Objective Mathematics
|
|
- Aileen Gilbert
- 5 years ago
- Views:
Transcription
1 . 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 fied points (d) three fied points. A variable tangent of ellipse meets the a b co-ordinate aes at A and B minimum area (in sq. units) of circumcircle of AOB, 'O' being the origin, is given by : (a) ( ) 4 a b. ( a b ). (c) ( ) 4 a b. (d) ( ) 4 a b.. Let P (, y) be any point on ellipse 9 + 5y = 5, if 'F ' and 'F ' are the focal points of ellipse perimeter of F PF is : (a) 0 8 (c) 5 (d) 0 4. The chords of contact of tangents t o curve + 8y = 8 from any point on its director circle intersect the director circle at 'C' and 'D' locus of the point of intersection of tangents to circle at 'C' and 'D' is : (a) 6 + y = y = 4. (c) 64 + y = 6. (d) None of these. 5. If normal at an end of latus rectum of an ellipse passes through one etremity of minor ais eccentricity 'e' satisfy : (a) e 4 + e = 0 e + e 5 = 0 (c) e = 5/ (d) e 4 e + = 0 6. If tangent is drawn at ' ' point to the ellipse 7 y 7, where 0, value of ' ' such that sum of intercepts on aes made by this tangent is minimum, is : (a) 8 (c) 6 (d) 4 7. The length of latus rectum of an ellipse is one third of the major ais eccentricity of ellipse is equal to : (a) (c) (d) 8. Minimum distance between the ellipse y 6 and the line y 7 0 is equal to : (a) 4 (c) 5 (d) 0 9. The line passing through the etremity A of the major ais and etremity B of the minor ais of the ellipse + 9y = 9 meets its auiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin O is equal to : (a) 0 (c) 0 sq. units 9 0 sq. unit (d) 7 0 sq. unit sq. units 0. The normal at a point P on the ellipse + 4y = 6 meets the -ais at Q. If M is the mid point of the line segment PQ the locus of M intersects the latus rectums of the given ellipse at the points 5 (a), 7 (c), 7 5 9, 4 4 (d), 7 [ 68 ] Mathematics for JEE-0
2 Ellipse. Maimum length of chord of ellipse, a b a > b, such that eccentric angles of the etremities of chord differ by is : 7. Let normals be drawn to the ellipse + y = from point (, ) the co-normal points lie on the curve : (a) y + 4y = 0 y + 4y = 0 (c) + 4y y = 0 (d) 4y + 4 y = 0 (a) a b (c) ab (d) b a. If an ellipse with major and minor aes of length 0 and 0 units respectively slides along the co-ordinate aes in the first quadrant length of the arc which is formed by the locus of centre of ellipse is given by : (a) (c) 5 (d). Area of ellipse for which focal points are (, 0) and (, 0) and point (4, ) lying on it, is given by : (a) 8 sq. units 9 sq. units (c) 4 sq. units (d) 8 sq. units 4. Let tangents drawn from point 'P' to the ellipse 4y 6 meets the co-ordinate aes at concylic points locus of point 'P' is given by : (a) y = 7 + y = 7 (c) y = 6 (d) + y = 6 5. Let the common tangent in I st quadrant to the circle y 6 and 4 5y 00 meet the aes at A and B area of (a) 4 AOB, where O is origin, is : 8 8. Let 'A' be the centre of ellipse 5 + 5y + 6y 8 = 0 and 'P', 'Q' points lie on the ellipse such that AP and AQ distances are maimum and minimum respectively AP + AQ is equal to : (a) 4 (c) (d) 5 9. Let 'AB' be the variable chord of the ellipse + y = and AOB, where 'O' is origin, then OA OB ( OA. OB) is equal to : (a).. (c) 4. (d) Let normal to the ellipse 4 + 5y = 0 at point P( ) touches the parabola y = 4 tan is equal to : (a) (c) (d) 4. Let circle 'C' with centre (, 0) be inscribed in the ellipse maimum 4y 6 and the area of circle 'C' is (c) 0 (d) none of these 6. Let ellipse, where a > b, be centered at a b 'O' and having AB and CD as its major and minor ais respectively. If one of the focus of ellipse is 'F ', the in-radius of triangle DOF is unit and OF = 6 units director circle of ellipse is given by : (a) + y = 00 + y = 97/ (c) + y = 50 (d) + y = 05/ [ 69 ] (a) equation of director circle of 'C' is given by 9( ) 9y equation of director circle of 'C' is given by ( ) y (c) area of circle 'C' is sq. units. (d) circle 'C' is auiliary circle for the ellipse 9( ) 5y Mathematics for JEE-0
3 . Let one of the focus point of ellipse a y b be at F (4, 0) and its intersection point with positive y-ais be 'B'. If the centre of ellipse is 'C' and circum-radius of CF B is.5 units which of the following statements are incorrect : (a) equation of director circle of ellipse is + y = 4. area of ellipse is 0 square units. (c) director circle of auiliary circle of the ellipse is + y = 50. (d) length of latus rectum of ellipse is 4 units.. Let ellipse E : + 4y = 4 is inscribed in a rectangle aligned with co-ordinate aes, which in turn is inscribed in another ellipse E that passes through the point (4, 0). With reference to ellipse E and E which of the following statements are true : (a) If point (, ) lies in between the boundary of the director circle of E and E 5 5. If point (, ) lies outside the ellipse E R [, ]. (c) Total number of integral points inside the ellipse E are four. (d) If point (, ) lies inside the ellipse E,. 4. Let point 'P' lies on the ellipse and normal 5 6 to ellipse at 'P' meets the co-ordinate aes at A and B. If 'O' is the origin and M is the foot of perpendicular from origin to AB (a) maimum area of AOB is.05 square units. maimum value of OM is units. (c) maimum value of OM is unit. (d) maimum area of AOB is 8 square. units Let variable point 'P' lies on the curve y and PA, PB are tangents to the ellipse + y = 9. If APB is an acute angle co-ordinate of point 'P' can be given by : (a) e e (c) ln (d) 9 tan Following questions are assertion and reasoning type questions. Each of these questions contains two statements, Statement (Assertion) and Statement (Reason). Each of these questions has four alternative answers, only one of them is the correct answer. Select the correct answer from the given options : (a) Both Statement and Statement are true and Statement is the correct eplanation of Statement. Both Statement and Statement are true but Statement is not the correct eplanation of Statement. (c) Statement is true but Statement is false. (d) Statement is false but Statement is true. 6. Statement : Total number of distinct normals which can be drawn to the ellipse point (0, 6) are three. from 69 5 Statement : Maimum number of normals which can be drawn to any given ellipse from a point are four. 7. Let any point 'P' lies on the ellipse and 6 PM, PM are the distances of 'P' from 8 0 and 8 0 respectively. Statement : For point 'P' maimum value of (PM ) (PM ) cannot eceed 64 square units Statement : Area of PF F, where F and F are foci of ellipse, can't eceed 4 square units. 8. Let C and C be two ellipse which are given by + 4y = 4 and + y = 6 respectively and any tangent to curve C meets the curve C at A and B. Statement : If tangents drawn to curve C at points A and B meet at point P APB Statement : Locus of point 'P' is the director circle of curve 'C '. [ 70 ] Mathematics for JEE-0
4 Ellipse 9. Statement : Let 'L' be variable line which is tangential to fied ellipse with foci F and F locus of the foot of perpendicular from foci to line 'L' is the auiliary circle of ellipse Statement : Product of the length of perpendiculars from foci F and F to the line 'L' is always the square of semi-minor ais of ellipse. 0. Statement : If point 'P' lies on a given ellipse with foci at F and F perimeter of PF F is constant Statement : Perimeter of the ellipse is given by ( F F )( e ) e eccentricity of ellipse. units, where 'e' is the [ 7 ] Mathematics for JEE-0
5 Comprehension passage () ( Questions No. - ) Let tangent at any point on the curve E : 4 + 9y = 6 meets the curve E :0 5 y 50 at P and Q. If tangents drawn at P and Q to curve E meets at point 'R' and locus of 'R' is given by the curve 'C ' then answer the following questions.. Locus of point from which perpendicular tangents can be drawn to curve 'C ' is : (a) + y = 50 + y = 60 (c) y 8 = 0 (d) y 9 = 0. Positive slope of the common tangent to curve 'C ' and + y = 60 is : (a) (c) (d). If from any point 'A' on the line + y = 0 tangents AB and AC are drawn to curve 'C ' locus of the circumcentre of ABC is : (a) 4 + 6y = 7 + y = 5 (c) y = 0 (d) + y = 0 Comprehension passage () ( Questions No. 4-6 ) 6. If 'O' is origin and the area of OPQ is square units value of 'k' is (a) (c) 5 4 (d) Comprehension passage () ( Questions No. 7-9 ) Let L : y m = 0 and L : y m = 0 be the variable lines for which m m is negative, and lines L and L are tangential to the variable ellipse 'E' at the points T and T respectively. If the ellipse 'E' is rotating about the point (, 0) and initially its equat ion is given by b ( ) a y ( ab), where R answer the following questions. 7. If 0 and the angle TOT is constant for all the positions of variable ellipse 'E', where 'O' is origin, then the ordered pair (a, b) can be given by : (a) (7, ) (4, 6) (c) (8, 6) (d) (, 6) 8. If a = 4b = and the angle TOT remains acute for all the positions of the variable ellipse 'E', where 'O' is origin the possible value of ' ' can be : (a) e (c) e (d) tan Let variable ellipse + 4y = 4k, where k R, and a fied parabola y = 8 is having a common tangent which meets the co-ordinate aes at P and Q answer the following questions. 4. Let A be the point of contact of the common tangent 9. If the T OT remains obtuse for all the positions of the variable ellipse 'E', where O is origin which one of the following relation must hold true : (a) a b 0 min{ a, b} a b with the ellipse and the eccentric angle of A is, then value of 'k' is equal to : (a) 4 8 (c) 6 (d) 5 (c) (d) ma{ a, b} a b a b a b 5. Locus of the mid-point of the intercepted length PQ is : (a) y + 4 = 0 y + = 0 (c) y + = 0 (d) 4y + = 0 [ 7 ] 0. Let tangent and normal be drawn at any point 'P' on the ellipse + y =, and rectangle PAOB is completed, where 'O' is the origin. Maimum area (in square units) of the rectangle PAOB is... Mathematics for JEE-0
6 . Let common tangents of the curves y = 4 and + 4y = 8 meets on the -ais at A and intersects the positive and negative y-ais at B and C respectively. If parabola with its ais along the -ais and verte at A passes through B and C length of latus rectum of the parabola is... Ellipse 4. Let tangents drawn at A and B points on the ellipse 4 + 9y = 6 meet at point P(, ). If 'C' is the centre of ellipse and the area of quadrilateral PACB is square units value of [ ], where [.] represents the greatest integer function, is equal to.... Let points A, B and C lie on the curve y, 4 y and y respectively maimum value of (AB + AC) is equal to Let ABCD is a square of side length 8 units, and an ellipse of eccentricity 0.5 is drawn touching the sides of the square, where the aes of symmetry being along the diagonals of square. If the major ais and minor ais is of length ' a' and ' b' units respectively. If line y meet the ellipse 4 9y 6 at points 'A' and 'B', where AOB 90, 'O' being the origin positive value of is equal to... value of sec sin b a is Match the following columns (I) and (II) Column (I) Column (II) (a) Number of points on the ellipse + 5y = 00 from (p) 0 which pair of perpendicular tangents can be drawn to the ellipse is / are : (q) 6 9 If the lines y = m + c and y = m + c intersect the ellipse a y at four concyclic points (m b + m ) must be : (r) (c) If all the normals of ellipse intersects or touches 5 6 the circle + y = r minimum value of 'r' is : (s) 4 (d) If the equation + 4y 8 + 6y + 4 k = 0 represents an ellipse values of 'k' can be : [ 7 ] Mathematics for JEE-0
7 7. Let C : + y = a and C : + y = b be two circles, where b > a > 0, and 'O' is origin. A line OPQ is drawn which meets C and C at points P and Q respectively. If 'R' is the moving point for which PR and QR is parallel to the y-ais and -ais respectively and the locus of 'R' is an ellipse 'E' match the following columns for eccentricity 'e' of the ellipse 'E' and the position of foci F and F of 'E'. Column (I) Column (II) (a) If F and F lie on the circle 'C ' eccentricity 'e' can be : If F and F lie inside the circle 'C ' eccentricity 'e' can be : (p) (q) sec sin (c) If F and F lie inside the circle 'C ' eccentricity 'e' can be : (r) cos 4 (d) If F and F don't lie inside the circle 'C ' eccentricity 'e' (s) cos() can be : [ 74 ] Mathematics for JEE-0
8 Ellipse.. (d). 4. (d) 5. (a) E 6. (c) (d) 0. (c). (a). (c). 4. (a) (a) 8. (c) (a). (b, c). (b, d). (a, b) 4. (c, d) 5. (a, b, d) (c) (a). (a). 4. (c) 5. E (c) 8. (c) 9. (c) 0. ( ). ( ). ( 6 ). ( 6 ) 4. ( 7 ) 5. ( 4 ) 6. (a) s 7. (a) r p q, s (c) q (c) p, q, r, s (d) q, r, s (d) p, r [ 75 ] Mathematics for JEE-0
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 information1 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 informationQ.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 informationTARGET : 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(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 informationby 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 informationTime : 3 hours 02 - Mathematics - July 2006 Marks : 100 Pg - 1 Instructions : S E CT I O N - A
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
More informationPREPARED 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( 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 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 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 informationl (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 informationObjective Mathematics
. In BC, if angles, B, C are in geometric seq- uence with common ratio, then is : b c a (a) (c) 0 (d) 6. If the angles of a triangle are in the ratio 4 : :, then the ratio of the longest side to the perimeter
More informationMULTIPLE 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 informationPOINT. 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 informationTrans 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 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 informationConic 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 information1 (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 information2. (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 informationObjective Mathematics
Chapter No - ( Area Bounded by Curves ). Normal at (, ) is given by : y y. f ( ) or f ( ). Area d ()() 7 Square units. Area (8)() 6 dy. ( ) d y c or f ( ) c f () c f ( ) As shown in figure, point P is
More informationEdexcel 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 informationJEE-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 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 informationVKR Classes TIME BOUND TESTS 1-7 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, C-9-0, Indra Vihar, Kota. Mob. No. 9890605 Single Choice Question : PRACTICE TEST-. The smallest integer greater than log +
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 informationy 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 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 informationHEAT-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 informationEinstein 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 informationAREA RELATED TO CIRCLES
CHAPTER 11 AREA RELATED TO CIRCLES (A) Main Concepts and Results Perimeters and areas of simple closed figures. Circumference and area of a circle. Area of a circular path (i.e., ring). Sector of a circle
More information5 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 informationDEEPAWALI ASSIGNMENT CLASS 11 FOR TARGET IIT JEE 2012 SOLUTION
DEEPAWALI ASSIGNMENT CLASS FOR TARGET IIT JEE 0 SOLUTION IMAGE OF SHRI GANESH LAXMI SARASWATI Director & H.O.D. IITJEE Mathematics SUHAG R. KARIYA (S.R.K. Sir) DOWNLOAD FREE STUDY PACKAGE, TEST SERIES
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 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 informationPARABOLA. 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 informationPRACTICE 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 informationMockTime.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 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 informationQ1. 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 informationCURVATURE 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= ( +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 informationADDITIONAL MATHEMATICS
005-CE A MATH HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 005 ADDITIONAL MATHEMATICS :00 pm 5:0 pm (½ hours) This paper must be answered in English 1. Answer ALL questions in Section A and any FOUR
More informationPractice 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 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 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 information63487 [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 informationConic 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 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 informationIIT 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 informationI 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 informationMathematics. 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 informationd) Find the equation of the circle whose extremities of a diameter are (1,2) and (4,5).
` KUKATPALLY CENTRE IPE MAT IIB Imortant Questions a) Find the equation of the circle whose centre is (-, ) and which asses through (,6) b) Find the equation of the circle assing through (,) and concentric
More informationGrade XI Mathematics
Grade XI Mathematics Exam Preparation Booklet Chapter Wise - Important Questions and Solutions #GrowWithGreen Questions Sets Q1. For two disjoint sets A and B, if n [P ( A B )] = 32 and n [P ( A B )] =
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 informationMockTime.com. (b) 9/2 (c) 18 (d) 27
212 NDA Mathematics Practice Set 1. Let X be any non-empty set containing n elements. Then what is the number of relations on X? 2 n 2 2n 2 2n n 2 2. Only 1 2 and 3 1 and 2 1 and 3 3. Consider the following
More informationBOARD QUESTION PAPER : MARCH 2016 GEOMETRY
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
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 informationCIRCLES. ii) P lies in the circle S = 0 s 11 = 0
CIRCLES 1 The set of points in a plane which are at a constant distance r ( 0) from a given point C is called a circle The fixed point C is called the centre and the constant distance r is called the radius
More informationIMPORTANT 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 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 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 information10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2)
10. Circles Q 1 True or False: It is possible to draw two circles passing through three given non-collinear points. Mark (1) Q 2 State the following statement as true or false. Give reasons also.the perpendicular
More informationMockTime.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 informationChapter-wise questions
hapter-wise questions ircles 1. In the given figure, is circumscribing a circle. ind the length of. 3 15cm 5 2. In the given figure, is the center and. ind the radius of the circle if = 18 cm and = 3cm
More information(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 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 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 informationSolutionbank C2 Edexcel Modular Mathematics for AS and A-Level
file://c:\users\buba\kaz\ouba\c_rev_a_.html Eercise A, Question Epand and simplify ( ) 5. ( ) 5 = + 5 ( ) + 0 ( ) + 0 ( ) + 5 ( ) + ( ) 5 = 5 + 0 0 + 5 5 Compare ( + ) n with ( ) n. Replace n by 5 and
More informationQ.1 If a, b, c are distinct positive real in H.P., then the value of the expression, (A) 1 (B) 2 (C) 3 (D) 4. (A) 2 (B) 5/2 (C) 3 (D) none of these
Q. If a, b, c are distinct positive real in H.P., then the value of the expression, b a b c + is equal to b a b c () (C) (D) 4 Q. In a triangle BC, (b + c) = a bc where is the circumradius of the triangle.
More information2016 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 informationSpecial 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 informatione x for x 0. Find the coordinates of the point of inflexion and justify that it is a point of inflexion. (Total 7 marks)
Chapter 0 Application of differential calculus 014 GDC required 1. Consider the curve with equation f () = e for 0. Find the coordinates of the point of infleion and justify that it is a point of infleion.
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 informationComplete 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 information2013 Sharygin Geometry Olympiad
Sharygin Geometry Olympiad 2013 First Round 1 Let ABC be an isosceles triangle with AB = BC. Point E lies on the side AB, and ED is the perpendicular from E to BC. It is known that AE = DE. Find DAC. 2
More informationPage 1
Pacing Chart Unit Week Day CCSS Standards Objective I Can Statements 121 CCSS.MATH.CONTENT.HSG.C.A.1 Prove that all circles are similar. Prove that all circles are similar. I can prove that all circles
More information( Bifurcated Syllabus ) ( According to Syllabus of Class X only) PART - I
Karunamoyee, Salt Lake, Kolkata : 70009 Mathematics (COMPULSORY) (Compulsory) Full marks : NEW 90 - For SYLLABUS Regular Candidates { Time 00 ---3 Hours - For 5 Eternal Minutes Candidates ( First 5 minutes
More informationSOLVED SUBJECTIVE EXAMPLES
Example 1 : SOLVED SUBJECTIVE EXAMPLES Find the locus of the points of intersection of the tangents to the circle x = r cos, y = r sin at points whose parametric angles differ by /3. All such points P
More informationPractice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? A. (1,10) B. (2,7) C. (3,5) D. (4,3) E.
April 9, 01 Standards: MM1Ga, MM1G1b Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? (1,10) B. (,7) C. (,) (,) (,1). Points P, Q, R, and S lie on a line
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 informationThe region enclosed by the curve of f and the x-axis is rotated 360 about the x-axis. Find the volume of the solid formed.
Section A ln. Let g() =, for > 0. ln Use the quotient rule to show that g ( ). 3 (b) The graph of g has a maimum point at A. Find the -coordinate of A. (Total 7 marks) 6. Let h() =. Find h (0). cos 3.
More informationSTRAIGHT LINES EXERCISE - 3
STRAIGHT LINES EXERCISE - 3 Q. D C (3,4) E A(, ) Mid point of A, C is B 3 E, Point D rotation of point C(3, 4) by angle 90 o about E. 3 o 3 3 i4 cis90 i 5i 3 i i 5 i 5 D, point E mid point of B & D. So
More informationCOORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE. To find the length of a line segment joining two points A(x 1, y 1 ) and B(x 2, y 2 ), use
COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE I. Length of a Line Segment: The distance between two points A ( x1, 1 ) B ( x, ) is given b A B = ( x x1) ( 1) To find the length of a line segment joining
More information11. Concentric Circles: Circles that lie in the same plane and have the same center.
Circles Definitions KNOW THESE TERMS 1. Circle: The set of all coplanar points equidistant from a given point. 2. Sphere: The set of all points equidistant from a given point. 3. Radius of a circle: The
More informationMathematics Extension 2
009 TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Etension General Instructions o Reading Time- 5 minutes o Working Time hours o Write using a blue or black pen o Approved calculators may be
More informationSYSTEM 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 informationMATHEMATICS EXTENSION 2
Sydney Grammar School Mathematics Department Trial Eaminations 008 FORM VI MATHEMATICS EXTENSION Eamination date Tuesday 5th August 008 Time allowed hours (plus 5 minutes reading time) Instructions All
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
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 informationGOVERNMENT 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 informationCircles, Mixed Exercise 6
Circles, Mixed Exercise 6 a QR is the diameter of the circle so the centre, C, is the midpoint of QR ( 5) 0 Midpoint = +, + = (, 6) C(, 6) b Radius = of diameter = of QR = of ( x x ) + ( y y ) = of ( 5
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 informationMath : Analytic Geometry
7 EP-Program - Strisuksa School - Roi-et Math : Analytic Geometry Dr.Wattana Toutip - Department of Mathematics Khon Kaen University 00 :Wattana Toutip wattou@kku.ac.th http://home.kku.ac.th/wattou 7 Analytic
More informationTrigonometry. Sin θ Cos θ Tan θ Cot θ Sec θ Cosec θ. Sin = = cos = = tan = = cosec = sec = 1. cot = sin. cos. tan
Trigonometry Trigonometry is one of the most interesting chapters of Quantitative Aptitude section. Basically, it is a part of SSC and other bank exams syllabus. We will tell you the easy method to learn
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 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 informationLecture 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 informationMATHEMATICS. r Statement I Statement II p q ~p ~q ~p q q p ~(p ~q) F F T T F F T F T T F T T F T F F T T T F T T F F F T T
MATHEMATICS Directions : Questions number to 5 are Assertion-Reason type questions. Each of these questions contains two statements : Statement- (Assertion) and Statement- (Reason). Each of these questions
More informationADDITIONAL MATHEMATICS
00-CE MTH HONG KONG EXMINTIONS UTHORITY HONG KONG CERTIFICTE OF EDUCTION EXMINTION 00 DDITIONL MTHEMTICS 8.0 am.00 am (½ hours) This paper must be answered in English. nswer LL questions in Section and
More information1 / 24
CBSE-XII-017 EXAMINATION CBSE-X-01 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 information