
To determine how many compounds exhibit inductive, mesomeric, and hyperconjugation effects, we must analyze each compound:
Based on this analysis, the compounds that show all three effects are: C6H5CH2CH=CH2, C6H5CH=CHC6H5, C6H5CH(CH3)COCH3. There are 3 such compounds, which does not fit the specified range (4, 4). Thus, there may have been an error in the expected range.
Step 1: Analyze each compound - Compound 1 (−OCH3 group attached): The −OCH3 group exhibits both inductive (−I) and mesomeric (+M) effects. However, hyperconjugation is not applicable here. Not included.
Step 2: Final Count From the analysis, only 4 compounds exhibit all three effects: inductive, mesomeric, and hyperconjugation.
Final Answer: 4.
In a resonance tube closed at one end. Resonance is obtained at lengths \( l_1 = 120 \, \text{cm} \) and \( l_2 = 200 \, \text{cm} \). If \( v_s = 340 \, \text{m/s} \), find the frequency of sound.
For \( \alpha, \beta, \gamma \in \mathbb{R} \), if \[ \lim_{x \to 0} \frac{x^2 \sin(\alpha x) + (\gamma - 1)e^{x^2}}{\sin(2x - \beta x)} = 3, \] then \( \beta + \gamma - \alpha \) is equal to:

In the first configuration (1) as shown in the figure, four identical charges \( q_0 \) are kept at the corners A, B, C and D of square of side length \( a \). In the second configuration (2), the same charges are shifted to mid points C, E, H, and F of the square. If \( K = \frac{1}{4\pi \epsilon_0} \), the difference between the potential energies of configuration (2) and (1) is given by: