Scribd
Upload
262 views2 pages

RMO Math Problems 2003

This document contains 23 questions that are part of an RMO (Orissa) exam from 2003. The questions are divided into two groups: Group A contains 10 questions worth 4 marks each, and Group B contains 10 questions worth 6 marks each. There are also 3 bonus questions worth 10 marks each that would be used in the case of a tie. The questions cover a range of math topics including algebra, geometry, number theory, and combinatorics. Calculators and protractors are not allowed, but rulers and compasses are permitted. Examinees are instructed to attempt as many questions as possible within the 3 hour time limit.

Uploaded by

drssagrawal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
262 views2 pages

RMO Math Problems 2003

This document contains 23 questions that are part of an RMO (Orissa) exam from 2003. The questions are divided into two groups: Group A contains 10 questions worth 4 marks each, and Group B contains 10 questions worth 6 marks each. There are also 3 bonus questions worth 10 marks each that would be used in the case of a tie. The questions cover a range of math topics including algebra, geometry, number theory, and combinatorics. Calculators and protractors are not allowed, but rulers and compasses are permitted. Examinees are instructed to attempt as many questions as possible within the 3 hour time limit.

Uploaded by

drssagrawal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

RMO QUESTIONS

RMO(ORISSA) 2003
Max Mark 100
Time 3 Hrs
Instructions:
Calculators (in any form) and protractors are not allowed.
Ruler and compass allowed.
Answer as many questions as you can.
Group A Q. 1 to Q.10 carry 4 marks each & Group B Q. 11 to Q. 20 carry 6 marks each.
Bonus question each carry 10 marks will taken into account in case of tie.
Group A
1. If one thing sold in Rs x it gives 15% loss, but if it sold in Rs y then it gives 15% gain. Then find the
ratio of y to x.
2. Solve for x and y : ( x y 3) 2 ( x 2 y 3) 2 0 .
3. There are 35 coins with ten numbers of students. Out of ten students at least one has exactly 1 coin,
at least one student having exactly 2 coins and at least one student having exactly 3 coins. Then
prove that at least one student having 5 or more than 5 coins.
4. Out of four whole numbers taking three at a time their sum is as follows: 180, 197, 208 and 222.
Then find the largest number amongst them.
5. Lengths of sides of a triangle are integers. If perimeter of triangle is 8 then find its area..
6. In a marriage party 13 pairs (husband & wife) joined. Each male handshakes with all other female
except his wife. No female handshake with females. Find the number of handshakes between them.
7. Find the 2000th letter in the sequence ABCDEDCBAABCDEDCBAABCDEDCBAABC...
4x
9 x y
8. If x and y are real numbers such that x y 8 and 5 y 243 , then find value of xy .
2
3
9. One right angled triangle is drawn by touching the circumference of a circle with radius 5. Find the
length of its hypotenuse.
10. If m 777...77 and n 999...99 multiplied together then what is the sum of digits of resulting
99 digits

77 digits

number.
Group B
2 f (n) 1
, n1,2,3... and f (1) 2 then find f (101) ?
2
12. Find the remainder when 20052002 2002 2005 divided by 2003.
13. From the figure find mA mB mC mD mE mF mG ?

11. If f (n 1)

Dr. Shyam Sundar Agrawal

RMO QUESTIONS

14. Triangle ABC is an acute angled triangle with mA 30 0 . H is the point of intersection of altitudes
from the vertices A, B and C. Midpoint of BC is M. T lies on side HM such that HM = MT. Prove
that AT = 2BC.
a
b
c
15. Let 0 a, b, c 1 and a b c 2 , prove that

8.
1 a 1 b 1 c
19 x 16 4 x 7
16. Find the real roots of the equation

, where x means greatest integer value less


10
3
than equal to x.
BD 3
17. From the given figure
and 6BE = AE, prove that 2AF = 9CF.
DC 4

18. By using 0, 1, 2, 3, 5 without repetition of digits how many numbers lies between 100 to 1000 and
how many of them are divisible by 6?
19. Find by which highest power of 2 the product of first 100 natural numbers is divisible.
20. If x y z 1, x 2 y 2 z 2 2, x 3 y 3 z 3 3 , find value of xyz .
(BONUS QUESTION)
21. Prove that there is no integral solution of the equation 1 x 2 3 y .
22. There is one 1 n chess board. If each square of chess board colored with red or white or blue such
that no two consecutive squares having same color. Let we can do it in an different ways. Find the
relation between an , an1 and an2 .
23. Find out for what natural number n, 16n 4 1 is not a prime number?
******
****
**
Dr. Shyam Sundar Agrawal
2

You might also like