Question

1) A spherical mammalian cell of radius ‘R’ is infected by a single coccus bacterium having 100 times
smaller radius. Given that the host cell will lyse when 1/2 of the cell volume is taken up by the
bacterium, approximately how many times will the bacterium divide before the host cell is lysed?
Options :
1. 19
2. 3X105
3. 106
4. 40

2) Two experiments were conducted with an enzyme following Michaelis Menten kinetics at substrate
concentrations of 0.5 g/l and 1 g/l. If the enzymatic reaction velocity increases approximately 2-fold
at the higher substrate concentration, the Km for the enzyme would be around: (The answer is 1g/L. Please explain why this is the answer with diagram if applicable)
Options :
1. 0.001 g/l
2. 0.01 g/l
3. 0.1 g/l
4. 1 g/l

3) An essential oil has antimicrobial activity with an MIC of 15 mg/Kg and can be used as a biopreservative.
This activity is lost at the rate of 1% of the remaining concentration, per day. The
minimum amount of oil to be added (mg) to 1 Kg of food product that is stored for 30 days is:
Options :
1. 21.43
2. 17.65
3. 20.28
4. 19.50

4) An unbiased coin is tossed 100 times in experiment I and 1000 times in experiment II. Which one of
the following statements is most likely to be TRUE regarding the ratio between heads and tails in
experiment I and II?
options:
1. It will be closer to one in experiment I
2. It will be closer to one in experiment II
3. It will be equal to one in both experiments
4. It will be equally away from one in both experiments

Answer 1

1) The answer will be 19 (Option 1).

Explanation: Mammalian cell's radius = R, Bacterium's radius = R/100 (As radius of bacterium is 100 times smaller than radius of mammalian cell)

So, volume of mammalian cell = $\frac{4}{3}\pi R^{3}$ , volume of bacterium =

4 , R 3 100

Now, host cell will lyse when 1/2 of the cell volume or $\frac{2}{3}\pi {R}^{3}$ is taken up by the bacterium.

So, number of bacterium require = $\frac{2}{3}\pi {R}^{3}$ / = 500,000

4 , R 3 100

Now, N_t = N₀ x 2ⁿ, where N_t = Population at time t, N₀ = Initial population, n = number of generation

We have, N₀ = 1, N_t = 500,000

So, number of generation (n) =
logNt logNo log2
(Derived from equation N_t = N₀ x 2ⁿ) =
log500,000 -logl log2
= 18.93 $\approx$19

So, the bacterium will divide approximately 19 times before the host cell is lysed. Thus the correct answer will be option 1.

4) The answer will be closer to one in experiment II (Option 2).

Explanation: As the coin is unbiased theoretically ratio of heads & tails will be 1:1. Now, experimental result will closer to the theoretical ratio if the number of trials is more. As in experiment I the coin is tossed only 100 times & in experiment II the same coin is tossed 1000 times, the probability that the experimental result will be closer to theoretical result will be higher in experiment II. So, correct answer will be option 2.