After $280\,days$,the activity of a radioactive sample is $6000\,dps$. The activity reduces to $3000\,dps$ after another $140\,days$. The initial activity of the sample in $dps$ is

$A$ bar magnet of magnetic moment $M$ and moment of inertia $I$ is freely suspended such that the magnetic axial line is in the direction of the magnetic meridian. If the magnet is displaced by a very small angle $\theta$,the angular acceleration is (Magnetic induction of earth's horizontal field $= B_H$)

If $[x]$ denotes the greatest integer not exceeding $x$ and if the function $f$ defined by $f(x)= \begin{cases} \frac{a+2 \cos x}{x^2} & , x < 0 \\ b \tan \frac{\pi}{[x+4]} & , x \geq 0 \end{cases}$ is continuous at $x=0$,then the ordered pair $(a, b)$ is equal to

In contrast to annelids,the Platyhelminthes show:

The Cartesian form of the polar equation $\theta = \tan^{-1} 2$ is

At high temperatures,which of the following are present?