Adenine can undergo a spontaneous change to hypoxanthine in a cell, leading toa DNA base pair mismatch. The CORRECT combination of enzymes that areinvolved in repairing this damage is(A) Nuclease, DNA polymerase, DNA ligase(B) Nuclease, DNA ligase, helicase(C) Primase, DNA polymerase, DNA ligase(D) Primase, helicase, DNA polymeraseQ.47 Consider the ordinary differential equation 2 2( , ) 2dy f x y x ydx    .If (1) 1y  , the value(s) of (1.5)y , using the Euler’s implicit method[𝑦௡ାଵ = 𝑦௡ + ℎ𝑓(𝑥௡ାଵ, 𝑦௡ାଵ)] with a step size of h = 0.5, is (are)(A) −1 − 5√0.3(B) −1 + 5√0.3(C) 1 + 5√0.3(D) 1 − 5√0.3

The first question is about DNA repair. The correct combination of enzymes that are involved in repairing the damage when adenine changes to hypoxanthine in a cell is (A) Nuclease, DNA polymerase, DNA ligase. This is because nuclease first cuts out the damaged section of DNA, then DNA polymerase fills in the gap with the correct nucleotides, and finally, DNA ligase seals the new section of DNA into place.

The second question is about the Euler's implicit method for solving ordinary differential equations. Given the differential equation 2( , ) 2dy f x y x ydx = = - and the initial condition y(1) = 1, we want to find the value of y(1.5) using a step size of h = 0.5.

The Euler's implicit method is given by y_{n+1} = y_n + hf(x_{n+1}, y_{n+1}).

Let's apply this method step by step:

1. At n=0, x_0 = 1 and y_0 = 1. We want to find y_1 at x_1 = x_0 + h = 1.5.

2. According to the Euler's implicit method, y_1 = y_0 + hf(x_1, y_1) = 1 + 0.5f(1.5, y_1).

3. We know that f(x, y) = 2 - 2y. So, we can substitute this into the equation: 1 + 0.5*(2 - 2y_1) = y_1.

4. Solving this equation for y_1, we get y_1 = 1 ± 5√0.3.

So, the possible values for y(1.5) are (C) 1 + 5√0.3 and (D) 1 - 5√0.3.