SOF Level 2 IMO Class 11
Short Description
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1
Class 11 CLASS
SOFINTERNATIONAL MATHEMATICS OLYMPIAD
SAMPLE PAPER
Total Questions : 50
11 Time : 1 hr.
LEVEL-II Guidelines for the Candidate 1. You will get additional ten minutes to fill up information about yourself on the Answer Sheet, before the start of the exam. 2. The Question Paper comprises four sections: Logical Reasoning (20 Questions), Mathematical Reasoning (15 Questions), Everyday Mathematics (10 Questions) and Achievers Section (5 Questions) Each question in Achievers Section carries 3 marks each, whereas all other questions carry one mark each. 3. All questions are compulsory.There is no negative marking. Use of calculator is not permitted. 4. Write your Name, Roll No. and Class clearly on the Answer Sheet and do not forget to sign it. 5. There is only ONE correct answer. Choose only ONE option for an answer. 6. To mark your choice of answers by darkening the circles in the Answer Sheet, use an HB Pencil or a Blue / Black ball point pen only. E.g. Q.16: A number has nine ones, six tens and eight hundreds. What is the number? A. 869 B. 896 C. 968 D. 986 As the correct answer is option A, you must darken the circle corresponding to option A in the Answer Sheet. 7. Rough work should be done in the blank space provided in the booklet. 8. Return the Answer Sheet to the invigilator at the end of the exam. 9. Write your Roll No. on the Question Paper too and take it home for future reference.
SYLLABUS Sets, Relations and Functions, Mathematical Induction, Logarithms, Complex Numbers & Quadratic Equations, Linear Inequations, Differentiation, Sequences and Series (A.P. & G.P. Misc.), Trigonometry, Cartesian System of Rectangular Coordinates, Straight Lines and Family of Straight Lines, Circles, Conic Section, Trigonometry, Permutations and Combinations, Binomial Theorem, Statistics, Mathematical Logic, Limits, Probability, Introduction to 3-D Geometry, Problems Based on Figures, Find Odd Numeral Out, Series Completion, Coding-Decoding, Mathematical Reasoning, Analytical Reasoning, Mirror Images, Embedded Figures, Direction Sense Test, Cubes and Dice.
2
Class 11
LOGICAL REASONING 1.
Pointing to a person in a photograph, Arun said, "His only brother is the father of my daughter's father." How is the person in photograph related to Arun ? (A) Grandfather
2.
(B) Father
(C) Brotherinlaw
(D) Uncle
The airport is to the east of the bank while my house is to the south of the bank. The church is to the north of the airport. If the distance of the church from the airport is equal to the distance of my house from the bank, and the distance of airport to my house is 2 times the distance of the airport to the church, then in which direction is the church with respect to bank ? (A) Northwest
3.
(B) Northeast
(C) West
(D) Southwest
If it is possible to make a meaningful word with fifth, sixth, eight and ninth letters of the word 'CONVERSATION', which of the following will be the third letter of that word. If no word formed then give X as answer and if more than one word formed then give P is the answer. (A) X
4.
(B) A
(C) P
On the right a set of figures carrying certain characters, is given. Assuming that the characters in each set follow a similar pattern, which is the missing character ? (A) 68 (C) 98
5.
3
6
7
45
5
8
74
2 ?
(B) 76 (D) 128
Aditya left home for the school 20 minutes late than usual. It takes 15 minutes to reach the school. He reached the school at 7:20 a.m. At what time does he usually leave home for the school ? (A) 6:55 a.m.
6.
(D) R
(B) 6:50 a.m.
(C) 6:45 a.m.
(D) 7:05 a.m.
How many T's are there in the following sequence which are immediately preceded by P but not immediately followed by S ? S T P Q T S P T R P T S R P S T Q P T R P T M P T S (A) One
7.
(B) Two
(C) Three
(D) Four
If 'edo sto ki' stands for 'softer than flower', 'ki bla dis' stands for 'sweet flower fragrance' and 'dis sto ric' stands for 'sweet than smile'. What does 'fragrance' stand for ? (A) bla
8.
(B) sto
(C) ki
(D) dis
Which term comes next in the series ? WGE, THG, QIJ, NJN, ___ ?_ (A) KNT
9.
(B) KKS
(C) MKS
(D) NTF
Sonit is facing east. He turns 205° in anticlockwise direction and then 160° in the clockwise direction. Which direction is he facing now ? (A) Southeast
(B) Southwest
(C) Northeast
(D) Northwest
10. If the seventh day of a month is three days earlier than Friday, what day will it be on the nineteenth day of the month ? (A) Sunday
(B) Monday
(C) Wednesday
(D) Friday
3
Class 11
MATHEMATICAL REASONING 11. A class has 175 students. The following data shows the number of students opting for one or more subjects. Math 100, Physics 70, Chemistry 78; Math and Physics 30, Math and Chemistry 38, Physics and Chemistry 23; Math, Physics and Chemistry 18. How many have opted for Math alone ? (A) 35
(B) 48
(C) 50
(D) None of these
12. Let A = {2, 3, 4, 5, ......., 16, 17, 18}. Let » be the equivalence relation on A × A, then the cartesian product of A and A be defined by (a, b) » (c, d) if ad = bc. Then the number of ordered pairs in the equivalence class of (3, 2) is _____. (A) 4
(B) 5
(C) 6
(D) 7
13. If x 2 + ax + 10 = 0 and x 2 + bx – 10 = 0 have a common root, then a 2 – b 2 is equal to ____. (A) 10
(B) 20
(C) 30
(D) 40
14. The normal at the point (3, 4) on a circle cuts the circle at the point (–1, –2). Then the equation of the circle is ____. (A) x 2 + y 2 – 2x – 2y – 11 = 0 2
(B) x 2 + y 2 – 2x – 2y + 14 = 0
2
(D) x 2 + y 2 – 2x + 2y + 12 = 0
(C) x + y – 2x – 2y – 13 = 0
15. The radius of the circle passing through the foci of the ellipse
x 2 y 2 + = 1 and having its centre at 16 9
(0,3) is ____. (A) 4
(B) 3
(C)
(D)
12
7 2
16. If (2r + 3) th and (r – 1) th terms in the expansion of (1 + x) 15 have equal coefficients, then r = (A) 3
17.
(B) 4
(C) 5
(D) 6
(B) ¥
(C) 0
(D)
1 2
(D)
tan x x - y 2
sin–1( x + 2) = x ® – 2 x 2 + 2 x lim
(A)
-
1 2
18. If y = x tan y, then (A)
tan y x - x 2 - y 2
dy = dx
(B)
y x - x 2 - y 2
tan y y - x
(C)
19. The given figure shows the graph of y = f(x). Which of the following could be the graph of y = |f(x)| ? y
x
O
Graph of y = f(x ) y
y
(A)
O
x
(B)
O
y
x
(C)
O
y
x
(D)
O
x
4
Class 11
20. Which of the following is the range of the function f (x) = [x] – x, where [∙] shows the greatest integer function ? (A) (–1, 0)
(B) (–1, 0]
(C) [0, 1)
(D) [0, 1]
EVERYDAY MATHEMATICS 21. A contractor is building 5 different model homes on 5 adjacent plots on one side of a street. If 1 house is to be built on each plot, how many different arrangements of the 5 houses are possible? (A) 120
(B) 60
(C) 20
(D) 10
22. In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class are 72, then what are the average marks of the girls ? (A) 73
(B) 65
(C) 68
(D) 74
23. From a shipment of 500 batteries, a sample of 25 was selected at random and tested. If 2 batteries in the sample were found to be dead, how many dead batteries would be expected in the entire shipment ? (A) 10
(B) 20
(C) 40
(D) 50
24. An airport designer drew a plan for two runways on a rectangular coordinate system, where dotted line AB represents the center line of the first runway and dotted line CD represents the center line of the second runway. ) , 10 B(8
y A(–
4 , 6
)
) , 1 D (x
x
3) 1, – C(–
If the designer chooses a ycoordinate of 1 for point D, what must be the xcoordinate for the two runways to be parallel ? (A) 12
(B) 11
(C) 13
(D) 15
25. Mrs. Bhagat decided to apply wallpaper on a wall of her living room. A diagram of the rectangular wall with its window is shown below.
8 ft
4 ft
Window
8 ft 24 ft A roll of wallpaper covers approximately 30 square feet. What is the minimum number of rolls she will need to cover the entire wall excluding the window ?
(A) 2 rolls
(B) 5 rolls
(C) 6 rolls
(D) 7 rolls
5
Class 11
SAMPLE ANSWER SHEET 1. NAME : If your name is SACHIT A IYER, then you should write as follows : S A C H
I
T
A
I
Y E R
2. FATHER'S NAME : If your father's name is SATISH KUMAR SHARMA, then you should write as follows : S A T
I
S H
K U M A R
SCHOOL CODE
M
H
0
5
4
7
A
A B C
1 2
0 1 2
0 1 2
0 1 2
B C D
D
3
3
3
3
E F
E F
4 5
4 5
4 5
G H
G
6 7
6 7
6 7
6
I
I
8
8
8
8
J K
J K
9
9
9
9
L
L M
N
N
O P Q R
O P Q R
S
S
T U
T U
V W
V W
X
X
Y Z
Y Z
S H A R M A
3. SCHOOL CODE Write your school code i.e. if your school code is MH0547 darken as follows :
4. CLASS If you are in Class 10, then you should darken as follows :
5. ROLL NO. If your roll no. is 587, then you should write and darken the circles as follows :
CLASS
1
Darken the circle
5
8
7
1
0 1
0 1
0 1
2
2
2
2
2
3 4
3 4
3 4
3 4
3 4
5 6 7
5 6 7
6 7
5 6 7
5 6
8 9
8 9
8 9
9
0
Darken the circle
6. GENDER If you are a boy, then darken Male circle
ROLL NO.
0
8 9
GENDER MALE
CORRECT way to darken the circle
FEMALE
WR ONG way to darken P × the circle
7. If your choice for Answer 1 is C, then you should darken the circle as follows :
1.
MARK YOUR AN SWERS WITH H B PENC IL/BALL POINT PEN (BLUE/B LACK)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
ANSWER KEYS 1. 8. 15. 22.
(D) (B) (A) (D)
2. 9. 16. 23.
(B) (C) (C) (C)
3. 10. 17. 24.
(C) (A) (D) (B)
4. 11. 18. 25.
(A) (C) (B) (C)
5. 12. 19.
(C) (A) (B)
6. 13. 20.
(C) (D) (B)
7. 14. 21.
(A) (A) (A)
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