If $|a| = 2$,$|b| = 3$ and $a, b$ are mutually perpendicular,then the area of the triangle whose vertices are $0, a + b, a - b$ is

$A$ force of $100 \ dynes$ acts on a mass of $5 \ g$ for $10 \ s$. The velocity produced is .......... $cm/s$.

$A$ vibratory motion is represented by $x = 2A \cos \omega t + A \cos (\omega t + \frac{\pi}{2}) + A \cos (\omega t + \pi) + \frac{A}{2} \cos (\omega t + \frac{3\pi}{2})$. The resultant amplitude of the motion is:

Let $z = a - \frac{i}{2}$,where $a \in R$. Then $|i + z|^2 - |i - z|^2$ is equal to

If the coordinate axes are the bisectors of the angles between the pair of lines $ax^2 + 2hxy + by^2 = 0$ where $h^2 > ab$ and $a \neq b$,then

The difference between the fundamental frequencies of an open pipe and a closed pipe of the same length is $100 \ Hz$. The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is: (in $Hz$)