CBSE 12th KVS Junior Mathematics Olympiad 2009 Question paper

Course: SSLC

University: CBSE


Junior Mathematics Olympiad

KENDRIYA VIDYALAYA SANGATHAN

12th KVS Junior Mathematics Olympiad – 2009

Time: 3 Hours Max.Mark 100

NOTE: Attempt all questions. All questions carry equal marks. The use of electronic devices are strictly prohibited.

1. Consider the following multiplication in decimal notations (999).(abc)= def132, determine the digits a,b,c,d,e,f.

2. Find the greatest number of 4 digits, which when divided by 3,5,7, and 9 leaves remainder 1,3,5 and 7 respectively.

3. If n is a positive integer such that n/810 = 0d25d25

where d is a single digit in decimal base. Find 'n'.

4. Solve in integers: 3x2-3xy + y2=7 and 2x2- 3xy + 2y2 = 14

5. Let x be the LCM of 32002 – 1 and 32002 + 1. Find the last digit of x.

6. Let f0(x)=1/1-x and fn(x)= f0(fn-1-(x)) Where n= 1,2,3Calculate f2009(2009)

7. Triangles ABC and DAG are two isosceles triangles with BAC = 20° and ADC= 100°. Show that AB = BC + CD.

8. Two intersecting circles E1 and E2 have a common tangent which touches E1 at P and E2 at Q. These two circles meet at M and N where N is nearer to PQ than M. The line PN meets the circle E2 again at R. Prove that MQ bisects angle PMR.

9. AB is a line segment of length 24 cm. and C is its middle point. On AB, AC and CB semi circles are described. Determine the radius of the circle which touches all the three semi circles.

10. Prove that a4 + b4+ c4 >= abc( a + b + c)