The eccentricity of the conic $\frac{5}{r}=2+3 \cos \theta+4 \sin \theta$ is

$A$ straight line which makes equal intercepts on positive $X$ and $Y$ axes and which is at a distance of $1$ unit from the origin intersects the straight line $y = 2x + 3 + \sqrt{2}$ at $(x_0, y_0)$. Then $2x_0 + y_0$ is equal to

Tubectomy is a method of sterilization in which

The time taken for a calorimeter containing $75 \ g$ of water at $62^{\circ} C$ to cool to $58^{\circ} C$ is $9 \ \text{minutes}$. When the calorimeter contains $105 \ g$ of water, it takes $12 \ \text{minutes}$ to cool from $62^{\circ} C$ to $58^{\circ} C$. The water equivalent of the calorimeter is: (in $g$)

What is the volume (in litres) of oxygen at $STP$ required for complete combustion of $32 \ g$ of $CH_4$ ? (Molecular weight of $CH_4$ is $16$ )

The value of $m$,such that the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2}$ lies in the plane $2x-4y+z=7$,is