MATHEMATICS SOLUTION
|
|
|
- Jessie Douglas
- 5 years ago
- Views:
Transcription
1 MATHEMATICS SOLUTION MHT-CET 6 (MATHEMATICS). (A) (A) If the school bus does not come) (I will not go to school) ( I shall meet my friend) (I shall go out for a movie) ~ p ~ q r s ~ p q r s [De Morgan s law]. (C) p : is an even prime number q : 6 is a divisor of and r : HCF of and 6 is ~ p q r is true.. (B) C centre of the balloon, r = radius, O eye of the observer. POQ By geometry, POC QOC COH Height of the centre h CH OC sin CP cosec sin r cosec sin h r cosec sin...() CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI #
2 5. (C) A.(cos sin ) Now, A adja adja A 6. (B) We have sin x 0 cos x 6 0 cos x cos x 0 cos x or x n cos cos x [ cos x ] 7. (B) Let OAP be the tree. When broken by the wind at A, let its top P strike the ground at M so that OM = 0 m. OMA 0, AP AM in rt. d AOM, we have, 0 OA tan 0 OM 0 OA OM tan 0 0 m AM AM Also, sec0 OM 0 0 AM m Height of the tree = OP = OA + AP = OA + AM m Height 0 m..() CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI #
3 8. (B) Let y mx and y mx be the lines represented by the given equation 9. (A) 0. (B) h a Then, m m and mm b b We have m : m : m m h b h a m and m b b h a m and m b b m m and mm h The equation h a ab b b x hxy y 0 a b Will represents a pair of real and distinct lines if h h 0 0 Which is true for all h R. The distance between the parallel straight lines given by by g ac d a a b Here, a = 8, b =, c = 5 and g = Required distance units (C) We have sin (x x) sin x (x x) n ( ) x either x x m x x m z Where K is odd OR x x k x x x k 0 n 8K x For least positive non-integral solution, ax hxy by gx fy c 0 is given CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI #
4 8K q x, where q is an odd integer.. (D) Given, a, b and c are three non-coplanar vectors and p, q and r defined by the relations b p c, q c a a b and r abc abc abc b c abc c a abc a b c a p a abc And. (D) a ca a q a 0 abc Similarly, b q cr and a r b q cq b r 0 a bp b cq c a r a p b p bq cq c r a r We have, a ˆi ˆj kˆ And b i ˆ a i ˆ ˆ ja ˆ j k ˆ a k ˆ a a a ˆi j ˆ kˆ b (A) 5. (D) Let a ˆi ˆj k, ˆ b i ˆ j ˆ kˆ And x ˆi ˆj kˆ a b c CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI #
5 6. (A) 7. (A) Vectors are collinear tan h ab a b y cosec x 5 8 dy 7 cosec x. cos ecx cot x. x dx x cosec 5 x cosec x.cot x 8. (D) The direction ratios of the given line are, 7,. The given line is parallel to i ˆ 7ˆj kˆ From the cartesian equation of the given line, it is clear that it passes through the point The vector equation of the line is r 5i ˆ j ˆ 6kˆ i ˆ 7j ˆ kˆ 9. (A) If l, m, n are the direction cosines of the line, then l m n 0 And l m 0n 0 l m n 0 0 Hence, the direction ratios of the line are,, 0. (A) q Short cut. p ,,6. (A) Let the DR s of a required line be a, b and c. Since, the normal to the given planes x y z and 6x 8y z are perpendicular to the line. a b c 0 CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI # 5
6 a b c a b c a b c Or Also, line passes through (,, ). Equation is x y z. (C) Equation of any plane passing through given line is a x by cz 0... Above plane is perpendicular to the plane x y z a b c 0 Also, normal to the plane is perpendicular to the line a b c 0 a b c 8 a b c 9 5 9x y 5z 0 9x y 5z 0 a 9, b, c 5. (C) Direction ratios of given planes are a, b, c and a, b, c cos 6 cos 7. (A) In a right < 5. (A) cos cos cos CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI # 6
7 6. (C) We want to check the continuity of the function at x = For this, we have to prove that LHL = RHL = f() f h LHL lim f x limf h lim x h0 h0 RHL lim f x lim f h x h0 lim h h h0 Thus, LHL = RHL = f() = Hence, function is continuous at x =. 7. (C) Put x h as x, h 0 8. (B) Given limit h tan cos h lim h0 h h tan h h sin lim tan h0 8h h h tan sin lim tan h0 h h h h tan tan lim x0 h h We have, f x cos x..(i) On differentiating Eq. (i) w.r.t.x, we get f ' x sin x cos x cos x f ' x (x) sin x cos x x..(ii) CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI # 7
8 Put x in Eq. (ii) we get sin sin f ' (B) 0. (A) Given, x y y Applying componendo and dividendo, we get y y x x y y x x y x y x On differentiating w.r.t. we get x x x x x x x x x x x x x dy dx x y mx b m is a tangent to the circle x y b for all values of m. If it also touches second circle x a y b then the length of perpendicular from its centre (a, 0) on this line is equal to the radius b of circle ma b m m b taking positive value m ma b m b b m a b a b. (A) x sin a.cot (a + y) Now, differentiating w.r.t. y, we get dx sin a.cos ec a y dy CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI # 8
9 dy sin (a y) dx sin a. (D) Given, x t, y t On differentiating w.r.t. t, we get dx dy and t dt dt dy dy dt t dx dx t dt. (C) Given x xy y 7 On differentiating w.r.t. x, we get dy dy x x y y 0 dx dx dy x y dx x y dy dx, 5. (C) As the curve crosses Y axis i.e. x = 0 0 y e y Given, x y e dy e e dx dy 0 e dx 0, x x Equation of tangent at (0, ) is y x 0 x y 5. (C) If X and Y are number of heads obtained by A and B, then : X B( n, p / ) and Y B( n, p / ). P( x) P( y) C r chance that both get the same no. of heads P( X 0) P( Y 0) P( X ) P( Y ) P( X ) P( Y ) P( X ) P( Y ) CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI # 9
10 [ P( X 0)] [ P( X )] [ P( X )] [ P( X )] [( C0) ( C) ( C) ( C ) ] 0 5 [ 9 9 ] (A) x x x x x 7 x x x dx x x x x dx C (C) sin x cos x dx Let sin x t dt cos x dx dt dx cos x sin x cos x dx dt t cos x cos x t dt 8. (A) / t / C t C sin x C Given, log log x dx x f x g x C log x log log x dx dx II I log x LHS x log log x dx dx log x / log x x x log log x dx dx C log x log x log x x log log x C log x f x loglog x, g x log x CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI # 0
11 9. (D) Let 0. (B) x dx dx x x dx x x I x x x x x x x x I log tan C x x But x a, b Let I a log b tan C I dx dx x x dx 5 x x Put t dx dt 5 x x x x x t t / / I f dt C t C / / C x x / C x. (C) Let / / sin x I dx... i 0 I / / sin x cos x / 0 / / sin x cos x / sin x dx a a f xdx f a xdx 0 0 CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI #
12 0 x / / cos I dx... ii / / cos x sin x Adding Eqs. (i) and (ii), we get / I dx I 0. (C). (B). (A) Required area (shown in shaded region) 8 8 5x 7 ydx dx 8 5x x = 96 sq. units CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI #
13 5. (A) x y... i x y... ii Given curve is And For intersection point put the value of y from eq. (i) in Eq. (ii), we get x x x x 0 x x 0 x, When x, When x, y then from Eq. (ii), we get y y y then from Eq. (ii) we get The line meets the parabola at the points B, A,. and Required area = (Area under the line x = y ) (Area under the parabola x x dx dx x x x sq. units 8 8 Therefore, required area is 9 sq. units. 8 x y ) 6. (B) Let the numbers be a, ar, ar, where r > Then, a, ar, ar are in A.P. ar a ar ( a, b, c are in A.P. b = a+) CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI #
14 6r r r 6r 0 r ( 6) ( 6) 7. (A) Given, x x x y Ae Be Ce... i y Ae Be Ce From Eq. (i), x x x x x x Ae y Be Ce x x y y Be Ce.. ii x y y y Ce... iii Again, differentiating w.r.t., we get x y y y 6Ce From Eq. (iii), x Ce y y y y y y y y y y 6y y 6y 0 8. (D) The given distribution will be a probability distribution, if PX 0 PX PX PX k k k k k 8 CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI #
15 9. (B) p th, q th and n th terms are in G.P. aq ar a a () p q using a n = a + (n ) d, a (q )d a (r )d a (p )d a (q )d By subtracting from both sides (q p)d (r q)d a (p )d a (q )d q p r q a (p )d a (q )d q p r q a a p p a : a (q p) : (r q) q q () becomes: 50. (A) Let the probability of success and failure are p and q respectively. p q and p q q q and Required probability p C C5 C CENTERS: MUMBAI /DELHI / AKOLA / LUCKNOW / NASHIK /PUNE /NAGPUR / BOKARO /DUBAI # 5
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 ()
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.](/thumbs/89/97771760.jpg "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].
JEE MAIN 2013 Mathematics
JEE MAIN 01 Mathematics 1. The circle passing through (1, ) and touching the axis of x at (, 0) also passes through the point (1) (, 5) () (5, ) () (, 5) (4) ( 5, ) The equation of the circle due to point
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..
WBJEEM Answer Keys by Aakash Institute, Kolkata Centre MATHEMATICS
WBJEEM - 05 Answer Keys by, Kolkata Centre MATHEMATICS Q.No. μ β γ δ 0 B A A D 0 B A C A 0 B C A * 04 C B B C 05 D D B A 06 A A B C 07 A * C A 08 D C D A 09 C C A * 0 C B D D B C A A D A A B A C A B 4
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
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
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.
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
Question Paper Set MHT CET
Target s 0 Question Paper Set MHT CET Physics, Chemistry, Mathematics & Biology Salient Features Set of 0 question papers with solutions each for Physics, Chemistry, Mathematics and Biology. Prepared as
Rao IIT Academy/ ISC - Board 2018_Std XII_Mathematics_QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS. XII - ISC Board
Rao IIT Academy/ ISC - Board 8_Std XII_Mathematics_QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS XII - ISC Board MATHEMATICS - QP + SOLUTIONS Date: 6..8 Ma. Marks : Question SECTION - A (8 Marks)
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
ADDITIONAL 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
Objective 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
1 are perpendicular to each other then, find. Q06. If the lines x 1 z 3 and x 2 y 5 z
Useful for CBSE Board Examination of Math (XII) for 6 For more stuffs on Maths, please visit : www.theopgupta.com Time Allowed : 8 Minutes Max. Marks : SECTION A 3 Q. Evaluate : sin cos 5. Q. State the
Board Answer Paper: MARCH 2014
Board Answer Paper: MARCH 04 and Statistics SECTION I Q.. (A) Select and write the correct answer from the given alternatives in each of the following: i. (C) Let l 0, m 3, n be the direction cosines of
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
1 / 23
CBSE-XII-017 EXAMINATION CBSE-X-008 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
PART B MATHEMATICS (2) (4) = +
JEE (MAIN)--CMP - PAR B MAHEMAICS. he circle passing through (, ) and touching the axis of x at (, ) also passes through the point () (, ) () (, ) () (, ) (4) (, ) Sol. () (x ) + y + λy = he circle passes
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII:
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII: 05-6 Question numbers to 6 carry mark each. SAMPLE PAPER II Section A Q. Evaluate: - 3 sin(cos (- )). 5 Q. State the reason for the following Binary Operation
( )( 2 ) n n! n! n! 1 1 = + + C = +
Subject : Mathematics MARKING SCHEME (For Sample Question Paper) Class : Senior Secondary. ( )( )( 9 )( 9 ) L.H.S. ω ω ω. ω ω. ω ( ω)( ω )( ω)( ω ) [ ω ] ω ω ( )( ) ( ) 4 ω +ω +ω. [ 4 ] + + 49 R.H.S (Since
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
Sec 4 Maths SET D PAPER 2
S4MA Set D Paper Sec 4 Maths Exam papers with worked solutions SET D PAPER Compiled by THE MATHS CAFE P a g e Answer all questions. Write your answers and working on the separate Answer Paper provided.
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
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
CBSE X Mathematics 2012 Solution (SET 1) Section B
CBSE X Mathematics 01 Solution (SET 1) Section B Q11. Find the value(s) of k so that the quadratic equation x kx + k = 0 has equal roots. Given equation is x kx k 0 For the given equation to have equal
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
HSC - BOARD MATHEMATICS (40) - SOLUTIONS
Date: 8..5 Q. (A) SECTION - I (i) (d) A () (ii) (c) A A I 6 6 6 A I 64 I I A A 6 (iii) (a) fg cos A cos HSC - BOARD - 5 MATHEMATICS (4) - SOLUTIONS cos cos ch () hy g fy c...(i) Comparing with A Hy By
QUESTION PAPER CODE 65/2/2/F EXPECTED ANSWER/VALUE POINTS
QUESTION PAPER CODE EXPECTED ANSWER/VALUE POINTS SECTION A. P 6 (A A ) P 6 9. (a b c) (a b c) 0 a b c (a b b c c a) 0 a b b c c a. a b sin θ a b cos θ 400 b 4 4. x z 5 or x z 5 mark for dc's of normal
Rao IIT Academy/ 2015/ XII - CBSE - Board Mathematics Code(65 /2 /MT) Set-2 / Solutions XII - CBSE BOARD CODE (65/2/MT) SET - 2
Rao IIT Academ/ 5/ XII - CBSE - Board Mathematics Code(65 / /MT) Set- / Solutions XII - CBSE BOARD CODE (65//MT) SET - Date: 8.3.5 MATHEMATICS - SOLUTIONS. Let a iˆ 3iˆ kˆ b iˆ ˆj and a b 3 5, b a b Projection
38. The total number of carboxylic acid groups in the product P is 38. [2] O C HO 3 O C C O C O C O. Total no. of carboxylic group = 2
![38. The total number of carboxylic acid groups in the product P is 38. [2] O C HO 3 O C C O C O C O. Total no. of carboxylic group = 2](/thumbs/78/77697004.jpg "38. The total number of carboxylic acid groups in the product P is 38. [2] O C HO 3 O C C O C O C O. Total no. of carboxylic group = 2")
(6) Vidyalankar : IIT JEE 0 Advanced : Question Paper & Solution 8. The total number of carboxylic acid groups in the product P is 8. [] C.... + H Heat C Total no. of carboxylic group = C C H 9. A tetrapeptide
CIRCLES. 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
63487 [Q. Booklet Number]
![63487 [Q. Booklet Number]](/thumbs/88/114675139.jpg "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
KEY FOR MATHS EXAMINATION PART - I 25. b d inverse axiom 27. d [3] 1. a 1 2. c k a 1 4. c
![KEY FOR MATHS EXAMINATION PART - I 25. b d inverse axiom 27. d [3] 1. a 1 2. c k a 1 4. c](/thumbs/82/85468270.jpg "KEY FOR MATHS EXAMINATION PART - I 25. b d inverse axiom 27. d [3] 1. a 1 2. c k a 1 4. c")
MODEL HIGHER SECONDARY EXAMINATION KEY FOR MATHS PART - I Q. No. Key. a 2. c k - 3. a. c u = 0 5. a tan - /3 6. d abc 7. a (0, 0, -) 8. a (-, - 8) 2 9. a purely imaginary 0. a the straight line x = /.
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII ( ) BLUE PRINT. Unit VSA (1) SA (4) LA (6) Total. I. Relations and Functions 1 (1) 4 (1) 5 (2)
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII (2013-14) BLUE PRINT Unit VSA (1) SA (4) LA (6) Total I. Relations and Functions 1 (1) 4 (1) 5 (2) Inverse Trigonometric Functions 1 (1) *4 (1) 5 (2) II. Matrices
Saturday, March 27, :59 PM Annexure 'F' Unfiled Notes Page 1
Annexure 'F' CLASS-XII SAMPLE QUESTION PAPER MATHEMATICS CLASS XII (2013-14) BLUE PRINT Unit VSA (1) SA (4) LA (6) Total I. Relations and Functions 1 (1) 4 (1) 5 (2) Inverse Trigonometric Functions
ANNUAL EXAMINATION - ANSWER KEY II PUC - MATHEMATICS PART - A
. LCM of and 6 8. -cosec ( ) -. π a a A a a. A A A A 8 8 6 5. 6. sin d ANNUAL EXAMINATION - ANSWER KEY -7 + d + + C II PUC - MATHEMATICS PART - A 7. or more vectors are said to be collinear vectors if
RAJASTHAN P.E.T. MATHS-1995
RAJASTHAN P.E.T. MATHS-1995 1. The equation of the normal to the circle x2 + y2 = a2 at point (x y ) will be : (1) x y - xy = (2) xx - yy = (3) x y + xy = (4) xx + yy = 2. Equation of the bisector of the
Marking Scheme (Mathematics XII )
Sr. No. Marking Scheme (Mathematics XII 07-8) Answer Section A., (, ) A A: (, ) A A: (,),(,) Mark(s). -5. a iˆ, b ˆj. (or an other correct answer). 6 6 ( ), () ( ) ( ). Hence, is not associative. Section
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 =,
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
Part r A A A 1 Mark Part r B B B 2 Marks Mark P t ar t t C C 5 Mar M ks Part r E 4 Marks Mark Tot To a t l
Part Part P t Part Part Total A B C E 1 Mark 2 Marks 5 Marks M k 4 Marks CIRCLES 12 Marks approximately Definition ; A circle is defined as the locus of a point which moves such that its distance from
MockTime.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
Maharashtra 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
CHAPTER 10 VECTORS POINTS TO REMEMBER
For more important questions visit : www4onocom CHAPTER 10 VECTORS POINTS TO REMEMBER A quantity that has magnitude as well as direction is called a vector It is denoted by a directed line segment Two
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..
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.
All Rights Reserved Wiley India Pvt. Ltd. 1
Question numbers to carry mark each. CBSE MATHEMATICS SECTION A. If R = {(, y) : + y = 8} is a relation of N, write the range of R. R = {(, y)! + y = 8} a relation of N. y = 8 y must be Integer So Can
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII :
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII : 05-6 TYPOLOGY VSA ( M) L A I (4M) L A II (6M) MARKS %WEIGHTAGE Remembering 3, 6, 8, 9, 5 0 0% Understanding, 9, 0 4, 6 % Applications 4 3, 5, 6, 7, 0 9 9%
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
QUESTION BOOKLET 2016 Subject : Paper III : Mathematics
QUESTION BOOKLET 06 Subject : Paper III : Mathematics ** Question Booklet Version Roll No. Question Booklet Sr. No. (Write this number on your Answer Sheet) Answer Sheet No. (Write this number on your
(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
Individual Events 1 I2 x 0 I3 a. Group Events. G8 V 1 G9 A 9 G10 a 4 4 B
Answers: (99-95 HKMO Final Events) Created by: Mr. Francis Hung Last updated: July 08 I a Individual Events I x 0 I3 a I r 3 I5 a b 3 y 3 b 8 s b c 3 z c t 5 c d w d 0 u d 6 3 6 G6 a 5 G7 a Group Events
MATHS X STD. Try, try and try again you will succeed atlast. P.THIRU KUMARESA KANI M.A., M.Sc.,B.Ed., (Maths)
MATHS X STD Try, try and try again you will succeed atlast P.THIRU KUMARESA KANI M.A., M.Sc.,B.Ed., (Maths) Govt.Girls High School,Konganapuram Salem (Dt.) Cell No. 9003450850 Email : kanisivasankari@gmail.com
SOLVED 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
Time : 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
QUESTION BOOKLET 2016 Subject : Paper III : Mathematics
QUESTION BOOKLET 06 Subject : Paper III : Mathematics ** Question Booklet Version Roll No. Question Booklet Sr. No. (Write this number on your Answer Sheet) Answer Sheet No. (Write this number on your
QUESTION BOOKLET 2016 Subject : Paper III : Mathematics
QUESTION BOOKLET 06 Subject : Paper III : Mathematics ** Question Booklet Version Roll No. Question Booklet Sr. No. (Write this number on your Answer Sheet) Answer Sheet No. (Write this number on your
( )( ) PR PQ = QR. Mathematics Class X TOPPER SAMPLE PAPER-1 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
Consortium of Medical Engineering and Dental Colleges of Karnataka (COMEDK-2007)
Consortium of Medical Engineering and Dental Colleges of Karnataka (COMEDK-007) MATHEMATICS. Log'f/ is equal to 7 Log 35 5. In the group (G 5 ), where G = {3, 6, 9, }; 5 is multiplication modulo 5, the
NARAYANA IIT/PMT ACADEMY
CPT-_XI (LJ) 6.0.08 NARAYANA IIT ACADEMY ANSWER KEY XI STUD (LJ) IITJEE MAINS MODEL Exam Date :6-0-08 physics Chemistry Mathematics. (C). (C) 6. (A). (A). (B) 6. (C). (B). (A) 6. (B) 4. (A) 4. (D) 64.
CBSE 2018 ANNUAL EXAMINATION DELHI
CBSE 08 ANNUAL EXAMINATION DELHI (Series SGN Code No 65/ : Delhi Region) Ma Marks : 00 Time Allowed : Hours SECTION A Q0 Find the value of tan cot ( ) Sol 5 5 tan cot ( ) tan tan cot cot 6 6 6 0 a Q0 If
Transweb Educational Services Pvt. Ltd Tel:
. An aeroplane flying at a constant speed, parallel to the horizontal ground, km above it, is observed at an elevation of 6º from a point on the ground. If, after five seconds, its elevation from the same
KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE S. S. L. C. EXAMINATION, MARCH/APRIL, » D} V fl MODEL ANSWERS
CCE RF CCE RR O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALE 560 00 G È.G È.G È.. Æ fioê,» ^È% / HØ È 08 S. S. L. C. EXAMINATION,
Indefinite Integration
Indefinite Integration 1 An antiderivative of a function y = f(x) defined on some interval (a, b) is called any function F(x) whose derivative at any point of this interval is equal to f(x): F'(x) = f(x)
So, 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
*P46958A0244* IAL PAPER JANUARY 2016 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA. 1. f(x) = (3 2x) 4, x 3 2
Edexcel "International A level" "C3/4" papers from 016 and 015 IAL PAPER JANUARY 016 Please use extra loose-leaf sheets of paper where you run out of space in this booklet. 1. f(x) = (3 x) 4, x 3 Find
Page 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
1 / 23
CBSE-XII-07 EXAMINATION CBSE-X-009 EXAMINATION MATHEMATICS Series: HRL Paper & Solution Code: 0/ Time: Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question paper
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
ICSE Solved Paper, 2018
ICSE Solved Paper, 018 Class-X Mathematics (Maximum Marks : 80) (Time allowed : Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to
STD. XII ISC - BOARD MATHEMATICS - SOLUTIONS
Rao IIT Academ/XII-ISC-Board -05_Mathematics_SOLUTIONS Date: 6.0.05 Question STD. XII ISC - BOARD MATHEMATICS - SOLUTIONS SECTION A (i) 4 6 M 6 4 9 5 8 M 8 km k k k k M km I 0 5 8 k k 0 0 0 8 k k 0 0 0
Mathematics Class XII
Mathematics Class XII Time: hour Total Marks: 00. All questions are compulsory.. The question paper consist of 9 questions divided into three sections A, B, C and D. Section A comprises of 4 questions
Coordinate goemetry in the (x, y) plane
Coordinate goemetr in the (x, ) plane In this chapter ou will learn how to solve problems involving parametric equations.. You can define the coordinates of a point on a curve using parametric equations.
2001 Higher Maths Non-Calculator PAPER 1 ( Non-Calc. )
001 PAPER 1 ( Non-Calc. ) 1 1) Find the equation of the straight line which is parallel to the line with equation x + 3y = 5 and which passes through the point (, 1). Parallel lines have the same gradient.
CIRCLES PART - II Theorem: The condition that the straight line lx + my + n = 0 may touch the circle x 2 + y 2 = a 2 is
CIRCLES PART - II Theorem: The equation of the tangent to the circle S = 0 at P(x 1, y 1 ) is S 1 = 0. Theorem: The equation of the normal to the circle S x + y + gx + fy + c = 0 at P(x 1, y 1 ) is (y
QUESTION BOOKLET 2016 Subject : Paper III : Mathematics
QUESTION BOOKLET 06 Subject : Paper III : Mathematics ** Question Booklet Version Roll No. Question Booklet Sr. No. (Write this number on your Answer Sheet) Answer Sheet No. (Write this number on your
XII HSC - BOARD
Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS Date: 0.0.08 XII HSC - BOARD - 08 MATHEMATICS (40) - SOLUTIONS Q. (A) SECTION - I (i) If
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
SOLUTION CLASS-XII / (CBSE)
CBSE XII EXAMINATION-6 SOLUTION--6 CBSE th Board MATHEMATICS SET- CLASS-XII / CBSE Corporate Office : CG Tower, A-6 &, IPIA, Near Cit Mall, Jhalawar Road, Kota Raj.- PCCP Head Office: J-, Jawahar Nagar,
Practice Assessment Task SET 3
PRACTICE ASSESSMENT TASK 3 655 Practice Assessment Task SET 3 Solve m - 5m + 6 $ 0 0 Find the locus of point P that moves so that it is equidistant from the points A^-3, h and B ^57, h 3 Write x = 4t,
Worksheet A VECTORS 1 G H I D E F A B C
Worksheet A G H I D E F A B C The diagram shows three sets of equally-spaced parallel lines. Given that AC = p that AD = q, express the following vectors in terms of p q. a CA b AG c AB d DF e HE f AF
SAMPLE QUESTION PAPER MATHEMATICS (041) CLASS XII Time allowed : 3 Hours MAX.MARKS 100 Blue Print. Applicatoin.
Knowledge Understanding Applicatoin HOTS Evaluation Knowledge Understanding Applicatoin HOTS Evaluation Knowledge Understanding Applicatoin HOTS Evaluation Knowledge Understanding Applicatoin HOTS Evaluation
Paper: 03 Class-X-Math: Summative Assessment - I
1 P a g e Paper: 03 Class-X-Math: Summative Assessment - I Total marks of the paper: 90 Total time of the paper: 3.5 hrs Questions: 1] Triangle ABC is similar to triangle DEF and their areas are 64 cm
Marking Scheme. Section A 3. 2 [1] l m n 1 n 1 cos [1] Direction ratios of the given line are 2, 1, 2.
![Marking Scheme. Section A 3. 2 [1] l m n 1 n 1 cos [1] Direction ratios of the given line are 2, 1, 2.](/thumbs/91/106056849.jpg "Marking Scheme. Section A 3. 2 [1] l m n 1 n 1 cos [1] Direction ratios of the given line are 2, 1, 2.")
Marking Scheme Section A. B. AB 6 A B 6. sin( ) cos( ) or sin( ). 4. l m n n cos 45 or 6 4 OR Direction ratios of the given line are,,. [/] Hence, direction cosines of the line are:,, or,, [/] Section
SMT Power Round Solutions : Poles and Polars
SMT Power Round Solutions : Poles and Polars February 18, 011 1 Definition and Basic Properties 1 Note that the unit circles are not necessary in the solutions. They just make the graphs look nicer. (1).0
NARAYANA IIT ACADEMY
CPT-_XI (LJ) 7..7 NARAYANA IIT ACADEMY ANSWER KEY XI STUD (LJ) IITJEE MAINS MODEL Exam Date :7--7 physics Chemistry Mathematics. (C) 3. (B) 6. (C). (C) 3. (D) 6. (A) 3. (B) 33. (A) 63. (B) 4. (D) 34. (A)
Cambridge International Examinations Cambridge International General Certificate of Secondary Education
www.xtremepapers.com Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 8 0 2 3 6 5 2 7 1 3 * ADDITIONAL MATHEMATICS 0606/11 Paper 1 October/November
Delhi Public School, Jammu Question Bank ( )
Class : XI Delhi Public School, Jammu Question Bank (07 8) Subject : Math s Q. For all sets A and B, (A B) (A B) A. LHS (A B) (A B) [(A B) A] [(A B) B] A A B A RHS Hence, given statement is true. Q. For
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
(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
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
MT - 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
1 / 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
Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths
![Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths](/thumbs/86/93150791.jpg "Topic 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
CBSE 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.
( 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
Question 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
Answers for NSSH exam paper 2 type of questions, based on the syllabus part 2 (includes 16)
Answers for NSSH eam paper type of questions, based on the syllabus part (includes 6) Section Integration dy 6 6. (a) Integrate with respect to : d y c ( )d or d The curve passes through P(,) so = 6/ +
WBJEE Answer Keys by Aakash Institute, Kolkata Centre
WBJEE - 08 Answer Keys by, Kolkata Centre MATHEMATICS Q.No. 0 A B C D 0 C D A B 0 B D A C 04 C B A B 05 C A C C 06 A C D C 07 B A C C 08 B *C,D C A 09 C D D B 0 D A C D B A B C C D A B B A A C 4 C C B