GATE CS 2004 Q7 — Arrays, Stacks and Queues

The hash function is defined as $h(x) = x \pmod{10}$, which simply returns the last digit (units digit) of the integer $x$.

Let's compute the hash value for each element in the input list:

• $h(4322) = 4322 \pmod{10} = 2$
• $h(1334) = 1334 \pmod{10} = 4$
• $h(1471) = 1471 \pmod{10} = 1$
• $h(9679) = 9679 \pmod{10} = 9$
• $h(1989) = 1989 \pmod{10} = 9$
• $h(6171) = 6171 \pmod{10} = 1$
• $h(6173) = 6173 \pmod{10} = 3$
• $h(4199) = 4199 \pmod{10} = 9$

Now, let's evaluate the given statements:

• Statement I: $9679, 1989, 4199$ hash to the same value.
  Since $h(9679) = h(1989) = h(4199) = 9$, this statement is True.
• Statement II: $1471, 6171$ hash to the same value.
  Since $h(1471) = h(6171) = 1$, this statement is True.
• Statement III: All elements hash to the same value.
  This is False as different elements yield different hash values (e.g., $2, 4, 1, 9, 3$).
• Statement IV: Each element hashes to a different value.
  This is False because there are multiple collisions (e.g., $1471$ and $6171$ both hash to $1$).

Therefore, only statements I and II are true, which corresponds to option C.