Acid hydrolysis of $X$ yields two different organic compounds. Which one of the following is $X$?

The work function of a substance is $4.0 \, eV$. The longest wavelength of light that can cause photoelectron emission from this substance is approximately ............ $nm$.

Two particles $P$ and $Q$ start from the origin and execute simple harmonic motion along the $X$-axis with the same amplitude but with periods $3 \ s$ and $6 \ s$,respectively. The ratio of the velocities of $P$ and $Q$ when they meet is

Let $n = 1! + 4! + 7! + \ldots + 400!$. Then the ten's digit of $n$ is

Observe the following statements :
$A: \int \left(\frac{x^2-1}{x^2}\right) e^{\frac{x^2+1}{x}} d x = e^{\frac{x^2+1}{x}} + c$
$R: \int f^{\prime}(x) e^{f(x)} d x = f(x) + c$
Then which of the following is true?

$A$ body constrained to move along the $y$-axis is subjected to a constant force $\vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \, \text{N}$. The work done by this force in moving the body a distance of $4 \, \text{m}$ along the $y$-axis is ............... $\text{J}$.