Work done in increasing the size of a soap bubble from a radius of $3\, cm$ to $5\, cm$ is nearly (Surface tension of soap solution $= 0.03\, Nm^{-1}$). (in $\pi \,mJ$)

$A$ parallel plate capacitor has circular plates of $10\, cm$ radius separated by an air-gap of $1\, mm$. It is charged by connecting the plates to a $100\, V$ battery. What is the change in energy stored in the capacitor when the plates are moved to a distance of $1\, cm$ while remaining connected to the battery?

If $x^2+\alpha y^2+2 \beta y=a^2$ represents a pair of perpendicular lines,then $\beta$ equals to

For a suitably chosen real constant $a$,let a function $f: R - \{-a\} \rightarrow R$ be defined by $f(x) = \frac{a-x}{a+x}$. Further,suppose that for any real number $x \neq -a$ and $f(x) \neq -a$,$(f \circ f)(x) = x$. Then $f\left(\frac{-1}{2}\right)$ is equal to

On addition of $1 \, mL$ solution of $10\% \, NaCl$ to $10 \, mL$ gold sol in the presence of $0.0250 \, g$ of starch,the coagulation is just prevented. What is the gold number of starch?

Which one of the following is an outer orbital complex and exhibits paramagnetic behavior?