$A$ disc has mass $m$ and radius $R$. How much tangential force should be applied to the rim of the disc so as to rotate it with angular velocity $\omega$ in time $t$?

Which of the following reactions will yield $2-$propanol? Select the correct answer from $a, b, c$ and $d$.
$(I)$ $CH_2=CH-CH_3 + H_2O \xrightarrow{H^+} $
$(II)$ $CH_3CHO \xrightarrow[(ii) H_2O]{(i) CH_3MgI}$
$(III)$ $CH_2O \xrightarrow[(ii) H_2O]{(i) C_2H_5MgI}$
$(IV)$ $CH_2=CH-CH_3 \xrightarrow{\text{neutral } KMnO_4}$

$A$ monoatomic gas is supplied heat $Q$ very slowly keeping pressure constant. The work done by the gas will be

$A$ Carnot engine,having an efficiency of $\eta = 1/10$ as a heat engine,is used as a refrigerator. If the work done on the system is $10 \ J$,the amount of energy absorbed from the reservoir at a lower temperature is .......... $J$.

In $Bryophytes$,sexual reproduction occurs through which organs?

In order to eliminate the first degree terms from the equation $2x^2+4xy+5y^2-4x-22y+7=0$,the point to which the origin is to be shifted is