According to the carbinol system,tert-butyl alcohol is named as:

Gas is being pumped into a spherical balloon at the rate of $30 \ ft^3 / min$. The rate at which the radius increases when it reaches the value $15 \ ft$,is:

The statement $(p$ $\rightarrow q)$ $\rightarrow [(\sim p$ $\rightarrow q)$ $\rightarrow q]$ is

If $\log (1+x) - \frac{2x}{2+x}$ is increasing,then

Carbon,Silicon,and Germanium atoms have four valence electrons each. Their valence and conduction bands are separated by energy band gaps represented by $(E_g)_C$,$(E_g)_{Si}$,and $(E_g)_{Ge}$ respectively. Which one of the following relationships is true in their case?

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is $\mu = 1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ is given by