$A$ sample of a radioactive element has a mass of $10 \, g$ at an instant $t = 0$. The approximate mass of this element in the sample after two mean lives is ........ $g$.

$A$ segment of wire vibrates with a fundamental frequency of $450 ~Hz$ under a tension of $9 ~kg-wt$. The tension at which the fundamental frequency of the same wire becomes $900 ~Hz$ is

Two dice are thrown simultaneously,the probability of obtaining a total score of $5$ is

$A$ body of weight $64\, N$ is pushed with just enough force to start it moving across a horizontal floor and the same force continues to act afterwards. If the coefficients of static and dynamic friction are $0.6$ and $0.4$ respectively,the acceleration of the body will be (Acceleration due to gravity $= g$)

Compound $PdCl_4 \cdot 6H_2O$ is a hydrated complex; $1 \, m$ aqueous solution of it has a freezing point of $269.28 \, K$. Assuming $100 \%$ ionization of the complex,calculate the molecular formula of the complex ($K_f$ for water $= 1.86 \, K \, kg \, mol^{-1}$,freezing point of pure water $= 273.15 \, K$).

$A$ wheel of mass $m$ has charges $+q$ and $-q$ at diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of a uniform vertical electric field $E$. Find the value of $E$.