Problems And Solutions SEAMO PAPER F 2016

MATH CONTEST SEAMO SMA

21. Find coefficient in the expansion of

\(\left(1+x+\frac{1}{x^2}\right)^{10}\)


22. \(PA\) and \(PB\) are tangential to the circle with centre \(O. OA=OB=1\) cm. Find the least possible value of \(PA·PB\).


23. The parabola \(y=x^2 +mx – \frac{3}{4}m^2\), where \(m>0\), intersects the x-axist at points \(A\) and \(B\). Suppose \(\frac{1}{OB}-\frac{1}{OB}=\frac{2}{3}\), find the value of \(m\)


24. In \(ΔABC, ∠BCA=90°, m\) is the midpoint of \(BC\). It is given that \(\sin∠BAM=\frac{1}{3}\). Find \(\sin∠BAC\)


25. Suppose \(f(x) = \ln{(1+x)} – \ln{(1-x)}\), for \(x∈(-1,1)\).
which of the following is/are true?
(i) \(f(\frac{2x}{1+x^2}=2f(x)\)
(ii) \(|f(x)|>2f(x)\)


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