The topicity relationship of \(H_a\) and \(H_b\) in X, Y and Z (as drawn in the figure) are, respectively,
Step 1: Molecule X. The two hydrogens \(H_a\) and \(H_b\) lie on a carbon in a highly symmetric (meso/C\(_2\)) environment bearing identical HO− and −CO2H substituent sets on opposite sides. A \(C_2\) rotation superposes \(H_a\) and \(H_b\); replacing either gives the same molecule \(⇒\) homotopic.
Step 2: Molecule Y. In the bridged/aromatic framework, \(H_a\) and \(H_b\) are related by an improper/mirror operation: replacement of \(H_a\) versus \(H_b\) generates non-superposable mirror-image products, while the parent is achiral. Thus they are enantiotopic.
Step 3: Molecule Z. For the prochiral vinyl \({CH_2}\) adjacent to −Cl, the two vinylic hydrogens are in an enantiotopic relationship (replacing one or the other creates enantiomeric \(E/R_e\) vs \(S_i\) labeled products). Hence enantiotopic.
Step 4: Collecting: \(X\) homotopic, \(Y\) enantiotopic, \(Z\) enantiotopic \(⇒\) option (B).
The reaction(s) in which inversion of configuration occur(s) is(are)
The acetolysis product(s) of the given reaction (solvolysis of the benzylic tosylate in AcOH) is(are)
A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are:
The number of patients per shift (X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹1000(X - 0.2), what is the average amount (in ₹) she has earned per shift in the past 100 shifts?
In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?
The Lineweaver-Burk plot for an enzyme obeying the Michaelis-Menten mechanism is given below.
The slope of the line is \(0.36 \times 10^2\) s, and the y-intercept is \(1.20\) mol\(^{-1}\) L s. The value of the Michaelis constant (\(K_M\)) is ________ \( \times 10^{-3} \) mol L\(^{-1}\) (in integer). [Note: \(v\) is the initial rate, and \([S]_0\) is the substrate concentration]
Consider a Carnot engine with a hot source kept at 500 K. From the hot source, 100 J of energy (heat) is withdrawn at 500 K. The cold sink is kept at 300 K. The efficiency of the Carnot engine is ___________ (rounded off to one decimal place).