GATE 2022 CS question paper PDF and answer key

“Fare” means price or charge, while “fair” means reasonable.

So the correct sentence is:

The fare is too high for it to be considered fair.

Therefore, the correct answer is Option D.

Use total probability.

If the first ball is green:

• probability = $\frac{3}{5}$
• green is not replaced, so next orange probability = $\frac{2}{4} = \frac{1}{2}$

If the first ball is orange:

• probability = $\frac{2}{5}$
• orange is replaced with another orange, so composition stays the same
• next orange probability = $\frac{2}{5}$

Hence,

Therefore, the correct answer is Option D.

• (A) is undecidable: equivalence of Turing machine languages is undecidable.
• (B) is undecidable by Rice’s theorem, since regularity is a non-trivial semantic property of the language recognized by a Turing machine.
• (C) is undecidable: deciding whether a Turing machine accepts all strings is the universality problem.

But (D) is decidable because the bound $1073$ is a fixed constant. A machine cannot inspect arbitrarily much input in at most $1073$ steps, so one can effectively analyze all relevant bounded computations and decide the property.

Therefore, the correct answers are A, B and C.

TCP sequence numbers count bytes, not bits.

At 1 Gbps,

In 60 seconds, the maximum number of bytes sent is

We need

Now,

but

Hence the minimum number of bits required is

Therefore, the answer is 33.

Before failure, router $P$ reaches $R$ via $Q$.

After link $Q-R$ fails:

• if Q informs P first, then $P$ updates correctly and no loop forms
• if P sends its stale route to Q first, then Q may believe that R is reachable through P, and a loop forms

Since P and Q send updates at random times with the same average rate, each of these two cases is equally likely.

So the probability of loop formation is

Therefore, the answer is 0.5.