A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation

y(x, t) = (0.01 m) sin[(62.8 m^$$-$$1)x] cos[(628 s^$$-$$1)t]

Assuming $$\pi$$ = 3.14, the correct statement(s) is(are)

A particle of mass M and positive charge Q, moving with a constant velocity $${\overrightarrow u _1} = 4\widehat i$$ ms^$$-$$1 enters a region of uniform static magnetic field, normal to the xy plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after 10 ms with a velocity $${\overrightarrow u _2} = 2\left( {\sqrt 3 \widehat i + \widehat j} \right)$$ ms^$$-$$1. The correct statement(s) is(are)

The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is ___________.

A freshly prepared sample of a radioisotope of half-life 1386 s has activity 10³ disintegrations per second. Given that ln2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is __________.