3 7th IMO - Set B A. 15 B. 17 C. 18 D. 21 8. In the following question, a set of figures is carrying certain numbers. Assuming that the numbers in each set follow a similar pattern, find the missing number. A. 2 B. 3 C. 4 D. 5 9. What number is opposite to 3, if four different positions of a dice are shown below?
A. 6 B. 4 C. 3 D. 2
10. In the following question, find out how will the Figure (X) look like after rotation?
Figure (X) A.
B. C. D.
11. Between two book-ends in your study are displayed your five favourite puzzle books. If you decide to arrange the five books in every possible combination and move just one book every minute, how long would it take you? A. 1 hour B. 2 hours C. 3 hours D. 4 hours 12. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure that would replace the question mark (?) in figure (4). A. B. C. D.
13. Examine the following relationships among members of a family of six persons—A, B, C, D, E and F. 1. The number of males equals that of females. 2. A and E are sons of F.
3. D is the mother of two, one boy and one girl. 4. B is the son of A.
5. There is one married couple in the family at present.
Which one of the following is true from the above information?
A. A, B and C are all females. B. A is the husband of D. C. D is the grand daughter of F. D. E and F are children of D.
14. Select the correct mirror image of Figure (X). A.
Figure (X) B.
C.
15. If + means ÷ , ÷ means –, – means ×, × means +, then 12 + 6 ÷ 3 – 2 × 8 = A. – 2 B. 2 C. 4 D. 8
16. In a class, among the passed students, Amisha is twenty-second from the top and Sajal, who is 5 ranks below Amisha, is thirty-fourth from the bottom. All the students from the class appeared for the exam. If the ratio of the students who passed in the exam to those who failed is 4 : 1 in that class, how many students are there in the class?
A. 60 B. 75 C. 90
D. Data inadequate
17. If SCOTLAND is written as 12345678, LOAN is written as 1435, LOTS is written as 8124, DAN is written as 537 and SON is written as 458, then what will be the code for ‘C’?
A. 0 B. 4 C. 5 D. 6
18. A family consists of six members P, Q, R, S, T and U. There are two married couples. Q is a doctor and the father of T. U is grandfather of R and is a contractor. S is grandmother of T and is a housewife. There is one doctor, one contractor, one nurse, one housewife and two students in the family.
Who is the sister/brother of T?
A. R B. U C. T D. Information insufficient 19. Study the given information carefully to answer the following question. M K K I D N E T T Q O B F H A A G T U U X W L S R I Each of these letters gets a numerical value based on its position in the above arrangement, such as, 1 for M, 2 for K, 4 for I and so on.
Value of A is exactly equal to the total value of which of the following pairs?
1. DO 2. QE 3. MH A. Only 1 B. Only 2 C. Only 3 D. Both 1 and 3
20. In the given figure, if the centres of all the circles are joined by horizontal and vertical lines, then find the number of squares that can be formed.
A. 16 B. 17 C. 18 D. 14
MatheMatical reasoning
21. ABCD is a quadrilateral with right angles at A andC. Points E and F are on the diagonal AC such
that DE and BF are both perpendicular to AC. If
AE = 3 cm, DE = 5 cm and CE = 7 cm then the length
of BF is _______ cm. A. 3.2 B. 3.4 C. 4 D. 4.2 22. The value of x x x x x x l m l m m n m n n l n l 2 2 2 2 2 2 + ´ + ´ + = A. 2 B. –1 C. 0 D. 1
23. If (aa + b)–2 + (ab + b)–2 = 1, where a, b are the
roots of ax2 + bx + c = 0, then ac (ac + 2) = _____
A. b2 2 B. b3
C. 2b D. b2
5
7th IMO - Set B
24. Two candidates attempt to solve a quadratic equation of the form x2 + px + q = 0. One starts with a wrong
value of p and finds the roots to be 2 and 6. The other starts with a wrong value of q and finds the roots to be 2 and –9. Find the correct roots.
A. 2, 6 B. 2, –9
C. 4, 8 D. –3, –4
25. In the diagram, PQ and QR are tangents to the circle, with centre O at P and R respectively. Find the value of x.
A. 25° B. 30° C. 55° D. 65°
26. Let Sn denote the sum of the first ‘n’ terms of an A.P. and
S2n = 3Sn. Then the ratio S3n is to Sn is equal to_____.
A. 4 : 2 B. 6 : 1 C. 8 : 2 D. 3 : 1
27. The L.C.M. of two numbers is 45 times their H.C.F. If one of the numbers is 125 and the sum of H.C.F. and L.C.M. is 1150, then the sum of two numbers is _____. A. 215
B. 220 C. 225 D. 350
28. ABCD is a trapezium, in which AD||BC, E and F are the mid-points of AB and CD respectively, then
EF is A. (AD BC+ ) 2 B. (AB CD+ ) 2 C. DF CF AE BE ´ ´ D. AD EF+ +BC 2
29. If A is 1/4 of a complete revolution, then 3 2 1 2 1 2 3 2 3 3 + - æ è çç ç ö ø ÷÷÷÷ + +æèççç - ö ø ÷÷÷÷ = - - cos sin sin cos A A A A A. 1 B. 3 C. 0 D. –1
30. The sums of n terms of two arithmetic series are in the ratio of 7 1
4 27
n n
+
+ . Find the ratio of their 11
th terms.
A. 4 : 3 B. 5 : 4 C. 7 : 4
D. None of these
31. Points A(6, 6), B(2, 3) and C(4, 7) are the vertices of a triangle which is _______.
A. Right angled B. Acute angled C. Obtuse angled D. None of these
32. If cosec q – sin q = a3 and sec q – cos q = b3, then a2b2(a2 + b2) =
A. 1 B. –1 C. 2 D. 0
33. Each observation in a raw data is first multiplied by 3, then 6 is added. It is then divided by 3 and subsequently reduced by 6, then ____
A. The new mean is equal to the original mean. B. The new mean is 4 more than the original mean. C. The new mean is 4 less than the original mean. D. The new mean is 2 more than the original mean. 34. If N is the sum of first 13986 prime numbers, then
N is always divisible by
A. 6 B. 4 C. 8
D. None of these
35. In a right triangle ABC is right-angled at B. If P and
Q are points on the sides AB and BC respectively,
then A. AQ2 + CP2 = 2(AC2 + PQ2) B. 2(AQ2 + CP2) = AC2 + PQ2 C. AQ2 + CP2 = AC2 + PQ2 D. AQ + CP = 1 2 (AC + PQ)