Instructions

For the following questions answer them individually

Question 11

A stationary source emits sound of frequency $$f_0 = 492 Hz$$. The sound is reflected by a large car approaching the source with a speed of $$2 ms^{-1}$$. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is $$330 ms^{-1}$$ and the car reflects the sound at the frequency it has received).

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Question 12

$$^{131}I$$ is an isotope of Iodine that $$\beta$$ decays to an isotope of Xenon with a half-life of 8 days. A small amount of a serum labelled with $$^{131}I$$ is injected into the blood of a person. The activity of the amount of $$^{131}I$$ injected was $$2.4 \times 10^5$$ Becquerel (Bq). It is known that the

injected serum will get distributed uniformly in the blood stream in less than half an hour. After 11.5 hours, 2.5 ml of blood is drawn from the personâ€™s body, and gives an activity of 115 Bq. The total volume of blood in the personâ€™s body, in liters is approximately (you may use $$e^x \approx 1 + x$$ for $$\mid x \mid \ll 1$$ and $$\ln 2 \approx 0.7$$).

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Instructions

Answer the Questions by appropriately matching the information given in the three columns of the following table.

A charged particle (electron or proton) is introduced at the origin $$(x = 0, y = 0, z = 0)$$ with a given initial velocity $$\overrightarrow{v}$$. A uniform electric field $$\overrightarrow{E}$$ and a uniform magnetic field $$\overrightarrow{B}$$ exist everywhere. The velocity $$\overrightarrow{v}$$, electric field $$\overrightarrow{E}$$ and magnetic field $$\overrightarrow{B}$$ are given in columns 1, 2 and 3 respectively. The quantities $$E_0, B_0$$ are positive in magnitude.

Question 14

In which case will the particle describe a helical path with axis along the positive z direction?

Question 15

In which case would the particle move in a straight line along the negative direction of y-axis (i.e., move along $$-\hat{y}$$)?

Instructions

Answer the Questions by appropriately matching the information given in the three columns of the following table.

An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P - V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here $$\gamma$$ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n.

Question 16

Which of the following options is the only correct representation of a process in which $$\triangle U = \triangle Q - P \triangle V$$?

Question 18

Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?

Instructions

For the following questions answer them individually

Question 19

An ideal gas is expanded from $$(p_1, V_1, T_1)$$ to $$(p_2, V_2, T_2)$$ under different conditions. The correct statement(s) among the following is(are)

Question 20

For a solution formed by mixing liquids L and M, the vapour pressure of L plotted against the mole fraction of M in solution is shown in the following figure. Here $$x_L$$ and $$x_M$$ represent mole fractions of L and M, respectively, in the solution. The correct statement(s) applicable to this system is(are)