Two spherical conductors each of capacity $C$ are charged to potentials $V$ and $-V$. These are then connected by means of a fine conducting wire. The loss of energy will be

In an experiment on photoelectric emission from a metallic surface,the wavelength of incident light is $2 \times 10^{-7} \ m$ and the stopping potential is $2.5 \ V$. The threshold frequency of the metal (in $Hz$) is approximately (charge of electron $e = 1.6 \times 10^{-19} \ C$,Planck's constant $h = 6.6 \times 10^{-34} \ J \cdot s$):

What does the given structural formula represent?

Which of the following electronic configurations represents a transition element?

Let $f(x) = \frac{2\sin^2 x - 1}{\cos x} + \frac{\cos x(2\sin x + 1)}{1 + \sin x}$. Then find $\int e^x (f(x) + f'(x)) dx$ (where $c$ is the constant of integration).

If $\int(1-\cos x) \operatorname{cosec}^2 x \, dx = f(x) + c$, then $f(x)$ is equal to