| List I | Species | List II | Geometry/ Shape |
| A | H3 O+ | I | Tetrahedral |
| B | Acetylide anion | II | Linera |
| C | NH4 + | III | Pyramidal |
| D | ClO2– | IV | Bent |
What is the empirical formula of a compound containing 40% sulfur and 60% oxygen by mass?
Match the LIST-I with LIST-II.
Choose the correct answer from the options given below :
Which of the following molecules(s) show/s paramagnetic behavior?
$\mathrm{O}_{2}$
$\mathrm{N}_{2}$
$\mathrm{F}_{2}$
$\mathrm{S}_{2}$
Given below are two statements:
Statement I : The N-N single bond is weaker and longer than that of P-P single bond
Statement II : Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions.
In the light of above statements, choose the correct answer from the options given below


For the circuit shown above, the equivalent gate 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: