Which of the following compounds when heated with $CO$ at $150^{\circ} C$ and $500 \ atm$ pressure in the presence of $BF_3$ forms ethyl propionate?

As shown in the figure,a block of mass $10 \, kg$ lying on a horizontal surface is pulled by a force $F$ acting at an angle of $30^{\circ}$ with the horizontal. For $\mu_{s} = 0.25$,the block will just start to move for the value of $F$ in $N$ is: [Given $g = 10 \, ms^{-2}$]

The limiting points of the co-axial system containing the two circles $x^2+y^2+2x-2y+2=0$ and $25(x^2+y^2)-10x-80y+65=0$ are

Energy of an electron in the ground state of the hydrogen atom is $-2.18 \times 10^{-18} \, J$. Calculate the ionization enthalpy of atomic hydrogen in terms of $J \, mol^{-1}$.

The angles of a triangle are in the ratio $3: 5: 10$. Then the ratio of the smallest side to the greatest side is:

$\frac{1}{2 \cdot 3} + \frac{1}{4 \cdot 5} + \frac{1}{6 \cdot 7} + \frac{1}{8 \cdot 9} + \dots$ is equal to