The wavelengths of two sound notes in air are $\frac{40}{195} ~m$ and $\frac{40}{193} ~m$. Each note produces $9$ beats per second separately with a third note of fixed frequency. The velocity of sound in air in $m/s$ is

$A$ spring of spring constant $5 \times 10^3 \, N/m$ is stretched initially by $5 \, cm$ from the unstretched position. Then the work required to stretch it further by another $5 \, cm$ is .............. $N-m$.

$\int_{-\pi / 2}^{\pi / 2} \sin ^4 x \cos ^6 x \, dx$ is equal to

In a meter bridge experiment,a resistance of $9 \Omega$ is connected in the left gap and an unknown resistance $x$ (where $x > 9 \Omega$) is connected in the right gap. If the resistances in the gaps are interchanged,the balancing point shifts by $10 \text{ cm}$. The value of the unknown resistance is: (in $\Omega$)

The image of the point $(3, 8)$ in the line $x + 3y = 7$ is

Two thermometers $X$ and $Y$ have ice points marked at $15^o$ and $25^o$ and steam points marked as $75^o$ and $125^o$ respectively. When thermometer $X$ measures the temperature of a bath as $60^o$ on it,what would thermometer $Y$ read when it is used to measure the temperature of the same bath?