GATE 2026 CS (Set 1) question paper PDF and answer key

A protagonist is the main or leading character in a story. Its opposite is the antagonist, the character who opposes the protagonist.

So the correct answer is Option B.

From the graph:

• For $S \le 10$, the value is 0
• For $10 < S < 20$, the graph rises linearly from 0 to 10, so $$N(S)=S-10$$
• For $S \ge 20$, the graph stays constant at 10

Now examine:

$$H_{10}(S)-H_{20}(S)$$

Piecewise:

• If $S \le 10$: $$H_{10}(S)=0,\quad H_{20}(S)=0 \Rightarrow N(S)=0$$
• If $10 < S \le 20$: $$H_{10}(S)=S-10,\quad H_{20}(S)=0 \Rightarrow N(S)=S-10$$
• If $S > 20$: $$H_{10}(S)=S-10,\quad H_{20}(S)=S-20$$ so $$N(S)=(S-10)-(S-20)=10$$

This matches the graph exactly.

Therefore, the correct answer is Option A.

From the control flow graph:

• B1 computes $a=b+i$
• B2 computes $a=g*k$, then other assignments
• B3 computes $t=g*k$ and then assigns $b=c+m$
• B4 computes $x=g*k$ and $y=b+i$
• B5 computes $z=c+m$

At the entry of B4, an expression is redundant only if it is available along all incoming paths.

• The expression $g*k$ is computed in both B2 and B3, and neither $g$ nor $k$ is modified before reaching B4. So $g*k$ is redundant in B4.
• The expression $b+i$ is available from B1 along the B2 path, but along the B3 path the variable $b$ is redefined by $b=c+m$. So $b+i$ is not available on all paths to B4.

At B5, the expression $c+m$ is not available along all paths from the entry because it is computed in B3 but not in B2, and B4 does not compute it.

So:

• B4: $\{g*k\}$
• B5: $\{\}$

Therefore, the correct answer is Option D.

The client needs at least 6000 addresses. The smallest CIDR block that can provide this is:

$$2^{13} = 8192$$

addresses, which corresponds to a /19 block.

A /19 block advances in steps of 32 in the third octet.

The ISP block 202.16.0.0/15 covers:

• 202.16.0.0 to 202.16.255.255
• 202.17.0.0 to 202.17.255.255

Now check alignment:

• 202.16.0.0/19 → valid
• 202.17.64.0/19 → valid
• 202.16.32.0/19 → valid
• 202.17.24.0/19 → invalid, because 24 is not a multiple of 32

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

The function bar(n) computes:

$$\lfloor \log_2 n \rfloor$$

for positive integers $n$.

Now define the smallest positive integer $a_k$ such that

$$foo(a_k)=k.$$

From the definition of foo:

• $foo(1)=1$, so $$a_1 = 1$$
• to get $foo(n)=k+1$, we need $$foo(bar(n)) = k$$ so the smallest such $n$ is the smallest integer for which $$\lfloor \log_2 n \rfloor = a_k,$$ namely $$n = 2^{a_k}.$$

Therefore:

$$a_2 = 2^{a_1} = 2$$ $$a_3 = 2^{a_2} = 4$$ $$a_4 = 2^{a_3} = 16$$ $$a_5 = 2^{a_4} = 65536$$

Therefore, the answer is 65536.