$\sqrt{2+\sqrt{5}-\sqrt{6-3 \sqrt{5}+\sqrt{14-6 \sqrt{5}}}}$ is equal to

In a compound microscope,the focal lengths of two lenses are $1.5 \, cm$ and $6.25 \, cm$. An object is placed at $2 \, cm$ from the objective lens and the final image is formed at $25 \, cm$ from the eye lens. The distance between the two lenses is.....$cm$

$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is

Consider the following statements $A$ and $B$ and identify the correct answer given below.
$A$. Peltier coefficient is numerically equal to the potential difference across the junctions of the thermocouple through which current is flowing.
$B$. According to Thomson,energy is neither absorbed nor evolved at the junction of a thermocouple but is absorbed or evolved only along the lengths of both the conductors.

The $pK_a$ values of four carboxylic acids are given below. Identify the weakest carboxylic acid.

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