Question

bounded by the axes of reference and the normal
to y=logex(log base e)  at the point (1, 0) is 
(a)1unitsquare                               (b)2unitsquare                              (c)1/2unit square                     (d)
none of these

Answer 1

First of all find the equation of normal to curve at (1, 0)

$y = log_ex \\ \frac{dy}{dx} = \frac{1}{x} \\ (\frac{dy}{dx})_(_x _= _1_, _y _= _0_) = 1$

This is slope of tangent so slope of normal is -1.
So equation of line -> (y - 0) = (-1) * (x - 1) -> x + y = 1

This is the line intersection x-axis at (1, 0) and y-axis at (0, 1), forming a right angle triangle with height = 1 unit and base = 1 unit.

So area = $\frac{1}{2} * 1 * 1$

Answer
(c)