Science Numericals for RRB ALP and JE: The Short Answer
RRB ALP and RRB JE CBT 1 test Physics, Chemistry and Life Sciences of Class 10 level, and a good share of the physics and chemistry questions are short numericals. They need only about 20 formulas: Ohm's law, electric power and energy, lens power and the lens formula, the three equations of motion, F = ma, work, kinetic energy, heat (Q = mcΔT), pressure, density, wave speed and the mole concept. Learn the formulas below, keep units in SI, and these become the most reliable marks in the science section.
Key takeaway: In RRB JE CBT 1, General Science has 30 of the 100 questions (CEN 05/2025). In RRB ALP, General Science (Class 10 level) is part of CBT 1, and CBT 2 Part A's Basic Science and Engineering names units, work power and energy, speed and velocity, heat and temperature, basic electricity and mass, weight and density (CEN 01/2025). Every answer below was computed in Python.
Science Numericals Formula Sheet
| Topic | Formula | Unit |
|---|---|---|
| Ohm's law | V = IR | volt (V) |
| Series resistance | R = R₁ + R₂ + … | ohm (Ω) |
| Parallel resistance | 1/R = 1/R₁ + 1/R₂ (two resistors: R₁R₂ ÷ (R₁ + R₂)) | ohm (Ω) |
| Electric power | P = VI = I²R = V²/R | watt (W) |
| Heating effect | H = I²Rt | joule (J) |
| Electric energy | units (kWh) = watts × hours ÷ 1000 | kWh |
| Stretched wire | R ∝ l² when volume is constant | Ω |
| Lens power | P = 1/f (f in m) = 100/f (f in cm); convex +, concave − | dioptre (D) |
| Lens formula | 1/v − 1/u = 1/f; magnification m = v/u | – |
| Equations of motion | v = u + at; s = ut + ½at²; v² = u² + 2as | m, m/s |
| Newton's second law | F = ma = m(v − u)/t | newton (N) |
| Work | W = Fs; against gravity W = mgh | J |
| Kinetic energy | KE = ½mv² | J |
| Power | P = W/t | W |
| Heat | Q = mcΔT | J |
| Pressure | P = F/A | pascal (Pa) |
| Density | ρ = m/V | kg/m³ or g/cm³ |
| Wave speed | v = fλ | m/s |
| Weight | W = mg (Moon: g ÷ 6) | N |
| Mole concept | n = given mass ÷ molar mass; N = n × 6.022 × 10²³ | mol |
| Percentage composition | (mass of element in formula ÷ molar mass) × 100 | % |
Electricity Numericals (Solved)
Q1. Two resistors of 6 Ω and 3 Ω are joined in parallel and this pair is joined in series with a 2 Ω resistor. Find the equivalent resistance. Answer: Parallel: 6 × 3 ÷ (6 + 3) = 2 Ω; total = 2 + 2 = 4 Ω.
Q2. A heater of resistance 44 Ω works on 220 V. What is its power? Answer: P = V² ÷ R = 220 × 220 ÷ 44 = 1,100 W.
Q3. A current of 3 A flows through a 10 Ω wire for 1 minute. How much heat is produced? Answer: H = I²Rt = 3² × 10 × 60 = 5,400 J.
Q4. A house runs 4 fans of 60 W each for 5 hours a day. At ₹7 per unit, what is the bill for 30 days? Answer: Energy = 4 × 60 × 5 × 30 ÷ 1000 = 36 kWh (units); bill = 36 × 7 = ₹252.
Q5. A wire of resistance 5 Ω is stretched to 3 times its length (volume unchanged). Find the new resistance. Answer: R ∝ length², so new R = 5 × 3² = 45 Ω.
Light (Lens) Numericals (Solved)
Sign convention: distances are measured from the optical centre; an object in front of the lens has a negative u, and a convex lens has a positive f.
Q6. Find the power of a convex lens of focal length 40 cm. Answer: P = 100 ÷ f (in cm) = 100 ÷ 40 = +2.5 D.
Q7. An object is placed 30 cm in front of a convex lens of focal length 20 cm. Find the image distance and magnification. Answer: 1/v − 1/u = 1/f with u = −30: 1/v = 1/20 − 1/30 = 1/60, so v = 60 cm (real, behind the lens); magnification = v ÷ u = −2 (inverted, 2 times the size).
Motion and Force Numericals (Solved)
Q8. A car moving at 5 m/s accelerates uniformly at 2 m/s² for 6 s. Find its final velocity and the distance covered. Answer: v = u + at = 5 + 2 × 6 = 17 m/s; s = ut + ½at² = 30 + 36 = 66 m.
Q9. A train at 20 m/s is stopped by a uniform retardation of 4 m/s². What distance does it cover before stopping? Answer: v² = u² − 2as ⇒ s = u² ÷ 2a = 400 ÷ 8 = 50 m.
Q10. The velocity of a 5 kg body rises from 4 m/s to 12 m/s in 2 s. What force acts on it? Answer: F = m(v − u) ÷ t = 5 × 8 ÷ 2 = 20 N.
Work, Energy and Power Numericals (Solved)
Q11. How much work is done in lifting a 40 kg load through 3 m? (g = 10 m/s²) Answer: W = mgh = 40 × 10 × 3 = 1200 J.
Q12. Find the kinetic energy of a 6 kg body moving at 5 m/s. Answer: KE = ½mv² = ½ × 6 × 25 = 75 J.
Q13. A motor does 1,200 J of work in 1 minute. What is its power? Answer: P = W ÷ t = 1200 ÷ 60 = 20 W.
Heat, Pressure, Density, Waves and Gravitation (Solved)
Q14. How much heat raises 3 kg of water by 15 °C? (specific heat of water = 4200 J/kg °C) Answer: Q = mcΔT = 3 × 4200 × 15 = 189,000 J.
Q15. A force of 600 N acts on an area of 3 m². Find the pressure. Answer: P = F ÷ A = 600 ÷ 3 = 200 Pa.
Q16. A metal block of mass 270 g has a volume of 100 cm³. Find its density. Answer: ρ = m ÷ V = 270 ÷ 100 = 2.7 g/cm³.
Q17. A sound wave of frequency 340 Hz has a wavelength of 0.5 m. Find its speed. Answer: v = fλ = 340 × 0.5 = 170 m/s.
Q18. A body has a mass of 72 kg on Earth. What is its weight on the Moon? (g = 10 m/s²; Moon's gravity = 1/6 of Earth's) Answer: Mass stays 72 kg; weight on Moon = 72 × 10 ÷ 6 = 120 N.
Chemistry Numericals: Mole Concept (Solved)
Q19. How many moles are there in 88 g of CO₂? (C = 12, O = 16) Answer: Molar mass = 12 + 2 × 16 = 44 g/mol; n = 88 ÷ 44 = 2 mol.
Q20. What is the percentage of nitrogen by mass in NH₃? (N = 14, H = 1) Answer: Molar mass = 14 + 3 = 17; % N = 14 ÷ 17 × 100 = 82.35% (approx.).
Q21. Find the molar mass of H₂SO₄. (H = 1, S = 32, O = 16) Answer: 2 × 1 + 32 + 4 × 16 = 98 g/mol.
Q22. How many molecules are in 0.5 mol of water? (Avogadro number = 6.022 × 10²³) Answer: 0.5 × 6.022 × 10²³ = 3.011 × 10²³ molecules.
Tricks to Score in Science Numericals
- Convert units first. cm to m, g to kg, minutes to seconds, watts × hours ÷ 1000 for kWh.
- Pick the formula from the given data. Given V and R with power asked, use P = V²/R directly instead of finding I.
- Lens power uses metres. With f in cm, use P = 100/f; a concave lens always gives a negative power.
- Mass never changes, weight does. On the Moon only g changes (one-sixth).
- Check with the options. Wrong options are often the result of a missed square (I² or v²) or a missed ½.
Science Numericals FAQs
What level of science is asked in RRB ALP and RRB JE?
The CENs set General Science at the 10th standard level: Physics, Chemistry and Life Sciences (RRB JE specifies the CBSE syllabus up to Class 10).
How many science questions come in RRB JE CBT 1?
30 out of 100 questions, as per the section-wise table in CEN 05/2025 (the CEN calls the split indicative).
Which numerical topics should I revise first?
Electricity (Ohm's law, power, energy bills), lenses, equations of motion and the mole concept give the most direct questions.
Are calculators allowed for these numericals?
Physical calculators are banned at the exam centre. The RRB JE CEN provides a virtual on-screen calculator only in CBT 2; CBT 1 has none, and the ALP CEN does not mention one, so practise these sums by hand.