$A$ car is fitted with a convex side-view mirror of focal length $20\ cm$. $A$ second car $2.8\ m$ behind the first car is overtaking the first car at a relative speed of $15\ m/s$. The speed of the image of the second car as seen in the mirror of the first one is

The more commonly used baking powder contains about $30 \% NaHCO_3, 20 \% NaAl(SO_4)_2, 10 \% Ca(H_2PO_4)_2$ and $40 \% $ starch. Which of the following statements is/are correct?

In a Young's double-slit experiment,the fringe width is $0.2 \, mm$. If the wavelength of light used is increased by $10\%$ and the separation between the slits is also increased by $10\%$,the fringe width will be.......$mm$.

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$,the piston moves through a length of $5 ~cm$. The total length of the cylindrical vessel in $cm$ is:

The probability distribution of a random variable $X$ is given by:

$X=x$	$P(X=x)$
$0$	$0.4$
$1$	$0.3$
$2$	$0.1$
$3$	$0.1$
$4$	$0.1$

The variance of $X$ is:

In order to eliminate the first degree terms from the equation $2x^2+4xy+5y^2-4x-22y+7=0$,the point to which the origin is to be shifted is