City Montessori School IYMC Senior Prelims Question Paper : cmseducation.org

Name of the Organisation : City Montessori School
Exam : International Young Mathematicians’ Convention
Subject : IYMC Senior Prelims
Year : 2012
Document Type : Model & Past Question Papers
Website : http://www.cmseducation.org/
Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/13370-IYMCSENIORPRELIMS.docx

IYMC Senior Prelims Question Paper :

Quick Facts :
** 25 Questions
** No Negative Marking
** Duration: 1 hour.
** In built Tie-Breakers

Related : City Montessori School IYMC Relay Round Question Paper : https://www.pdfquestion.in/13363.html

1. If |a| = |b| = 0 and then az+bz+c= 0 represents
A) A circle
B) An ellipse
C) A straight line
D) A point

2. If a, ß, and d are the roots of (x2+x+4)2 + 3x(x2+x+4) + 2×2 = 0, then |a| + |ß| + |y| + |d| is equal to?
A)6
B) 8
C) 12
D) 25

3. If a and b are two positive real numbers and A, G, H are arithmetic mean, geometric mean and harmonic between a and b respectively, then A=G=H and the equality holds if and only if
A) a>b
B) a<b
C) a=b
D) None of the above

4. Let an = 111……1 (n times). The remainder when a124 is divided by 271 is
A) 23
B) 25
C) 27
D) 29

5. The number log27 is
A) An integer
B) A rational number
C) An irrational number
D) A prime number

6. The number of non negative integral solutions of x1+x2+…..+xr = n is
A) n+r-1Cr-1
B) nCr
C) n-rCr-1
D) n+rCr-1

7. log(x) f(x) = log(x) f(x)+ 0<f(x)=g(x) is true for what range of f(x)?
A) q(x) > 1
B) q(x) < 0
C) 0<q(x)<1
D) None of these

8. Number of solutions of log4(x-1) = log2(x-3) is
A) 3
B) 1
C) 2
D) 0

9. Number of zeroes at the end of 100! Is
A) 20
B) 22
C) 24
D) 26

10. For what value(s) of n, is C1-2C2+3C3-….+(-1)n-1 nCn = 0?
A) n<0
B) n>0
C) 0<n<1
D) n>1

11. If a = 99100, b = 10099, then
A) a>b
B) a=b
C) a<b
D) a+2b = 101100

12. If A=1 and b=1/3 then the value of a for which A2 = B is
A) 1
B) -1
C) i
D) No real values

13. The inverse of a Skew symmetric matrix of odd order is?
A) A symmetric matrix
B) A skew symmetric matrix
C) Diagonal matrix
D) Does not exist

14. If cos 2ß = cos (a+?)/cos (a-?), then tan a, tan ß and tan ? are in
A) A.P
B) G.P
C) H.P
D) None of these

15. What is the sum to infinity of s = 1 + (-1) + 1 + (-1) +……
A) 0
B) 1
C) 1/2
D) Indeterminate

16. Compute : (100-1)(100-2)(100-3)…..(100+1)(100+2)(100+3)
A) 0
B) 11110000
C) 111110000
D) 999200000

18. Which is the only number which can be represented as the sum of two cubes in two different ways?
A)769
B) 1729
C) 482
D) 1168

19. The inequality sin-1x > cos-1x holds for
A) All values of x
B) x (0, 1/ )
C) x (1/ , 1]
D) No value of x

20. The point (a, b+c), (b, c+a) and (c, a+b) are
A) Vertices of an equilateral triangle
B) Concyclic
C) Vertices of a right angled triangle
D) None of these

21. If the two circles x2+y2+2gx+2fy = 0 and x2+y2+2g 1x+2f1y = 0 touch each other, then
A) f1g = fg1
B) ff1 = gg1
C) f2+g2 = f12+g12
D) None of these

22. The sine of the angle between the pair of lines represented by the equation x2-7xy+12y2=0 is
A) 1/12
B) 1/13
C) 1/v170
D) None of these

23. If e and e1 are the eccentricities of a hyperbola and its conjugate, then 1/e2 + 1/e12 is equal to
A)-1
B) 0
C) 1
D) None of these

24. In the domains of functions, dom (f+g) gives
A) dom f n {x: f(x) = 0}
B) dom f n dom g
C) dom f n dom g n {x:g(x) ?0}
D) None of these

25. If f(x) = then at x = 1
A) f is not continuous
B) f is continuous but not differential
C)f is differentiated
D) the derivative is 1

Rules & Regulations :
** A team participating in the IYMC- Mathematica should consist of eight contestants – two from the Primary Level (10-13 years of age), three for the Middle School Level (14-15 years of age) and three for the Senior Level ( 16-18 years of age and not enrolled for an Undergraduate Programme at a College or University).

** A Teacher-Team Leader must accompany the team. The participation of the Mathematics Teacher as the Team Leader is desirable.
** Competition is open only for Registered schools. Coaching Centres/institutes or tutorials are not eligible for participation.

** As IYMC Mathematica is being organized from the 2nd to the 5th of December, 2018 teams are requested to arrive before 12 noon of 2nd December, 2018. Teams are, however, welcome a day earlier and may leave a day after. We will be happy to extend hospitality to all outstation teams during their entire stay in Lucknow.

** Participating teams with Team Leaders must be present at the venue at all times. The Leaders are responsible for good conduct of their team members.
** Only writing and drawing instruments are permitted at the contest venue. Books, papers, tables, calculators and computers will not be allowed in the examination rooms.