The value of $c$ in the Lagrange's mean value theorem for $f(x)=\sqrt{x-2}$ in the interval $[2,6]$ is

The displacement of a particle executing $SHM$ is given by $y=5 \sin \left(4 t+\frac{\pi}{3}\right)$. If $T$ is the time period and the mass of the particle is $2 \text{ g}$,the kinetic energy of the particle when $t=\frac{T}{4}$ is given by (in $J$)

$A$ gamma ray photon creates an electron-positron pair. If the rest mass energy of an electron is $0.5\, MeV$ and the total kinetic energy of the electron-positron pair is $0.78\, MeV$,then the energy of the gamma ray photon must be $......\, MeV$.

Which one of the following sets correctly represents the increase in the paramagnetic property of the ions?

For $x \in \mathbb{R}$,the least value of $\frac{x^2-6x+5}{x^2+2x+1}$ is

If $f(x) = \sin^2 \left( \frac{\pi}{8} + \frac{x}{2} \right) - \sin^2 \left( \frac{\pi}{8} - \frac{x}{2} \right)$,then the period of $f$ is