A particular straight line passes through origin and a point whose abscissa is double of ordinate of the point. The equation of such straight line is :
$y=\frac{x}{2}$
$y=2 x$
$y=-4 x$
$y=-\frac{x}{4}$
If $F = \frac{2}{{\sin \,\theta + \sqrt 3 \,\cos \,\theta }}$, then minimum value of $F$ is
Two particles $A$ and $B$ are moving in $X Y$-plane.
Their positions vary with time $t$ according to relation :
$x_A(t)=3 t, \quad x_B(t)=6$
$y_A(t)=t, \quad y_B(t)=2+3 t^2$
Distance between two particles at $t =1$ is :
The sum of the series $1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\ldots \ldots . \infty$ is