Statement I: In the lac operon, the z gene does indeed code for β-galactosidase, the enzyme that hydrolyzes lactose into galactose and glucose. This statement is true.
Statement II: The lac operon is induced by the presence of lactose (or allolactose, a lactose isomer). The presence of glucose actually represses the lac operon, even if lactose is present. This phenomenon is called catabolite repression. Galactose doesn’t directly induce the lac operon; it’s the presence of lactose that matters. Therefore, statement II is false.
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Match the LIST-I with LIST-II. \[ \begin{array}{|l|l|} \hline \textbf{LIST I} & \textbf{LIST II} \\ \hline A. \ \text{Franklin Stahl} & I. \ \beta\text{-form of DNA} \\ B. \ \text{Maurice Wilkins} & II. \ \text{Estimated absolute amount of each Base} \\ C. \ \text{Erwin Chargaff} & III. \ \text{Proposed two polynucleotide chain} \\ D. \ \text{Watson and Crick} & IV. \ \text{Individual strands of Duplexes are entirely heavy or light} \\ \hline \end{array} \]
Consider a water tank shown in the figure. It has one wall at \(x = L\) and can be taken to be very wide in the z direction. When filled with a liquid of surface tension \(S\) and density \( \rho \), the liquid surface makes angle \( \theta_0 \) (\( \theta_0 < < 1 \)) with the x-axis at \(x = L\). If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is: (take \(g\) as the acceleration due to gravity) 
AB is a part of an electrical circuit (see figure). The potential difference \(V_A - V_B\), at the instant when current \(i = 2\) A and is increasing at a rate of 1 amp/second is:
Among the following, choose the ones with an equal number of atoms.
Choose the correct answer from the options given below:
In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency ω(t) and average amplitude A(t) of the system change with time t. Which one of the following options schematically depicts these changes correctly? 