How many 4-digit positive integers divisible by 3 can be formed using only the digits $\{1,3,4,6,7\}$, such that no digit appears more than once in a number ?

The sum of the following infinite series is

$$ 2+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{8}+\frac{1}{9}+\frac{1}{16}+\frac{1}{27}+\ldots $$

In an election, the share of valid votes received by the four candidates $A, B, C$, and $D$ is represented by the pie chart shown. The total number of votes cast in the election were $1,15,000$, out of which 5,000 were invalid.

A $4 \times 4$ digital image has pixel intensities $(U)$ as shown in the figure. The number of pixels with $U \leq 4$ is: