When light of wavelength $\lambda$ is incident on a photosensitive surface,the stopping potential is $V$. When light of wavelength $3 \lambda$ is incident on the same surface,the stopping potential is $\frac{V}{6}$. The threshold wavelength for the surface is:

Observe the following statements:
$I. f(x) = a x^{41} + b x^{-40} \Rightarrow \frac{f^{\prime \prime}(x)}{f(x)} = 1640 x^{-2}$
$II. \frac{d}{d x} \tan ^{-1}\left(\frac{2 x}{1-x^2}\right) = \frac{1}{1+x^2}$
Which of the following is correct?

Let $P$ be a plane passing through the points $(2,1,0)$,$(4,1,1)$ and $(5,0,1)$ and $R$ be the point $(2,1,6)$. Then the image of $R$ in the plane $P$ is

The end correction for the vibrations of air column in a tube of circular cross-section will be more if the tube is

If $m_1, m_2, m_3$ and $m_4$ are respectively the magnitudes of the vectors $\overrightarrow{a}_1=2 \hat{i}-\hat{j}+\hat{k}$,$\overrightarrow{a}_2=3 \hat{i}-4 \hat{j}-4 \hat{k}$,$\overrightarrow{a}_3=\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{a}_4=-\hat{i}+3 \hat{j}+\hat{k}$,then the correct order of $m_1, m_2, m_3$ and $m_4$ is

Which of the following compounds when heated with $CO$ at $150^{\circ} C$ and $500 \ atm$ pressure in the presence of $BF_3$ forms ethyl propionate?