Energy consumed in a home is 250 units then the total energy in Joule will be :

Question

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Correct — C, 9×10⁸. The whole question rests on knowing what a 'unit' means on an electricity bill. One unit is the Board of Trade unit, which is one kilowatt-hour: the energy delivered when a load of one kilowatt runs for one hour. Convert it to SI step by step and nothing is left to memory — one kilowatt is 1,000 watts, one watt is one joule per second, and one hour is 3,600 seconds, so 1 kWh = 1,000 J/s × 3,600 s = 3,600,000 J = 3.6 × 10⁶ J. A month's consumption of 250 units is therefore 250 × 3.6 × 10⁶ = 900 × 10⁶ = 9 × 10⁸ joules, which is option (c). The Commission printed this same working in the remarks it published on 31 October 2025 while disposing of candidate objections, setting out the energy consumed as 250 kWh and equating it to 9 × 10⁸ J. Two habits make this a ten-second question rather than a thirty-second one. First, fix 3.6 × 10⁶ J per unit in memory as a single number, the way you would fix 4.186 J per calorie; every domestic-electricity numerical in every state PSC paper reduces to multiplying by it. Second, do the arithmetic in powers of ten and let the exponent do the checking: 250 is 2.5 × 10², so 2.5 × 3.6 = 9 and 10² × 10⁶ = 10⁸, giving 9 × 10⁸ with no long multiplication at all. Note also what the question is really testing, because it is not arithmetic. It is the distinction between power and energy — the kilowatt is a rate of using energy while the kilowatt-hour is a quantity of energy, and the electricity board bills you for the second, never the first. A candidate who half-remembers the conversion as 3,600 J, which is the value for one watt-hour rather than one kilowatt-hour, lands squarely on option (a); the factor of a thousand between the watt and the kilowatt is the only thing separating the two answers on this paper. For a feel for the size of the number, 9 × 10⁸ J is the energy a single 100-watt bulb would consume if it burned continuously for 2,500 hours, that is for more than a hundred days without a break — which is precisely why the joule is useless for billing and the kilowatt-hour exists.

Why the other options are wrong — (a) The most reasoned wrong answer on the list, and the one the option set was built to catch. It is 250 × 3,600, the figure you get by treating one unit as one WATT-hour (3.6 × 10³ J) instead of one KILOWATT-hour (3.6 × 10⁶ J) — a slip of exactly a factor of a thousand. In real terms 9 × 10⁵ J is a quarter of a single unit, less than what one ceiling fan draws in a night, so it cannot be a household's monthly bill.  (b) No standard slip in the conversion produces this figure; it sits on the list as a magnitude decoy between the two derivable values, so that a candidate who guesses by 'feel' rather than converting cannot land on the answer. Checked against the meter it is absurd: 8 × 10⁶ J divided by 3.6 × 10⁶ J per unit is about 2.2 units, that is under one per cent of the 250 units the stem states.  (d) Smaller still, and the easiest to eliminate on sight. 10⁵ J is 0.028 kWh — about one thirty-sixth of a single unit, or the energy a 100-watt bulb uses in roughly seventeen minutes. Candidates reach it by treating the '250 units' as though the unit were already a joule-scale quantity. Any answer that makes a month of household electricity smaller than one billed unit has failed the reality check before the arithmetic begins.

Concept: Energy and power are different physical quantities and the exam tests the boundary between them relentlessly. Energy is the capacity to do work; its SI unit is the joule, defined as the work done when a force of one newton moves its point of application through one metre, and named after James Prescott Joule (1818-1889), whose paddle-wheel experiments established the mechanical equivalent of heat. Power is the RATE at which energy is transferred, measured in watts, where one watt is one joule per second. Rearranged, energy = power × time, and that single rearrangement generates the kilowatt-hour: a kilowatt of load running for an hour delivers 1,000 × 3,600 = 3.6 × 10⁶ joules. Electricity utilities bill in kilowatt-hours, called 'units' on Indian bills, for the practical reason that the joule is far too small a parcel to be convenient — a household month written in joules runs to nine hundred million of them. The same logic produces the whole family of energy units the exam uses: the calorie (4.186 J) for food and heat, the erg (10⁻⁷ J) in the older CGS system, the electronvolt (1.602 × 10⁻¹⁹ J) for atomic and nuclear physics, and, at national scale, the billion unit or BU (10⁹ kWh, equal to 3.6 × 10¹⁵ J) in which India's annual electricity generation is reported. Every one of them is a joule with a different number of zeroes attached, chosen so that the numbers people actually quote stay between one and a thousand.

State PCS 2025 Q123 — Science & Technology PYQ with Answer

State PCS 2025 Q123 — Science & Technology PYQ with Answer