TS EAMCET 2022 (Online) 20th July Morning Shift

Statement I An object subjected to velocities $\mathbf{v}_1$ and $\mathbf{v}_2$ has a resultant velocity with magnitude $|\mathbf{v}|=\left|\mathbf{v}_1\right|+\left|\mathbf{v}_2\right|$.

Statement II The magnitude of displacement is either less or equal to the path length of an object between two points.

Statement III The instantaeous acceleration is the limiting value of the average acceleration as the time interval approaches zero.

Which of the following is correct?

The approximate ratio of the speed of light in vacuum to that of an electron in the first Bohr orbit of hydrogen atom is

$\{x \in[0,2 \pi] / \sin x+i \cos 2 x$ and $\cos x-i \sin 2 x$ are conjugate to each other} $=$

For a projectile, if $\alpha$ is the angle of projection, $R$ is the range, $h$ is the maximum height, $t$ is the time of flight then

The maximum number of orbitals present in $n=4$ energy level of an atom and the maximum number of electrons with spin value $+\frac{1}{2}$ in the same orbitals are respectively

If $1, \omega, \omega^2$ are the cube roots of unity and $1, \alpha, \alpha^2, \alpha^3$ are the fourth roots of unity in usual notation, then $\alpha+\alpha \omega-\alpha^3 \omega^2=$