Filiform apparatus is a characteristic feature of

Two blocks of masses $10\,kg$ and $4\,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $14\,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ......... $m/s$.

Which of the following is the strongest conjugate base?

Molar volume $( V_m )$ of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_m$ as the variable. The ratio $($in $mol dm ^{-3} )$ of the coefficient of $V_m^2$ to the coefficient of $V_m$ for a gas having van der Waals constants $a=6.0 dm ^6 atm \ mol ^{-2}$ and $b=0.060 dm ^3 mol^{-1}$ at $300 K$ and $300 atm$ is $....$ .
Use: Universal gas constant $(R)=0.082 dm ^3 atm \ mol { }^{-1} K^{-1}$

The number of proper subsets of the set ${1, 2, 3}$ is

In a $U$-tube experiment,a column $AB$ of water is balanced by a column $CD$ of oil,as shown in the figure. Then the relative density of oil is