A water tank in the form of a right rectangular parallelepiped, with 4 m in length, 3 m in width, and 2 m in height, needs to be sanitized. In this operation, the tank will need to be emptied in 20 minutes at most. The water will be removed with the help of a pump with constant flow rate, where flow rate is the volume of liquid that passes through the pump per unit of time.
The minimum flow rate, in liters per second, that this pump should have so that the tank is emptied in the stipulated time is
(A) 2.
(B) 3.
(C) 5.
(D) 12.
(E) 20.

A blood bank receives 450 mL of blood from each donor. After separating blood plasma from red blood cells, the former is stored in bags with 250 mL capacity. The blood bank rents refrigerators from a company for storage of plasma bags, according to its needs. Each refrigerator has a storage capacity of 50 bags. Over the course of a week, 100 people donated blood to that bank.
Assume that from every 60 mL of blood, 40 mL of plasma is extracted.
The minimum number of freezers that the bank needed to rent to store all the plasma bags from that week was
(A) 2.
(B) 3.
(C) 4.
(D) 6.
(E) 8.

The package of snacks preferred by a girl is sold in packages with different quantities. Each package is assigned a number of points in the promotion: ``When you total exactly 12 points in packages and add another R\$ 10.00 to the purchase value, you will win a stuffed animal''.
This snack is sold in three packages with the following masses, points, and prices:

\begin{tabular}{ c } Package

mass (g)

&

Package

points

& Price (R\$) \hline 50 & 2 & 2.00 \hline 100 & 4 & 3.60 \hline 200 & 6 & 6.40 \hline \end{tabular}
The smallest amount to be spent by this girl that allows her to take the stuffed animal in this promotion is
(A) R\$ 10.80.
(B) R\$ 12.80.
(C) R\$ 20.80.
(D) R\$ 22.00.
(E) R\$ 22.80.

The venue for Olympic swimming competitions uses the most advanced technology to provide swimmers with ideal conditions. This involves reducing the impact of undulation and currents caused by swimmers in their movement. To achieve this, the competition pool has a uniform depth of 3 m, which helps reduce the ``reflection'' of water (the movement against a surface and the return in the opposite direction, reaching the swimmers), in addition to the already traditional 50 m length and 25 m width. A club wishes to reform its pool of 50 m length, 20 m width and 2 m depth so that it has the same dimensions as Olympic pools.
After the reform, the capacity of this pool will exceed the capacity of the original pool by a value closest to
(A) $20\%$.
(B) $25\%$.
(C) $47\%$.
(D) $50\%$.
(E) $88\%$.

A couple is moving to a new home and needs to place a cubic object, with 80 cm edges, in a cardboard box, which cannot be disassembled. They have five boxes available, with different dimensions, as described:

• Box 1: $86 \mathrm{~cm} \times 86 \mathrm{~cm} \times 86 \mathrm{~cm}$
• Box 2: $75 \mathrm{~cm} \times 82 \mathrm{~cm} \times 90 \mathrm{~cm}$
• Box 3: $85 \mathrm{~cm} \times 82 \mathrm{~cm} \times 90 \mathrm{~cm}$
• Box 4: $82 \mathrm{~cm} \times 95 \mathrm{~cm} \times 82 \mathrm{~cm}$
• Box 5: $80 \mathrm{~cm} \times 95 \mathrm{~cm} \times 85 \mathrm{~cm}$

The couple needs to choose a box in which the object fits, so that the least free space remains in its interior.
The box chosen by the couple should be number
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.

The following is a graph showing the velocity $v ( t )$ at time $t$ ( $0 \leqq t \leqq d$ ) of a point P moving on a number line starting from the origin.
When $\int _ { 0 } ^ { a } | v ( t ) | d t = \int _ { a } ^ { d } | v ( t ) | d t$, which of the following statements in are correct? (Here, $0 < a < b < c < d$.) [3 points]
Remarks ㄱ. Point P passes through the origin again after starting. ㄴ. $\int _ { 0 } ^ { c } v ( t ) d t = \int _ { c } ^ { d } v ( t ) d t$ ㄷ. $\int _ { 0 } ^ { b } v ( t ) d t = \int _ { b } ^ { d } | v ( t ) | d t$
(1) ㄴ
(2) ㄷ
(3) ㄱ, ㄴ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ

The position $x ( t )$ of a point P moving on a number line at time $t$ is given by $$x ( t ) = t ( t - 1 ) ( a t + b ) \quad ( a \neq 0 )$$ for two constants $a , b$. The velocity $v ( t )$ of point P at time $t$ satisfies $\int _ { 0 } ^ { 1 } | v ( t ) | d t = 2$. Which of the following statements in the given options are correct? [4 points]
Given statements: ᄀ. $\int _ { 0 } ^ { 1 } v ( t ) d t = 0$ ㄴ. There exists $t _ { 1 }$ in the open interval $( 0,1 )$ such that $\left| x \left( t _ { 1 } \right) \right| > 1$. ㄷ. If $| x ( t ) | < 1$ for all $t$ with $0 \leq t \leq 1$, then there exists $t _ { 2 }$ in the open interval $( 0,1 )$ such that $x \left( t _ { 2 } \right) = 0$.
(1) ᄀ
(2) ᄀ, ㄴ
(3) ᄀ, ㄷ
(4) ㄴ, ㄷ
(5) ᄀ, ㄴ, ㄷ

Water falls from a tap of circular cross section at the rate of 2 metres/sec and fills up a hemispherical bowl of inner diameter 0.9 metres. If the inner diameter of the tap is 0.01 metres, then the time needed to fill the bowl is
(A) 40.5 minutes
(B) 81 minutes
(C) 60.75 minutes
(D) 20.25 minutes

Water falls from a tap of circular cross section at the rate of 2 metres/sec and fills up a hemispherical bowl of inner diameter 0.9 metres. If the inner diameter of the tap is 0.01 metres, then the time needed to fill the bowl is
(A) 40.5 minutes
(B) 81 minutes
(C) 60.75 minutes
(D) 20.25 minutes