Consider a hash table of size 10 with indices $\{0,1, \ldots, 9\}$, with the hash function

$$ h(x)=3 x(\bmod 10) $$

where linear probing is used to handle collisions. The hash table is initially empty and then the following sequence of keys is inserted into the hash table: 1 , $4,5,6,14,15$. The indices where the keys 14 and 15 are stored are, respectively

If a relational decomposition is not dependency-preserving, which one of the following relational operators will be executed more frequently in order to maintain the dependencies?

Consider the following three relations:

Car (model, year, serial, color)

Make (maker, model)

Own (owner, serial)

A tuple in Car represents a specific car of a given model, made in a given year, with a serial number and a color. A tuple in Make specifies that a maker company makes cars of a certain model. A tuple in Own specifies that an owner owns the car with a given serial number. Keys are underlined; (owner, serial) together form key for Own. ( $\bowtie $ denotes natural join)

$$ \pi_{\text {owner }}(\text { Own } \bowtie \left(\sigma_{\text {color="red" }}\right. $$

$\left(\right.$ Car $\triangleright \triangleleft\left(\sigma_{\text {maker }=\text { "ABC }}\right.$ Make $\left.\left.\left.)\right)\right)\right)$

Which one of the following options describes what the above expression computes?

$$ \text { On a relation named Loan of a bank: } $$

The following SQL query is executed

SELECT L1.loan_number

FROM Loan L1

WHERE L1.amount > (SELECT MAX

(L2.amount)

FROM Loan L2

WHERE L2.branch_name $=$ 'SR Nagar');

The number of rows returned by the query is _________