The uncertainties in the velocities of two particles $A$ and $B$ are $0.05 \ m \ s^{-1}$ and $0.02 \ m \ s^{-1}$ respectively. The mass of $B$ is five times that of mass $A$. What is the ratio of uncertainties $\left(\frac{\Delta x_A}{\Delta x_B}\right)$ in their positions?

If $\int \frac{dx}{(1+\sqrt{x}) \sqrt{x-x^2}} = \frac{A \sqrt{x}}{\sqrt{1-x}} + \frac{B}{\sqrt{1-x}} + C$,where $C$ is a real constant,then $A+B$ equals to

Which of the following is not aromatic?

$50 \, g$ of copper is heated to increase its temperature by $10 \, ^\circ C$. If the same quantity of heat is given to $10 \, g$ of water,the rise in its temperature is ........ $^\circ C$ (Specific heat of copper $= 420 \, J \cdot kg^{-1} \cdot ^\circ C^{-1}$,Specific heat of water $= 4200 \, J \cdot kg^{-1} \cdot ^\circ C^{-1}$)

If the line joining $A(1, 3, 4)$ and $B$ is divided by the point $P(-2, 3, 5)$ in the ratio $1: 3$,then the coordinates of $B$ are:

If $f(x) = \frac{x^2-10x+25}{x^2-7x+10}$ and $f$ is continuous at $x = 5$,then $f(5)$ is equal to