Let $f(x)=a_n x^n+a_{n-1} x^{n-1}+\cdots+a_1 x+a_0$ be a polynomial. Suppose that $f(0)=0$,

$$ \left.\left.\frac{d f}{d x}\right]_{x=0}=1, \frac{d^2 f}{d x^2}\right]_{x=0}=4 $$

and

$$ \frac{d^3 f}{d x^3}=\frac{d^5 f}{d x^5} $$

Then $f(5)=$

Let $S$ be the set of all unit vectors in the $X Y$-plane. Then the set $S$ has

A lab reports that the global average temperature in the year 2020 was $14.9^{\circ} \mathrm{C}$ and predicts that the global average temperature will increase at the rate of $1 \%$ per year. What will be the global average temperature in the year 2035?

Let $X$ be the set of all $2 \times 2$ matrices with real entries and $R \subset X \times X$ be the relation $R=$ $\{(A, B): A B=B A\}$. Which of the following statements is true?