If the mass number of an atom is $A = 40$ and its electron configuration is $1s^2, 2s^2, 2p^6, 3s^2, 3p^6$,the number of neutrons and protons in its nucleus will be

The value of $\int_{-1}^{1} (\sqrt{1 + x + x^2} - \sqrt{1 - x + x^2}) \, dx$ is

We have two spheres,one of which is hollow and the other solid. They have identical masses and moments of inertia about their respective diameters. The ratio of their radii is given by:

If the circle $x^2+y^2+8x-4y+c=0$ touches the circle $x^2+y^2+2x+4y-11=0$ externally and cuts the circle $x^2+y^2-6x+8y+k=0$ orthogonally,then $k=$

If $\tan \theta + \cot \theta = 2$,then $\sin \theta$ is equal to

$A$ particle of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x$-direction. It enters a region containing a uniform magnetic field $B$ directed along the negative $z$-direction,extending from $x = a$ to $x = b$. The minimum value of $v$ required so that the particle can just enter the region $x > b$ is