÙ ª¤ÁæüÐ (2) ·¤æÕüÙ ·¤è ÂãÜè ¿æÚU ¥æØÙÙ ª¤Áæü°¡Ð (3) H2 ·¤è çßØæðÁÙ ª¤Áæü ¥æñÚU ·¤æÕüÙ (»ýð\$È¤æ§Å)U ·¤è ª¤ßüÂæÌÙ ª¤ÁæüÐ (4) ·¤æÕüÙ ·¤è ÂýÍ× ¿æÚU ¥æØÙÙ ª¤Áæü°¡ ¥æñÚ ãæ§ÇþUæðÁÙ ·¤è §ÜñÅþUæòÙ ÕÏéÌæÐ
21. 21. English : 21 Set : 06 Hindi : 21 Set : 06 41. Which of the following xenon-OXO compounds may not be obtained by hydrolysis of xenon fluorides ? (1) Xe O2F2 (2) Xe O F4 (3) Xe O3 (4) Xe O4 42. Excited hydrogen atom emits light in the ultraviolet region at 2.4731015 Hz. With this frequency, the energy of a single photon is : (h56.63310234 Js) (1) 8.041310240 J (2) 2.680310219 J (3) 1.640310218 J (4) 6.111310217 J 43. Which one of the following exhibits the largest number of oxidation states ? (1) Ti (22) (2) V(23) (3) Cr (24) (4) Mn (25) 41. \$ÁèÙæÙ ÜæðÚUæ§ÇUæð´ ·ð¤ ÁÜèØ ¥ÂæÅUÙ âð çÙÙ \$ÁèÙæÙ- ¥æâæð-Øæñç»·¤æð´ ×ð´ âð ç·¤â·¤æð Âýææ Ùãè´ ç·¤Øæ Áæ â·¤Ìæ ãñ? (1) Xe O2F2 (2) Xe O F4 (3) Xe O3 (4) Xe O4 42. 2.4731015 Hz ÂÚU ÂÚUæÕñ´»Ùè ÿæðæ ×ð´ ©æðçÁÌ ãæ§ÇþUæðÁÙ ÂÚU×ææé Âý·¤æàæ ©âçÁüÌ ·¤ÚUÌæ ãñÐ §â ¥æßëçæ ·ð¤ âæÍ °·¤ ¥·ð¤Üð È¤æðÅUæòÙ ·¤è ª¤Áæü ãæð»è Ñ (h56.63310234 Js) (1) 8.041310240 J (2) 2.680310219 J (3) 1.640310218 J (4) 6.111310217 J 43. çÙÙæð´ ×ð´ âð ·¤æñÙ °·¤ ¥çÏ·¤Ì× â´Øæ ×ð´ ¥æòâè·¤ÚUæ ¥ßSÍæ°¡ çÎ¹æÌæ ãñ? (1) Ti (22) (2) V(23) (3) Cr (24) (4) Mn (25)
22. 22. English : 22 Set : 06 Hindi : 22 Set : 06 44. Copper becomes green when exposed to moist air for a long period. This is due to : (1) the formation of a layer of cupric oxide on the surface of copper. (2) the formation of a layer of basic carbonate of copper on the surface of copper. (3) the formation of a layer of cupric hydroxide on the surface of copper. (4) the formation of basic copper sulphate layer on the surface of the metal. 45. Among the following species the one which causes the highest CFSE, Do as a ligand is : (1) CN2 (2) NH3 (3) F2 (4) CO 46. Similarity in chemical properties of the atoms of elements in a group of the Periodic table is most closely related to : (1) atomic numbers (2) atomic masses (3) number of principal energy levels (4) number of valence electrons 44. ÜÕð â×Ø Ì·¤ »èÜè ßæØé ·ð¤ âÂ·ü¤ ×ð´ ÚUãÙð ÂÚU ·¤æÂÚU ãÚUæ ãæð ÁæÌæ ãñÐ §â·¤æ ·¤æÚUæ ãæðÌæ ãñ Ñ (1) ·¤æÂÚU ÌÜ ÂÚU ØêçÂý·¤ ¥æòâæ§ÇU ·¤æ ÂÚUÌ ÕÙÙæÐ (2) ·¤æÂÚU ÌÜ ÂÚU ·¤æÂÚU ·ð¤ ÿææÚUèØ ·¤æÕæðüÙðÅU ·¤æ ÂÚUÌ ÕÙÙæÐ (3) ·¤æÂÚU ÌÜ ÂÚU ØêçÂý·¤ ãæ§ÇþU¥æòâæ§ÇU ·¤æ ÂÚUÌ ÕÙÙæÐ (4) ÏæÌé ÌÜ ÂÚU ÿææÚUèØ ·¤æÂÚU âË\$Èð¤ÅU ·¤æ ÂÚUÌ ÕÙÙæÐ 45. çÙÙ ÂÎæÍæðZ ×ð´ âð ·¤æñÙ °·¤ çÜ»ñÇU M¤Â ×ð´ ¥çÏ·¤Ì× CFSE, Do ·¤æ ·¤æÚUæ ÕÙÌæ ãñ? (1) CN2 (2) NH3 (3) F2 (4) CO 46. ¥æßÌü âæÚUæè ·ð¤ ç·¤âè »ýéÂ ×ð´ Ìß ·ð¤ ÂÚU×ææé¥æð´ ·ð¤ ÚUæâæØçÙ·¤ »éææð´ ×ð´ ¥çÏ·¤Ì× â×æÙÌæ ·ð¤ ·¤æÚUæ ãæðÌð ãñ´ Ñ (1) ÂÚU×ææé·¤ ÙÕÚU (2) ÂÚU×ææé·¤ ÎýÃØ×æÙ (3) ÕÇ¸ð (Principal) ª¤Áæü SÌÚUæð´ ·¤è â´Øæ (4) ßñÜðâè §ÜñÅþUæòÙæð´ ·¤è â´Øæ
23. 23. English : 23 Set : 06 Hindi : 23 Set : 06 47. çÙÙ ÃØßSÍæ¥æð´ ×ð´ âð ·¤æñÙ çÎØð »Øð ÂÎæÍæðZ O22, S22, N32, P32 ·¤è ¥æØçÙ·¤ çæØæ¥æð´ ·ð¤ ÕÉ¸Ìð ·ý¤× (ØêÙÌ× âð ßëãæ×) ·¤æð ÂýSÌéÌ ·¤ÚUÌè ãñ? (1) O22< N32< S22 < P32 (2) O22< P32< N32 < S22 (3) N32 < O22< P32 < S22 (4) N32< S22< O22 < P32 48. â´âæçÚU·¤ ©ææÂÙ ·¤æ ·¤æÚUæ ãæðÌæ ãñ ßæØé×ÇUÜ ×ð´ ÕÉ¸Ùæ Ñ (1) ×èÍðÙ ¥æñÚU Ùæ§ÅþUâ ¥æòâæ§ÇU ·¤æÐ (2) ×èÍðÙ ¥æñÚU CO2 ·¤æÐ (3) ×èÍðÙ ¥æñÚU O3 ·¤æÐ (4) ×èÍðÙ ¥æñÚU CO ·¤æÐ 49. ãæ§ÇþUæðÁÙ ÂÚU¥æòâæ§ÇU ¥Â¿æØ·¤ ÌÍæ ©Â¿æØ·¤ ÎæðÙæð´ Âý·¤æÚU âð ÃØßãæÚU ·¤ÚUÌæ ãñ ¥æñÚU Øã çÙÖüÚU ·¤ÚUÌæ ãñ ¥çæç·ý¤Øæ ·¤ÚUÙð ßæÜð SÂèàæè\$Á ·ð¤ SßæÖæß ÂÚUÐ çÙÙ ×ð´ âð ç·¤â·ð¤ âæÍ H2O2 ¥ÜèØ ×æØ× ×ð´ ¥Â¿æØ·¤ ·ð¤ M¤Â ×ð´ ç·ý¤Øæ ·¤ÚUÌæ ãñ? (1) MnO4 2 (2) 2 2 7 Cr O 2 (3) 2 3 SO 2 (4) KI 47. Which of the following arrangements represents the increasing order (smallest to largest) of ionic radii of the given species O22, S22, N32, P32 ? (1) O22< N32< S22 < P32 (2) O22< P32< N32 < S22 (3) N32 < O22< P32 < S22 (4) N32< S22< O22 < P32 48. Global warming is due to increase of : (1) methane and nitrous oxide in atmosphere (2) methane and CO2 in atmosphere (3) methane and O3 in atmosphere (4) methane and CO in atmosphere 49. Hydrogen peroxide acts both as an oxidising and as a reducing agent depending upon the nature of the reacting species. In which of the following cases H2O2 acts as a reducing agent in acid medium ? (1) MnO4 2 (2) 2 2 7 Cr O 2 (3) 2 3 SO 2 (4) KI
24. 24. English : 24 Set : 06 Hindi : 24 Set : 06 50. Which one of the following complexes will most likely absorb visible light ? (At nos. Sc521, Ti522, V523, Zn530) (1) [Sc(H2O)6]31 (2) [Ti (NH3)6]41 (3) [V(NH3)6]31 (4) [Zn(NH3)6]21 51. on mercuration- demercuration produces the major product : (1) (2) (3) (4) 52. In the Victor-Meyers test, the colour given by 18, 28 and 38 alcohols are respectively : (1) Red, colourless, blue (2) Red, blue, colourless (3) Colourless, red, blue (4) Red, blue, violet 50. çÙÙ ·¤æòÜðâæð´ (â´·¤ÚUæð´) ×ð´ âð ·¤æñÙ ÎëàØ Âý·¤æàæ ·¤æð ¥ßàææðçáÌ ·¤ÚUÙð ·¤è âßæüçÏ·¤ â´ÖæßÙæ ÚU¹Ìæ ãñ? ( ÂÚU×ææé ·ý¤×æ´·¤ Sc521, Ti522, V523, Zn530) (1) [Sc(H2O)6]31 (2) [Ti (NH3)6]41 (3) [V(NH3)6]31 (4) [Zn(NH3)6]21 51. ×ÚUØêÚðUàæÙ-¥×ÚUØêÚðUàæÙ ÂÚ Uâð Âýææ ×éØ ç·ý¤ØæÈ¤Ü ãæðÌæ ãñ Ñ (1) (2) (3) (4) 52. çßÅUÚU ×ðØÚU ·ð¤ ÂÚUèÿææ ç·ý¤Øæ ×ð´ 18, 28 ¥æñÚU 38 ·ð¤ °ðË·¤æðãæÜæð´ mæÚUæ çÎØæ Ú´U» ·ý¤×æÙéâæÚU ãæðÌæ ãñ Ñ (1) ÜæÜ, Ú´U»ãèÙ, ÙèÜæ (2) ÜæÜ, ÙèÜæ, Ú´U»ãèÙ (3) Ú´U»ãèÙ, ÜæÜ, ÙèÜæ (4) ÜæÜ, ÙèÜæ, Áæ×Ùè
25. 25. English : 25 Set : 06 Hindi : 25 Set : 06 53. Conversion of benzene diazonium chloride to chloro benzene is an example of which of the following reactions ? (1) Claisen (2) Friedel-craft (3) Sandmeyer (4) Wurtz 54. In the presence of peroxide, HCl and HI do not give anti-Markownikoffs addition to alkenes because : (1) One of the steps is endothermic in HCl and HI (2) Both HCl and HI are strong acids (3) HCl is oxidizing and the HI is reducing (4) All the steps are exothermic in HCl and HI 55. The major product obtained in the photo catalysed bromination of 2-methylbutane is : (1) 1-bromo-2-methylbutane (2) 1-bromo-3-methylbutane (3) 2-bromo-3-methylbutane (4) 2-bromo-2-methylbutane 53. Õñ\$ÁèÙ ÇUæØæ\$ÁæðçÙØ× ÜæðÚUæ§ÇU ·¤æ ÜæðÚUæð Õñ\$ÁèÙ ×ð´ ÕÎÜÙæ §Ù×ð´ âð ç·¤â ¥çÖç·ý¤Øæ ·¤æ ©ÎæãÚUæ ãæðÌæ ãñ? (1) Üð\$ÁÙ (2) Èý¤èÇUÜ-·ý¤æ\$\$ÅU (3) âñ´ÇU×æØÚU (4) ßéÅ÷üUU\$Á 54. ÂÚU¥æòâæ§ÇU ·¤è ©ÂçSÍçÌ ×ð´ °ðË·¤èÙæð´ ·¤æð HCl ¥æñÚU HI °ðÅUè×æÚU·¤æðÙè·¤æÈ¤ Øæð» Ùãè´ ÎðÌð Øæð´ ç·¤ Ñ (1) HCl ¥æñÚU HI ·ð¤ âÕÏ ×ð´ °·¤ ¿ÚUæ ª¤c×æàææðáè ãñÐ (2) HCl ¥æñÚU HI ÎæðÙæð´, ÂýÕÜ ¥Ü ãñ´Ð (3) HCl ©Â¿æØ·¤ ¥æñÚU HI ¥Â¿æØ·¤ ãñÐ (4) HCl ¥æñÚU HI ·ð¤ âÕÏæð´ ×ð´ âÖè ¿ÚUæ ª¤c×æÂýÎ ãñ´Ð 55. 2- ×ðçÍÜØéÅðUÙ ·ð¤ Âý·¤æàæ mæÚUæ ©ÂýðçÚUÌ Õýæð×èÙðàæÙ ×ð´ ÕÇ¸æ ç·ý¤ØæÈ¤Ü ãæðÌæ ãñ Ñ (1) 1-Õýæð×æð-2-×ðçÍÜØéÅðUÙ (2) 1-Õýæð×æð-3-×ðçÍÜØéÅðUÙ (3) 2-Õýæð×æð-3-×ðçÍËæØéÅðUÙ (4) 2-Õýæð×æð-2-×ðçÍÜØéÅðUÙ
26. 26. English : 26 Set : 06 Hindi : 26 Set : 06 56. Which of the following molecules has two sigma(s) and two pi(p) bonds ? (1) C2H4 (2) N2F2 (3) C2H2Cl2 (4) HCN 57. Which one of the following acids does not exhibit optical isomerism ? (1) Lactic acid (2) Tartaric acid (3) Maleic acid (4) a-amino acids 58. Aminoglycosides are usually used as : (1) antibiotic (2) analgesic (3) hypnotic (4) antifertility 59. Which of the following will not show mutarotation ? (1) Maltose (2) Lactose (3) Glucose (4) Sucrose 56. çÙÙ ¥æé¥æð´ ×ð´ âð ç·¤â ¥æé ×ð´ Îæð çâ×æ (s) ¥æñÚU Îæð Âæ§ü (p) ¥æÕÏ ãæðÌð ãñ´? (1) C2H4 (2) N2F2 (3) C2H2Cl2 (4) HCN 57. çÙÙ ¥Üæð´ ×ð´ âð ·¤æñÙ Âý·¤æàæèØ â×æßØßÌæ Ùãè´ çÎ¹æÌæ? (1) ÜñçÅU·¤ °ðçâÇU (2) ÅUæÚUÅñUçÚU·¤ °çâÇU (3) ×ñÜè·¤ °çâÇU (4) a- °×æØÙæð´ °ðçâÇU 58. ¥×æØÙæðÜæ§·¤æðâæ§ÇUæð´ ·¤æð ÂýæØÑ çÙÙ ç·¤â Âý·¤æÚU ÂýØæð» ç·¤Øæ ÁæÌæ ãñ? (1) °ðÅUè ÕæØæðçÅU·¤ M¤Â ×ð´ (ÂýçÌ Áñçß·¤) (2) °ðÙÜÁñçâ·¤ M¤Â ×ð´ (ÂèÇ¸æ Ùæàæ·¤) (3) çãÂÙæçÅU·¤ M¤Â ×ð´ (çÙÎýæ ÂýÎ) (4) °ðÅUè È¤ÚUçÅUçÜÅUè M¤Â ×ð´ (°ðÅUè çÙáð¿·¤) 59. §Ù×ð´ âð ·¤æñÙ ØêÅUæÚUæðÅðUàæÙ Ùãè´ çÎ¹æØð»æ? (1) ×æËÅUæð\$Á (2) ÜñÅUæð\$Á (3) Üê·¤æð\$Á (4) âê·ý¤æð\$Á
27. 27. English : 27 Set : 06 Hindi : 27 Set : 06 60. Phthalic acid reacts with resorcinol in the presence of concentrated H2SO4 to give : (1) Phenolphthalein (2) Alizarin (3) Coumarin (4) Fluorescein 60. âæÎý H2SO4 ·¤è ©ÂçSÍçÌ ×ð´ ÍñçÜ·¤ °ðçâÇU çÚU\$ÁæÚUâèÙæÜ âð ¥çÖç·ý¤Øæ ·¤ÚU ÎðÌæ ãñ Ñ (1) çÈ¤ÙæËÈ¤ÍðÜèÙ (2) °ðçÜ\$ÁðÚUèÙ (3) ·é¤×ýèÙ (4) \$\$ÜæðÚðUâèÙ
28. 28. English : 28 Set : 06 Hindi : 28 Set : 06 PART C  MATHEMATICS 61. A relation on the set A5{x : ?x? < 3, xeZ}, where Z is the set of integers is defined by R5{(x, y) : y5?x?, 1x ≠2 }. Then the number of elements in the power set of R is : (1) 32 (2) 16 (3) 8 (4) 64 62. Let z ¹ 2i be any complex number such that z i z i 2 1 is a purely imaginary number. Then z1 1 z is : (1) 0 (2) any non-zero real number other than 1. (3) any non-zero real number. (4) a purely imaginary number. 63. The sum of the roots of the equation, x21?2x23?2450, is : (1) 2 (2) 22 (3) 2 (4) 22 Öæ» C  »çæÌ 61. â×éæØ A5{x : ?x? < 3, xeZ}, Áãæ¡ Z ÂêææZ·¤æð´ ·¤æ â×éæØ ãñ, ÂÚU °·¤ â´Õ´Ï R, R5{(x, y) : y5?x?, 1x ≠2 } mæÚUæ ÂçÚUÖæçáÌ ãñÐ Ìæð R ·ð¤ ææÌ â×éæØ ×ð´ ¥ßØßæð´ ·¤è â´Øæ ãñ Ñ (1) 32 (2) 16 (3) 8 (4) 64 62. ×æÙæ z ¹ 2i ·¤æð§ü °ðâè âç×æ â´Øæ ãñ ç·¤ z i z i 2 1 °·¤ àæéh ·¤æËÂçÙ·¤ â´Øæ ãñ, Ìæð z1 1 z ãñ Ñ (1) 0 (2) 1 ·ð¤ ¥çÌçÚUæ ·¤æð§ü àæêØðæÚU ßæSÌçß·¤ â´ØæÐ (3) ·¤æð§ü àæêØðæÚU ßæSÌçß·¤ â´ØæÐ (4) °·¤ àæéh ·¤æËÂçÙ·¤ â´ØæÐ 63. â×è·¤ÚUæ x21?2x23?2450, ·ð¤ ×êÜæð´ ·¤æ Øæð»È¤Ü ãñ Ñ (1) 2 (2) 22 (3) 2 (4) 22
29. 29. English : 29 Set : 06 Hindi : 29 Set : 06 64. If ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 22 2 22 2 a b c a b c a b c k a b c , 0, 1 1 1a b c ≠1l 1l 1l 5 l l 2l 2l 2l then k is equal to : (1) 4labc (2) 24labc (3) 4l2 (4) 24l2 65. If 1 2 A 3 1 2 x      5 2 and B 1 y x          5 be such that 6 AB 8       5 , then : (1) y52x (2) y522x (3) y5x (4) y52x 66. 8 - digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do not occupy odd places, is : (1) 160 (2) 120 (3) 60 (4) 48 64. ØçÎ ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 22 2 22 2 a b c a b c a b c k a b c , 0, 1 1 1a b c ≠1l 1l 1l 5 l l 2l 2l 2l ãñ, Ìæð k ÕÚUæÕÚU ãñ Ñ (1) 4labc (2) 24labc (3) 4l2 (4) 24l2 65. ØçÎ 1 2 A 3 1 2 x      5 2 ÌÍæ B 1 y x          5 °ðâð ãñ´ ç·¤ 6 AB 8       5 , ãñ, Ìæð Ñ (1) y52x (2) y522x (3) y5x (4) y52x 66. ¥´·¤æð´ 1, 1, 2, 2, 2, 3, 4, 4 ·ð¤ ÂýØæð» âð, ¥æÆU ¥´·¤èØ â´Øæ°¡ ÕÙæ§ü »§ü ãñ´Ð °ðâè â´Øæ¥æð´ ·¤è â´Øæ çÁÙ×ð´ çßá× ¥´·¤ çßá× SÍæÙæð´ ÂÚU Ù ¥æØð´, ãñ Ñ (1) 160 (2) 120 (3) 60 (4) 48
30. 30. English : 30 Set : 06 Hindi : 30 Set : 06 67. If 55 2 3 x      1 is expanded in the ascending powers of x and the coefficients of powers of x in two consecutive terms of the expansion are equal, then these terms are : (1) 7th and 8th (2) 8th and 9th (3) 28th and 29th (4) 27th and 28th 68. Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of 1 a and 1 b . If 1 : G M is 4 : 5, then a : b can be : (1) 1 : 4 (2) 1 : 2 (3) 2 : 3 (4) 3 : 4 69. The least positive integer n such that 2 n 1 2 2 2 1 1 3 1003 3 ........ ,<2 2 2 2 2 is : (1) 4 (2) 5 (3) 6 (4) 7 67. ØçÎ 55 2 3 x      1 ·¤æ x ·¤è ¥æÚUæðãè ææÌæð´ ×ð´ ÂýâæÚU ·¤ÚUÙð ÂÚU, ÂýâæÚU ×ð´ Îæð ·ý¤ç×·¤ ÂÎæð´ ×ð´ x ·¤è ææÌð´ â×æÙ ãñ´, Ìæð Øã ÂÎ ã´ñ Ñ (1) 7 ßæ¡ ÌÍæ 8 ßæ¡ (2) 8 ßæ¡ ÌÍæ 9 ßæ¡ (3) 28 ßæ¡ ÌÍæ 29 ßæ¡ (4) 27 ßæ¡ ÌÍæ 28 ßæ¡ 68. ×æÙæ Îæð ÏÙ â´Øæ¥æð´ a ÌÍæ b ·¤æ »éææðæÚU ×æØ G ãñ ÌÍæ 1 a ÌÍæ 1 b ·¤æ â×æÌÚU ×æØ M ãñÐ ØçÎ 1 : G M 5 4 : 5 ãñ, Ìæð a : b ãæð â·¤Ìð ãñ´ Ñ (1) 1 : 4 (2) 1 : 2 (3) 2 : 3 (4) 3 : 4 69. ÏÙ ÂêææZ·¤ n ·¤æ ßã ØêÙÌ× ×æÙ çÁâ·ð¤ çÜØð 2 n 1 2 2 2 1 1 3 1003 3 ........ ,<2 2 2 2 2 ãñ, ãñ Ñ (1) 4 (2) 5 (3) 6 (4) 7
31. 31. English : 31 Set : 06 Hindi : 31 Set : 06 70. Let f, g : R®R be two functions defined by f (x) 1 sin 0 , and ( ) ( ) 0 , 0 x , x g x x f xx x    ≠      5 5 5 Statement I : f is a continuous function at x50. Statement II : g is a differentiable function at x50. (1) Both statements I and II are false. (2) Both statements I and II are true. (3) Statement I is true, statement II is false. (4) Statement I is false, statement II is true. 71. If f(x)5x22x15, 1 > 2 x , and g(x) is its inverse function, then g9(7) equals : (1) 1 3 2 (2) 1 13 (3) 1 3 (4) 1 13 2 70. ×æÙæ f, g : R®R Îæð È¤ÜÙ ãñ´ Áæð f (x) 1 sin 0 , ( ) ( ) 0 , 0 x , x g x x f xx x    ≠      5 5 5 ±²Ë mæÚUæ ÂçÚUÖæçáÌ ãñ´ Ñ ·¤ÍÙ I : x50 ÂÚU f °·¤ âÌÌ È¤ÜÙ ãñÐ ·¤ÍÙ II : x50 ÂÚU g °·¤ ¥ß·¤ÜèØ È¤ÜÙ ãñÐ (1) ·¤ÍÙ I ÌÍæ II ÎæðÙæð´ ¥âØ ãñ´Ð (2) ·¤ÍÙ I ÌÍæ II ÎæðÙæð´ âØ ãñ´Ð (3) ·¤ÍÙ I âØ ãñ, ·¤ÍÙ II ¥âØ ãñÐ (4) ·¤ÍÙ I ¥âØ ãñ, ·¤ÍÙ II âØ ãñÐ 71. ØçÎ f(x)5x22x15, 1 > 2 x ,ÌÍæ g(x) §â·¤æ ÃØé·ý¤× È¤ÜÙ ãñ, Ìæð g9(7) ÕÚUæÕÚU ãñ Ñ (1) 1 3 2 (2) 1 13 (3) 1 3 (4) 1 13 2
32. 32. English : 32 Set : 06 Hindi : 32 Set : 06 72. Let f and g be two differentiable functions on R such that f 9(x) > 0 and g9(x) < 0, for all x e R. Then for all x : (1) f(g(x)) > f (g(x21)) (2) f(g(x)) > f (g(x11)) (3) g(f(x)) > g (f(x21)) (4) g(f(x)) < g (f(x11)) 73. If 11x41x55 ( ) 5 i i i 0 a 1 x∑ 5 1 , for all x in R, then a2 is : (1) 24 (2) 6 (3) 28 (4) 10 74. The integral ( ) 2 2 23 3 sin cos d sin cos x x x x x ∫ 1 is equal to : (1) ( )3 1 c 1 cot x 1 1 (2) ( )3 1 c 3 1 tan x 2 1 1 (3) ( ) 3 3 sin c 1 cos x x 1 1 (4) ( ) 3 3 cos c 3 1 sin x x 2 1 1 72. ×æÙæ R ÂÚU f ÌÍæ g Îæð °ðâð ¥ß·¤ÜÙèØ È¤ÜÙ ãñ ç·¤ âÖè x e R ·ð¤ çÜ° f 9(x) > 0 ÌÍæ g9(x) < 0 ãñ, Ìæð âÖè x ·ð¤ çÜ° Ñ (1) f(g(x)) > f(g(x21)) (2) f(g(x)) > f(g(x11)) (3) g(f(x)) > g(f(x21)) (4) g(f(x)) < g(f(x11)) 73. ØçÎ âÖè x e R ·ð¤ çÜ° 11x41x55 ( ) 5 i i i 0 a 1 x∑ 5 1 ãñ, Ìæð a2 ãñ Ñ (1) 24 (2) 6 (3) 28 (4) 10 74. â×æ·¤Ü ( ) 2 2 23 3 sin cos d sin cos x x x x x ∫ 1 ÕÚUæÕÚU ãñ Ñ (1) ( )3 1 c 1 cot x 1 1 (2) ( )3 1 c 3 1 tan x 2 1 1 (3) ( ) 3 3 sin c 1 cos x x 1 1 (4) ( ) 3 3 cos c 3 1 sin x x 2 1 1
33. 33. English : 33 Set : 06 Hindi : 33 Set : 06 75. If [ ] denotes the greatest integer function, then the integral [ ] 0 cos dx x∫ p is equal to : (1) 2 p (2) 0 (3) 21 (4) 2 p 2 76. If for a continuous function f(x), ( ) t 2 2 ( ) d t ,f x x x∫ 2p 1 5 p 2 for all t/2p, then 3 f       p 2 is equal to : (1) p (2) 2 p (3) 3 p (4) 6 p 75. ØçÎ [ ] °·¤ ×ãæ× ÂêææZ·¤èØ È¤ÜÙ ãñ, Ìæð â×æ·¤Ü [ ] 0 cos dx x∫ p ÕÚUæÕÚU ãñ Ñ (1) 2 p (2) 0 (3) 21 (4) 2 p 2 76. ØçÎ °·¤ âÌÌ È¤ÜÙ f(x) ·ð¤ çÜ°, âÖè t /2p ·ð¤ çÜ° ( ) t 2 2 ( ) d tf x x x∫ 2p 1 5 p 2 ãñ, Ìæð 3 f       p 2 ÕÚUæÕÚU ãñ Ñ (1) p (2) 2 p (3) 3 p (4) 6 p
34. 34. English : 34 Set : 06 Hindi : 34 Set : 06 77. The general solution of the differential equation, sin 2x d tan 0 d y x y x       2 2 5 , is : (1) y tan x 5x1c (2) y cot x 5tan x1c (3) y tan x 5cot x1c (4) y cot x 5x1c 78. If a line intercepted between the coordinate axes is trisected at a point A(4, 3), which is nearer to x-axis, then its equation is : (1) 4x23y57 (2) 3x12y518 (3) 3x18y536 (4) x13y513 79. If the three distinct lines x12ay1a50, x13by1b50 and x14ay1a50 are concurrent, then the point (a, b) lies on a : (1) circle (2) hyperbola (3) straight line (4) parabola 77. ¥ß·¤Ü â×è·¤ÚUæ sin 2x d tan 0 d y x y x       2 2 5 ·¤æ ÃØæÂ·¤ ãÜ ãñ Ñ (1) y tan x 5x1c (2) y cot x 5tan x1c (3) y tan x 5cot x1c (4) y cot x 5x1c 78. çÙÎðüàææ´·¤ ¥ÿææð´ ·ð¤ Õè¿ ¥´ÌÑ¹´çÇUÌ °·¤ ÚðU¹æ, °·¤ çÕ´Îé A(4, 3) Áæð x- ¥ÿæ ·ð¤ Âæâ ãñ, ÂÚU Sæ×çæÖæçÁÌ ãæðÌè ãñ, Ìæð ©â·¤æ â×è·¤ÚUæ ãñ Ñ (1) 4x23y57 (2) 3x12y518 (3) 3x18y536 (4) x13y513 79. ØçÎ ÌèÙ çßçÖóæ ÚðU¹æ°¡ x12ay1a50, x13by1b50 ÌÍæ x14ay1a50 â´»æ×è ã´ñ, Ìæð çÕ´Îé (a, b) °·¤ Ñ (1) ßëæ ÂÚU çSÍÌ ãñ (2) ¥çÌ ÂÚUßÜØ ÂÚU çSÍÌ ãñ (3) âÚUÜ ÚðU¹æ ÂÚU çSÍÌ ãñ (4) ÂÚUßÜØ ÂÚU çSÍÌ ãñ
35. 35. English : 35 Set : 06 Hindi : 35 Set : 06 80. For the two circles x21y2516 and x21y222y50, there is/are : (1) one pair of common tangents (2) two pairs of common tangents (3) three common tangents (4) no common tangent 81. Two tangents are drawn from a point (22, 21) to the curve, y254x. If a is the angle between them, then ?tan a? is equal to : (1) 1 3 (2) 1 3 (3) 3 (4) 3 82. The minimum area of a triangle formed by any tangent to the ellipse 22 1 16 81 yx 1 5 and the co-ordinate axes is : (1) 12 (2) 18 (3) 26 (4) 36 80. Îæð ßëææð´ x21y2516 ÌÍæ x21y222y50, ·ð¤ çÜ° ãñ/ã´ñ Ñ (1) ©ÖØçÙcÆU SÂàæü ÚðU¹æ¥æð´ ·¤æ °·¤ Øé×Ð (2) ©ÖØçÙcÆU SÂàæü ÚðU¹æ¥æð´ ·ð¤ Îæð Øé×Ð (3) ÌèÙ ©ÖØçÙcÆU SÂàæü ÚðU¹æ°´Ð (4) ·¤æð§ü ©ÖØçÙcÆU SÂàæü ÚðU¹æ Ùãè´Ð 81. °·¤ çÕ´Îé (22, 21) âð °·¤ ß·ý¤ y254x ÂÚU Îæð SÂàæü ÚðU¹æ°¡ ¹è´¿è »§ü ãñ, ØçÎ ©Ù·ð¤ Õè¿ ·¤æ ·¤æðæ a ãñ, Ìæð ?tan a? ÕÚUæÕÚU ãñ Ñ (1) 1 3 (2) 1 3 (3) 3 (4) 3 82. Îèæüßëæ 22 1 16 81 yx 1 5 ÂÚU ¹è´¿è »§ü ç·¤âè SÂàæü ÚðU¹æ ÌÍæ çÙÎðüàææ´·¤ ¥ÿææð´ mæÚUæ ÕÙè çæÖéÁ ·¤æ ØêÙÌ× ÿæðæÈ¤Ü ãñ Ñ (1) 12 (2) 18 (3) 26 (4) 36
36. 36. English : 36 Set : 06 Hindi : 36 Set : 06 83. A symmetrical form of the line of intersection of the planes x5ay1b and z5cy1d is : (1) 1b d a 1 c yx z22 2 5 5 (2) 1b a d c a 1 c yx z22 2 2 2 5 5 (3) 0a c b 1 d yx z22 2 5 5 (4) 1b a d c b 0 d yx z22 2 2 2 5 5 84. If the distance between planes, 4x22y24z1150 and 4x22y24z1d50 is 7, then d is : (1) 41 or 242 (2) 42 or 243 (3) 241 or 43 (4) 242 or 44 85. If x ∧ , y ∧ and z ∧ are three unit vectors in three-dimensional space, then the minimum value of 2 2 2 x y y z z x ∧ ∧ ∧ ∧ ∧ ∧ ? 1 ? 1 ? 1 ? 1 ? 1 ? is : (1) 3 2 (2) 3 (3) 3 3 (4) 6 83. â×ÌÜæð´ x5ay1b ÌÍæ z5cy1d ·¤è ÂýçÌÀðUÎè ÚðU¹æ ·¤æ â×ç×Ì M¤Â ãñ Ñ (1) 1b d a 1 c yx z22 2 5 5 (2) 1b a d c a 1 c yx z22 2 2 2 5 5 (3) 0a c b 1 d yx z22 2 5 5 (4) 1b a d c b 0 d yx z22 2 2 2 5 5 84. ØçÎ â×ÌÜæð´ 4x22y24z1150 ÌÍæ 4x22y24z1d50 ·ð¤ Õè¿ ·¤è ÎêÚUè 7, Ìæð d ãñ Ñ (1) 41 ¥Íßæ 242 (2) 42 ¥Íßæ 243 (3) 241 ¥Íßæ 43 (4) 242 ¥Íßæ 44 85. ØçÎ çæ-çß×èØ ¥æ·¤æàæ ×ð´ x ∧ , y ∧ ÌÍæ z ∧ ÌèÙ ×ææ·¤ âçÎàæ ãñ´, Ìæð 2 2 2 x y y z z x ∧ ∧ ∧ ∧ ∧ ∧ ? 1 ? 1 ? 1 ? 1 ? 1 ? ·¤æ ØêÙÌ× ×æÙ ãñ Ñ (1) 3 2 (2) 3 (3) 3 3 (4) 6
37. 37. English : 37 Set : 06 Hindi : 37 Set : 06 86. Let X and M.D. be the mean and the mean deviation about X of n observations xi, i51, 2, ....., n. If each of the observations is increased by 5, then the new mean and the mean deviation about the new mean, respectively, are : (1) X , M.D. (2) X 15, M.D. (3) X , M.D.15 (4) X 15, M.D.15 87. A number x is chosen at random from the set {1, 2, 3, 4, ....., 100}. Define the event : A5 the chosen number x satisfies ( 10) ( 50) 0 ( 30) x x x 2 2 / 2 Then P(A) is : (1) 0.71 (2) 0.70 (3) 0.51 (4) 0.20 86. ×æÙæ n Âýðÿæææð´ xi, i51, 2, ....., n ·¤æ ×æØ X ÌÍæ X ·ð¤ âæÂðÿæ ©Ù·¤æ ×æØ çß¿ÜÙ M.D. ãñÐ ØçÎ ÂýØð·¤ Âýðÿææ ×ð´ 5 ÕÉ¸æ çÎØæ Áæ° Ìæð ÙØæ ×æØ ÌÍæ æØð ×æØ ·ð¤ âæÂðÿæ ©Ù·¤æ ×æØ çß¿ÜÙ ·ý¤×àæÑ ãñ Ñ (1) X , M.D. (2) X 15, M.D. (3) X , M.D.15 (4) X 15, M.D.15 87. â×éæØ {1, 2, 3, 4, ....., 100} ×ð´ âð °·¤ â´Øæ x ØæÎëÀUØæ ¿éÙè »§üÐ æÅUÙæ A ·¤æð ÂçÚUÖæçáÌ ·¤èçÁ° Ñ A5 ¿éÙè »§ü â´Øæ x ( 10) ( 50) 0 ( 30) x x x 2 2 / 2 ·¤æð â´ÌécÅ ·¤ÚUÌè ãñÐ Ìæð P(A) ãñ Ñ (1) 0.71 (2) 0.70 (3) 0.51 (4) 0.20
38. 38. English : 38 Set : 06 Hindi : 38 Set : 06 88. Statement I : The equation (sin21x)31(cos21x)32ap350 has a solution for all a/ 1 32 . Statement II : For any x e R, sin21x1cos21x5 2 p and 0 [ 2 1 sin 4 x       2 p 2 [ 2 9 16 p . (1) Both statements I and II are true. (2) Both statements I and II are false. (3) Statement I is true and statement II is false. (4) Statement I is false and statement II is true. 89. If 1 cos 1 ( ) sin 1 cos and 1 sin 1 f u u 5 2 u 2 u 2 u A and B are respectively the maximum and the minimum values of f (u), then (A, B) is equal to : (1) (3, 21) (2) (4, 2 22 ) (3) ( )2 2 2 2,1 2 (4) ( )2 2 1,1 2 88. ·¤ÍÙ I : â×è·¤ÚUæ (sin21x)31(cos21x)32ap350 ·¤æ âÖè a/ 1 32 ·ð¤ çÜ° °·¤ ãÜ ãñÐ ·¤ÍÙ II : ç·¤âè x e R ·ð¤ çÜ° sin21x1cos21x5 2 p ÌÍæ 0 [ 2 1 sin 4 x       2 p 2 [ 2 9 16 p . (1) ·¤ÍÙ I ÌÍæ II ÎæðÙæð´ âØ ãñ´Ð (2) ·¤ÍÙ I ÌÍæ II ÎæðÙæð´ ¥âØ ãñ´Ð (3) ·¤ÍÙ I âØ ãñ ÌÍæ ·¤ÍÙ II ¥âØ ãñÐ (4) ·¤ÍÙ I ¥SæØ ãñ, ÌÍæ ·¤ÍÙ II âØ ãñÐ 89. ØçÎ 1 cos 1 ( ) sin 1 cos 1 sin 1 f u u 5 2 u 2 u 2 u ãñ, ÌÍæ A ÌÍæ B ·ý¤×àæÑ f (u) ·ð¤ ¥çÏ·¤Ì× ÌÍæ ØêÙÌ× ×æÙ ãñ´, Ìæð (A, B) ÕÚUæÕÚU ãñ Ñ (1) (3, 21) (2) (4, 2 22 ) (3) ( )2 2 2 2,1 2 (4) ( )2 2 1,1 2
39. 39. English : 39 Set : 06 Hindi : 39 Set : 06 90. Let p, q, r denote arbitrary statements. Then the logically equivalent of the statement p Þ (q Ú r) is : (1) (p Ú q) Þ r (2) (p Þ q) Ú (p Þ r) (3) (p Þ ~q) Ù (p Þ r) (4) (p Þ q) Ù (p Þ ~r) - o 0 o - 90. ×æÙæ p, q, r SßðÀU ·¤ÍÙ ÎàææüÌð ãñ´Ð ·¤ÍÙ p Þ (q Ú r) ·¤æ Ìæç·ü¤·¤ â×ÌéËØ ãñ Ñ (1) (p Ú q) Þ r (2) (p Þ q) Ú (p Þ r) (3) (p Þ ~q) Ù (p Þ r) (4) (p Þ q) Ù (p Þ ~r) - o 0 o -