All India - 2012

The binary operation * : R × R → R is defined as a * b = 2a + b. Find (2 * 3) * 4

Find the principal value of tan^–1√3 - sec^–1 (-2).

Find the value of x + y from the following equation:

Let A be a square matric of order 3 × 3. Write the value of |2A|, where |A| = 4.

Evaluate:

Given :

Write f(x) satisfying the above.

Write the value of

Find the scalar components of the vector

with initial point A (2,1) and terminal point B (–5, 7).

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