🧬 Q.1 Founder effect · genetic drift biology
What is Founder effect? — A small group breaks away from a big population, carrying only a fraction of the genetic diversity. Allele frequencies in the new colony are randomly different from the original. That random change is the signature of genetic drift.
Founder effect is a special case of genetic drift (like bottleneck effect). It’s not about adaptation, survival, or new mutations — just sampling error when a few individuals start a new population.
🚫 Why other options are incorrect:
- ❌ Natural selection → non‑random, based on fitness. Founder effect is random.
- ❌ Genetic recombination → reshuffles alleles (meiosis), but doesn’t change overall frequencies by random sampling.
- ❌ Mutations → create new alleles, not just change frequencies of existing ones.
✅ Correct option: 1. Genetic drift
📐 Q.2 Derivative of x·logₑ(x) calculus
First, recognise: 〖log〗_e (x) = ln x. So we differentiate x·ln x.
= 1 · ln x + x · (1/x)
= ln x + 1 → 1 + ln x
🔍 Step‑by‑step:
- Product rule (u·v)' = u'v + uv'
- u = x → u' = 1
- v = ln x → v' = 1/x
- = 1·ln x + x·(1/x) = ln x + 1
🧠 Common pitfalls — why others are wrong:
- Option 1 (1) → forgot the ln x part, treated as derivative of x only.
- Option 2 (e^x) → confused ln x with e^x. d(ln x)/dx = 1/x, not e^x.
- Option 3 (0) → treating x ln x as constant — impossible, function changes with x.
➕ Extra insight: setting derivative = 0 gives ln x = –1 → x = e⁻¹, important in optimisation.
🎯 memory anchors
Founder effect → “few colonists by chance” → genetic drift (random). Not selection, not mutation.
x ln x derivative → product rule always: (1)(ln x) + x(1/x) = ln x + 1. No shortcuts!
📌 Exams test if you mix up random vs directed evolution, and product rule vs simple log derivative.
⚡ Q.3 ATP-dependent transporter cell biology
🧠 Core concept – active vs passive
🔹 Passive transport = no ATP, down gradient (like sliding).
🔹 Active transport = needs energy, against gradient. But only primary active uses ATP directly.
e.g. Na⁺/K⁺‑ATPase, Ca²⁺ pump.
Without ATP → pump stops.
❌ Why others are wrong:
- Symporters (2) – secondary active transport; use ion gradient (e.g. Na⁺‑glucose). They don’t bind ATP.
- Antiporters (3) – also secondary active; move opposite directions using gradient energy. No ATP hydrolysis.
- Ion channels (4) – passive (facilitated diffusion). Ions move through pores according to electrochemical gradient. Like doors – they open, but don't push.
| Protein class | ATP used directly? | transport type |
|---|---|---|
| Pumps | ✅ YES | primary active |
| Symporters | ❌ no | secondary active |
| Antiporters | ❌ no | secondary active |
| Ion channels | ❌ no | passive |
📨 Q.4 Second messenger? signaling
📡 What is a second messenger? — intracellular small molecule/ion produced after receptor activation, relays & amplifies signal.
First messenger (hormone) → receptor → second messenger (cAMP, Ca²⁺, DAG, IP₃ …) → cellular response.
🔍 per option:
- 1. Calcium ion — YES, released from ER, binds calmodulin, triggers contraction/secretion.
- 2. Cyclic AMP — YES, prototypical second messenger (from ATP via adenylyl cyclase), activates PKA.
- 4. Diacyl glycerol (DAG) — YES, from PIP₂ breakdown, activates PKC, stays in membrane.
- 3. Potassium ion (K⁺) — ❌ NOT a second messenger. Maintains resting potential, involved in electrical signalling but not produced as a signal amplifier inside the cell.
- Thinking “all ions = second messengers” — but only Ca²⁺ is specifically regulated and acts as a messenger.
- Overlooking the word “NOT”; they mark cAMP (which IS a messenger).
- Confusing electrical role (K⁺ in action potentials) with biochemical second messenger role.
| Molecule | Second messenger? | Role |
|---|---|---|
| Ca²⁺ | ✅ yes | activates calmodulin, enzymes |
| cAMP | ✅ yes | PKA activation, gene regulation |
| DAG | ✅ yes | PKC activation |
| K⁺ | ❌ no | membrane potential, repolarisation |
Potassium = office furniture — important, but doesn't relay messages.
📋 exam cheat sheet – membrane & signaling
🔋 ATP users (direct)
- Pumps (Na⁺/K⁺, Ca²⁺ ATPase)
- ATPases / transport ATPases
🚫 No direct ATP
- Symporters, Antiporters
- Ion channels (always passive)
📨 second messengers
- cAMP, cGMP, Ca²⁺, IP₃, DAG, NO
- K⁺ is NOT one
‼️ trap word “NOT” changes everything – circle it in exams.
📐 Q.5 d²y/dx² of 15cos x – 13sin x calculus
🧠 Step 1 – recognise the pattern
Function is a linear combo of sine and cosine. Their second derivatives are the negative of themselves:
d²/dx² (sin x) = –sin x d²/dx² (cos x) = –cos x
y = 15cos x – 13sin x
dy/dx = 15(–sin x) – 13(cos x) = –15sin x – 13cos x
d²y/dx² = –15cos x + 13sin x
Factor –1 : = –(15cos x – 13sin x) = –y
🎯 result: d²y/dx² = –y → option 3 ✅
- π/y – π never appears; no division.
- 2 – constant only if y were quadratic; trig derivatives aren’t constant.
- y²/x – no squares or x‑division emerge from differentiating sin/cos.
🧪 Q.6 non‑essential amino acid biochemistry
🧠 Essential = cannot be synthesised by body → must come from diet.
The 9 essentials: Histidine, Isoleucine, Leucine, Lysine, Methionine, Phenylalanine, Threonine, Tryptophan, Valine.
Notice tyrosine is missing – it’s made from phenylalanine.
| Amino acid | Essential? | Reason |
|---|---|---|
| Threonine | ✅ Yes | cannot be synthesised |
| Valine | ✅ Yes | BCAA, must eat |
| Tryptophan | ✅ Yes | precursor of serotonin |
| Tyrosine | ❌ No | synthesised from phenylalanine |
Tyrosine is formed by hydroxylation of phenylalanine. If you have enough phenylalanine (essential), the body makes tyrosine. That’s why it’s conditionally essential only in disorders like PKU.
- Assuming all aromatic amino acids are essential (tryptophan is, but tyrosine isn’t).
- Memorising list without logic – use mnemonic “PVT TIM HALL” (includes Phe, Val, Thr, Trp, Ile, Met, His, Arg?, Leu, Lys) – tyrosine absent.
- Confusing “important” (tyrosine makes dopamine, hormones) with “essential”. Importance ≠ dietary essentiality.
📋 exam recap
🔢 Q5 second derivative
- y = A cos x + B sin x → y'' = –y
- Always compare with original
🥚 Q6 essential amino acids
- 9 essentials – learn “PVT TIM HALL”
- Tyrosine made from Phe → not essential
- Read carefully: “NOT”
🧫 Q.7 E. coli membrane microbiology
🧠 Step 1 – context: E. coli = prokaryote → membrane ≠ eukaryote
Major phospholipids in E. coli: Phosphatidylethanolamine (PE) (~70–80%), Phosphatidylglycerol, Cardiolipin.
❌ Why others are not abundant in E. coli:
- 2. Phosphatidyl choline (PC) – most abundant in mammalian membranes; bacteria (especially E. coli) have very little PC. Classic eukaryote/prokaryote trap.
- 3. Phosphatidyl serine (PS) – present in small amounts, often intermediate for PE synthesis. Not major.
- 4. Phosphatidyl inositol (PI) – key signaling lipid in eukaryotes (IP₃/DAG pathway); bacteria rarely use PI as a bulk component.
| Lipid | Abundance in E. coli | Typical in eukaryotes? |
|---|---|---|
| Phosphatidylethanolamine | 70–80% (major) | present, but not always dominant |
| Phosphatidylcholine | very low / absent | dominant in mammalian membranes |
| Phosphatidylserine | minor | small amount, signalling |
| Phosphatidylinositol | rare | signalling hub |
🧪 Q.8 Coenzyme A – vitamin source biochemistry
🧠 Core fact: coenzymes are often vitamin derivatives. Coenzyme A (CoA) is derived from pantothenic acid (vitamin B5).
CoA is central to metabolism: acetyl‑CoA formation, fatty acid oxidation, TCA cycle, etc. Its structure includes pantothenic acid + ADP + cysteamine.
B5 (pantothenic acid) → Coenzyme A
B2 (riboflavin) → FAD, FMN
B6 (pyridoxine) → PLP
B9 (folic acid) → THF
❌ Distractor breakdown:
- 1. Riboflavin (B2) – forms FAD/FMN (redox cofactors), not CoA.
- 2. Pyridoxine (B6) – forms PLP (amino acid metabolism), unrelated to CoA.
- 3. Folic acid (B9) – forms tetrahydrofolate (one‑carbon transfer), not CoA.
- 4. Pantothenic acid (B5) – direct precursor of CoA → correct.
| Vitamin | Coenzyme form | Main function |
|---|---|---|
| Riboflavin (B2) | FAD, FMN | redox, ETC |
| Pyridoxine (B6) | PLP | transamination, decarboxylation |
| Folic acid (B9) | THF | one‑carbon transfer, DNA synthesis |
| Pantothenic acid (B5) | Coenzyme A | acyl group transfer, metabolism |
📋 exam nutshell
🦠 E. coli membrane
- ~75% Phosphatidylethanolamine
- PC, PS, PI are minor / eukaryotic
- trap: don’t pick phosphatidylcholine
💊 Coenzyme A vitamin
- Pantothenic acid (B5) → CoA
- B2 → FAD, B6 → PLP, B9 → THF
- straight cofactor mapping
⚛️ Q.9 Electron Gain Enthalpy order periodic trends
🧠 Step 1 – Understand “magnitude of electron gain enthalpy”
Electron gain enthalpy (ΔegH) is usually negative (energy released). “Magnitude” means we compare the absolute value (how much energy is released). More negative → larger magnitude.
Expected order (ignoring fluorine exception): Cl > Br > I > At.
🧪 Why chlorine has the highest magnitude among these four:
- Cl (small size, strong nuclear pull, 3p orbital) → releases most energy upon gaining electron.
- Br (larger than Cl, 4p) → less energy released.
- I (even larger, 5p) → lower magnitude.
- At (very large, radioactive, 6p, high shielding) → least negative, smallest magnitude.
- Br > Cl > At > I (opt 1) – incorrect because Cl has higher magnitude than Br. First comparison itself is wrong.
- I > Br > Cl > At (opt 2) – reverses the group trend (says electron gain enthalpy increases down the group).
- At > Br > Cl > I (opt 4) – Astatine is the largest, least attraction → cannot be highest. Opposite of actual order.
| Element | Atomic size trend | Electron gain enthalpy magnitude |
|---|---|---|
| Cl (Chlorine) | smallest among these | highest (most negative) |
| Br (Bromine) | larger than Cl | ▼ decreases |
| I (Iodine) | even larger | ▼ further down |
| At (Astatine) | largest, high shielding | lowest magnitude |
Chlorine: “Come here! I’ve been waiting!” (strong attraction)
Bromine: “Yeah okay, come if you want.” (weaker)
Iodine: “Hmm… fine.”
Astatine: “Who even are you?” (almost indifferent) 😄
So order: Cl > Br > I > At.
📊 Periodic pulse – halogen electron gain enthalpy
✅ correct order (magnitude)
- Cl > Br > I > At
- Fluorine (not here) would be between Cl and Br due to small size repulsion.
🚫 common mistakes
- Confusing electronegativity with electron gain enthalpy
- Blindly saying “increases up the group” without checking actual values
- Forgetting “magnitude” → mixing up signs
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