IISER Aptitude Test (IAT) - Advanced Practice PDF

IISER Aptitude Test (IAT) - Advanced Practice Questions ======================================================= Total Questions: 60 (Physics - 15, Chemistry - 15, Mathematics - 15, Biology - 15) Difficulty Distribution: 100% Hard Level Instructions ------------ Total Time: 180 minutes Each ques...

IISER Aptitude Test (IAT) - Advanced Practice Questions ======================================================= Total Questions: 60 (Physics - 15, Chemistry - 15, Mathematics - 15, Biology - 15) Difficulty Distribution: 100% Hard Level Instructions ------------ Total Time: 180 minutes Each question carries 4 marks. Negative marking: 1 mark deducted for each incorrect answer. Choose the correct option from the four given choices. No electronic devices allowed. Physics ------- 1. 1\. A satellite orbits a planet in an elliptical path. If its speed at perigee is 8 km/s and the orbit has an eccentricity of 0.5, what is its approximate speed at apogee? - 4.0 km/s - 3.2 km/s - 6.4 km/s - 5.0 km/s 2. 2\. A 2 kg particle moving at 10 m/s in a horizontal circle of radius 3 m is released. What is its centripetal acceleration at the moment of release? - 33.3 m/s² - 111.1 m/s² - 50 m/s² - 100 m/s² 3. 3\. An electron is accelerated through a potential difference of 150 V. What is its approximate de Broglie wavelength? - 0.33 nm - 0.25 nm - 0.50 nm - 0.10 nm 4. 4\. In a double-slit experiment, if the slit separation is halved while keeping the wavelength and screen distance constant, the fringe spacing will: - Double - Quadruple - Halve - Remain unchanged 5. 5\. A resistor of 10 Ω is connected across a 20 V battery. What is the power dissipated by the resistor? - 40 W - 20 W - 200 W - 400 W 6. 6\. In an LC circuit, if the inductance is doubled and the capacitance is halved, the resonant frequency will: - Remain unchanged - Increase by a factor of 2 - Increase by √2 - Decrease by a factor of 2 7. 7\. A metal rod moving with constant velocity in a uniform magnetic field experiences an induced emf. If the velocity is doubled, the induced emf will: - Halve - Quadruple - Remain the same - Double 8. 8\. Two parallel plates are separated by 5 cm and have a potential difference of 100 V. What is the electric field between them? - 1000 V/m - 200 V/m - 500 V/m - 2000 V/m 9. 9\. In a diffraction grating experiment, if the grating spacing is halved, how does the angular position of the first-order maximum change (assuming small angles)? - It quadruples - It approximately doubles - It halves - It remains the same 10. 10\. A projectile is launched at 45° with an initial speed of 20 m/s. What is its maximum height? - 15.3 m - 5.1 m - 20.4 m - 10.2 m 11. 11\. In a perfectly elastic collision between two identical masses where one is initially at rest, what is the speed of the formerly stationary mass after the collision if the moving mass had speed v? - 2v - v/2 - 0 - v 12. 12\. In a nuclear reaction, a 0.1% mass defect occurs in a 1 kg mass. Using c = 3×10\^8 m/s, what is the energy released? - 9×10\^15 J - 9×10\^13 J - 9×10\^14 J - 9×10\^16 J 13. 13\. A converging lens of focal length 15 cm forms a real image of an object placed 30 cm away. What is the image distance? - 15 cm - 10 cm - 20 cm - 30 cm 14. 14\. For an isothermal expansion of an ideal gas, the work done is given by: - nCΔT - ½ nRT - nRΔT ln(V\_f/ V\_i) - nRT ln(V\_f/ V\_i) 15. 15\. If two waves of equal amplitude and frequency are 180° out of phase, what is their resulting amplitude? - Double the individual amplitude - √2 times the individual amplitude - Same as the individual amplitude - Zero Chemistry --------- 16. 1\. For the reaction with rate law r = k\[A\]²\[B\], how does the rate change if \[A\] is tripled and \[B\] is halved? - Decreases by 3/2 - Increases by 9/2 - Increases by 9 - Increases by 3 17. 2\. Which of the following compounds exhibits significant resonance stabilization? - Cyclopentane - Benzene - Naphthalene - Cyclohexane 18. 3\. What is the oxidation state of chromium in potassium dichromate (K₂Cr₂O₇)? - +6 - +3 - 0 - +2 19. 4\. Which of the following substances exhibits the strongest intermolecular forces? - Methane - Carbon dioxide - Fluorine - Water 20. 5\. Predict the major product when 1‑bromobutane reacts with excess KOH in an alcoholic solution. - 1‑Butanol - But‑2‑ene - But‑1‑ene - 2‑Butanol 21. 6\. In molecular orbital theory, which orbital in O₂ is responsible for its paramagnetism? - π\*2p - π2p - σ2p - σ\*2s 22. 7\. For an SN1 reaction, which factor predominantly determines the reaction rate? - Nucleophile strength - Solvent polarity - Leaving group ability - Carbocation stability 23. 8\. Order the acidity of the following compounds: acetic acid, phenol, water, and ethanol. - Acetic acid \> Water \> Phenol \> Ethanol - Water \> Acetic acid \> Phenol \> Ethanol - Phenol \> Acetic acid \> Water \> Ethanol - Acetic acid \> Phenol \> Water \> Ethanol 24. 9\. A catalyst increases the rate of a reaction primarily by: - Changing the reaction mechanism - Increasing the equilibrium constant - Increasing the temperature - Lowering the activation energy 25. 10\. During titration of a weak acid with a strong base, the pH at the equivalence point is typically: - Equal to 7 - Greater than 7 - Highly variable - Less than 7 26. 11\. Cis--trans isomerism is a type of: - Optical isomerism - Positional isomerism - Geometrical isomerism - Chain isomerism 27. 12\. In a polar aprotic solvent, the nucleophilicity order of the halide ions is: - I⁻ \> Br⁻ \> Cl⁻ \> F⁻ - Br⁻ \> I⁻ \> Cl⁻ \> F⁻ - F⁻ \> Cl⁻ \> Br⁻ \> I⁻ - Cl⁻ \> F⁻ \> I⁻ \> Br⁻ 28. 13\. For an endothermic reaction, increasing the temperature will: - Reverse the reaction - Decrease the equilibrium constant - Have no effect - Increase the equilibrium constant 29. 14\. What is the hybridization of the central atom in SF₆? - sp³d - sp³ - sp³d² - d²sp³ 30. 15\. Which reagent is best for oxidizing a primary alcohol to an aldehyde without further oxidation to a carboxylic acid? - H₂O₂ - CrO₃ - KMnO₄ - PCC Biology ------- 31. 1\. Which feature of mitochondria supports the endosymbiotic theory? - Double membrane structure - Presence of circular DNA - Bacterial-like ribosomes - All of the above 32. 2\. During protein synthesis, which step is directly energy-dependent? - Protein folding - tRNA charging - mRNA transcription - Peptide bond formation 33. 3\. What is the primary role of telomerase in eukaryotic cells? - Initiating replication - DNA repair - mRNA degradation - Extending telomeres 34. 4\. Which process during meiosis is chiefly responsible for genetic diversity? - Crossing over - Mitosis - Cytokinesis - Binary fission 35. 5\. What is the main function of lysosomes in the cell? - Storing genetic information - ATP production - Protein synthesis - Digesting macromolecules 36. 6\. Which type of RNA is a key component of ribozymes? - mRNA - tRNA - snRNA - rRNA 37. 7\. Which statement about gene regulation in prokaryotes is correct? - Operons allow coordinated gene expression - Only eukaryotes have operons - Genes are regulated independently - Prokaryotes use introns for regulation 38. 8\. What is the significance of the lac operon in E. coli? - It controls protein synthesis - It directs flagellar motion - It regulates lactose metabolism - It manages cell division 39. 9\. How can mutations in the DNA sequence affect proteins? - They may be silent, missense, or nonsense - They invariably enhance protein function - They always produce nonfunctional proteins - They are instantly repaired 40. 10\. Which method is a form of horizontal gene transfer in bacteria? - Binary fission - Mitosis - Conjugation - Meiosis 41. 11\. In evolution, what does \'genetic drift\' refer to? - Mutation - Natural selection - Random changes in allele frequencies - Gene flow 42. 12\. What is the primary role of microRNAs in cells? - Protein folding - Transcription initiation - DNA replication - Post-transcriptional regulation 43. 13\. Which process is responsible for the formation of gametes in animals? - Binary fission - Meiosis - Mitosis - Budding 44. 14\. The endoplasmic reticulum is chiefly involved in: - DNA replication - Protein folding and modification - Detoxification - Lipid storage 45. 15\. Which hormone is primarily responsible for increasing the basal metabolic rate in humans? - Thyroxine - Insulin - Cortisol - Glucagon Mathematics ----------- 46. 1\. Evaluate the limit: limₓ→0 (sin(3x)/x). - Undefined - 3 - 1/3 - 0 47. 2\. Evaluate the integral: ∫₀¹ x eˣ dx. - e - 2 - e - 1 - 2 48. 3\. If the determinant of a 2×2 matrix A is 5, what is the determinant of 2A? - 10 - 5 - 20 - 40 49. 4\. Solve for x: e\^(2x) - 5eˣ + 6 = 0. - x = ln 2 or x = ln 3 - x = ln 2 only - x = 0 and ln2 - x = ln3 only 50. 5\. Find the derivative of f(x) = ln(x² + 1). - 1/(x²+1) - 2/(x²+1) - 2x/(x²+1) - x/(x²+1) 51. 6\. Determine the convergence of the series ∑ (1/n²) from n = 1 to ∞. - Conditionally convergent - Oscillatory - Divergent - Convergent 52. 7\. What is the sum of the infinite geometric series: 4 + 2 + 1 +... ? - 4 - 7 - Infinite - 8 53. 8\. Solve for x: log₂(x) + log₂(x - 2) = 3. - x = 5 - x = 4 - x = 6 - x = 3 54. 9\. If f(x) = x³ - 3x, for what values of x does f\'(x) = 0? - x = -1 and 1 - x = -√3, 0, √3 - x = -1, 0, and 1 - x = 0 55. 10\. Find the sum of the first 20 terms of an arithmetic series with first term 5 and common difference 3. - 630 - 620 - 670 - 625 56. 11\. Determine the radius of convergence for the power series ∑ n! xⁿ. - 0 - Converges for all x - ∞ - 1 57. 12\. Solve the differential equation dy/dx = 3y with the initial condition y(0) = 2. - y = 2e\^(x/3) - y = 2e\^(x+3) - y = 2e\^(3x) - y = 2e\^(x) 58. 13\. Find the eigenvalues of the matrix \[\[2, 1\], \[1, 2\]\]. - 3 and 1 - 0 and 4 - 2 and 2 - 1 and 1 59. 14\. If f(x) = x² sin(1/x) for x ≠ 0 (and f(0) = 0), is f differentiable at x = 0? - Yes - Only if extended continuously - No - Insufficient information 60. 15\. Evaluate the limit: limₓ→∞ ((2x²+3)/(x²-5)). - 2 - ∞ - 3 - 0 End of the Test Paper