IISER Aptitude Test Practice Set 1

Explanation: Mitochondria produce ATP through oxidative phosphorylation, providing the cell with its primary source of energy, hence the name 'powerhouse of the cell.'

Explanation: Leucine has an isobutyl group as its side chain, which is hydrophobic and non-polar. Serine has a hydroxyl group (polar), lysine has an amino group (positively charged), and glutamic acid has a carboxyl group (negatively charged).

Explanation: Crossing over (recombination) occurs during Prophase I of meiosis, specifically at the pachytene stage, when homologous chromosomes form bivalents and exchange segments of chromatids at chiasmata.

Explanation: In a monohybrid cross (Aa × Aa), the F₂ generation shows a 3:1 phenotypic ratio (3 dominant : 1 recessive), while the genotypic ratio is 1:2:1 (AA : Aa : aa).

Explanation: Experiments using isotopic tracers (H₂¹⁸O) by Ruben and Kamen showed that the oxygen released during photosynthesis comes entirely from the photolysis of water molecules in the light reactions.

Explanation: Starfish belong to phylum Echinodermata, characterized by a water vascular system, pentaradial symmetry in adults, and an endoskeleton of calcareous ossicles with spines.

Explanation: Hydrochloric acid (HCl) secreted by parietal cells of the stomach provides the acidic pH needed to convert inactive pepsinogen into active pepsin by removing a short peptide segment.

Explanation: Gause's competitive exclusion principle states that two species competing for identical resources cannot stably coexist — the species with even a slight competitive advantage will eventually dominate and drive the other to local extinction.

Explanation: The d subshell has 5 orbitals (mₗ = −2, −1, 0, +1, +2), and each orbital holds a maximum of 2 electrons. So the maximum occupancy is 5 × 2 = 10 electrons.

Explanation: The Gibbs free energy criterion for spontaneity states ΔG < 0 at constant T and P. A process can be spontaneous even with ΔH > 0 (endothermic) as long as TΔS is large enough to make ΔG negative.

Explanation: By Le Chatelier's principle, increasing pressure favors the side with fewer moles of gas. Reactants have 4 moles (1 + 3) while products have 2 moles, so equilibrium shifts to the right toward NH₃.

Explanation: For a first-order reaction, t₁/₂ = ln 2 / k = 0.693 / 0.0693 = 10 minutes. The half-life of a first-order reaction is independent of the initial concentration.

Explanation: Atomic radius increases down a group due to addition of electron shells. Potassium (K) is in period 4 of group 1, making it larger than Na (period 3), Li (period 2), and Be (group 2, period 2).

Explanation: Benzene's aromatic stabilization energy (~150 kJ/mol) from delocalized π electrons makes substitution reactions (which preserve aromaticity) energetically favored over addition reactions (which would destroy the aromatic ring).

Explanation: In transition metal complexes, the d orbitals split into different energy levels due to the crystal field. Electrons undergo d-d transitions between these split levels, absorbing specific wavelengths of visible light and producing complementary colors.

Explanation: In aqueous solution, the basic strength order is (CH₃)₂NH > CH₃NH₂ > NH₃. Methyl groups increase electron density on nitrogen (inductive effect), enhancing basicity. (CH₃)₃N is less basic than (CH₃)₂NH in water due to steric hindrance to solvation.

Explanation: (g ∘ f)(x) = g(f(x)) = √(x²) = |x|. Since x² ≥ 0 for all real x, the argument of √ is always non-negative. The domain is all of ℝ = (−∞, ∞).

Explanation: For an n×n matrix, det(kA) = kⁿ · det(A). Here n = 3 and k = 2, so det(2A) = 2³ × 5 = 8 × 5 = 40.

Explanation: f(x) = |x − 1| is continuous everywhere (absolute value of a continuous function). However, at x = 1, the left derivative is −1 and the right derivative is +1, so f is not differentiable at x = 1.

Explanation: ∫₀^π sin x dx = [−cos x]₀^π = −cos π − (−cos 0) = −(−1) + 1 = 2.

Explanation: The order is 2 (the highest derivative present is d²y/dx²). The degree of a differential equation is defined only when the equation is polynomial in all derivatives. Since sin(dy/dx) is transcendental, the degree is not defined.

Explanation: Squaring both sides: (sin θ + cos θ)² = 2, giving sin²θ + 2sin θ cos θ + cos²θ = 2. Since sin²θ + cos²θ = 1, we get 1 + 2sin θ cos θ = 2, so sin θ cos θ = 1/2.

Explanation: Favorable outcomes: sum = 10: (4,6),(5,5),(6,4) = 3; sum = 11: (5,6),(6,5) = 2; sum = 12: (6,6) = 1. Total favorable = 6 out of 36. Probability = 6/36 = 1/6.

Explanation: By Newton's second law, F = ma, so a = F/m = 20/10 = 2 m/s².

Explanation: Elastic potential energy = ½kx² = ½ × 200 × (0.1)² = ½ × 200 × 0.01 = 1 J.

Explanation: T = 2π√(L/g). On the Moon, g_Moon = g/6, so T_Moon = 2π√(L/(g/6)) = √6 × T = 2√6 ≈ 4.9 s.

Explanation: At the midpoint, the electric fields due to the two equal positive charges are equal in magnitude but point in opposite directions (each pointing away from its source). They cancel exactly, giving a net field of zero.

Explanation: Self-inductance L = μ₀N²A/l, where N is the number of turns, A is the cross-sectional area, and l is the length. Thus L is proportional to N², the square of the number of turns.

Explanation: Fringe width β = λD/d. With d' = d/2 and D' = 2D: β' = λ(2D)/(d/2) = 4λD/d = 4β. The fringe width becomes four times the original.

Explanation: The binding energy per nucleon curve peaks around mass number A ≈ 56 (iron-56). Nuclei lighter than iron release energy through fusion, while heavier nuclei release energy through fission, both moving toward the iron peak.