Amino acids are soluble in polar solvents due to their zwitterionic nature.
• Arginine is a polar amino acid and exists as a zwitterion in aqueous solutions.
• It is not soluble in nonpolar solvents like benzene.
• It has multiple pKa values, high melting point, and exists as a crystalline solid
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 |

Let $ a_1, a_2, a_3, \ldots $ be in an A.P. such that $$ \sum_{k=1}^{12} 2a_{2k - 1} = \frac{72}{5}, \quad \text{and} \quad \sum_{k=1}^{n} a_k = 0, $$ then $ n $ is:
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:
Let \( A = \begin{bmatrix} \alpha & -1 \\ 6 & \beta \end{bmatrix} , \ \alpha > 0 \), such that \( \det(A) = 0 \) and \( \alpha + \beta = 1. \) If \( I \) denotes the \( 2 \times 2 \) identity matrix, then the matrix \( (I + A)^8 \) is:
Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is: