$A$ random variable $X$ takes the values $0, 1, 2, 3, \ldots$ with probability $P(X=x)=k(x+1)\left(\frac{1}{5}\right)^x$,where $k$ is a constant. Then $P(X=0)$ is

There is some change in length when a $33000 ~N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} ~m^2$. The change of temperature required to produce the same elongation,if the steel rod is heated,is (The modulus of elasticity is $3 \times 10^{11} ~N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ} C$). (in $^{\circ} C$)

Which of the following is true for the gaseous state?

$A$ gaseous mixture consists of $16\,g$ of helium and $16\,g$ of oxygen. The ratio $(C_p/C_v)$ of the mixture is

Which region is considered the secondary center of origin for coffee production?

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 $g=10 \ m/s^2$)