The time period of a second's pendulum is $2\, s$. The spherical bob,which is empty from inside,has a mass of $50\, g$. This is now replaced by another solid bob of the same radius but having a mass of $100\, g$. The new time period will be .... $s$.

If the wavelengths of maximum intensity of radiations emitted by the sun and the moon are $0.5 \times 10^{-6} \ m$ and $10^{-4} \ m$ respectively,the ratio of their temperatures is:

Check whether the following pair of statements are negations of each other. Give reasons for your answer.
$I$: $x+y=y+x$ is true for every real number $x$ and $y$.
$II$: There exists real numbers $x$ and $y$ for which $x+y \neq y+x$.

The four distinct points $(0,0), (2,0), (0,-2)$ and $(k,-2)$ are concyclic,if $k$ is equal to

The excess pressure inside a spherical soap bubble of radius $1 ~cm$ is balanced by a column of oil (specific gravity $= 0.8$), $2 ~mm$ high. The surface tension of the bubble is: (in $~N/m$)

If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k}$,$\overrightarrow{b}=\hat{i}+\hat{j}$,$\overrightarrow{c}=\hat{i}$ and $(\overrightarrow{a} \times \overrightarrow{b}) \times \overrightarrow{c}=\lambda \overrightarrow{a}+\mu \overrightarrow{b}$,then $\lambda+\mu$ is equal to: