If $\theta$ is the angle between vectors $\vec{a}$ and $\vec{b}$ and $|\vec{a} \times \vec{b}| = |\vec{a} \cdot \vec{b}|$,then $\theta$ is equal to

There is a horizontal film of soap solution. On it,a thread is placed in the form of a loop. The film is pierced inside the loop,and the thread becomes a circular loop of radius $R$. If the surface tension of the soap solution is $T$,then what will be the tension in the thread?

Which one of the following equations is correct for the reaction $N_{2(g)} + 3H_{2(g)} \longrightarrow 2NH_{3(g)}$?

Which of the following radiations has the least wavelength?

Consider the following reaction,
$C_2H_5Cl + AgCN \xrightarrow{EtOH / H_2O} \underline{X} \text{ (major)}$
Which one of the following statements is true for $\underline{X}$?
$(I)$ It gives propionic acid on hydrolysis
$(II)$ It has an ester functional group
$(III)$ It has a nitrogen linked to ethyl carbon
$(IV)$ It has a cyanide group

$A$ particle is projected up along a rough inclined plane of inclination $45^{\circ}$ with the horizontal. If the coefficient of friction is $0.5$, the acceleration is ($g=$ Acceleration due to gravity).