The family of curves in which the sub-tangent at any point to any curve is double the abscissa is given by

The de-Broglie wavelength of the electron in the ground state of the hydrogen atom is . . . . . . $\mathring{A}$ (radius of the first orbit of hydrogen atom $= 0.53 \ \mathring{A}$).

On heating one end of a rod,the temperature of the whole rod will be uniform when

If $-\frac{\pi}{4} < x < \frac{\pi}{4}$,then the general solution of the differential equation $\cos ^2 x \cdot \frac{d y}{d x}-(\tan 2 x) y=\cos ^4 x$ is

If the axes are rotated through an angle $45^{\circ}$ in the positive direction without changing the origin,then the coordinates of the point $(\sqrt{2}, 4)$ in the old system are