Tuesday’s GATE CS set

In a hostel, every resident prefers exactly one of tea and coffee, and the ratio of tea drinkers to coffee drinkers is $5:3$. Then 12 new residents, all coffee drinkers, move in and 5 tea drinkers move out. The ratio of tea drinkers to coffee drinkers is now $5:4$.

How many tea drinkers were there in the hostel originally?

A disk rotates at 12000 rpm and has 500 sectors per track. Moving the head from a track to an adjacent track takes 0.5 ms, and seek time is proportional to the number of tracks crossed. The head is initially on track 20. A request reads, in this order:

1. 6 randomly located sectors on track 35;
2. a run of 200 consecutive sectors on track 10;
3. 6 randomly located sectors on track 50.

Assume that each randomly located sector is preceded by an average rotational latency of half a rotation; the run of consecutive sectors is preceded by one such average latency and is then read in a single sweep; reading one sector takes $\frac{1}{500}$ of a rotation; and all other overheads are zero.

The total time to serve the request, in milliseconds, is

Assume int is 4 bytes. What does the following C program print?

#include <stdio.h>
int main(void) {
    int a[6] = {4, 9, 2, 7};
    int *p = a + 3;
    int *q = &a[1];
    *q += *p;
    p--;
    *p = p - q;
    printf("%d %d %d", a[1], a[2], *(q + 3));
    return 0;
}

Consider the following two context-free grammars over the terminal alphabet $\{a,b\}$. In each grammar $S$ is the only non-terminal and the start symbol, and $ϵ$ denotes the empty string.

Which one of the following statements is CORRECT?

Consider the context-free grammar $G$ with start symbol $S$, non-terminals $\{S,A,B\}$ and terminals $\{a,b,c,d\}$:

$$S\to Aa\mid Bb\mid cAb$$ $$A\to d$$ $$B\to d$$

Which ONE of the following statements is TRUE?

A relation $R(A,B,C)$ is stored as a data file sorted on attribute $A$; the file is not sorted on $B$. A sparse index has entries for only some search-key values (for example, one entry per data block), and a lookup for a key that has no entry uses the entry with the largest indexed key not greater than it.

Which one of the following indexes on this file can be sparse?

A host sends one UDP datagram carrying 2928 bytes of application data over IPv4. The UDP header is 8 bytes and every IPv4 header is 20 bytes (no options). The datagram must cross a link whose MTU is 1000 bytes, including the IP header. The DF bit is not set. Assume the router fragments greedily: while the remaining data does not fit in one fragment, it emits the largest fragment allowed and repeats on the rest; once the remaining data fits within the MTU, it sends it as the last fragment.

Which ONE of the following gives the number of IP fragments and the fragment offset field value of the last fragment?