All India-2009

Let * be a binary operation on N Given: by
a * b = HCF (a, b) a, b, ∈ N. Write the value of 22 * 4.

Evaluate:

Evaluate:

Write the principal value of,

Write the value of the following determinant:

Find the value of x, from the following:

Find the value of p, if

Write the direction cosines of a line equally inclined to the three coordinate axes.

If is a unit vector and then find