DO NOT OPEN THIS BOOKLET UNTIL ASKED TO DO SO Roll No. Total Questions: 50
Time: 1 hr hr.
CLASS
8
SOF INTERNATIONAL MATHEMATICS OLYMPIAD
Level-2
SET-2
Guidelines for the Candidate 1.
You will get additional ten minutes to ll up information about yourself on the OMR Sheet, before the start of the exam.
2.
The Question Paper comprises two sections : Mathematics (45 Questions) and Achievers Section (5 Questions) Each question in Achievers Section carries 3 marks, whereas all other questions carry one mark each.
3.
All questions are compulsory. compulsory. There There is no negative marking. Use Use of calculator is not permitted.
4.
Write your Name, Roll No. and Class clearly on the OMR Sheet and do not forget to sign it.
5.
There is only ONE correct answer. answer. Choose only ONE ONE option for an answer.
6.
To mark your choice of answers by darkening the circles in the OMR 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 16. the circle corresponding to option C.
A
B
C
D
7.
Rough work should be done in the blank space provided in the booklet.
8.
Return the OMR Sheet and question paper to the invigilator at the end of the exam.
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MATHEMATICS
8. 1.
A. C. 2.
3 + 3+8 7 − 4 3
Find the value of 0 1
B. D.
2 4
Three pipes A, B and C can ll a cistern in 10 hours, 12 hours and 15 hours respectively. First A was opened. After 1 hour, B was opened and then after 1 hour C was also opened. Find the time taken to ll the cistern. A. B. C. D.
4 3 4 3
hours hours hours hours
32 52 52 32
A. B. C. D. 9.
If A. C.
4.
60 km 45 km 36 km None of these
One of the factor of the following equation 8(a + b)2 + 14(a + b) + 3 is
mins mins mins mins
x + 1 15 1 = of ÷ 2 , then the value of x is 16 5 8
A. B. C. D.
2
3.
Ram travels from P to Q at 10 km/hr and returns at 15 km/hr. Shyam travels from P to Q at 12.5 km/hr and returns at 12.5 km/hr. If he takes 12 minutes less than Ram, then what is the distance between P and Q?
7 2
B.
2 2
4 2
D.
6 2
10.
(2a + (4a + (2a + (2a +
2b + 4b + 2b + 4b +
2) 4) 3) 1)
Find the area of the given gure if AB || DC and BC || EF. 20 cm
D E
m m c c
If the number obtained by interchanging the digits
5 6 1
F
of a two-digit number is 18 more than the original
A
number and the sum of the digits is 8, then what is 53 32
B. D.
A. C.
35 23 11.
5.
In the gure given below, BCDE is a trapezium with BC || ED, EQ || DR. Find ∠ BCD. Q E
D
52°
A. C. 6.
B. D.
74° 38°
Radius of a cylinder is 2 x cm and its height is
2 x
π
cm.
If the volume of the cylinder is equal to the volume of a cube. Find the total surface area of the cube. A. C. 7.
If P = 999, then A. B. C. D.
2
42 x2 cm 2 24 x3 cm 3
100 999 1002 998
B. D. 3
2 x2 cm 2 24 x2 cm 2
P ( P + 2) + 1 =
384 cm2 379 cm2
In a group of children each child gives a gift to every other child. If the number of gifts are 132, nd the number of children. 11 13
B. D.
12 14
If a =
(
3+ 2
)
−3
and b =
(
3− 2
)
−3
, then the value
of (a + 1) –1 + (b + 1) –1 is
C
36° 54°
B. D.
126°
12. B
389 cm2 364 cm2
A. C.
R
52°
B
28 cm
the original number? A. C.
C
13.
A.
0
B.
1
C.
48 2
D.
5
Match the following. Column-I
Column-II
(a) Number of edges of a triangular pyramid is
(i)
12
(b) Number of vertices of a square prism is
(ii)
8
(c) Number of faces of a triangular prism is
(iii)
6
(d) Number of edges of a cube is
(iv)
5
| Class-8 | Set-2 | Level 2
A. B. C. D. 14.
(a) (iv) (iii) (iii) (iv)
(b) (iii) (i) (ii) (iii)
(c) (i) (ii) (iv) (ii)
(d) (ii) (iv) (i) (i)
20.
A. B. C. D.
After allowing a discount of 25% on marked price of a trouser, it is sold for ` 240. Find the marked price of the trouser. A. B. C. D.
` 240
21.
` 320 ` 115
The rational expression form is A. C.
16.
4 x + 20 x + 25
17.
(2 x + 5)
2 x 2 x + 5
B. D.
1
1
If 2 x −
2 x
A.
= 1 , then 2 x +
2 x
in its simplest
5 2 x – 5
C. 22.
=
2
B.
3
C.
4
D.
5
23.
(a + b )( x − y )
+
by − cz (b + c )( y − z )
+
cz − ax (c + a )(z − x )
24.
is equal to 1 3
18.
The value of ( −1)
A. C.
0 –2
B. D. 235
+ ( −1)
368
B. D.
2 0
b
Q
106°
C
1
b
3
c
= ,
100°
= 2,
c d
1
d
2
e
= ,
P
D
e
= 3 and
f
=
1 4
, then
abc def
is 2 None of these
Draw AB = 5.2 cm. With A as centre and radius 3.2 cm, draw an arc. Step-III : With B as centre and radius 3 cm draw another arc, cutting the previous arc at O. Step-IV : Join OA and OB. Step-V : Produce DO to C such that OC = DO and produce BO to D such that OD = OB. Step-VI : Join AD, BC and CD. ABCD is the required parallelogram.
C. 25.
Class-8 | Set-2 | Level 2 |
8
B.
8 1
64 6
D.
64
81
33 24
B. D.
44 25
4 8
B. D.
6 10
22
15
B.
15 21
21 15
D.
15
22
Find the value of P and Q respectively. P Q × 6
Step-I : Step-II :
Step-II Step-III Step-IV Step-V
3
The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator is decreased by 6, the new numerator becomes 2. Find the original number. A.
Which of the following steps is INCORRECT while constructing a parallelogram, one of whose sides is 5.2 cm and whose diagonals are 6 cm and 6.4 cm?
A. B. C. D.
B
The number of edges in a pyramid with square base is: A. C.
If x : a = y : b = z : c then ax − by
19.
A
39° 21° 41° 53° a
135°
How many sides does a regular polygon have, if each of its interior angle is 165°? A. C.
A.
A. C.
If
R
is
` 200 2
15.
In the gure given below, CDP is a straight line, D AQD is equilateral. Find ∠ PDQ.
QQQ A. B. C. D. 26.
7, 4, 7, 8,
5 7 4 5 2
Find the value of 1+
1 1−
A. B. C. D.
× 1
5 6
of
3 3 2
÷
1
.
4
2
0 1/5 2/5 3/5 3
27. A can do a piece of work in 25 days and B can nish it in 20 days. They work together for 5 days and then A leaves. In how many days will B nish the remaining work? A. B. C. D. 28.
C.
x + z xz 2( z − x)
B. D.
xz 2( x − z ) 2 xz ( x − z )
20 years 35 years
B. D.
28 years 42 years
37.
38.
22 + 42 + 6 2 + … + 1024 2 is equal to
31.
C.
2 1 4
B. D.
39.
2 1
10% 14%
B. D.
40.
3
12% 18%
500 m 200 m
B. D.
450 m 350 m
If X and Y together lent ` 84100 at 5% compounded annually and the amount which X gets at the end of 3 years is the same as Y gets at the end of 5 years,
8
10
42.
4
21 : 20 441 : 400 400 : 441 41 : 40
×
5 12
×… ×
32 16
31 64
B. D.
1
=
x
2
, then the value
36 12
50115 cm3 2000 cm3
B. D.
27000 cm3 15550 cm3
Rectangular pyramid Pentagonal prism Hexagonal prism Square pyramid
The average of the age of a husband and wife, ve years ago was 25 years. The average of the present age of husband, wife and a child born during the time is 21 years. Find the present age of the child. 1 year 3 years
B. D.
2 years 5 years
6 typists working 5 hours a day can type the manuscript of a book in 16 days. How many days will 4 typists take to do the same job, each working 6 hours a day? 10 20
B. D.
15 25
The difference between compound interest and simple interest at the same rate on ` 5000 for 2 years is ` 72. What is the rate of interest per annum? 11% 15%
B. D.
10% 12%
The value of [1 – {1 – (1 – a 4) –1} –1] –1/4 is A.
a4
B.
C.
a
D.
a2 1 a
The pie chart drawn here represents the amount spent on different sports by a school in a year. If the money spent on football is ` 9000, answer the following questions. Football
Tennis Basket ball
then nd the ratio of shares of X and Y . A. B. C. D.
× × ×
Name the solid that would be formed by using the given net.
A. C. 41.
1
Find the volume of wood used to make a closed rectangular box of outer dimensions 50 cm × 35 cm × 22 cm, the thickness of wood being 2.5 cm all around.
A. C.
3
The time taken by a train at a speed of 120 km/hr crosses an electric pole in 9 seconds and a platform in 24 seconds. What is the length of the platform? A. C.
34.
1
4 6 of x is
A. C.
4m m3
A fair price shopkeeper takes 10% prot on his goods. If he lost 20% of his goods, then what is the loss perce nt? A. C.
33.
B. D.
A die is tossed once. What is the probabil ity of appearing an odd prime number? A.
32.
3m m2
4
A. B. C. D.
If 12 + 2 2 + 32 + … + 512 2 = m, then
A. C.
3
A. C.
Ten years ago, Savita's age was half of Rajan's age. If the ratio of their present age is 3 : 4, what will be the sum of their present age? A. C.
30.
36.
2 xz
2
If
A. C.
If a x = b y = c z and b 2 = ac, then y equals A.
29.
10 11 12 13
35.
45° Hockey 100° 30° 25° 160° Cricket
(a) (b)
What is the total amount spent on sports? How much amount is spent on hockey? | Class-8 | Set-2 | Level 2
(a) ` 30,000 ` 80000 ` 72000 ` 28000
A. B. C. D. 43.
(b) ` 9000 ` 30000 ` 20000 ` 25000
A. B. C. D.
The following bar graph shows the number of students in a hostel speaking different languages. Study the bar graph and answer the following questions.
44.
Punjabi
s e g a u g n a L
Bengali
A.
2
C.
2
2 3 1 3
kg
B.
1
kg
D.
3
English
45.
After dividing the sum of
Tamil 5
10
15
20 25 30 35 40 Number of students
45
50
55
What is the ratio of the number of students speaking Punjabi to those speaking English? What is percentage of the students speaking Marathi over those speaking English?
5 8
and
2 3 2 3
kg kg
−3
by the reciprocal
10
−15 3 , we get ______. 8 − 4
of
(b)
(b) 63% 65% 60% 63%
How many kg of pure salt must be added to 30 kg of 2% solution of salt and water to increase it to a 10% solution?
Marathi
Hindi
(a)
(a) 7:5 5:7 7:5 5:7
A.
13 105 273
C.
320
B. D.
−273 320
−15 113
ACHIEVERS SECTION 46.
A. B. C. D. 47.
E
108° 132° 124° 96°
49. f
B
a
D
y x
b
C
e P
c Q
S
R
A train starts with full number of passengers. At the rst station, the train drops one-third of the passengers and takes in 96 more. At the next station, one half of the passengers on board get down while 12 new passengers get on board. If the passengers on board now are 240, the number of passengers in the beginning was A. C.
48.
A
Polygon ABCDE is a regular pentagon and polygon PQRSCD is a regular hexagon. Find x.
540 444
B. D.
600 430
A number is increased by 20% and then again increased by 20%. By what per cent should the increased number be reduc ed so as to get back the original number? A.
5 30 % 9
B.
2 40 % 7
C.
3 30 % 7
D.
4 30 % 7
Class-8 | Set-2 | Level 2 |
Water flows out through a circular pipe whose diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60 cm. By how much will the level of water rise in 30 minutes? A.
2m
B.
3m
C.
4m
D.
5m
6
50.
1/ 2
2 (625)3/ 5 × (1024) −6 / 5 ÷ (25)3/ 5
3 128 −5/ 2 × (125)1/ 5 ) (
(10 ) ÷ (10 ) 3 2
÷
2 3
(102 ) 3 ÷ (103 )2
equals A.
1 5
B.
0
C.
1
D.
1 10
5
SPACE FOR ROUGH WORK
6
| Class-8 | Set-2 | Level 2
