$$A(2,6,2), B(-4,0, \lambda), C(2,3,-1)$$ and $$D(4,5,0),|\lambda| \leq 5$$ are the vertices of a quadrilateral $$A B C D$$. If its area is 18 square units, then $$5-6 \lambda$$ is equal to __________.

If $$f(x)=x^{2}+g^{\prime}(1) x+g^{\prime \prime}(2)$$ and $$g(x)=f(1) x^{2}+x f^{\prime}(x)+f^{\prime \prime}(x)$$, then the value of $$f(4)-g(4)$$ is equal to ____________.

Let $$\sigma$$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $$E_{I}, E_{I I}$$ and $$E_{I I I}$$ are:

'$$n$$' polarizing sheets are arranged such that each makes an angle $$45^{\circ}$$ with the preceeding sheet. An unpolarized light of intensity I is incident into this arrangement. The output intensity is found to be $$I / 64$$. The value of $$n$$ will be: