If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then for every $x \in R, f(g(x))$ is equal to

If a solid sphere of mass $1 \ kg$ and radius $0.1 \ m$ rolls without slipping at a uniform velocity of $1 \ m/s$ along a straight line on a horizontal floor,the kinetic energy is

On closing an open organ pipe from one end,it is noticed that the frequency of the third harmonic is $50 ~Hz$ more than the fundamental frequency of vibration in the open organ pipe. The fundamental frequency of the open organ pipe is (in $~Hz$)

If the pair of lines given by $(x^2+y^2) \cos^2 \theta = (x \cos \theta + y \sin \theta)^2$ are perpendicular to each other,then $\theta$ is equal to

When a positively charged particle enters a uniform magnetic field with uniform velocity,its trajectory can be :
$(1)$ a straight line
$(2)$ a circle
$(3)$ a helix

If $a > 0$ and $b^2 - 4ac = 0$,then the curve $y = ax^2 + bx + c$