The equation of a wave on a string of linear mass density $0.04 \, kg \cdot m^{-1}$ is given by: $y = 0.02 \, \sin \left[ 2\pi \left( \frac{t}{0.04} - \frac{x}{0.50} \right) \right]$. The tension in the string is ..... $N$.

Which one of the following compounds does not decolourise an acidified aqueous solution of $KMnO_4$?

The graph in the figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t$. The relationship between $A$ and $t$ is: (Assume $\ln 12 = 2.6$)

When the same quantity of electricity is passed through aqueous $AgNO_3$ and $H_2SO_4$ solutions connected in series,$5.04 \times 10^{-2} \ g$ of $H_2$ is liberated. What is the mass of silver (in grams) deposited? (Eq. wts. of hydrogen $= 1.008$,silver $= 108$)

If the length of a stretched string is shortened by $x \%$ and the tension is increased by $44 \%$,then the ratio of the final and initial fundamental frequencies is $2:1$. The value of $x$ is:

Two lenses in contact made of materials with dispersive powers in the ratio $2 : 1$,behave as an achromatic convex lens of focal length $10\, cm$. The individual focal lengths of the lenses are