If the position vectors of the vertices of a triangle are $2 \hat{i}-\hat{j}+\hat{k}$, $\hat{i}-3 \hat{j}-5 \hat{k}$, and $3 \hat{i}-4 \hat{j}-4 \hat{k}$, then the triangle is

An iron rod is placed parallel to a magnetic field of intensity $2000 \ A \ m^{-1}$. The magnetic flux through the rod is $6 \times 10^{-4} \ Wb$ and its cross-sectional area is $3 \ cm^2$. The magnetic permeability of the rod in $Wb \ A^{-1} \ m^{-1}$ is:

$\lim _{x \rightarrow \infty}\left[\sqrt{x^2+2 x-1}-x\right]$ is equal to :

If $\frac{dy}{dx} + 2x \tan(x-y) = 1$,then $\sin(x-y)$ is equal to

Identify the basic amino acid from the following.

Two point white dots are $1 \, mm$ apart on black paper. They are viewed by an eye with a pupil diameter of $3 \, mm$. Approximately,what is the maximum distance at which these dots can be resolved by the eye? (Take $\lambda = 500 \, nm$)