Using properties of determinants, show that

Find the distance of the plane 3x – 4y + 12z = 3 from the origin.

Prove the following:

Show that f : N → N, given by

is both one-one and onto.

OR

Consider the binary operations * : R × R → R and o : R × R → R defined as a * b =| a -b| and aob = a for all a, b ∈ R. Show that ‘*’ is commutative but not associative, ‘o’ is associative but not commutative.

If show that.

OR

Differentiate with respect to x.