The value of '$$a$$' for which one root of the quadratic equation $$$\left( {{a^2} - 5a + 3} \right){x^2} + \left( {3a - 1} \right)x + 2 = 0$$$
is twice as large as the other is

The number of real solutions of the equation $${x^2} - 3\left| x \right| + 2 = 0$$ is

The real number $$x$$ when added to its inverse gives the minimum sum at $$x$$ equal :

If $$x$$ is positive, the first negative term in the expansion of $${\left( {1 + x} \right)^{27/5}}$$ is