KVS Junior
Mathematics Olympiad (JMO) – 2001
M.M. 100 Time
: 3 hours
Note : (i) Please check that there are two printed
pages and ten question in all.
(ii) Attempt all questions. All questions carry
equal marks.
1. Fill in the
blanks :
(a)
If x + y = 1, x3 + y3 = 4, then x2
+ y2 = ……..
(b)
After 15 litres of petrol was added to the fuel tank of
a car, the tank was 75% full. If the capacity of the tank is 28 litres, then
the number of litres in the tank before adding the petrol was ……
(c)
The perimeter of a rectangle is 56 metres. The ratio of
its length to width is 4:3. The length of the diagonal in metres is ……..
(d)
If April 23 falls on Tuesday, then March 23 of the same
year was a ……..
(e)
The sum of the digits of the number 2200052004
is ….
2. (a) Arrange the
following in ascending order :
25555,
33333, 62222
(b) Two rectangles, each measuring 3 cm x 7 cm,
are placed as in the adjoining
figure :
Find the area of
the overlapping
portion (shaded)
in cm2.
3. (a) Factorize :
(x-y)3+(y-z)3+(z-x)3
(b)
If x2-x-1=0, then find the value of x3-2x
+1
4. (a) Find all integers n such that (n2-n-1)n+2
= 1
(b)
If x = , find the value of
5. (a) Find all the positive perfect cubes that
divide 99.
(b)
Find the integer closest to 100 (12-)
6. An ant
crawls 1 centimetre north, 2 centimetres west, 3 centimetres south, 4
centimetres east, 5 centimetres north and so on, at 1 centimetre per second.
Each segment is 1 centimetre longer than the preceding one, and at the end of a
segment, the ant makes a left turn. In which direction is the ant moving 1
minute after the start ?
7. Find the
lengths of the sides of a triangle with 20, 28 and 35 as the lengths of its
altitudes.
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