If a random variable $X$ has the following probability distribution, then its variance is nearly

$$ \begin{array}{clllllll} \hline X=x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline P(X=x) & 0.05 & 0.1 & 2 K & 0 & 0.3 & K & 0.1 \\ \hline \end{array} $$

A radar system can detect an enemy plane in one out of 10 consecutive scans. The probability that it cannot detect an enemy plane at least two times in four consecutive scans, is

The locus of a variable point which forms a triangle of fixed area with two fixed points is

If the axes are rotated through angle ' $\alpha$ ', then the number of values of a such that the transformed equation of $x^2+y^2+2 x+2 y-5=0$ contains no liner terms is