UNIFIED COUNCIL An ISO 9001: 2008 Certified Organisation

HYPERBOLA. AIEEE Syllabus. Total No. of questions in Ellipse are: Solved examples Level # Level # Level # 3..

HYPERBOLA AIEEE Sllus. Stndrd eqution nd definitions. Conjugte Hperol. Prmetric eqution of te Hperol. Position of point P(, ) wit respect to Hperol 5. Line nd Hperol 6. Eqution of te Tngent Totl No. of

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

1. If y 2 2x 2y + 5 = 0 is (A) a circle with centre (1, 1) (B) a parabola with vertex (1, 2) 9 (A) 0, (B) 4, (C) (4, 4) (D) a (C) c = am m.

SET I. If y x y + 5 = 0 is (A) circle with centre (, ) (B) prbol with vertex (, ) (C) prbol with directrix x = 3. The focus of the prbol x 8x + y + 7 = 0 is (D) prbol with directrix x = 9 9 (A) 0, (B)

Time : 3 hours 03 - Mathematics - March 2007 Marks : 100 Pg - 1 S E CT I O N - A

Time : hours 0 - Mthemtics - Mrch 007 Mrks : 100 Pg - 1 Instructions : 1. Answer ll questions.. Write your nswers ccording to the instructions given below with the questions.. Begin ech section on new

A P P E N D I X POWERS OF TEN AND SCIENTIFIC NOTATION A P P E N D I X SIGNIFICANT FIGURES

A POWERS OF TEN AND SCIENTIFIC NOTATION In science, very lrge nd very smll deciml numbers re conveniently expressed in terms of powers of ten, some of wic re listed below: 0 3 0 0 0 000 0 3 0 0 0 0.00

Lesson-5 ELLIPSE 2 1 = 0

Lesson-5 ELLIPSE. An ellipse is the locus of point which moves in plne such tht its distnce from fied point (known s the focus) is e (< ), times its distnce from fied stright line (known s the directri).

Chapter 2 Differentiation

Cpter Differentition. Introduction In its initil stges differentition is lrgely mtter of finding limiting vlues, wen te vribles ( δ ) pproces zero, nd to begin tis cpter few emples will be tken. Emple..:

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

Version 001 HW#6 - Electromagnetism arts (00224) 1

Version 001 HW#6 - Electromgnetism rts (00224) 1 This print-out should hve 11 questions. Multiple-choice questions my continue on the next column or pge find ll choices efore nswering. rightest Light ul

Data Provided: A formula sheet and table of physical constants is attached to this paper.

PHY15-B PHY47 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 009-010 ASTRONOMY DEPARTMENT

, MATHS H.O.D.: SUHAG R.KARIYA, BHOPAL, CONIC SECTION PART 8 OF

DOWNLOAD FREE FROM www.tekoclsses.com, PH.: 0 903 903 7779, 98930 5888 Some questions (Assertion Reson tpe) re given elow. Ech question contins Sttement (Assertion) nd Sttement (Reson). Ech question hs

Mathematics Extension 2

00 HIGHER SCHOOL CERTIFICATE EXAMINATION Mthemtics Etension Generl Instructions Reding time 5 minutes Working time hours Write using blck or blue pen Bord-pproved clcultors my be used A tble of stndrd

15 - TRIGONOMETRY Page 1 ( Answers at the end of all questions )

- TRIGONOMETRY Pge P ( ) In tringle PQR, R =. If tn b c = 0, 0, then Q nd tn re the roots of the eqution = b c c = b b = c b = c [ AIEEE 00 ] ( ) In tringle ABC, let C =. If r is the inrdius nd R is the

Ellipse. 1. Defini t ions. FREE Download Study Package from website: 11 of 91CONIC SECTION

FREE Downlod Stud Pckge from wesite: www.tekoclsses.com. Defini t ions Ellipse It is locus of point which moves in such w tht the rtio of its distnce from fied point nd fied line (not psses through fied

ICSE Board Class IX Mathematics Paper 4 Solution

ICSE Bord Clss IX Mthemtics Pper Solution SECTION A (0 Mrks) Q.. () Consider x y 6 5 5 x y 6 5 5 0 6 0 6 x y 6 50 8 5 6 7 6 x y 6 7 6 x y 6 x 7,y (b) Dimensions of the brick: Length (l) = 0 cm, bredth

PLK VICWOOD K.T. CHONG SIXTH FORM COLLEGE Form Six AL Physics Optical instruments

AL Pysics/pticl instruments/p.1 PLK VICW K.T. CHNG SIXTH FRM CLLEGE Form Six AL Pysics pticl Instruments pticl instruments Mgniying glss Microscope Rercting telescope Grting spectrometer Qulittive understnding

CONIC SECTIONS. Chapter 11

CONIC SECTIONS Chpter. Overview.. Sections of cone Let l e fied verticl line nd m e nother line intersecting it t fied point V nd inclined to it t n ngle α (Fig..). Fig.. Suppose we rotte the line m round

JEE Advnced Mths Assignment Onl One Correct Answer Tpe. The locus of the orthocenter of the tringle formed the lines (+P) P + P(+P) = 0, (+q) q+q(+q) = 0 nd = 0, where p q, is () hperol prol n ellipse

Higher Checklist (Unit 3) Higher Checklist (Unit 3) Vectors

Vectors Skill Achieved? Know tht sclr is quntity tht hs only size (no direction) Identify rel-life exmples of sclrs such s, temperture, mss, distnce, time, speed, energy nd electric chrge Know tht vector

Average Rate of Change (AROC) The average rate of change of y over an interval is equal to change in

Averge Rte o Cnge AROC Te verge rte o cnge o y over n intervl is equl to b b y y cngein y cnge in. Emple: Find te verge rte o cnge o te unction wit rule 5 s cnges rom to 5. 4 4 6 5 4 0 0 5 5 5 5 & 4 5

Linear Inequalities: Each of the following carries five marks each: 1. Solve the system of equations graphically.

Liner Inequlities: Ech of the following crries five mrks ech:. Solve the system of equtions grphiclly. x + 2y 8, 2x + y 8, x 0, y 0 Solution: Considerx + 2y 8.. () Drw the grph for x + 2y = 8 by line.it

Math 20C Multivariable Calculus Lecture 5 1. Lines and planes. Equations of lines (Vector, parametric, and symmetric eqs.). Equations of lines

Mt 2C Multivrible Clculus Lecture 5 1 Lines nd plnes Slide 1 Equtions of lines (Vector, prmetric, nd symmetric eqs.). Equtions of plnes. Distnce from point to plne. Equtions of lines Slide 2 Definition

03 Qudrtic Functions Completing the squre: Generl Form f ( x) x + x + c f ( x) ( x + p) + q where,, nd c re constnts nd 0. (i) (ii) (iii) (iv) *Note t

A-PDF Wtermrk DEMO: Purchse from www.a-pdf.com to remove the wtermrk Add Mths Formule List: Form 4 (Updte 8/9/08) 0 Functions Asolute Vlue Function Inverse Function If f ( x ), if f ( x ) 0 f ( x) y f

SSC MAINS (MATHS) MOCK TEST-1 (SOLUTION)

007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI-09 SSC MINS (MTHS) MOCK TEST- (SOLUTION). (B) Order of surds re,,. LCM of, nd is. So, convert ec surd into surd of order 0 0 0 6

Unique Solutions R. Amazing World of Carbon Compounds. C h a p t e r. G l a n c e

9. C h p t e r t G l n c e Hydrocrbons - The fundmentl orgnic compounds : All orgnic compounds contin hydrogen long with crbon. They re the fundmentl orgnic compounds lso known s "Prent" compounds. These

Mathematics. Sample Question Paper. Class 10th. (Detailed Solutions) Mathematics Class X. 2. Given, equa tion is 4 5 x 5x

Sample Question Paper (Detailed Solutions Matematics lass 0t 4 Matematics lass X. Let p( a 6 a be divisible by ( a, if p( a 0. Ten, p( a a a( a 6 a a a 6 a 6 a 0 Hence, remainder is (6 a.. Given, equa

k ) and directrix x = h p is A focal chord is a line segment which passes through the focus of a parabola and has endpoints on the parabola.

Stndrd Eqution of Prol with vertex ( h, k ) nd directrix y = k p is ( x h) p ( y k ) = 4. Verticl xis of symmetry Stndrd Eqution of Prol with vertex ( h, k ) nd directrix x = h p is ( y k ) p( x h) = 4.

/ 3, then (A) 3(a 2 m 2 + b 2 ) = 4c 2 (B) 3(a 2 + b 2 m 2 ) = 4c 2 (C) a 2 m 2 + b 2 = 4c 2 (D) a 2 + b 2 m 2 = 4c 2

SET I. If the locus of the point of intersection of perpendiculr tngents to the ellipse x circle with centre t (0, 0), then the rdius of the circle would e + / ( ) is. There re exctl two points on the

Prerequisite Knowledge Required from O Level Add Math. d n a = c and b = d

Prerequisite Knowledge Required from O Level Add Mth ) Surds, Indices & Logrithms Rules for Surds. b= b =. 3. 4. b = b = ( ) = = = 5. + b n = c+ d n = c nd b = d Cution: + +, - Rtionlising the Denomintor

1. If * is the operation defined by a*b = a b for a, b N, then (2 * 3) * 2 is equal to (A) 81 (B) 512 (C) 216 (D) 64 (E) 243 ANSWER : D

. If * is the opertion defined by *b = b for, b N, then ( * ) * is equl to (A) 8 (B) 5 (C) 6 (D) 64 (E) 4. The domin of the function ( 9)/( ),if f( ) = is 6, if = (A) (0, ) (B) (-, ) (C) (-, ) (D) (, )

Physics 2135 Exam 3 April 21, 2015

Em Totl hysics 2135 Em 3 April 21, 2015 Key rinted Nme: 200 / 200 N/A Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. 1. C Two long stright

Homework Assignment 6 Solution Set

Homework Assignment 6 Solution Set PHYCS 440 Mrch, 004 Prolem (Griffiths 4.6 One wy to find the energy is to find the E nd D fields everywhere nd then integrte the energy density for those fields. We know

Use of Trigonometric Functions

Unit 03 Use of Trigonometric Functions 1. Introduction Lerning Ojectives of tis UNIT 1. Lern ow te trigonometric functions re relted to te rtios of sides of rigt ngle tringle. 2. Be le to determine te

Chapter 23. Geometric Optics

Cpter 23 Geometric Optic Ligt Wt i ligt? Wve or prticle? ot Geometric optic: ligt trvel i trigt-lie pt clled ry Ti i true if typicl ditce re muc lrger t te wvelegt Geometric Optic 2 Wt it i out eome ddreed

In-Class Problems 2 and 3: Projectile Motion Solutions. In-Class Problem 2: Throwing a Stone Down a Hill

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deprtment of Physics Physics 8T Fll Term 4 In-Clss Problems nd 3: Projectile Motion Solutions We would like ech group to pply the problem solving strtegy with the

( β ) touches the x-axis if = 1

Generl Certificte of Eduction (dv. Level) Emintion, ugust Comined Mthemtics I - Prt B Model nswers. () Let f k k, where k is rel constnt. i. Epress f in the form( ) Find the turning point of f without

Actual Formula Test #1 Test #2 Formula. (x h) 2 + (y k) 2 = r 2 General equation of a circle

Actul Formul Test # Test # Formul ( + b)( b + b ) 3 + b 3 = ( b)( + b + b ) 3 b 3 = x = b ± b 4c f(x) = f( x) f( x) = f(x) Qurtic Formul Test for even functions Test for o functions (x h) + (y k) = r Generl

Partial Derivatives. Limits. For a single variable function f (x), the limit lim

Limits Prtil Derivtives For single vrible function f (x), the limit lim x f (x) exists only if the right-hnd side limit equls to the left-hnd side limit, i.e., lim f (x) = lim f (x). x x + For two vribles

First Semester Review Calculus BC

First Semester Review lculus. Wht is the coordinte of the point of inflection on the grph of Multiple hoice: No lcultor y 3 3 5 4? 5 0 0 3 5 0. The grph of piecewise-liner function f, for 4, is shown below.

PHYSICS ASSIGNMENT-9

MPS/PHY-XII-11/A9 PHYSICS ASSIGNMENT-9 *********************************************************************************************************** 1. A wire kept long the north-south direction is llowed

PKK Energy chains. PKK 320 / 200 x 2340 / 200; 5Pz, 1PT55

Energy cins Te order for plstic energy cin sould contin te following dt: Type / dius x Lengt / Widt "Arrngement"; Seprtor rrngement 1 3 Type selection is in ccordnce wit dimeter nd quntity of te lines

REVIEW Chapter 1 The Real Number System

Mth 7 REVIEW Chpter The Rel Number System In clss work: Solve ll exercises. (Sections. &. Definition A set is collection of objects (elements. The Set of Nturl Numbers N N = {,,,, 5, } The Set of Whole

Thomas Whitham Sixth Form

Thoms Whithm Sith Form Pure Mthemtics Unit C Alger Trigonometry Geometry Clculus Vectors Trigonometry Compound ngle formule sin sin cos cos Pge A B sin Acos B cos Asin B A B sin Acos B cos Asin B A B cos

HKDSE2018 Mathematics (Compulsory Part) Paper 2 Solution 1. B 4 (2 ) = (2 ) 2. D. α + β. x x. α β 3. C. h h k k ( 4 ) 6( 2 )

HKDSE08 Mthemtics (Compulsory Prt) Pper Solution. B n+ 8 n+ 4 ( ) ( ) n+ n+ 6n+ 6n+ (6n+ ) (6n+ ). D α β x x α x β ( x) α x β β x α x + β x β ( α + β ) x β β x α + β. C 6 4 h h k k ( 4 ) 6( ) h k h + k

( ) Same as above but m = f x = f x - symmetric to y-axis. find where f ( x) Relative: Find where f ( x) x a + lim exists ( lim f exists.

AP Clculus Finl Review Sheet solutions When you see the words This is wht you think of doing Find the zeros Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor Find

Math 113 Exam 1-Review

Mth 113 Exm 1-Review September 26, 2016 Exm 1 covers 6.1-7.3 in the textbook. It is dvisble to lso review the mteril from 5.3 nd 5.5 s this will be helpful in solving some of the problems. 6.1 Are Between

Mathematics Extension 2

00 HIGHER SCHOOL CERTIFICATE EXAMINATION Mthemtics Extension Generl Instructions Reding time 5 minutes Working time hours Write using blck or blue pen Bord-pproved clcultors m be used A tble of stndrd

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes

PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write

JEE(MAIN) 2015 TEST PAPER WITH SOLUTION (HELD ON SATURDAY 04 th APRIL, 2015) PART B MATHEMATICS

JEE(MAIN) 05 TEST PAPER WITH SOLUTION (HELD ON SATURDAY 0 th APRIL, 05) PART B MATHEMATICS CODE-D. Let, b nd c be three non-zero vectors such tht no two of them re colliner nd, b c b c. If is the ngle

Conducting Ellipsoid and Circular Disk

1 Problem Conducting Ellipsoid nd Circulr Disk Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 (September 1, 00) Show tht the surfce chrge density σ on conducting ellipsoid,

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

MH CET 2018 (QUESTION WITH ANSWER)

( P C M ) MH CET 8 (QUESTION WITH ANSWER). /.sec () + log () - log (3) + log () Ans. () - log MATHS () 3 c + c C C A cos + cos c + cosc + + cosa ( + cosc ) + + cosa c c ( + + ) c / / I tn - in sec - in

Section 15.6 Directional Derivatives and the Gradient Vector

Section 15.6 Directional Derivatives and te Gradient Vector Finding rates of cange in different directions Recall tat wen we first started considering derivatives of functions of more tan one variable,

Solutions to Mock IIT Advanced/Test - 2[Paper-1]/2013

Solutions to Mock IIT Advnced/Test - [Pper-]/3 [HEMISTRY].(D n 3 r hnge in entropy for reversible dibtic process is zero. (Alwys..(B V Litre T 3 K P 9/76 Since t t, 39 mm of Hg pressure is observed It

fractions Let s Learn to

5 simple lgebric frctions corne lens pupil retin Norml vision light focused on the retin concve lens Shortsightedness (myopi) light focused in front of the retin Corrected myopi light focused on the retin

Drill Exercise Find the coordinates of the vertices, foci, eccentricity and the equations of the directrix of the hyperbola 4x 2 25y 2 = 100.

Drill Exercise - 1 1 Find the coordintes of the vertices, foci, eccentricit nd the equtions of the directrix of the hperol 4x 5 = 100 Find the eccentricit of the hperol whose ltus-rectum is 8 nd conjugte

CET MATHEMATICS 2013

CET MATHEMATICS VERSION CODE: C. If sin is the cute ngle between the curves + nd + 8 t (, ), then () () () Ans: () Slope of first curve m ; slope of second curve m - therefore ngle is o A sin o (). The

Section 14.3 Arc Length and Curvature

Section 4.3 Arc Length nd Curvture Clculus on Curves in Spce In this section, we ly the foundtions for describing the movement of n object in spce.. Vector Function Bsics In Clc, formul for rc length in

spring from 1 cm to 2 cm is given by

Problem [8 pts] Tre or Flse. Give brief explntion or exmple to jstify yor nswer. ) [ pts] Given solid generted by revolving region bot the line x, if we re sing the shell method to compte its volme, then

Version 001 HW#6 - Electromagnetic Induction arts (00224) 1 3 T

Version 001 HW#6 - lectromgnetic Induction rts (00224) 1 This print-out should hve 12 questions. Multiple-choice questions my continue on the next column or pge find ll choices efore nswering. AP 1998

BRIEF NOTES ADDITIONAL MATHEMATICS FORM

BRIEF NOTES ADDITIONAL MATHEMATICS FORM CHAPTER : FUNCTION. : + is the object, + is the imge : + cn be written s () = +. To ind the imge or mens () = + = Imge or is. Find the object or 8 mens () = 8 wht

1 (=0.5) I3 a 7 I4 a 15 I5 a (=0.5) c 4 N 10 1 (=0.5) N 6 A 52 S 2

Answers: (98-84 HKMO Finl Events) Creted by Mr. Frncis Hung Lst updted: December 05 Individul Events SI 900 I 0 I (=0.5) I 7 I4 5 I5 80 b 7 b b 5 b 6 b 8 b 4 c c 4 c 0 x (=0.5) c 4 N 0 d 9 d 5 d 5 y d

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,

I. Equations of a Circle a. At the origin center= r= b. Standard from: center= r=

11.: Circle & Ellipse I cn Write the eqution of circle given specific informtion Grph circle in coordinte plne. Grph n ellipse nd determine ll criticl informtion. Write the eqution of n ellipse from rel

FINALTERM EXAMINATION 2011 Calculus &. Analytical Geometry-I

FINALTERM EXAMINATION 011 Clculus &. Anlyticl Geometry-I Question No: 1 { Mrks: 1 ) - Plese choose one If f is twice differentible function t sttionry point x 0 x 0 nd f ''(x 0 ) > 0 then f hs reltive...

DEFINITION OF A DERIVATIVE

DEFINITION OF A DERIVATIVE Section 2.1 Calculus AP/Dual, Revised 2017 viet.dang@umbleisd.net 2.1: Definition of a Derivative 1 DEFINITION A. Te derivative of a function allows you to find te SLOPE OF THE

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK 11 WRITTEN EXAMINATION 2 SOLUTIONS SECTION 1 MULTIPLE CHOICE QUESTIONS

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK WRITTEN EXAMINATION SOLUTIONS FOR ERRORS AND UPDATES, PLEASE VISIT WWW.TSFX.COM.AU/MC-UPDATES SECTION MULTIPLE CHOICE QUESTIONS QUESTION QUESTION

IMPORTANT. Read these directions carefully:

Physics 208: Electricity nd Mgnetism Finl Exm, Secs. 506 510. 7 My. 2004 Instructor: Dr. George R. Welch, 415 Engineering-Physics, 845-7737 Print your nme netly: Lst nme: First nme: Sign your nme: Plese

MATHEMATICS PART A. 1. ABC is a triangle, right angled at A. The resultant of the forces acting along AB, AC

FIITJEE Solutions to AIEEE MATHEMATICS PART A. ABC is tringle, right ngled t A. The resultnt of the forces cting long AB, AC with mgnitudes AB nd respectively is the force long AD, where D is the AC foot

Logarithms and Exponential Functions. Gerda de Vries & John S. Macnab. match as necessary, or to work these results into other lessons.

Logritms nd Eponentil Functions Gerd de Vries & Jon S. Mcn It is epected tt students re lred fmilir wit tis mteril. We include it ere for completeness. Te tree lessons given ere re ver sort. Te tecer is

13.4 Work done by Constant Forces

13.4 Work done by Constnt Forces We will begin our discussion of the concept of work by nlyzing the motion of n object in one dimension cted on by constnt forces. Let s consider the following exmple: push

1 Calculus. 1.1 Gradients and the Derivative. Q f(x+h) f(x)

Calculus. Gradients and te Derivative Q f(x+) δy P T δx R f(x) 0 x x+ Let P (x, f(x)) and Q(x+, f(x+)) denote two points on te curve of te function y = f(x) and let R denote te point of intersection of

Math 0230 Calculus 2 Lectures

Mth Clculus Lectures Chpter 7 Applictions of Integrtion Numertion of sections corresponds to the text Jmes Stewrt, Essentil Clculus, Erly Trnscendentls, Second edition. Section 7. Ares Between Curves Two

= 9 4 = = = 8 2 = 4. Model Question paper-i SECTION-A 1.C 2.D 3.C 4. C 5. A 6.D 7.B 8.C 9.B B 12.B 13.B 14.D 15.

www.rktuitioncentre.blogspot.in Page 1 of 8 Model Question paper-i SECTION-A 1.C.D 3.C. C 5. A 6.D 7.B 8.C 9.B 10. 11.B 1.B 13.B 1.D 15.A SECTION-B 16. P a, b, c, Q g,, x, y, R {a, e, f, s} R\ P Q {a,

SOLUTION OF TRIANGLE GENERAL NOTATION : 1. In a triangle ABC angles at vertices are usually denoted by A, B, C

GENERL NOTTION : SOLUTION OF TRINGLE In tringle BC ngles t vertices re usully denoted by, B, C PGE # sides opposite to these vertices re denoted by, b, c respectively Circumrdius is denoted by R 3 Inrdius

Time: 3 Hrs. M.M. 90

Class: X Subject: Mathematics Topic: SA1 No. of Questions: 34 Time: 3 Hrs. M.M. 90 General Instructions: 1. All questions are compulsory. 2. The questions paper consists of 34 questions divided into four

PARABOLA EXERCISE 3(B)

PARABOLA EXERCISE (B). Find eqution of the tngent nd norml to the prbol y = 6x t the positive end of the ltus rectum. Eqution of prbol y = 6x 4 = 6 = / Positive end of the Ltus rectum is(, ) =, Eqution

F is on a moving charged particle. F = 0, if B v. (sin " = 0)

F is on moving chrged prticle. Chpter 29 Mgnetic Fields Ech mgnet hs two poles, north pole nd south pole, regrdless the size nd shpe of the mgnet. Like poles repel ech other, unlike poles ttrct ech other.

US01CMTH02 UNIT Curvature

Stu mteril of BSc(Semester - I) US1CMTH (Rdius of Curvture nd Rectifiction) Prepred by Nilesh Y Ptel Hed,Mthemtics Deprtment,VPnd RPTPScience College US1CMTH UNIT- 1 Curvture Let f : I R be sufficiently

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams

Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz

Integration Techniques

Integrtion Techniques. Integrtion of Trigonometric Functions Exmple. Evlute cos x. Recll tht cos x = cos x. Hence, cos x Exmple. Evlute = ( + cos x) = (x + sin x) + C = x + 4 sin x + C. cos 3 x. Let u

JUST THE MATHS UNIT NUMBER INTEGRATION APPLICATIONS 6 (First moments of an arc) A.J.Hobson

JUST THE MATHS UNIT NUMBER 13.6 INTEGRATION APPLICATIONS 6 (First moments of n rc) by A.J.Hobson 13.6.1 Introduction 13.6. First moment of n rc bout the y-xis 13.6.3 First moment of n rc bout the x-xis

Math Week 5 concepts and homework, due Friday February 10

Mt 2280-00 Week 5 concepts nd omework, due Fridy Februry 0 Recll tt ll problems re good for seeing if you cn work wit te underlying concepts; tt te underlined problems re to be nded in; nd tt te Fridy

SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014

SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 014 Mrk Scheme: Ech prt of Question 1 is worth four mrks which re wrded solely for the correct nswer.

Sample Problems for the Final of Math 121, Fall, 2005

Smple Problems for the Finl of Mth, Fll, 5 The following is collection of vrious types of smple problems covering sections.8,.,.5, nd.8 6.5 of the text which constitute only prt of the common Mth Finl.

USA Mathematical Talent Search Round 1 Solutions Year 21 Academic Year

1/1/21. Fill in the circles in the picture t right with the digits 1-8, one digit in ech circle with no digit repeted, so tht no two circles tht re connected by line segment contin consecutive digits.

Board Answer Paper: October 2014

Trget Pulictions Pvt. Ltd. Bord Answer Pper: Octoer 4 Mthemtics nd Sttistics SECTION I Q.. (A) Select nd write the correct nswer from the given lterntives in ech of the following su-questions: i. (D) ii..p

Trigonometric Functions

Trget Publictions Pvt. Ltd. Chpter 0: Trigonometric Functions 0 Trigonometric Functions. ( ) cos cos cos cos (cos + cos ) Given, cos cos + 0 cos (cos + cos ) + ( ) 0 cos cos cos + 0 + cos + (cos cos +

0, i.e. forces act in the same direction. , i.e. forces act in opposite direction. The resultant of two forces is closer to the larger force.

Sttics. Introduction. Sttics is tt brnc of mecnics wic dels wit te study of te system of forces in equilibrium. Mtter : Mtter is nyting wic cn be perceived by our senses of wic cn exert, or be cted on,

SAINT IGNATIUS COLLEGE

SAINT IGNATIUS COLLEGE Directions to Students Tril Higher School Certificte 0 MATHEMATICS Reding Time : 5 minutes Totl Mrks 00 Working Time : hours Write using blue or blck pen. (sketches in pencil). This

Coimisiún na Scrúduithe Stáit State Examinations Commission

M 30 Coimisiún n Scrúduithe Stáit Stte Exmintions Commission LEAVING CERTIFICATE EXAMINATION, 005 MATHEMATICS HIGHER LEVEL PAPER ( 300 mrks ) MONDAY, 3 JUNE MORNING, 9:30 to :00 Attempt FIVE questions

Calculus AB Section I Part A A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION

lculus Section I Prt LULTOR MY NOT US ON THIS PRT OF TH XMINTION In this test: Unless otherwise specified, the domin of function f is ssumed to e the set of ll rel numers for which f () is rel numer..

1. Weak acids. For a weak acid HA, there is less than 100% dissociation to ions. The B-L equilibrium is:

th 9 Homework: Reding, M&F, ch. 15, pp. 584-598, 602-605 (clcultions of ph, etc., for wek cids, wek bses, polyprotic cids, nd slts; fctors ffecting cid strength). Problems: Nkon, ch. 18, #1-10, 16-18,

Unique Solutions R. All about Electromagnetism. C h a p t e r. G l a n c e

5. C h p t e r t G l n c e When electric current is pssed through conductor, it produces mgnetic field round it. The first discovery of the connection between electricity nd mgnetism ws mde by H. C. Oersted.

Improper Integrals, and Differential Equations

Improper Integrls, nd Differentil Equtions October 22, 204 5.3 Improper Integrls Previously, we discussed how integrls correspond to res. More specificlly, we sid tht for function f(x), the region creted

MDPT Practice Test 1 (Math Analysis)

MDPT Prctice Test (Mth Anlysis). Wht is the rdin mesure of n ngle whose degree mesure is 7? ) 5 π π 5 c) π 5 d) 5 5. In the figure to the right, AB is the dimeter of the circle with center O. If the length

APPLICATIONS OF THE DEFINITE INTEGRAL

APPLICATIONS OF THE DEFINITE INTEGRAL. Volume: Slicing, disks nd wshers.. Volumes by Slicing. Suppose solid object hs boundries extending from x =, to x = b, nd tht its cross-section in plne pssing through

Math 100 Review Sheet

Mth 100 Review Sheet Joseph H. Silvermn December 2010 This outline of Mth 100 is summry of the mteril covered in the course. It is designed to be study id, but it is only n outline nd should be used s

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

7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus

7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e