Pre-REGIONAL MATHEMATICAL OLYMPIAD, 2013

May 12th, 2015
Studypool Tutor
Price: $10 USD

Tutor description

• There are 20 questions in this question paper. Each question carries 5 marks. • Answer all questions • Time allotted: 2 hours QUESTIONS 1. What is the smallest positive integer k such that k(33 + 43 + 53 ) = an for some positive integers a and n, with n > 1?

Word Count: 858
Showing Page: 1/4
Pre Rmo 2013 Question Paper Set ANATIONAL BOARD FOR HIGHER MATHEMATICSANDHOMI BHABHA CENTRE FOR SCIENCE EDUCATIONTATA INSTITUTE OF FUNDAMENTAL RESEARCHPre-REGIONAL MATHEMATICAL OLYMPIAD, 2013Mumbai RegionOctober 20, 2013QUESTION PAPER SET: A There are 20 questions in this question paper. Each question carries 5 marks. Answer all questions. Time allotted: 2 hours.QUESTIONS1. What is the smallest positive integer k such that k(33 + 43 + 53 ) = an for some positive integers a and n, with n > 1?n2. Let Sn =k=01 . What is the value ofk+1+ k991?n=1 Sn + Sn13. It is given that the equation x2 + ax + 20 = 0 has integer roots. What is the sum of all possible values of a?4. Three points X, Y, Z are on a striaght line such that XY = 10 and XZ = 3. What is the product of all possible values of Y Z?5. There are n 1 red balls, n green balls and n + 1 blue balls in a bag. The number of ways of choosing two balls from the bag that have different colours is 299. What is the value of n? 6. Let S(M ) denote the sum of the digits of a positive integer M written in base 10. Let N be the smallest positive integer such that S(N ) = 2013. What

Review from student

Studypool Student
" Very Satisfied. "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1823 tutors are online

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors