Time : 3 hours 02 - Mathematics - July 2006 Marks : 100 Pg - 1 Instructions : S E CT I O N - A

Size: px
Start display at page:

Download "Time : 3 hours 02 - Mathematics - July 2006 Marks : 100 Pg - 1 Instructions : S E CT I O N - A"

Transcription

1 Time : 3 hours 0 Mathematics July 006 Marks : 00 Pg Instructions :. Answer all questions.. Write your answers according to the instructions given below with the questions. 3. Begin each section on a new page. S E CT I O N A Given below are to 5 multiple choice questions. Each carries one mark. Write the serial number ( a or b or c or d ) in your answer book of the alternative which you feel is the correct answer of the question.. d [ ( l 7 l, 8 ), ( l 7 l, 3 ) ] =? ( a ) 5 ( b ) ( c ) 5 ( d ). The Cartesian equation of the line passing through ( 5, 6 ) and ( 3, 6 ) is ( a ) y 6 = 0 ( b ) y + 6 = 0 ( c ) 5 = 0 ( d ) + 3 = 0 3. The equation of the circle touching the y ais and having its centre at ( 3, 4 ) is ( a ) + y y + 6 = 0 ( b ) + y 6 + 8y + 9 = 0 ( c ) + y 6 8y + 9 = 0 ( d ) + y 6 + 8y + 6 = 0 4. The end points of the latus rectum for parabola = 6y are 3 3 ( a ) ± 3, ( b ), 3 ( c ) 3, 3 ( d ) 3 ± 3, 5. Measure of the angle between asymptotes of 4 y = 9 is 4 ( a ) tan 4 ( b ) tan 4 ( c ) ( d ) tan Which is a unit vector? ( a ) ( cosα, sinα ) ( b ) (sinα, cosα ) ( c ) (, ) ( d ) (cosα, sinα ) 7. = (, ) and y = (, 0 ), then cos ^ y = ( a ) ( b ) 0 ( c ) ( d ) y 8. Measure of the angle between + y + z = and r = ( 0, 0, 0 ) + k (,, ), k R is ( a ) ( b ) ( c ) ( d ) 6 3 4

2 Time : 3 hours 0 Mathematics July 006 Marks : 00 Pg 9. The plane r. (,, ) = touches the sphere + y + z 4y + z 3 = 0, then the point of contact is ( a ) (, 4, ) ( b ) (, 4, ) ( c ) (, 4, ) ( d ) none of these 0. 4 e e lim 4 4 ( a ) 4e ( b ) =? e 4 ( c ) 4e ( d ) log e 4. The derivative of sin with respect to cos is ( a ) ( b ) ( c ) 0 ( d ) none of these. Radius of a circular metal plate, when heated, increases by %. If its radius is 0 cm., then the increase in its area is ( a ) 4 cm ( b ) 4 cm ( c ) 0 cm ( d ) cm 3. 0 l l = ( a ) ( b ) ( c ) ( d ) none of these 4. The degree and order of the differential equation d y dy = + are ( a ) 6 and ( b ) 3 and ( c ) and ( d ) and 5. A body projected in vertical direction attains maimum height 50 m. Its velocity at 5 m height is ( a ) 7 0 m/s ( b ) 7 0 m/s ( c ) 7 0 m/s ( d ) 490 m S E C T I O N B Answer the following 6 to 30 questions. Each question carries one mark In which ratio does the ais divide the line segment joining A ( 3, 5 ) and B (, 6 )? 7. Obtain the equation of the circle which has a diagonal of rectangle formed by =, =, y = 3 and y =. Obtain the equation of a circle with radius 5/, if it passes through (, ) and (, 4).

3 Time : 3 hours 0 Mathematics July 006 Marks : 00 Pg 3 8. There is a point on the parabola y = whose coordinate is two times the y coordinate. If this point is not the verte of the parabola, find the point. y 9. Find the parametric equation of the director circle of the ellipse + = Find a unit vector orthogonal to both (,, ) and ( 3,, ).. Find the projection of (,, ) on (,, ).. Find the perpendicular distance of the point P ( 4, 5, 3 ) from the line 5 y + z 6 = = d 3 ( ) Find d 006 loge e 3. Find ( sin ). e 4. Evaluate Find the area of the region bounded by the curve y = cos, ais and the lines = 0 and =. 6. Evaluate tan sec Evaluate Evaluate ( cosec sec + ), l l. 8. Obtain the differential equation representing all the lines of family y = m + c ( where m and c are arbitrary constants ). 9. If the distance of a particle eecuting rectilinear motion is from a fied point at time t, where = t 3 9t + t + 8, then when will the velocity become Two balls are thrown vertically upwards with velocities 9.6 m/s and 9.8 m/s. Find the height of the second ball, when the first ball attains maimum height.

4 Time : 3 hours 0 Mathematics July 006 Marks : 00 Pg 4 S EC T I O N C Answer the following 3 to 40 questions as directed. Each question carries two marks Prove by using slopes that A (, 8 ) B (, 6 ) and C ( 6, 0 ) are the vertices of a right triangle. Find the equation of the perpendicular bisector of AB where A is ( 3, ) and B is ( 7, 6 ). 3. For the parabola = y, find the area of the triangle whose vertices are the verte of the parabola and two end points of its latus rectum. 33. If the end points of a chord of the ellipse b + a y a b = 0 have eccentric angles with measure α and β, then prove that the equation of the line containing the chord is α + β y α + β α β cos + sin = cos. a b y 34. If the eccentricities of = ± are e and e respectively, then prove that a b e + e = e. e. If the chord of hyperbola joining P ( α ) and Q ( β ) on the hyperbola subtends a right angle at the centre C ( 0, 0 ), then prove that a + b sinα sinβ = Prove that : [ + y y + z z + ] = [ y z ]. 36. If, y, z are coplanar vectors, then prove that + y, y + z, and z + are coplanar. If ( + y ). ( y ) = 63 and l l = 8 l y l, then find l l. 37. Get the radius of the circle that is the intersection of the sphere + y + z = 49 and the plane + 3y z = If = a ( cosθ ), y = a ( θ sinθ ), θ [ 0, ], a 0, then find d y.

5 Time : 3 hours 0 Mathematics July 006 Marks : 00 Pg Verify Rolle s theorem for f ( ) = sin + cos, 0,. If it is applicable, find c. In which interval the function f ( ) = is increasing and in which interval is it decreasing? sin 40. Evaluate. + sin S E C T I O N D Answer the following 4 to 50 questions as directed. Each question carries 3 marks A is (, 0 ) and B is (, 0 ). If l AP PB l = 4, then find the equation of locus of P. Origin is circumcentre of triangle with vertices A (, tan ), B (, tan ) and C (, tan ) ( 0 < θ I < /, i > 0, i =,, 3 ). θ θ 3 3 θ3 y sin θ + sin θ + sin θ3 If the centroid of Δ ABC is (, y ), prove that =. cos θ + cosθ + cosθ3 4. If the equation 3 + ( 3 p ) y + qy p = 8pq represents a circle, find p and q. Also determine the centre and radius of the circle. 43. Forces measuring 5, 3 and unit act in the direction ( 6,, 3 ), ( 3,, 6 ), (, 3, 6 ) respectively. As a result, the particle moves from (,, 3 ) to ( 5,, ). Find the resultant force and work done. 44. Find the vector and Cartesian equations of the line passing through (,, 3 ) and perpendicular to the two lines y z r = ( 0, 0, 0 ) + K (,, ), K R and = =. 3 6 Find the measure of the angle between two lines, if their direction cosines l, m, n satisfy l + m + n = 0, l + m n = Find the vector and Cartesian equations of the plane containing the lines y z 5 r = (,, 3 ) + K (, 3, 4 ), K R and = = Find lim cos ( sin ). tan ( sin )

6 Time : 3 hours 0 Mathematics July 006 Marks : 00 Pg Prove that if > 0, then < tan < Obtain sin as the limit of a sum Prove that = log dy 50. Solve y = y +. If y ( ) = 0, then find the particular solution of the given differential equation. The population of a city increases at the rate of 3 % per year. How many years will it take for the population to double? S E C T I O N E Answer the following 5 to 54 questions. Each question carries 5 marks A is ( 4, 5 ) in Δ ABC and the lines 5 + 3y 4 = 0 and 3 + 8y + 3 = 0 contain two of the altitudes of the triangle. Find the coordinates of B and C. 5. If f ( ) = e e e + e, 0, f ( 0 ) =, then prove that f is not continuous at = 0. ( + m) n ( + n) m Find lim, 0 m, n N. 53. If = sin t and y = sin pt, then prove that ( ) d y dy + p y = Evaluate + 5e + 6e sec Evaluate. + cosec

Objective Mathematics

Objective 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 information

Conic section. Ans: c. Ans: a. Ans: c. Episode:43 Faculty: Prof. A. NAGARAJ. 1. A circle

Conic section. Ans: c. Ans: a. Ans: c. Episode:43 Faculty: Prof. A. NAGARAJ. 1. A circle Episode:43 Faculty: Prof. A. NAGARAJ Conic section 1. A circle gx fy c 0 is said to be imaginary circle if a) g + f = c b) g + f > c c) g + f < c d) g = f. If (1,-3) is the centre of the circle x y ax

More information

PRACTICE PAPER 6 SOLUTIONS

PRACTICE PAPER 6 SOLUTIONS PRACTICE PAPER 6 SOLUTIONS SECTION A I.. Find the value of k if the points (, ) and (k, 3) are conjugate points with respect to the circle + y 5 + 8y + 6. Sol. Equation of the circle is + y 5 + 8y + 6

More information

IIT JEE Maths Paper 2

IIT JEE Maths Paper 2 IIT JEE - 009 Maths Paper A. Question paper format: 1. The question paper consists of 4 sections.. Section I contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for

More information

MULTIPLE CHOICE QUESTIONS SUBJECT : MATHEMATICS Duration : Two Hours Maximum Marks : 100. [ Q. 1 to 60 carry one mark each ] A. 0 B. 1 C. 2 D.

MULTIPLE CHOICE QUESTIONS SUBJECT : MATHEMATICS Duration : Two Hours Maximum Marks : 100. [ Q. 1 to 60 carry one mark each ] A. 0 B. 1 C. 2 D. M 68 MULTIPLE CHOICE QUESTIONS SUBJECT : MATHEMATICS Duration : Two Hours Maimum Marks : [ Q. to 6 carry one mark each ]. If sin sin sin y z, then the value of 9 y 9 z 9 9 y 9 z 9 A. B. C. D. is equal

More information

1 is equal to. 1 (B) a. (C) a (B) (D) 4. (C) P lies inside both C & E (D) P lies inside C but outside E. (B) 1 (D) 1

1 is equal to. 1 (B) a. (C) a (B) (D) 4. (C) P lies inside both C & E (D) P lies inside C but outside E. (B) 1 (D) 1 Single Correct Q. Two mutuall perpendicular tangents of the parabola = a meet the ais in P and P. If S is the focus of the parabola then l a (SP ) is equal to (SP ) l (B) a (C) a Q. ABCD and EFGC are squares

More information

QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)

QUESTION 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 information

63487 [Q. Booklet Number]

63487 [Q. Booklet Number] WBJEE - 0 (Answers & Hints) 687 [Q. Booklet Number] Regd. Office : Aakash Tower, Plot No., Sector-, Dwarka, New Delhi-0075 Ph. : 0-7656 Fa : 0-767 ANSWERS & HINTS for WBJEE - 0 by & Aakash IIT-JEE MULTIPLE

More information

y mx 25m 25 4 circle. Then the perpendicular distance of tangent from the centre (0, 0) is the radius. Since tangent

y mx 25m 25 4 circle. Then the perpendicular distance of tangent from the centre (0, 0) is the radius. Since tangent Mathematics. The sides AB, BC and CA of ABC have, 4 and 5 interior points respectively on them as shown in the figure. The number of triangles that can be formed using these interior points is () 80 ()

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.

( 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 information

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

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

More information

2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is

2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is . If P(A) = x, P = 2x, P(A B) = 2, P ( A B) = 2 3, then the value of x is (A) 5 8 5 36 6 36 36 2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time

More information

by Abhijit Kumar Jha

by Abhijit Kumar Jha SET I. If the locus of the point of intersection of perpendicular tangents to the ellipse x a circle with centre at (0, 0), then the radius of the circle would e a + a /a ( a ). There are exactl two points

More information

( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear.

( 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 information

TARGET QUARTERLY MATHS MATERIAL

TARGET QUARTERLY MATHS MATERIAL Adyar Adambakkam Pallavaram Pammal Chromepet Now also at SELAIYUR TARGET QUARTERLY MATHS MATERIAL Achievement through HARDWORK Improvement through INNOVATION Target Centum Practising Package +2 GENERAL

More information

QUESTION BANK ON STRAIGHT LINE AND CIRCLE

QUESTION 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 information

FIITJEE SOLUTION TO AIEEE-2005 MATHEMATICS

FIITJEE SOLUTION TO AIEEE-2005 MATHEMATICS FIITJEE SOLUTION TO AIEEE-5 MATHEMATICS. If A A + I =, then the inverse of A is () A + I () A () A I () I A. () Given A A + I = A A A A + A I = A (Multiplying A on both sides) A - I + A - = or A = I A..

More information

Trans Web Educational Services Pvt. Ltd B 147,1st Floor, Sec-6, NOIDA, UP

Trans Web Educational Services Pvt. Ltd B 147,1st Floor, Sec-6, 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

(c) n (d) n 2. (a) (b) (c) (d) (a) Null set (b) {P} (c) {P, Q, R} (d) {Q, R} (a) 2k (b) 7 (c) 2 (d) K (a) 1 (b) 3 (c) 3xyz (d) 27xyz

(c) n (d) n 2. (a) (b) (c) (d) (a) Null set (b) {P} (c) {P, Q, R} (d) {Q, R} (a) 2k (b) 7 (c) 2 (d) K (a) 1 (b) 3 (c) 3xyz (d) 27xyz 318 NDA Mathematics Practice Set 1. (1001)2 (101)2 (110)2 (100)2 2. z 1/z 2z z/2 3. The multiplication of the number (10101)2 by (1101)2 yields which one of the following? (100011001)2 (100010001)2 (110010011)2

More information

GLOBAL TALENT SEARCH EXAMINATIONS (GTSE) CLASS -XI

GLOBAL TALENT SEARCH EXAMINATIONS (GTSE) CLASS -XI GLOBAL TALENT SEARCH EXAMINATIONS (GTSE) Date: rd November 008 CLASS -XI MATHEMATICS Max Marks: 80 Time: :0 to :5 a.m. General Instructions: (Read Instructions carefully). All questions are compulsory.

More information

POINT. Preface. The concept of Point is very important for the study of coordinate

POINT. Preface. The concept of Point is very important for the study of coordinate POINT Preface The concept of Point is ver important for the stud of coordinate geometr. This chapter deals with various forms of representing a Point and several associated properties. The concept of coordinates

More information

Practice Set for IIT JEE. Paper I

Practice Set for IIT JEE. Paper I Objective Questions I [Only one correct option] Practice Set for IIT JEE Paper I Q 1. The number of lines in the xy-plane, Whose distance from (-1, 2) is 2 and from (2, 6) is 3, is a. 2 b. 3 c. 4 d. None

More information

SET-I SECTION A SECTION B. General Instructions. Time : 3 hours Max. Marks : 100

SET-I SECTION A SECTION B. General Instructions. Time : 3 hours Max. Marks : 100 General Instructions. All questions are compulsor.. This question paper contains 9 questions.. Questions - in Section A are ver short answer tpe questions carring mark each.. Questions 5- in Section B

More information

MATHEMATICS EXTENSION 2

MATHEMATICS EXTENSION 2 PETRUS KY COLLEGE NEW SOUTH WALES in partnership with VIETNAMESE COMMUNITY IN AUSTRALIA NSW CHAPTER JULY 006 MATHEMATICS EXTENSION PRE-TRIAL TEST HIGHER SCHOOL CERTIFICATE (HSC) Student Number: Student

More information

TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad

TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad TARGT : J 01 SCOR J (Advanced) Home Assignment # 0 Kota Chandigarh Ahmedabad J-Mathematics HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP 1. If x + y = 0 is a tangent at the vertex of a parabola and x + y 7 =

More information

Code : N. Mathematics ( ) ( ) ( ) Q c, a and b are coplanar. x 2 = λ µ... (ii) 1. If (2, 3, 5) is one end of a diameter of the sphere

Code : N. Mathematics ( ) ( ) ( ) Q c, a and b are coplanar. x 2 = λ µ... (ii) 1. If (2, 3, 5) is one end of a diameter of the sphere Mathematics. If (, 3, ) is one end of a diameter of the sphere x + y + z 6x y z + 0 = 0, then the coordinates of the other end of the diameter are () (4, 3, 3) () (4, 9, 3) (3) (4, 3, 3) (4) (4, 3, ) Sol.

More information

JEE-ADVANCED MATHEMATICS. Paper-1. SECTION 1: (One or More Options Correct Type)

JEE-ADVANCED MATHEMATICS. Paper-1. SECTION 1: (One or More Options Correct Type) JEE-ADVANCED MATHEMATICS Paper- SECTION : (One or More Options Correct Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR

More information

IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB

IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB ` KUKATPALLY CENTRE IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHS-IB 017-18 FIITJEE KUKATPALLY CENTRE: # -97, Plot No1, Opp Patel Kunta Huda Park, Vijaynagar Colony, Hyderabad - 500

More information

(iii) For each question in Section III, you will be awarded 4 Marks if you darken only the bubble corresponding to the

(iii) For each question in Section III, you will be awarded 4 Marks if you darken only the bubble corresponding to the FIITJEE Solutions to IIT - JEE 8 (Paper, Code 4) Time: hours M. Marks: 4 Note: (i) The question paper consists of parts (Part I : Mathematics, Part II : Physics, Part III : Chemistry). Each part has 4

More information

Q.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or

Q.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. A variable rectangle PQRS has its sides parallel to fied directions. Q and S lie respectivel on the lines = a, = a and P lies on the ais. Then the locus of R

More information

KEAM (ENGINEERING) ANSWER KEY 2017

KEAM (ENGINEERING) ANSWER KEY 2017 MTHMTICS KM KY 07 PG: KM (NGINRING) KY 07 PPR II MTHMTICS QUSTIONS & S. p q r p q r + is equal to () q p () q + p (C) q () p () 0 5 0. Let = 0 5 5 () 0 and () 0 = 0. If + 5 C = 0, then C is 0 5 5 5 5 0

More information

are in c) A B (D) 2 = {4,5,6} by = {(4,4), (5,5), (6,6)} is (C) (B) 0 < (C) 0 = 8, = 5 = 8, = 8 (B) (D) (C) 2 +

are in c) A B (D) 2 = {4,5,6} by = {(4,4), (5,5), (6,6)} is (C) (B) 0 < (C) 0 = 8, = 5 = 8, = 8 (B) (D) (C) 2 + 1. If are in GP then AP GP are in HP 2. The sum to infinity of the series 1 3. The set B-A a subset of a) A c) A B b) B d)null set 4. The converse of the statement if 3 3 6 then I am the president of USA

More information

Edexcel GCE A Level Maths. Further Maths 3 Coordinate Systems

Edexcel GCE A Level Maths. Further Maths 3 Coordinate Systems Edecel GCE A Level Maths Further Maths 3 Coordinate Sstems Edited b: K V Kumaran kumarmaths.weebl.com 1 kumarmaths.weebl.com kumarmaths.weebl.com 3 kumarmaths.weebl.com 4 kumarmaths.weebl.com 5 1. An ellipse

More information

RAJASTHAN P.E.T. MATHS 1997

RAJASTHAN P.E.T. MATHS 1997 RAJASTHAN P.E.T. MATHS 1997 1. The value of k for which the points (0,0), (2,0), (0,1) and (0,k) lies on a circle is : (1) 1,2 (2) -1,2 (3) 0,2 (4) 0, 1 2. The area of the triangle formed by the tangent

More information

02. If (x, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) x + y = 0 (B) bx ay = 0 (C) ax by = 0 (D) bx + ay = 0 (E) ax + by =

02. If (x, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) x + y = 0 (B) bx ay = 0 (C) ax by = 0 (D) bx + ay = 0 (E) ax + by = 0. π/ sin d 0 sin + cos (A) 0 (B) π (C) 3 π / (D) π / (E) π /4 0. If (, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) + y = 0 (B) b ay = 0 (C) a by = 0 (D) b + ay = 0 (E) a + by = 0 03.

More information

SUBJECT : PAPER I MATHEMATICS

SUBJECT : PAPER I MATHEMATICS Question Booklet Version SUBJECT : PAPER I MATHEMATICS Instruction to Candidates. This question booklet contains 50 Objective Type Questions (Single Best Response Type) in the subject of Mathematics..

More information

Conic Sections Session 2: Ellipse

Conic Sections Session 2: Ellipse Conic Sections Session 2: Ellipse Toh Pee Choon NIE Oct 2017 Toh Pee Choon (NIE) Session 2: Ellipse Oct 2017 1 / 24 Introduction Problem 2.1 Let A, F 1 and F 2 be three points that form a triangle F 2

More information

SYSTEM OF CIRCLES OBJECTIVES (a) Touch each other internally (b) Touch each other externally

SYSTEM OF CIRCLES OBJECTIVES (a) Touch each other internally (b) Touch each other externally SYSTEM OF CIRCLES OBJECTIVES. A circle passes through (0, 0) and (, 0) and touches the circle x + y = 9, then the centre of circle is (a) (c) 3,, (b) (d) 3,, ±. The equation of the circle having its centre

More information

I K J are two points on the graph given by y = 2 sin x + cos 2x. Prove that there exists

I K J are two points on the graph given by y = 2 sin x + cos 2x. Prove that there exists LEVEL I. A circular metal plate epands under heating so that its radius increase by %. Find the approimate increase in the area of the plate, if the radius of the plate before heating is 0cm.. The length

More information

CHAPTER-1. SETS. Q.4 Write down the proper subsets of { a, b, Q.5 Write down the power set of { 5,6,7 }? Verify the following result :

CHAPTER-1. SETS. Q.4 Write down the proper subsets of { a, b, Q.5 Write down the power set of { 5,6,7 }? Verify the following result : CHAPTER-. SETS Q. Write the following sets in roster form (i) A = { : is an integer and 5 5 } (ii) B = { : is a natural number and < < 4} (iii) C= { : is a two- digit natural number such that sum of digit

More information

Mathematics. Single Correct Questions

Mathematics. Single Correct Questions Mathematics Single Correct Questions +4 1.00 1. If and then 2. The number of solutions of, in the interval is : 3. If then equals : 4. A plane bisects the line segment joining the points and at right angles.

More information

Lecture 17. Implicit differentiation. Making y the subject: If xy =1,y= x 1 & dy. changed to the subject of y. Note: Example 1.

Lecture 17. Implicit differentiation. Making y the subject: If xy =1,y= x 1 & dy. changed to the subject of y. Note: Example 1. Implicit differentiation. Lecture 17 Making y the subject: If xy 1,y x 1 & dy dx x 2. But xy y 2 1 is harder to be changed to the subject of y. Note: d dx (f(y)) f (y) dy dx Example 1. Find dy dx given

More information

CURVATURE AND RADIUS OF CURVATURE

CURVATURE AND RADIUS OF CURVATURE CHAPTER 5 CURVATURE AND RADIUS OF CURVATURE 5.1 Introduction: Curvature is a numerical measure of bending of the curve. At a particular point on the curve, a tangent can be drawn. Let this line makes an

More information

PARABOLA. AIEEE Syllabus. Total No. of questions in Parabola are: Solved examples Level # Level # Level # Level # 4..

PARABOLA. AIEEE Syllabus. Total No. of questions in Parabola are: Solved examples Level # Level # Level # Level # 4.. PRBOL IEEE yllabus 1. Definition. Terms related to Parabola 3. tandard form of Equation of Parabola 4. Reduction to standard Equation 5. General Equation of a Parabola 6. Equation of Parabola when its

More information

KEAM (ENGINEERING) ANSWER KEY 2018

KEAM (ENGINEERING) ANSWER KEY 2018 MTHEMTIS KEM KEY 08 PGE: M.O: Kunnumpuram, yurveda ollege Jn., Trivandrum-, (: 047-57040, 47040 E-mail: info@zephyrentrance.in, Website: www.zephyrentrance.in KOHI KOLLM RNHES Puthussery uilding, Kaloor

More information

TS EAMCET 2016 SYLLABUS ENGINEERING STREAM

TS EAMCET 2016 SYLLABUS ENGINEERING STREAM TS EAMCET 2016 SYLLABUS ENGINEERING STREAM Subject: MATHEMATICS 1) ALGEBRA : a) Functions: Types of functions Definitions - Inverse functions and Theorems - Domain, Range, Inverse of real valued functions.

More information

Name of Exam. Centre...Exam. Centre No.:... Test Booklet Code :... Test Booklet No.:...

Name of Exam. Centre...Exam. Centre No.:... Test Booklet Code :... Test Booklet No.:... Test Booklet Code A ME-2008 i Test Booklet No. This booklet contains 12 pages. DO NOT open this Test Booklet until you are asked to do so. 7468 5 Important Instructions :- 1. The MATHEMATICS test is consist

More information

22 (Write this number on your Answer Sheet)

22 (Write this number on your Answer Sheet) Question Booklet Version (Write this number on your Answer Sheet) Day and Date : Thursday, 0th May, 08 QUESTION BOOKLET (MHT-CET - 08) Subjects : Paper I : Mathematics MH-CET 08 Roll No. Question Booklet

More information

MATHEMATICS Code No. 13 INSTRUCTIONS

MATHEMATICS Code No. 13 INSTRUCTIONS DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO COMBINED COMPETITIVE (PRELIMINARY) EXAMINATION, 00 Serial No. MATHEMATICS Code No. A Time Allowed : Two Hours Maximum Marks : 00 INSTRUCTIONS.

More information

The Distance Formula. The Midpoint Formula

The Distance Formula. The Midpoint Formula Math 120 Intermediate Algebra Sec 9.1: Distance Midpoint Formulas The Distance Formula The distance between two points P 1 = (x 1, y 1 ) P 2 = (x 1, y 1 ), denoted by d(p 1, P 2 ), is d(p 1, P 2 ) = (x

More information

Reg. No. : Question Paper Code : B.E./B.Tech. DEGREE EXAMINATION, JANUARY First Semester. Marine Engineering

Reg. No. : Question Paper Code : B.E./B.Tech. DEGREE EXAMINATION, JANUARY First Semester. Marine Engineering WK Reg No : Question Paper Code : 78 BE/BTech DEGREE EXAMINATION, JANUARY 4 First Semester Marine Engineering MA 65 MATHEMATICS FOR MARINE ENGINEERING I (Regulation ) Time : Three hours Maimum : marks

More information

Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in

Chapter (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 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

(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 information

MockTime.com. NDA Mathematics Practice Set 1.

MockTime.com. NDA Mathematics Practice Set 1. 346 NDA Mathematics Practice Set 1. Let A = { 1, 2, 5, 8}, B = {0, 1, 3, 6, 7} and R be the relation is one less than from A to B, then how many elements will R contain? 2 3 5 9 7. 1 only 2 only 1 and

More information

1. Which of the following defines a function f for which f ( x) = f( x) 2. ln(4 2 x) < 0 if and only if

1. Which of the following defines a function f for which f ( x) = f( x) 2. ln(4 2 x) < 0 if and only if . Which of the following defines a function f for which f ( ) = f( )? a. f ( ) = + 4 b. f ( ) = sin( ) f ( ) = cos( ) f ( ) = e f ( ) = log. ln(4 ) < 0 if and only if a. < b. < < < < > >. If f ( ) = (

More information

GOVERNMENT OF KARNATAKA KARNATAKA STATE PRE-UNIVERSITY EDUCATION EXAMINATION BOARD SCHEME OF VALUATION. Subject : MATHEMATICS Subject Code : 35

GOVERNMENT OF KARNATAKA KARNATAKA STATE PRE-UNIVERSITY EDUCATION EXAMINATION BOARD SCHEME OF VALUATION. Subject : MATHEMATICS Subject Code : 35 GOVERNMENT OF KARNATAKA KARNATAKA STATE PRE-UNIVERSITY EDUCATION EXAMINATION BOARD II YEAR PUC EXAMINATION MARCH APRIL 0 SCHEME OF VALUATION Subject : MATHEMATICS Subject Code : 5 PART A Write the prime

More information

Complete Syllabus of Class XI & XII

Complete Syllabus of Class XI & XII Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-0005 Ph.: 0-7656 Fa : 0-767 MM : 0 Sample Paper : Campus Recruitment Test Time : ½ Hr. Mathematics (Engineering) Complete Syllabus of Class XI & XII

More information

1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3.

1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3. Higher Maths Non Calculator Practice Practice Paper A. A sequence is defined b the recurrence relation u u, u. n n What is the value of u?. The line with equation k 9 is parallel to the line with gradient

More information

MockTime.com. (a) 36 (b) 33 (c) 20 (d) 6

MockTime.com. (a) 36 (b) 33 (c) 20 (d) 6 185 NDA Mathematics Practice Set 1. Which of the following statements is not correct for the relation R defined by arb if and only if b lives within one kilometer from a? R is reflexive R is symmetric

More information

2. (i) Find the equation of the circle which passes through ( 7, 1) and has centre ( 4, 3).

2. (i) Find the equation of the circle which passes through ( 7, 1) and has centre ( 4, 3). Circle 1. (i) Find the equation of the circle with centre ( 7, 3) and of radius 10. (ii) Find the centre of the circle 2x 2 + 2y 2 + 6x + 8y 1 = 0 (iii) What is the radius of the circle 3x 2 + 3y 2 + 5x

More information

Mathematics Extension 2

Mathematics Extension 2 0 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Etension General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Black pen is preferred Board-approved calculators

More information

5 Find an equation of the circle in which AB is a diameter in each case. a A (1, 2) B (3, 2) b A ( 7, 2) B (1, 8) c A (1, 1) B (4, 0)

5 Find an equation of the circle in which AB is a diameter in each case. a A (1, 2) B (3, 2) b A ( 7, 2) B (1, 8) c A (1, 1) B (4, 0) C2 CRDINATE GEMETRY Worksheet A 1 Write down an equation of the circle with the given centre and radius in each case. a centre (0, 0) radius 5 b centre (1, 3) radius 2 c centre (4, 6) radius 1 1 d centre

More information

Math Bank - 9. If cos ecθ= x + then the value of cos ecθ + cot θ is. (a) 2x (b) -2x. = and ( ) sec A + C = 2, then. (b), (c), (d) None of these

Math Bank - 9. If cos ecθ= x + then the value of cos ecθ + cot θ is. (a) 2x (b) -2x. = and ( ) sec A + C = 2, then. (b), (c), (d) None of these Math Bank - 9. If cos ecθ= + then the value of cos ecθ + cot θ - / (d) -/. If sin ( A + B + C) =, tan ( A B) = and ( ) 0 0 0 A= 90,B= 60,C= 0 0 0 0 A = 0,B = 60,C = 0 0 0 0 A= 60,B= 0,C= 0. 9 5 The value

More information

ANSWER KEY 1. [A] 2. [C] 3. [B] 4. [B] 5. [C] 6. [A] 7. [B] 8. [C] 9. [A] 10. [A] 11. [D] 12. [A] 13. [D] 14. [C] 15. [B] 16. [C] 17. [D] 18.

ANSWER KEY 1. [A] 2. [C] 3. [B] 4. [B] 5. [C] 6. [A] 7. [B] 8. [C] 9. [A] 10. [A] 11. [D] 12. [A] 13. [D] 14. [C] 15. [B] 16. [C] 17. [D] 18. ANSWER KEY. [A]. [C]. [B] 4. [B] 5. [C] 6. [A] 7. [B] 8. [C] 9. [A]. [A]. [D]. [A]. [D] 4. [C] 5. [B] 6. [C] 7. [D] 8. [B] 9. [C]. [C]. [D]. [A]. [B] 4. [D] 5. [A] 6. [D] 7. [B] 8. [D] 9. [D]. [B]. [A].

More information

CALCULUS BASIC SUMMER REVIEW

CALCULUS BASIC SUMMER REVIEW NAME CALCULUS BASIC SUMMER REVIEW Slope of a non vertical line: rise y y y m run Point Slope Equation: y y m( ) The slope is m and a point on your line is, ). ( y Slope-Intercept Equation: y m b slope=

More information

Special Mathematics Notes

Special Mathematics Notes Special Mathematics Notes Tetbook: Classroom Mathematics Stds 9 & 10 CHAPTER 6 Trigonometr Trigonometr is a stud of measurements of sides of triangles as related to the angles, and the application of this

More information

Q1. If (1, 2) lies on the circle. x 2 + y 2 + 2gx + 2fy + c = 0. which is concentric with the circle x 2 + y 2 +4x + 2y 5 = 0 then c =

Q1. If (1, 2) lies on the circle. x 2 + y 2 + 2gx + 2fy + c = 0. which is concentric with the circle x 2 + y 2 +4x + 2y 5 = 0 then c = Q1. If (1, 2) lies on the circle x 2 + y 2 + 2gx + 2fy + c = 0 which is concentric with the circle x 2 + y 2 +4x + 2y 5 = 0 then c = a) 11 b) -13 c) 24 d) 100 Solution: Any circle concentric with x 2 +

More information

PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared by IITians.

PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared by IITians. www. Class XI TARGET : JEE Main/Adv PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) ALP ADVANCED LEVEL PROBLEMS Straight Lines 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared b IITians.

More information

Mathematics Extension 1

Mathematics Extension 1 013 HIGHER SCHL CERTIFICATE EXAMINATIN Mathematics Etension 1 General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Black pen is preferred Board-approved calculators

More information

Created by T. Madas LINE INTEGRALS. Created by T. Madas

Created by T. Madas LINE INTEGRALS. Created by T. Madas LINE INTEGRALS LINE INTEGRALS IN 2 DIMENSIONAL CARTESIAN COORDINATES Question 1 Evaluate the integral ( x + 2y) dx, C where C is the path along the curve with equation y 2 = x + 1, from ( ) 0,1 to ( )

More information

MockTime.com. (b) (c) (d)

MockTime.com. (b) (c) (d) 373 NDA Mathematics Practice Set 1. If A, B and C are any three arbitrary events then which one of the following expressions shows that both A and B occur but not C? 2. Which one of the following is an

More information

Basic Mathematics - XII (Mgmt.) SET 1

Basic Mathematics - XII (Mgmt.) SET 1 Basic Mathematics - XII (Mgmt.) SET Grade: XII Subject: Basic Mathematics F.M.:00 Time: hrs. P.M.: 40 Model Candidates are required to give their answers in their own words as far as practicable. The figures

More information

l (D) 36 (C) 9 x + a sin at which the tangent is parallel to x-axis lie on

l (D) 36 (C) 9 x + a sin at which the tangent is parallel to x-axis lie on Dpp- to MATHEMATICS Dail Practice Problems Target IIT JEE 00 CLASS : XIII (VXYZ) DPP. NO.- to DPP- Q. If on a given base, a triangle be described such that the sum of the tangents of the base angles is

More information

CBSE 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 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 information

1 (C) 1 e. Q.3 The angle between the tangent lines to the graph of the function f (x) = ( 2t 5)dt at the points where (C) (A) 0 (B) 1/2 (C) 1 (D) 3

1 (C) 1 e. Q.3 The angle between the tangent lines to the graph of the function f (x) = ( 2t 5)dt at the points where (C) (A) 0 (B) 1/2 (C) 1 (D) 3 [STRAIGHT OBJECTIVE TYPE] Q. Point 'A' lies on the curve y e and has the coordinate (, ) where > 0. Point B has the coordinates (, 0). If 'O' is the origin then the maimum area of the triangle AOB is (A)

More information

DIRECTORATE OF EDUCATION GOVT. OF NCT OF DELHI

DIRECTORATE OF EDUCATION GOVT. OF NCT OF DELHI 456789045678904567890456789045678904567890456789045678904567890456789045678904567890 456789045678904567890456789045678904567890456789045678904567890456789045678904567890 QUESTION BANK 456789045678904567890456789045678904567890456789045678904567890456789045678904567890

More information

DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO

DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO T.B.C. : P-AQNA-L-ZNGU Serial No.- TEST BOOKLET MATHEMATICS Test Booklet Series Time Allowed : Two Hours and Thirty Minutes Maximum Marks : 00

More information

GAT-UGTP-2018 Page 1 of 5

GAT-UGTP-2018 Page 1 of 5 SECTION A: MATHEMATICS UNIT 1 SETS, RELATIONS AND FUNCTIONS: Sets and their representation, Union, Intersection and compliment of sets, and their algebraic properties, power set, Relation, Types of relation,

More information

SECTION A Time allowed: 20 minutes Marks: 20

SECTION A Time allowed: 20 minutes Marks: 20 Mathcity.org Merging man and maths Federal Board HSSC-II Eamination Mathematics Model Question Paper Roll No: Answer Sheet No: FBISE WE WORK FOR EXCELLENCE Signature of Candidate: Signature of Invigilator:

More information

Mathematics Extension 2

Mathematics Extension 2 00 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Board-approved calculators may be used A table

More information

CO-ORDINATE GEOMETRY

CO-ORDINATE GEOMETRY CO-ORDINATE GEOMETRY 1 To change from Cartesian coordinates to polar coordinates, for X write r cos θ and for y write r sin θ. 2 To change from polar coordinates to cartesian coordinates, for r 2 write

More information

Analytic Geometry MAT 1035

Analytic Geometry MAT 1035 Analytic Geometry MAT 035 5.09.04 WEEKLY PROGRAM - The first week of the semester, we will introduce the course and given a brief outline. We continue with vectors in R n and some operations including

More information

2016 SEC 4 ADDITIONAL MATHEMATICS CW & HW

2016 SEC 4 ADDITIONAL MATHEMATICS CW & HW FEB EXAM 06 SEC 4 ADDITIONAL MATHEMATICS CW & HW Find the values of k for which the line y 6 is a tangent to the curve k 7 y. Find also the coordinates of the point at which this tangent touches the curve.

More information

BASIC MATHEMATICS - XII SET - I

BASIC MATHEMATICS - XII SET - I BASIC MATHEMATICS - XII Grade: XII Subject: Basic Mathematics F.M.:00 Time: hrs. P.M.: 40 Candidates are required to give their answers in their own words as far as practicable. The figures in the margin

More information

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 4 UNIT (ADDITIONAL) Time allowed Three hours (Plus 5 minutes reading time)

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 4 UNIT (ADDITIONAL) Time allowed Three hours (Plus 5 minutes reading time) N E W S O U T H W A L E S HIGHER SCHOOL CERTIFICATE EXAMINATION 996 MATHEMATICS 4 UNIT (ADDITIONAL) Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions.

More information

Centres at Pallavaram Opp. St. therasa s School Pammal Krishna Nagar Adyar Kasturiba Nagar Chrompet - Opp. MIT Selaiyur Near Camp Road Junction

Centres at Pallavaram Opp. St. therasa s School Pammal Krishna Nagar Adyar Kasturiba Nagar Chrompet - Opp. MIT Selaiyur Near Camp Road Junction Adyar Adambakkam Pallavaram Pammal Chromepet Now also at SELAIYUR Day - wise Portions Day 1 : Day 2 : Day 3 : Matrices and Determinants, Complex Numbers and Vector Algebra Analytical Geometry, Discrete

More information

= 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.

= 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,

More information

JEE (Advanced) 2018 MATHEMATICS QUESTION BANK

JEE (Advanced) 2018 MATHEMATICS QUESTION BANK JEE (Advanced) 08 MATHEMATICS QUESTION BANK Ans. A [ : a multiple of ] and B [ : a multiple of 5], then A B ( A means complement of A) A B A B A B A B A { : 5 0}, B {, }, C {,5}, then A ( B C) {(, ), (,

More information

Page 1 MATHEMATICS

Page 1 MATHEMATICS PREPARED BY :S.MANIKANDAN., VICE PRINCIPAL., JOTHI VIDHYALAYA MHSS., ELAMPILLAI., SALEM., 94798 Page + MATHEMATICS PREPARED BY :S.MANIKANDAN., VICE PRINCIPAL., JOTHI VIDHYALAYA MHSS., ELAMPILLAI., SALEM.,

More information

X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS. 1. Commutative property i ii. 2. Associative property i ii

X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS. 1. Commutative property i ii. 2. Associative property i ii X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS 1. Commutative property i ii 2. Associative property i ii 3. Distributive property i ii 4. De Morgan s laws i ii i ii 5. Cardinality of

More information

Analytic Geometry MAT 1035

Analytic Geometry MAT 1035 Analytic Geometry MAT 035 5.09.04 WEEKLY PROGRAM - The first week of the semester, we will introduce the course and given a brief outline. We continue with vectors in R n and some operations including

More information

HEAT-3 APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA MAX-MARKS-(112(3)+20(5)=436)

HEAT-3 APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA MAX-MARKS-(112(3)+20(5)=436) HEAT- APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA TIME-(HRS) Select the correct alternative : (Only one is correct) MAX-MARKS-(()+0(5)=6) Q. Suppose & are the point of maimum and the point of minimum

More information

a Write down the coordinates of the point on the curve where t = 2. b Find the value of t at the point on the curve with coordinates ( 5 4, 8).

a Write down the coordinates of the point on the curve where t = 2. b Find the value of t at the point on the curve with coordinates ( 5 4, 8). Worksheet A 1 A curve is given by the parametric equations x = t + 1, y = 4 t. a Write down the coordinates of the point on the curve where t =. b Find the value of t at the point on the curve with coordinates

More information

Total marks 70. Section I. 10 marks. Section II. 60 marks

Total marks 70. Section I. 10 marks. Section II. 60 marks THE KING S SCHOOL 03 Higher School Certificate Trial Eamination Mathematics Etension General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Board-approved calculators

More information

6675/01 Edexcel GCE Pure Mathematics P5 Further Mathematics FP2 Advanced/Advanced Subsidiary

6675/01 Edexcel GCE Pure Mathematics P5 Further Mathematics FP2 Advanced/Advanced Subsidiary 6675/1 Edecel GCE Pure Mathematics P5 Further Mathematics FP Advanced/Advanced Subsidiary Monday June 5 Morning Time: 1 hour 3 minutes 1 1. (a) Find d. (1 4 ) (b) Find, to 3 decimal places, the value of.3

More information

Mathematics Advanced Extension Award. Candidates may NOT use a calculator in answering this paper.

Mathematics Advanced Extension Award. Candidates may NOT use a calculator in answering this paper. Paper Reference(s) 9801/01 Edecel Mathematics Advanced Etension Award Monday 7 June 011 Afternoon Time: 3 hours Materials required for eamination Answer book (AB16) Graph paper (ASG) Mathematical Formulae

More information

MA 162 FINAL EXAM PRACTICE PROBLEMS Spring Find the angle between the vectors v = 2i + 2j + k and w = 2i + 2j k. C.

MA 162 FINAL EXAM PRACTICE PROBLEMS Spring Find the angle between the vectors v = 2i + 2j + k and w = 2i + 2j k. C. MA 6 FINAL EXAM PRACTICE PROBLEMS Spring. Find the angle between the vectors v = i + j + k and w = i + j k. cos 8 cos 5 cos D. cos 7 E. cos. Find a such that u = i j + ak and v = i + j + k are perpendicular.

More information

JEE MAIN 2016 ONLINE EXAMINATION DATE : SUBJECT : MATHEMATICS TEST PAPER WITH SOLUTIONS & ANSWER KEY

JEE MAIN 2016 ONLINE EXAMINATION DATE : SUBJECT : MATHEMATICS TEST PAPER WITH SOLUTIONS & ANSWER KEY JEE MAIN 06 ONLINE EXAMINATION DATE : 0-0-06 SUBJECT : MATHEMATICS TEST PAPER WITH SOLUTIONS & ANSWER KEY CORPORATE OFFICE : CG TOWER, A-6 & 5, IPIA, NEAR CITY MALL, JHALAWAR ROAD, KOTA (RAJ.) - 005 REG.

More information

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

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : , MCN COMPLEX NUMBER C The complex number Complex number is denoted by ie = a + ib, where a is called as real part of (denoted by Re and b is called as imaginary part of (denoted by Im Here i =, also i =,

More information

LEAVING CERTIFICATE EXAMINATION, 2001 MATHEMATICS HIGHER LEVEL

LEAVING CERTIFICATE EXAMINATION, 2001 MATHEMATICS HIGHER LEVEL M 30 AN ROINN OIDEACHAIS AGUS EOLAÍOCHTA LEAVING CERTIFICATE EXAMINATION, 001 MATHEMATICS HIGHER LEVEL PAPER (300 marks) MONDAY, 11 JUNE MORNING, 930 to 100 Attempt FIVE questions from Section A and ONE

More information