The number of integral values of m for which the quadratic expression, (1 + 2m)x² – 2(1 + 3m)x + 4(1 + m), x $$ \in $$ R, is always positive, is :

The total number of irrational terms in the binomial expansion of (7^1/5 – 3^1/10)⁶⁰ is :

The set of all values of $$\lambda $$ for which the system of linear equations
x – 2y – 2z = $$\lambda $$x
x + 2y + z = $$\lambda $$y
– x – y = $$\lambda $$z
has a non-trivial solutions :

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :