

 Why constant of integration will absent in definite integration
Science [12], Mathematics  Trigonometry,
Central Board of Secondary Education
8/19/2009
 A trapezium ABCD, in which AB is parallel to CD, is inscribed in a circle with centre O. Suppose the diagonals AC and BD of the trapezium intersect at M and OM = 2.
Science [12], Mathematics  Olympiad,
Central Board of Secondary Education
2/7/2009
Trapezium, Circle
 Let a, b , c be three natural numbers such that a< b < c and GCD ( c  a, c  b) =1. Suppose there exists an integer d such that a + d, b + d, c + d form the sides of a right  angle triangle. Prove that there exist integers l, m such that c + d = l^{2} = m^{2}.
Science [12], Mathematics  Olympiad,
Central Board of Secondary Education
2/7/2009
 How many 6 digit numbers are there such that (1) The digits of each number are all from the set {1, 2 ,3 ,4, 5} (2) Any digit that appears in the number appears at least twice ?
Science [12], Mathematics  Olympiad,
Central Board of Secondary Education
2/7/2009
Possibilities, Interchangeable, Desired Number
 Prove that: (a) 5 < √5 + 3√5 + 4√5; 8 > √8 + 3√8 + 4√8; n > √n + 3√n + 4√n for all integers n ≥ 9
Science [12], Mathematics  Olympiad,
Central Board of Secondary Education
2/7/2009
 Find all pairs (a, b) of real numbers such that whenever [alfa] is a root of x2 + ax + b = 0 [alfa]2  2 is also a root of the equation.
Science [12], Mathematics  Olympiad,
Central Board of Secondary Education
2/7/2009
 Let ABC be an acuteangled triangle; AD be the bisector of [angle] BAC with D on BC: and BE be the altitude from B on AC. Show that [angle] CED > 45 [degree]
Science [12], Mathematics  Olympiad,
Central Board of Secondary Education
2/7/2009

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