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Let $a, b, x, y$ be real numbers such that $a^2+b^2=81$,$x^2+y^2=121$ and $ax+by=99$. Then,the set of all possible values of $ay-bx$ is

$A$ container is filled with water $(\mu = 1.33 \approx 4/3)$ up to a height of $33.25 \, cm$. $A$ concave mirror is placed $15 \, cm$ above the water level. The image of an object placed at the bottom is formed by the mirror at $25 \, cm$ below the water level. The focal length of the mirror is: (in $, cm$)

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The Henry's law constant for the solubility of $N_2$ gas in water at $298 \ K$ is $1.0 \times 10^5 \ atm$. The mole fraction of $N_2$ in air is $0.8$. The number of moles of $N_2$ from air dissolved in $10 \ moles$ of water at $298 \ K$ and $5 \ atm$ pressure will be:

$A$ rectangle $ABCD$ is inscribed in a circle whose center lies on the line $3y = x + 10$. If $A$ and $B$ are the points $(-6, 7)$ and $(4, 7)$ respectively,find the area of the rectangle.

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