The correct relation between the degree of freedom $f$ and the ratio of specific heat $\gamma$ is -

Needles $N_1, N_2$ and $N_3$ are made of a ferromagnetic,a paramagnetic and a diamagnetic substance respectively. $A$ magnet when brought close to them will

The amplitude of a wave represented by the displacement equation $y = \frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$ will be

Along the $X$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at $x=a+r$ (if $a \ll r$) is: ($\varepsilon_0$ is the permittivity of free space)

Two identical flutes produce fundamental notes of frequency $300\,Hz$ at $27\,^{\circ}C.$ If the temperature of air in one flute is increased to $31\,^{\circ}C,$ the number of beats heard per second will be

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\frac{\pi}{3}$. Then,the perimeter of the triangle is