$A$ particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then,its time period of vibration will be

The distance between the lines represented by $4x^2 + 20xy + 25y^2 + 2x + 5y - 12 = 0$ is equal to

An earthquake generates both transverse $(S)$ and longitudinal $(P)$ waves in the earth. The speed of $S$ waves is about $4.5 \, km/s$ and that of $P$ waves is about $8.0 \, km/s$. $A$ seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0 \, min$ before the first $S$ wave. The epicenter of the earthquake is located at a distance of about ..... $km$.

If the angle between the pair of lines $x^2+2 \sqrt{2} x y+k y^2=0, k>0$ is $45^{\circ}$,then the area (in square units) of the triangle formed by the pair of bisectors of the angles between these lines and the line $x+2 y+1=0$ is

Which one is an incorrect statement?

The average degree of freedom per molecule of a gas is $6$. The gas performs $25 \ J$ of work while expanding at constant pressure. The heat absorbed by the gas is .... $J$