In the following reactions

The major compound Y is

Suppose that all the terms of an arithmetic progression (A.P) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is

For any integer k, let $${a_k} = \cos \left( {{{k\pi } \over 7}} \right) + i\,\,\sin \left( {{{k\pi } \over 7}} \right)$$, where $$i = \sqrt { - 1} \,$$. The value of the expression $${{\sum\limits_{k = 1}^{12} {\left| {{\alpha _{k + 1}} - {a_k}} \right|} } \over {\sum\limits_{k = 1}^3 {\left| {{\alpha _{4k - 1}} - {\alpha _{4k - 2}}} \right|} }}$$ is

Suppose that $$\overrightarrow p ,\overrightarrow q $$ and $$\overrightarrow r $$ are three non-coplanar vectors in $${R^3}$$. Let the components of a vector $$\overrightarrow s $$ along $$\overrightarrow p ,$$ $$\overrightarrow q $$ and $$\overrightarrow r $$ be $$4, 3$$ and $$5,$$ respectively. If the components of this vector $$\overrightarrow s $$ along $$\left( { - \overrightarrow p + \overrightarrow q + \overrightarrow r } \right),\left( {\overrightarrow p - \overrightarrow q + \overrightarrow r } \right)$$ and $$\left( { - \overrightarrow p - \overrightarrow q + \overrightarrow r } \right)$$ are $$x, y$$ and $$z,$$ respectively, then the value of $$2x+y+z$$ is