Two unequal masses ' \(\mathrm{A}\) ' and ' \(\mathrm{B}\) ' moving along a straight line are brought to rest by equal retarding forces. If 'A' takes double the time taken by 'B' to come to rest and 'A' travels \(\frac{2}{3} \mathrm{rd}\) of the distance covered by ' \(\mathrm{B}\) ' before coming to rest, then the ratio of masses of ' \(\mathrm{A}\) ' and ' \(\mathrm{B}\) ' is _________ .

Consider a circular ring of radius \(1,4 \mathrm{~cm}\) lying on the surface of a liquid. If a vertical force of \(0.022 \mathrm{~N}\) greater than the weight of the ring is required to lift this ring from the liquid surface, then the surface tension of the liquid is

A TV tower has a height of \(150 \mathrm{~m}\). If the population density around the TV tower is \(10^3 \mathrm{~km}^{-2}\) then the population covered by the tower is (Radius of the earth, \(\mathrm{R}=6.4 \times 10^6 \mathrm{~m}\))

An open air pipe of length \(80 \mathrm{~cm}\) has the second harmonic frequency equal to the fundamental frequency of a closed organ air pipe. The length of the closed pipe is

Calculate the wavelength of the \(k_a\) line for \(z=31\), when \(a=5 \times 10^7 \mathrm{~Hz}^{1 / 2}\) for a characteristic X-ray spectrum.

In the given circuit, the potential difference across the plates of the capacitor C in steady state is

The coefficient of viscosity of an ideal fluid is

If the circles \(x^2+y^2-2 x-2 y-7=0\) and \(x^2+y^2+4 x+2 y+k=0\) cut orthogonally, then the length of their common chord is units

The initial rate of increase of current when a battery of emf \(6 \mathrm{~V}\) is connected in series with an inductance of \(2 \mathrm{H}\) and resistance of \(12 \Omega\) is

The combined equation of the lines passing through the origin and having slopes \(\frac{2}{3}\) and \(\frac{-2}{3}\) is

If \(A=(a, 0)\) and \(B=(-a, 0)\), then the locus of a point \(\mathrm{P}\) such that \(\mathrm{PA}^2-\mathrm{PB}^2=a^2\) is.

When a wire made of material with Young's modulus Y is subjected to a stress S, the elastic potential energy per unit volume stored in the wire is

From the following data
\[
\begin{aligned}
& \mathrm{CH}_3 \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g)+2 \mathrm{H}_2 \mathrm{O}(l) \\
& \Delta_r H^{\circ}=-726 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{H}_2 \mathrm{O}(l) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{C}(\text { graphite })+\mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g}) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-393 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
&
\end{aligned}
\]
The standard enthalpy of formation of \(\mathrm{CH}_3 \mathrm{OH}(l)\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is