$A$ magnetized wire of magnetic moment $M$ and length $L$ is bent into an arc of a circle subtending an angle of $60^\circ$ at the center. The new magnetic moment is:

Four massless springs whose force constants are $2k, 2k, k$ and $2k$ respectively are attached to a mass $M$ kept on a frictionless plane (as shown in figure). If the mass $M$ is displaced in the horizontal direction,then the frequency of oscillation of the system is

If $T$ is the surface tension of a soap solution,the amount of work done in blowing a soap bubble from a diameter $D$ to $2D$ is (in $\pi D^2T$)

$ABCD$ is a square with side $16$ units and $A$ is the origin. If the equation of the circle circumscribing the square $ABCD$ is $x^2+y^2=4k(x+y)$,then $k=$

$50 \ \Omega$ and $100 \ \Omega$ resistors are connected in series. This connection is connected with a battery of $2.4 \ V$. When a voltmeter of $100 \ \Omega$ resistance is connected across the $100 \ \Omega$ resistor,the reading of the voltmeter will be $.......... \ V$.

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