Q6 of 52 Page 1

Evaluate:

Or

Evaluate:

Let

Let f(x) = (1 - x²) sin x cos²x

f(-x) = (1 - (-x)²) sin(-x) cos²(-x)

= -(1 - x²) sin x cos²x

= - f(x)

Hence f(x) is an odd function.

Using if f(x) is an odd function, we get I = 0.

Consider

Let

|x|=-x, if x<0

And |x|=x, if x≥0

Hence,

= [-0 - (-1)] + [2 - 0]

= [0 + 1] + [2-0]

= 1 + 2

If a line makes angles 90°, 135°, 45° with x, y and z axes respectively, find its direction cosines.

Find the vector equation of the line which passes through the point (3,4,5) and is parallel to the vector .

Find:

Examine whether the operation * defined on R by a*b=ab+1 is

(i) a binary or not.

(ii) if a binary operation, is it associative or not?

Find a matrix A such that 2A-3B+5C=O, where and .