For the following questions answer them individually
If $$A, B \& C$$ are vectors and $$A = 1.u_{x} + 2.u_{y} + 3.u_{z}, B = 1.u_{x} + 1.u_{y} + 1.u_{z}$$ and $$C = 3.u_{x} + 2.u_{y} + 1.u_{z}$$, then $$(A \times B).C$$
The eigen values of the matrix are $$\begin{bmatrix}\cos \alpha & \sin \alpha \\ \sin \alpha & \cos \alpha \end{bmatrix}$$
The Laplace Transform of x(t) formed by convolution operator is:
$$x(t) = \left\{t.u(t)\right\}\otimes \left\{\cos 2 \pi t.u(t)\right\}$$
A random variable X has $$\overline{X} = 0 \& \sigma_{x}^{2} = 1$$. Form a new random variable $$Y = 2X + 1$$. The values of $$\overline{Y} \& \sigma_{y}^{2}$$ are:
Person X can solve 80% of the ISRO question paper and Person Y can solve 60%. The probability that at least one of them will solve a problem from the question paper, selectedat random is :