IMO sample papers for classes 6 to 12

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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
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athematics
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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)jij§im ,,~tic?J~~.H·9.F.& L8,M., Ration~ number & it~operations, ty1ultipli-
& ion 01 ra at number, 8impla',& compoundtnterest, Percenta§e. 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

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. NEW DELHI. INDIA
Organized by :
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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
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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 ~--~-----
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Oy piadof
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MATHEMATICS OLYMPIAD
FOUNDATION (NGO)
New Delhi, India
Promoting Mathematics Education
www.mathsolympiad.orgN£W 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 (243t·8
+(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
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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
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ympiad f
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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
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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 to·In 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
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lympiadof
athematics
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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
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18. TechnicalSupportprovided by
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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 2x·th - -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
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