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Four matrices M1, M2, M3 and M4 are dimensions p × q, q × r, r × s and s × t respectively can be multiplied in several ways with different number of total scalar multiplications. For example When multiplied as ((M1 *M2) (M3* M4 )) 1 2 3 4 M ×M × M ×M the total number of scalar multiplications is pqr+rst+prt. When multiplied as ((( M1 * M2) *M3 ) *M4 ) the total number of scalar multiplications is pqr+prs+pst. If p=10, q=100, r=20, s=5 and t=80, then the minimum number of scalar multiplications needed is

Definition of a language L with alphabet {a} is given as following { nk } L = a |k > 0, and n is a positive integer constant What is the minimum number of states needed in a DFA to recognize L?

An 8 KB direct mapped write-back cache is organized as multiple blocks, each of size 32-bytes. The processor generates 32-bit addresses. The cache controller maintains the tag information for each cache block comprising of the following. 1 Valid bit 1 modified bit As many bits as the minimum needed to identify the memory block mapped in the cache. What is the total size of memory needed at the cache controller to store metadata (tags) for the cache?

An application loads 100 libraries at start up. Loading each library requires exactly one disk access. The seek time of the disk to a random location is given as 10 ms. Rotational speed of disk is 6000 rpm. If all 100 libraries are loaded from random locations on the disk, how long does it take to load all libraries? (The time to transfer data from the disk block once the head has been positioned at the start of the block may be neglected)

Database table by name Loan_Records is given below.

Borrower Bank_Manager Loan_ Amount

Ramesh Sunderajan 10000.00

Suresh Ramgopal 5000.00

Mahesh Sunderajan 7000.00

What is the output of the following SQL query?

SELECT count(*)

FROM(

(SELECT Borrower. Bank_Manager FROM Loan_Records) AS S

NATURAL JOIN

(SELECT Bank_Manager, Loan_Amount FROM Loan_Records) AS T

);

Which of the following statements is NOT TRUE?

We are given a set of n distinct elements and an unlabeled binary tree with n nodes. In how many ways can we populate the tree with the given set so that it becomes a binary search tree?

Consider a database table T containing two columns X and Y each of type integer.

After the creation of the table, one record (X= 1, Y=l) is inserted in the table. Let MX and MY denote the respective maximum values of X and Y among all records in the table at any point in time. Using MX and MY, new records are inserted in the table 128 times with X and Y values being MX+1, 2*MY+1 respectively. It may be noted that each time after the insertion, values of MX and MY change. What will be the output of the following SQL query after the steps mentioned above are carried out?

SELECT Y FROM T WHERE X=7;

Consider the following table of arrival time and burst time for three processes P0, P1 and P2.

Process Arrival time Burst Time

P0 0 ms 9 ms

P1 1 ms 4ms

P2 2 ms 9ms

The pre-emptive shortest job first scheduling algorithm is used. Scheduling is carried out only at arrival or completion of processes. What is the average waiting time for the three processes?

Consider evaluating the following expression tree on a machine with load-store architecture in which memory can be accessed only through load and store instructions. The variables a, b, c, d and e are initially stored in memory. The binary operators used in this expression tree can be evaluated by the machine only when the operands are in registers. The instructions produce result only in a register. If no intermediate results can be stored in memory, what is the minimum number of registers needed to evaluate this expression?

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