



The given compound is \( \text{HOCH(CN)}_2 \). This indicates a carbon atom bonded to a hydroxyl group (\(-\text{OH}\)) and two cyano groups (\(-\text{CN}\)).
The correct bond-line formula for this structure is represented by option (4).
Explanation: The central carbon atom is bonded to one hydroxyl group (\(-\text{OH}\)) and two cyano groups (\(-\text{CN}\)). This structure matches the representation of option (4), showing two cyano groups attached to the central carbon atom along with the hydroxyl group.
Match List-I with List-II: List-I
The correct increasing order of stability of the complexes based on \( \Delta \) value is:
| List I (Molecule) | List II (Number and types of bond/s between two carbon atoms) | ||
| A. | ethane | I. | one σ-bond and two π-bonds |
| B. | ethene | II. | two π-bonds |
| C. | carbon molecule, C2 | III. | one σ-bonds |
| D. | ethyne | IV. | one σ-bond and one π-bond |


Two cells of emf 1V and 2V and internal resistance 2 \( \Omega \) and 1 \( \Omega \), respectively, are connected in series with an external resistance of 6 \( \Omega \). The total current in the circuit is \( I_1 \). Now the same two cells in parallel configuration are connected to the same external resistance. In this case, the total current drawn is \( I_2 \). The value of \( \left( \frac{I_1}{I_2} \right) \) is \( \frac{x}{3} \). The value of x is 1cm.
If $ \theta \in [-2\pi,\ 2\pi] $, then the number of solutions of $$ 2\sqrt{2} \cos^2\theta + (2 - \sqrt{6}) \cos\theta - \sqrt{3} = 0 $$ is:
The term independent of $ x $ in the expansion of $$ \left( \frac{x + 1}{x^{3/2} + 1 - \sqrt{x}} \cdot \frac{x + 1}{x - \sqrt{x}} \right)^{10} $$ for $ x>1 $ is: