Figure shows a circuit diagram comprising Boolean logic gates and the corresponding timing diagrams showing digital signals at various points in the circuit. Which of the following is/are true? 
Step 1: Analyze circuit behavior.
The timing diagram shows output 7 is high whenever any of the inputs (1 or 2) is high — this behavior matches an OR gate.
Step 2: Compare with given circuit.
Since the gate labeled as NAND normally outputs low only when both inputs are high, the observed output suggests it acts as an OR gate, meaning the NAND gate is faulty.
Step 3: Verify other possibilities.
- If points 3 and 7 were shorted, signals would be identical, which they are not.
- The NOT gate and AND gate behave as expected per waveforms.
Step 4: Conclusion.
Hence, the NAND gate is faulty and behaves like an OR gate.
Match the LIST-I with LIST-II
| LIST-I (Logic Gates) | LIST-II (Expressions) | ||
|---|---|---|---|
| A. | EX-OR | I. | \( A\bar{B} + \bar{A}B \) |
| B. | NAND | II. | \( A + B \) |
| C. | OR | III. | \( AB \) |
| D. | EX-NOR | IV. | \( \bar{A}\bar{B} + AB \) |
Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I (Counters) | List-II (Delay/Number of States) |
|---|---|
| (A) n-bit ring counter | (I) Number of states is \( 2^n \) |
| (B) MOD-\(2^n\) asynchronous counter | (II) Fastest counter |
| (C) n-bit Johnson counter | (III) Number of used states is \( n \) |
| (D) Synchronous counter | (IV) Number of used states is \( 2n \) |
Choose the correct answer from the options given below:
A MOD 2 and a MOD 5 up-counter when cascaded together results in a MOD ______ counter.

At a particular temperature T, Planck's energy density of black body radiation in terms of frequency is \(\rho_T(\nu) = 8 \times 10^{-18} \text{ J/m}^3 \text{ Hz}^{-1}\) at \(\nu = 3 \times 10^{14}\) Hz. Then Planck's energy density \(\rho_T(\lambda)\) at the corresponding wavelength (\(\lambda\)) has the value \rule{1cm}{0.15mm} \(\times 10^2 \text{ J/m}^4\). (in integer)
[Speed of light \(c = 3 \times 10^8\) m/s]
(Note: The unit for \(\rho_T(\nu)\) in the original problem was given as J/m³, which is dimensionally incorrect for a spectral density. The correct unit J/(m³·Hz) or J·s/m³ is used here for the solution.)