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?

The equation of the common tangent to the curves $y^2 = 8x$ and $xy = -1$ is

When $MgSO_4$ reacts with $NH_4OH$ and $Na_2HPO_4$,it forms a white crystalline substance. What is the formula of that substance?

The following diagram indicates the energy levels of a certain atom. When the system moves from the $4E$ level to the $E$ level, a photon of wavelength $\lambda_1$ is emitted. The wavelength of the photon produced during its transition from the $\frac{7}{3}E$ level to the $E$ level is $\lambda_2$. The ratio $\frac{\lambda_1}{\lambda_2}$ will be:

If $f(x) = \sin^6 x + \cos^6 x$ for $x \in R$,then $f(x)$ lies in the interval

$x=\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right), y=\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right) \Rightarrow \frac{d y}{d x}$ is equal to