When light of wavelength $\lambda$ is incident on a photosensitive surface,the stopping potential is $V$. When light of wavelength $3 \lambda$ is incident on the same surface,the stopping potential is $\frac{V}{6}$. The threshold wavelength for the surface is:

Assertion : $\text{Trans-}2\text{-butene}$ on reaction with $Br_2$ gives $\text{meso-}2,3\text{-dibromobutane}$.
Reason : The reaction involves $\text{syn-addition}$ of bromine.

If $\alpha, \beta, \gamma$ are the roots of $x^3+4x+1=0$,then the equation whose roots are $\frac{\alpha^2}{\beta+\gamma}, \frac{\beta^2}{\gamma+\alpha}, \frac{\gamma^2}{\alpha+\beta}$ is

$A$ body is projected from the earth at an angle of $30^{\circ}$ with the horizontal with some initial velocity. If its range is $20 \ m$,the maximum height reached by it is (in meters):

If $f$ is a differentiable function such that $f(2x+1) = f(1-2x)$ for all $x \in R$,then what is the minimum number of roots of the equation $f'(x) = 0$ in the interval $x \in (-5, 10)$,given that $f(2) = f(5) = f(10)$?

An earthquake generates both transverse $(S)$ and longitudinal $(P)$ waves in the earth. The speed of $S$ waves is about $4.5 \, km/s$ and that of $P$ waves is about $8.0 \, km/s$. $A$ seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0 \, min$ before the first $S$ wave. The epicenter of the earthquake is located at a distance of about ..... $km$.