If the circle $x^2 + y^2 + 6x - 2y + k = 0$ bisects the circumference of the circle $x^2 + y^2 + 2x - 6y - 15 = 0$,then $k =$

$A$ soap bubble,having a radius of $1 \ mm$,is blown from a detergent solution having a surface tension of $2.5 \times 10^{-2} \ N/m$. The pressure inside the bubble is equal to the pressure at a point $Z_0$ below the free surface of water in a container. Taking $g = 10 \ m/s^2$ and the density of water $\rho = 10^3 \ kg/m^3$,the value of $Z_0$ is: (in $cm$)

The average kinetic energy of a gas molecule at $27\,^{\circ}C$ is $6.21 \times 10^{-21}\,J$. Its average kinetic energy at $227\,^{\circ}C$ will be

One end of a uniform glass capillary tube of radius $r=0.025 \ cm$ is immersed vertically in water to a depth $h=1 \ cm$. The excess pressure in $N/m^2$ required to blow an air bubble out of the tube is: (Surface tension of water $T=7 \times 10^{-2} \ N/m$,Density of water $\rho=10^3 \ kg/m^3$,Acceleration due to gravity $g=10 \ m/s^2$)

The number of solutions for $z^3+\bar{z}=0$ is

$A$ wire of area of cross-section $10^{-6} \ m^2$ is increased in length by $0.1\%$. The tension produced is $1000 \ N$. The Young's modulus of the wire is: