A musical instrument is made using four different metal strings 1, 2, 3 and 4 with mass per unit length μ, 2μ, 3μ and 4μ 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 (μ) at free length L₀ and tension T₀ the fundamental mode frequency is f₀. List - I List - II (I) String - 1 (μ) (P) 1 (II) String - 2 (2μ) (Q) 1/2 (III) String - 3 (3μ) (R) 1/√2 (IV) String - 4 (4μ) (S) 1/√3 (T) 3/16 (U) 1/16 Answer the following by appropriately matching the lists based on the information given in the paragraph. If the tension in each string is T₀, the correct match for the highest fundamental frequency in f₀ units will be :<p></p>

A musical instrument is made using four different metal strings 1, 2, 3 and 4 with mass per unit length μ, 2μ, 3μ and 4μ 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 (μ) at free length L₀ and tension T₀ the fundamental mode frequency is f₀. List - I List - II (I) String - 1 (μ) (P) 1 (II) String - 2 (2μ) (Q) 1/2 (III) String - 3 (3μ) (R) 1/√2 (IV) String - 4 (4μ) (S) 1/√3 (T) 3/16 (U) 1/16 Answer the following by appropriately matching the lists based on the information given in the paragraph. If the tension in each string is T₀, the correct match for the highest fundamental frequency in f₀ units will be :

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