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 ............. $\mathring{A}$.

In a $\triangle ABC$,the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ is equal to:

The value of $\lambda$ with $|\lambda| < 16$ such that $2 x^2-10 x y+12 y^2+5 x+\lambda y-3=0$ represents a pair of straight lines,is

The complex $[Pt(py)(NH_3)(Br)(Cl)]$ will have how many geometrical isomers?

The work function of a metal is $2 \text{ eV}$. If a radiation of wavelength $3000 \text{ Å}$ is incident on it,the maximum kinetic energy of the emitted photoelectrons is (Planck's constant $h = 6.6 \times 10^{-34} \text{ J s}$; velocity of light $c = 3 \times 10^8 \text{ m/s}$; $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$)

The angle between the curves $y=\sin x$ and $y=\cos x$ is