BOARD QUESTION PAPER : MARCH 2016 GEOMETRY


 Eileen Stafford
 4 years ago
 Views:
Transcription
1 BOARD QUESTION PAPER : MARCH 016 GEOMETRY Time : Hours Total Marks : 40 Note: (i) Solve All questions. Draw diagram wherever necessary. (ii) Use of calculator is not allowed. (iii) Diagram is essential for writing the proof of the theorem. (iv) Marks of constructions should be distinct. They should not be rubbed off. Q.1. Attempt any five of the following subquestions: [5] (1) DEF ~ MNK. If DE 5. MN 6, then find the value of A( DEF). A( MNK) () In the adjoining figure, in ABC, B 90 O, C60 O, A0 O, AC 18 cm. Find BC. () In the adjoining figure, m(arc PMQ) 10 o, find PQS. 0 (4) If the angle θ 60, find the value of cos θ. (5) Find the slope of the line with inclination 0 o. (6) Using Euler s formula, find V if E 0, F 1. Q.. Solve any four subquestions: [8] (1) In the following figure, in PQR, is the bisector of PRQ. If PS 6, SQ 8, PR 15, find QR. () In the following figure, a tangent segment PA touching a circle in A and a scant PBC shown. If AP 15, BP 10, find BC. () Draw an equilateral ABC with side 6. cm and construct is circumcircle. (4) For the angle in standard position if the initial arm rotates 5 o in anticlockwise direction, then state the quadrant in which terminal arm leis. (Draw the figure and write the answer.) (5) Find the area of sector whose arc length and radius are 10 cm and 5 cm respectively.
2 (6) Find the surface area of a sphere of radius 4. cm. π Q.. Attempt any three of the following subquestion: [9] (1) Adjacent sides of a parallelogram are 11 cm and 17 cm. of the length of one its diagonal is 6 cm, find the length of the other. () In the following figure, secants containing chords RS and PQ of a circle intersects each other in point A in the exterior of a circle. If m(arc PCR) 6 o, m(arc QDS) 48 o, then find. () Draw a circle of radius.5 cm. take any point K on it. Draw a tangent to the circle at K without using centre of the circle. (4) If sec α, then find the value of 1 cos 1+ cos 7 ec α, where α is in IV quadrant. ec α (5) Write the equation of the line passing through the pair of pints (, ) and (4, 7) in the form of y m x + c. Q.4. Attempt any two of the following subquestions: [8] (1) Prove that The length of the two tangent segments to a circle drawn from an external point are equal. () A Person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60 o. When he movies 40 m away from the bank, he finds the angle of elevation to be 0 o. Find the height of the tree and width of the river. ( 1.7) () A(5, 4), B(, ) and C(1, 8) are the vertices of a triangle ABC. Find the equations of median AD and line parallel to AC passing through the point B. Q.5. Attempt any two of the following subquestions: [10] (1) In the following figure, AE EF AF BE CF a, AT BC. Show that AB AC a. () SHR SVU. In SHR, SH 4.5 cm, HR HR 5. cm, SR 5.8 cm and SV 5. Construct SVU. () Water flows at the rate of 15 m per minute through a cylindrical pipe, having the diameter 0 mm. how much time will it take to fill a conical vessel of base diameter 40 cm and depth 45 cm?
3 BOARD ANSWER PAPER : MARCH 016 GEOMETRY Q.1. Attempt any five of the following subquestions: [5] (1) Solution: DEF ~ MNK () Solution: A( DEF) DE A( MNK) MN... (Given) ( 5 ) ( 6 ) A( DEF ) 5 A( MNK ) 6 In ABC, B 90 o, C 60 o, A 0 o... (Given) BC 1 AC... (Side opposite to 0 o )... (Ratio of areas of similar s ratio of squares of the corresponding sides.) BC 1 18 BC 9 cm. () Solution: m PQS 1 m( arc PMQ )... (Tangent  secant Th.) m PQS 1 10 (4) Solution: m PQS 60 o cos θ cos ( 60 o ) cos 60 o o cos 1 (5) Solution: Inclination (θ) 0 slope of line (m) tan θ 0 1 m tan 0 slope of line is 1
4 (6) Solution: Since solid figure is prism (polyhedron) By Eulers formula, F + V E 1 + V V V + 18 V 0 Q.. Attempt any four of the following subquestions: [8] (1) Solution: In PQR, seg RS bisects PRQ... (Given) PS PR... (Angle bisector property) QS QR QR QR QR 0 () Solution: Ray PA is a tangent and PBC is a secant PA PB PC [Tangent secant property] ( 15) 10 PC 10PC 5 PC 5 10 PC.5 PB + BC.5... (P  B  C) 10 + BC.5 BC.5 10 BC 1.5 () Solution: Steps of construction (a) To draw ABC. (b) To draw perpendicular bisectors of seg AC and seg BC intersecting at O. (c) To draw circumcircle.
5 (4) Solution: If the initial arm rotates 5 0 in anticlockwise direction, the terminal arm lies in I quadrant. 0 y 5 x (5) Solution: 1 Area of sector r length of arc cm The Area of sector is 5 cm (6) Solution: Surface area of a sphere 4πr cm The Total surface area of a sphere is 1.76 cm Q.. Attempt any three of the following subquestion: [9] (1) Solution : ABCD is a m AD 11 cm, AB 17 cm Diagonal AC 6 cm In a parallelogram diagonals bisect each other. O is the mid  point of AC and BD AO 1 AC In ADB, seg AO is the median By Apollonius principle, AB + AD AO + BO ( ) ( ) ( ) cm BO BO ( ) BO BO 7 BO BO 6 BO 6 BD BO 6 1 length of the other diagonal is 1 cm. 11 cm B A O 17 cm C D
6 () Solution : i) PQR 1 marcpcr ( )... (Inscribed angle Th.) 1 o o 6 1 ii) SPQ 1 marcsdq ( )... (Inscribed angle Th.) 1 o o 48 4 iii) SPQ SRQ... (Angles inscribed in the same arc) SRQ 4 o SRQ is an exterior angle of ARQ. () Solution : SRQ RAQ + RQA... (Remote interior angle Th.) 4 o RAQ + 1 o RAQ 11 o Steps of construction : (i) (ii) Draw a circle with.5 cm radius. Marks point K on the circle, draw chord KQ. (iii) Mark point P on the major segment. (iv) At K draw QKM congruent to QPK. (4) Solution : Line KM is tangent to the circle at K. As α is in IV quadrant is a negative acute angle x is positive & y is negative cos α and sec α are positive 1) 1 + tan α sec α [Identity] tan α sec α tanα 1 [Taking square root on both sides] 1 tan α [α is in IV quadrant]
7 ) cotα cotα 1 tanα 1 1 [Relation] cot α ) 1 + cot α cosec α [Identity] 1 + ( ) cosec α 1 + cosec α 4 cosec α cosecα cosecx The value of [Taking square root on both sides].[α is in IV quadrant] 1 cosecα 1 ( ) [Substituting the values] 1+ cos ecα 1 + ( ) 1 1 cosecα 1+ cos ecα (5) Solution: Let P (, ) (x1,y1), Q (4,7) (x, y) Since the line passes through points P and Q Equation of line in two point form is x x1 y y1 x x y y 1 1 x y 4 7 x y 4 (x ) y 4 4 (x ) y x 4 y x 4 + y x 1 y y x 1 Equation of line is y x 1.
8 Q.4. Attempt any two of the following subquestions: [8] (1) Solution : Given : A circle with centre O, an external point P of the circle. The two tangents through the point P touches the circle at the points A and B. O To prove : PA PB Construction : Draw seg OA, seg OB and seg OP. Proof : PAO PBO... (Radius is perpendicular to tangent) In the right angled PAO and the right angled PBO. Seg OA seg OB... (Radii of same circle) hypotenuse PO hypotenuse PO... (common side) PAO PBO... (Hypotenuse side theorem) seg PA seg PB... (c.s.c.t) PA PB Hence, the length of the two tangent segments to a circle drawn from an external point are equal. A B P () Solution: In the given figure, AB represents the height of the tree & BC represents the width of the river. The person at the beginning is at point C observing the top of the tree & making an angle of elevation. moving 40m away again makes an angle of elevation with the top of tree. ACB & ADB is an angle of elevation ACB 60 0 & BC x BD BC + CD (BCD) 1) BD (x + 40)m ) In ABC, ABC 90 0 & ACB 60 0 ) tan θ AB BC θ 60 0 D 0 60 C x A y B tan 60 y x y [ tan60 ] x x 4) In ABD y (i) ADB 0 0 & ABD 90 0 θ 0 0 5) tanθ AB BD tan0 y x + 40
9 6) 1 y x 40 + x + 40 y (ii) x + 40 x [from (i) & (ii)] x x + 40 x x 40 x 0 Substituting x 0 in eqn (i) [ tan0 ] x y 0 y y 17. y 4.6 y Height of tree 4.6 m & Width of river 0 m () Solution: A (5,4), B (, ), C (l, 8) seg AD is the median D is the midpoint of BC By midpoint formula D, 10 D, D ( 1, 5) For median AD, Let A (5, 4) (x1, y1), D ( 1, 5) (x, y) Equation of median AD in two point form is x x y y x x y y x 5 y 4 5 ( 1) 4 ( 5) x 5 y x 5 y (x 5) 6(y 4) 9x 45 6y 4
10 9x 6y x 6y 1 0 x y (divide by ) Equation of median AD is x y 7 0 Slope of line AC slope of line AC line BP line AC slope of line BP slope of line AC slope of line BP (m) For line BP,... [given] Equation of line BP with slope (m) and passing through point B(, ) (x1, y1) in slope point form is y y1 m(x x1) y ( ) [x ( )] y + (x + ) y + x + 9 x + y x + y 7 0 x y Equation of line parallel to AC is x y Q.5. Attempt any two of the following subquestions: [10] (1) Solution: Given: Proof: AT BC. AE EB AF RN FC a. To Prove : AB BC a. In ABF, EB EF a [Given] E is the midpoint of BF (i). AE is a median. [From (i)]. AB + AF AE + EB [By Appollonius Theorem] AB + a a + a AB + a 4a AB 4a a AB a AB a AB a. (ii)
11 Similarly, we can prove AC.a AB AC.a () Solution: (Analytical Figure) (iii) (From (ii) & (iii)) (Required triangle) () Solution : Cylindrical pipe, d 0 mm, r 10 mm 1 cm Rate of water flow 15 m / min h 1500 cm / min Conical vessel, D 40 cm R 0 cm and H 45 cm Let the conical vessel be filled in x minutes. Volume of water flowing through cylindrical pipe in x min. Volume of conical vessel 45 cm d 40 cm πr h x 1 πr H x x 1500 x 4 minutes. It will take 4 minutes to fill the conical vessel.
Maharashtra State Board Class X Mathematics  Geometry Board Paper 2016 Solution
Maharashtra State Board Class X Mathematics  Geometry Board Paper 016 Solution 1. i. ΔDEF ΔMNK (given) A( DEF) DE A( MNK) MN A( DEF) 5 5 A( MNK) 6 6...(Areas of similar triangles) ii. ΔABC is 060 90
More informationTime : 2 Hours (Pages 3) Max. Marks : 40. Q.1. Solve the following : (Any 5) 5 In PQR, m Q = 90º, m P = 30º, m R = 60º. If PR = 8 cm, find QR.
Q.P. SET CODE Q.1. Solve the following : (ny 5) 5 (i) (ii) In PQR, m Q 90º, m P 0º, m R 60º. If PR 8 cm, find QR. O is the centre of the circle. If m C 80º, the find m (arc C) and m (arc C). Seat No. 01
More informationBOARD ANSWER PAPER :OCTOBER 2014
BRD NSWER PPER :CTBER 04 GEETRY. Solve any five subquestions: BE i. BE ( BD) D BE 6 ( BD) 9 ΔBE (ΔBD) [Ratio of areas of two triangles having equal base is equal to the ratio of their corresponding
More informationSolved Paper SSC Maharashtra Exam March 207 Class  X Geometry Time : 2 Hours Max. Marks : 40 Note : (i) Solve all questions. Draw diagrams wherever necessary. (ii) Use of calculator is not allowed. (iii)
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 informationMaharashtra State Board Class X Mathematics Geometry Board Paper 2015 Solution. Time: 2 hours Total Marks: 40
Maharashtra State Board Class X Mathematics Geometry Board Paper 05 Solution Time: hours Total Marks: 40 Note: () Solve all questions. Draw diagrams wherever necessary. ()Use of calculator is not allowed.
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 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 informationTopic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths
Topic 2 [312 marks] 1 The rectangle ABCD is inscribed in a circle Sides [AD] and [AB] have lengths [12 marks] 3 cm and (\9\) cm respectively E is a point on side [AB] such that AE is 3 cm Side [DE] is
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 information0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.
0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,
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 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 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 informationGeometry 3 SIMILARITY & CONGRUENCY Congruency: When two figures have same shape and size, then they are said to be congruent figure. The phenomena between these two figures is said to be congruency. CONDITIONS
More information0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?
0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30
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 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 informationMT  GEOMETRY  SEMI PRELIM  I : PAPER  4
07 00 MT A.. Attempt ANY FIVE of the following : (i) Slope of the line (m) 4 y intercept of the line (c) 0 By slope intercept form, The equation of the line is y m + c y (4) + (0) y 4 MT  GEOMETRY  SEMI
More informationchapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
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 informationMT  MATHEMATICS (71) GEOMETRY  PRELIM II  PAPER  6 (E)
04 00 Seat No. MT  MTHEMTIS (7) GEOMETRY  PRELIM II  (E) Time : Hours (Pages 3) Max. Marks : 40 Note : ll questions are compulsory. Use of calculator is not allowed. Q.. Solve NY FIVE of the following
More informationMT  GEOMETRY  SEMI PRELIM  I : PAPER  1
07 00 MT A.. Attempt ANY FIVE of the following : (i) Slope of the line (m) 5 intercept of the line (c) B slope intercept form, The equation of the line is m + c 5 () + ( ) 5 MT  GEOMETRY  SEMI PRELIM
More informationIt is known that the length of the tangents drawn from an external point to a circle is equal.
CBSE MATHSSET 12014 Q1. The first three terms of an AP are 3y1, 3y+5 and 5y+1, respectively. We need to find the value of y. We know that if a, b and c are in AP, then: b a = c b 2b = a + c 2 (3y+5)
More informationMathematics Class X Board Paper 2011
Mathematics Class X Board Paper Solution Section  A (4 Marks) Soln.. (a). Here, p(x) = x + x kx + For (x) to be the factor of p(x) = x + x kx + P () = Thus, () + () k() + = 8 + 8  k + = k = Thus p(x)
More informationSOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)
1. (A) 1 1 1 11 1 + 6 6 5 30 5 5 5 5 6 = 6 6 SOLUTIONS SECTION A. (B) Let the angles be x and 3x respectively x+3x = 180 o (sum of angles on same side of transversal is 180 o ) x=36 0 So, larger angle=3x
More informationTriangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z.
Triangles 1.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm. (B) 17 cm. (C) 23 cm. of these. 2.Can 80, 75 and 20 form a triangle?
More informationBOARD ANSWER PAPER : MARCH 2015 ALGEBRA
BOARD ANSWER PAPER : MARCH 015 ALGEBRA Algebra Q.1. Attempt any five of the following subquestions: i. The given sequence is 1, 4, 7, 10, Here, t 1 = 1, t = 4, t 3 = 7, t 4 = 10 t t 1 = 4 1 = 3 t 3 t
More informationRao IIT Academy/ SSC  Board Exam 2018 / Mathematics CodeA / QP + Solutions JEE MEDICALUG BOARDS KVPY NTSE OLYMPIADS SSC  BOARD
Rao IIT cademy/ SSC  oard Exam 018 / Mathematics Code / QP + Solutions JEE MEDICLUG ORDS KVPY NTSE OLYMPIDS SSC  ORD  018 Date: 1.0.018 MTHEMTICS  PPER  SOLUTIONS Q.1 ttempt any FIVE of the following
More information1 / 23
CBSEXII07 EXAMINATION CBSEX009 EXAMINATION MATHEMATICS Series: HRL Paper & Solution Code: 0/ Time: Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question paper
More information= 9 4 = = = 8 2 = 4. Model Question paperi SECTIONA 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 paperi SECTIONA 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 SECTIONB 16. P a, b, c, Q g,, x, y, R {a, e, f, s} R\ P Q {a,
More informationTRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions
CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)
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 information1 / 23
CBSEXII017 EXAMINATION CBSEX008 EXAMINATION MATHEMATICS Series: RLH/ Paper & Solution Code: 30//1 Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question
More information0114ge. Geometry Regents Exam 0114
0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?
More informationCBSE CLASS X MATH SOLUTION Therefore, 0.6, 0.25 and 0.3 are greater than or equal to 0 and less than or equal to 1.
CBSE CLASS X MATH SOLUTION 011 Q1 The probability of an event is always greater than or equal to zero and less than or equal to one. Here, 3 5 = 0.6 5% = 5 100 = 0.5 Therefore, 0.6, 0.5 and 0.3 are greater
More information0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
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 informationTriangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?
Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel
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 24AD 2 (D) 4AD 23AC 2 2.Which of the following statement is true? Any two right triangles are similar
More informationCBSE Class X Mathematics Board Paper 2019 All India Set 3 Time: 3 hours Total Marks: 80
CBSE Class X Mathematics Board Paper 2019 All India Set 3 Time: 3 hours Total Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided
More informationSSC EXAMINATION GEOMETRY (SETA)
GRND TEST SS EXMINTION GEOMETRY (SET) SOLUTION Q. Solve any five subquestions: [5M] ns. ns. 60 & D have equal height ( ) ( D) D D ( ) ( D) Slope of the line ns. 60 cos D [/M] [/M] tan tan 60 cos cos
More informationCBSE CLASS10 MARCH 2018
CBSE CLASS10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION & ANSWER Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four
More informationSimilarity of Triangle
Similarity of Triangle 95 17 Similarity of Triangle 17.1 INTRODUCTION Looking around you will see many objects which are of the same shape but of same or different sizes. For examples, leaves of a tree
More information0811ge. Geometry Regents Exam
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationQuestion 1 ( 1.0 marks) places of decimals? Solution: Now, on dividing by 2, we obtain =
Question 1 ( 1.0 marks) The decimal expansion of the rational number places of decimals? will terminate after how many The given expression i.e., can be rewritten as Now, on dividing 0.043 by 2, we obtain
More informationSM2H Unit 6 Circle Notes
Name: Period: SM2H Unit 6 Circle Notes 6.1 Circle Vocabulary, Arc and Angle Measures Circle: All points in a plane that are the same distance from a given point, called the center of the circle. Chord:
More informationPage 1 of 15. Website: Mobile:
Exercise 10.2 Question 1: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5
More informationSAMPLE QUESTION PAPER Summative Assessment II ClassX ( ) Mathematics. Time Allowed: 3 Hours Max. Marks: 90
SAMPLE QUESTION PAPER Summative Assessment II ClassX (2016 17) Mathematics Time Allowed: 3 Hours Max. Marks: 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of31
More information2012 GCSE Maths Tutor All Rights Reserved
2012 GCSE Maths Tutor All Rights Reserved www.gcsemathstutor.com This book is under copyright to GCSE Maths Tutor. However, it may be distributed freely provided it is not sold for profit. Contents angles
More information2005 Palm Harbor February Invitational Geometry Answer Key
005 Palm Harbor February Invitational Geometry Answer Key Individual 1. B. D. C. D 5. C 6. D 7. B 8. B 9. A 10. E 11. D 1. C 1. D 1. C 15. B 16. B 17. E 18. D 19. C 0. C 1. D. C. C. A 5. C 6. C 7. A 8.
More informationPractice Test Student Answer Document
Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
More information0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.
Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would
More informationPart (1) Second : Trigonometry. Tan
Part (1) Second : Trigonometry (1) Complete the following table : The angle Ratio 42 12 \ Sin 0.3214 Cas 0.5321 Tan 2.0625 (2) Complete the following : 1) 46 36 \ 24 \\ =. In degrees. 2) 44.125 = in degrees,
More informationMT  GEOMETRY  SEMI PRELIM  I : PAPER  2
07 00 MT MT  GEOMETRY  SEMI PRELIM  I : PAPER  Time : Hours Model Answer Paper Ma. Marks : 40 A.. Attempt ANY FIVE of the following : (i) Slope of the line (m) 4 intercept of the line (c) 3 B slope
More informationCHAPTER 7 TRIANGLES. 7.1 Introduction. 7.2 Congruence of Triangles
CHAPTER 7 TRIANGLES 7.1 Introduction You have studied about triangles and their various properties in your earlier classes. You know that a closed figure formed by three intersecting lines is called a
More informationVKR Classes TIME BOUND TESTS 17 Target JEE ADVANCED For Class XI VKR Classes, C , Indra Vihar, Kota. Mob. No
VKR Classes TIME BOUND TESTS 7 Target JEE ADVANCED For Class XI VKR Classes, C90, Indra Vihar, Kota. Mob. No. 9890605 Single Choice Question : PRACTICE TEST. The smallest integer greater than log +
More information3. AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is:
Solved Paper 2 Class 9 th, Mathematics, SA 2 Time: 3hours Max. Marks 90 General Instructions 1. All questions are compulsory. 2. Draw neat labeled diagram wherever necessary to explain your answer. 3.
More information1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM.
1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM. 2. Let ABCD be a cyclic quadrilateral inscribed in a circle
More information1 / 22
CBSEXII017 EXAMINATION MATHEMATICS Paper & Solution Time: 3 Hrs. Max. Marks: 90 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 31 questions divided into
More informationMathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions
Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Quiz #1. Tuesday, 17 January, 2012. [10 minutes] 1. Given a line segment AB, use (some of) Postulates I V,
More informationClass X Delhi Math Set3 Section A
Class X Delhi Math Set3 Section A 1. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30. The distance of the car from the base of the tower (in m.) is:
More informationCBSE Board Class X Mathematics
CBSE Board Class X Mathematics Time: 3 hrs Total Marks: 80 General Instructions: 1. All questions are compulsory.. The question paper consists of 30 questions divided into four sections A, B, C, and D.
More information0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.
0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD
More informationClass X Mathematics Sample Question Paper Time allowed: 3 Hours Max. Marks: 80. SectionA
Class X Mathematics Sample Question Paper 089 Time allowed: Hours Max. Marks: 80 General Instructions:. All the questions are compulsory.. The questions paper consists of 0 questions divided into sections
More information0612ge. Geometry Regents Exam
0612ge 1 Triangle ABC is graphed on the set of axes below. 3 As shown in the diagram below, EF intersects planes P, Q, and R. Which transformation produces an image that is similar to, but not congruent
More informationImportant Instructions for the School Principal. (Not to be printed with the question paper)
Important Instructions for the School Principal (Not to be printed with the question paper) 1) This question paper is strictly meant for use in school based SAII, March2012 only. This question paper
More informationAREAS OF PARALLELOGRAMS AND TRIANGLES
AREAS OF PARALLELOGRAMS AND TRIANGLES Main Concepts and Results: The area of a closed plane figure is the measure of the region inside the figure: Fig.1 The shaded parts (Fig.1) represent the regions whose
More information( )( ) PR PQ = QR. Mathematics Class X TOPPER SAMPLE PAPER1 SOLUTIONS. HCF x LCM = Product of the 2 numbers 126 x LCM = 252 x 378
Mathematics Class X TOPPER SAMPLE PAPER SOLUTIONS Ans HCF x LCM Product of the numbers 6 x LCM 5 x 378 LCM 756 ( Mark) Ans The zeroes are, 4 p( x) x + x 4 x 3x 4 ( Mark) Ans3 For intersecting lines: a
More informationMaharashtra State Board Class IX Mathematics Geometry Board Paper 1 Solution
Maharashtra State Board Class IX Mathematics Geometry Board Paper Solution Time: hours Total Marks: 40. i. Let the measure of each interior opposite angle be x. Since, Sum of two interior opposite angles
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) Nonintersecting line: The line AB and the circle
More informationSURA's Guides for 3rd to 12th Std for all Subjects in TM & EM Available. MARCH Public Exam Question Paper with Answers MATHEMATICS
SURA's Guides for rd to 1th Std for all Subjects in TM & EM Available 10 th STD. MARCH  017 Public Exam Question Paper with Answers MATHEMATICS [Time Allowed : ½ Hrs.] [Maximum Marks : 100] SECTION 
More informationUNIT8 SIMILAR TRIANGLES Geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art. 1. ABC is a rightangled triangle, rightangled
More informationCAREER POINT PRE FOUNDATION DIVISON CLASS9. IMO StageII Exam MATHEMATICS Date :
CAREER POINT PRE FOUNDATION DIVISON IMO StageII Exam.07 CLASS9 MATHEMATICS Date : 007 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 information1 / 24
CBSEXII017 EXAMINATION CBSEX01 EXAMINATION MATHEMATICS Paper & Solution Time: 3 Hrs. Max. Marks: 90 General Instuctions : 1. All questions are compulsory.. The question paper consists of 34 questions
More information1 / 23
CBSEXII07 EXAMINATION CBSEX00 EXAMINATION MATHEMATICS Series: LRH/ Paper & Solution Code: 30// Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question
More information1 What is the solution of the system of equations graphed below? y = 2x + 1
1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x
More information[ClassX] MATHEMATICS SESSION:
[ClassX] MTHEMTICS SESSION:01718 Time allowed: 3 hrs. Maximum Marks : 80 General Instructions : (i) ll questions are compulsory. (ii) This question paper consists of 30 questions divided into four sections,
More information= 0 1 (3 4 ) 1 (4 4) + 1 (4 3) = = + 1 = 0 = 1 = ± 1 ]
STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. If the lines x + y + = 0 ; x + y + = 0 and x + y + = 0, where + =, are concurrent then (A) =, = (B) =, = ± (C) =, = ± (D*) = ±, = [Sol. Lines are x + y + = 0
More informationMathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2.
() Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2. If EF = 15.4 cm, find BC. Answer 1: 1 () Question 2: Diagonals of a trapezium ABCD with AB DC intersect each other
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 informationHonors Geometry MidTerm Exam Review
Class: Date: Honors Geometry MidTerm Exam Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Classify the triangle by its sides. The
More informationMathematics. A basic Course for beginers in G.C.E. (Advanced Level) Mathematics
Mathematics A basic Course for beginers in G.C.E. (Advanced Level) Mathematics Department of Mathematics Faculty of Science and Technology National Institute of Education Maharagama Sri Lanka 2009 Director
More informationC=2πr C=πd. Chapter 10 Circles Circles and Circumference. Circumference: the distance around the circle
10.1 Circles and Circumference Chapter 10 Circles Circle the locus or set of all points in a plane that are A equidistant from a given point, called the center When naming a circle you always name it by
More informationMATHS QUESTION PAPER CLASSX (MARCH, 2011) PARTA
MATHS QUESTION PAPER CLASSX (MARCH, 011) PARTA Time : 75 minutes Maximum Marks : 50 Instructions : (1) There are 50 objective typequestions in this part and all are compulsory. () The questions are
More informationCBSE MATHEMATICS (SET2)_2019
CBSE 09 MATHEMATICS (SET) (Solutions). OC AB (AB is tangent to the smaller circle) In OBC a b CB CB a b CB a b AB CB (Perpendicular from the centre bisects the chord) AB a b. In PQS PQ 4 (By Pythagoras
More informationRMT 2013 Geometry Test Solutions February 2, = 51.
RMT 0 Geometry Test Solutions February, 0. Answer: 5 Solution: Let m A = x and m B = y. Note that we have two pairs of isosceles triangles, so m A = m ACD and m B = m BCD. Since m ACD + m BCD = m ACB,
More informationQUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)
QUESTION BANK ON CONIC SECTION (Parabola, Ellipse & Hyperbola) Question bank on Parabola, Ellipse & Hyperbola Select the correct alternative : (Only one is correct) Q. Two mutually perpendicular tangents
More informationMATHEMATICS. IMPORTANT FORMULAE AND CONCEPTS for. Summative Assessment II. Revision CLASS X Prepared by
MATHEMATICS IMPORTANT FORMULAE AND CONCEPTS for Summative Assessment II Revision CLASS X 06 7 Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist (Elect.), B. Ed. Kendriya Vidyalaya GaCHiBOWli
More information0609ge. Geometry Regents Exam AB DE, A D, and B E.
0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible
More informationTrans Web Educational Services Pvt. Ltd B 147,1st Floor, Sec6, NOIDA, UP
Solved Examples Example 1: Find the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4, x + 2y = 5. Method 1. Consider the equation (x + y 6) (2x + y 4) + λ 1
More information(A) 50 (B) 40 (C) 90 (D) 75. Circles. Circles <1M> 1.It is possible to draw a circle which passes through three collinear points (T/F)
Circles 1.It is possible to draw a circle which passes through three collinear points (T/F) 2.The perpendicular bisector of two chords intersect at centre of circle (T/F) 3.If two arcs of a circle
More informationMaharashtra Board Class IX Mathematics (Geometry) Sample Paper 3 Solution
Maharashtra Board Class IX Mathematics (Geometry) Sample Paper Solution Time: hours Total Marks: 40. i. Three sides of an equilateral triangle are congruent. Perimeter of an equilateral triangle = side
More informationSo, eqn. to the bisector containing (1, 4) is = x + 27y = 0
Q.No. The bisector of the acute angle between the lines x  4y + 7 = 0 and x + 5y  = 0, is: Option x + y  9 = 0 Option x + 77y  0 = 0 Option x  y + 9 = 0 Correct Answer L : x  4y + 7 = 0 L :x 5y
More informationHigher Order Thinking Skill questions
Higher Order Thinking Skill questions TOPIC Constructions (Class X) 1. Draw a triangle ABC with sides BC = 6.3cm, AB = 5.2cm and ÐABC = 60. Then construct a triangle whose sides are times the corresponding
More informationMATHEMATICS. Time allowed : 3 hours Maximum Marks : 100 QUESTION PAPER CODE 30/1/1 SECTION  A
MATHEMATICS Time allowed : 3 hours Maximum Marks : 100 GENERAL INSTRUCTIONS : 1. All questions are compulsory 2. The question paper consists of 30 questions divided into four sections  A, B, C and D.
More informationICSE QUESTION PAPER Class X Maths (2016) Solution
ICSE QUESTION PAPER Class X Maths (016) Solution SECTION A 1. (a) Let f(x) x x kx 5 Using remainder theorem, f() 7 () () k() 5 7 (8) (4) k() 5 7 16 1 k 5 7 k 16 1 5 7 k 6 k 1 (b) A = 9A + MI A 9A mi...
More informationObjective Mathematics
. A tangent to the ellipse is intersected by a b the tangents at the etremities of the major ais at 'P' and 'Q' circle on PQ as diameter always passes through : (a) one fied point two fied points (c) four
More informationTriangles. Chapter Flowchart. The Chapter Flowcharts give you the gist of the chapter flow in a single glance.
Triangles Chapter Flowchart The Chapter Flowcharts give you the gist of the chapter flow in a single glance. Triangle A plane figure bounded by three line segments is called a triangle. Types of Triangles
More information1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.
1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)
More information