Two simple harmonic motion, are represented by the equations $${y_1} = 10\sin \left( {3\pi t + {\pi \over 3}} \right)$$ $${y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)$$ Ratio of amplitude of y₁ to y₂ = x : 1. The value of x is ______________.

X different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number n = 6 ? The value of X is ______________.

A zener diode of power rating 2W is to be used as a voltage regulator. If the zener diode has a breakdown of 10 V and it has to regulate voltage fluctuated between 6 V and 14 V, the value of R_s for safe operation should be ___________ $$\Omega$$.

Wires W₁ and W₂ are made of same material having the breaking stress of 1.25 $$\times$$ 10⁹ N/m². W₁ and W₂ have cross-sectional area of 8 $$\times$$ 10^$$-$$7 m² and 4 $$\times$$ 10^$$-$$7 m², respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is ____________ kg. (Use g = 10 m/s²)