In a nuclide,one $a.m.u.$ of mass is dissipated into energy to bind its nucleons. The energy equivalent of this mass is

Which sample contains a greater number of nuclei: a $5.00 \, \mu Ci$ sample of $^{240}Pu$ (half-life $6560 \, y$) or a $4.45 \, \mu Ci$ sample of $^{243}Am$ (half-life $7370 \, y$)?

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the centre of mass of the system is

If $(1+x+x^2+x^3)^5 = \sum_{k=0}^{15} a_k x^k$,then $\sum_{k=0}^7 a_{2k}$ is equal to

$A$ hyperbola passes through a focus of the ellipse $\frac{x^2}{169} + \frac{y^2}{25} = 1$. Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse. The product of their eccentricities is $1$. Then,the equation of the hyperbola is:

How many $g$ of a dibasic acid $(Mol. wt. = 200)$ should be present in $100 \ ml$ of its aqueous solution to give a decinormal strength?