Let the lines

$${L_1}:\overrightarrow r = \lambda \left( {\widehat i + 2\widehat j + 3\widehat k} \right),\,\lambda \in R$$

$${L_2}:\overrightarrow r = \left( {\widehat i + 3\widehat j + \widehat k} \right) + \mu \left( {\widehat i + \widehat j + 5\widehat k} \right);\,\mu \in R$$,

intersect at the point S. If a plane ax + by $$-$$ z + d = 0 passes through S and is parallel to both the lines L₁ and L₂, then the value of a + b + d is equal to ____________.

Let A be a 3 $$\times$$ 3 matrix having entries from the set {$$-$$1, 0, 1}. The number of all such matrices A having sum of all the entries equal to 5, is ___________.

The greatest integer less than or equal to the sum of first 100 terms of the sequence $${1 \over 3},{5 \over 9},{{19} \over {27}},{{65} \over {81}},$$ ...... is equal to ___________.

If $$Z = {{{A^2}{B^3}} \over {{C^4}}}$$, then the relative error in Z will be :