The area of the triangle $ABC$ is $10 \sqrt{3} \text{ cm}^2$,angle $B$ is $60^{\circ}$ and its perimeter is $20 \text{ cm}$,then $\ell(AC) = $ (in $text{ cm}$)

In a resonance pipe,the first and second resonances are obtained at lengths $22.7 \ cm$ and $70.2 \ cm$ respectively. What will be the end correction in $cm$?

The integral $\int \frac{3x^{13} + 2x^{11}}{(2x^4 + 3x^2 + 1)^4} dx$ is equal to (where $C$ is a constant of integration)

Which classification system was proposed by $R.H. Whittaker$?

Which of the following compounds is both paramagnetic and colored?

For the reaction $A + B \rightarrow C$,experiments were performed in the presence of a large amount of $B$ to measure the initial reaction rate $(V_f)$ as a function of the initial concentration of $A ([A]_0)$. The data from the experiments are plotted as shown below. The order of the reaction with respect to $A$ is $.....$