Biology Set-1

Q1. A double-stranded DNA molecule of $1000$ base pairs contains $30\%$ adenine. Assuming Watson–Crick pairing ($A$–$T$ pairs have $2$ hydrogen bonds and $G$–$C$ pairs have $3$ hydrogen bonds), the total number of hydrogen bonds in the molecule is:

Q2. Consider the following double-stranded DNA fragment; only the sense (coding) strand is shown $5'\rightarrow3'$: $5'$-ATGCCATTAGGCTGAACGGATCCGTAATGC-$3'. You plan a PCR to amplify an$18$-nucleotide fragment. Which of the following primer pairs (forward ; reverse — both given$5'\rightarrow3'$) will yield a PCR product of length$18$ nucleotides? (Forward primers are given as matching the sense strand.)

Q3. In E. coli a lac operon mutant carries two mutations: (i) an operator mutation that prevents lac repressor binding (so the repressor cannot block transcription), and (ii) a mutation in the CAP‑binding site that prevents CAP–cAMP activation. Predict the level of expression of lac structural genes under these four environmental states: (1) glucose present, lactose absent; (2) glucose absent, lactose present; (3) glucose absent, lactose absent; (4) glucose present, lactose present.

Q4. Assertion (A): Telomerase is active in most somatic human cells.
Reason (R): DNA polymerases require an RNA primer and synthesize DNA only in the $5'\!\rightarrow\!3'$ direction, producing the end‑replication problem on linear chromosomes.

Q5. A linear DNA molecule of length $3000\ \text{bp}$ gives the following digestion pattern: enzyme $X$ → fragments of $900\ \text{bp}$ and $2100\ \text{bp}$; enzyme $Y$ → fragments of $1200\ \text{bp}$ and $1800\ \text{bp}$; double digest $X+Y$ → fragments of $300\ \text{bp}$, $900\ \text{bp}$ and $1800\ \text{bp}$. Which one of the following linear maps (positions measured from the left end at $0\ \text{bp}$) is consistent with these data?

Q6. A PCR reaction is set up with an initial number of $10$ double-stranded target molecules and is run for $30$ cycles with perfect efficiency (each cycle doubles the number of target molecules). Assuming no loss and perfect doubling each cycle, how many double-stranded target molecules will be present at the end?

Q7. A circular plasmid of length $6000\ \mathrm{bp}$ has a single recognition site for enzyme A and two recognition sites for enzyme B. Digestion results: A alone → one fragment of $6000\ \mathrm{bp}$ (linear), B alone → two fragments of $2000\ \mathrm{bp}$ and $4000\ \mathrm{bp}$, and A+B (double digest) → three fragments of $1000\ \mathrm{bp}$, $2000\ \mathrm{bp}$ and $3000\ \mathrm{bp}$. Which of the following best describes the relative positions of the restriction sites?

Q8. E. coli cells are grown for many generations in medium containing $^{15}\mathrm{N}$ so that all genomic DNA is heavy (HH). They are then shifted to medium containing $^{14}\mathrm{N}$ and allowed to replicate for $4$ generations. Assuming semiconservative replication and no selection, what fraction of the DNA molecules extracted after the fourth generation will be hybrid (one heavy strand + one light strand)?

Q9. Assertion (A): In a merodiploid bacterium where the chromosomal lac operon carries an operator-constitutive mutation ($\mathrm{lac}^{\mathrm{Oc}}$) and a second copy on a plasmid supplies a wild-type repressor gene ($\mathrm{lac}I^{+}$), the chromosomal lac structural genes will be expressed constitutively even in the absence of lactose.
Reason (R): Operator sequences act in cis, so a functional repressor supplied in trans from a different DNA molecule cannot bind and repress expression at a mutated operator on the chromosome.

Q10. During DNA replication in E. coli a G:T mismatch occurs such that the parental (original) strand contains G and the newly synthesized strand contains T. In wild-type cells Dam methylase methylates adenine in GATC and the mismatch repair (MMR) system uses this methylation to identify and remove the newly synthesized strand; in a Dam-deficient mutant there is no methylation and MMR cannot distinguish strands and instead excises one strand at random. Under these assumptions, what is the probability that after MMR the original (parental) base G is retained at that locus in the Dam-deficient strain?

Q11. A double-stranded DNA fragment contains 300 base pairs and has GC content of 40%. Using the relation $H = 3N_{GC} + 2N_{AT}$, where $N_{GC}$ and $N_{AT}$ are numbers of GC and AT base pairs respectively, what is the total number of hydrogen bonds in the fragment?

Q12. Consider a eukaryotic diploid cell whose haploid genome size is $3\times10^{9}$ bp. DNA polymerase incorporates wrong nucleotides at a rate $r_0=10^{-6}$ per base. Proofreading reduces this error rate by 100-fold and mismatch-repair reduces the remaining errors by another 100-fold. Using $N = G\times r$ (where $G$ is the diploid genome size and $r$ is the final error rate), estimate the expected number of replication errors per cell division across the entire diploid genome.

Q13. In a bacterium mRNA is synthesized at rate $S=20$ molecules min$^{-1}$ and degrades with first-order kinetics having half-life $t_{1/2}=2$ min. Using $k=\dfrac{\ln 2}{t_{1/2}}$ and steady state $M_{ss}=\dfrac{S}{k}$, calculate (i) the steady-state number of mRNA molecules, and (ii) if a mutation increases the half-life to $4$ min, the new steady-state number and the fold-change relative to the original. Choose the option that correctly states (original $M_{ss}$; new $M_{ss}$; fold-change).

Q14. Assertion (A): In a Meselson–Stahl type experiment starting from a single $HH$ (heavy–heavy) DNA molecule, the absolute number of hybrid ($HL$) DNA molecules remains constant in all generations after the first replication in light medium.
Reason (R): Each original heavy strand continues to serve as a template in every subsequent replication and therefore produces exactly one $HL$ molecule per original heavy strand in each generation.

Q15. A linear eukaryotic chromosome has length $L=96\times10^{6}$ bp. Replication forks move at speed $v=2\ \text{kb min}^{-1}$. Assume all origins fire synchronously at the start of S-phase, each origin gives bidirectional replication, and no additional origins fire later. To finish replication within S-phase duration $T=120$ min, the minimum number of origins required is given by $N_{\min}=\dfrac{L}{2vT}$. What is $N_{\min}$ (nearest integer)?