Two plane polarized light waves combine at a certain point whose electric field components are

$$\begin{aligned} & E_1=E_0 \operatorname{Sin} \omega t \\ & E_2=E_0 \operatorname{Sin}\left(\omega t+\frac{\pi}{3}\right) \end{aligned}$$

Find the amplitude of the resultant wave.

Uniform magnetic fields of different strengths $\left(B_1\right.$ and $\left.B_2\right)$, both normal to the plane of the paper exist as shown in the figure. A charged particle of mass $m$ and charge $q$, at the interface at an instant, moves into the region 2 with velocity $v$ and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface?

(Consider the velocity of the particle to be normal to the magnetic field and $\mathrm{B}_2>\mathrm{B}_1$ )

Two projectiles are fired from ground with same initial speeds from same point at angles $\left(45^{\circ}+\right.$ $\alpha)$ and $\left(45^{\circ}-\alpha\right)$ with horizontal direction. The ratio of their times of flights is

In a hydrogen like ion, the energy difference between the $2^{\text {nd }}$ excitation energy state and ground is 108.8 eV . The atomic number of the ion is: