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Frequently Asked maths olympiad Latest Exam Pattern - maths olympiad Sample Question with Solutions Page 15

(#M40030614) MATHS OLYMPIAD QUESTION Logic Keep an EYE

Q. Sum of all triple digit numbers divisible by 7.

Asked In Maths Olympiad Harsh Poddar (11 years ago)

Solved RAKESH Read Solution (5)

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(#M40022014) MATHS OLYMPIAD QUESTION GEOMETRY Keep an EYE

Let ABCD be a quadrilateral inscribed p in a circle. Suppose AB = 2 + p2 and AB subtends 135 at the centre of the circle. Find the maximum possible area of ABCD

Asked In Maths Olympiad MAN (12 years ago)

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(#M40022013) MATHS OLYMPIAD QUESTION GEOMETRY Keep an EYE

Let ABC be a triangle. An interior point P of ABC is said to be good if we can find exactly 27 rays emanating from P intersecting the sides of the triangle ABC such that the triangle is divided by these rays into 27 smaller triangles of equal area. Determine the number of good points for a given triangle ABC.

Asked In Maths Olympiad MAN (12 years ago)

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(#M40022012) MATHS OLYMPIAD QUESTION GEOMETRY Keep an EYE

Let ABC be an acute-angled triangle, and let D, E, F be points on BC, CA, AB respectively such that AD is the median, BE is the internal angle bisector and CF is the altitude. Suppose FDE = C, DEF = A and EFD = B. Prove that ABC is equilateral.

Asked In Maths Olympiad MAN (12 years ago)

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(#M40022011) MATHS OLYMPIAD QUESTION ALGEBRA Keep an EYE

Let f : Z ! Z be a function satisfying f(0) = 0, f(1) = 0 and
(i) f(xy) + f(x)f(y) = f(x) + f(y);
(ii)f(x y) − f(0)


f(x)f(y) = 0,
for all x, y 2 Z, simultaneously.
(a) Find the set of all possible values of the function f.
(b) If f(10) 6= 0 and f(2) = 0, find the set of all integers n such that
f(n) 6= 0

Asked In Maths Olympiad MAN (12 years ago)

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(#M40022010) MATHS OLYMPIAD QUESTION ALGEBRA Keep an EYE

Define a sequence hf0(x), f1(x), f2(x), . . .i of functions by
f0(x) = 1, f1(x) = x,
􀀀
fn(x)

2
− 1 = fn+1(x)fn−1(x), for n  1.
Prove that each fn(x) is a polynomial with integer coefficients

Asked In Maths Olympiad MAN (12 years ago)

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(#M40022006) MATHS OLYMPIAD QUESTION ALGEBRA Keep an EYE

Find all functions f : R + R such that
f(x + y)f(x - y) = f(x) + f(y)

2 - 4x^2f(y), (1)
for all x, y - R, where R denotes the set of all real numbers.

Asked In Maths Olympiad MAN (12 years ago)

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(#M40022005) MATHS OLYMPIAD QUESTION GEOMETRY Keep an EYE

Let ABCD be a quadrilateral inscribed in a circle. Let E, F, G, H be the midpoints of the arcs AB, BC, CD, DA of the circle. Suppose AC· BD = EG · FH. Prove that AC, BD, EG, FH are concurrent.

Asked In Maths Olympiad MAN (12 years ago)

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(#M40022004) MATHS OLYMPIAD QUESTION GEOMETRY Keep an EYE

Suppose five of the nine vertices of a regular nine-sided polygon are arbitrarily chosen. Show
that one can select four among these five such that they are the vertices of a trapezium.

Asked In Maths Olympiad MAN (12 years ago)

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(#M40022000) MATHS OLYMPIAD QUESTION GEOMETRY Keep an EYE

How many 6-tuples (a1, a2, a3, a4, a5, a6) are there such that each of a1, a2, a3, a4, a5, a6 is from the set {1, 2, 3, 4} and the six expressions a2 j - ajaj +1 + a2 j+1
for j = 1, 2, 3, 4, 5, 6(where a7 is to be taken as a1) are all equal to one another?

Asked In Maths Olympiad MAN (12 years ago)

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