July

Vol. - 4, Issue XII, July - September 2008

"I Started my life selling Idlis in my slum," Sarathbabu an alumnus from IIM-A.

An in-house publication of Resonance

Main hoon na Resonating The

of Education

July - September 2008

CONT E NT S Quotes RKV Sir's Message Cover Story

4 5 6

Ankit Fadia, the young Indian is recognized across the world as a authentic computer security guru, cyber terrorism expert and computer security trainer.

IIT Success Story News & Views gkj u ekuh thou esa Sandipan Deb Reso Reaper Math Magic Winners Olympiad Opulence Reso Family Function- VILAY

9 10 11 12 14 15 16 18 19

VICTORY - Felicitation Function 2008 Reso PCCP Accomplishments Talent Hunt Think To Win Reso Boost IIT - Kharagpur The Inspiring Account of Sarathbabu Rainbow Spot Light Eureka Khul ja sim sim Reso Repertoire

20 22 23 26 27 28 30 32 33 34 37 39

Dear Students, Winning brings immense pleasure and happiness. It instills confidence and consolidates our position among the people we love to be with. The words of Mount Everest conqueror Bachendri pal are inspiring;” I don't think I have conquered mountains; I've conquered weaknesses and fears with my practice and training.” winning is inspiration to work harder. It's a responsibility because a winner gives hope to all those who share similar aspirations. In IIT-JEE results on 30 May 08, Resonance hogged lime light and there is a winning smile on Resonites' faces radiating the winner's energy. From the various teaching programmes, Resonance contributes 1064 students in the list of successful 8652 students, which is striking as the overall success rate this year is 2.78% in IIT-JEE. From our list of selected students, 612 students come from the regular class room contact programmes and 452 count from the distance learning programmes, registering 17 ranks in the top 100 students, 09 (18, 24, 42, 58, 77, 85, 92, 95, 100) are from regular class room contact programmes and 08 students (05, 23, 33, 39, 49, 55, 76, and 94) from various distance learning programmes. I appreciate the efforts of all the successful students. They have achieved their goal facing many hardships and their success reflects commitment and dedication with continued focus on their target staying away from their homes. The Resonance faculty members and the support from the administrative team have contributed significantly in their success. I would like to make a special mention of Jaipur and Bhopal study centers which have earned laurels as their students achieved remarkable success- 48 out of 240, and 8 out of 24 respectively. To our new students, my best advice is to be attentive during the lectures in the classroom which prove most useful and the important points noted by them in the classroom shall help them most in meeting success. The results are the mirror reflection of the competitive excellence originating from accumulation of merit and enterprise, involving sincere efforts and hard work. I expect all of you to essentially follow a winner's road map to be successful in life. Winning is where wholesome growth is. I wish to complete my words with the following urdu verse. *gok esa rk'k dk ?kj ugha curk] jksus ls fcxM+k eqdn~nj ugha curk] nqfu;k thrus dk gkSlyk j[kks ;kjksa] ,d thr ls dksbZ fldUnj ugha curk----

R K Verma

Awards & Recognition For his outstanding contributions in the field of computer security globally, Fadia has been honored with numerous awards namely. m Person of the Year India 2002’ by Limca Book of Records. m Gold Medal from Singapore Government. (IDSS, Singapore) m Mention in Limca Book of Records 2002, Limca Book of Records 2003 & Limca Bookof Records 2004. m ‘Hall of Fame’ Award by The Hindustan Times. Books: He has authored several internationally best-selling books on numerous topics related to Computer Security that have been widely appreciated by both professionals and industry leaders the world over. His books have sold a record 2 million copies across the globe, have been translated into Japanese, Korean, Portuguese and Polish and are also being used as reference textbooks in some of the most prestigious academic institutions in Asia and North America. His few books includes: The Unofficial Guide to Ethical Hacking, N e t w o r k S e c u r i t y : A H a c k e r ’s Perspective, The Ethical Hacking Guide to Corporate Security, Hacking Mobile Phones, Email Hacking, Windows Hacking, Google Hacking, Intrusion Alert, Encryption & Tips and tricks on Linux

Anunaad, July - September 2008

Milestones in Ankit Fadia’s Life AGE 10 - Gifted a computer at home by his parents. AGE 12 - Developed an interest in Computer Hacking. AGE 14 – Published his first book titled 'The Unofficial Guide to Ethical Hacking' which became an instant bestseller worldwide, sold 500 000 copies and was translated into 11 languages. AGE 16 – After the Sept. 11th attacks, cracked an encrypted email sent by the Al-Qaeda terrorist network for a classified intelligence agency. AGE 21 - Widely recognized as an Ethical Hacker, Computer Security Expert and Cyber Terrorism guru. Written many best selling books, delivered more than 1000 seminars in 25 countries, received 45 awards, provide certification courses on Computer Security, is writing a script for a movie, runs his own consulting company and is a student at Stanford University.

m ‘Ambassy State Award’- State L e v e l Aw a r d o f I n d i a . (Rajasthan) m B e s t S p e a k e r Aw a r d ( 5 occasions). m Silicon-India Person of the Week. m Outstanding Young Achiever Award. m Student Achiever of the Year 2002-2003. m Stanford University Asia Technology Initiative (ATI) 2004 Fellow m IT Leader Award 2005. m Indo-American Society Young Achiever Award 2005. m Industry leaders like Mr. Phiroze Vandrewala, Ganesh Ayyar, Mr. Kiran Karnik, and Research Pioneers like Jennifer Grannick and Indian icons like Dr. A.P.J. Kalam Mr. Chandra Babu Naidu Mr. Murali Manohar Joshi have also felicitated Fadia’s work.

08

IIT Success Story

IIT SUCCESS STORY

For any multinational in India, especially the food retailer, the thumb rule is to have 30% localisation and 70% global content. What is more important to succeed here is to have a 'global brand with local heart'. And that’s what we have been doing. - Muktesh Pant

M

Muktesh Pant is the chief marketing officer of $ 13b i l l i o n Yu m ! B r a n d s ' international division, Yum! Restaurant International. It is the world's largest restaurant company with 35,000 restaurants.

Muktesh Pant belongs to Kumaon. He did his schooling at Saint Joseph’s School Nainital. His mother, Shivani, is a famous Hindi novelist. The only son and the youngest of four children, Pant excelled in school. He wanted to study chemistry so he took the entrance exam and joined the IIT – Kanpur. Muktesh got his M. Tech. degree in 1976 in Chemical Engg. At the end of his fourth year at IIT, he went to Nocil for industrial training. "That’s when he realized that engineering by itself would get him nowhere. Engineers are given a pat on the back and the best employee award, while it’s the marketing and finance guys who got good money”. So, when some months later, Hindustan Lever came to the IIT campus to recruit engineers, Muktesh Pant asked them if it was possible to accommodate him in the marketing department. Pant wasn’t too hopeful of getting a positive response and had already Anunaad, July - September 2008

secured admission at IIM - Ahmedabad, But Levers invited him to Mumbai for another round of interviews. It was unusual in those days to appoint someone in the marketing department who didn’t have an MBA degree, but Pant clinched it in the interview. That was the end of chemistry. Muktesh (Micky) Pant spent 15 years in the company, from 1976 to 1991. According to Pant “Hindustan Lever, is the most preeminent company in India. It ingrained in me the very best management practices”.

consumer attention, Pant carved out more than 50 per cent share of India's premium footwear market for Reebok. Then he moved to Boston as Reebok's global brand manager. He was employee number one at Reebok, India, and helped build the company and its brand in India. Mr Pant, who came close to the top spot at Reebok, threw up a high profile marketing job, for the sweat and risk of an entrepreneurial venture, which was close to his heart. In 2004 Muktesh Pant has resigned as CMO of Reebok in order to pursue his life-long dream of establishing a yoga business that connects him to his roots in India. After following his dream of Yoga start-up, Muktesh Pant returned to the big corporate world as Chief Marketing Officer in Yum! Restaurants international divisions in mid 2005. A division of Yum! Brands Inc, a leading restaurant company with more than 33,000 restaurants in over 100 countries and territories, Yum! Inc, is the secondlargest food franchiser in the world, after McDonald's, in terms of sales. It is alsoOwner of leading restaurant brands like

In 1991 he moved from Hindustan Lever to Pepsi. Pant joined Pepsi for a four-year stint in 1991, where he headed the exports division, and later its bottling operations. He took another leap in 1996 when he moved from Pepsi to Reebok as its country head in India. He helped found Reeboks' India office, and eventually became the Chief Marketing Officer of Reebok. In a market where global brands like Adidas, Nike, Lotto and Pump were jostling for

KFC, Pizza Hut, Taco Bell and Long John Silver's. In his new role as worldwide chief marketing officer, Pant is working out in the company's Dallas headquarters. For Mr. Pant, the move from Reebok International to Yum! would mean moving from a single-brand company to a multibrand environment. He is among a handful of Indians who have earned their megaspurs on home soil. R.K. Sharma, SW & PR 09

News & Views

IIT SNIPPETS Indian Institute of Technology, Kanpur, has a task on hand excavating a 600 BC township, known as Gautam Buddha's monsoon haunts for 24 years. After carrying out an assessment study of the ruins and terraces 6 kilometers from Shravasti district, ASI saught IIT-K's assistance, for archeo scientific investigations of the pocket. ASI has signed an MoU with IIT- K for lending technical expertise to ASI project in terrain mapping, satellite imaging, laser scanning, Soil/pollen analysis and dating among others. The Shravasti find could turn out to be one of the most ambitious projects undertaken. ASI had earlier teamed up with the IIT- K in the Ahichhtra excavation near Bareilly, which was the capital of King Dhrupad, father of Draupadi the fiery consort of Pandavas. Work on the project has been underway since February 2007. The IITians would also be helping in restoration of historical monuments as part of the pact. The Monument protection Group-a core team comprising five senior faculty members and professors Omkar Dixit, Bharat Lohani, SK Jain and DC Roy, had come down to carry out a preliminary survey of the three century old 60 foot- tall Roomi Gate.The team intends to undertake seismic analysis to asses' damage to the structure.

IIT-M Grade Prefer old economy to new

IIT - Kanpur helps ASI in excavation

To be fading for budding engineers, the best technocrats from the Indian Institute of Technology, Madras, have shifted their attention to the manufacturing sector, which is today seen a better long term career bet. Besides, the core engineering sector offers better salaries than IT companies too are becoming bigger draw than IT. This is born out by campus placements over two years. IIT Madras deputy registrar (training placements & PR) Jaikumar said, “In the current season, of the 1,098 student, 51% placements were in the core sector, 25% in IT companies, while finance and firms accounted for another 17%, FMCG and PSU companies mopped up the remaining 7%.” Core sector companies have hired 560 students this year, Professor T T Narendran, Dean, Industrial consultancy and sponsored research, IIT Madras, explained, “We found IT firms don't pay much. IT firms, which were earlier recruiting 50 students, are now talking 5-10 moving to tier-II engineering colleges for their manpower needs.

Techniche is the annual-techno management Festival of IIT Guwahati. The national school championship, Technothlon is one of the major attraction of Techniche IITG’s Techno Management festival. Technothlon is aimed at initiating, moulding and sharpening the scientific outlook of the next wave of youth. Technothlon is conducted in two stages, Prelims and Mains. Prelims is nationwide aptitude exam for class 9-12 conducted by IIT Guwahati in 21 cities across the country on the 20th July, 2008 (Sunday). Top 60 teams selected in each module will take part in Technothlon mains held at IIT Guwahati. Apart from this, various on line events will be held which starts one or two weeks before Technotulon commences. Some of the major events in online module are, I Kaaru, Arbit , Online VSM. Lectures by eminent personalities are held during the 3 days of Techniche. Some of the finalized dignitaries this year are, James Matuer (Nobel Prize in Physics 2006), H.C. Verma (Professor in IIT-Kanpur), Michael Danino (Franch Author), C. Mohan (Chief Scientist IBM, USA), Prabhu Chawla (Editor – Indiatoday, Seadhibaat- Aajtak).- News courtesy : Mayank Goyal, IIT G.

The annual-techno management Festival of IIT Guwahati.

Manoj Sharma, General Manager -Academics


10

^^gkj u ekuh thou esa** gtkjksa vU; Nk=ksa dh rjg eSa Hkh vkbZvkbZVh&tsbZbZ dh rS;kjh djus ds fy, dksVk esa v/;;ujr FkkA vkbZvkbZVh&tsbZbZ 2007 dh ijh{kk dk og egRoiw.kZ fnu cgqr djhc vk pqdk Fkk] eSa fnu jkr viuh i] Numerical Problems Solve djus dk t+Tck vkSj lgh ekxZn'kZuA iz-3 D;k IIT-Kharagpur dk okrkoj.k vU; IIT laLFkkuksa ls fdlh Hkh izdkj ls fHkUu gS \ m- IIT- Kharagpur dks Mother of all IITs dgrs gSaA ;g lcls cM+h] lcls iqjkuh ,oa lHkh IITs ls fcYdqy fHkUu gSA IIT Kharagpur us 2000 vkS j 2001 esa vius Campus esa M a n a g e m e n t School (VGSOM) vkSj P r i v e t f u n d e d professional institute dh LFkkiuk dh o ckdh lHkh IIT laLFkkuksa us IIT- Kgp ds bl dne ls izsj.kk ysdj Management vkSj Privet funded professional institute dh LFkkiuk dhA vr% IIT Kharagpur vU; IITs ds fy, Hkh ,d Role Model gSA iz-5 IIT-Kgp ds 'kS{kf.kd ekgkSy ls tqM+s dqN ;knxkj yEgkas ds ckjs esa crk,aA m- Final semester esa tc eSa viuk project iwjk dj jgk Fkk] rc eSaus viuk fcLrj lab esa gh yxk fy;k FkkA vkSj yxHkx ,d eghus rd lab esa gh can lk gks x;k Fkk] vFkkZr iwjk le; lab esa gh dke djrk j g r k FkkA ;g ,d ,slk vuqHko Fkk tks vkxs eq>s vius professional life esa cgqr dke vk;kA iz-6 IIT-Kgp dh isaA rLdjh esa iSlk dekdj mlls dFkk djkdj iq.; izkIr djus fd ekU;rk ls cpsaA 8- viuk igukok vkSj O;ogkj ges'kk 'kkyhu j[ksaA 9- u fdlh ds lkFk vuqfpr O;ogkj djsaA u vuqfpr O;ogkj lgsaA 10- vius vfr fof'k"V gksus dk Hkze u ikysaA uSfrdrk ,d ,slk vkpj.k gS ftldh ped dHkh de ugha gksrh] ml ij fdlh Hkh ckgjh izsjd dk izHkko ugha iM+rkA bl ij dHkh tax ugha yxrkA

Virendra Saxena Front Line, Administration Anunaad, July - September 2008

32

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vuqukn dks is bl ckr dh gS fd vkt Hkh gesa vkSj gekjs cPps dks jst+ksusUl vius ifjokj dh rjg gh ;kn dj jgk gSA vkt gekjs cPps us tkss eqdke gkfly fd;k oks jst+ks&ifjokj ds lg;ksx ds fcuk laHko ugha FkkA eSa vki lHkh dk ân; dh xgjkbZ;ksa ls vkHkkj O;Dr djrh gw¡A Chandra Laxmi Agrawal Mother of Rohit Agrawal Reso Roll No. :- 36686 Currently doing B.Tech. Mining ISMU Dhanbad

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Anunaad is truly inspiring, educational magazine. I would like to say thanks to Resonance for this magazine. Please extend the number of articles.

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RESONANCE Appreciation Different Organisations have different ways of displaying their appreciations for excellence. Rewards for great performance need to be instantaneous and appropriate. It gives the employees a sense of dignity & respect. We touch their heart and increase emotional bonding with the organisation. Resonance Rewards its employee to make them feel highly valued and praise worthy. It has introduced the concept of EMPLOYEE OF THE MONTH (EOM) in recognition of their contribution and to infuse motivation among others.


APPLAUDS A JOB WELL DONE!

EMPLOYEE OF THE MONTH March 2008

March 2008

March 2008

March 2008

Mr. C. M. Verma Mr. Praveen Verma Mr. Bhuvnesh Sharma Mr. Dewank Executive (HRD) Sr. Office Assistant (Oprt.) Executive (PCCP) Jr. Office Asstt. (Admn.)

April 2008

May 2008

May 2008

Mr. Jitendra Singh Rajawat Office Assistant (PCCP)

Mr. Jijit Nair Sr. Office Asstt. (Admn.)

Mr. D. S. Parihar (Suraj) B.D. Executive (Lucknow)

33

EUREKA! Physics R E S O Q . 1 0 Physics : 1. A rigid bar of negligible weight is supported by steel and bronze wires as shown in figure. If w = 25kN, compute the temperature change that will cause the stress in the steel bar to be 50 N/mm2. For steel wire : as = 2 × 10–6 /ºC , ls = 2m, For bronze wire : aB = 8 × 10–6 /ºC , lB = 4m,

Bronze steel,s,A s, s,as,

w 1m 4m

Solution by : J.K. Pandey Faculty - Physics

ys = 1.5 × 1012 N/m2 As = 3 cm2 yB = 1.5 × 1011 N/m2 AB = 10 cm2

3m

Sol.

Tension in steel bar Ts = 50 × 106 × 3 × 10–4 = 15 kN.

WINNER Saurabh Agarwal Roll No. - 503364 Batch -G1

Bronze steel TB

Ts S

Tension in bronze wire : TS × 1 + TB × 4 = 25 × 3 TB = 15kN For steel :

B

3m

From constrain : dB × 4 = dS × 1 ds = 4dB For Bronze :

Ts  s   s  s T Asys

ds =

dB =

3

15  10  2 =

w=25kN

1m 4m

3  10  4  2  1012

 2  10 6  2T =

= 5 × 10–5 + 4 × 10–6 DT.

TB  B   B  B T A B yB 15  10 3  4

10  10

4

 1.5  10

11

 8  10 6  4T

= 4 × 10–4 + 32 × 10–6 DT

We know : dS = 4dB 5 × 10–5 + 4 × 10–6 DT = 16 × 10–4 + 128 × 10–6 DT – 124 × 10–6 DT = 155 × 10–5

115 X 10 5 50 = = – 12.5ºC. 4 124 X 10 6 The given circular loop is made up of uniform resistance wire of 4W. If wire of resistance 1W is connected across PT and a constant potential difference is applied across PR. For what value of ‘q ’ the points Q and T will be equipotential. Q DT =

2.

Sol.

Simplified circuit:- Resistance of RT =

2    Resistance of PST =  2    

4 2r

rq = 1

1

P

R 1 2/

2 6 4   2   

2   2     

4q2 – 8pq + 2p2 = 0 q=

4  16 2  8 2 4


R

= ?

T

2   2  1 2     For Q & T to be equipotential : 2  2 1 

S

S

2

2

P

2 

T

2q2 – 4pq + p2 = 0 =

4  2 2  4

=

  (2  2 ) 2

= 

 2

34

EUREKA! Chemistry R E S O Q . 1 0 Chemistry : Q. 1 An organic compound C5H8O2 gives effervescence of CO2 with sodium bicarbonate. Two forms are possible for (A) neither of which is optically active. (A) on catalytic reduction gives (B) C5H10O2 which can be separated into enantiomorphs.

Solution by : Girijesh Dubey Faculty - Chemistry

Ans.

Q. 2

An aliphatic monoamine (vapour density of 36) on treating with excess of CH3I for a long time, a quaternary salt containing 55.5% of iodine is produced. Write the possible structure of amine.

Ans.

(i) CH3 – NH – CH2 – CH2 – CH3

WINNER Vaibhav Gupta Roll No. - 709076 Batch - PB1

(ii) CH3 – CH2 – NH – CH2 – CH3

(iii)

WINNER Saurabh Agarwal Roll No. - 503364 Batch -G1

Maths R E S O Q . 1 0 Maths: 1.

Solution by Safdar Seraj Faculty - Maths

If (a, b) is the centroid of a triangle P Q R where P, 2. Let ABC be a triangle and P an interior point of D ABC. Show Q and R three points lying on the parabola (y - 4)2 that at least one of the angles Ð PBA, Ð PBC and Ð PCA is less = 15 (x+3) and normals at, P and Q meet at R. Find than or equal to 30°. the largest value of m satisfying a + b > m for all Sol (2). Assume that 30º < a1, b1, g1 < 150º possible value of a and b. Hence, if the feet of the ^ s from P to AB, BC, CA and C', A', B' respectively, then

Sin α1 

Sol (1). Let y – 4 = Y & x + 3 = X Y2 = 15x

Again a let

t1 t2 = 2 & t1 + t2 + t3 = 0 2 1

2 2 2 3

(t  t t )   3 3 5 2 2 (2t1  2t 2  2t1t 2 ) 4

 15 15  P   t12 , t1  2  4  15 15     t 22 , t 2  2  4  15 15  R   t 32 , t 3  2  4

Similarly, 2PA' > PB, 2PB' > PC Thus PA' + PB' + PC' >

a + b > 16

\ Largest value of m = 16. Anunaad, April - June 2008

PA  PB  PC 2

..........(I)

PA  PB  PC but PA'  PB'  PC'  2 \ from (i) & (ii) our assumption is wrong \at least one of a1, b1 & g1 is less than 30.

5 2 4 (t1  2  2)  15 (t1  t 2 ) 4 t1  12 15 (t1  t 2  t3 )  4 0 2 3 b=4

PC ' 1  sin30  i.e., 2PC '  PA PA 2

.........(ii)

C P

A

B

WINNER WINNER Navin Kumar Phool Chand Yadav Roll No. - 700603 Roll No. - 713194 Batch - PA1 Batch - PB1

35

Sim Sim

Khul Ja CHEMISTRY CATALYST: (C)

II.

cyclohexanone will be obtained on heating cyclic b-keto acid

Ans.

I.

(D)

Ans :

Formation of glycollic acid from F on treating with alkali indicates that F is glyoxal

which is hydrolysis product of cyclic

CH = O CH = O

CH = O

CH2O

CH2OH

H – C – O–

C=O

C–O

O–H

O Glycollate ion

–

OH

O–H

O

b-keto-ester (B)

COO C2H5

–

Since Intramolecular claisen ester condensation of (A) gives B and COOC2H5 (ethyl ester of adipic COOC2H5

C2H5OH structure of (A) is (CH2) 4 Formation of ethane on electrolysis of sodium alkanoate tells that (H) is sodium acetate because on electrolysis we get alkane corresponding to dimer of alkyl part of acid salt as Cathode –

2R COONa

 +2e 2Na

acid)

The reactions of given question is as follows O

2Na

C – OC2H5

Anode 

–

2RCOO

(I) –2e 2Rº (II) –2CO2

Rº + ºR R – R

 CO 2

(A)

C – OC2H5



O

COOH

O

H2O/H

O

LiAlH4

O

H2SO4/

OH

and then C will be

(D)

CH = O CH2

. Structure of E tells that

CH = O +

alcKOH

Ozonolysis

CH = O (F)

(E) –

[O]  CH3COOH CH2 (H) –CO2 NaOH CH COONa electrolysis 3

Anunaad, April - June 2008

OC2H5 O–H

NBS

(C)

(G)

D is

–C2H5OH

(B)

–CO2 

CH = O

O

C – OC2H5

COOC2H5 +

CH = O

On basis of G & F, E will be

BH

O

Br

G = CH2

&

O–

O

COOH Thus G = CH2

OC2H5

–BH

COOH

CH = O 1

C – OC2H5

–

B(C2H5ONa)



G   G'  CH3 COOH

O



C – OC2H5

Since R—R is ethane hence H is CH3COOH Acetic acid is obtained from (G) which is one of the ozonolysis product of E as [O]

O C – OC2H5

COOH

OH intramolecular cannizzarorean –

COO COOH

CH2OH Glycollate ion CH– 3 CH3

36

Khul Ja Sim Sim (D)

2.

PHYSICS FORCE :

Ans.

1.

(D)

Ans :

C5H10O2 follows general formula CnH2nO2 which may

be carboxylic acid or ester. According to question (A) is not carboxylic acid because it gives CH4 with CH3 – MgI. Thus (A) is ester. Since we get B & C (which undergo iodoform reaction) on treating (A) with excess of CH3 MgI hence (B)

Sol. 1 a + 2b = 180° -------(1) & b + 90 -2a + 90 = 180 b = 2a -------(2) Hence

5 a = 180° a = 36°

will be 2º alcohol as it is known that alkyl format with grignard reagent given 2º alcohol.

o=

CH-MgI 3

( )

( )

H3 O

OH Br I CH-CH - CH+ 3 R OH + Mg 3 ( ) ( ) OH

According to given question molecular formula for RI can be determined as :O

H – C – OR' = C5 H10 O 2

Sol. 2

v u v = mu u+v=a then u  a , v  ma 1 m 1 m uv ma f  u  v (1  m) 2 m

Sol. 3 For achromatic combination then f   2 f 1

R'  C 5H10 O 2 – CHO 2  C 4H9 Thus RI OH (C) is C4H9OH. As (C) gives (+) ve iodoform test hence it must contain CH3– CH -group hence (C) will be.

But

w w1 w  1  0 But 1  2 f f w

1 1 1   1 f f f

1 1 1 1 1   1 Þ  1 10  2 f 1 f 2f 10

OH CH3– CH – R . According to molecular formula of C,

f1 = 5cm f = -10 cm

OH R = – CH2 – CH3

Sol. 4

A x B  iˆ ˆj kˆ  8iˆ  8 ˆj  8k 3 1 2 2 2 4 The magnitude =

MATH EXPONENT : 1. 6.

C A

2. 7.

B A

3. 8.

B A

4. 9.

A A

5. 10.

A C

The unit vector perpendicular to

A and B

AxB

1 ˆ ˆ ˆ   (i  j  k ) 3 AxB Angle between


82  (8) 2  (8) 2  8 3

    |A x B | 8 3 2 A & B, sinθ      | A | | B| 14 x 24 7  | A |  9  1  4  14  | B |  4  4  16  24

37

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