Let z be complex number such that
$$\left| {{{z - i} \over {z + 2i}}} \right| = 1$$ and |z| = $${5 \over 2}$$.
Then the value of |z + 3i| is :

If the number of five digit numbers with distinct digits and 2 at the 10^th place is 336 k, then k is equal to :

A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness the melts at a rate of 50 cm³/min. When the thickness of ice is 5 cm, then the rate (in cm/min.) at which of the thickness of ice decreases, is :

The number of real roots of the equation,
e^4x + e^3x – 4e^2x + e^x + 1 = 0 is :