The common characteristics between tomato and potato will be maximum at the level of their . . . . . . .

If $3$ is a root of $x^2+kx-24=0$,then it is also a root of which of the following equations?

The wavelength of the first line of the Lyman series for a hydrogen atom is equal to that of the second line of the Balmer series for a hydrogen-like ion. The atomic number $Z$ of the hydrogen-like ion is

If $\vec{a} = \hat{i} - \hat{j} - \hat{k}$ and $\vec{b} = \lambda\hat{i} - 3\hat{j} + \hat{k}$ and the orthogonal projection of $\vec{b}$ on $\vec{a}$ is $\frac{4}{3}(\hat{i} - \hat{j} - \hat{k})$,then $\lambda$ is equal to:

$A$ diode detector is used to detect an amplitude-modulated wave of $60\%$ modulation by using a capacitor of capacity $250 \text{ pF}$ in parallel with a load resistance of $100 \text{ k}\Omega$. Find the maximum modulation frequency which could be detected by it.