The magnetic susceptibility of a paramagnetic material at $-73^{\circ} C$ is $0.0075$. What will be its value at $-173^{\circ} C$?

The variance of $20$ observations is $5$. If each observation is multiplied by $2$,then the variance of the resulting observations is:

Two blocks of masses $1 \ kg$ and $2 \ kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{40}{3 \pi} \times 10^6 \ N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $\left(g = 10 \ m s^{-2}\right)$

The equation of trajectory of a projectile is $y=10 x-\left(\frac{5}{9}\right) x^2$. If we assume $g=10 \ m/s^2$,the range of the projectile (in metres) is:

The maximum value of $xy$ subject to $x+y=7$ is

$A$ tension of $20 ~N$ is applied to a copper wire of cross-sectional area $0.01 ~cm^2$. The Young's modulus of copper is $1.1 \times 10^{11} ~N/m^2$ and the Poisson's ratio is $0.32$. The decrease in the cross-sectional area of the wire is: