A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length $$\mu $$, 2$$\mu $$, 3$$\mu $$ and 4$$\mu $$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range L0 and 2L0. It is found that in string-1$$\mu $$ at free length L0 and tension T0 the fundamental mode frequency is f0.
List-I gives the above four strings while list-II lists the magnitude of some quantity.
If the tension in each string is T0, the correct match for the highest fundamental frequency in f0 units will be
A
I $$ \to $$ P, II $$ \to $$ Q, III $$ \to $$ T, IV $$ \to $$ S
B
I $$ \to $$ P, II $$ \to $$ R, III $$ \to $$ S, IV $$ \to $$ Q
C
I $$ \to $$ Q, II $$ \to $$ S, III $$ \to $$ R, IV $$ \to $$ P
D
I $$ \to $$ Q, II $$ \to $$ P, III $$ \to $$ R, IV $$ \to $$ T
2
JEE Advanced 2019 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length $$\mu $$, 2$$\mu $$, 3$$\mu $$ and 4$$\mu $$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range L0 and 2L0. It is found that in string-1$$\mu $$ at free length L0 and tension T0 the fundamental mode frequency is f0.
List-I gives the above four strings while list-II lists the magnitude of some quantity.
The length of the strings 1, 2, 3 and 4 are kept fixed at L0, $${{3{L_0}} \over 2}$$, $${{5{L_0}} \over 4}$$ and $${{7{L_0}} \over 4}$$ respectively. Strings 1, 2, 3 and 4 are vibrated at their 1st, 3rd, 5th and 14th harmonies, respectively such that all the strings have same frequency.
The correct match for the tension in the four strings in the units of T0 will be
A
I $$ \to $$ P, II $$ \to $$ R, III $$ \to $$ T, IV $$ \to $$ U
B
I $$ \to $$ P, II $$ \to $$ Q, III $$ \to $$ R, IV $$ \to $$ T
C
I $$ \to $$ P, II $$ \to $$ Q, III $$ \to $$ T, IV $$ \to $$ U
D
I $$ \to $$ T, II $$ \to $$ Q, III $$ \to $$ R, IV $$ \to $$ U
3
JEE Advanced 2019 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by T$$\Delta $$X where T is temperature of the system and $$\Delta $$X is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas, $$X = {3 \over 2}R\,\ln \left( {{T \over {{T_A}}}} \right) + R\,\ln \left( {{V \over {{V_A}}}} \right)$$
Here, R is gas constant, V is volume of gas, TA and VA are constants.
The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.
If the process on one mole of monatomic ideal gas is as shown in the TV-diagram with $${P_0}{V_0} = {1 \over 3}R{T_0}$$, the correct match is,
A
I $$ \to $$ P, II $$ \to $$ R, III $$ \to $$ T, IV $$ \to $$ S
B
I $$ \to $$ P, II $$ \to $$ T, III $$ \to $$ Q, IV $$ \to $$ T
C
I $$ \to $$ S, II $$ \to $$ T, III $$ \to $$ Q, IV $$ \to $$ U
D
I $$ \to $$ P, II $$ \to $$ R, III $$ \to $$ T, IV $$ \to $$ P
4
JEE Advanced 2019 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by T$$\Delta $$X where T is temperature of the system and $$\Delta $$X is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas, $$X = {3 \over 2}R\,\ln \left( {{T \over {{T_A}}}} \right) + R\,\ln \left( {{V \over {{V_A}}}} \right)$$
Here, R is gas constant, V is volume of gas, TA and VA are constants.
The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.
If the process carried out on one mole of monoatomic ideal gas is as shown in the PV-diagram with $${p_0}{V_0} = {1 \over 3}R{T_0}$$, the correct match is,
A
I$$ \to $$S, II $$ \to $$ R, III $$ \to $$ Q, IV $$ \to $$ T
B
I $$ \to $$ Q, II $$ \to $$ R, III $$ \to $$ P, IV $$ \to $$ U
C
I $$ \to $$ Q, II $$ \to $$ S, III $$ \to $$ R, IV $$ \to $$ U
D
I $$ \to $$ Q, II $$ \to $$ R, III $$ \to $$ S, IV $$ \to $$ U
