Frequency $f$ of a simple pendulum depends on its length $\ell$ and acceleration $g$ due to gravity according to the following equation $f=\frac{1}{2 \pi} \sqrt{\frac{ g }{\ell}}$. Graph between which of the following quantities is a straight line?
$f$ on the ordinate and $\ell$ on the abscissa
$f$ on the ordinate and $\sqrt{ \ell }$ on the abscissa
$f ^2$ on the ordinate and $\ell$ on the abscissa
$f ^2$ on the ordinate and $1 / \ell$ on the abscissa
If $\tan \theta=\frac{1}{\sqrt{5}}$ and $\theta$ lies in the first quadrant, the value of $\cos \theta$ is :
The coordinates of a particle moving in $XY$-plane vary with time as $x=4 t ^2 ; y=2 t$. The locus of the particle is a :-
The slope of the tangent to the curve $y = ln\, (cos\,x)$ a $x = \frac{3\pi}{4}$ is