If the series limit of the Lyman series for a Hydrogen atom is equal to the series limit of the Balmer series for a hydrogen-like atom,then the atomic number of this hydrogen-like atom will be:

In the figure,the potentiometer wire $AB$ of length $L$ and resistance $9r$ is joined to the cell $D$ of $emf$ $\varepsilon$ and internal resistance $r$. The cell $C$'s $emf$ is $\varepsilon / 2$ and its internal resistance is $2r$. The galvanometer $G$ will show no deflection when the length $AJ$ is

Let $A, B$ and $C$ be three points in a plane. The locus of a point $P$ moving such that $PA^2 + PB^2 = 2PC^2$ is a

The length of the subtangent at any point $(x_1, y_1)$ on the curve $y=5^x$ is

The layer of cells outside the phloem meant for giving rise to the root branches is called

The position of a projectile launched from the origin at $t=0$ is given by $\vec{r}=(40 \hat{i}+50 \hat{j}) \text{ m}$ at $t=2 \text{ s}$. If the projectile was launched at an angle $\theta$ from the horizontal,then $\theta$ is (take $g = 10 \text{ m/s}^2$)