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
Magnitude of slope of the shown graph.
The greatest value of the function $-5 \sin \theta+12 \cos \theta$ 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 :-
In the given figure, each box represents a function machine. A function machine illustrates what it does with the input.Which of the following statements is correct?
As $\theta$ increases from $0^{\circ}$ to $90^{\circ}$, the value of $\cos \theta$ :-