In the following structure,the double bonds are marked as $I, II, III$ and $IV$. Geometrical isomerism is not possible at site$(s)$:

$A$ weight $W$ can be hung in any of the following four ways by using the same string. In which case is the string more likely to break?

$A$ charge $Q$ is enclosed by a Gaussian spherical surface of radius $R$. If the radius is doubled,then the outward electric flux will

$CH_3CN \xrightarrow{Na + C_2H_5OH} X$. The compound $X$ is:

In the measurement of a physical quantity $X = \frac{A^2 B}{C^{1/3} D^3}$,the percentage errors in the measurements of $A, B, C$,and $D$ are $2\%, 2\%, 4\%$,and $5\%$,respectively. The minimum percentage error in the measurement of $X$ is contributed by:

$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620 \, years$ and $810 \, years$. The time (in years) after which one-fourth of the material remains is