IITJEE Foundation Math and PRMO (preRMO) practice: another random collection of questions

Problem 1: Find the value of \frac{x+2a}{2b--x} + \frac{x-2a}{2a+x} + \frac{4ab}{x^{2}-4b^{2}} when x=\frac{ab}{a+b}

Problem 2: Reduce the following fraction to its lowest terms:

(\frac{1}{x} + \frac{1}{y} + \frac{1}{z}) \div (\frac{x+y+z}{x^{2}+y^{2}+z^{2}-xy-yz-zx} - \frac{1}{x+y+z})+1

Problem 3: Simplify: \sqrt[4]{97-56\sqrt{3}}

Problem 4: If a+b+c+d=2s, prove that 4(ab+cd)^{2}-(a^{2}+b^{2}-c^{2}-d^{2})^{2}=16(s-a)(s-b)(s-c)(s-d)

Problem 5: If a, b, c are in HP, show that (\frac{3}{a} + \frac{3}{b} - \frac{2}{c})(\frac{3}{c} + \frac{3}{b} - \frac{2}{a})+\frac{9}{b^{2}}=\frac{25}{ac}.

May u discover the joy of Math! πŸ™‚ πŸ™‚ πŸ™‚

Nalin Pithwa.

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