Let the image of the point $\mathrm{P}(0,-5,0)$ in the line $\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2}$ be the point R and the image of the point $\mathrm{Q}\left(0, \frac{-1}{2}, 0\right)$ in the line $\frac{x-1}{-1}=\frac{y+9}{4}=\frac{z+1}{1}$ be the point S . Then the square of the area of the parallelogram PQRS is $\_\_\_\_$ .
Let $f(x)=\left\{\begin{array}{ll}x^3+8 ; & x<0, \\ x^2-4 ; & x \geq 0,\end{array}\right.$ and $g(x)= \begin{cases}(x-8)^{1 / 3} ; & x<0, \\ (x+4)^{1 / 2} ; & x \geq 0 .\end{cases}$
Then the number of points, where the function $g \circ f$ is discontinuous, is $\_\_\_\_$ .
The percentage error in the calculated volume of a sphere, if there is $2 \%$ error in its diameter measurement, is $\_\_\_\_$ .
$$ \text { Match List - I with List - II. } $$
| $$ \text { List - I } $$ |
$$ \text { List - II } $$ |
||
|---|---|---|---|
| A. | Boltzmann constant | I. | $$ \left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right] $$ |
| B. | Stefan's constant | II. | $$ \left[\mathrm{M} \mathrm{~L}^2 \mathrm{~T}^{-1}\right] $$ |
| C. | Planck's constant | III. | $$ \left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right] $$ |
| D. | Gravitational constant | IV. | $$ \left[\mathrm{M} \mathrm{~L}^0 \mathrm{~T}^{-3} \mathrm{~K}^{-4}\right] $$ |
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