Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
IIT-JEE 2010 EXAMINATION                                                         PAPER - 1                                ...
IIT-JEE 2010 EXAMINATION                                                     PAPER - 1                                    ...
IIT-JEE 2010 EXAMINATION                                                         PAPER - 1                                ...
IIT-JEE 2010 EXAMINATION                                                       PAPER - 1                                  ...
IIT-JEE 2010 EXAMINATION                                                    PAPER - 1                                     ...
IIT-JEE 2010 EXAMINATION                                                  PAPER - 1                                       ...
IIT-JEE 2010 EXAMINATION                                                         PAPER - 1                                ...
IIT-JEE 2010 EXAMINATION                                                   PAPER - 1                                      ...
IIT-JEE 2010 EXAMINATION                                                         PAPER - 1                                ...
IIT-JEE 2010 EXAMINATION                                                     PAPER - 1                                    ...
IIT-JEE 2010 EXAMINATION                                                         PAPER - 1                                ...
IIT-JEE 2010 EXAMINATION                                                     PAPER - 1                                    ...
IIT-JEE 2010 EXAMINATION                                                         PAPER - 1                                ...
Upcoming SlideShare
Loading in …5
×

C:\Documents And Settings\Shweta\Desktop\Answerkey Paper 1

375 views

Published on

Published in: Business, Technology
  • Be the first to comment

  • Be the first to like this

C:\Documents And Settings\Shweta\Desktop\Answerkey Paper 1

  1. 1. IIT-JEE 2010 EXAMINATION PAPER - 1 PART - I (CHEMISTRY) (HELD ON : 11 - 04 - 2010) ÕÇÅÖËÑÐĘË" ¼" (Õëðéîç" Åñôôçåö" Åêñëå ç" Öû òç+ Öêëõ" õçåöëñð" åñðöãëðõ" º" ï÷îöëòîç" åêñëåç" ó÷çõöëñðõ°" Çãåê" ó÷çõöëñð" êãõ" èñ÷ô" åêñëåçõ" (Ã+." (Ä+." (Å+" ãðæ" (Æ+." ñ÷ö ñè" ùêëåê" ÑÐÎÛ" ÑÐÇ" ëõ" åñôôçåö°³° Öêç" õûðöêçõëõ" ñè" µĘñåöûðç" ëõ" ãåêëçøçæ" äû" ãææëðé" ã" äôñïñãîíãðç" ëðöñ" ã" ïëúö÷ôç" ñè" õñæë÷ï" ãïëæç" ãðæ" ãð" ãîíûðç° Öêç "äôñïñãîíãðç "ãðæ "ãîíûðç "ôçõòçåöëøçîû "ãôç "Ę (Ã+" ÄôÅÊ ´ÅÊ ´ÅÊ ´ÅÊ ´ÅÊ µ" ãðæ "ÅÊ µÅÊ ´ÅºÅÊ (Ä+" ÄôÅÊ ´ÅÊ ´ÅÊ µ" ãðæ "ÅÊ µÅÊ ´ÅÊ ´ÅºÅÊ (Å+" ÄôÅÊ ´ÅÊ ´ÅÊ ´ÅÊ ´ÅÊ µ" ãðæ "ÅÊ µÅºÅÊ (Æ+" ÄôÅÊ´ÅÊ ´ÅÊ ´ÅÊ µ" ãðæ "ÅÊ µÅÊ ´ÅºÅÊÃðõ°" (Æ+´° Öêç "åñôôçåö "õöãöçïçðö "ãäñ÷ö "öêç "èñîîñùëðé "æëõãååêãôëæç "ëõ "Ę CH2OH O H CH2OH H (a) O H H EN OH OH H H OH (Ã+" Ôëðé" (ã+" ëõ "òûôãðñõç "ùëöê "aĘéîûåñõëæëå" îëðí (Å+" Ôëðé" (ä+" ëõ" è÷ôãðñõç" ùëöê" aĘéîûåñõëæëå" îëðíÃðõ°" (Ã+ OCH 2CH2 O H OH (b) OH H CH2OH (Ä+" Ôëðé" (ã+" ëõ" è÷ôãðñõç" ùëöê" aĘéîûåñõëæëå" îëðí (Æ+" Ôëðé" (ä+" ëõ "òûôãðñõç "ùëöê "bĘéîûåñõëæëå" îëðí LLµ° Ëð" öêç" ôçãåöëñð" HBr OCH3 " ¾¾¾ " öêç" òôñæ÷åöõ" ãôç" ¼¯ ® (Ã+" Br OCH3 " ãðæ "Ê´ (Ä+" Br " ãðæ "ÅʵÄô (Å+" Br " ãðæ "ÅʵÑÊ (Æ+" OH " ãðæ "ÅÊ µÄô AÃðõ°" (Æ+¶° Òîñöõ "õêñùëðé "öêç "øãôëãöëñð "ñè "öêç "ôãöç "åñðõöãðö "(í+ "ùëöê "öçïòçôãö÷ôç "(Ö+ "ãôç "éëøçð "äçîñù° "Öêç "òîñö "öêãö "èñîîñùõ Ãôôêçðë÷õ" çó÷ãöëñð" ëõ" Ę k k (Ã+" (Ä+" T T k k (Å+" (Æ+" T TÃðõ°" (Ã+·° Öêç" õòçåëçõ" ùêëåê" äû" æçèëðëöëñð" êãõ" ÜÇÔÑ" õöãðæãôæ "ïñîãô "çðöêãîòû "ñè "èñôïãöëñð "ãö "´»º "Í "ëõ "Ę (Ã+" Äô ´(é+ (Ä+" Åî´(é+ (Å+" Ê´Ñ(é+ (Æ+" Åʶ(é+Ãðõ°" (Ä+ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in 1 / 13
  2. 2. IIT-JEE 2010 EXAMINATION PAPER - 1 (HELD ON : 11 - 04 - 2010) Ę³¸° Öêç" äñðæ" çðçôéû" (ëð" íåãî" ïñî + "ñè "ã "ÅĘÅ "õëðéîç "äñðæ "ëõ "ãòòôñúëïãöçîû "Ę (Ã+" ³ (´+" ³² (Å+" ³²² (Æ+" ³²²²Ãðõ°" (Å+¹° Öêç" åñôôçåö" õöô÷åö÷ôç" ñè" çöêûîçðçæëãïëðçöçöôããåçöëå" ãåëæ" (ÇÆÖÃ+" ëõ" Ę HOOC–CH2 CH 2–COOH HOOC COOH (Ã+" N–CH=CH–N (Ä+" N–CH 2–CH 2–N HOOC–CH2 CH 2–COOH HOOC COOH COOH CH 2 HOOC–CH2 H HOOC–CH2 CH 2–COOH N–CH–CH–N (Å+" N–CH2–CH2 –N (Æ+" H CH2–COOH HOOC–CH2 CH2–COOH CH 2 HOOCÃðõ°" (Å+º° Öêç "ëñðëüãöëñð "ëõñïçô "ñè "ÝÅô(Ê´Ñ+ ¶Åî(ÐÑ´+ßÅî" ëõ" ĘÃðõ°" (Ä+ EN (Ã+" ÝÅô(Ê ´Ñ+ ¶(Ñ ´Ð+ßÅî ´ (Ä+" ÝÅô(Ê ´Ñ+ ¶Åî ´ß(ÐÑ ´+ (Å+" ÝÅô(Ê ´Ñ+¶Åî(ÑÐÑ+ßÅî (Æ+" ÝÅô(Ê ´Ñ+ ¶Åî ´(ÐÑ ´+ß°Ê ´Ñ ÕÇÅÖËÑÐĘËË" ¼" (Ï÷îöëòîç" Åñôôçå ö" Åêñëåç" Öûòç+ Öêëõ" õçåöëñð" åñðöãëðõ" ·" ï÷îöëòîç" åêñëåç" ó÷çõöëñðõ°" Çãåê" ó÷çõöëñð" êãõ" èñ÷ô" åêñëåçõ" (Ã+." (Ä+." (Å+" ãðæ" (Æ+." ñ÷ö ñè" ùêëåê" ÑÐÇ" ÑÔ" ÏÑÔ Ç" ïãû" äç" åñôôçåö° LL»° Ëð" öêç" Ðçùïãð" òôñìçåöëñð" èñô" ´.´Ęæëïçöêûîä÷öãðç X H3C CH3 A H H Y Ú" ãðæ" Û" åãð "ôçõòçåöëøçîû "äç "Ę (Ã+ "Ê "ãðæ "Ê (Ä+ "Ê "ãðæ "Å ´Ê · (Å+" Å´Ê ·" ãðæ "Ê (Æ+" ÅÊ µ" ãðæ "ÅÊ µÃðõ°" (Æ+³²° Ãó÷çñ÷õ "õñî÷öëñðõ "ñè "ÊÐѵ." ÍÑÊ." ÅʵÅÑÑÊ" ãðæ" ÅʵÅÑÑÐã" ñè" ëæçðöëåãî" åñðåçðöôãöëñðõ" ãôç" òôñøëæçæ°" Öêç òãëô(õ+ "ñè "õñî÷öëñðõ "ùêëåê "èñôï "ã "ä÷èèçô "÷òñð "ïëúëðé "ëõ(ãôç+ "Ę (Ã+" ÊÐѵ" ãðæ "ÅÊ µÅÑÑÊ (Ä+ "ÍÑÊ "ãðæ "ÅÊ µÅÑÑÐã (Å+" ÊÐÑ µ" ãðæ "ÅÊ µÅÑÑÐã (Æ+" ÅÊ µÅÑÑÊ" ãðæ" ÅÊ µÅÑÑÐãÃðõ°" (Å." Æ+ OH³³° Ëð" öêç" ôçãåöëñð" NaOH(aq ) / Br " ¾¾¾¾¾¾ " öêç "ëðöçôïçæëãöç(õ+ "ëõ(ãôç+ "Ę ® 2 O O O O Br (Ã+" (Ä+" (Å+" (Æ+" Br Br Br Br BrÃðõ°" (Ã." Ä." Å+ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 2 / 13 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in
  3. 3. IIT-JEE 2010 EXAMINATION PAPER - 1 (HELD ON : 11 - 04 - 2010)³´° Öêç "ôçãéçðö(õ+ "÷õçæ "èñô "õñèöçðëðé "öêç "öçïòñôãôû "êãôæðçõõ "ñè "ùãöçô "ëõ(ãôç+ "Ę (Ã+" Åã µ(ÒÑ ¶+ ´ (Ä+" Åã(ÑÊ+ ´ (Å+" Ðã ´ÅÑ µ (Æ+" ÐãÑÅîÃðõ°" (Ä." Å+³µ° Ãïñðé" öêç" èñîîñùëðé." öêç" ëðöçðõëøç" òôñòçôöû" ëõ" (òôñòçôöëçõ" ãôç+" Ę (Ã+" Ïñîãô" åñðæ÷åöëøëöû (Ä+" Çîçåöôñïñöëøç" èñôåç (Å+" Ôçõëõöãðåç (Æ+" Êçãö" åãòãåëöûÃðõ°" (Ã." Ä+ ÕÇÅÖËÑÐĘËËË" ¼" (Ò ãôãé ôãòê" Öûòç+ Öêëõ" õçåöëñð" åñðöãëðõ" ´" òãôãéôãòêõ°" Äãõçæ" ÷òñð" öêç" èëôõö" òãôãéôãòê." ´" ï÷îöëòîç" åêñëåç" ó÷çõöëñðõ" ãðæ" äãõçæ ÷òñð" öêç" õçåñðæ" òãôãéôãòê" µ" ï÷îöëòîç" åêñëåç" ó÷çõöëñðõ" êãøç" öñ" äç" ãðõùçôçæ°" Çãåê" ñè" öêçõç" ó÷çõöëñðõ" êãõ èñ÷ô" åêñëåçõ" (Ã+." (Ä+." (Å+" ãðæ" (Æ+." ñ÷ö" ñè" ùêëåê" ÑÐÎÛ" ÑÐÇ" ëõ" åñôôçåö° Ò ã ôã é ô ãò ê "èñ ô "Ó÷ çõ öë ñð õ " ³¶ "ö ñ "³· Öêç" åñðåçðöôãöëñð" ñè" òñöãõõë÷ï" ëñðõ" ëðõëæç" ã" äëñîñéëåãî" åçîî" ëõ" ãö" îçãõö" öùçðöû" öëïçõ" êëéêçô" öêãð" öêç" ñ÷öõëæç° Öêç" ôçõ÷îöëðé" òñöçðöëãî" æëèèçôçðåç" ãåôñõõ" öêç" åçîî" ëõ" ëïòñôöãðö" ëð" õçøçôãî" òôñåçõõçõ" õ÷åê" ãõ" öôãðõïëõõëñð" ñè" ðçôøç ëõ "¼ EN ëïò÷îõçõ "ãðæ "ïãëðöãëðëðé "öêç "ëñð "äãîãðåç° "à "õëïòîç "ïñæçî "èñô "õ÷åê "ã "åñðåçðöôãöëñð "åçîî "ëðøñîøëðé "ã "ïçöãî "Ï Ï(õ+"þÏ +(ãó "½ "²°²· "ïñîãô+ "þ "Ï +(ãó" ½" ³" ïñîãô+"þ" (õ+³ ¶ ° Èñô" öêç" ãäñøç" åçîî" ¼¯ þ Ï Èñô "öêç "ãäñøç "çîçåöôñîûöëå "åçîî "öêç "ïãéðëö÷æç "ñè "öêç "åçîî "òñöçðöëãî "þÇ åçî îþ "¿ "¹² "ïØ° (Ã+" Ç åçîî " ¾ "² "½ "DÉ "À "² (Ä+ "Ç åçîî" À "² "½ "DÉ" ¾" ² (Å+" Ç åçîî" ¾ "² "½ "DÉ ²" À "² (Æ+ "Ç åçîî " À "² "½ "DÉ ²" ¾ "²Ãðõ°" (Ä+ LL³·° Ëè "öêç "²°²· "ïñîãô "õñî÷öëñð "ñè "Ï +" ëõ "ôçòîãåçæ "äû "ã "²°²²´· "ïñîãô "Ï +" õñî÷öëñð." öêçð" öêç" ïãéðëö÷æç" ñè" öêç" åçîî òñöçðöëãî" ùñ÷îæ" äç" ¼¯ (Ã+ "µ· "ïØ (Ä+ "¹² "ïØ (Å+" ³¶²" ïØ (Æ+" ¹²²" ïØÃðõ°" (Å+ Ò ã ôã é ô ãòê" è ñô" Ó÷ çõ öë ñð" ³¸" ö ñ" ³º Åñòòçô "ëõ "öêç "ïñõö "ðñäçî "ñè "öêç "èëôõö "ôñù "öôãðõëöëñð "ïçöãîõ "ãðæ "ñåå÷ôõ "ëð "õïãîî "æçòñõëöõ "ëð "õçøçôãî "åñ÷ðöôëçõ° A Ñôçõ "ñè "åñòòçô "ëðåî÷æç "åêãîåãðöêëöç "(Å÷ÕÑ ¶" ° "·Ê ´Ñ+." ãöãåãïëöç" (Å÷ ´Åî(ÑÊ+ µ+." å÷òôëöç" (Å÷ ´Ñ+." åñòòçô" éîãðåç (Å÷ ´Õ+" ãðæ" ïãîãåêëöç" (Å÷ ´(ÑÊ+ ´ÅÑ µ+° "Êñùçøçô. "º²% "ñè "öêç "ùñôîæ "åñòòçô "òôñæ÷åöëñð "åñïçõ "èôñï "öêç "ñôç åêãîåñòûôëöç" (Å÷ÈçÕ ´+°" Öêç" çúöôãåöëñð" ñè" åñòòçô" èôñï" åêãîåñòûôëöç" ëðøñîøçõ" òãôöëãî" ôñãõöëðé." ôçïñøãî" ñè" ëôñð ãðæ" õçîè¯ôçæ÷åöëñð°³ ¸ ° Òãôöëãî" ôñãõöëðé" ñè" åêãîåñòûôëöç" òôñæ÷åçõ" ¼¯ (Ã+" Å÷ ´Õ "ãðæ "ÈçÑ (Ä+ "Å÷ ´Ñ "ãðæ "ÈçÑ (Å+ "Å÷Õ "ãðæ "Èç ´Ñ µ (Æ+" Å÷ ´Ñ "ãðæ "Èç ´Ñ µÃðõ°" (Ã+³¹° Ëôñð" ëõ" ôçïñøçæ" èôñï" åêãîåñòûôëöç" ãõ" ¼¯ (Ã+" ÈçÑ (Ä+" ÈçÕ (Å+" Èç ´Ñ µ (Æ+" ÈçÕëÑ µÃðõ°" (Æ+³º° Ëð" õçîè¯ôçæ÷åöëñð." öêç" ôçæ÷åëðé" õòçåëçõ" ëõ" ¼¯ (Ã+ "Õ (Ä+" Ñ´Ę (Å+" Õ ´Ę (Æ+" ÕÑ ´Ãðõ°" (Å+ ÕÇÅÖËÑÐĘËØ" ¼" (Ëðöçéçô" Öûòç+ Öêëõ"Õçåöëñð"åñðöãëðõ"ÖÇÐ"ó÷çõöëñðõ°"Öêç"ãðõùçô"öñ"çãåê"ó÷çõöëñð"ëõ"ã"õëðéîç"æëéëö"ëðöçéçô"ôãðéëðé"èôñï"²"öñ"»°"Öêç åñôôçåö"æëéëö"äçîñù"öêç"ó÷çõöëñð"ð÷ïäçô"ëð"öêç"ÑÔÕ"ëõ"öñ"äç"ä÷ääîçæ°³»° à "õö÷æçðö "òçôèñôïõ "ã "öëöôãöëñð "ùëöê "æëèèçôçðö "ä÷ôçööçõ "ãðæ "èëðæõ "öëöôç "øãî÷çõ "ñè "´·°´ "ïÎ. "´·°´· "ïÎ. "ãðæ ´·°² "ïΰ "Öêç "ð÷ïäçô "ñè "õëéðëèëåãðö "èëé÷ôçõ "ëð "öêç "ãøçôãéç "öëöôç "øãî÷ç "ëõ "¼¯Ãðõ° "µ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in 3 / 13
  4. 4. IIT-JEE 2010 EXAMINATION PAPER - 1 (HELD ON : 11 - 04 - 2010)´²° Öêç "åñðåçðöôãöëñð "ñè "Ô "ëð "öêç "ôçãåöëñð "Ô "® Ò "ùãõ "ïçãõ÷ôçæ "ãõ "ã "è÷ðåöëñð "ñè "öëïç "ãðæ "öêç "èñîîñùëðé "æãöã "ëõ ñäöãëðçæ" ¼ [R] (molar) 1.0 0.76 0.40 0.10 t(min.) 0.0 0.05 0.12 0.18 Öêç "ñôæçô "ñè "öêç "ôçãåöëñð "ëõ°Ãðõ° "² 235 142 90´³° Öêç" ð÷ïäçô" ñè" ðç÷öôñðõ" çïëööçæ" ùêçð" 92 U " ÷ðæçôéñçõ" åñðöôñîîçæ" ð÷åîçãô" èëõõëñð" öñ" 54 Xe " ãðæ" 38 Sr " ëõ°Ãðõ° "¶´´° Öêç "öñöãî "ð÷ïäçô "ñè "äãõëå "éôñ÷òõ "ëð "öêç "èñîîñùëðé "èñôï "ñè "îûõëðç "ëõ "¼ + H3N–CH2–CH2–CH2–CH2 O CH–CÃðõ° "´ EN H2N O –´ µ ° Öêç "öñöãî "ð÷ïäçô "ñè "åûåîëå "ëõñïçôõ "òñõõëäîç "èñô "ã "êûæôñåãôäñð "ùëöê "öêç "ïñîçå÷îãô "èñôï÷îã "Å ¶Ê ¸" ëõ°Ãðõ° "·´¶° Ëð" öêç" õåêçïç" éëøçð" äçîñù." öêç" öñöãî" ð÷ïäçô" ñè" ëðöôãïñîçå÷îãô" ãîæñî" åñðæçðõãöëñð" òôñæ÷åöõ" èñôïçæ" èôñï" ēÛĔ ëõ" ¼¯ LL 1. O3 1. NaOH (aq) 2. Zn, H2O Y 2. heatÃðõ° "³´·° Ãïñðéõö "öêç "èñîîñùëðé. "öêç "öñöãî "ð÷ïäçô "ñè "åñïòñ÷ðæõ "õñî÷äîç "ëð "ãó÷çõñ÷õ "ÐãÑÊ "ëõ "¼ H3C CH3 A N COOH OCH2CH3 OH CH2OH NO2 OH CH2CH3 COOH CH2CH3 N H3C CH3Ãðõ° "·´¸° Ãïñðéõö "öêç "èñîîñùëðé. "öêç "öñöãî "ð÷ïäçô "ñè "åñïòñ÷ðæõ "ùêñõç "ãó÷çñ÷õ "õñî÷öëñð "ö÷ôðõ "ôçæ "îëöï÷õ "òãòçô "äî÷ç ëõ "¼ ÍÅÐ Í ´ ÕÑ ¶ (ÐÊ ¶+ ´Å ´Ñ ¶ ÐãÅî Üð(ÐÑ µ + ´ ÈçÅî µ Í ´ÅÑ µ ÐÊ ¶ÐÑ µ ÎëÅÐÃðõ° "µ´ ¹ ° Äãõçæ "ñð "ØÕÇÒÔ "öêçñôû. "öêç "ð÷ïäçô "ñè "»² "æçéôçç "ÈĘÄôĘÈ "ãðéîçõ "ëð "ÄôÈ ·" ëõ°Ãðõ° "¶´ º ° Öêç "øãî÷ç "ñè "ð "ëð "öêç "ïñîçå÷îãô "èñôï÷îã "Äç ðÃî ´Õë ¸Ñ ³º" ëõ°Ãðõ° "µ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 4 / 13 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in
  5. 5. IIT-JEE 2010 EXAMINATION PAPER - 1 PART - II (MATHEMATICS) (HELD ON : 11 - 04 - 2010) ÕÇÅÖËÑÐĘË" ¼" (Õëðéîç" Åñôôçåö" Åêñëå ç" Öû òç+ Öêëõ" õçåöëñð" åñðöãëðõ" º" ï÷îöëòîç" åêñëåç" ó÷çõöëñðõ°" Çãåê" ó÷çõöëñð" êãõ" èñ÷ô" åêñëåçõ" (Ã+." (Ä+." (Å+" ãðæ" (Æ+." ñ÷ö ñè" ùêëåê" ÑÐÎÛ" ÑÐÇ" ëõ" åñôôçåö°´»° Îçö" w" äç "ã "åñïòîçú "å÷äç "ôññö "ñè "÷ðëöû "ùëöê "w" ¹" ³° "à "èãëô "æëç "ëõ "öêôñùð "öêôçç "öëïçõ° "Ëè "ô³. "ô´" ãðæ "ô´" ãôç "öêç ð÷ïäçôõ" ñäöãëðçæ" ñð" öêç" æëç." öêçð" öêç" òôñäãäëîëöû" öêãö" wr1 + wr2 + wr3 = 0 " ëõ 1 1 2 1 (Ã+" (Ä+" (Å+" (Æ+" 18 9 9 36Ãðõ° (Å+µ²° Îçö "Ò. "Ó. "Ô "ãðæ "Õ "äç "öêç "òñëðöõ "ñð "öêç "òîãðç "ùëöê "òñõëöëñð "øçåöñôõ "Ę 2i - ˆ 4i,3i + 3j " ãðæ" -3i + 2j " ôçõòçåöëøçîû° ˆ j, ˆ ˆ ˆ ˆ ˆ ° Öêç "ó÷ãæôëîãöçôãî "ÒÓÔÕ "ï÷õö "äç "ã (Ã+" òãôãîîçîñéôãï." ùêëåê" ëõ" ðçëöêçô" ã" ôêñïä÷õ" ðñô" ã" ôçåöãðéîç (Ä+" õó÷ãôçµ³° EN (Å+ "ôçåöãðéîç. "ä÷ö "ðñö "ã "õó÷ãôç (Æ+ "ôêñïä÷õ. "ä÷ö "ðñö "ã "õó÷ãôçÃðõ °" (Ã+ é x ù é1 ù Öêç "ð÷ïäçô "ñè "µ "Ù "µ "ïãöôëåçõ "à "ùêñõç "çðöôëçõ "ãôç "çëöêçô "² "ñô "³ "ãðæ "èñô "ùêëåê "öêç "õûõöçï " A ê y ú = ê0 ú " êãõ çúãåöîû" öùñ" æëõöëðåö" õñî÷öëñðõ." ëõ ê ú ê ú ê z ú ê0 ú ë û ë û LL (Ã+" ² (Ä+ "´ »" Ę "³ (Å+" ³¸º (Æ+" ´Ãðõ °" (Ã+ x 1 tln(1 + t)µ´° lim Öêç "øãî÷ç "ñè " x ®0 x 3 ò t4 + 4 dt " ëõ 0 1 1 1 (Ã+" ² (Ä+" (Å+" (Æ+" A 12 24 64Ãðõ°" (Ä+µ µ ° Îçö "ò "ãðæ "ó "äç "ôçãî "ð÷ïäçôõ "õ÷åê "öêãö "ò "¹" ². "òµ" ¹" ó "ãðæ "òµ" ¹ Ęó°" Ëè" a" ãðæ" b" ãôç" ðñðüçôñ" åñïòîçú" ð÷ïäçôõ a b õãöëõèûëðé" a + b" ¿ "Ę "ò "ãðæ "aµ" +" b µ" ¿ "ó. "öêçð "ã "ó÷ãæôãöëå "çó÷ãöëñð "êãøëðé " " ãðæ" " ãõ "ëöõ "ôññöõ "ëõ b a µ ´ µ µ µ ´ µ µ (Ã+" (ò " + "ó+ú " Ę "(ò " +" ´ó+ú" +" (ò " +" ó+" ¿" ² (Ä+" (ò " + "ó+ú " Ę" (ò " Ę "´ó+ú "+ "(ò " + "ó+ "¿ "² µ ´ µ µ µ ´ µ µ (Å+" (ò " Ę "ó+ú " Ę "(·ò " Ę "´ó+ú "+ "(ò " Ę "ó+ "¿ "² (Æ+ "(ò " Ę "ó+ú " Ę "(·ò " + "´ó+ú "+ "(ò " Ę "ó+ "¿ "²Ãðõ°" (Ä+ 2 2 2 x 2-xµ¶° Îçö" è." é" ãðæ" ê" äç" ôçãî¯øãî÷çæ" è÷ðåöëñðõ" æçèëðçæ" ñð" öêç" ëðöçôøãî" ݲ." ³ß" äû" è(ú+" ¿" e x + e- x ." é(ú+" ¿" xe + e 2 2 ãðæ" ê(ú+" ¿" x2e x + e - x ° "Ëè "ã. "ä "ãðæ "å "æçðñöç. "ôçõòçåöëøçîû. "öêç "ãäõñî÷öç "ïãúëï÷ï "ñè "è. "é "ãðæ "ê "ñð "ݲ. "³ß. öêçð (Ã+" ã" ¿" ä" ãðæ" å" ¹" ä (Ä+ "ã "¿ "å "ãðæ "ã "¹" ä (Å+" ã" ¹" ä "ãðæ "å "¹" ä (Æ+ "ã "¿ "ä "¿ "åÃðõ °" (Æ+µ · ° Ëè "öêç "ãðéîçõ "Ã. "Ä "ãðæ "Å "ñè "ã "öôëãðéîç "ãôç "ëð "ãð "ãôëöêïçöëå "òôñéôçõõëñð "ãðæ "ëè "ã. "ä "ãðæ "å "æçðñöç "öêç "îçðéöêõ a c ñè" öêç" õëæçõ" ñòòñõëöç" öñ" Ã." Ä" ãðæ" Å" ôçõòçåöëøçîû." öêçð" öêç" øãî÷ç" ñè" öêç" çúòôçõõëñð" sin2C + sin2A " ëõ c a 1 3 (Ã+" (Ä+" (Å+" ³ (Æ+" 3 2 2Ãðõ °" (Æ+ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in 5 / 13
  6. 6. IIT-JEE 2010 EXAMINATION PAPER - 1 (HELD ON : 11 - 04 - 2010) x y zµ¸° Çó÷ãöëñð" ñè" öêç" òîãðç" åñðöãëðëðé" öêç" õöôãëéêö" îëðç" = = " ãðæ" òçôòçðæëå÷îãô" öñ" öêç" òîãðç" åñðöãëðëðé" öêç 2 3 4 x y z x y z õöôãëéêö" îëðçõ" = = " ãðæ" = = " ëõ 3 4 2 4 2 3 (Ã+ "ú "+ "´û "Ę "´ü "¿ "² (Ä+ "µú "+ "´û "Ę "´ü "¿ "² (Å+ "ú "Ę "´û "+ "ü "¿ "² (Æ+ "·ú "+ "´û "Ę "¶ü "¿ "²Ãðõ°" (Å+ ÕÇÅÖËÑÐĘËË" ¼" (Ï÷îöëòîç" Åñôôçå ö" Åêñëåç" Öûòç+ Öêëõ" õçåöëñð" åñðöãëðõ" ·" ï÷îöëòîç" åêñëåç" ó÷çõöëñðõ°" Çãåê" ó÷çõöëñð" êãõ" èñ÷ô" åêñëåçõ" (Ã+." (Ä+." (Å+" ãðæ" (Æ+." ñ÷ö ñè" ùêëåê" ÑÐÇ" ÑÔ" ÏÑÔ Ç" ïãû" äç" åñôôçåö°µ¹° Îçö "ü ³" ãðæ "ü ´" äç "öùñ "æëõöëðåö "åñïòîçú "ð÷ïäçôõ "ãðæ "îçö "ü "¿ "(³ "Ę "ö+ü ³" + "öü ´" èñô "õñïç "ôçãî "ð÷ïäçô "ö "ùëöê ² "¾ "ö "¾ "³° "Ëè "Ãôé(ù+ "æçðñöçõ "öêç "òôëðåëòãî "ãôé÷ïçðö "ñè "ã "ðñðüçôñ "åñïòîçú "ð÷ïäçô "ù. "öêçð (Ã+" þü " Ę "ü ³þ+þü " Ę "ü ´þ¿þü ³" Ę "ü ´ þ (Ä+ "Ãôé(ü "Ę "ü³+" ¿ "Ãôé(ü "Ę "ü´+ z - z1 z - z1 (Å+ z - z =0 (Æ+ "Ãôé(ü "Ę "ü ³+ " ¿" Ãôé(ü´" Ę "ü ³+Ãðõ°" (Ã.Å.Æ+µº° 2 EN 1 z2 - z1 Öêç" øãî÷ç(õ+" ñè" 1 ò 0 x 4 (1 - x)4 1 + x2 dx " ëõ" (ãôç+ 22 2 71 3 p -p - LL (Ã+" (Ä+" (Å+" ² (Æ+" 7 105 15 2Ãðõ °" (Ã+ pµ»° Îçö "ÃÄÅ "äç "ã "öôëãðéîç "õ÷åê "öêãö " ÐACB = " ãðæ "îçö "ã. "ä "ãðæ "å "æçðñöç "öêç "îçðéöêõ "ñè "öêç "õëæçõ "ñòòñõëöç "öñ 6 Ã. "Ä "ãðæ "Å "ôçõòçåöëøçîû° "Öêç "øãî÷ç(õ+ "ñè "ú "èñô "ùêëåê "ã "¿ "ú ´" + "ú "+ "³. "ä "¿ "ú ´" Ę "³ "ãðæ "å "¿ "´ú "+ "³ "ëõ "(ãôç+ A (Ã+" -(2 + 3) (Ä+" 1 + 3 (Å+" 2 + 3 (Æ+" 4 3Ãðõ°" (Ä+¶ ² ° Îçö "à "ãðæ "Ä "äç "öùñ "æëõöëðåö "òñëðöõ "ñð "öêç "òãôãäñîã "û´" ¿ "¶ú° "Ëè "öêç "ãúëõ "ñè "öêç "òãôãäñîã "öñ÷åêçõ "ã "åëôåîç "ñè ôãæë÷õ "ô "êãøëðé "ÃÄ "ãõ "ëöõ "æëãïçöçô. "öêçð "öêç "õîñòç "ñè "öêç "îëðç "ìñëðëðé "à "ãðæ "Ä "åãð "äç "¯ 1 1 2 2 (Ã+ "Ę (Ä+" (Å+" (Æ+" Ę r r r rÃðõ °" (Å.Æ+ x¶³° Îçö" è" äç" ã" ôçãî¯øãî÷çæ" è÷ðåöëñð" æçèëðçæ" ñð" öêç" ëðöçôøãî" (²." ¥+" äû" f(x) = lnx + ò 1 + sin tdt °" Öêçð" ùêëåê" ñè" öêç 0 èñîîñùëðé" õöãöçïçðö(õ+" ëõ" (ãôç+" öô÷çÁ (Ã+" è))(ú+" çúëõöõ" èñô" ãîî" ú" Î" (²." ¥+ (Ä+" è)(ú+" çúëõöõ" èñô" ãîî" ú" Î" (²." ¥+ "ãðæ "è) "ëõ "åñðöëð÷ñ÷õ "ñð "(². "¥+. "ä÷ö "ðñö "æëèèçôçðöëãäîç "ñð "(². "¥+ (Å+" öêçôç" çúëõöõ" a" À "³ "õ÷åê "öêãö "þè)(ú+þ "¾ "þè(ú+þ "èñô "ãîî "ú "Î" (a." ¥+ (Æ+" öêçôç" çúëõöõ" b" À" ²" õ÷åê" öêãö" þè(ú+þ+þè)(ú+þ¾" b" èñô" ãîî" ú" Î" (0." ¥+Ãðõ °" (Ä.Å+ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 6 / 13 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in
  7. 7. IIT-JEE 2010 EXAMINATION PAPER - 1 (HELD ON : 11 - 04 - 2010) ÕÇÅÖËÑÐĘËËË" ¼" (Ò ãôãé ôãòê" Öûòç+ Öêëõ" õçåöëñð" åñðöãëðõ" ´" òãôãéôãòêõ°" Äãõçæ" ÷òñð" öêç" èëôõö" òãôãéôãòê." ´" ï÷îöëòîç" åêñëåç" ó÷çõöëñðõ" ãðæ" äãõçæ ÷òñð" öêç" õçåñðæ" òãôãéôãòê" µ" ï÷îöëòîç" åêñëåç" ó÷çõöëñðõ" êãøç" öñ" äç" ãðõùçôçæ°" Çãåê" ñè" öêçõç" ó÷çõöëñðõ" êãõ èñ÷ô" åêñëåçõ" (Ã+." (Ä+." (Å+" ãðæ" (Æ+." ñ÷ö" ñè" ùêëåê" ÑÐÎÛ" ÑÐÇ" ëõ" åñôôçåö° Ò ã ôã é ô ãò ê "èñ ô "Ó÷ çõ öë ñð "¶ ´ "ãð æ "¶µ x2 y 2 Öêç "åëôåîç "ú ´" + "û ´" Ę "ºú "¿ "² "ãðæ "êûòçôäñîã " - = 1 " ëðöçôõçåö "ãö "öêç "òñëðöõ "à "ãðæ "Ä° 9 4¶´° Çó÷ãöëñð "ñè "ã "åñïïñð "öãðéçðö "ùëöê "òñõëöëøç "õîñòç "öñ "öêç "åëôåîç "ãõ "ùçîî "ãõ "öñ "öêç "êûòçôäñîã "ëõ "¯ (Ã+" 2x - 5y - 20 = 0 (Ä+" 2x - 5y + 4 = 0 (Å+ "µú "Ę "¶û "+ "º "¿ "² (Æ+ "¶ú "Ę "µû "+ "¶ "¿ "²Ãðõ°" (Ä+¶µ° Çó÷ãöëñð "ñè "öêç "åëôåîç "ùëöê "ÃÄ "ãõ "ëöõ "æëãïçöçô "ëõ "¯ (Ã+" ú ´ " + "û ´" Ę "³´ú "+ "´¶ "¿ "² (Ä+ "ú ´" + "û ´ " + "³´ú "+ "´¶ "¿ "²Ãðõ °" (Ã+ EN (Å+" ú ´ " + "û ´" + "´¶ú "Ę "³´ "¿ "² ì (Æ+" ú ´" + "û ´" Ę "´¶ú "Ę "³´ "¿ "² Ò ã ôã é ô ãòê" è ñô" Ó÷ çõ öë ñð" ¶¶" ö ñ" ¶¸ Îçö "ò "äç "ãð "ñææ "òôëïç "ð÷ïäçô "ãðæ "Ö ò" äç "öêç "èñîîñùëðé "õçö "ñè "´ "Ù "´ "ïãöôëåçõ "¼ é a bù ü ï ï Tp = í A = ê ú : a,b,c Î {0,1,2,.....,p - 1}ý LL ï î ëc aû ï þ¶¶° Öêç "ð÷ïäçô "ñè "à "ëð "Ö ò" õ÷åê "öêãö "à "ëõ "çëöêçô "õûïïçöôëå "ñô "õíçù¯õûïïçöôëå "ñô "äñöê. "ãðæ "æçö "(Ã+ "æëøëõëäîç "äû ò" ëõ¯ (Ã+ "(ò "Ę "³+ ´ (Ä+ "´ "(ò "Ę "³+ (Å+" (ò" Ę" ³+ ´" + "³ (Æ+" ´ò" Ę³Ãðõ °" (Æ+ A¶·° Öêç "ð÷ïäçô "ñè "à "ëð "Ö ò" õ÷åê "öêãö "öêç "öôãåç "ñè "à "ëõ "ðñö "æëøëõëäîç "äû "ò "ä÷ö "æçö "(Ã+ "ëõ "æëøëõëäîç "äû "ò "ëõ¯ ÝÐñöç "¼" Öêç "öôãåç "ñè "ã "ïãöôëú "ëõ "öêç "õ÷ï "ñè "ëöõ "æëãéñðãî "çðöôëçõ°ß ´ µ ´ ´ ´ (Ã+" (ò" Ę" ³+" (ò " Ę "ò "+ "³+ (Ä+ "ò " Ę "(ò "Ę "³+ (Å+ "(ò "Ę "³+ (Æ+" (ò" Ę" ³+" (ò " Ę "´+Ãðõ°" (Å+¶¸° Öêç "ð÷ïäçô "ñè "à "ëð "Ö ò" õ÷åê "öêãö "æçö "(Ã+ "ëõ "ðñö "æëøëõëäîç "äû "ò "ëõ¯ (Ã+" ´ò ´ (Ä+ "ò µ" Ę" ·ò (Å+" ò µ" Ę "µò (Æ+ "ò µ" Ę "ò ´Ãðõ °" (Æ+ ÕÇÅÖËÑÐĘËØ" ¼" (Ëðöçéçô" Öûòç+ Öêëõ"Õçåöëñð"åñðöãëðõ"ÖÇÐ"ó÷çõöëñðõ°"Öêç"ãðõùçô"öñ"çãåê"ó÷çõöëñð"ëõ"ã"õëðéîç"æëéëö"ëðöçéçô"ôãðéëðé"èôñï"²"öñ"»°"Öêç åñôôçåö"æëéëö"äçîñù"öêç"ó÷çõöëñð"ð÷ïäçô"ëð"öêç"ÑÔÕ"ëõ"öñ"äç"ä÷ääîçæ° k -1¶¹° Îçö "Õí." í" ¿" ³.´.°°°°°°°.³²²." æçðñöç" öêç" õ÷ï" ñè" öêç" ëðèëðëöç" éçñïçöôëå" õçôëçõ" ùêñõç" èëôõö" öçôï" ëõ" " ãðæ "öêç k! 1 1002 100 2 åñïïñð" ôãöëñ"ëõ" k ° "Öêçð "öêç "øãî÷ç "ñè " 100! k =1 ( + å k - 3k + 1 S k " ëõ )Ãðõ ° "¶ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in 7 / 13
  8. 8. IIT-JEE 2010 EXAMINATION PAPER - 1 (HELD ON : 11 - 04 - 2010)¶º° Öêç "ð÷ïäçô "ñè "ãîî "òñõõëäîç "øãî÷çõ "ñè "q. "ùêçôç "² "¾ "q" ¾" p. "èñô "ùêëåê "öêç "õûõöçï "ñè "çó÷ãöëñðõ (û"+"ü+"åñõ"µq"¿"(úûü+"õëð"µq 2cos3q 2sin 3q x sin 3q = + y z (úûü+"õëð"µq"¿"(û"+"´ü+"åñõ"µq"+"û"õëð"µq êãøç" ã" õñî÷öëñð" (ú².û². "ü²+ "ùëöê "û²ü²" ¹" ²." ëõÃðõ ° "µ¶ » ° Îçö "è "äç "ã "ôçãî¯øãî÷çæ "æëèèçôçðöëãäîç "è÷ðåöëñð "ñð "Ô "(öêç "õçö "ñè "ãîî "ôçãî "ð÷ïäçôõ+ "õ÷åê "öêãö "è(³+ "¿ "³° "Ëè "öêç "û¯ëðöçôåçòö ñè "öêç "öãðéçðö "ãö "ãðû "òñëðö "Ò(ú.û+ "ñð "öêç "å÷ôøç "û "¿ "è(ú+ "ëõ "çó÷ãî "öñ "öêç "å÷äç "ñè "öêç "ãäõåëõõã "ñè "Ò. "öêçð "öêç "øãî÷ç "ñè è(ʵ+" ëõ" çó÷ãî" öñÃðõ ° "» æ p pö np·²° Öêç "ð÷ïäçô "ñè "øãî÷çõ "ñè "q" ëð" öêç" ëðöçôøãî" ç - , ÷ " õ÷åê" öêãö" q ¹ " èñô "ð "¿ "². "³³. "³´ "ãðæ "öãðq" ¿ "åñö "·q" ãõ" ùçîî è 2 2ø 5 ãõ"õëð"´q"¿"åñõ¶q"ëõÃðõ ° "µ 1·³°Ãðõ ° "´·´° ( r r r EN Öêç "ïãúëï÷ï "øãî÷ç "ñè "öêç "çúòôçõõëñð " ) ( r r r r ) ( r 2a + b . é a ´ b ´ a - 2b ù "ëõ ë û ) sin q + 3 sin q cos q + 5 cos2 q 2 r ˆ - 2ˆ Ëè" a " ãðæ" b " ãôç "øçåöñôõ "ëð "õòãåç "éëøçð "äû " a = i 5 j r 2i + ˆ + 3k " ãðæ" b = ˆ j 14 ˆ " ëõ . "öêçð "öêç "øãî÷ç "ñè LLÃðõ ° "· x2 y 2·µ° Öêç" îëðç" ´ú" +" û" ¿³" ëõ" öãðéçðö" öñ" öêç" êûòçôäñîã" - = 1 ° "Ëè "öêëõ "îëðç "òãõõçõ "öêôñ÷éê "öêç "òñëðö "ñè "ëðöçôõçåöëñð "ñè a 2 b2 öêç" ðçãôçõö" æëôçåöôëú" ãðæ" öêç" ú¯ãúëõ." öêçð" öêç" çååçðöôëåëöû" ñè" öêç" êûòçôäñîã" ëõÃðõ ° "´ x -1 y - 2 z - 3 A·¶° Ëè "öêç "æëõöãðåç "äçöùççð "öêç "òîãðç "Ãú "Ę "´û "+ "ü "¿ "æ "ãðæ "öêç "òîãðç "åñðöãëðëðé "öêç "îëðçõ " = = " ãðæ 2 3 4 x-2 y -3 z -4 = = " ëõ" 6 ." öêçð" þæþ" ëõ 3 4 5Ãðõ ° "¸· · ° Èñô "ãðû "ôçãî "ð÷ïäçô "ú. "îçö "Ýúß "æçðñöç "öêç "îãôéçõö "ëðöçéçô "îçõõ "öêãð "ñô "çó÷ãî "öñ "ú° "Îçö "è "äç "ã "ôçãî "øãî÷çæ "è÷ðåöëñð æçèëðçæ" ñð" öêç" ëðöçôøãî" ÝĘ³²." ³²ß" äû ì x - [x] if [x]is odd, f(x) = í î1 + [x] - x if [x]is even 10 p2 10 -ò " Öêçð "öêç "øãî÷ç "ñè " f(x) cos px dx " ëõ 10Ãðõ ° "¶ 2p 2p·¸° Îçö" w" äç" öêç" åñïòîçú" ð÷ïäçô" cos + i sin °" Öêçð" öêç" ð÷ïäçô" ñè" æëõöëðåö" åñïòîçú" ð÷ïäçôõ" ü" õãöëõèûëðé 3 3 z +1 w w2 w z + w2 1 = 0 " ëõ "çó÷ãî "öñ 2 w 1 z+wÃðõ ° "³ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 8 / 13 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in
  9. 9. IIT-JEE 2010 EXAMINATION PAPER - 1 PART-III (PHYSICS) (HELD ON : 11 - 04 - 2010) UGEVKQP˜K" <" *Ukping" Eqttgev" Ejqke g" V{ rg+ Vjku" ugevkqp" eqpvckpu" :" ownvkrng" ejqkeg" swguvkqpu0" Gcej" swguvkqp" jcu" hqwt" ejqkegu" *C+." *D+." *E+" cpf" *F+." qwv qh" yjkej" QPN[" QPG" ku" eqttgev0790 Kpecpfguegpv" dwndu" ctg" fgukipgf" d{" mggrkpi" kp" okpf" vjcv" vjg" tgukuvcpeg" qh" vjgkt" hkncogpv" kpetgcugu" ykvj" vjg" kpetgcug kp "vgorgtcvwtg0 "Kh "cv "tqqo "vgorgtcvwtg. "322 "Y. "82 "Y "cpf "62 "Y "dwndu "jcxg "hkncogpv "tgukuvcpeg "T322. "T82" cpf "T62. tgurgevkxgn{." vjg" tgncvkqp" dgvyggp" vjgug" tgukuvcpegu" ku 1 1 1 1 1 1 *C+" R = R + R *D+ "T 322" ? "T 62" - "T 82 *E+" T 322" @ "T 82" @ "T 62 *F+" R > > R 60 R 40 100 40 60 100Cpu0" *F+7:0 Vq "xgtkh{ "Qjo”u "ncy. " "c "uvwfgpv "ku "rtqxkfgf "ykvj "c "vguv "tgukuvqt "TV. "c "jkij "tgukuvcpeg "T3." c"uocnn" tgukuvcpeg" T4."vyq EN kfgpvkecn"icnxcpqogvgtu" I3" cpf "I4." cpf"c"xctkcdng"xqnvcig"uqwteg"X0" Vjg"eqttgev" ektewkv"vq"ectt{" qwv"vjg" gzrgtkogpv ku" <˜ LL *C+" *D+" A *E+" *F+"Cpu0" *E+7;0 Cp "CE "xqnvcig "uqwteg "qh "xctkcdng "cpiwnct "htgswgpe{ "w" cpf" hkzgf" cornkvwfg" X2" ku" eqppgevgf" kp" ugtkgu" ykvj" c ecrcekvcpeg "E "cpf "cp "gngevtke "dwnd "qh "tgukuvcpeg "T "*kpfwevcpeg "|gtq+0 "Yjgp "w" " ku" kpetgcugf *C+ "vjg "dwnd "inqyu "fkoogt *D+" vjg" dwnd" inqyu" dtkijvgt *E+" vqvcn" korgfcpeg" qh" vjg" ektewkv" ku" wpejcpigf *F+" vqvcn" korgfcpeg" qh" vjg" ektewkv" kpetgcuguCpu0 *D+ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in 9 / 13
  10. 10. IIT-JEE 2010 EXAMINATION PAPER - 1 (HELD ON : 11 - 04 - 2010)820 C" vjkp" hngzkdng" yktg" qh" ngpivj" N" ku" eqppgevgf" vq" vyq" cflcegpv" hkzgf" rqkpvu" cpf" ecttkgu" c" ewttgpv" K" kp" vjg" enqemykug fktgevkqp. "cu "ujqyp "kp "vjg "hkiwtg0 "Yjgp "vjg "u{uvgo "ku "rwv "kp "c "wpkhqto "ocipgvke "hkgnf "qh "uvtgpivj "D "iqkpi "kpvq "vjg rncpg "qh "vjg "rcrgt. "vjg "yktg "vcmgu "vjg "ujcrg "qh "c "ekteng0 "Vjg "vgpukqp "kp "vjg "yktg "ku """""""""" IBL IBL IBL *C+" KDN *D+" *E+" *F+" p 2p 4pCpu0 *E+8 3 0 C "dnqem "qh "ocuu "o "ku "qp "cp "kpenkpgf "rncpg "qh "cping "q0" Vjg" eqghhkekgpv" qh" htkevkqp dgvyggp" vjg"dnqem" cpf"vjg"rncpg"ku" m"cpf"vcpq" @m0"Vjg"dnqem"ku" jgnf"uvcvkqpct{"d{ EN crrn{kpi "c "hqteg "R "rctcnngn "vq "vjg "rncpg0 "Vjg "fktgevkqp "qh "hqteg "rqkpvkpi "wr "vjg rncpg "ku "vcmgp "vq "dg "rqukvkxg0 "Cu "R "ku "xctkgf "htqo "R 3" ? "oi "*ukpq" ˜" mequq+" vq R4?oi*ukpq" -" m" equq+. "vjg "htkevkqpcn "hqteg "h "xgtuwu "R "itcrj "yknn "nqqm "nkmg LL *C+" *D+" ""*E+" "*F+"Cpu0" *C+8 4 0 C "vjkp "wpkhqto "cppwnct "fkue "*ugg "hkiwtg+ "qh "ocuu "O "jcu "qwvgt "tcfkwu "6T "cpf "kppgt "tcfkwu "5T0 " " AVjg" yqtm" tgswktgf" vq" vcmg" c" wpkv" ocuu" htqo" rqkpv" R" qp" kvu" czku" vq" kphkpkv{" ku 2GM 2GM *C+" ( 4 2 - 5) *D+" - ( 4 2 - 5) 7R 7R GM 2GM *E+" *F+" ( 2 - 1) 4R 5RCpu0" " *C+8 5 0 Eqpukfgt" c" vjkp" uswctg" ujggv" qh" ukfg" N" cpf" vjkempguu" v." ocfg" qh" c" ocvgtkcn" qh" tgukuvkxkv{" r0" Vjg" tgukuvcpeg" dgvyggp vyq "qrrqukvg "hcegu. "ujqyp "d{ " "vjg "ujcfgf "ctgcu "kp "vjg "hkiwtg "ku *C+" fktgevn{" rtqrqtvkqpcn" vq" N *D+" fktgevn{" rtqrqtvkqpcn" vq" v *E+" kpfgrgpfgpv" qh" N *F+" kpfgrgpfgpv" qh" vCpu0" *E+860 C" tgcn" icu" dgjcxgu" nkmg" cp" kfgcn" icu" kh" kvu *C+" rtguuwtg" cpf" vgorgtcvwtg" ctg" dqvj" jkij *D+" rtguuwtg" cpf" vgorgtcvwtg" ctg" dqvj" nqy *E+ " "rtguuwtg "ku "jkij "cpf "vgorgtcvwtg "ku "nqy *F+" rtguuwtg" ku" nqy" cpf" vgorgtcvwtg" ku" jkijCpu0 *F+ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 10 / 13 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in
  11. 11. IIT-JEE 2010 EXAMINATION PAPER - 1 (HELD ON : 11 - 04 - 2010) UGEVKQP˜KK" <" *Ownvkrng" Eqttge v" Ejqkeg" V{rg+ Vjku" ugevkqp" eqpvckpu" 7" ownvkrng" ejqkeg" swguvkqpu0" Gcej" swguvkqp" jcu" hqwt" ejqkegu" *C+." *D+." *E+" cpf" *F+." qwv qh" yjkej" QPG" QT" OQT G" oc{" dg" eqttgev0870 C "rqkpv "ocuu "qh "3 "mi "eqnnkfgu "gncuvkecnn{ "ykvj "c "uvcvkqpct{ "rqkpv "ocuu "qh "7 "mi0 "Chvt "vjgkt "eqnnkukqp. "vjg "3 "mi "ocuu tgxgtugu" kvu" fktgevkqp" cpf" oqxgu" ykvj" c" urggf" qh" 4" ou˜30 "Yjkej "qh "vjg "hqnnqykpi "uvcvgogv*u+ "ku "*ctg+ "eqttgev "hqt "vjg u{uvgo" qh" vjgug" vyq" ocuuguA *C+ "Vqvcn "oqogpvwo "qh "vjg "u{uvgo "ku "5 "mi "ou˜3 *D+ "Oqogpvwo "qh "7 "mi "ocuu "chvgt "eqnnkukqp "ku "6 "mi "ou˜3 *E+ "Mkpgvke "gpgti{ "qh "vjg "egpvtg "qh "ocuu "ku "2097 "L *F+ "Vqvcn "mkpgvke "gpgti{ "qh "vjg "u{uvgo "ku "6LCpu0" " *CE+8 8 0 Qpg "oqng "qh "cp "kfgcn "icu "kp "kpkvkcn "uvcvg "C "wpfgtiqgu "c "e{enke "rtqeguu "CDEC. "cu "ujqyp "kp "vjg "hkiwtg0 "Kvu "rtguuwtg cv "C "ku "R20" Ejqqug" vjg" eqttgev" qrvkqp*u+" htqo" vjg" hqnnqykpi EN *C+ "Kpvgtpcn "gpgtikgu "cv "C "cpf "D "ctg "vjg "ucog *D+ "Yqtm "fqpg "d{ "vjg "icu "kp "rtqeguu "CD "ku "R2X2" lp "6 *E+" Rtguuwtg"cv"E"ku" P0 4 *F+" Vgorgtcvwtg" cv" E" ku" T0 4 LLCpu0" *CD+8 9 0 C "uvwfgpv "wugu "c "ukorng "rgpfwnwo "qh "gzcevn{ "3o "ngpivj "vq "fgvgtokpg "i. "vjg "ceegngtcvkqp "fwg "vq "itcxkv{0 "Jg "wugu "c uvqr "ycvej "ykvj "vjg "ngcuv "eqwpv "qh "3 "uge "hqt "vjku "cpf "tgeqtfu "62 "ugeqpfu "hqt "42 "queknncvkqpu0 "Hqt "vjku "qdugtxcvkqp. yjkej" qh" vjg" hqnnqykpi" uvcvgogpv*u+" ku" *ctg+" vtwgA *C+" Gttqt" DV "kp "ogcuwtkpi "V. "vjg "vkog "rgtkqf "ku "2027 "ugeqpfu *D+" Gttqt" DV" kp" ogcuwtkpi" V." vjg" vkog" rgtkqf" ku" 3" ugeqpf A *E+" Rgtegpvcig" gttqt" kp" vjg" fgvgtokpcvkqp" qh" i" ku" 7 *F+" Rgtegpvcig" gttqt" kp" vjg" fgvgtokpcvkqp" qh" i" ku" 407Cpu0" *CE+8 : 0 C "hgy "gngevtke "hkgnf "nkpgu "hqt "c "u{uvgo "qh "vyq "ejctigu "S3" cpf "S4" hkzgf "cv "vyq fkhhgtgpv "rqkpvu "qp "vjg "z˜czku "ctg "ujqyp "kp "vjg "hkiwtg0 "Vjgug "nkpgu "uwiiguv "vjcv *C+" ~S 3~" @" ~S 4 ~ *D+" " ~S 3~" >" ~S 4~ *E+ "cv "c "hkpkvg "fkuvcpeg "vq "vjg "nghv "qh "S3" vjg" gngevtke" hkgnf" ku" |gtq *F+ "cv "c "hkpkvg "fkuvcpeg "vq "vjg "tkijv "qh "S4" vjg" gngevtke" hkgnf" ku" |gtqCpu 0" *CF+8 ; 0 " C "tc{ "QR "qh "oqpqejtqocvke "nkijv "ku "kpekfgpv "qp "vjg "hceg "CD "qh "rtkuo "CDEF pgct "xgtvgz "D "cv "cp "kpekfgpv "cping "qh "82² "*ugg "hkiwtg+0 "Kh "vjg "tghtcevkxg "kpfgz "qh vjg" ocvgtkcn" qh" vjg" rtkuo" ku" 3 ." yjkej" qh" vjg" hqnnqykpi" ku" *ctg+" eqttgevA *C+ "Vjg "tc{ "igvu "vqvcnn{ "kpvgtpcnn{ "tghngevgf "cv "hceg "EF *D+ "Vjg "tc{ "eqogu "qwv "vjtqwij "hceg "CF *E+ "Vjg "cping "dgvyggp "vjg "kpekfgpv "tc{ "cpf "vjg "gogtigpv "tc{ "ku ";2² *F+" Vjg" cping" dgvyggp" vjg" kpekfgpv" tc{" cpf" vjg" gogtigpv" tc{" ku" 342²Cpu 0" *CDE+ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in 11 / 13
  12. 12. IIT-JEE 2010 EXAMINATION PAPER - 1 (HELD ON : 11 - 04 - 2010) UGEVKQP˜KKK" <" *R ctci tcrj" V{rg+ Vjku" ugevkqp" eqpvckpu" 4" rctcitcrju0" Dcugf" wrqp" vjg" hktuv" rctcitcrj." 4" ownvkrng" ejqkeg" swguvkqpu" cpf" dcugf wrqp" vjg" ugeqpf" rctcitcrj" 5" ownvkrng" ejqkeg" swguvkqpu" jcxg" vq" dg" cpuygtgf0" Gcej" qh" vjgug" swguvkqpu" jcu hqwt" ejqkegu" *C+." *D+." *E+" cpf" *F+." qwv" qh" yjkej" QPN[" QPG" ku" eqttgev0 Rctcitcrj" hqt" Swguvkqpu" 92" vq" 93 Gngevtkecn" " tgukuvcpeg" qh" egtvckp" ocvgtkcnu." mpqyp" cu" uwrgteqpfwevqtu." ejcpigu """"""" cdtwrvn{ "htqo "c "pqp|gtq "xcnwg "vq "|gtq "cu "vjgkt "vgorgtcvwtg "ku "nqygtgf " "dgnqy "c etkvkecn" vgorgtcvwtg" V E*2+0" Cp" kpvgtguvkpi" rtqrgtv{" qh" uwrgteqpfwevqtu" ku" vjcv vjgkt" etkvkecn" vgorgtcvwtg" dgeqogu" uocnngt" vjcp" V E*2+ "kh "vjg{ "ctg "rncegf "kp "c ocipgvke" hkgnf." k0g0." vjg" etkvkecn" vgorgtcvwtg" V E*D+ "ku "c "hwpevkqp "qh "vjg "ocipgvke hkgnf" uvtgpivj" D0" Vjg" fgrgpfgpeg" qh" VE" *D+ "qp "D "ku "ujqyp "kp "vjg "hkiwtg0920 Kp "vjg "itcrju "dgnqy. "vjg "tgukuvcpeg "T "qh "c "uwrgteqpfwevqt "ku "ujqyp "cu "c "hwpevkqp "qh "kvu "vgorgtcvwtg "V "hqt "vyq fkhhgtgpv" ocipgvke" hkgnfu" D3*uqnf" nkpg+" cpf" D4" *fcujgf" nkpg+0" Kh" D4" ku "nctigt "vjcp "D3. "yjkej "qh "vjg "hqnnqykpi "itcrju ujqyu" vjg" eqttgev" xctkcvkqp" qh" T" ykvj" V" kp" vjgug" hkgnfuA *C+"Cp u 0* C+ EN *D+" " *E+" *F+"930 C" uwrgteqpfwevqt" jcu" VE*2+ "? "322 "M0 "Yjgp "c "ocipgvke "hkgnf "qh "907 "Vgunc "ku "crrnkgf. "kvu "VE" fgetgcugu "vq "97 "M0 "Hqt LL vjku" ocvgtkcn" qpg" ecp" fghkpkvgn{" uc{" vjcv" yjgp *C+ "D?7 "Vgunc. "VE" *D+ "? ":2 "M *D+ "D?7 "Vgunc. "97 "M "> "VE*D+ "> "322 "M *E+ "D? "32 "Vgunc. "97 "M "> "VE *D+" >" 322M *F+ " "D "? "32 "Vgunc. "VE*D+ "? "92 "MCpu0" *D+ Rc tcitcrj" hqt" swguvkqpu" 94" vq" 96 Yjgp "c "rctvkeng "qh "ocuu "o "oqxgu "qp "vjg "z˜czku "kp "c "rqvgpvkcn "qh "vjg "hqto X*z+ "? "mz4." kv" rgthqtou" ukorng" jctoqpke" oqvkqp0" Vjg" eqttgurqpfkpi" vkog A m rgtkqf" ku" rtqrqtvkqpcn" vq" ." cu" ecp" dg" uggp" gcukn{" wukpi" fkogpukqpcn k cpcn{uku0" Jqygxgt." vjg" oqvkqp" qh" c" rctvkeng" ecp" dg" rgtkqfke" gxgp" yjgp" kvu rqvgpvkcn" gpgti{" kpetgcugu" qp" dqvj" ukfgu" qh" z?2" kp" c" yc{" fkhhgtgpv" htqo mz4" cpf" kvu" vqvcn"gpgti{" ku" uwej" vjcv" vjg" rctvkeng" fqgu" pqv"guecrg" vq"kphkpkv{0 Eqpukfgt" c" rctvkeng" qh" ocuu" o" oqxkpi" qp" vjg" z˜czku0" Kvu" rqvgpvkcn" gpgti{ ku" X*z+" ?" az 6" *a" @ "2+ "hqt "~z~ "pgct "vjg "qtkikp "cpf "dgeqogu "c "eqpuvcpv gswcn "vq "X2" hqt" ~z~" ³" Z2" *ugg" hkiwtg+940 Kh" vjg" vqvcn" gpgti{" qh" vjg" rctvkeng" ku" G." kv" yknn" rgthqto" rgtkqfke" oqvkqp" qpn{" kh *C+ "G "> "2 *D+ "G "@ "2 *E+" X2" @ "G "@ "2 *F+ "G "@ "X2Cpu0" *E+9 5 0 Hqt "rgtkqfke "oqvkqp "qh "uocnn "cornkvwfg "C. "vjg "vkog "rgtkqf "V "qh "vjku "rctvkeng "ku "rtqrqtvkqpcn "vq m 1 m a 1 a *C+" A *D+" *E+" A *F+" a A a m A mCpu0" *D+960 Vjg "ceegngtcvkqp "qh "vjku "rctvkeng "hqt "~z~ "@ "Z2" ku V0 V0 *C+" rtqrqtvkqpcn" vq" X2 *D+" rtqrqtvkqpcn" vq" mX *E+" rtqrqtvkqpcn" vq" mX 0 *F+" gtq 0Cpu0 *F+ Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 12 / 13 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in
  13. 13. IIT-JEE 2010 EXAMINATION PAPER - 1 (HELD ON : 11 - 04 - 2010) UGEVKQP˜KX" <" *Kpvgigt" V{rg+ Vjku"Ugevkqp"eqpvckpu"VGP"swguvkqpu0"Vjg"cpuygt"vq"gcej"swguvkqp"ku"c"ukping"fkikv"kpvgigt"tcpikpi"htqo"2"vq";0"Vjg eqttgev"fkikv"dgnqy"vjg"swguvkqp"pwodgt"kp"vjg"QTU"ku"vq"dg"dwddngf0 6970 Itcxkvcvkqpcn" ceegngtcvkqp" qp" vjg" uwthceg" qh" c" rncpgv" ku" g . "yjgtg "i "ku "vjg "itcxkvcvkqpcn "ceegngtcvkqp "qp "vjg 11 2 uwthceg" qh" vjg" gctvj0" Vjg" cxgtcig" ocuu" fgpukv{" qh" vjg" rncpgv" ku" " vkogu "vjcv "qh "vjg "Gctvj0 "Kh "vjg "guecrg "urggf "qp 3 vjg "uwthceg "qh "vjg "gctvj "ku "vcmgp "vq "dg "33 "mou˜3. "vjg "guecrg " "urggf "qp "vjg "uwthceg "qh "vjg "rncpg "kp "mou˜3" yknn" dgCpu0 "59 8 0 C "rkgeg "qh "keg "*jgcv "ecrcekv{ "? "4322 "L "mi˜3" ²E˜3" cpf "ncvgpv "jgcv "? "5058 "Ù "327" L" mi˜3+ "qh "ocuu "o "itcou "ku "cv "˜7²E cv" cvoqurjgtke" rtguuwtg0" Kv" ku" ikxgp" 642" L" qh" jgcv" uq" vjcv" vjg" keg" uvctvu" ognvkpi0" Hkpcnn{" yjgp" vjg" keg˜ycvgt" okzvwtg ku" kp" gswknkdtkwo." kv" ku" hqwpf" vjcv" 3" io" qh" keg" jcu" ognvgf0" Cuuwokpi" vjgtg" ku" pq" qvjgt" jgcv" gzejcpig" kp" vjg" rtqeguu. vjg" xcnwg" qh" o" kuCpu0 ":9:0 EN9 9 0 C" uvcvkqpct{" uqwteg" ku" gokvvkpi" uqwpf" cv" c" hkzgf" htgswgpe{" h2." yjkej" ku" tghngevgf" d{" vyq" ectu" crrtqcejkpi" vjg" uqwteg0 Vjg" fkhhgtgpeg" dgvyggp" vjg" htgswgpekgu" qh" uqwpf" tghngevgf" htqo" vjg" ectu" ku" 304" qh" h20 "Yjcv "ku "vjg "fkhhgtgpeg "kp "vjg urggfu" qh" vjg" ectu" *kp" mo" rgt" jqwt+" vq" vjg" pgctguv" kpvgigtA" Vjg" ectu" ctg" oqxkpi" cv" eqpuvcpv" urggfu" owej" uocnngt vjcp "vjg "urggf "qh "uqwpf "yjkej "ku "552 "ou˜30Cpu0 "9 Vjg "hqecn "ngpivj "qh "c "vjkp "dkeqpxgz "ngpu "ku "42 "eo0 "Yjgp "cp "qdlgev "ku "oqxgf "htqo "c "fkuvcpeg "qh "47 "eo "kp "htqpv "qh "kv m25 LL vq "72 "eo. "vjg "ocipkhkecvkqp "qh "kvu "kocig "ejcpigu "htqo "o47" vq "o720" Vjg" tcvkq" m " ku 50Cpu0 "89 ; 0 Cp" a˜rctvkeng" cpf" c" rtqvqp" ctg" ceegngtcvgf" htqo" tguv" d{" c" rqvgpvkcn" fkhhgtgpeg" qh" 322" X0" Chvgt" vjku." vjgkt" fg" Dtqinkg lp ycxgngpivju" ctg" la" cpf" lr" tgurgevkxgn{0" Vjg" tcvkq" . "vq "vjg "pgctguv "kpvgigt. "ku la ACpu0 "5: 2 0 Yjgp" vyq" kfgpvkecn" dcvvgtkgu" qh" kpvgtpcn" tgukuvcpeg" 3W" " gcej" ctg" eqppgevgf" kp" ugtkgu" cetquu" c" tgukuvqt" T." vjg" tcvg" qh jgcv" rtqfwegf" kp" T" ku" L30" Yjgp" vjg" ucog" dcvvgtkgu" ctg" eqppgevgf" kp" rctcnngn" cetquu" T." vjg" tcvg" ku" L40 "Kh "L3" ?" 4047" L4 vjgp "vjg "xcnwg "qh "T "kp "W" kuCpu0 "6: 3 0 Vyq "urjgtkecn "dqfkgu "C "*tcfkwu "8 "eo+ "cpf "D "*tcfkwu "3: "eo+ "ctg "cv "vgorgtcvwtgu "V3" cpf "V 4." tgurgevkxgn{0" Vjg oczkowo" kpvgpukv{" kp" vjg" gokuukqp"urgevtwo" qh"C" ku" cv" 722"po" cpf" kp" vjcv"qh" D" ku" cv"3722" po0"Eqpukfgtkpi" vjgp" vq dg "dncem "dqfkgu. "yjcv "yknn "dg "vjg "tcvkq "qh "vjg "tcvg "qh "vqvcn " "gpgti{ "tcfkcvgf "d{ "C "vq "vjcv "qh "DACpu0 ; æ pö:40 Yjgp" vyq" rtqitguukxg" ycxgu" {3?6" ukp*4z" ˜" 8v+" cpf" {4" ?5" ukp" ç 2x - 6t - ÷ " ctg" uwrgtkorqugf." vjg" cornkvwfg" qh è 2ø vjg" tguwnvcpv" ycxg" kuCpu0 "7: 5 0 C" 203" mi" ocuu" " ku" uwurgpfgf" htqo" c" yktg" qh" pginkikdng" ocuu0" Vjg" ngpivj" qh" vjg" yktg" ku" 3o" cpf" kvu" etquu˜ugevkqpcn ctgc "ku "60; "Ù "32˜9" o40" Kh" vjg" ocuu" ku" rwnngf" c" nkvvng" kp" vjg" xgtvkecnn{" fqypyctf" fktgevkqp" cpf" tgngcugf." kv" rgthqtou ukorng "jctoqpke "oqvkqp "qh "cpiwnct "htgswgpe{ "362 "tcf "u˜30 "Kh "vjg "[qwpi”u "oqfwnwu "qh "vjg "ocvgtkcn "qh "vjg "yktg "ku "p " "Ù 32;" Po˜4. "vjg "xcnwg "qh "p "kuCpu0 "6: 6 0 C"dkpct{" uvct"eqpukuvu" qh"vyq" uvctu" C"*ocuu"404"OU+ "cpf "D "*ocuu "33 "OU+."yjgtg" OU" ku "vjg "ocuu "qh "vjg "uwp0 "Vjg{ "ctg ugrctcvgf "d{ "fkuvcpeg "f "cpf "ctg "tqvcvkpi "cdqwv "vjgkt "egpvtg "qh "ocuu. "yjkej "ku "uvcvkqpct{0 "Vjg "tcvkq "qh "vjg "vqvcn cpiwnct" oqogpvwo" qh" vjg" dkpct{" uvct" vq" vjg" cpiwnct" oqogpvwo" qh" uvct" D" cdqwv" vjg" egpvtg" qh" ocuu" kuCpu0 "8 Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, INDRA VIHAR, KOTA-324005 PHONE : +91 - 744 - 2436001 (4 Lines), Fax : +91-744-2435003, E-mail: info@allen.ac.in Website: www.allen.ac.in 13 / 13

×