Which of the following rational numbers are equivalent to $-7\frac{4}{6}$?

Raji created a number line. $A, B, P, Q, R,$and $S$ represent rational numbers.

Which of these is representing the number closest to $A\times B$?

Ajit subtracted a rational number $x$ from $1$. Then he subtracted another rational number $y$ from $1$. He found that, $(1-x) > (1-y)$.

Which of these is true about the rational numbers $x$, and $y$?

Rani pasted marbles with lables bearing rational numbers, and then tries to arrange them in increasing and decreasing order. She found that one particular ball is always comes in the middle.

Which of these balls come in the middle?

A student was converting the speed of a car from $\mathrm{km}/\mathrm{h}\to \mathrm{m}/\mathrm{s}$. The speed was given in $\mathrm{km}/\mathrm{h}$ and the student is supposed to multiply the given speed by $\frac{5}{18}$. But by mistake the student multiplied the given speed by $\frac{18}{5}$.  As the result the student got a number $299$ more than the correct value.

What was the speed of the car in $\mathrm{km}/\mathrm{h}$?

Sudha's teacher asked her to find the number of rational numbers between $\sqrt{2}$ and $\sqrt{3}$. Her teacher told her that $\sqrt{2}\approx 1.414$ and $\sqrt{3}\approx 1.732$. The teacher also told Sudha that $\sqrt{2}$, and $\sqrt{3}$ are not rational numbers.

How many rational numbers can be found between $\sqrt{2}$ and $\sqrt{3}$?

A ball is dropped from a height as indicated in the figure below. It goes deep into a pit, rebounds at the bottom of the pit, and goes up to $\frac{2}{3}$ of its previous height.

Which of these gives the ball's closest position when its reaches its maximum height between its $2$nd and $3$rd bounce? (The second figure is not to scale)