Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$,then the probability of non-occurrence of at least one of the events $E$ and $F$ is

Two fair dice are rolled. The probability of the sum of digits on their faces being greater than or equal to $10$ is

$A$ tank with vertical walls is mounted so that its base is at a height $H$ above the horizontal ground. The tank is filled with water to a depth $h$. $A$ hole is punched in the side wall of the tank at a depth $x$ below the water surface. To have maximum range of the emerging stream, the value of $x$ is

When radiation of wavelength $\lambda$ is incident on a metallic surface,the stopping potential is $4.8 \ V$. If the same surface is illuminated with radiation of double the wavelength,then the stopping potential becomes $1.6 \ V$. Then the threshold wavelength for the surface is

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} ~kg ~m^{-1}$ is represented by the equation $y=0.2 \sin (1.5 x+60 t)$,where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

If $S_{n} = 1^3 + 2^3 + \ldots + n^3$ and $T_{n} = 1 + 2 + \ldots + n$,then