BPSC TRE 1 PYQ Quiz – Science Subject for Secondary Teacher

To just lift off, the upward thrust must equal the rocket’s weight.

• Total mass = 50 kg + 450 kg = 500 kg.

• Weight, W = mg = 500 × 9.8 = 4900 N.

• Thrust, F = v_exhaust × (dm/dt) = 5000 × (dm/dt).

• For lift-off: 5000 × (dm/dt) = 4900.

• Therefore, dm/dt = 4900 / 5000 = 0.98 kg/sec.

For a central force, F ∝ 1/r^(n 1). For a circular orbit, centripetal force equals central force: mv²/r ∝ 1/r^(n 1), so v ∝ 1/r^(n/2). Time period T = 2πr/v ∝ r^(1 n/2). Thus, T₂/T₁ = (2R/R)^(1 n/2) = 2^((n 2)/2). This expression is not listed in the options.

The total kinetic energy in the lab frame is the sum of the kinetic energy of the center of mass and the kinetic energy in the CM frame: T_L = T_CM T_C. The ratio T_L / T_CM is (m₁ m₂)/m₁. The question likely refers to this ratio, as T_C is the energy available for the reaction.

A streamline is defined as a curve that is everywhere tangent to the velocity vector of the flow at a specific instant in time.

The mean free path l is inversely proportional to the number density n (n = N/V). Since N is the same for both boxes, l ∝ V. Therefore, l/V is a constant, so l_A/V_A = l_B/V_B.

According to Wien’s displacement law, the wavelength of peak emission is inversely proportional to temperature (λ_max ∝ 1/T). Therefore, as temperature increases, the peak shifts towards lower, not higher, wavelengths.

With one slit, amplitude = a, so intensity I₀ ∝ a².
With two slits at maxima, amplitudes add: A = a + a = 2a, so intensity I ∝ (2a)² = 4a².
Thus, I = 4I₀.

For the first minimum in single-slit diffraction: a sinθ = λ.
For small angles, sinθ ≈ y/D, where y = 4 mm = 0.004 m, D = 2 m.
So, a (y/D) = λ → a = λD / y = (600 × 10⁻⁹ m × 2 m) / 0.004 m = 3 × 10⁻⁴ m = 0.3 mm.

A quarter-wave plate introduces a π/2 phase difference. For the output to be circularly polarized, the incident plane-polarized light must be oriented at 45° to the optic axis. This ensures equal amplitudes for the ordinary and extraordinary waves, which, when combined with a π/2 phase difference, results in circular polarization.

For light waves in a medium, the product of group velocity (v_g) and phase velocity (v_p) is c².
v_g × v_p = c² → v_p = c² / v_g = (3 × 10⁸)² / (2 × 10⁸) = 9 × 10¹⁶ / 2 × 10⁸ = 4.5 × 10⁸ m/s.

The given equation is y = 0.5 sin(3x – 32π t). Comparing with standard form y = A sin(kx – ωt), we find ω = 32π rad/s.
Frequency f = ω / (2π) = 32π / (2π) = 16 Hz.
Since 16 Hz is not among the options, the correct answer is “None of the above”.

All three given equations are indeed Maxwell’s equations:

1. Ampère-Maxwell law

2. Faraday’s law

3. Gauss’s law for magnetism
   Therefore, none of them is “not Maxwell’s equation”.

According to Faraday’s law, voltage is induced only when there is a change in magnetic flux. With a stationary conductor and a static magnetic field, the flux is constant, so the induced voltage is zero.

The magnetic flux Φ = B ⋅ A = BA cosθ, where θ is the angle between the field and the area vector (perpendicular to the plane of the loop). If the magnetic field is parallel to the plane of the loop, then θ = 90° and cosθ = 0, resulting in zero flux. This is a common scenario in such problems.

The Biot-Savart law is dB = (μ₀/4π) I (dl × r̂)/r².
(i) True: dB ∝ |dl|
(ii) False: It deals with magnetic field, not electric field.
(iii) True: dB ∝ I

The 10Ω and 15Ω resistors are in parallel: R_parallel = (10×15)/(10+15) = 150/25 = 6Ω.
This combination is in series with the 4Ω resistor: R_total = 6Ω + 4Ω = 10Ω.
Using Ohm’s law: i = V/R_total = 20V / 10Ω = 2A.

In a parallel resonance circuit, the Q-factor provides current magnification, not voltage magnification. Voltage magnification is a characteristic of series resonance circuits.

For tungsten: K_max = eV_s = hν – φ → 1.8 eV = hν – 4.5 eV → hν = 6.3 eV.
For sodium: eV_s = hν – φ = 6.3 eV – 2.3 eV = 4.0 eV.
So, stopping potential for sodium is 4.0 V.

The fine structure in atomic spectra is due to the interaction between the electron’s spin and its orbital motion (spin-orbit coupling).

An alpha particle is ⁴₂He. In alpha decay:

• New proton number = 84 – 2 = 82

• New nucleon number = 216 – 4 = 212

We need to check conservation laws. For Λ + Σ⁺ → n + p + π⁺:

• Charge: 0 + 1 = 0 + 1 + 1 → conserved (1=1)

• Baryon number: 1 + 1 = 1 + 1 + 0 → conserved (2=2)

• Strangeness: -1 + (-1) = 0 + 0 + 0 → not conserved (-2 ≠ 0)
  Strangeness is not conserved, so this reaction is not allowed by the strong or electromagnetic interaction.

Explanation:
Donor impurities have 5 valence electrons (e.g., phosphorus, arsenic) and belong to group V of the periodic table. When added to silicon (group IV), they provide an extra electron for conduction.

Explanation:
In an n-type semiconductor, donor impurities add extra electrons, increasing the electron concentration in the conduction band. This shifts the Fermi level upward, closer to the conduction band.

The maximum theoretical efficiency of a half-wave rectifier is (1/π)² × 100% ≈ (0.318)² × 100% ≈ 40.6%.

In traditional analog TV broadcasting:

• Video information is transmitted using Amplitude Modulation (AM)

• Audio information is transmitted using Frequency Modulation (FM)

Explanation:
The reverse saturation current approximately doubles (increases by 2 times) for every 10°C rise in temperature.

Explanation:
Cut-off wavelength λ_c = 1240 / E_g (where E_g is in eV and λ_c in nm).
For silicon: λ_c = 1240 / 1.1 ≈ 1127.27 nm
For germanium: λ_c = 1240 / 0.67 ≈ 1850.75 nm

Explanation:
The coprecipitation method allows for mixing at the molecular level in solution, resulting in highly homogeneous products like ZnFe₂O₄ spinel.

Explanation:
The unit cell is the smallest repeating unit that, when repeated in three dimensions, generates the entire crystal lattice.

Explanation:
Chemical dissociation can be exothermic (releases heat), endothermic (absorbs heat), or reversible depending on the specific reaction and conditions.

Explanation:
Nuclear radii are typically of the order of 1-10 femtometers (1 fm = 10⁻¹⁵ m = 10⁻¹³ cm).

Explanation:
An atomic orbital is defined as a region in space around the nucleus where there is a high probability (typically 90%) of finding an electron.

Explanation:
For a reaction with rate law: rate = k[A]^m[B]^n, when [A] = [B] = 1, then rate = k. So the rate equals the specific rate constant.

Explanation:
Assuming the rate law is rate = k[A]²[B]:
New rate = k(2[A])²([B]/2) = k(4[A]²)([B]/2) = 2k[A]²[B] = 2 × original rate.

Explanation:
For first-order kinetics: k = (2.303/t) log([A]₀/[A]) = (2.303/200) log(2.00/0.15) = (2.303/200) log(13.33) ≈ (2.303/200) × 1.125 ≈ 0.01295 min⁻¹.
Half-life t₁/₂ = 0.693/k = 0.693/0.01295 ≈ 53.51 minutes (closest to 53.72 minutes).

Explanation:
A mercury cell is a primary (non-rechargeable) cell. Primary cell reactions cannot be reversed by applying an external potential. Nickel-Cadmium cells are secondary (rechargeable) cells.

A catalyst works by providing an alternative reaction pathway with a lower activation energy. It does not change the thermodynamic parameters (entropy, internal energy, enthalpy) of the reaction.

Explanation:
Photochemistry is the branch of chemistry concerned with chemical effects caused by absorption of visible or ultraviolet light.

Explanation:
Intensity of light is defined as the number of photons crossing a unit area per unit time, or equivalently, the power per unit area.

Explanation:
Predissociation occurs when a molecule in a stable excited state makes a radiationless transition to a repulsive (unstable) excited state, leading to dissociation of the molecule.

Explanation:
Sodium carbonate reacts with copper sulphate to form a basic copper carbonate (like CuCO₃·Cu(OH)₂), sodium sulphate, and carbon dioxide. It does not form simple copper carbonate or copper hydroxide as the main product.

Explanation:
Due to lanthanoid contraction, the expected increase in atomic radius from the 4d to the 5d series elements is canceled out. This results in elements in the second and third transition series (e.g., Zr and Hf, Nb and Ta, Mo and W) having nearly identical atomic radii.

Explanation:
The nitroprusside ion is [Fe(CN)₅(NO)]²⁻. In this complex, the iron is in the +2 oxidation state (ferrate(II)), it is coordinated by five cyanide (cyano) ligands and one nitrosyl (nitrosyl) ligand.

Explanation:
Heating limestone (CaCO₃) in the absence of air is calcination: CaCO₃(s) → CaO(s) + CO₂(g). The product, calcium oxide (CaO or quicklime), is slaked with water to form Ca(OH)₂ (slaked lime), which is the actual compound used in whitewashing.

Explanation:
In acidified medium, KMnO₄ (purple) is a strong oxidizing agent. It oxidizes Fe²⁺ ions from FeSO₄ to Fe³⁺ and is itself reduced to colorless Mn²⁺ ions. This decolorization is a characteristic test for oxidizing agents like permanganate.

Explanation:
Diphenylmethane (C₆H₅–CH₂–C₆H₅) has a -CH₂- bridge. The four non-equivalent positions for chlorine substitution are: two positions on one ring (ortho and meta/para to the bridge, considering symmetry), and the two positions on the other ring (which are equivalent to the first due to symmetry), and the bridge carbon itself. A detailed count shows 4 distinct monochloro structural isomers.

Explanation:
The reaction is: 2AgCl(s) → 2Ag(s) + Cl₂(g). The grey color is due to the formation of fine silver metal (i). Chlorine gas is produced and escapes (iii). This is a decomposition reaction (iv), but the specific products listed in (i) and (iii) are the direct cause of the observation.

Explanation:
While HDPE is linear, Low-Density Polyethylene (LDPE) is a common example of a branched chain polymer. Polyvinyl Chloride (PVC) can also have branched structures depending on the polymerization conditions. Teflon (PTFE) is generally linear. Since at least one common form of polyethylene is branched, the correct choice is “More than one of the above”.

Explanation:
Polymers like Polylactic Acid (PLA) and Polyglycolic Acid (PGA), derived from lactic acid and glycolic acid respectively, are well-known biodegradable polymers used in medical sutures and packaging. Styrene, acrylonitrile, and vinyl chloride form non-biodegradable plastics like polystyrene, ABS, and PVC.

Explanation:
In polar protic solvents (like water), nucleophilicity increases down a group in the periodic table due to poorer solvation of larger ions. Thus, the order for halides is F⁻ < Cl⁻ < Br⁻ < I⁻. Acetate (CH₃COO⁻) is a very poor nucleophile because the negative charge is resonance-stabilized. Therefore, CH₃COO⁻ is the weakest nucleophile among the given ions.

Explanation:
Carbocation stability increases with the number of alkyl groups attached to the positively charged carbon due to the inductive electron-donating effect and hyperconjugation of the alkyl groups. Thus, tertiary (3°) carbocations are the most stable, followed by secondary (2°), then primary (1°), and methyl (CH₃⁺) is the least stable.

Explanation:
The carbonyl (C=O) stretching vibration gives a strong, sharp peak in the infrared (IR) spectrum around 1700 cm⁻¹ (typically between 1650-1750 cm⁻¹ depending on the specific compound).

Explanation:
ortho-Nitrophenol has intramolecular hydrogen bonding, which makes it more volatile. para-Nitrophenol has intermolecular hydrogen bonding, making it less volatile. Steam distillation selectively vaporizes the more volatile ortho-isomer, allowing for their separation

Explanation:
tert-Butyl chloride ((CH₃)₃C-Cl) forms a stable tertiary carbocation. This high stability favors the two-step SN1 mechanism. Primary alkyl halides like n-butyl chloride favor SN2, and secondary alkyl halides like sec-butyl chloride can undergo both SN1 and SN2 depending on conditions.

Explanation:
Phytophagous (plant-eating) nematodes, such as root-knot nematodes (Meloidogyne), are predominantly parasites of plant roots, where they cause galls and other damage.

Explanation:
Secondary treatment uses aerobic microorganisms to biologically degrade organic matter in wastewater. This process significantly reduces the Biochemical Oxygen Demand (BOD), which is a measure of the amount of oxygen consumed by microorganisms while decomposing organic waste.

Explanation:
The majority of economically important plant pathogenic bacteria, such as those in the genera Pseudomonas, Xanthomonas, and Erwinia, are rod-shaped (bacilli) and Gram-negative.

Explanation:
Albugo (e.g., Albugo candida, which causes white rust in plants) is an obligate parasite, meaning it can only grow and reproduce on living host tissue.

Explanation:
The Compositae (or Asteraceae) family is characterized by having many small flowers aggregated into a composite head (inflorescence that looks like a single flower), not large individual flowers and seeds.

Explanation:
Uttar Pradesh, along with Punjab and Haryana, is a major producer of Basmati rice in India. Kerala and Andhra Pradesh are not traditionally known for Basmati cultivation.

Explanation:
A somaclone is a plant generated from tissue culture, particularly from somatic cells. While it is genetically identical (a clone) to the original plant, the term specifically refers to the plants that are regenerated and are morphologically similar, though somaclonal variation can sometimes occur.

Explanation:
A polysome (or polyribosome) is a complex of an mRNA molecule and two or more ribosomes that actively translate the mRNA into a polypeptide chain. It is the functional unit for the simultaneous synthesis of multiple copies of a protein.

Explanation:
Active transport moves molecules or ions across a membrane against their concentration gradient (from low to high concentration). This process requires energy, typically in the form of ATP.

Explanation:
Tropical evergreen forests in India are found in areas with very high rainfall, such as the Western Ghats, parts of the Northeast (including Assam), and the Andaman and Nicobar Islands. Madhya Pradesh has predominantly deciduous forests.

Explanation:
The term “ozone hole” refers to a severe thinning of the ozone layer in a particular area, specifically a large and rapid decrease in the total ozone column. It is not a literal hole but a region of exceptionally depleted ozone.

Explanation:
Groundnut oil is extracted from the seeds of Arachis hypogaea, the peanut plant. Brassica juncea is mustard, and Artabotrys odoratissimus is a flowering plant not used for oil.

Explanation:
Roughage, or dietary fiber, is indigestible by humans and does not provide energy or nutrients in the conventional sense. However, it is essential for adding bulk to feces and facilitating bowel movements.

Explanation:
The plasma membrane is primarily composed of a phospholipid bilayer with proteins embedded in it (fluid mosaic model). Carbohydrates are also present, attached to lipids (glycolipids) or proteins (glycoproteins), on the outer surface.

Explanation:
Gregor Mendel formulated his laws of inheritance by conducting cross-pollination (sexual reproduction) experiments on pea plants and observing the inheritance of traits from one generation to the next.

Explanation:
A decrease in blood oxygen (hypoxemia) is detected by chemoreceptors, primarily in the carotid and aortic bodies. They send signals to the respiratory center in the medulla oblongata, which increases the breathing rate to take in more oxygen.

Explanation:
Parathyroid hormone (PTH) increases blood calcium levels by stimulating bone resorption, increasing calcium reabsorption in the kidneys, and promoting vitamin D activation (which increases intestinal calcium absorption). It decreases blood phosphate levels.

Explanation:
Epinephrine (adrenaline) is released rapidly by the adrenal medulla in response to stress (the “fight-or-flight” response). Corticosteroids from the adrenal cortex are involved in the longer-term stress response.

Explanation:
Cimex hemipterus, commonly known as the tropical bed bug, is an ectoparasite that feeds on human blood.

Explanation:
Schistosoma species are trematode worms (flukes) that live in the blood vessels of their human hosts, causing the disease schistosomiasis. Enterobius is a pinworm (nematode), and Wuchereria is a filarial worm (nematode) that causes elephantiasis.

Explanation:
In the chick embryo, the allantois functions as a respiratory organ. It fuses with the chorion to form the chorioallantoic membrane, which lies close to the eggshell and facilitates gas exchange.

Explanation:
With aging, arteries lose elasticity, and the heart muscle may undergo hypertrophy (thickening) in response to increased pressure. Stress-related fat deposition can also occur in adulthood. The question is poorly phrased, but multiple options describe age-related changes.

Explanation:
Eugenics is the practice or advocacy of improving the human species by selectively mating people with specific desirable hereditary traits.

Explanation:
Metamerism is the phenomenon of having a linear series of body segments (metameres) fundamentally similar in structure, with at least some organs (e.g., muscles, nerves, excretory organs) repeated in each segment. This is seen in annelids, arthropods, and chordates

Explanation:
The nauplius is a characteristic larval stage of most crustaceans. It is a free-swimming larva with three pairs of appendages and a single median eye.