ENTHUSIAST, LEADER & ACHIEVER COURSE TARGET : PRE-MEDICAL 2016 Test Type : MAJOR Test Pattern : AIPMT

Size: px
Start display at page:

Download "ENTHUSIAST, LEADER & ACHIEVER COURSE TARGET : PRE-MEDICAL 2016 Test Type : MAJOR Test Pattern : AIPMT"

Transcription

1 LSSROO ONTT PROGRE (cdmic Sssion : 0-06) ENTHUSIST, LEDER & HIEER OURSE TRGET : PRE-EDIL 06 Tst Typ : JOR Tst Pttrn : IPT. omponnt of x on y xcos x y ( b) ( b) y b b b. J E I. x.0 cos(t + ).0 cost locity dx 0sin t dt d x cclrtion dt t t. sc, TEST DTE : TEST SYLLUS : FULL SYLLUS 0 cos t NSWER EY Qu ns Qu ns Qu ns Qu ns Qu ns Qu ns Qu ns Qu ns Qu ns HINT SHEET x.0 cos.0 ( ) locity dx 0 (zro) 0 dt cclrtion d x dt 0 ( ) 0 6. ccording to work nrgy thorm W mg + W F g(h + S) FS 0 [ i f 0] FS g(h + S) h F g+ S HS - /6

2 7. xi ˆ xj ˆ xi ˆ xj ˆ... () xj ˆ...() ultiply q. () by () nd subtrct q. () from it ( ) xi ˆ xj ˆ xi ˆ xj ˆ dir n. 8. u 0 x E tn S E tn S x f u 0 P D 0. No conduction is found btwn P & Q so both P & Q will b n-typ or p-typ. Thrfor R will b bs.. ftr 0 s dm F dt ftr 0 s. jor Tst For Trgt : Pr-dicl 06/ x x 4. T / 0.7 R. R T/ R k 00 4L L 00 L 00 L 7. F g p (u ) t t m/s 8.. R R R R 0 R 00 0 R 00 0 R 0 0 R R 0 R r, R r R r 9. R F 0. nt F 0 S s F F 0 F rmining rmining F [T, T 0, r, r sm] HS - /6

3 . T P blow (g + ) ( + )(0 + 0) 60N gsin. r r For shll r r g sin () but S g sin () diiding th two qutions r S. For isothrml procss P olum xpnds to doubl so prssur will b hld for dibtic procss P r const P P P / 6 P P P I R + E R R 8 k 7. Thrml Tnsion F Y 8.. r.40 olt P ir...(i) but i. 80 r...(ii) Pr-dicl : ENTHUSIST, LEDER & HIEER/ rms 0. On soling w gt r 0 W W W W W 6(H 4 ) dq T dt dq r dt ( r ).. Totl distnc cord by two whls is sm r n r n or n n 000 rpm 4. Phs diff Z 00 X sin Z X sin I lds E so rctnc is cpciti.. olum rmins sm L '(L) 6. ' ; R i (L) R f / %chng 60 b L 4R i Ri Ri 00 Ri 7. Sinc P' n P n P' 7P c 00% b HS - /6

4 8. pply nrgy consrtion Enrgy t surfc Enrgy t hight 9. HS - 4/6 G m G m m R (R h) but Hnc G R Gm Gm Gm R 4 R R h Hnc R + h n n h c c 4 R R n 700 n' 708 Hz 40. nr + potntil nr potntil (+) ( ) lso potntil t both & + r + domints So > uy u xuy g g g u x & u y tn f f o x uy u tn f o f f o + f 4 6f 4 f 4 nd f o 0 jor Tst For Trgt : Pr-dicl 06/ sol. P const. P T constnt T. di L dt 6 0 (,0) D D 7 0 Y (0,) (0, ) (,0) 4 in dirction of lctric fild potntil will b dcrsd So > D > 48. mino pyridin is not prsnt in nuclic cid 49. NERT (XII th ) Prt-II, Pg. # E 00 cc cc. NERT (XII th ) Prt-II, Pg. # H NO r Fr. H PO 4 n NOH n H H r Sn/Hl NO NH X r NNO Hl H r r NERT (XII th ) Prt-II, Pg. # 449 Hr ur H r N l

5 Pr-dicl : ENTHUSIST, LEDER & HIEER/ H z n.8 06 m/s m/s x m h 4 x ^ ^ x m ^ ^ ^ Ph N / liq.nh Ph Ph H H Ph (irch Rduction) 64. O HO O H H4 HO OH 4 O H H4 HO / 6. hcp nd ccp both h sm.n hlorobnzn on hydrolysis gis phnol. 69. h w 0 4 w 7 h H E f E b O E f E b E f E b O 7. N H H N,N Dimthyl yclopropn rboxmid 7. Rctiity of hlid stbility of crboction 74. FH OOH + OH FH OO + H O 0m mol m mol 0 0 m mol 0m mol m mol Slt For cidic buffr ph P + log cid P log 7. ST tm. 8.6 mm 78. NERT (XII th ) Prt-II, Pg. # grphit + O (g) O (g) It rprsnt nthlpy of combustion of grphit s wll s nthlpy of formtion of O (g) 8. (I) (II) -H 0 -H 0 + Hydrogn 8. NERT (XII th ) Prt-II, Pg. # In HIO 4 nd H O cntrl tom prsnt in highst oxidtion stt so ct s oxidnt only. 87. Q nd R shows romtic chrctr du to Huckl rul. 88. NERT (XII th ) Prt-II, Pg. # NERT XI Pg. # 97. NERT XI Pg. # odul () Pg. #,,4 00. NERT XI Pg. # NERT XII Pg. # 04. NERT XI Pg. # NERT XII Pg. # NERT XI Pg. # odul () Pg. # 7 0. NERT XII Pg. # 47 HS - /6

6 . NERT XII Pg. # NERT XI Pg. # 79. NERT XI Pg. # 9 6. NERT XI Pg. # NERT XI Pg. # NERT XII Pg. # 6 0. NERT XII Pg. #, pr NERT XI Pg. # 7. NERT XI Pg. # 04 pr 4 9. NERT XII Pg. # 4 0. NERT XII Pg. # 4, pr NERT XI Pg. # 97 & 98. NERT XI Pg. # NERT XII Pg. # NERT XII Pg. # 7 4. NERT XII Pg. # NERT XI Pg. # NERT XI Pg. # 4 jor Tst For Trgt : Pr-dicl 06/ NERT XI Pg. # 4 0. NERT XII Pg. # 0,. NERT XII Pg. # NERT XII Pg. # 7, pr NERT XII (E) Pg. # 68 pr 9.. NERT XII (H) Pg. # 8 pr NERT XII Pg. # 6. NERT XII Pg. # NERT XI Pg. # 0 6. NERT XI Pg. # 66. NERT XI Pg. # 68, pr- 67. NERT XI Pg. #,, 0, NERT XII Pg. # 60, 6 7. NERT XII Pg. # 9 7. NERT XII Pg. # NERT XI Pg. # 7. NERT XI Pg. # 77. NERT XI Pg. # 6, 7 HS - 6/6

INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x)

INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x) Chptr 7 INTEGRALS 7. Ovrviw 7.. Lt d d F () f (). Thn, w writ f ( ) d F () + C. Ths intgrls r clld indfinit intgrls or gnrl intgrls, C is clld constnt of intgrtion. All ths intgrls diffr y constnt. 7..

More information

UNIT # 08 (PART - I)

UNIT # 08 (PART - I) . r. d[h d[h.5 7.5 mol L S d[o d[so UNIT # 8 (PRT - I CHEMICL INETICS EXERCISE # 6. d[ x [ x [ x. r [X[C ' [X [[B r '[ [B [C. r [NO [Cl. d[so d[h.5 5 mol L S d[nh d[nh. 5. 6. r [ [B r [x [y r' [x [y r'

More information

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph?

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph? 95. Which of the following descries the net ionic rection for the hydrolysis of NH4Cl( s)? A. NH4 ( q) Cl & ( q) NH4Cl( s) B. NH Cl & 4 ( s) NH4 ( q) Cl ( q) C. Cl ( q) H O & 2 ( l) HCl( q) OH ( q) D.

More information

22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 8: Effect of a Vertical Field on Tokamak Equilibrium

22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 8: Effect of a Vertical Field on Tokamak Equilibrium .65, MHD Thory of usion Systms Prof. ridrg Lctur 8: Effct of Vrticl ild on Tokmk Equilirium Toroidl orc lnc y Mns of Vrticl ild. Lt us riw why th rticl fild is imortnt. 3. or ry short tims, th cuum chmr

More information

NARAYANA I I T / P M T A C A D E M Y. C o m m o n P r a c t i c e T e s t 05 XII-IC SPARK Date:

NARAYANA I I T / P M T A C A D E M Y. C o m m o n P r a c t i c e T e s t 05 XII-IC SPARK Date: 1. (A). (C). (B). (B) 5. (A) 6. (B) 7. (B) 8. (A) 9. (A) 1. (D) 11. (C) 1. (B) 1. (A) 1. (D) 15. (B) NARAYANA I I T / P M T A C A D E M Y C o m m o n P r a c t i c e T e s t 5 XII-IC SPARK Date: 9.1.17

More information

TOPIC 5: INTEGRATION

TOPIC 5: INTEGRATION TOPIC 5: INTEGRATION. Th indfinit intgrl In mny rspcts, th oprtion of intgrtion tht w r studying hr is th invrs oprtion of drivtion. Dfinition.. Th function F is n ntidrivtiv (or primitiv) of th function

More information

LEADER TEST SERIES / JOINT PACKAGE COURSE TARGET : PRE-MEDICAL 2017

LEADER TEST SERIES / JOINT PACKAGE COURSE TARGET : PRE-MEDICAL 2017 Tst Typ : MJR émù é. n n L ù ét ù ê m ú ê ú ê ú ë û ëlû ëtû DISTC LRIG PRGRMM (cadmic Sssion : 6 7) LDR TST SRIS / JIT PCKG CURS TRGT : PRMDICL 7 TST DT : 9 4 7 SWR KY HIT SHT Tst Pattrn : IIMS Qu. 4 5

More information

Lecture 11 Waves in Periodic Potentials Today: Questions you should be able to address after today s lecture:

Lecture 11 Waves in Periodic Potentials Today: Questions you should be able to address after today s lecture: Lctur 11 Wvs in Priodic Potntils Tody: 1. Invrs lttic dfinition in 1D.. rphicl rprsnttion of priodic nd -priodic functions using th -xis nd invrs lttic vctors. 3. Sris solutions to th priodic potntil Hmiltonin

More information

Cu 3 (PO 4 ) 2 (s) 3 Cu 2+ (aq) + 2 PO 4 3- (aq) circle answer: pure water or Na 3 PO 4 solution This is the common-ion effect.

Cu 3 (PO 4 ) 2 (s) 3 Cu 2+ (aq) + 2 PO 4 3- (aq) circle answer: pure water or Na 3 PO 4 solution This is the common-ion effect. CHEM 1122011 NAME: ANSWER KEY Vining, Exm # SHORT ANSWER QUESTIONS ============= 4 points ech ============ All work must be shown. 1. Wht re [H O ] nd [OH ] for solution tht hs ph of 9.0? Choose one. ()

More information

, between the vertical lines x a and x b. Given a demand curve, having price as a function of quantity, p f (x) at height k is the curve f ( x,

, between the vertical lines x a and x b. Given a demand curve, having price as a function of quantity, p f (x) at height k is the curve f ( x, Clculus for Businss nd Socil Scincs - Prof D Yun Finl Em Rviw vrsion 5/9/7 Chck wbsit for ny postd typos nd updts Pls rport ny typos This rviw sht contins summris of nw topics only (This rviw sht dos hv

More information

1. What colour would 1.0 M HCl be in an indicator mixture consisting of phenol red and

1. What colour would 1.0 M HCl be in an indicator mixture consisting of phenol red and cids Practice Test 2 1. What colour would 1.0 M Hl be in an indicator mixture consisting of phenol red and thymolphthalein? red blue yellow colourless 2. uring a titration, what volume of 0.500 M KOH is

More information

Chapter 16. 1) is a particular point on the graph of the function. 1. y, where x y 1

Chapter 16. 1) is a particular point on the graph of the function. 1. y, where x y 1 Prctic qustions W now tht th prmtr p is dirctl rltd to th mplitud; thrfor, w cn find tht p. cos d [ sin ] sin sin Not: Evn though ou might not now how to find th prmtr in prt, it is lws dvisl to procd

More information

FIITJEE JEE(Main)

FIITJEE JEE(Main) AITS-FT-II-PCM-Sol.-JEE(Main)/7 In JEE Advanced 06, FIITJEE Students bag 6 in Top 00 AIR, 75 in Top 00 AIR, 8 in Top 500 AIR. 54 Students from Long Term Classroom/ Integrated School Program & 44 Students

More information

Ch 1.2: Solutions of Some Differential Equations

Ch 1.2: Solutions of Some Differential Equations Ch 1.2: Solutions of Som Diffrntil Equtions Rcll th fr fll nd owl/mic diffrntil qutions: v 9.8.2v, p.5 p 45 Ths qutions hv th gnrl form y' = y - b W cn us mthods of clculus to solv diffrntil qutions of

More information

DISTANCE LEARNING PROGRAMME

DISTANCE LEARNING PROGRAMME DISTANCE EARNING PROGRAMME (Academic Session : - 7) EADER TEST SERIES / JOINT PACKAGE COURSE TARGET : PRE-MEDICA 7 Test Type : A INDIA OPEN TEST (MAJOR) Test Pattern : NEET-UG TEST DATE : - 4-7 ANSWER

More information

ME 522 PRINCIPLES OF ROBOTICS. FIRST MIDTERM EXAMINATION April 19, M. Kemal Özgören

ME 522 PRINCIPLES OF ROBOTICS. FIRST MIDTERM EXAMINATION April 19, M. Kemal Özgören ME 522 PINCIPLES OF OBOTICS FIST MIDTEM EXAMINATION April 9, 202 Nm Lst Nm M. Kml Özgörn 2 4 60 40 40 0 80 250 USEFUL FOMULAS cos( ) cos cos sin sin sin( ) sin cos cos sin sin y/ r, cos x/ r, r 0 tn 2(

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

More information

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9 Lctur contnts Bloch thorm -vctor Brillouin zon Almost fr-lctron modl Bnds ffctiv mss Hols Trnsltionl symmtry: Bloch thorm On-lctron Schrödingr qution ch stt cn ccommo up to lctrons: If Vr is priodic function:

More information

Narayana IIT Academy

Narayana IIT Academy INDIA Sec: Sr. IIT_IZ Jee-Advnced Dte: --7 Time: 09:00 AM to :00 Noon 0_P Model M.Mrks: 0 KEY SHEET CHEMISTRY C D 3 D B 5 A 6 D 7 B 8 AC 9 BC 0 ABD ABD A 3 C D 5 B 6 B 7 9 8 9 0 7 8 3 3 6 PHYSICS B 5 D

More information

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS SEMESTER TWO 2014 WEEK 11 WRITTEN EXAMINATION 1 SOLUTIONS

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS SEMESTER TWO 2014 WEEK 11 WRITTEN EXAMINATION 1 SOLUTIONS MASTER CLASS PROGRAM UNIT SPECIALIST MATHEMATICS SEMESTER TWO WEEK WRITTEN EXAMINATION SOLUTIONS FOR ERRORS AND UPDATES, PLEASE VISIT WWW.TSFX.COM.AU/MC-UPDATES QUESTION () Lt p ( z) z z z If z i z ( is

More information

I. The Connection between Spectroscopy and Quantum Mechanics

I. The Connection between Spectroscopy and Quantum Mechanics I. Th Connction twn Spctroscopy nd Quntum Mchnics On of th postults of quntum mchnics: Th stt of systm is fully dscrid y its wvfunction, Ψ( r1, r,..., t) whr r 1, r, tc. r th coordints of th constitunt

More information

SOLUTIONS TO CONCEPTS CHAPTER

SOLUTIONS TO CONCEPTS CHAPTER 1. m = kg S = 10m Let, ccelertion =, Initil velocity u = 0. S= ut + 1/ t 10 = ½ ( ) 10 = = 5 m/s orce: = = 5 = 10N (ns) SOLUIONS O CONCEPS CHPE 5 40000. u = 40 km/hr = = 11.11 m/s. 3600 m = 000 kg ; v

More information

Heat/Di usion Equation. 2 = 0 k constant w(x; 0) = '(x) initial condition. ( w2 2 ) t (kww x ) x + k(w x ) 2 dx. (w x ) 2 dx 0.

Heat/Di usion Equation.  2 = 0 k constant w(x; 0) = '(x) initial condition. ( w2 2 ) t (kww x ) x + k(w x ) 2 dx. (w x ) 2 dx 0. Hat/Di usion Equation @w @t k @ w @x k constant w(x; ) '(x) initial condition w(; t) w(l; t) boundary conditions Enrgy stimat: So w(w t kw xx ) ( w ) t (kww x ) x + k(w x ) or and thrfor E(t) R l Z l Z

More information

PHYSICS. (c) m D D m. v vt. (c) 3. Width of the river = d = 800 m m/s. 600m. B 800m v m,r. (b) 1000m. v w

PHYSICS. (c) m D D m. v vt. (c) 3. Width of the river = d = 800 m m/s. 600m. B 800m v m,r. (b) 1000m. v w PHYSICS T. T 8 k/hr = /s, ' Hz, ' 7 Hz T. r D D D,. r D D. D. D.... g/c. Width o the rier = d = 8 w /s B 8,r P O. sin t cos., on the copring this eqution, with sin t cos k =, k =. k. /s w Q. =, 9 9 = 8,

More information

ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o:

ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o: R TE EVTE (dhd H Hdg) L / Mld Kbrd gú s v l m sl c m qu gs v nns V n P P rs l mul m d lud 7 súb Fí cón ví f f dó, cru gs,, j l f c r s m l qum t pr qud ct, us: ns,,,, cs, cut r l sns m / m fí hó sn sí

More information

ALL INDIA TEST SERIES

ALL INDIA TEST SERIES AITS-FT-IV-(Pper-)-PCM(S)-JEE(Advnced)/4 From Clssroom/Integrted School Progrms 7 in Top 0, 3 in Top 00, 54 in Top 300, 06 in Top 500 All Indi Rnks & 34 Students from Clssroom /Integrted School Progrms

More information

Erlkönig. t t.! t t. t t t tj "tt. tj t tj ttt!t t. e t Jt e t t t e t Jt

Erlkönig. t t.! t t. t t t tj tt. tj t tj ttt!t t. e t Jt e t t t e t Jt Gsng Po 1 Agio " " lkö (Compl by Rhol Bckr, s Moifi by Mrk S. Zimmr)!! J "! J # " c c " Luwig vn Bhovn WoO 131 (177) I Wr Who!! " J J! 5 ri ris hro' h spä h, I urch J J Nch rk un W Es n wil A J J is f

More information

Calculus II (MAC )

Calculus II (MAC ) Calculus II (MAC232-2) Tst 2 (25/6/25) Nam (PRINT): Plas show your work. An answr with no work rcivs no crdit. You may us th back of a pag if you nd mor spac for a problm. You may not us any calculators.

More information

Q.28 Q.29 Q.30. Q.31 Evaluate: ( log x ) Q.32 Evaluate: ( ) Q.33. Q.34 Evaluate: Q.35 Q.36 Q.37 Q.38 Q.39 Q.40 Q.41 Q.42. Q.43 Evaluate : ( x 2) Q.

Q.28 Q.29 Q.30. Q.31 Evaluate: ( log x ) Q.32 Evaluate: ( ) Q.33. Q.34 Evaluate: Q.35 Q.36 Q.37 Q.38 Q.39 Q.40 Q.41 Q.42. Q.43 Evaluate : ( x 2) Q. LASS XII Q Evlut : Q sc Evlut c Q Evlut: ( ) Q Evlut: Q5 α Evlut: α Q Evlut: Q7 Evlut: { t (t sc )} / Q8 Evlut : ( )( ) Q9 Evlut: Q0 Evlut: Q Evlut : ( ) ( ) Q Evlut : / ( ) Q Evlut: / ( ) Q Evlut : )

More information

MATHEMATICS (Part II) (Fresh / New Course)

MATHEMATICS (Part II) (Fresh / New Course) Sig. of Supdt... MRD-XII-(A) MATHEMATICS Roll No... Time Allowed : Hrs. MATHEMATICS Totl Mrks: 00 NOTE : There re THREE sections in this pper i.e. Section A, B nd C. Time : 0 Mins. Section A Mrks: 0 NOTE

More information

Charging of capacitor through inductor and resistor

Charging of capacitor through inductor and resistor cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.

More information

Math Calculus with Analytic Geometry II

Math Calculus with Analytic Geometry II orem of definite Mth 5.0 with Anlytic Geometry II Jnury 4, 0 orem of definite If < b then b f (x) dx = ( under f bove x-xis) ( bove f under x-xis) Exmple 8 0 3 9 x dx = π 3 4 = 9π 4 orem of definite Problem

More information

Differential Equations

Differential Equations UNIT I Diffrntial Equations.0 INTRODUCTION W li in a world of intrrlatd changing ntitis. Th locit of a falling bod changs with distanc, th position of th arth changs with tim, th ara of a circl changs

More information

LEADER & ACHIEVER COURSE PHASE : MLA,MLB,MLC, MLD, MLE,MLF, MLG, MLH, MLI, MLJ, MAZA,MAZB & MAZC TARGET : PRE-MEDICAL 2016

LEADER & ACHIEVER COURSE PHASE : MLA,MLB,MLC, MLD, MLE,MLF, MLG, MLH, MLI, MLJ, MAZA,MAZB & MAZC TARGET : PRE-MEDICAL 2016 CLSSM CNTCT PGMME (cdemic Sessio : 5-6) LEDE & CHIEVE CUSE PHSE : ML,ML,MLC, MLD, MLE,MLF, MLG, MLH, MLI, MLJ, MZ,MZ & MZC Test Type : MJ TGET : PE-MEDICL 6 Test Ptter : IPMT TEST DTE : - 4-6 TEST SYLLUS

More information

Strong acids and bases. Strong acids and bases. Systematic Treatment of Equilibrium & Monoprotic Acid-base Equilibrium.

Strong acids and bases. Strong acids and bases. Systematic Treatment of Equilibrium & Monoprotic Acid-base Equilibrium. Strong cids nd bses Systemtic Tretment of Equilibrium & Monoprotic cid-bse Equilibrium onc. (M) 0.0.00 -.00-5.00-8 p Strong cids nd bses onc. (M) p 0.0.0.00 -.0.00-5 5.0.00-8 8.0? We hve to consider utoprotolysis

More information

Section 3: Antiderivatives of Formulas

Section 3: Antiderivatives of Formulas Chptr Th Intgrl Appli Clculus 96 Sction : Antirivtivs of Formuls Now w cn put th is of rs n ntirivtivs togthr to gt wy of vluting finit intgrls tht is ct n oftn sy. To vlut finit intgrl f(t) t, w cn fin

More information

df dx There is an infinite number of different paths from

df dx There is an infinite number of different paths from Integrl clculus line integrls Feb 7, 18 From clculus, in the cse of single vrible x1 F F x F x f x dx, where f x 1 x df dx Now, consider the cse tht two vribles re t ply. Suppose,, df M x y dx N x y dy

More information

CLASSROOM CONTACT PROGRAMME

CLASSROOM CONTACT PROGRAMME CLASSROOM CONTACT PROGRAMME (Academic Session : 05-06) ENTHUSIAST,LEADER & ACHIEVER COURSE PHASE : ENTHUSIAST, MLM, MLN, MLP, MLQ, MAZE, MAZF, MAZG, MAZH & MAZI TARGET : PRE-MEDICAL 06 Test Type : MAJOR

More information

1 ST ROUND, SOLUTIONS

1 ST ROUND, SOLUTIONS ST ROUND, SOLUTIONS Problem (Lithuni) Self destructing pper ( points) Solution ( ) ( ) ( ) [Al HO OH ) ph pk lg [Al H O ( ) ( ) [Al H O OH [Al ( ).9 [Al H O.9.47 [Al ( ) ( ) ( ) [Al H O OH.9 pk ph lg.

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

Solution: APPM 1360 Final (150 pts) Spring (60 pts total) The following parts are not related, justify your answers:

Solution: APPM 1360 Final (150 pts) Spring (60 pts total) The following parts are not related, justify your answers: APPM 6 Final 5 pts) Spring 4. 6 pts total) Th following parts ar not rlatd, justify your answrs: a) Considr th curv rprsntd by th paramtric quations, t and y t + for t. i) 6 pts) Writ down th corrsponding

More information

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016 Wintr 2016 COMP-250: Introduction to Computr Scinc Lctur 23, April 5, 2016 Commnt out input siz 2) Writ ny lgorithm tht runs in tim Θ(n 2 log 2 n) in wors cs. Explin why this is its running tim. I don

More information

Elliptical motion, gravity, etc

Elliptical motion, gravity, etc FW Physics 130 G:\130 lctur\ch 13 Elliticl motion.docx g 1 of 7 11/3/010; 6:40 PM; Lst rintd 11/3/010 6:40:00 PM Fig. 1 Elliticl motion, grvity, tc minor xis mjor xis F 1 =A F =B C - D, mjor nd minor xs

More information

HINTS & SOLUTIONS. Admission cum Scholarship Test for SUPER-50. Standard: 10 th (Stage I) Code: EG

HINTS & SOLUTIONS. Admission cum Scholarship Test for SUPER-50. Standard: 10 th (Stage I) Code: EG Delhi/ Ghzibd /Mumbi/ Pune / Go/ Akol/ Nshik/ Kolktt / Lucknow / Bokro/ Dubi Admission cum Scholrship Test for SUPER-50 Stndrd: 10 th (Stge I) Code: EG HINTS & SOLUTIONS H.O: nd Floor, C-8 & 9, Rj Ngr

More information

Hydronium or hydroxide ions can also be produced by a reaction of certain substances with water:

Hydronium or hydroxide ions can also be produced by a reaction of certain substances with water: Chpter 14 1 ACIDS/BASES Acids hve tste, rect with most metls to produce, rect with most crbontes to produce, turn litmus nd phenolphthlein. Bses hve tste rect very well well with most metls or crbontes,

More information

Single Correct Type. cos z + k, then the value of k equals. dx = 2 dz. (a) 1 (b) 0 (c)1 (d) 2 (code-v2t3paq10) l (c) ( l ) x.

Single Correct Type. cos z + k, then the value of k equals. dx = 2 dz. (a) 1 (b) 0 (c)1 (d) 2 (code-v2t3paq10) l (c) ( l ) x. IIT JEE/AIEEE MATHS y SUHAAG SIR Bhopl, Ph. (755)3 www.kolsss.om Qusion. & Soluion. In. Cl. Pg: of 6 TOPIC = INTEGRAL CALCULUS Singl Corr Typ 3 3 3 Qu.. L f () = sin + sin + + sin + hn h primiiv of f()

More information

Fundamentals of Continuum Mechanics. Seoul National University Graphics & Media Lab

Fundamentals of Continuum Mechanics. Seoul National University Graphics & Media Lab Fndmntls of Contnm Mchncs Sol Ntonl Unvrsty Grphcs & Md Lb Th Rodmp of Contnm Mchncs Strss Trnsformton Strn Trnsformton Strss Tnsor Strn T + T ++ T Strss-Strn Rltonshp Strn Enrgy FEM Formlton Lt s Stdy

More information

FULL MECHANICS SOLUTION

FULL MECHANICS SOLUTION FULL MECHANICS SOLUION. m 3 3 3 f For long the tngentil direction m 3g cos 3 sin 3 f N m 3g sin 3 cos3 from soling 3. ( N 4) ( N 8) N gsin 3. = ut + t = ut g sin cos t u t = gsin cos = 4 5 5 = s] 3 4 o

More information

CHEMISTRY 16 HOUR EXAM III March 26, 1998 Dr. Finklea - Answer key

CHEMISTRY 16 HOUR EXAM III March 26, 1998 Dr. Finklea - Answer key CHEMISTRY 16 HOUR EXAM III Mrch 26, 1998 Dr. Finkle - Answer key 1. Phenol, lso known s crbolic cid, is wek monoprotic cid (HA). A 1.0 M solution of phenol hs ph of 4.95. Wht is the K of phenol? 1. 2.0

More information

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued...

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued... Progrssiv Printing T.M. CPITLS g 4½+ Th sy, fun (n FR!) wy to tch cpitl lttrs. ook : C o - For Kinrgrtn or First Gr (not for pr-school). - Tchs tht cpitl lttrs mk th sm souns s th littl lttrs. - Tchs th

More information

TUESDAY JULY Concerning an Upcoming Change Order for the Clearwell Project. Pages 28 SALLISAW MUNICIPAL AUTHORITY SPECIAL MEETING

TUESDAY JULY Concerning an Upcoming Change Order for the Clearwell Project. Pages 28 SALLISAW MUNICIPAL AUTHORITY SPECIAL MEETING SSW MUCP UTHOT SPEC MEETG TUESD U 2 200 0 00M SSW WTE TETMET PT COEECE OOM EPPE OD GED Mg Cd T Od 2 Dc Quum 3 c B P m B P h H W Eg Ccg Upcmg Chg Od h C Pjc Cd d Cc d Ep Ph Pjc Pg 28 dju Pd u 22 200 Tm

More information

Narayana IIT Academy INDIA Sec: Sr. IIT_IZ Jee-Advanced Date: Time: 02:00 PM to 05:00 PM 2014_P2 MODEL Max.Marks:180 KEY SHEET

Narayana IIT Academy INDIA Sec: Sr. IIT_IZ Jee-Advanced Date: Time: 02:00 PM to 05:00 PM 2014_P2 MODEL Max.Marks:180 KEY SHEET INDIA Sec: Sr. IIT_IZ Jee-Advnced Dte: -9-8 Time: : PM to : PM 4_P MDEL M.Mrks:8 KEY SEET PYSICS A B C 4 A B 6 D 7 A 8 B 9 A D D C A 4 B D 6 B 7 A 8 D 9 A D CEMISTY B B C 4 D A 6 B 7 A 8 C 9 D C D D C

More information

Electrochemistry L E O

Electrochemistry L E O Rmmbr from CHM151 A rdox raction in on in which lctrons ar transfrrd lctrochmistry L O Rduction os lctrons xidation G R ain lctrons duction W can dtrmin which lmnt is oxidizd or rducd by assigning oxidation

More information

CLASS XII PHYSICS. (a) 30 cm, 60 cm (b) 20 cm, 30 cm (c) 15 cm, 20 cm (d) 12 cm, 15 cm. where

CLASS XII PHYSICS. (a) 30 cm, 60 cm (b) 20 cm, 30 cm (c) 15 cm, 20 cm (d) 12 cm, 15 cm. where PHYSICS combintion o two thin lenses with ocl lengths n respectively orms n imge o istnt object t istnce cm when lenses re in contct. The position o this imge shits by cm towrs the combintion when two

More information

MATHEMATICS PAPER IB COORDINATE GEOMETRY(2D &3D) AND CALCULUS. Note: This question paper consists of three sections A,B and C.

MATHEMATICS PAPER IB COORDINATE GEOMETRY(2D &3D) AND CALCULUS. Note: This question paper consists of three sections A,B and C. MATHEMATICS PAPER IB COORDINATE GEOMETRY(D &D) AND CALCULUS. TIME : hrs Ma. Marks.75 Not: This qustion papr consists of thr sctions A,B and C. SECTION A VERY SHORT ANSWER TYPE QUESTIONS. 0X =0.If th portion

More information

SAFE HANDS & IIT-ian's PACE EDT-15 (JEE) SOLUTIONS

SAFE HANDS & IIT-ian's PACE EDT-15 (JEE) SOLUTIONS It is not possibl to find flu through biggr loop dirctly So w will find cofficint of mutual inductanc btwn two loops and thn find th flu through biggr loop Also rmmbr M = M ( ) ( ) EDT- (JEE) SOLUTIONS

More information

The Fundamental Theorem of Calculus. The Total Change Theorem and the Area Under a Curve.

The Fundamental Theorem of Calculus. The Total Change Theorem and the Area Under a Curve. Clculus Li Vs The Fundmentl Theorem of Clculus. The Totl Chnge Theorem nd the Are Under Curve. Recll the following fct from Clculus course. If continuous function f(x) represents the rte of chnge of F

More information

Errata for Second Edition, First Printing

Errata for Second Edition, First Printing Errt for Scond Edition, First Printing pg 68, lin 1: z=.67 should b z=.44 pg 71: Eqution (.3) should rd B( R) = θ R 1 x= [1 G( x)] pg 1: Eqution (.63) should rd B( R) = x= R = θ ( x R) p( x) R 1 x= [1

More information

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator. Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r

More information

IV. CONDENSED MATTER PHYSICS

IV. CONDENSED MATTER PHYSICS IV. CONDENSED MATTER PHYSICS UNIT I CRYSTAL PHYSICS Lecture - II Dr. T. J. Shinde Deprtment of Physics Smt. K. R. P. Kny Mhvidyly, Islmpur Simple Crystl Structures Simple cubic (SC) Fce centered cubic

More information

MATH 253 WORKSHEET 24 MORE INTEGRATION IN POLAR COORDINATES. r dr = = 4 = Here we used: (1) The half-angle formula cos 2 θ = 1 2

MATH 253 WORKSHEET 24 MORE INTEGRATION IN POLAR COORDINATES. r dr = = 4 = Here we used: (1) The half-angle formula cos 2 θ = 1 2 MATH 53 WORKSHEET MORE INTEGRATION IN POLAR COORDINATES ) Find the volume of the solid lying bove the xy-plne, below the prboloid x + y nd inside the cylinder x ) + y. ) We found lst time the set of points

More information

Version 001 HW#6 - Circular & Rotational Motion arts (00223) 1

Version 001 HW#6 - Circular & Rotational Motion arts (00223) 1 Version 001 HW#6 - Circulr & ottionl Motion rts (00223) 1 This print-out should hve 14 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Circling

More information

(most) due to long range e m forces i.e. via atomic collisions or due to short range nuclear collisions or through decay ( = weak interactions)

(most) due to long range e m forces i.e. via atomic collisions or due to short range nuclear collisions or through decay ( = weak interactions) Spring 01, P67, YK Monday January 30, 01 8 Obsrvabl particl dtction ffcts ar : (most) du to long rang m forcs i.. via atomic collisions or du to short rang nuclar collisions or through dcay ( = wak intractions)

More information

Lecture 4. Conic section

Lecture 4. Conic section Lctur 4 Conic sction Conic sctions r locus of points whr distncs from fixd point nd fixd lin r in constnt rtio. Conic sctions in D r curvs which r locus of points whor position vctor r stisfis r r. whr

More information

CHEMISTRY. 31 (b) The term acid rain was coined by Robert Augus 32 (c)

CHEMISTRY. 31 (b) The term acid rain was coined by Robert Augus 32 (c) CHEMISTRY 31 (b) The term cid rin ws coined by Robert Augus 32 (c) Initil At (4-3 moles equilibrium mole mole Hence, mole Hence, number of moles of t equilibrium =2-1=1 mole Number of moles of t equilibrium

More information

SSC Mains Mock Test 227 [Answer with Solution]

SSC Mains Mock Test 227 [Answer with Solution] SS Mins Mock Test 7 [nswer with Solution]. (D) E ccording to question, G 00 00 8 0 G GF, F D Let, GF GF Now, eterior ngle FGE FGE FEG Now, eterior ngle D In DE, + + 80º 80º 7 5º (ppro.). () I st digit

More information

PHYSICS 211 MIDTERM I 21 April 2004

PHYSICS 211 MIDTERM I 21 April 2004 PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

Errata for Second Edition, First Printing

Errata for Second Edition, First Printing Errt for Scond Edition, First Printing pg 68, lin 1: z=.67 should b z=.44 pg 1: Eqution (.63) should rd B( R) = x= R = θ ( x R) p( x) R 1 x= [1 G( x)] = θp( R) + ( θ R)[1 G( R)] pg 15, problm 6: dmnd of

More information

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration

More information

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1 Mth 33 Volume Stewrt 5.2 Geometry of integrls. In this section, we will lern how to compute volumes using integrls defined by slice nlysis. First, we recll from Clculus I how to compute res. Given the

More information

[ ]:543.4(075.8) 35.20: ,..,..,.., : /... ;. 2-. ISBN , - [ ]:543.4(075.8) 35.20:34.

[ ]:543.4(075.8) 35.20: ,..,..,.., : /... ;. 2-. ISBN , - [ ]:543.4(075.8) 35.20:34. .. - 2-2009 [661.87.+661.88]:543.4(075.8) 35.20:34.2373-60..,..,..,..,.. -60 : /... ;. 2-. : -, 2008. 134. ISBN 5-98298-299-7 -., -,,. - «,, -, -», - 550800,, 240600 «-», -. [661.87.+661.88]:543.4(075.8)

More information

Verification Analysis of the Slope Stability

Verification Analysis of the Slope Stability Verifiction nul no. 3 Updte 04/016 Verifiction Anlysis of the Slope Stbility Progr: File: Slope Stbility Deo_v_en_03.gst In this verifiction nul you will find hnd-de verifiction nlysis of the stbility

More information

PHYSICS 116C Homework 4 Solutions

PHYSICS 116C Homework 4 Solutions PHYSICS 116C Homework 4 Solutions 1. ( Simple hrmonic oscilltor. Clerly the eqution is of the Sturm-Liouville (SL form with λ = n 2, A(x = 1, B(x =, w(x = 1. Legendre s eqution. Clerly the eqution is of

More information

The pn junction: 2 Current vs Voltage (IV) characteristics

The pn junction: 2 Current vs Voltage (IV) characteristics Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n

More information

PH427/PH527: Periodic systems Spring Overview of the PH427 website (syllabus, assignments etc.) 2. Coupled oscillations.

PH427/PH527: Periodic systems Spring Overview of the PH427 website (syllabus, assignments etc.) 2. Coupled oscillations. Dy : Mondy 5 inuts. Ovrviw of th PH47 wsit (syllus, ssignnts tc.). Coupld oscilltions W gin with sss coupld y Hook's Lw springs nd find th possil longitudinl) otion of such syst. W ll xtnd this to finit

More information

Limits Indeterminate Forms and L Hospital s Rule

Limits Indeterminate Forms and L Hospital s Rule Limits Indtrmint Forms nd L Hospitl s Rul I Indtrmint Form o th Tp W hv prviousl studid its with th indtrmint orm s shown in th ollowin mpls: Empl : Empl : tn [Not: W us th ivn it ] Empl : 8 h 8 [Not:

More information

AP PHYSICS C: ELECTRICITY AND MAGNETISM 2015 SCORING GUIDELINES

AP PHYSICS C: ELECTRICITY AND MAGNETISM 2015 SCORING GUIDELINES AP PHYSICS C: ELECTRICITY AND MAGNETISM 2015 SCORING GUIDELINES Qustion 1 15 points total Distribution of points (a) i. For at last on arrow btwn th plats pointing downward from th positiv plats toward

More information

ELECTROMAGNETIC INDUCTION CHAPTER - 38

ELECTROMAGNETIC INDUCTION CHAPTER - 38 . (a) CTOMAGNTIC INDUCTION CHAPT - 38 3 3.dl MT I M I T 3 (b) BI T MI T M I T (c) d / MI T M I T. at + bt + c s / t Volt (a) a t t Sc b t Volt c [] Wbr (b) d [a., b.4, c.6, t s] at + b. +.4. volt 3. (a)

More information

CONTINUITY AND DIFFERENTIABILITY

CONTINUITY AND DIFFERENTIABILITY MCD CONTINUITY AND DIFFERENTIABILITY NCERT Solvd mpls upto th sction 5 (Introduction) nd 5 (Continuity) : Empl : Chck th continuity of th function f givn by f() = + t = Empl : Emin whthr th function f

More information

Physics 241 Exam 1 February 19, 2004

Physics 241 Exam 1 February 19, 2004 Phsics 241 Em 1 Februr 19, 24 One (both sides) 8 1/2 11 crib sheet is llowed. It must be of our own cretion. k = 1 = 9 1 9 N m2 4p 2 2 = 8.85 1-12 N m 2 e =1.62 1-19 c = 2.99792458 1 8 m/s (speed of light)

More information

Mathematics Extension 2

Mathematics Extension 2 S Y D N E Y B O Y S H I G H S C H O O L M O O R E P A R K, S U R R Y H I L L S 005 HIGHER SCHOOL CERTIFICATE TRIAL PAPER Mthemtics Extension Generl Instructions Totl Mrks 0 Reding Time 5 Minutes Attempt

More information

Chemistry 2 Exam Roane State Academic Festival. Name (print neatly) School

Chemistry 2 Exam Roane State Academic Festival. Name (print neatly) School Name (print neatly) School There are fifteen question on this exam. Each question is weighted equally. n the answer sheet, write your name in the space provided and your answers in the blanks provided.

More information

AS 5850 Finite Element Analysis

AS 5850 Finite Element Analysis AS 5850 Finit Elmnt Analysis Two-Dimnsional Linar Elasticity Instructor Prof. IIT Madras Equations of Plan Elasticity - 1 displacmnt fild strain- displacmnt rlations (infinitsimal strain) in matrix form

More information

Lecture 6 Thermionic Engines

Lecture 6 Thermionic Engines Ltur 6 hrmioni ngins Rviw Rihrdson formul hrmioni ngins Shotty brrir nd diod pn juntion nd diod disussion.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion WARR M. ROHSOW HA AD MASS

More information

Math 307 Lecture 19. Laplace Transforms of Discontinuous Functions. W.R. Casper. Department of Mathematics University of Washington.

Math 307 Lecture 19. Laplace Transforms of Discontinuous Functions. W.R. Casper. Department of Mathematics University of Washington. Math 307 Lecture 19 Laplace Transforms of Discontinuous Functions W.R. Casper Department of Mathematics University of Washington November 26, 2014 Today! Last time: Step Functions This time: Laplace Transforms

More information

Mor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration

More information

Dr. Steward s CHM152 Exam #2 Review Spring 2014 (Ch ) KEY

Dr. Steward s CHM152 Exam #2 Review Spring 2014 (Ch ) KEY Dr. Stewrd s CHM152 Em #2 Review Spring 2014 (Ch. 16. 17) KEY 1. Eplin the commonion effect. Wek cid or wek bse s % dissocition will decrese if they re plced in solutions with one of the products of dissocition.

More information

x = b a n x 2 e x dx. cdx = c(b a), where c is any constant. a b

x = b a n x 2 e x dx. cdx = c(b a), where c is any constant. a b CHAPTER 5. INTEGRALS 61 where nd x = b n x i = 1 (x i 1 + x i ) = midpoint of [x i 1, x i ]. Problem 168 (Exercise 1, pge 377). Use the Midpoint Rule with the n = 4 to pproximte 5 1 x e x dx. Some quick

More information

Lecture Outline. Skin Depth Power Flow 8/7/2018. EE 4347 Applied Electromagnetics. Topic 3e

Lecture Outline. Skin Depth Power Flow 8/7/2018. EE 4347 Applied Electromagnetics. Topic 3e 8/7/018 Cours Instructor Dr. Raymond C. Rumpf Offic: A 337 Phon: (915) 747 6958 E Mail: rcrumpf@utp.du EE 4347 Applid Elctromagntics Topic 3 Skin Dpth & Powr Flow Skin Dpth Ths & Powr nots Flow may contain

More information

HOMEWORK SOLUTIONS MATH 1910 Sections 7.9, 8.1 Fall 2016

HOMEWORK SOLUTIONS MATH 1910 Sections 7.9, 8.1 Fall 2016 HOMEWORK SOLUTIONS MATH 9 Sections 7.9, 8. Fll 6 Problem 7.9.33 Show tht for ny constnts M,, nd, the function yt) = )) t ) M + tnh stisfies the logistic eqution: y SOLUTION. Let Then nd Finlly, y = y M

More information

This Week. Computer Graphics. Introduction. Introduction. Graphics Maths by Example. Graphics Maths by Example

This Week. Computer Graphics. Introduction. Introduction. Graphics Maths by Example. Graphics Maths by Example This Wk Computr Grphics Vctors nd Oprtions Vctor Arithmtic Gomtric Concpts Points, Lins nd Plns Eploiting Dot Products CSC 470 Computr Grphics 1 CSC 470 Computr Grphics 2 Introduction Introduction Wh do

More information

Math 34A. Final Review

Math 34A. Final Review Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right

More information

Total Score Maximum

Total Score Maximum Lst Nme: Mth 8: Honours Clculus II Dr. J. Bowmn 9: : April 5, 7 Finl Em First Nme: Student ID: Question 4 5 6 7 Totl Score Mimum 6 4 8 9 4 No clcultors or formul sheets. Check tht you hve 6 pges.. Find

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS

MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS VSRT MEMO #05 MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS 01886 Fbrury 3, 009 Tlphon: 781-981-507 Fx: 781-981-0590 To: VSRT Group From: Aln E.E. Rogrs Subjct: Simplifid

More information

Narayana IIT Academy

Narayana IIT Academy INDI Sec: LT-IIT-SPRK Jee-dvanced Date: -3-8 Time: 3. 4_P MODEL Ma.Marks:8 KEY SHEET RPT-4 PHYSICS,B,C,D,B,C,D 3 B,C 4,C,D 5,B,C 6,B,C,D 7,B,C,D 8,B,C,D 9,B,C,D,B,D 6 4 3 5 4 4 5 3 6 3 7 6 8 4 9 5 8 CHEMISTRY,C,D,C

More information

The two-body Kepler problem

The two-body Kepler problem The two-body Kepler problem set center of mass at the origin (X = 0) ignore all multipole moments (spherical bodies or point masses) define r := r 1 r 2,r:= r,m:= m 1 + m 2,µ:= m 1 m 2 /m reduces to effective

More information

Chem 104A, Fall 2016, Midterm 1 Key

Chem 104A, Fall 2016, Midterm 1 Key hm 104A, ll 2016, Mitrm 1 Ky 1) onstruct microstt tl for p 4 configurtion. Pls numrt th ms n ml for ch lctron in ch microstt in th tl. (Us th formt ml m s. Tht is spin -½ lctron in n s oritl woul writtn

More information

The Form of Hanging Slinky

The Form of Hanging Slinky Bulletin of Aichi Univ. of Eduction, 66Nturl Sciences, pp. - 6, Mrch, 07 The Form of Hnging Slinky Kenzi ODANI Deprtment of Mthemtics Eduction, Aichi University of Eduction, Kriy 448-854, Jpn Introduction

More information

SAMPLE LITANY OF THE SAINTS E/G. Dadd9/F. Aadd9. cy. Christ, have. Lord, have mer cy. Christ, have A/E. Dadd9. Aadd9/C Bm E. 1. Ma ry and. mer cy.

SAMPLE LITANY OF THE SAINTS E/G. Dadd9/F. Aadd9. cy. Christ, have. Lord, have mer cy. Christ, have A/E. Dadd9. Aadd9/C Bm E. 1. Ma ry and. mer cy. LTNY OF TH SNTS Cntrs Gnt flwng ( = c. 100) /G Ddd9/F ll Kybrd / hv Ddd9 hv hv Txt 1973, CL. ll rghts rsrvd. Usd wth prmssn. Musc: D. Bckr, b. 1953, 1987, D. Bckr. Publshd by OCP. ll rghts rsrvd. SMPL

More information