The remainder on dividing 1 + 3 + 3² + 3³ + ..... + 3²⁰²¹ by 50 is _________.

The area (in sq. units) of the region enclosed between the parabola y² = 2x and the line x + y = 4 is __________.

Let a circle C : (x $$-$$ h)² + (y $$-$$ k)² = r², k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ___________.

In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability $${3 \over 4}$$ and the remaining 6 questions correctly with probability $${1 \over 4}$$. If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is $${{{{27}k}} \over {{4^{10}}}}$$, then k is equal to ___________.