The centre of the circle $r^2-4r(\cos \theta+\sin \theta)-4=0$ in Cartesian coordinates is

On closing an open organ pipe from one end,it is noticed that the frequency of the third harmonic is $50 ~Hz$ more than the fundamental frequency of vibration in the open organ pipe. The fundamental frequency of the open organ pipe is (in $~Hz$)

Amongst the given taxonomic aids,how many are associated with the preservation of specimens? Monograph,Flora,Key,Museums,Botanical Gardens,Catalogue,Herbarium,Manual

An electron (mass = $9.1 \times 10^{-31} \ kg$; charge = $1.6 \times 10^{-19} \ C$) experiences no deflection if subjected to an electric field of $3.2 \times 10^5 \ V/m$ and a magnetic field of $2.0 \times 10^{-3} \ Wb/m^2$. Both the fields are normal to the path of the electron and to each other. If the electric field is removed,then the electron will revolve in an orbit of radius.......$m$

The point of intersection of the diagonals of a square is at the origin,and the coordinate axes are drawn along the diagonals. If the side length of the square is $a$,which of the following is $NOT$ a vertex of the square?

$\frac{1}{2 \cdot 3} + \frac{1}{4 \cdot 5} + \frac{1}{6 \cdot 7} + \frac{1}{8 \cdot 9} + \dots$ is equal to