Two waves $\mathrm{Y}_1=0.25 \sin 316 \mathrm{t} \quad$ and $\mathrm{Y}_2=0.25 \sin 310 \mathrm{t}$ are propagating along the same direction. The number of beats produced per second are

In a meter bridge experiment, the balance point is obtained if the gaps are closed by $2 \Omega$ and $3 \Omega$. A shunt of $\mathrm{X} \Omega$ is added to $3 \Omega$ resistor to shift the null point by 22.5 cm. The value of ' $x$ ' is

Water rises up to height ' $X$ ' in a capillary tube immersed vertically in water. When the whole arrangement is taken to a depth ' d ' in a mine, the water level rises up to height ' $Y$ '. If ' $R$ ' is the radius of earth then the ratio $\frac{Y}{X}$ is

In an equilateral prism the ray undergoes minimum deviation when it is incident at an angle of $50^{\circ}$. The angle of minimum deviation is