GATE 2016 CS (Set 2) question paper PDF and answer key

Among 150 faculty members in an institute, 55 are connected with each other through Facebook and 85 are connected through WhatsApp. 30 faculty members do not have Facebook or WhatsApp accounts.

The number of faculty members connected only through Facebook accounts is ______________.

Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or, more importantly, required.

Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph?

(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions.

The given diagram shows the flowchart for a recursive function $A(n)$.

Assume that all statements, except for the recursive calls, have $O(1)$ time complexity.

If the worst-case time complexity of this function is $O(n^\alpha)$, then the least possible value of $\alpha$, accurate up to two decimal places, is __________.

Consider a non-negative counting semaphore $S$.

The operation $P(S)$ decrements $S$, and $V(S)$ increments $S$.

During an execution, 20 $P(S)$ operations and 12 $V(S)$ operations are issued in some order.

The largest initial value of $S$ for which at least one $P(S)$ operation will remain blocked is __________.

Consider the following database table named water_schemes.

The number of tuples returned by the following SQL query is __________.

WITH total(name, capacity) AS (
  SELECT district_name, SUM(capacity)
  FROM water_schemes
  GROUP BY district_name
),
total_avg(capacity) AS (
  SELECT AVG(capacity)
  FROM total
)
SELECT name
FROM total, total_avg
WHERE total.capacity >= total_avg.capacity;