Freezing compartment of a refrigerator is at $0°\mathrm{C}$ and room temperature is $27.3°\mathrm{C}$. Work done by the refrigerator to freeze $1 \mathrm{g}$ of water at $0°\mathrm{C}$ is $\left(L_{\mathrm{ice}}=80 \mathrm{cal} {\mathrm{g}}^{-1}\right)$

Two identical piano wires have a fundamental frequency of 600 cycle per second when kept under the same tension. What fractional increase in the tension of one wires will lead to the occurrence of 6 beats per second when both wires vibrate simultaneously?

'A horizontal uniform glass tube of \(100 \mathrm{~cm}\), length sealed at both ends contains \(10 \mathrm{~cm}\) mercury column in the middle. The temperature and pressure of air on either side of mercury column are respectively \(31^{\circ} \mathrm{C}\) and \(76 \mathrm{~cm}\) of mercury. If the air column at one end is kept at \(0^{\circ} \mathrm{C}\) and the other end at \(273^{\circ} \mathrm{C}\), then the pressure of air which is at \(0^{\circ} \mathrm{C}\) is : (in \(\mathrm{cm}\) of \(\mathrm{Hg}\) )

Two charged particles each of mass \(9.8 \mathrm{~g}\) and charges \(+20 \mu \mathrm{C}\) and \(-20 \mu \mathrm{C}\) are attached to the two ends of a massless and rigid uniform non-conducting rod of length \(50 \mathrm{~cm}\). This arrangement is held in a uniform electric field of \(12.1 \mathrm{NC}^{-1}\), such that the rod makes a very small angle with the field direction. If the rod is set free, the minimum time needed for the rod to become parallel to the direction of the electric field is ................ seconds.

Which of the following is the property of Rydberg constant?

When a body is heated, then maximum rise will be in its

5 moles of Hydrogen \(\left(\gamma=\frac{7}{5}\right)\) initially at S.T.P. are compressed adiabatically so that its temperature becomes \(400^{\circ} \mathrm{C}\). The increase in the internal energy of the gas in kilo-joules is
\[
\left(R=8.30 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)
\]

The percentage of ionization of 1 L of \(x \mathrm{M}\) acetic acid is 4.242 and is called solution "A". The percentage of ionization of 1 L of \(y \mathrm{M}\) acetic acid is 3 and is called solution "B". Solution "A" is mixed with solution "B". What is the concentration of acetic acid in the resultant solution?
\(\left(\mathrm{K}_{\mathrm{a}} \text { of acetic acid }=1.8 \times 10^{-5}\right)\)

Lucas test is used for the determination of

If \(2 \sin x-\cos 2 x=1\), then \(\left(3-2 \sin ^2 x\right)=\)

If \(y=y(x)\) is the solution of \(\frac{d y}{d x}=\frac{x-y \cos x}{1+\sin x}, y\left(\frac{\pi}{2}\right)=\frac{\pi^2}{8}\), then \(y(\pi)=\)

The number of solutions of the system of equations \(2 x+y-z=7, x-3 y+2 z=1\), \(x+4 y-3 z=5\) is

Using the standard electrode potentials given below identify the correct statements from the following.
\[
\begin{aligned}
\mathrm{Fe}^{2+}+2 e^{-} \longrightarrow \mathrm{Fe} ; E^{\circ} & =-0.44 \mathrm{~V} \\
\mathrm{Cu}^{2+}+2 e^{-} \longrightarrow \mathrm{Cu} ; E^{\circ} & =+0.34 \mathrm{~V} \\
\mathrm{Ag}^{+}+e^{-} \longrightarrow \mathrm{Ag} ; E^{\circ} & =+0.80 \mathrm{~V}
\end{aligned}
\]
(i) Copper can displace iron from \(\mathrm{FeSO}_4\) solution.
(ii) Iron can displace copper from \(\mathrm{CuSO}_4\) solution.
(iii) Silver can displace copper from \(\mathrm{CuSO}_4\) solution.
(iv) Iron can displace silver from \(\mathrm{AgNO}_3\) solution.