Jmo Sample Paper

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KVS Junior Mathematics Olympiad (JMO)
M.M. 100Time : 3 hours
Note : Attempt all questions.
SAMPLE PAPER – I
All questions carry equal marks
Q.1Resolve into factors : 99899
Q.2The number 21328 has a unique feature :
The sum of first four digits equals the units digit. How many even five- digit number have this unique property? Q.3One vertex angle of a regular octagon that has side length 4 units is joined with two other vertex angles to form a kite as shown in the figure below. Determine the area of the kite ? [pic]

Q.4ABC is a triangle in which [pic] D is a point on side BC such that AD bisects [pic] and [pic]. Find the value of [pic] in degrees.

Q.5Find a number which when divided by 10 leaves remainder 9, when divided by 8 leaves remainder 7, etc. down to where when divided by 2, it leaves remainder 1.

Q. 6.A man went out after 3pm and on returning after half an hour, found that the minute hand was as much in advance of the hour hand when he went out. Find at what time he went out ?

Q.7Find the final digit of the millionth number of
[pic]
Q.8If a,b,c are real numbers such that
[pic]
then prove that
[pic]

Q.9In the multiplication example below p stands for prime digits. Reconstruct the problem by replacing p.

Ppp
Xpp
Pppp

Pppp

pPppp

Q.10In the grid below, how many ways you can spell MATHEM?

[pic]
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