Which of the following is least likely to behave as a Lewis base?

$\int_0^1 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right) d x$ is equal to :

Widal test is used for the diagnosis of

When concentrated ${H_2SO_4}$ reacts with $X$ at a temperature of $160-170 \, ^\circ C$,ethylene is obtained. What is $X$?

If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}+\vec{b}|=\sqrt{29}$ and $\vec{a} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \times \vec{b}$,then a possible value of $(\vec{a}+\vec{b}) \cdot(-7 \hat{i}+2 \hat{j}+3 \hat{k})$ is

As shown in the figure,two particles each of mass $m$ tied at the ends of a light string of length $2 a$ are kept on a frictionless horizontal surface. When the mid-point $(P)$ of the string is pulled vertically upwards with a small but constant force $F$,the particles move towards each other on the surface. The magnitude of acceleration of each particle,when the separation between them becomes $2 x$,is: