The lines represented by the equation $x^2-y^2-x+3y-2=0$ are :

$A$ converging beam of rays is incident on a diverging lens. Having passed through the lens,the rays intersect at a point $15 \, cm$ from the lens on the opposite side. If the lens is removed,the point where the rays meet will move $5 \, cm$ closer to the lens. The focal length of the lens is.....$cm$

The Vernier scale of a travelling microscope has $50$ divisions which coincide with $49$ main scale divisions. If each main scale division is $0.5 \text{ mm}$,then the least count of the microscope is

The equation of the locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$,where $z=x+iy$ is a complex number,is

For a cell,the terminal potential difference is $2.2 \, V$ when the circuit is open and reduces to $1.8 \, V$ when the cell is connected to an external resistance of $R = 5 \, \Omega$. Determine the internal resistance of the cell.

In the sequence of sets $(1,2,3), (4,5,6), (7,8,9,10), \ldots$,the sum of elements in the $50^{th}$ set is