Correct Answer: \(O_2: 1\sigma, 1\pi; \text{C}_2: 0\sigma, 2\pi\)
Explanation:
To determine the bonding in diatomic molecules like \(O_2\) and \(C_2\), we use Molecular Orbital Theory (MOT).
• O2 molecule:
- Total bond order: 2 (based on MO diagram)
- Bonding: 1 σ bond (from \(2s\) or \(2p_z\)) and 1 π bond (from \(2p_x\) & \(2p_y\))
⇒ So, bonding in \(O_2\): 1σ and 1π
• C2 molecule:
- Total bond order: 2
- Due to the electron configuration, the two bonds in C2 are both π bonds.
- There is no net σ bond from 2p orbitals.
⇒ So, bonding in \(C_2\): 0σ and 2π
Therefore, the correct bonding is:
\(O_2: 1σ, 1π; \text{C}_2: 0σ, 2π\)
From the given following (A to D) cyclic structures, those which will not react with Tollen's reagent are : 
Compound 'P' undergoes the following sequence of reactions : (i) NH₃ (ii) $\Delta$ $\rightarrow$ Q (i) KOH, Br₂ (ii) CHCl₃, KOH (alc), $\Delta$ $\rightarrow$ NC-CH₃. 'P' is : 

Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 
Choose the correct answer from the options given below:
For x < 0:
f(x) = ex + ax
For x ≥ 0:
f(x) = b(x - 1)2