Consider the following tables, Loan and Borrower, of a bank.

Query: $\quad \pi_{\text {branch_name, customer_name }}$ (Loan $\triangleright \triangleleft$

Borrower) $\div \pi_{\text {branch_name }}$ (Loan)

where $\triangleright \triangleleft$ denotes natural join.

The number of tuples returned by the above relational algebra query is

__________

Suppose $X$ and $Y$ are random variables. The conditional expectation of $X$ given $Y$ is denoted by $E[X \mid Y]$. Then $E[E[X \mid Y]]$ equals

The sum of the elements in each row of $A \in \mathbb{R}^{n \times n}$ is 1 . If $B=A^3-2 A^2+A$, which one of the following statements is correct (for $x \in \mathbb{R}^n$ )?

Let $f(x)=\frac{e^x-e^{-x}}{2}, x \in R$. Let $f^{(k)}(a)$ denote the $k^{\text {th }}$ derivative of $f$ evaluated at $a$. What is the value of $f^{(10)}(0)$ ?(Note: ! denotes factorial)