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

If $\vec{u}, \vec{v},$ and $\vec{w}$ are three non-coplanar vectors,then $(\vec{u} + \vec{v} - \vec{w}) \cdot ((\vec{u} - \vec{v}) \times (\vec{v} - \vec{w})) = \dots$

The Bulk modulus for an incompressible liquid is

The length of the subtangent at $(2,2)$ to the curve $x^5=2y^4$ is

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $(4/5) \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $(3/5) \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,its time period (in $seconds$) is

Calcium carbonate reacts with aqueous $HCl$ to give $CaCl_2$ and $CO_2$ according to the reaction given below: $CaCO_{3(s)} + 2HCl_{(aq)} \to CaCl_{2(aq)} + CO_{2(g)} + H_2O_{(l)}$
What mass of $CaCl_2$ will be formed when $250 \ mL$ of $0.76 \ M$ $HCl$ reacts with $1000 \ g$ of $CaCO_3$? Name the limiting reagent. Calculate the number of moles of $CaCl_2$ formed in the reaction.