Which variety of rice is an example of a naturally occurring mutation?

Let $u = i + j$,$v = i - j$ and $w = i + 2j + 3k$. If $n$ is a unit vector such that $u \cdot n = 0$ and $v \cdot n = 0$,then $|w \cdot n|$ is equal to

If $A$ is a non-zero square matrix of order $n$ with $\operatorname{det}(I+A) \neq 0$ and $A^3=O$,where $I$ and $O$ are the unit and null matrices of order $n \times n$ respectively,then $(I+A)^{-1}$ is equal to

The potential difference between $A$ and $B$ in the figure is ................. $V$.

The value of $\lim_{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n (k^2 x)$ is

In a meter bridge,a $30 \Omega$ resistance is connected in the left gap and a pair of resistances $P$ and $Q$ in the right gap. Measured from the left,the balance point is $37.5 \text{ cm}$ when $P$ and $Q$ are in series,and $71.4 \text{ cm}$ when they are in parallel. The values of $P$ and $Q$ (in $\Omega$) are: