The combined equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve $x^2+y^2+xy+x+3y+1=0$ and the line $x+y+2=0$ is

The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

The wavelength of the first line of the Lyman series for a hydrogen atom is equal to that of the second line of the Balmer series for a hydrogen-like ion. The atomic number $Z$ of the hydrogen-like ion is

Which of the following molecules does not have a linear arrangement of atoms?

In a compound microscope,the focal length of the objective lens is $f_o = 1.2 \ cm$ and the focal length of the eyepiece is $f_e = 3.0 \ cm$. When the object is kept at $u_o = -1.25 \ cm$ in front of the objective,the final image is formed at infinity. The magnifying power of the compound microscope is:

Consider the following two statements,$A$ and $B$ and identify the correct answer given below:
$A$. Nuclear density is same for all nuclei.
$B$. Radius of the nucleus $R$ and its mass number $A$ are related as $\sqrt{A} \propto R^{1 / 6}$.