ANSWER KEY PHYSICS. Workdone X

Similar documents
BINOMIAL THEOREM SOLUTION. 1. (D) n. = (C 0 + C 1 x +C 2 x C n x n ) (1+ x+ x 2 +.)

PROGRESSION AND SERIES

Electric Potential. and Equipotentials

We show that every analytic function can be expanded into a power series, called the Taylor series of the function.

For this purpose, we need the following result:

Semiconductors materials

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

Dynamically Equivalent Systems. Dynamically Equivalent Systems. Dynamically Equivalent Systems. ME 201 Mechanics of Machines

PLANCESS RANK ACCELERATOR

Advanced Higher Maths: Formulae

ANSWERS, HINTS & SOLUTIONS HALF COURSE TEST VII (Main)

MATH Midterm Solutions

DRAFT. Formulae and Statistical Tables for A-level Mathematics SPECIMEN MATERIAL. First Issued September 2017

ELECTROSTATICS. 4πε0. E dr. The electric field is along the direction where the potential decreases at the maximum rate. 5. Electric Potential Energy:

BINOMIAL THEOREM An expression consisting of two terms, connected by + or sign is called a

Advanced Higher Maths: Formulae

BINOMIAL THEOREM NCERT An expression consisting of two terms, connected by + or sign is called a

U>, and is negative. Electric Potential Energy

CHAPTER 18: ELECTRIC CHARGE AND ELECTRIC FIELD

3.1 Magnetic Fields. Oersted and Ampere

Mathematics. Trigonometrical Ratio, Functions & Identities

SOLUTIONS ( ) ( )! ( ) ( ) ( ) ( )! ( ) ( ) ( ) ( ) n r. r ( Pascal s equation ). n 1. Stepanov Dalpiaz

x a y n + b = 1 0<b a, n > 0 (1.1) x 1 - a y = b 0<b a, n > 0 (1.1') b n sin 2 + cos 2 = 1 x n = = cos 2 6 Superellipse (Lamé curve)

Multi-Electron Atoms-Helium

[Q. Booklet Number]

2012 GCE A Level H2 Maths Solution Paper Let x,

Electron states in a periodic potential. Assume the electrons do not interact with each other. Solve the single electron Schrodinger equation: KJ =

Summary: Binomial Expansion...! r. where

SULIT 3472/2. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.

10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = =

[ 20 ] 1. Inequality exists only between two real numbers (not complex numbers). 2. If a be any real number then one and only one of there hold.

UNIT V: Z-TRANSFORMS AND DIFFERENCE EQUATIONS. Dr. V. Valliammal Department of Applied Mathematics Sri Venkateswara College of Engineering

Induction. Induction and Recursion. Induction is a very useful proof technique

EXERCISE - 01 CHECK YOUR GRASP

Polymer A should have the medium T g. It has a larger sidechain than polymer B, and may also have hydrogen bonding, due the -COOH group.

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

NARAYANA I I T / P M T A C A D E M Y. C o m m o n Pr a c t i c e T e s t 0 9 XI-IC SPARK Date: PHYSICS CHEMISTRY MATHEMATICS

Progression. CATsyllabus.com. CATsyllabus.com. Sequence & Series. Arithmetic Progression (A.P.) n th term of an A.P.

Algebra Based Physics. Gravitational Force. PSI Honors universal gravitation presentation Update Fall 2016.notebookNovember 10, 2016

2002 Quarter 1 Math 172 Final Exam. Review

2a a a 2a 4a. 3a/2 f(x) dx a/2 = 6i) Equation of plane OAB is r = λa + µb. Since C lies on the plane OAB, c can be expressed as c = λa +

Chapter 28 Sources of Magnetic Field

1. The 0.1 kg particle has a speed v = 10 m/s as it passes the 30 position shown. The coefficient of kinetic friction between the particle and the

Mathematical Statistics

Technical Report: Bessel Filter Analysis

Mark Scheme (Results) January 2008

BINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k =

Ch 26 - Capacitance! What s Next! Review! Lab this week!

Numerical integration

Answers to test yourself questions

ME 501A Seminar in Engineering Analysis Page 1

General Physics (PHY 2140)

ATOMIC STRUCTURE EXERCISE # 1

Chapter Linear Regression

Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder


Graphing Review Part 3: Polynomials

CITY UNIVERSITY LONDON

B. Examples 1. Finite Sums finite sums are an example of Riemann Sums in which each subinterval has the same length and the same x i

Important Facts You Need To Know/Review:

Qn Suggested Solution Marking Scheme 1 y. G1 Shape with at least 2 [2]

By the end of this section you will be able to prove the Chinese Remainder Theorem apply this theorem to solve simultaneous linear congruences

The Pigeonhole Principle 3.4 Binomial Coefficients

DATE : HINTS & SOLUTIONS PAPER-1 PART-I : PHYSICS JEE PREPARATORY TEST-2 (JPT-2) (JEE ADVANCED PATTERN) TARGET : JEE (MAIN+ADVANCED) 2018

The Discrete Fourier Transform

ALGEBRA II CHAPTER 7 NOTES. Name

BINOMIAL THEOREM & ITS SIMPLE APPLICATION

CHAPTER 5 : SERIES. 5.2 The Sum of a Series Sum of Power of n Positive Integers Sum of Series of Partial Fraction Difference Method

1 Using Integration to Find Arc Lengths and Surface Areas

EXAMPLES. Leader in CBSE Coaching. Solutions of BINOMIAL THEOREM A.V.T.E. by AVTE (avte.in) Class XI

Simpson s 1/3 rd Rule of Integration

PhysicsAndMathsTutor.com

Limit of a function:

f(bx) dx = f dx = dx l dx f(0) log b x a + l log b a 2ɛ log b a.

M5. LTI Systems Described by Linear Constant Coefficient Difference Equations

Downloaded from

Lecture 38 (Trapped Particles) Physics Spring 2018 Douglas Fields

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3

Energy Dissipation Gravitational Potential Energy Power

Using Counting Techniques to Determine Probabilities

EXPANSION OF LIQUIDS

(A) 6.32 (B) 9.49 (C) (D) (E) 18.97

Using Difference Equations to Generalize Results for Periodic Nested Radicals

Consider unordered sample of size r. This sample can be used to make r! Ordered samples (r! permutations). unordered sample

«A first lesson on Mathematical Induction»

Physics 11b Lecture #11

Disjoint Sets { 9} { 1} { 11} Disjoint Sets (cont) Operations. Disjoint Sets (cont) Disjoint Sets (cont) n elements

Ch 3.4 Binomial Coefficients. Pascal's Identit y and Triangle. Chapter 3.2 & 3.4. South China University of Technology

7.5-Determinants in Two Variables

Auchmuty High School Mathematics Department Sequences & Series Notes Teacher Version

Mathematical Induction (selected questions)

Class Summary. be functions and f( D) , we define the composition of f with g, denoted g f by

Section 35 SHM and Circular Motion

Schrödinger Equation Via Laplace-Beltrami Operator

VECTOR MECHANICS FOR ENGINEERS: Vector Mechanics for Engineers: Dynamics. In the current chapter, you will study the motion of systems of particles.

In the case of a third degree polynomial we took the third difference and found them to be constants thus the polynomial difference holds.

[5 points] (c) Find the charge enclosed by the cylindrical surface of radius ρ 0 = 9 mm and length L = 1 m. [2

Physics 235 Final Examination December 4, 2006 Solutions

8. SIMPLE LINEAR REGRESSION. Stupid is forever, ignorance can be fixed.

Transcription:

ANSWER KEY PHYSICS 6 6 6 7 7 7 9 9 9 0 0 0 CHEMISTRY 6 6 6 7 7 7 9 9 9 0 0 60 MATHEMATICS 6 66 7 76 6 6 67 7 77 7 6 6 7 7 6 69 7 79 9 6 70 7 0 90 PHYSICS F L l. l A Y l A ;( A R L L A. W = (/ lod etesio = (/ mgl 6. wl bd y 7. YAl L F 0 0 L L 7 0 ( I L. PV V K p 000 ; V V 9. PV h p g K V V V 0.0 00 F / Y Fl Fl 0. Y ; l Y l l l o l l l /. Wok doe = lod etesio F F / A FL YA But Y o F / L A L YA YA Wokdoe X L L. Eegy /volume = stesssti Ystisti= Y(sti = 00 0.060-0.060 - =600Jm -. Bekig stess bekig foce cos tt e ( = o =. Eegy stoed pe uit volume = stess sti stess stess stess sti stess Y 6. Stem poit d ice poit tempetues depeds o pessue. Tiple poit hs uique tempetue. Tiple poit of wte is t 7. 6K d pessue 6. 0 - p. 7. Gses epd quickly th liquids. C F K 7. ; 9 O O O F C 0 C C 0 F 90 9. ; F 0 00 0 L 0. L L t; 00 L t 00 0 0000 0.% S Y

. legth iceses, peiod iceses time fo oe oscilltio iceses d thus time will loss l l. ; t l t 0. 99 o C 0.9.0. Pecetge chge i volume t 00 t 00 00 t 00 0-00=. l. 00 t 00 l. 0 00 0 0.0% 6. H = 0 0 + 0 00 + 0 0 = 700 cl.. L 0 (0 0 o 0 0 g 0g 0 9. Het gied by ice = het lost by wte; 0 0 + 0 θ = (0 - θ; o 00 + 0θ = 0 - θ o 00 6 θ = 00-00; o o C 6 0. Mss tio : ; hece T tio :. This fits 0 o C o [θ-0] = 0 [0-θ]; θ -0 = 00-0θ i.e. θ = 0; θ = 0 o CHEMISTRY. Volume is ot itesive popety.. the compesso hs to u fo loge time eleg moe het to the suoudigs.. 0 C d tm. Totl eegy of isolted system is costt.. Fomtio of CO is eothemic ectio; het is evolved fom the system, i.e. eegy is loweed. Thus, eothemic ectios occu spoteously o ccout of decese i ethlpy of system. Thus, E H. 6. H 7. Hess s lw. egtive 9. fo isotheml pocess: T 0 d E 0 d q 0 0. fo elemets, stdd ethlpy of fomtio is zeo.. W = 0 is ot tue.. q = 0J w = -J (wok doe by the system E q w 0 J.. give umbe of moles = Iitil tempetue = kj = 000J It will be (- becuse wok is doe by the system. Het cpcity t costt volume (C υ = 0J / K We kow tht wok doe W Cv ( T T; 000 0 ( T 00 000 0 T 6000 000 0 T 000; T 0K. 0. Chge i itel eegy is give by the eltio, E q w E q w (s het is give out by the system E E kj. fo isochoic pocess V 0 so q E i.e. het give to system ude costt volume is used up i iceg E. 6. It is o-metl 7. /p tio is cuse of dioctivity.. s lkli metls hve tedecy to loose e. 9. ech peiod cosists of seies of elemets whose tom hve the sme picipl qutum o. ( of the oute most shell i.e., i secod peiod =, this shell hs fou obitls (oe s d thee p which c hve eight electos, hece secod peiod cotis elemets fom tomic o. to 0. 0. Neils Boh developed the log fom of peiodic tble o the bsis of Moseley s piciple.. De Ch Coutois. Deceses 6 6. s s p s p s picipl qutum o. is so it belogs to th peiod.

. Elemets of secod d thid peiod Digol eltioship. Electoic cofigutio 6. Z =,,,. it would dote e moe esily. 7. Fist goup e.g.. the ode of sceeig effect fo give shell electo is s > p > d > f. 9. Elemets of goup hloge e: F, Cl, B l d At. 60. Vlece electos MATHEMATICS 6. Legth of wie = 7 cm, dius of the c = cm Agle subteded t the cete = Ac legth 7 dius 6 7 0 0 di degee 0 6 6. t (,, t e G.P 6. 6 mimum vlue. 6. I cyclic qudiltel A + C = A C A Similly B+D = ( c C B D B ( d D C DC D 0 6. If A B C the A B C [ mimum vlueof A is ] The A B C 0 If A, the A 0 A B C 0 66. ( 67. t t t 6 6 9 t( t t ( t t 7 7 6. t t0 t t t90 cot t t t t t A t A ta t A A t At A ta t At A t A t A ta t At AtA t A t A ta t A t A t At AtA 69.

A B y A B y A B A B A B A B 70. y y y y A B A B y t Acot B y t A y t B 7. Miimum vlue of 7. b Mimum vlue of b Miimum vlue of b b Mimum vlue of Poduct A A B A BA B; B = (A+B (A B (+ (- (+ (- 60 6 cot 60 cot6 606 6 6 0 ( 0 7. 6 0 0 6 0 7. Mimum vlue of But RHS = 7Thee is o solutio 7. t t t t t t whee t t t t (t t t 6t 0t 0 6t 0t 0 t t 0 t 6 7 7 7,, 6 6 6 Sice is cute t > 0 t 76. 90 9 90 9 90 79 90 9 9

... 79... 9 90 9 9... 79... 9 90... 9... 90. 77. Let t 7 t 7 the 7 7 0 (60 (60 7. [ 60 ] t t 0 60 0 6 0 0 (60 0 0 0(70 0 0 0 70 t 0 t 0 79. t(0 0 t 0t 0 t 60 t 0 t 0 t 0 t 0 t 0 t 0 t 0 t 0 0. t t b b b t b b. 76 6 76 9 6 6 6 7 ( is i the th qudt is gete th 0 t 7 7 7 t 7 7 7 7 7. cot.. t 0 t(70 0 t 70 t 0 t 70 t 0 t 70 t 0 t(90 0 t 0

t0 t 00 t 70 t 0 t 70 t 0 t 70 t 0 0 cot t 0 t 70...., if <... o 6. t 6 7 t( t t7 t7 t t7 t7 7 7 7 7 7. t sec 0 ( ( i.e. 0. 7, 0, But 0 7. :. 9. Give tht ( ( 0 90. 0 7 6 7 (0 7 6 6 0 ( 6 6 (90 6 7 6