2 7th IMO - Set A
1. Choose the correct option that will continue the same pattern and replace the question mark in the given series. 3, 12, 27, 48, 75, 108, ? A. 147 B. 162 C. 183 D. 192
2. In a certain code, PLEADING is written as FMHCQMFB. How is SHOULDER written in that code?
A. KCDQTIPV B. QDCKVPIT C. QDCKTIPV D. TIPVQDCK
3. Q's mother is sister of P and daughter of M. S is daughter of P and sister of T. How is M related to T?
A. Aunt B. Father C. Sister
D. Maternal Grandfather or Maternal Grandmother 4. Read the following information carefully and answer
the question that follows :
(i) Five friends P, Q, R, S and T travelled to five different cities; Chennai, Kolkata, Delhi, Bangalore and Hyderabad by different modes of transport; Bus, Train, Aeroplane, Car and Boat from Mumbai.
(ii) The person who travelled to Delhi did not travel by boat.
(iii) R went to Bangalore by car and Q went to Kolkata by aeroplane.
(iv) S travelled by boat whereas T travelled by train. (v) Mumbai is not connected by bus to Delhi and
Chennai.
Which of the following combinations of place and mode is NOT correct?
A. Delhi-Train B. Kolkata-Aeroplane C. Hyderabad-Car D. Chennai-Boat
5. The given question consists of five figures marked P, Q, R, S and T called the Problem Figures. Select a figure from the options which will continue the same series as established by the five Problem Figures.
A.
B. C.
D.
6. Find the number of triangles in the given figure.
A. 12 B. 15 C. 14
D. None of these
7. The door of Aditya's house faces East. From the back side of his house, he walks straight 50 metres, then turns to the right and walks 50 metres again. Finally, he turns towards left and stops after walking 25 metres. Now, Aditya is in which direction from the starting point?
A. South-east B. North-east C. West D. North-west
8. Forty boys are standing in a row facing the North. Arun is eleventh from the left and Deepak is thirty- first from the right end of the row. How far will Shreya, who is third to the right of Arun in the row, be from Deepak? A. 2nd B. 3rd C. 4th D. 5th
logical reasoning
9. If 'Q' denotes '+', 'J' denotes '×', 'T' denotes '–' and 'K' denotes '÷', then 30 K 2 Q 3 J 6 T 5 = ? A. 18 B. 28 C. 31 D. 103
10. Which of the following is the mirror image of the given word, if the mirror is placed vertically left? N O T I F I C AT I O N A. B. C. D.
11. Find out how many such pairs of letters are there in the given word each of which has as many letters between them in the word as in the English alphabet.
ADVERTISEMENT A. Three
B. Four C. Five
D. More than five
12. The triangle represents females, rectangle represents housewife and circle represents school teachers, then the number representing females who are school teachers but unmarried is
A. 2 B. 4 C. 3 D. 8
13. How many 8's are there in the following number series each of which is exactly divisible by its immediately preceding and also divisible by its immediately succeeding number? 8 2 4 5 1 7 2 8 4 8 4 2 2 8 2 6 9 8 4 5 4 8 3 2 8 4 3 1 8 3 A. 1 B. 4 C. 3 D. 2
14. Choose the group which is different from the rest. A. MEWGN
B. PBQTX C. DRYSN D. CGHKV
15. If the third, fourth, fifth, seventh and tenth letters of the word PERSONALITY forms a meaningful word then first letter of the word is the answer. If no word is possible, then 'X' is the answer and if more than one such word is formed, then 'M' is the answer. A. R
B. X C. O D. M
16. Find the missing character.
? T W 3 15 10 J T G P S D A. 5 B. 9 C. 11 D. 13
17. The number of cubes required to make the given figure is ______.
A. 31 B. 32 C. 33 D. 34
18. Select the figure from the options which is embedded in the given Fig. (X).
A. B. C. D.
4 7th IMO - Set A
19. In the given question, two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered. The operations of numbers progress from left to right.
Rules
I. If an odd number is followed by a two-digit even number, then they are to be added.
II. If an odd number is followed by a two-digit odd number, then the second number is to be subtracted from the first number.
III. If an even number is followed by a number which is a perfect square of a number, then the second number is to be divided by the first number. IV. If an even number is followed by a two-digit even
number, then the first number is to be multiplied by the second number.
13 11 4 17 13 12
If the resultant of the first set of numbers is multiplied by the resultant of the second set of numbers, what will be the outcome?
A. 48 B. 69 C. 75 D. 96
20. Which of the following options will complete the figure matrix? A. B. C. D.
MaTHeMaTical reasoning
21. If one root of the equation a(b – c)x2 + b(c – a)x +c(a – b) = 0 is 1, then the other root is ___.
A. b c a a b c ( ) ( ) − − B. a b c c a b ( ) ( ) − − C. a b c b c a ( ) ( ) − − D. c aa b bc ( ) ( ) − − 22. If H.C.F of (x – 5)(x2 – x – a) and (x – 4) (x2 – 2x – b) is
(x – 4)(x – 5), find the values of a and b respectively.
A. 15, 18 B. 10, 7 C. –8, 10 D. 12, 15
23. What is the sum of an A.P. whose first term is a, the second term is b and the last term is c?
A. ( )( ) ( ) b c a a c b a + − + − 2 2 B. (b c a a)( c) b a + + + − 2 C. 2(a c b)( c 2a) b a + − + + D. (b+ −cb2+a aa)( −c)
24. ABCD is a cyclic quadrilateral. AE is drawn parallel to CD and BA is produced. If ∠ABC = 92° and ∠FAE = 20°, then ∠BCD =
A. 88° B. 108° C. 115° D. 72°
25. If xcos3q + ysin3q = sinqcosq and xcosq = ysinq, then x2 + y2 =
A. 0 B. 4 C. 1 D. 2
26. Find the coordinates of the points which trisect the line joining (–3, 5) and (6, –7).
A. (0, 1) and (3, –3) B. (–1, –1) and (0, 3) C. (2, 0) and (1, 1) D. (2, 2) and (0, 1)
27. Express in lowest terms : x a x a 8 8 6−− 6 A. ( )( ) ( ) x a x a x ax a 2 2 2 2 2 2 2 + − + + B. ( )( ) ( )( ) x a x a x ax a x ax a 2 2 4 4 2+ ++ 2 2+− + 2 C. ( )( ) ( ) x a x a x ax a 2 2 4 4 2 2 2 + + − + D. ( )( ) ( )( ) x a x a x ax a x ax a 2 2 4 4 2+ +− 2 2+− + 2 28. Express as a rational expression.
1 1 11 22 1 44 1 x− −x+ −x + −x + A. (3 14) 1 2 2 x x − − B. (x ) x 2 4++31 C. (x88− 1) D. 2(xx 14) + +
29. A point D is on the side BC of an equilateral DABC such that DC = 1 4BC. Then AD 2 = A. 13 CD2 B. 9 AB2 C. 6 CD2 D. 12 BC2
30. In the given figure, AB, EF and CD are parallel lines. Given that EG = 5 cm, GC = 10 cm and DC = 18 cm, then EF =
A. 9 cm B. 25 cm C. 13 cm D. 16 cm
31. The product of 12% of an integer and 20% of the next integer is 61.2. Find the integer.
A. 50 B. –51 C. 63
D. Both A and B
32. Find the values of p and q respectively for which the following system of linear equations has infinite solutions. 2x + 3y = 7 (p + q)x + (2p – q)y = 21 A. 2, 6 B. –7, 3 C. –3, –5 D. 5, 1
33. Find the value of x in the given figure, where O is the centre of the circle.
A. 80° B. 160° C. 100° D. 105°
34. If sinq + cosq = 2 sin(90° – q), then cotq = A. 1
B. 2 1− C. 2 1+ D. –1
35. Find k, so that 4k + 8, k3 + 3k + 6 and 3k2 + 4k + 4
are three successive terms of an A.P.
A. 0 B. 2
C. –1 D. Both A and B