(Considering that all isomers satisfy the given conditions) Since given compound produces pink colour with neutral FeCl3. So, it must have at least one –OH group attached to benzene ring.
Also, given compound is optically active, it means it should have a chiral centre, which is only possible when it has –CH(OH)CH3.
DBE (Double bond equivalent) of C8H10O2 is
= \(\text{Number of carbon atoms} - \left(\frac{\text{Number of monovalent atoms}}{2}\right) + 1\)
= \(8 - \frac{10}{2} + 1 = 4\)
So, total isomeric structures = 6
Find the least horizontal force \( P \) to start motion of any part of the system of three blocks resting upon one another as shown in the figure. The weights of blocks are \( A = 300 \, {N}, B = 100 \, {N}, C = 200 \, {N} \). The coefficient of friction between \( A \) and \( C \) is 0.3, between \( B \) and \( C \) is 0.2 and between \( C \) and the ground is 0.1.
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.