If $P=(0,1,0)$ and $Q=(0,0,1)$, then the length of the projection of the line segment $PQ$ on the plane $x+y+z=3$ is

If $m$ and $\sigma^2$ are the mean and variance of the random variable $X$,whose distribution is given by:

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{3}$	$\frac{1}{2}$	$0$	$\frac{1}{6}$

Then:

The area (in sq units) of the quadrilateral formed by two pairs of lines $\lambda^2 x^2 - m^2 y^2 - n(\lambda x + m y) = 0$ and $\lambda^2 x^2 - m^2 y^2 + n(\lambda x + m y) = 0$ is:

$A$ ball $A$ of mass $m$ moving along the positive $x$-direction with kinetic energy $K$ and momentum $p$ undergoes an elastic head-on collision with a stationary ball $B$ of mass $M$. After the collision,ball $A$ moves along the negative $x$-direction with kinetic energy $K/9$. The final momentum of ball $B$ is:

The two lenses of an achromatic doublet should have:

For a constant hydraulic stress on an object,the fractional change in the object's volume $\left( \frac{\Delta V}{V} \right)$ and its bulk modulus $(B)$ are related as