In how many ways can $6$ persons be selected from $4$ officers and $8$ constables,if at least one officer is to be included?

Which domain of life is known for surviving in extreme environmental conditions?

$A$ column of water within xylem vessels of tall trees does not break under its weight because of

In the circuit shown in the figure,the $AC$ source gives a voltage $V = 20 \cos(2000t)$. Neglecting source resistance,the voltmeter and ammeter readings will be

$A$ parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is connected to another battery and is charged to potential difference $2V$. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is