CUET UG Science Practice Set 1

Explanation: Mitochondria are called the powerhouse of the cell because they produce ATP through oxidative phosphorylation during cellular respiration.

Explanation: Helicase is the enzyme that unwinds the DNA double helix by breaking the hydrogen bonds between complementary base pairs, creating the replication fork.

Explanation: Ovulation is the process by which a mature oocyte is released from the Graafian follicle of the ovary, typically around day 14 of the menstrual cycle, triggered by a surge in luteinising hormone (LH).

Explanation: In C4 plants, CO2 is first fixed in mesophyll cells by PEP carboxylase, which combines CO2 with phosphoenolpyruvate (PEP) to form oxaloacetate (a 4-carbon compound). This is distinct from C3 plants where RuBisCO fixes CO2 using RuBP.

Explanation: A test cross involves crossing the dihybrid (TtRr) with the homozygous recessive (ttrr). The dihybrid produces four types of gametes (TR, Tr, tR, tr) in equal proportions, and the recessive parent produces only tr gametes. This yields four phenotypes in a 1:1:1:1 ratio — tall round, tall wrinkled, dwarf round, and dwarf wrinkled.

Explanation: The pyramid of energy is always upright because energy is lost as heat at each trophic level due to respiration (second law of thermodynamics). Unlike pyramids of number or biomass, which can be inverted in certain ecosystems, the energy pyramid can never be inverted.

Explanation: Agrobacterium tumefaciens naturally infects plants and transfers a segment of its Ti plasmid (T-DNA) into the plant genome. Scientists exploit this mechanism by replacing the T-DNA with the gene of interest to create transgenic plants.

Explanation: Blood group O is called the universal donor because O-type red blood cells lack both A and B antigens on their surface, so they do not trigger an immune response when transfused into recipients of any ABO blood group.

Explanation: The capacitance of a parallel-plate capacitor is given by C = (K * epsilon_0 * A) / d. With air (K = 1), C_air = epsilon_0 * A / d. Inserting a dielectric of constant K multiplies the capacitance by K, giving the new capacitance KC.

Explanation: Power of a lens P = 1/f, where f is the focal length in metres. Here f = 20 cm = 0.20 m, so P = 1/0.20 = +5 D. The sign is positive because it is a convex (converging) lens.

Explanation: In a full-wave rectifier, both halves of the input AC cycle are utilised. Each complete input cycle produces two output pulses. Therefore, the output frequency is twice the input frequency: 2 x 50 = 100 Hz.

Explanation: At maximum height the final velocity is zero. Using v² = u² - 2gh: 0 = (20)² - 2(10)h, which gives h = 400/20 = 20 m.

Explanation: The peak EMF in an AC generator is given by E₀ = NBAω, where ω = 2πf. Here N = 100, B = 0.5 T, A = 0.01 m², and f = 30 rev/s. So ω = 2π(30) = 60π rad/s, and E₀ = 100 x 0.5 x 0.01 x 60π = 30π ≈ 94.2 V.

Explanation: Fringe width β = λD/d, where λ is wavelength, D is the screen distance, and d is slit separation. If d becomes d/2 and D becomes 2D, then β' = λ(2D)/(d/2) = 4λD/d = 4β. The fringe width is quadrupled.

Explanation: An isothermal process is one that occurs at constant temperature ('iso' = same, 'thermal' = temperature). For an ideal gas, the internal energy depends only on temperature, so both temperature and internal energy remain constant.

Explanation: The Bohr radius (radius of the first orbit, n = 1) of the hydrogen atom is a₀ = 0.529 angstroms, which is approximately 0.053 nm or 53 pm. This is a fundamental constant in atomic physics.

Explanation: In ethylene, each carbon forms two sigma bonds with hydrogen atoms and one sigma bond plus one pi bond with the other carbon (a double bond). This requires three hybrid orbitals, which corresponds to sp² hybridisation. The unhybridised p orbital forms the pi bond.

Explanation: For a first-order reaction, the half-life t₁/₂ = 0.693/k, where k is the rate constant. It depends only on the rate constant and is independent of the initial concentration of the reactant. This is a distinguishing feature of first-order kinetics.

Explanation: By IUPAC rules, ligands are listed alphabetically: ammine (NH₃) before chlorido (Cl⁻). The complex has five ammine and one chlorido ligand, giving 'pentaamminechlorido'. The cobalt oxidation state is +3 (total charge = +2 from two Cl⁻ counter ions, and one Cl⁻ inside = Co must be +3). The full name is pentaamminechloridocobalt(III) chloride.

Explanation: Fluorine (F) is the most electronegative element with a Pauling electronegativity of 3.98. Electronegativity generally increases across a period and up a group, placing fluorine at the top right of the periodic table (excluding noble gases).

Explanation: At 25°C, the ionic product of water Kw = [H⁺][OH⁻] = 1.0 x 10⁻¹⁴. In pure water, [H⁺] = [OH⁻] = 1.0 x 10⁻⁷ M, so pH = -log(10⁻⁷) = 7.

Explanation: Using ΔTf = Kf × m, where ΔTf = 0.93°C and Kf = 1.86 K·kg/mol: molality m = 0.93/1.86 = 0.5 mol/kg. Moles of solute = 0.5 x 0.200 = 0.1 mol. Molar mass = mass/moles = 18/0.1 = 180 g/mol.

Explanation: The -CHO (formyl) group is the defining functional group of aldehydes. Ketones contain -CO- (carbonyl between two carbon atoms), carboxylic acids contain -COOH, and alcohols contain -OH.

Explanation: For a square matrix of order n, |adj(A)| = |A|^(n-1). Here n = 3 and |A| = 5, so |adj(A)| = 5^(3-1) = 5² = 25.

Explanation: The highest order derivative is d²y/dx² (order 2). Its power is 1, so the degree is 1.

Explanation: Total outcomes when two dice are thrown = 6 x 6 = 36. Favourable outcomes for sum = 7 are: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Probability = 6/36 = 1/6.

Explanation: Using integration by parts with u = x and dv = sin(x)dx: du = dx, v = -cos(x). The integral becomes [-x cos(x)]₀^π + ∫₀^π cos(x) dx = [-π cos(π) + 0] + [sin(x)]₀^π = [-π(-1)] + [0 - 0] = π.

Explanation: This is a standard limit. As x approaches 0, sin(x)/x approaches 1. This can be proved geometrically using the squeeze theorem or verified by the Taylor expansion sin(x) = x - x³/3! + ..., so sin(x)/x = 1 - x²/6 + ... which tends to 1.

Explanation: The dot product a · b = (2)(1) + (3)(-1) + (1)(2) = 2 - 3 + 2 = 1.

Explanation: First write √3 + i in polar form: |√3 + i| = √(3 + 1) = 2, arg = arctan(1/√3) = π/6. So √3 + i = 2(cos π/6 + i sin π/6). By De Moivre's theorem, (√3 + i)⁶ = 2⁶(cos 6π/6 + i sin 6π/6) = 64(cos π + i sin π) = -64. The argument of -64 (a negative real number) is π.