1. TechnicalSupportprovided by Li'!Ni;j Z 0 N E I I N T NATIONAL Olympiad of Mathematics An ISO 9001 : 2000 Certified Organization Organized by : MATHEMATICS OLYMPIAD FOUNDATION (NGO) New Delhi, India Promoting Mathematics Education www.mathsolympiad.orgNEW DELHI. INDIA CLASS 6th .. SYLLABUS AND SAMPLE GUESTION PAPER SYLLABUS The Actual Q.uestion ~aper contains 40 questions. The duration of the test paper is 60 Minutes. cNUrriber system & its operation, indian & International System. BODMAS Rule. L.C.M. & H.C.F.. Fractional & Decimal Algebraic Expressions; Linear equations & its solution, About Lines, QuadrJlateral & type of quadrilateral, Triangle & its property, Area & perimeter of geometric figures !Triangle. circle, Quadrilateral) etc. Pictorial chart, Bar graph. 1. Complete the series 11, 13, 17, 19, 23, 25, (...) (a) 27 (b) 31 (c) 29 (d) 28 2. Horse is related to Mare as Bull is related to (a) Animal (b) Stable (c) Meat (d) Cow 3. If E = 5, then CAT means. (a) 23 (b) 24 (c) 3 (d) 25 4. Find the cost of fencing a rectangular field of length 175m & breadth 125m at the rate of Rs. 12 per meter. I (a) Rs. 7000/- (b) Rs. 6500/- (d) Rs. 7500/-(c) Rs. 7200/- 5. There are 20 girls and 15 boys in a class. What is the ratio of no. of girls to the total no. of students ~.... in the class. (a) 7: 4 (b) 2: 7 (d) 4: 7(c) 6: 7 6. A speed of 36 km/h is the same as (a) 10 m/sec (b) 12 m/sec (c) 129.6 m/sec (d) 3600 m/sec _______________________________________1 Page 13

2. EX/Tabus & Sample Questions - iOM .'0{) 1 _ 7. Simplify this: 312x312 - 218x 218 530 (b) 97 (c) 95 (d) 94(a) 93 8. Find the square root of 1225. (a) 25 (b) 45 (c) 35 (d) 15 9. The number x, x + 2 and x + 4 are all prime numbers. If (a) x == 2 (b) x = 3 (c) x == 5 (d) x = 7 10. A train, 480m long, passes a standing man in 24 sec. What is the speed of the train in km/h? (a) 72 km/h (b) 24 km/h (c) 20,km/h (d) None of these 11. A person buys a scooter for Rs. 4,500. For how much should he sell it to get gain 8%? (a) Rs. 4800/- (b) Rs. 4860/- (c) Rs. 5000/- (d) Rs. 4000/- 12. Find the average wages of the 5 workers, whose daily wages are Rs. 80, 70, 120, 100, 110. (a) Rs. 100/- (b) Rs. 90/- (c) Rs. 96/- (d) Rs. 95/- 13. Find the H.C.F of 18, 48, 72. (a) 4 (b) 9 (c) 16 (d) 6 14. Which one is not like the other words in the group? (a) March (b) July (c) August (d) April 15. The average of even numbers from 1 to 20 is __ . (a) 12 (b) 11 (c) 10 (d) 110. 16. (17)2+ (23)2 == ? (a) 718 (b) 818 (c) 988 (d) 828 17. Simplify: 2 - [2 - {2 - 2 - 2}] (a) 3 (b) 2 (c) 0 (d) 1 18. Find the value of 62 - 52 (a) 9 (b) 8 (c) 11 (d) 10 5. (d) 13. (d) 7. (d) 15. (b) 2. (d) 10. (a) 18. (c) 3. (b) 11. (b) 6. (a) 14. (d) 4. (c) 12. (c) 8. (c) 16. (b) 1. (c) 9. (b) 17. (b) Page 14 1--------------------------------------- '"

3. INTERNATIONAL Technical Support provided by @'hi;JZONEI NEW DELHI. INDIA ymptad of athematics An ISO 9001: 2000 Cerlified Organization Organized by : MATHEMATICS OLYMPIAD FOUNDATION (NGO) New Delhi. India Promoting Mathematics Education www.mathsolyrnpiad.orq CLASS 7th ' SYLLABUS AND SAMPLE GUESTIDN PAPER The Actual Question Paper contains 40 questions. The duration of the test paper is 60 Minutes. .~. 'A lTl)jijim ,,~tic?J~~.H9.F.& L8,M., Ration~ number & it~operations, ty1ultipli- & ion 01 ra at number, 8impla',& compoundtnterest, Percentae. Profit & Loss, Time ,&distance, Algebraic expression & Simple linear equations, Elementary Mensuration (triangle, circle quadrilateral) etc. Bar graph. 1. (4)2 +(3)2 = .fi (a) 25 (b) 5 (d) 125(e) 425 2, What will be the area of the square whose perimeter' is 320m. (a) 6500, m2 (b) 640 m" (e) 6000 m- (d) 6400 m" (a) 2 (e) 26(b) 27 (d) 25 4. 0.002 x 0.05 is equal to (a) O.OOlDO (e) 0.0001 (b) 0.01000 (d) None of these 5. What is the value of x, if 30 - 5(x - 1) = a (a) 7 (b) 6 (e) 5 (d) 4 _______________________________________1 Page 15

4. 6. Find the perimeter of the adjoining figure which is a semicircle including its diameter. (Where 1t = 3.147 ) ( ) 10m (a) 25 m (b) 20 m (c) 25.7 m (d) 20.7 m. 7. If m = 2, what is the value of 3m2 - 2m - 7 (a) 0 (b) 1 (c) 2 (d) 5 8. 651.2.;. 4 will be (a) 16.28 (b) 1.628 (c) 162.8 (d) 1628 9. If c Line a II band _cis a transversal line, L. y = ? (c) 1750 (d) None of these 10. In the adjoining figure, find the value of x. (d) None of these tz. What is the value of n? If fii = 64 0.835 x 0.835 x 0.835 + 0.165 x 0.165 x 0.165 11. Simplify: 0.835 x 0.835.0.835 x 0.165 +0.165 x 0.165 (a) 1 (b) 2 (c) 3 (d) 0.5 (a) n = 6 (b) n = 4 (c) n = 8 (d) . n = 12 13. The sum of lwo numbers is 20 & their difference is 10. Find the product of the two numbers. (a) 6u (b) 100 (c) 75 (d) 80 14. Two numbers are in the ratio of 3 : 1. If the sum of these two numbers is 440, find the numbers. Page 16 1 _ t.

5. ______________________ 1 Syllapus Sam Ie uestions- iOltf'i)9 (b) 200, 240 (c) 400, 40 (d) 330, 110.(a) 320, 120 15. A class has 20 boys & 30 girls. The average age of the boys is 12 years and that of the girls is 11 years what is the average age of the whole class? (a) 11.4 years . (b) 11.6 years (c) 11.2 years (d) 12 years I. 16. A man buys a toy for Rs. 25 and sells it for Rs. 30. Find his gain percentage. (a) 30% (b) 20% (c) 40% . (d) 10% 17. Which of the following venn diagram correctly represents Pet animals, Dog, Lion: ego (a) 0 (O)@ (d)@)(b)OO o 18. ANAEMIA is related to 'IRON' as 'GOITRE' is related to (a) Iodine (b) Blood (c) Weakness . (d) Vitamin 19. Which word cannot be made from the word REASONABLE? (a) BRAIN (b) BONES (c) NOBLE (d) ARSON 20. Which number is opposite to 3? (b) 2 (c) 4 (d) 6(a) 1 ANSWERS 1. . (a) 2. (d) 3. (c) 4. (c) 5. (a) 6. '(c) 7. (b) 8. (c) 9. (a) 10. (c) 11. (a) 12. (d) 13. (c) 14. (d) 15. (a) 16. (b) 17. (a) 18. (a) 19. (a) 20. (c) -------------------------------------1 Page 17

6. INTERNATIONAL Technical Support provided by i"98;1 ZO N E I An ISO 9001: 2000 Certified Organization Oympia of Mathematics . NEW DELHI. INDIA Organized by : MATHEMATICS OLYMPIAD FOUNDATION (NGO) New Delhi, India Promoting Mathematics Education www.mathsolympiad.org CLASS 8th SYLLABUS AND SAMPLE GUESTION PAPER SYLLABUS Thei1ctual Question Paper contains 40 questions, The duration of the test paper is 60 Minutes. Section- 1 : Number system, Mathematical modelling & reasoning, Completion 'of series, Odd man out, Problem related to cube & dice etc. Section - II: L.C.M & H.C.F., Square & Square roots, Cube & cube roots, Exponents &, Radici:ds, Time & work, Profit & loss, Equation of one & two variable, Parallel lines, Circ1es, A(ea, Surface area & volume of geometrical figure etc. :S~ction - ill : Blood Helationshiptest, Coding - decoding. 1. (105)3 is equal to (a) 1158625 (b) 1156525 (e) 1157625 (d) 1155625 2. Fill up the gap? 6 20 12 30 4j? J J26 42 114 (a) 89 (b) 72 (e) 74 (d) 81 3. If n is a whole number, n2(n2 - 1) is always divisible by (a) 12 (b) 24 (e) 36 (d) 4 5-2 x 3-2 x (125)2/3 4. (27)(-2/3) x (32f1l5 (a) 2 (b) 4 (e) 3 (d) 5 Page 18 I ~----------------~-------- '"

7. ________________~------------I~~--~~~--~~~~ 5; Mohan sold two horses for Rs. 15000 each. On one he gained 20% and on the other he lost 20%. Find his total loss or gain. (a) 1200 (b) 1280 (c) 1300 (d) 1250 6. At what rate percent per annum will a sum of Rs. 4000 yield compound interest of Rs. 410 in 2 years. (a) 5% (b) 4% (c) 10% (d) 6% 7. The sum of two numbers is 45 and their ratio is 7 : 8. Final the numbers. (a) 21, 22 (e) 20, 21 (b) 25, 26 (d) 21, 24 8. The perimeter of a rectangle is 640 m. and the length is to the breadth as 5 : 3, then what will be its area?' . (a) 2400 m2 (e) 2500 m2 (b) 24000 m" (d) can't be determined 9. Ratio of the area of two square is 25 : 9. Find the ratio of their perimeters. (a) 5: 9 (b) 9 : 5 (c) 5: 3 (d) 3: 5 10. The surface of a cube is 1176 cm-. The volume of this cube is--- (a) 7056 ern" (b) 4704 em" (e) 2744 ern" (d) 3528 em! 11. 300m from the foot of a cliff on level ground the angle of elevation of the top of a cliff is 30 then height of the cliff will be _ (a) 200.J3 m (b) lOO.J3 m (c) 300.J3 m (d) 150.J3 m 12. From the digit 1, 2, 3, 4. How many numbers of 3- digit can be formed? (a) 12 (b) 18 (c) 24 [c} 36 13. A = {1, 2, 3, 4, 5}. How many possible no. of subsets can be formed from set A? (a) 16 (b) 24 (e) 30 (d) 32 14. From the given figure, what will be the value of x (a) 45 (b) 60 (d) 30(c) 75 -------------------------------------1 Page 19 '"

8. 15. From the adjoining figure, what is the value of ? (a) 60 (b) 80 (c) 70 J5+1 J5:i a2 +ab+b2 16. Ifa= J5:i 'b = J5+i then the value of is 5-1 5+1 a2 -ab+b2 (a) 3/4 (b) 19/7 (c) 3/5 (d) 50 (d) 5/3 17. If DEAR is coded as FGCT, then how will READ be coded as (a) TGCF (b) FGCF (c) TSFC (d) TCGF 18. If day before yesterday it was Monday. What day will fall on a day after tomorrow? (a) Sunday (b) Friday . (c) Saturday (d) Thursday 19. If AT = 20, BAT = 40 then CAT will be equal to: (a) 30 (b) 50 (c) 60 (d) 70 20. Complete the series. 9, 12, 11, 14, 13, ( ), 15 (a) 12 (b) 16 (e) 10 (d) 17 A'N S WE'R, S 1. (c) 2. (b) 3. (d) 4. (c) 5. (d) 6. (a) 7. (d) 8. (b) 9. (c) 10. (c) 11. (b) 12. (c) 13. (d) 14. (b) 15. (c) 16. (b) 17. (a) 18. (b) 19. (c) 20. (b) Page 20 I ~--~----- '. .~.

9. TechnicalSupportprovided by ~il59i;JZ 0 N E I An ISO 9001: 2000 Certified Organization INTERNATIONAL Oy piadof Mathematics Organized by : MATHEMATICS OLYMPIAD FOUNDATION (NGO) New Delhi, India Promoting Mathematics Education www.mathsolympiad.orgNW DELHI. INDIA CLASS 9th SYLLABUS AND SAMPLE GUESTIDN PAPER SYLtABUS The Actual Question Paper contains 40 questions, The duration of the test paper is 60 Minutes. $e'Ctig,n - : P~~plef'! relat!d to. cube & dice, Number system, Mathematical Modelling & operations. Completion of .series & odd man out. $. Section - It' : Triangle & its properties. Simple & compound interest, Coordinate Geometry, Heron's formulae, Statistics, Linear Quadratic Equation. ii[ . _~*:_; , se - Ul :ProbablHty, Arrangement of things. 1. log tant? + logz" + logs'' + + log88 + log 89 is equal to (a) 1 (b) 0 (e) 2 (d) None of these '2. A leap year contains .....odd days W 1 ~) 2 (d) None of these(el 0 3. In the adjoining, ABeD is a parallelogram. Find the value of x and y. ,r---------~~~c " A~~~---------' 21 In = 1+2+3+4 + 21 is equal to. n=I 4. (b) 312(a) 213 (d) 231(e) 321 --------------------------------------1 Page 21 '.

10. SyUabu$ & Sam le stions - iOM '09 I 5. Convert 0.47 in the rational form 47 47 43 43 (a) - (b) 90 (c) - (d) - 99 90 99 6. What is the total surface area of a right circular cone, the radius of whose base is 21 ern and height is 28cm. (a) 1396 ern- (b) 3696 em- (c) 3966 em' (d) 6468 em- 2 7. Sita spends 66 3 % of her salary and can save Rs 300. What is her total salary? (a) Rs 900 (b) Rs 800 (c) Rs 1100 (d) 1000 8. Find the value of (243t8 +(243)4 (a) 49' (b) 25 (c) 9 (d) 16 9. (a) 1/3 (b) 2/3 (c) 1/2 (d) can't be determined 10. TheLCM of two number is 2079 and their HCF is 27. If one of the numbers is 189. Find the other number. (a) 297 (b) 279 (c) 792 (d) 279 11. If the price of a pencil is decreased by 16~ % and decrease is Rs. 3, find the new price of the 3 pencil. (a) Rs 18 (b) Rs 15 (c) Rs 24 (d) Rs 16 12. An umbrella was purchased at Rs. 80/- and sold forRs. 68/-. The rate of discount is : (a) 12% (b) 15% (d) 20% 13. In which quadrant point (-5, -7) lies (a) 1st quadrant (b) 2nd quadrant (c) 3rd quadrant (d) 4th quadrant 14. A & B together can do a piece of work in 6 days & A alone can do it in 9 days. In how many days can B alone do it? (a) 16 days (b) 15 days (c) 12 days (d) 18 days Page 22 I ~------------------~--------

11. ____________________ 1 Syllabus & Sample Questions - iOM '09 15. Lines AB & CD intersect at O. If LCOE = 90 . Find the value of a, band c c E (a) 30, 40, 15 (b) 30, 60, 12 (c) 30, 40, 12 (d) None of these 16. P(A) = 0.25, P(B) = 0.5, P( AnB)= 0.14 then P(AuB) = ? (a) 0.61 (b) 0.62 (c) 0.16 (d) None of these 17. Find the missing number 4, 196, 16, 144, 36, 100, 64, ? (a) 36 (b) 100 (c) 80 (d) 64 18. Find out the word which is of a different class. (a) BSF . (b) IAS (c) RPF (d) IAF 19. KWZ, MaX, ON, QET, ? (a) SAQ (b') SUR (c) RAP (d) SCR 20. 'Which figure of the following venn diagram represents. Anti-Social Elements, Pick Pocket, Blackmailers. (a) SWERS 4. (d) 12. (b) 20. (b) 1. (b). 9. (c) 17. (d) 2. (b) 10. (a) 18. (b) 5. (d) 14. (d) 3. (c) 11. (b) 19. (d) 7. (a) 15. (c) 8. (c) 16. (a) 5. (c) 13. (c) ~-------------------------------------I Page 23 '. '~.

12. TechnicalSupport provided by Lilh8;' Z 0 N E I An ISO 9001: 2000 Certified Organization INTER>JAT[ONAL ympiad f Mathematics Organized by : MATHEMATICS OLYMPIAD FOUNDATION (NGO) New Delhi. India Promoting Mathematics Education www.mathsolympiad.orgNEW DELHI, INDIA CLASS 10th SYLLABUS AND SAMPLE GUESTIDN PAPER scs SYLLABUS The Actual Question Paper contains 40 questions. The duration of the test paper is.60 Minutes. Section ,!: Nl:1lT!bers~stem",Oistance, Speed & Time, Profit and, los~., Codi!}9 - d~t Mathematical operatiotls, IQ Test, se .!A ,. Section - II : Sequence & Series; Unear Equation in two variable, PoJynomial Equation, Expression (up to 3 degrees), Similar Triangle, its properties, Circles, Trigonometrillden- tity, Property of Triangle, Height & distance, Coordinate Geometry. Surface area & vol~e ,0f,geometricaJ fig, ,. Section - III : Pr6babifity, Arrangement of thing, Statistics. 1. The point (8, 12), (7, 13), (5, 15) are (a) vertices of the equilateral triangle' (c) concyclic (b) collinear (d) None of these 2. In the adjoining fig. a circle is inscribed in a square of side 14 em. What is the area of the shaded region? (d) 28 cm.(a) 42 em. (b) 36 cm. (c) 44 cm. I ~--------Page 24 '"

13. ______________________________I~~~~~_~~~-~~~-- 3. Find the value of y, 2 1 2 y --Y=- 3 9 (d) ~ ~ 3 ' 4 5 4 (c) 3' 5" 4. If ex, ~, Y be the roots of the equations x(1+x2 )+Jt( 6+x)+2 = 0 then the value of 0(-1+~-1 +v' is equal to (a) - 3 (b) 1/2 (d) None of these(c) - 1/2 20 5. If' . n then L tn is equal toIn a senes tn =-- In+l n=l (a) 20!-1 (b) 20 1 (d) 21!-1 -- - (c) -- 21! 21! 2(n -1)! 21! 6. What is the sum of uptotu'" terms of the A.P. 5, 15, 25, ......... (a) 500 (b) 400 (c) 1000 (d) 1500 7. A cone of radius 12 cm. is divided into two parts by drawing a plane through the mid point of its axis parallel to the base. Compare the volumes of the two parts. (a) 7: 1 (b) 1 : 7 (e) 3: 5 (d) 5:.3 8. Ram went to a bank to withdraw Rs. 2000. Heasked the cashier to give him Rs 50 and Rs 100 . notes only. Ram got 25 notes in all. Find how many notes of Rs. 50 and Rs. 100 he received respectively. (a) 10, 20 (b) 15; 20 (c) 20, 5 (d) 10, 15 9. What is the area of the shaded region (to the nearest em") in the given figures where a is the centre of the circle. f I (a) 16 em (b) 14 em (c) 15 cm (d) 18 em 10. The median can graphically be found from. (a) Ogive (b) histogram (c) frequency eurve (d) None of these --------------------------------------1 Page 25 ...

14. Syllabus & Sample uestio~s - iOM '09 1 .....:... ---,::-- 11. The mean of variates 5, 7, 8, 11, 13, 17 with frequencies 4, 6, 9, 10, 12, 11 respectively is (a) 8 (b) 11.3 (c) 12 (d) 13 12. 100 cards marked with numbers 2 to 101 are placed in a bag and mixed thoroughly. Ram draws a cards from the bag. Find the probability that the number on the card is a number which is a square of. 2 (a) 25 (b) 9 100. 1 50 (d) None of these(c) 13. Two cards are drawn at random from a pack of 52 cards. The probability of getting at least a spade and an ace is (a) 2 51 (d) 1 34 (b) 8 221 1 (c) 26 14. The number of 5 digit even numbers that can be made with the digits 0, 1, 2, 3 is (a) 192 (b) 384 (c) 768 (d) None of these 15. Find the number in the unit place in 96'2-x 966 x 454 x 959 (a) 2 (b) 4 (c) 6 (d) 8 16. A man spends 60% of his income. His income increased by 15% and his expenditure also increases by 5%. Find the percentage of increase in his saving. (a) 30% (b) 15% (c) 20% (d) 25% p. A sells an article to B at a profit of 5% and B sells it to C at a loss of 5%. If C pays Rs. 23.94 for it, what did it cost to A. (a) Rs.24 (b) Rs. 25 (c) Rs.26 (d) Rs. 30 18. 10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men & 15 women work together, in how many days will the work get completed? (a) 6 (b) 7 ~ 3 (c) 6~ 3 19. ABXW, EFTS,?, MNLK (a) IJOP (b) IJPO (c) JIOP (d) JIPO ANSWERS .: 1. (b) 2. (a) 3. (a) 4. (c) 5. (d) 6. (a) 7. (b) 8. (d) 9. (b) 10. (a) 11. (b) 12. (b) 13. (c) 14. (b) 15. (a) 16. (a) 17. (a) 18. (c) 19. (b) Page 26 I------~--------~--------~-------- '"

15. Technical Support provided by 1O.1'rii;JZONEI lNTERNATIONAL lympiadof athematics An ISO 9001: 2000 Certified Organization Organized by : MATHEMATICS OLYMPIAD FOUNDATION (NGO) New Delhi. India Promoting Mathematics Education www.mathsolympiad.orgNEW DELHI, INDIA CLASS 11th SYLLABUS AND SAMPLE QUESTION PAPER SYLLABUS ~ Sets, Relations and functions, Coordinate Geometric:- Straight line, pair of St. line, Conic. $ection. Basic concept about 3- dimension (Solid geometry) Sequence and series, Com- plex Number, Quadratic Equation and expression, Binomial theorem, Permutation and Com- bination,-Probability, Non-Verbal Reasoning (1.0.), Central Tendency, Variance & Stan- dard Deviation 1. Let A = {1, 2, 3, 4} and R be a relation in A given by R = (1, 1), (2, 2), (3, 3), (1, 2), (3, 1), (4, 4), (2, 1), (1, 3) Then R is (a) reflexive (c) transitive (b) symmetric (d) both reflexive & transitive 2. Let f : R -? R such that f(x) =~' XE R. Then f is l+x (aJ injective (bJ surjective .. (d) none of these(c) bijective 3. The range of the function f(x) = 7- x Px_3 is [Q nPr = In~r] (a) {I, 2, 3} (b) {I, 2, 3, 4, 5, 6} (c) {I, 2, 3,4 } (d) {I, 3} 4. Let A and B be two sets. Then (AuB)'u(A'nB) is equal to (a) A' (b) A (d) none of these(c) B' 5. The distance between the lines 3x + 4y = 9 and 6x + By + 15 = a is 3 (a) - 10 (b) 33 10 33 (c) 5 (d) none of these --~---------------------------------I Page 27 '..

16. (a) AP (b) GP 6. If CasA + CosB + 2CosC = 2. Then Side of the VABC are in- (c) HP (d) None of these 7. The equation X2+ y2 - 2x + 4y + 5 = 0 represents (a) a point (b) a pair of straight lines (c) a circle of non-zero radius (d) none of these 8. The points (4, 11), (5, 10), (6, 9) are (aj vertices of an. equilateral triangle (c) concyclic (b) collinear (d) none of these g. The vertex of the parabola (y - a)2 = 4a (x + a) is _ (a) (- a, a) (b) (a, - a) (c) (- 2a, 2a) (d) 10. If A =[~ ~ ~lthen in which option is true. 111 (a) A3 =9A (b) A3 = 27A 11. aD +bD is the H.M. between a and b if n is aD - 1 + bD - 1 (c) A+A=A2 (DL A-I does not exist. (a) 0 1 (b) 2 12. The value of cosec Ifl" - ../3seclOo is equal to: 1 (a) 2 (b) 2 (c) 4 13. If cas 20 - sin 20 = P then cas 40 is equal to: (a) _p~2_p2 14. The value of cas go - sin go is equal to: ~5-J5(a) - --'----- 2 5+J5 (b) 4 -1 (c) 2 (d) 1 Page 28 (c) p+2~2-p2 (d) none of these (c) ~~5-J5 2 (d) none of these I----------------------------~------ '"

17. ___________________________I~~~~~~~~~~~~~~ 15. In a group of boys, the no. of arrangements of 4 boys is 12 times the no. of arrangements of 2 boys. The no. of boys in a group is (a) 10 (b) 8 (c) 6 (d) none of these 16. Find r, if 54Pr = 6 SPr_1 (a) 4 (b) 5 (c) 2 (d) 3 xIS -1 17. Evaluate Um-- is equal to : x~lxlO -1 2 3 5 5 (a) - (b) - (c) - (d) - 3 2 2 3 18. In a single cast with two dice the odds against drawing 7 is: (a) 1 6 (b) ~ . 12 (c) 5: 1 (d) 1: 5 19. 10 apples are distributed at random among 6 persons. The probability that at least one of them will receive none is 6 (a) 143 (d) none of these 137 (c) 143 '20. Which of the following comes out next in the series below? JAZ, LEX, NN, POT, ? (a) QUR (b) RSR (c) RUS (d) SUR k " ':aJ ANSWERS ." "', 1. (d) 2. (d) 3. (d) 4. (a) 5. (b) 6. (a) 7. (a) B. (b) 9. (a) 10. (b) 11. (a) 12. (c) 13. (b) 14. (c) 15. (c) 16. (d) 17. (b) lB. (c) 19. (c) 20. (c) .I Page 29 '"

18. TechnicalSupportprovided by ...1'4i;'Z CJ N E I INTERNATIONAL Promoting Mathematics Education www.mathsolympiad.org An ISO 9001: 2000 Certified Organization Organized by : MATHEMATICS OLYMPIAD FOUNDATION (NGO) New Delhi, India NEW DELHI. INDIA CLASS 12th SYLLABUS AND SAMPLE GUESTIDN PAPER 1. Let A = {I, 2, 3} and B = {a, b} then which of the following subsets of Ax B is a mapping from A to B? (a) {(l, 0), (3, b), (2, a)} (b) {(l, b), (2, a). (3, an (c) {(l, a). (2, b)} (d) none of these 2. On the set A =' {i, 2, 3, 4}, a relation is R = {(l, 3). (4, 2), (2, 4) (2, 3), (3, l)}. The relation R is (a) a function (b) transitive (c) not symmetric (d) reflexive 3. The relation "congruence modulo" is (a) reflexive only (c) -symmetric only (b) transitive only (d) an equivalence relation 4. If A arid B are two sets. Then (A - B) U (B - A) U (A I B) is equal to (a) AUB (b) AI B (d) B'(c) A 5. sincot-1tancos-1x is equal to (a) x (b) ~1-x2 1 (d) none of these(c) x Page 30 I ~----------------------------~---

19. 6. If A be a sequence matrix of order 2x 2 then I KA I is equal to (a) KIAI (b) K31AI (c) 3KIAI (d) K21AI 7. If 10g45 = a and 10g56 = b then 10g32 is equal to 1 1 1 (a) -- (b) 2b+1 (c) 2ab+1 (d) -- 2a+l 2ab-l 8. In a AABC, A = 900 , then t -I ( b) -I ( c )an -- + tan -- is equal to a+c a+b 1t (a) 4 (d) none of these(b) 1t 2 (c) tan-I 9. The points (- 1, 1) and (1, - 1) are symmetrical about the line _ (a) x + y = a (b) y = x ec) x + y = 1 (d) none of these 10. The range of the real-valued function rex) = ~9 - x2 is (a) [0, 3) (b) [- 3, 3) (d) none of these(c) [- 3, 0) x-I 11. If rex) = -- then f (ax) : x, the term of f (x) is equal to x+l . f(x)+a (a) l+af(x) (b) (a-1)f(x)+a+l (a+1)f(x)+a-1 (a +l)f(x) +a= l (c) (d) none of these (a -1)f(x) +a +1 dy 12. If y = sin XO and z = cos x then - is equal to dz (a) - cosec x . cos x 1t 1tX (b) -cosec-.cosx 180 180 -1t 1tX (c) -.cosecx.cos- 180 180 (d) none of these ta -I 2xth - -I 2x 13. The derivative of n --2 WI respect to SID--2 is I-x l+x 1 (a) l+x2 (b) 1 l-x2 (c) a (d) 1 ________________________~--~--------I Page 31 " .~.

20. ~~--~~~~~--~~I----------------------------~ (a) 1 (b) a 1 (d) 2(c) 2 l-sinx 1t 1t (1t)15. Let f(x) = ., x ! - . If f (x) is continuous at x = - then f -2 should be sin2x 2 . 2 (a) 1 (b) a 1 (c) 2 (c) none of these XO yO . x 16. The curve -; + -; = 2 touches the line - + I = 2 at the point a b ab --- (a) (b. a) (d) (~,~)(b) (a. b) (c) (1. 1) 17. J'~2+ x dx is equal to _ 2-x . o (a) 1t+2 (b) 1+~ 2 3 (c) 1t+-2 (d) none of these 1 18. The value of fx.exdx is o (a) 2 1 (b) 2 (c) a (d) 1 - 19. What is order and degree of this differ~ntial equation? x ::; + 2(:~r-xy + x2 - i = 0 (a) (1. 2) (b) (2. 1) (c) (2. 2) (d) (1. 3) 20. A dice is tossed thrice. What is the probability of getting a odd number at least once? 5 (b) l 1 7 (a) - (c) - (d) - 8 8 8 8 ~.NSWERS " , - .. 'J. . . 1. (b) 2. (c) 3. (d) 4. (a) 5. (a) 6.. (d) 7. (d) 8. (a) 9. (b) 10. (b) 11. (c) 12.. (c) 13. (c) 14. (d) 15. (b) 16. (b) 17. (a) 18. (d) 19. '(b) 20. (d) Page 32 1-------------------------------------- '.