One root of the equation $\cos x - x + \frac{1}{2} = 0$ lies in the interval

If $200 \text{ MeV}$ of energy is released in the fission of one nucleus of ${}_{92}^{236}U$,the number of nuclei that must undergo fission to release an energy of $1000 \text{ J}$ is

Two slits separated by a distance of $1\, mm$ are illuminated with red light of wavelength $6.5 \times 10^{-7}\, m$. The interference fringes are observed on a screen placed $1\, m$ from the slits. Find the distance between the third dark fringe and the fifth bright fringe on the same side of the central maxima.

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth,is

The normal to the curve $x = a(1 + \cos \theta)$,$y = a \sin \theta$ at $\theta$ always passes through which fixed point?

If $\sigma_1$,$\sigma_2$,and $\sigma_3$ are the conductivities of three conductors,what will be the equivalent conductivity when they are connected in series?