• $NH_{4}NO_{2} \xrightarrow{\Delta} N_{2} + 2H_{2}O$
• $Ba(N_{3})_{2} \xrightarrow{\Delta} Ba + 3N_{2}$
• $(NH_{4})_{2}Cr_{2}O_{7} \xrightarrow{\Delta} N_{2} + Cr_{2}O_{3} + 4H_{2}O$
• $(NH_{4})_{2}SO_{4}$ decomposes to release $NH_{3}$ (Ammonia) gas, not $N_{2}$.

To solve this, you have to break it down into the same "Select then Arrange" flow:

1. Selection ($C$): * We need 3 Physics books. Since P1 is mandatory, we only need to choose 2 more from the remaining 4. Calculation: $\binom{4}{2} = 6$.

   • We need 2 Math books from 4. Calculation: $\binom{4}{2} = 6$.

   • Total selection combinations: $6 \times 6 = 36$.

2. Arrangement ($P$): * We have 5 books (3 Physics, 2 Math).

   • The "Gap Method" is best for the constraint "Math books not together."

   • First, arrange the 3 Physics books: $3! = 6$ ways.

   • This creates 4 possible gaps ( _ P _ P _ P _ ).

   • We must place the 2 Math books into these 4 gaps: $^4P_2 = 12$ ways.

   • Total arrangements per selection: $6 \times 12 = 72$.

3. Final Calculation:

   • $36 \text{ (selections)} \times 72 \text{ (arrangements)} = 2592$.

Correct Answer: D (1200 or more)

Disproportionation occurs when an element in an intermediate oxidation state simultaneously undergoes oxidation and reduction.

• $\text{BrO}^-$ (Br = +1): can disproportionate to Br$^-$ ($-1$) and BrO$_3^-$ ($+5$) ✓
• $\text{BrO}_2^-$ (Br = +3): can disproportionate to $\text{BrO}^-$ and $\text{BrO}_3^-$ ✓
• $\text{BrO}_3^-$ (Br = +5): can disproportionate under certain conditions ✓
• $\text{BrO}_4^-$ (Br = +7): Br is in its highest oxidation state for bromine — it cannot be further oxidised, so disproportionation is not possible.

$\text{BrO}_4^-$ does not undergo disproportionation.

The sentence sets up a contrast: the reputation was harmed during the ordeal, but came out fine after it. Shaken...unscathed perfectly fits — 'shaken' means temporarily disturbed, and 'unscathed' means without lasting damage. 'Destroyed...intact' is contradictory. 'Damaged...impaired' gives no contrast. 'Tarnished...sullied' are both negative with no recovery implied.