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Fundamental Information Technology Engineer Examination (FE) | Section A Comprehensive Mock Test 01

1 / 100.0s

Problem 1

Signed integers are represented in 8-bit two's complement. 01111100 and 00001010 are added, and the result is also stored in 8 bits.

Which combination gives the bit pattern stored and an account of the operation?

View explanation

01111100 is 124 and 00001010 is 10, so the mathematical sum is 134. But 8-bit two's complement covers only −128 to 127, and 134 falls outside that range. The low-order eight bits, 10000110, represent −122 when signed, and the moment the sum of two positive numbers turns negative you can tell an overflow has occurred.

Problem 2

The CPU always checks a cache with an access time of 10 nanoseconds first. Only on a cache miss does it then check main memory, with an access time of 100 nanoseconds. The cache hit rate is 90%.

What is the effective access time of this configuration, in nanoseconds?

View explanation

The 10 nanoseconds for the cache is needed whether it hits or misses. The miss rate is 10%, so the average additional time for main memory is 0.1 × 100 = 10 nanoseconds. The effective access time is therefore 10 + 10 = 20 nanoseconds. The figure of 19 comes from 0.9 × 10 + 0.1 × 100, which drops the cache check on a miss.

Problem 3

A binary search for 25 is performed on the ascending array A = [3, 8, 12, 17, 25, 31, 44]. Subscripts start at 1, and the lower and upper ends of the search range are low and high. The middle position mid is found each time by: mid = floor((low + high) / 2) If A[mid] is less than 25, low is updated to mid + 1; if it is greater, high is updated to mid − 1.

How many elements of A are compared before 25 is found, and in what order are those values compared?

View explanation

At the start low = 1 and high = 7, so mid = 4 and 17 is compared. Since 25 is larger, the range narrows to 5–7, giving mid = 6 and a comparison with 31. This time 25 is smaller, so the range becomes 5–5 and the third comparison finds 25 at A[5]. It does not work through the array from the front as a linear search would.

Problem 4

There is a relation "OrderDetail (order number, order date, product number, product name, quantity)" whose primary key is (order number, product number). Each order number has exactly one order date, and each product number has exactly one product name.

Which table structure best removes the partial functional dependencies and avoids duplicated updates of the same order date or product name?

View explanation

The order date depends only on the order number and the product name only on the product number, which are partial functional dependencies on part of the composite key. Moving orders and products into tables of their own, and leaving in OrderDetail only the quantity that is specific to a combination of order and product, satisfies second normal form. Moving quantity into the product table would make it impossible to record different quantities per order.

Problem 5

There are a customer table Customers(customer_id, name) and an order table Orders(order_id, customer_id). order_id is never NULL. You want the number of orders per customer, including customers with no orders at all.

Which SQL statement meets this requirement?

View explanation

A LEFT JOIN keeps every customer on the left and leaves the order side NULL for customers with no orders. Counting the non-NULL order_id therefore gives 0 for those customers. INNER JOIN and WHERE o.order_id IS NOT NULL both exclude customers without orders. COUNT(*) counts the customer rows left by the outer join, so it returns 1 even with no orders.

Problem 6

You are assigning IPv4 addresses to devices that communicate directly with the host 192.168.10.77/27 on the same subnet. As is normal for a subnet, the network address and the broadcast address are not assigned to devices.

Which address can be assigned?

View explanation

A /27 subnet mask is 255.255.255.224, which divides the last octet into blocks of 32. 77 falls in the block from 64 to 95, where 64 is the network address and 95 the broadcast address. The usable range for devices is 65 to 94, so of the options only 192.168.10.94 qualifies. 96 is the start of the next subnet.

Problem 7

A web application builds its search conditions by concatenating user input directly into an SQL statement. You want to reduce the risk of SQL injection without changing the database structure.

Which is the most appropriate fix?

View explanation

Placeholders separate the instruction part of the SQL statement from the values the user supplies, making it much harder for symbols in the input to be interpreted as SQL commands. HTML escaping is mainly a defense against XSS when displaying in a browser, not a defense for SQL. Granting administrator privileges only widens the impact if an attack succeeds.

Problem 8

An input field accepts only integers from 1 to 100 inclusive as valid.

Which set of test values is representative of boundary value analysis on the lower and upper limits?

View explanation

With inclusive boundaries you check just outside the lower limit (0) and on it (1), and on the upper limit (100) and just outside it (101). That exercises the points at which the valid/invalid decision flips at each end. The values 1, 50 and 100 are all valid, which makes it hard to find a defect that wrongly accepts values outside the range.

Problem 9

Task A (3 days) and task B (4 days) can start at the same time. Task C (2 days) starts after A finishes. Task D (5 days) starts after both B and C have finished. The duration of each task is fixed and there are no resource constraints.

Which combination gives the shortest completion time for the project and the critical path?

View explanation

A through C takes 3 + 2 = 5 days, while B, running in parallel, finishes in 4. D waits for both B and C, so it starts on day 5 and takes a further 5 days, giving 10 days overall. The longest path is A → C → D. B → D takes 9 days, so it has one day of slack and is not the critical path.

Problem 10

A product sells for 5,000 yen per unit, the variable cost is 3,000 yen per unit, and fixed costs for the period are 800,000 yen. Sales volume equals production volume, and the unit price and variable cost are constant.

How many units is the break-even sales volume?

View explanation

The marginal profit available to recover fixed costs on each unit sold is 5,000 − 3,000 = 2,000 yen. Dividing the fixed costs of 800,000 yen by 2,000 yen gives 400 units, at which sales of 2,000,000 yen equal total costs of 2,000,000 yen. Dividing the fixed costs by the selling price alone gives 160 units, which would not recover the variable costs.