$A$ concave mirror gives an image three times as large as the object placed at a distance of $20 \ cm$ from it. For the image to be real,the focal length should be ...... $cm$.

In a meter bridge experiment,a null point is obtained at $l \text{ cm}$ from the left end. If the meter bridge wire is replaced by a wire of the same material but twice the area of cross-section,then the null point is obtained at a distance:

Which of the following has the lowest thermal stability?

Silviculture is the cultivation of which of the following?

Given the circle $C$ with the equation $x^2+y^2-2x+10y-38=0$. Match the List-$I$ with the List-$II$ given below concerning $C$.

$A$. The equation of the polar of $(4, 3)$ with respect to $C$	$I$. $y + 5 = 0$
$B$. The equation of the tangent at $(9, -5)$ on $C$	$II$. $x = 1$
$C$. The equation of the normal at $(-7, -5)$ on $C$	$III$. $3x + 8y = 27$
$D$. The equation of the diameter passing through $(1, -5)$ and $(1, 3)$	$IV$. $x = 9$

The $P-V$ diagram of $2\,g$ of $He$ gas for the process $A \to B$ is shown. What is the heat given to the gas (in $,P_0V_0$)?