If the lines $4x + 3y - 1 = 0$,$x - y + 5 = 0$,and $kx + 5y - 3 = 0$ are concurrent,then $k$ is equal to:

When a bucket is half full,the weight of the bucket and the water is $10 \ kg$. When the bucket is two-thirds full,the total weight is $11 \ kg$. What is the total weight (in $kg$),when the bucket is completely full?

The distance between two coherent sources is $0.1 \, mm$. The fringe-width on a screen $1.2 \, m$ away from the source is $6.0 \, mm$. The wavelength of light used is $\dots \, \mathring{A}$.

Let $\overline{a}, \overline{b}$ and $\overline{c}$ be three non-zero vectors such that no two of them are collinear and $(\overline{a} \times \overline{b}) \times \overline{c}=\frac{1}{3}|\overline{b}||\overline{c}| \overline{a}$. If $\theta$ is the angle between the vectors $\overline{b}$ and $\overline{c}$,then the value of $\sin \theta$ is

The correct floral formula of chilli is

In the circuit shown below,the $AC$ source has voltage $V = 20 \cos(\omega t)$ with $\omega = 2000 \, rad/sec$. The amplitude of the current will be nearest to.....$A$