If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

If $a = \log_{24} 12$,$b = \log_{36} 24$,and $c = \log_{48} 36$,then $1 + abc$ is equal to:

After $280\,days$,the activity of a radioactive sample is $6000\,dps$. The activity reduces to $3000\,dps$ after another $140\,days$. The initial activity of the sample in $dps$ is

At $27^{\circ} C$,$500 \ mL$ of helium diffuses in $30 \ minutes$. What is the time (in hours) taken for $1000 \ mL$ of $SO_2$ to diffuse under the same experimental conditions?

$A$ torch bulb rated as $4.5\, W, 1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ............. $V$.

$CFCl_3$ is responsible for the decomposition of ozone to oxygen. Which of the following reacts with ozone to form oxygen?