+ R 2 where R 1. MULTIPLE CHOICE QUESTIONS (MCQ's) (Each question carries one mark)
|
|
- August Barton
- 5 years ago
- Views:
Transcription
1 2. C h p t e r t G l n c e is the set of ll points in plne which re t constnt distnce from fixed point clled centre nd constnt distnce is known s rdius of circle. A tngent t ny point of circle is perpendiculr to the rdius through the point of contct nd the line perpendiculr to rdius of circle t its outer end is tngent to the circle. Two tngents cn be drwn from point outside the circle nd the lengths of such tngents re equl. If two circles re touching then the common point lies on the line joining their centres nd if the circles touch internlly the distnce between their centres is R 1 - R 2 nd if the circles touch externlly the distnt between centres is R 1 + R 2 where R 1 + R 2 re their rdii. The mesure of n ngle subtended by n rc t point on the circle is hlf of the mesure of the ngle subtended by the rc t the centre. An ngle subtended by semicircle t point on the circle is 90º Angles subtended by the sme rc re congruent A. The opposite ngles of cyclic qudrilterl CNC supplementry nd its converse is true. If n ngle with its vertex on the circle whose one side is tngent of circle nd other side is secnt then the mesure of the ngle is hlf of the mesure of the intercepted rc. If secnt is drwn through the point of contct of tngent to circle then the ngle which this tngent mkes with the chord contined the secnt re equl to the ngles subtended by the chord in the corresponding lternte segment. If two secnts of circle intersect inside or outside the circle then the re of the rectngle formed by the two line segments corresponding to one secnt is equl to re of the rectngle formed by the two line segments corresponding to other. If secnt nd tngent of circle intersect in point outside the circle then the re of the rectngle formed by the two line segments corresponding to the secnt is equl to the re of the squre formed by the line segment corresponding to the tngent. MULTIPLE CHOICE QUESTIONS (MCQ's) (Ech question crries one mrk) 1. A tngent t ny point of circle is... to the rdius through the point of contct. prllel b intersecting c perpendiculr d slnting 2. Three congruent circles with centres A, B nd C nd with rdius 5 cm touch ech other. Then perimeter of ABC is... cm. 15 b 20 c 30 d Rdius of the circle pssing through the vertices of right ngled tringle with sides 6 cm, 8 cm nd 10 cm is... cm. 3 b 4 c 5 d The opposite ngles of cyclic qudrilterl re.... supplementry b cute c obtuse d complementry
2 40 Unique MCQ's 5. Mesure of ngle inscribed in semicircle is º b 45º c 30º d 90º 6. A chord intersects circle in... points. one b mny c two d more thn two 7. The length of one tngent drwn from point outside circle is 7 cm the length of other tngent is... cm. 7 b 3.5 c 14 d Two circles with rdius 6 cm nd 4 cm touch ech other externlly the distnce between their centres is... cm. 5 b 24 c 6 d A chord divides circle is two rcs mesuring 2x nd 7x. The mesure of minor rc is º b 140º c 80º d 20º 10. An ngle subtended by semicircle t point outside the circle is... ngle. right b n cute c n obtuse d 180º 11. A cyclic prllelogrm is.... squre b rhombus c rectngle d kite 12. Angle subtended by sme rc re.... equl b unequl c congruent d cute 13. If two secnts of circle intersect in point 'P' then; AP BP = CP b AP = BP c CP = CD d AP BP = CP DP PD 14. The mesure of n inscribed ngle is... the mesure of the intercepted rc. Twice b hlf c one-fourth d equl 15. PQRS is cyclic qudritterl if m P = 4m R then m P =...? 36º b 144º c 9º d 46º 16. Mesure of n rc is equl to the mesure of...? inscribed ngle b semicircle c centrl ngle d circle 17. In the djoining figure, if m QPR = 50º, then m(rc QSR) =...? 25º b 80º c 100º d 130º 18. Two circles with centre P nd Q touch internlly. The rdius of smller circle is 8 cm. The distnce between their centre is 3 cm then find the dimeter of the lrger circle. 5 cm b 11 cm c 22 cm d 5.5 cm 19. A line which intersects the circle in two distinct points is clled... chord b tngent c secnt d rdius 20. In the djoining figure, if AD = 5, AB = 10 then OD =? 14 b 7.5 c 20 d 10
3 GEOMETRY - S.S.C (c) perpendiculr 2. (c) (c) 5 4. () supplementry 5. (d) 90º 6. (c) two 7. () 7 8. (d) (c) 80º 10. (b) n cute 11. (c) rectngle 12. (c) congruent 13. (d) AP BP = CP DP 14. (b) hlf 15. (b) 144º P + R = 180º [Opposite ngles of cyclic qudrilterl] 4 R + R = 180º 5 R = 180º R = = 36º P = 180º 36º = 144º 16. (c) centrl ngle 17. (d) m(rc QSR) = 130º Joing QO nd RO 1. Line QR is tngent t R. PQ = 13 cm, QR =12cm. Then rdius PR =... cm. 25 b 5 c 10 d 1 2. Q is the centre of circle. Answers Problems For Prctice OQP + ORP = 90º [Tngent perpendiculrity theorem] OQP + ORP = 90º + 90º = 180º PQRO is cyclic qudrilterl. QPR + QOR = 180º QOR = 180º 50º QOR = 130º QOR = m(rc QSR) [Centrl ngle property] m(rc QSR) = 130º 18. (c) D = 22 cm R r = 3 R 8 = 3 R = = 11 D = 2R = 2 11 = 22 cm 19. (c) secnt 20. (b) OD = 7.5 AB 2 = AD AC (10) 2 = 5 AC 100 = AC 5 AC = 20 CD = 20 5 = 15 OD = 1 CD 2 3. ABC is isosceles tringle with perimeter 34 cm. AB = AC nd BC = 10 cm. If circle touches the sides PM nd PN re tngents. If MPN = 50º then MQN = º b 100 c 130º d 310º of tringle, AP = cm b 5 cm c 7 cm d 10 cm 4. Two circles with centres P nd Q touch internlly. If their rdii re 10 cm nd 26 cm, then PQ =... cm. 16 b 36 c 13 d 6 = 1 15 = 7.5 2
4 42 Unique MCQ's 5. The rdii of two circles re 25 cm nd 9 cm nd CD = 34 cm AB = cm b 20 cm c 30 cm d 15 cm 6. If m(rc PMR) = 110º, then PQR = º b 55º c 60º d 120º 7. If m(rc AB) = 20º, m(rc CD) = 30º; then AMB = º b 30º c 50º d 25º 8. If BAC = 30 ; then m(rc BC) = b 60º c 30º d 10º 9. If BAC = 70º nd if rc intercepted by both the ngles is sme, PQR = º b 68º c 35º d 70º 10. If ABCD is cyclic; then.... = c b b = c c d = x d = x Answers 11. If m(rc PMQ) = 140º. Then PQR = º b 40º c 80º d 110º 12. seg AB nd seg AD re chords of the circle nd AC is tngent. If m(rc APB) = 70º, m(rc BQD) = 16º; then m CAD = º b 43º c 32º d 27º 13. seg PA is tngent nd seg PC is secnt. If AP = 12 cm, BP = 9 cm PC =... cm. 9 b 12 c 16 d In figure seg PB nd seg PD re secnt nd PA = 12 cm, PB = 15 cm, PC = 10 cm; then PD =... cm. 27 b 9 c 18 d In figure seg PT is tngent nd seg PB is secnt. PTA.... PAT b PBT c BPT d TAB 1 - b 2 - c 3 - c c 6 - b 7 - d 8 - b 9 - d 10 - d 11 - d 12 - b 13 - c 14 - c 15 - b
5
GEOMETRICAL PROPERTIES OF ANGLES AND CIRCLES, ANGLES PROPERTIES OF TRIANGLES, QUADRILATERALS AND POLYGONS:
GEOMETRICL PROPERTIES OF NGLES ND CIRCLES, NGLES PROPERTIES OF TRINGLES, QUDRILTERLS ND POLYGONS: 1.1 TYPES OF NGLES: CUTE NGLE RIGHT NGLE OTUSE NGLE STRIGHT NGLE REFLEX NGLE 40 0 4 0 90 0 156 0 180 0
More informationAnswers to Exercises. c 2 2ab b 2 2ab a 2 c 2 a 2 b 2
Answers to Eercises CHAPTER 9 CHAPTER LESSON 9. CHAPTER 9 CHAPTER. c 9. cm. cm. b 5. cm. d 0 cm 5. s cm. c 8.5 cm 7. b cm 8.. cm 9. 0 cm 0. s.5 cm. r cm. 7 ft. 5 m.. cm 5.,, 5. 8 m 7. The re of the lrge
More informationGEOMETRY OF THE CIRCLE TANGENTS & SECANTS
Geometry Of The ircle Tngents & Secnts GEOMETRY OF THE IRLE TNGENTS & SENTS www.mthletics.com.u Tngents TNGENTS nd N Secnts SENTS Tngents nd secnts re lines tht strt outside circle. Tngent touches the
More information/ 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
More informationMDPT 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
More informationJEE 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
More information15 - 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
More informationAlg. Sheet (1) Department : Math Form : 3 rd prep. Sheet
Ciro Governorte Nozh Directorte of Eduction Nozh Lnguge Schools Ismili Rod Deprtment : Mth Form : rd prep. Sheet Alg. Sheet () [] Find the vlues of nd in ech of the following if : ) (, ) ( -5, 9 ) ) (,
More informationLesson-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).
More informationLLT Education Services
8. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. (a) 4 cm (b) 3 cm (c) 6 cm (d) 5 cm 9. From a point P, 10 cm away from the
More information1. 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)
More informationTime : 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
More informationICSE 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
More informationPARABOLA 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
More informationSOLUTION OF TRIANGLES
SOLUTION OF TIANGLES DPP by VK Sir B.TEH., IIT DELHI VK lsses, -9-40, Indr Vihr, Kot. Mob. No. 989060 . If cos A + cosb + cos = then the sides of the AB re in A.P. G.P H.P. none. If in tringle sin A :
More informationR(3, 8) P( 3, 0) Q( 2, 2) S(5, 3) Q(2, 32) P(0, 8) Higher Mathematics Objective Test Practice Book. 1 The diagram shows a sketch of part of
Higher Mthemtics Ojective Test Prctice ook The digrm shows sketch of prt of the grph of f ( ). The digrm shows sketch of the cuic f ( ). R(, 8) f ( ) f ( ) P(, ) Q(, ) S(, ) Wht re the domin nd rnge of
More informationSet 1 Paper 2. 1 Pearson Education Asia Limited 2017
. A. A. C. B. C 6. A 7. A 8. B 9. C. D. A. B. A. B. C 6. D 7. C 8. B 9. C. D. C. A. B. A. A 6. A 7. A 8. D 9. B. C. B. D. D. D. D 6. D 7. B 8. C 9. C. D. B. B. A. D. C Section A. A (68 ) [ ( ) n ( n 6n
More informationMEP Practice Book ES3. 1. Calculate the size of the angles marked with a letter in each diagram. None to scale
ME rctice ook ES3 3 ngle Geometr 3.3 ngle Geometr 1. lculte the size of the ngles mrked with letter in ech digrm. None to scle () 70 () 20 54 65 25 c 36 (d) (e) (f) 56 62 d e 60 40 70 70 f 30 g (g) (h)
More information2) Three noncollinear points in Plane M. [A] A, D, E [B] A, B, E [C] A, B, D [D] A, E, H [E] A, H, M [F] H, A, B
Review Use the points nd lines in the digrm to identify the following. 1) Three colliner points in Plne M. [],, H [],, [],, [],, [],, M [] H,, M 2) Three noncolliner points in Plne M. [],, [],, [],, [],,
More informationVAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)
BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ
More informationPrerequisite 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
More informationCONIC 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
More informationChapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in
Chapter - 10 (Circle) Key Concept * Circle - circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle - Circle having same centre called concentric circle.
More informationLinear 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
More informationUdaan School Of Mathematics Class X Chapter 10 Circles Maths
Exercise 10.1 1. Fill in the blanks (i) The common point of tangent and the circle is called point of contact. (ii) A circle may have two parallel tangents. (iii) A tangent to a circle intersects it in
More informationIMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB
` K UKATP ALLY CE NTRE IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB 7-8 FIITJEE KUKATPALLY CENTRE: # -97, Plot No, Opp Ptel Kunt Hud Prk, Vijngr Colon, Hderbd - 5 7 Ph: -66 Regd
More informationA LEVEL TOPIC REVIEW. factor and remainder theorems
A LEVEL TOPIC REVIEW unit C fctor nd reminder theorems. Use the Fctor Theorem to show tht: ) ( ) is fctor of +. ( mrks) ( + ) is fctor of ( ) is fctor of + 7+. ( mrks) +. ( mrks). Use lgebric division
More informationDownloaded from
Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2 - AD 2 AD 2 - AC 2 3AC 2-4AD 2 (D) 4AD 2-3AC 2 2.Which of the following statement is true? Any two right triangles are similar
More informationUS01CMTH02 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
More informationAnswers: ( HKMO Heat Events) Created by: Mr. Francis Hung Last updated: 15 December 2017
Answers: (0- HKMO Het Events) reted y: Mr. Frncis Hung Lst updted: 5 Decemer 07 - Individul - Group Individul Events 6 80 0 4 5 5 0 6 4 7 8 5 9 9 0 9 609 4 808 5 0 6 6 7 6 8 0 9 67 0 0 I Simplify 94 0.
More information(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2
CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5
More informationCoimisiún 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
More informationEllipse. 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
More information1. 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) (, )
More informationTime : 2 Hours Preliminary Model Answer Paper Max. Marks : 40. [Given] [Taking square roots]
.P. SET CODE MT - w 05 00 - MT - w - MTHEMTICS (7) GEOMETRY - (E) Time : Hours Preliminary Model nswer Paper Max. Marks : 40.. ttempt NY FIVE of the following : (i) BC ~ PQ [Given] ( BC) ( PQ) BC PQ [reas
More informationTHE KENNESAW STATE UNIVERSITY HIGH SCHOOL MATHEMATICS COMPETITION PART I MULTIPLE CHOICE NO CALCULATORS 90 MINUTES
THE 08 09 KENNESW STTE UNIVERSITY HIGH SHOOL MTHEMTIS OMPETITION PRT I MULTIPLE HOIE For ech of the following questions, crefully blcken the pproprite box on the nswer sheet with # pencil. o not fold,
More informationAnswers for Lesson 3-1, pp Exercises
Answers for Lesson -, pp. Eercises * ) PQ * ) PS * ) PS * ) PS * ) SR * ) QR * ) QR * ) QR. nd with trnsversl ; lt. int. '. nd with trnsversl ; lt. int. '. nd with trnsversl ; sme-side int. '. nd with
More informationDrill 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
More information, 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
More informationUse the diagram to identify each angle pair as a linear pair, vertical angles, or neither.
inl xm Review hpter 1 6 & hpter 9 Nme Use the points nd lines in the digrm to identify the following. 1) Three colliner points in Plne M. [],, H [],, [],, [],, [],, M [] H,, M 2) Three noncolliner points
More information03 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
More informationI. 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
More informationQuestion Bank Tangent Properties of a Circle
Question Bank Tangent Properties of a Circle 1. In quadrilateral ABCD, D = 90, BC = 38 cm and DC = 5 cm. A circle is inscribed in this quadrilateral which touches AB at point Q such that QB = 7 cm. Find
More information10 If 3, a, b, c, 23 are in A.S., then a + b + c = 15 Find the perimeter of the sector in the figure. A. 1:3. A. 2.25cm B. 3cm
HK MTHS Pper II P. If f ( x ) = 0 x, then f ( y ) = 6 0 y 0 + y 0 y 0 8 y 0 y If s = ind the gretest vlue of x + y if ( x, y ) is point lying in the region O (including the boundry). n [ + (n )d ], then
More informationUnit 5 Review. For each problem (1-4) a and b are segment lengths; x and y are angle measures.
For ech problem (1-4) nd b re segment lengths; x nd y re ngle mesures. 1. Figure is Prllelogrm 2. Figure is Squre 21 36 16 b 104 3 2 6 b = 21 b = 16 x = 104 y = 40 = 3 2 b = 6 x = 45 y = 90 3. Figure is
More informationAndrew Ryba Math Intel Research Final Paper 6/7/09 (revision 6/17/09)
Andrew Ryb Mth ntel Reserch Finl Pper 6/7/09 (revision 6/17/09) Euler's formul tells us tht for every tringle, the squre of the distnce between its circumcenter nd incenter is R 2-2rR, where R is the circumrdius
More informationSCORE JEE (Advanced)
SLUTIN. ns. (D) L : x + y 0 S L : x + y 0 L : x + y 7 0 Point of intersection of L 0 & L 0 is (,9) Point of intersection of L 0 & L 0 is (0,) line perpendiculr to L nd pssing through (, 9) isx y + 0...
More informationJEE(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
More information( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear.
Problems 01 - POINT Page 1 ( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. ( ) Prove that the two lines joining the mid-points of the pairs of opposite sides and the line
More informationMaharashtra Board Class X Mathematics - Geometry Board Paper 2014 Solution. Time: 2 hours Total Marks: 40
Maharashtra Board Class X Mathematics - Geometry Board Paper 04 Solution Time: hours Total Marks: 40 Note: - () All questions are compulsory. () Use of calculator is not allowed.. i. Ratio of the areas
More informationQUESTION BANK ON STRAIGHT LINE AND CIRCLE
QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,
More informationForm 5 HKCEE 1990 Mathematics II (a 2n ) 3 = A. f(1) B. f(n) A. a 6n B. a 8n C. D. E. 2 D. 1 E. n. 1 in. If 2 = 10 p, 3 = 10 q, express log 6
Form HK 9 Mthemtics II.. ( n ) =. 6n. 8n. n 6n 8n... +. 6.. f(). f(n). n n If = 0 p, = 0 q, epress log 6 in terms of p nd q.. p q. pq. p q pq p + q Let > b > 0. If nd b re respectivel the st nd nd terms
More information= ( +1) BP AC = AP + (1+ )BP Proved UNIT-9 CIRCLES 1. Prove that the parallelogram circumscribing a circle is rhombus. Ans Given : ABCD is a parallelogram circumscribing a circle. To prove : - ABCD is
More informationMATHEMATICS 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
More informationMath 1102: Calculus I (Math/Sci majors) MWF 3pm, Fulton Hall 230 Homework 2 solutions
Mth 1102: Clculus I (Mth/Sci mjors) MWF 3pm, Fulton Hll 230 Homework 2 solutions Plese write netly, nd show ll work. Cution: An nswer with no work is wrong! Do the following problems from Chpter III: 6,
More information21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.
21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 22. Prove that If two sides of a cyclic quadrilateral are parallel, then
More information2 Calculate the size of each angle marked by a letter in these triangles.
Cmridge Essentils Mthemtics Support 8 GM1.1 GM1.1 1 Clculte the size of ech ngle mrked y letter. c 2 Clculte the size of ech ngle mrked y letter in these tringles. c d 3 Clculte the size of ech ngle mrked
More informationGeometry of the Circle - Chords and Angles. Geometry of the Circle. Chord and Angles. Curriculum Ready ACMMG: 272.
Geometry of the irle - hords nd ngles Geometry of the irle hord nd ngles urriulum Redy MMG: 272 www.mthletis.om hords nd ngles HRS N NGLES The irle is si shpe nd so it n e found lmost nywhere. This setion
More informationAngles and triangles. Chapter Introduction Angular measurement Minutes and seconds
hpter 0 ngles nd tringles 0.1 Introduction stright line which crosses two prllel lines is clled trnsversl (see MN in igure 0.1). Trigonometry is suject tht involves the mesurement of sides nd ngles of
More informationGeometry AP Book 8, Part 2: Unit 3
Geometry ook 8, rt 2: Unit 3 IMRTNT NTE: For mny questions in this unit, there re multiple correct nswers, e.g. line segment cn e written s, RST is the sme s TSR, etc. Where pproprite, techers should e
More information( 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
More informationCET 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
More informationFill in the blanks Chapter 10 Circles Exercise 10.1 Question 1: (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater
More informationDEEPAWALI ASSIGNMENT
DEEPWLI SSIGNMENT CLSS & DOPPE FO TGET IIT JEE Get Solution & Video Tutorils online www.mthsbysuhg.com Downlod FEE Study Pckges, Test Series from w ww.tekoclsses.com Bhopl : Phone : (0755) 00 000 Wishing
More informationLevel I MAML Olympiad 2001 Page 1 of 6 (A) 90 (B) 92 (C) 94 (D) 96 (E) 98 (A) 48 (B) 54 (C) 60 (D) 66 (E) 72 (A) 9 (B) 13 (C) 17 (D) 25 (E) 38
Level I MAML Olympid 00 Pge of 6. Si students in smll clss took n em on the scheduled dte. The verge of their grdes ws 75. The seventh student in the clss ws ill tht dy nd took the em lte. When her score
More informationIndicate whether the statement is true or false.
PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.
More informationSSC CGL Tier 1 and Tier 2 Program
Gurudwara Road Model Town, Hisar 9729327755 www.ssccglpinnacle.com SSC CGL Tier 1 and Tier 2 Program -------------------------------------------------------------------------------------------------------------------
More informationMORE FUNCTION GRAPHING; OPTIMIZATION. (Last edited October 28, 2013 at 11:09pm.)
MORE FUNCTION GRAPHING; OPTIMIZATION FRI, OCT 25, 203 (Lst edited October 28, 203 t :09pm.) Exercise. Let n be n rbitrry positive integer. Give n exmple of function with exctly n verticl symptotes. Give
More informationMathematics 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
More informationTriangles The following examples explore aspects of triangles:
Tringles The following exmples explore spects of tringles: xmple 1: ltitude of right ngled tringle + xmple : tringle ltitude of the symmetricl ltitude of n isosceles x x - 4 +x xmple 3: ltitude of the
More informationPRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES
PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES 1. Find the value of k, if x =, y = 1 is a solution of the equation x + 3y = k.. Find the points where the graph of the equation
More informationArcs and Inscribed Angles of Circles
Arcs and Inscribed Angles of Circles Inscribed angles have: Vertex on the circle Sides are chords (Chords AB and BC) Angle ABC is inscribed in the circle AC is the intercepted arc because it is created
More informationELLIPSE. Standard equation of an ellipse referred to its principal axes along the co-ordinate axes is. ( a,0) A'
J-Mthemtics LLIPS. STANDARD QUATION & DFINITION : Stndrd eqution of n ellipse referred to its principl es long the co-ordinte es is > & = ( e ) = e. Y + =. where where e = eccentricit (0 < e < ). FOCI
More informationNOT TO SCALE. We can make use of the small angle approximations: if θ á 1 (and is expressed in RADIANS), then
3. Stellr Prllx y terrestril stndrds, the strs re extremely distnt: the nerest, Proxim Centuri, is 4.24 light yers (~ 10 13 km) wy. This mens tht their prllx is extremely smll. Prllx is the pprent shifting
More informationCIRCLES MODULE - 3 OBJECTIVES EXPECTED BACKGROUND KNOWLEDGE. Circles. Geometry. Notes
Circles MODULE - 3 15 CIRCLES You are already familiar with geometrical figures such as a line segment, an angle, a triangle, a quadrilateral and a circle. Common examples of a circle are a wheel, a bangle,
More informationUNCORRECTED. 9Geometry in the plane and proof
9Geometry in the plne nd proof Ojectives To consider necessry nd sufficient conditions for two lines to e prllel. To determine the ngle sum of polygon. To define congruence of two figures. To determine
More informationQ1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. askiitians
Class: VII Subject: Math s Topic: Properties of triangle No. of Questions: 20 Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. Greater
More informationSimilarity and Congruence
Similrity nd ongruence urriculum Redy MMG: 201, 220, 221, 243, 244 www.mthletics.com SIMILRITY N ONGRUN If two shpes re congruent, it mens thy re equl in every wy ll their corresponding sides nd ngles
More information13.3 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS
33 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS As simple ppliction of the results we hve obtined on lgebric extensions, nd in prticulr on the multiplictivity of extension degrees, we cn nswer (in
More informationEdexcel GCE Core Mathematics (C2) Required Knowledge Information Sheet. Daniel Hammocks
Edexcel GCE Core Mthemtics (C) Required Knowledge Informtion Sheet C Formule Given in Mthemticl Formule nd Sttisticl Tles Booklet Cosine Rule o = + c c cosine (A) Binomil Series o ( + ) n = n + n 1 n 1
More informationExercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior)
Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater than its radius lies
More informationMathematics. Area under Curve.
Mthemtics Are under Curve www.testprepkrt.com Tle of Content 1. Introduction.. Procedure of Curve Sketching. 3. Sketching of Some common Curves. 4. Are of Bounded Regions. 5. Sign convention for finding
More informationPrerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) ,
R rern Tower, Rod No, Contrctors Are, Bistupur, Jmshedpur 800, Tel 065789, www.prernclsses.com IIT JEE 0 Mthemtics per I ART III SECTION I Single Correct Answer Type This section contins 0 multiple choice
More informationPolynomials and Division Theory
Higher Checklist (Unit ) Higher Checklist (Unit ) Polynomils nd Division Theory Skill Achieved? Know tht polynomil (expression) is of the form: n x + n x n + n x n + + n x + x + 0 where the i R re the
More information( 1 ) Find the co-ordinates of the focus, length of the latus-rectum and equation of the directrix of the parabola x 2 = - 8y.
PROBLEMS 04 - PARABOLA Page 1 ( 1 ) Find the co-ordinates of the focus, length of the latus-rectum and equation of the directrix of the parabola x - 8. [ Ans: ( 0, - ), 8, ] ( ) If the line 3x 4 k 0 is
More informationAlg 3 Ch 7.2, 8 1. C 2) If A = 30, and C = 45, a = 1 find b and c A
lg 3 h 7.2, 8 1 7.2 Right Tringle Trig ) Use of clcultor sin 10 = sin x =.4741 c ) rete right tringles π 1) If = nd = 25, find 6 c 2) If = 30, nd = 45, = 1 find nd c 3) If in right, with right ngle t,
More information6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.
6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has
More informationClass IX - NCERT Maths Exercise (10.1)
Class IX - NCERT Maths Exercise (10.1) Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/interior) (ii) A point, whose distance from the centre of a circle is greater
More informationCAREER POINT PRE FOUNDATION DIVISON CLASS-9. IMO Stage-II Exam MATHEMATICS Date :
CAREER POINT PRE FOUNDATION DIVISON IMO Stage-II Exam.-07 CLASS-9 MATHEMATICS Date : -0-07 Q. In the given figure, PQR is a right angled triangle, right angled at Q. If QRST is a square on side QR and
More informationMath 9 Chapter 8 Practice Test
Name: Class: Date: ID: A Math 9 Chapter 8 Practice Test Short Answer 1. O is the centre of this circle and point Q is a point of tangency. Determine the value of t. If necessary, give your answer to the
More informationChapter 3. - parts of a circle.
Chapter 3 - parts of a circle. 3.1 properties of circles. - area of a sector of a circle. the area of the smaller sector can be found by the following formula: A = qº 360º pr2, given q in degrees, or!
More informationEuclidian Geometry Grade 10 to 12 (CAPS)
Euclidian Geometry Grade 10 to 12 (CAPS) Compiled by Marlene Malan marlene.mcubed@gmail.com Prepared by Marlene Malan CAPS DOCUMENT (Paper 2) Grade 10 Grade 11 Grade 12 (a) Revise basic results established
More information1 cos. cos cos cos cos MAT 126H Solutions Take-Home Exam 4. Problem 1
MAT 16H Solutions Tke-Home Exm 4 Problem 1 ) & b) Using the hlf-ngle formul for cosine, we get: 1 cos 1 4 4 cos cos 8 4 nd 1 8 cos cos 16 4 c) Using the hlf-ngle formul for tngent, we get: cot ( 3π 1 )
More informationMT - w A.P. SET CODE MT - w - MATHEMATICS (71) GEOMETRY- SET - A (E) Time : 2 Hours Preliminary Model Answer Paper Max.
.P. SET CODE.. Solve NY FIVE of the following : (i) ( BE) ( BD) ( BE) ( BD) BE D 6 9 MT - w 07 00 - MT - w - MTHEMTICS (7) GEOMETRY- (E) Time : Hours Preliminary Model nswer Paper Max. Marks : 40 [Triangles
More informationIndividual Events I3 a 10 I4. d 90 angle 57 d Group Events. d 220 Probability
Answers: (98-8 HKMO Finl Events) Creted by: Mr. Frncis Hung Lst updted: 8 Jnury 08 I 800 I Individul Events I 0 I4 no. of routes 6 I5 + + b b 0 b b c *8 missing c 0 c c See the remrk 600 d d 90 ngle 57
More informationProperties of the Circle
9 Properties of the Circle TERMINOLOGY Arc: Part of a curve, most commonly a portion of the distance around the circumference of a circle Chord: A straight line joining two points on the circumference
More informationLUMS School of Science and Engineering
LUMS School of Science nd Engineering PH- Solution of ssignment Mrch, 0, 0 Brvis Lttice Answer: We hve given tht c.5(î + ĵ + ˆk) 5 (î + ĵ + ˆk) 0 (î + ĵ + ˆk) c (î + ĵ + ˆk) î + ĵ + ˆk + b + c î, b ĵ nd
More informationieducation.com Tangents given as follows. the circle. contact. There are c) Secant:
h Tangents and Secants to the Circle A Line and a circle: let us consider a circle and line say AB. There can be three possibilities given as follows. a) Non-intersecting line: The line AB and the circle
More informationMATHEMATICS (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 informationJUST THE MATHS SLIDES NUMBER INTEGRATION APPLICATIONS 12 (Second moments of an area (B)) A.J.Hobson
JUST THE MATHS SLIDES NUMBER 13.12 INTEGRATION APPLICATIONS 12 (Second moments of n re (B)) b A.J.Hobson 13.12.1 The prllel xis theorem 13.12.2 The perpendiculr xis theorem 13.12.3 The rdius of grtion
More information