The Bohr orbit radius for the hydrogen atom $(n = 1)$ is approximately $0.530 \ \mathring{A}$. The radius for the first excited state $(n = 2)$ is ............. $\mathring{A}$.

$A$ magnetized wire of magnetic moment $M$ and length $l$ is bent into the form of a semicircle of radius $r$. Then its new magnetic moment is:

If $x=a\left[\cos \theta+\log \left\{\tan \left(\frac{\theta}{2}\right)\right\}\right]$ and $y=a \sin \theta$,then $\frac{dy}{dx}$ is equal to

Which structure in the embryo is considered the precursor to the urinary bladder?

There is a uniform electric field of strength $10^3 \ Vm^{-1}$ along the $Y$-axis. $A$ body of mass $1 \ g$ and charge $10^{-6} \ C$ is projected into the field from the origin along the positive $X$-axis with a velocity of $10 \ ms^{-1}$. Its speed in $ms^{-1}$ after $10 \ s$ is (Neglect gravitation).

$A$ pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2+y^2=4$ with $x+y=a$. The set containing the value of $a$ is