If , find .

OR

If and , find when .

A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

Using properties of determinants, prove that = 9(3xyz + xy + yz + zx).

If y = sin(sinx), prove that

Find the equations of the tangent and the normal, to the curve 16x² + 9y² = 145 at the point (x₁, y₁) where x₁ = 2 and y₁ > 0.

OR

Find the intervals in which the function f(x) = is

(a) Strictly increasing,

(b) Strictly decreasing.