For $x \in \mathbb{R}$,the range of $3 \cos (4x - 5) + 4$ lies in the interval

The numbers $a_n = 6^n - 5n$ for $n = 1, 2, 3, \ldots$ when divided by $25$ leave the remainder:

The number of ways that $8$ beads of different colours can be strung as a necklace is

Diffraction effects are easier to notice in the case of sound waves than in the case of light waves because

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of $4: 3$. If the effective focal length of the two lenses is $+60 ~cm$,then the focal lengths of the lenses should be:

Three point charges $1 \ C$,$-2 \ C$,and $-2 \ C$ are placed at the vertices of an equilateral triangle of side $1 \ m$. The work done by an external force to increase the separation of the charges to $2 \ m$ in joules is $(\varepsilon_0 = \text{permittivity of air})$