A body weight \(50 \mathrm{~g}\) in air and \(40 \mathrm{~g}\) in water. How much would it weight in a liquid of specific gravity \(1.5\) ?

Maximum amplitude of message signal in amplitude modulation is \(20 \mathrm{~cm}\). If the amplitude of carrier wave is \(40 \mathrm{~cm}\), then modulation index of modulated wave is

Choose the wrong statement.

Two capacitors \(\mathrm{C}_1\) and \(\mathrm{C}_2\) are charged to 100 V and 120 V respectively. It is found that upon connecting them together in parallel, the potential on each one of them is zero. Therefore

To the potentiometer wire of length \(L\) and \(10 \Omega\) resistance, a battery of emf \(2.5 \mathrm{~V}\) and a resistance \(R\) are connected in series. If a potential difference of \(1 \mathrm{~V}\) is balanced across \(L\) / 2 length, the value of \(R\) in \(\Omega\) will be

A \(5.80 \mu \mathrm{~F}\) parallel plate air capacitor has a plate separation of 5 mm and is charged to a potential difference of 400 V . The energy density in the region between the plates is

The heat required to increase the temperature of 4 moles of a mono-atomic ideal gas from \(273^{\circ} \mathrm{C}\) to \(473^{\circ} \mathrm{C}\) at constant volume is

Dalton's law of partial pressures is applicable to which one of the following systems?

The ratio of the coefficient of \(x^3\) to the term independent of \(x\) in the expansion of \(\left(2 x+\dfrac{1}{x^2}\right)^{12}\) is

If \(150 \mathrm{~J}\) of heat is added to a system and the work done by the system is \(110 \mathrm{~J}\), then change in internal energy will be

Presence of peroxides in old stocks of ethers can be tested by first treating them with \(\mathrm{Fe}^{2+}\) ions and then adding an aqueous solution of

In which one of the case the chemical reaction given in Column I does not match with the name of the reaction given in Column II?
\(\begin{array}{|l|l|l|} \hline \text{S.No.} & \text{Column I - Reactions} & \text{Column II - Name of reaction.} \\ \hline \text{A} & \mathrm{C}_6 \mathrm{H}_5 \mathrm{CHO}+ \text{Conc. NaOH, heat} \rightarrow \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{OH}+\mathrm{C}_6 \mathrm{H}_5 \mathrm{COONa} & \text{Cannizzaro's reaction} \\ \hline \text{B} & \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_3+ \text{ (i) } \mathrm{CrO}_2 \mathrm{Cl}_2 / \mathrm{CS}_2 \text{ (ii) } \mathrm{H}_3 \mathrm{O}^{+} \rightarrow \mathrm{C}_6 \mathrm{H}_5 \mathrm{CHO} & \text{Etard reaction.} \\ \hline \text{C} & \mathrm{C}_6 \mathrm{H}_6+\mathrm{CO} / \mathrm{HCl} \text{ (anh. } \mathrm{AlCl}_3 \rightarrow \mathrm{C}_6 \mathrm{H}_5 \mathrm{CHO} & \text{Kolbe's reaction} \\ \hline \text{D} & \mathrm{RCN}+ \text{ (i) } \mathrm{SnCl}_2+\mathrm{HCl} \text{ (ii) } \rightarrow \mathrm{RCHO} & \text{Stephen's reaction.} \\ \hline \end{array}\)

If \(y=\tan ^{-1}\left(\frac{a-x}{1+a x}\right)\), then \(\frac{d y}{d x}=\)