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

Dimensions of a block are $1\,cm \times 1\,cm \times 100\,cm$. If the specific resistance of its material is $3 \times 10^{-7}\, \Omega \cdot m$, then the resistance between the opposite rectangular faces (the square ends) is:

Identify $B$ in the following reaction:
$H_4SiO_4$ $\xrightarrow[1000^{\circ}C]{-2H_2O} A$ $\xrightarrow[\Delta]{\text{Carbon}} B + CO$

Molar volume $( V_m )$ of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_m$ as the variable. The ratio $($in $mol dm ^{-3} )$ of the coefficient of $V_m^2$ to the coefficient of $V_m$ for a gas having van der Waals constants $a=6.0 dm ^6 atm \ mol ^{-2}$ and $b=0.060 dm ^3 mol^{-1}$ at $300 K$ and $300 atm$ is $....$ .
Use: Universal gas constant $(R)=0.082 dm ^3 atm \ mol { }^{-1} K^{-1}$

If $y=a \cos (\log x)+b \sin (\log x)$,where $a, b$ are parameters,then $x^2 y^{\prime \prime}+x y^{\prime}$ is equal to

Which of the following statements are correct?
$(i)$ In prokaryotic cells,a special membranous structure formed by the extension of the plasma membrane into the cell is known as polysome.
$(ii)$ The smooth endoplasmic reticulum is the major site for synthesis of glycoproteins.
$(iii)$ $RuBisCO$ is the most abundant protein in the whole biosphere.
$(iv)$ Mitochondria,chloroplasts and peroxisomes are not considered as part of endomembrane system.
Of the above statements: