How to Solve Physics Numericals: 4 Steps for HSC and MHT-CET

Students who know the formula still lose marks because they never fix what the question gives and asks. A hidden Given such as "from rest" is missed, km/h goes straight into a formula, or a formula is chosen by memory. In our experience of teaching, these setup slips cost more marks than arithmetic.

"Formula yaad hai, phir bhi answer galat" (I remember the formula, still the answer is wrong) is the usual complaint. Freezing often comes from hunting for a formula first, which needs insight you may not have yet. The routine below starts with a move that needs none: write down what the question tells you. Writing the Given list first removes the guesswork, and the habit is fixable.

The card is a four-line reminder you copy onto an index card or the inside cover of your notebook and run on every numerical. It contains only the routine, not chapter formulas.

List Given and Required by reading the question twice, sketching it quickly, and writing each known quantity and the one unknown with their units. Read once for the story and once for the numbers. Write each value with the unit the question uses, for example 72 km/h. The conversion to SI comes in Step 3.

Look for Givens the question hides in words. "From rest" means the starting velocity is 0. "At the highest point" means the velocity there is 0. The sketch is one line in any topic: a motion line, a ray diagram, a circuit. If you study mechanics, the "draw the free body diagram first" version (a free body diagram is a sketch showing every force on one object) is in our Engineering Mechanics study plan, written for first-year students of Savitribai Phule Pune University (SPPU). For a body held in equilibrium by three forces, Lami's theorem shows how to pair each angle with its force.

You pass this step when every Given has a unit and exactly one quantity is marked Required.

Choose the formula that contains the Required letter and no other unknown, then write it in symbols before any number goes in. Writing symbols first makes rearranging safer and shows exactly which letters you are using. The same test works in every chapter. For chapter formulas, use our HSC Physics formula sheet for Maharashtra Class 12.

Before you match letters, name the concept the question is about. A question about position, velocity, and time under constant acceleration points to the equations of motion. A force and an acceleration point to Newton's second law. Speed changing over a distance under a force points to work and energy.

Once the concept is named, only a few formulas are left to match, and our guides to simple harmonic motion formulas and wave optics formulas show the same matching test for those two Std XII topics.

For motion in a straight line with constant acceleration, matching looks like this:

Here u is starting velocity, v is final velocity, a is acceleration, t is time and s is displacement (distance measured in the chosen positive direction). These hold only when acceleration is constant. NCERT's Class 11 Physics, Chapter 2 develops them.

The pass test is a count: the formula should have exactly one unknown. If it has two, try another row or look for a hidden Given.

Change units before substituting, never after. Every Given must be in SI units (the International System of Units, built on metre, kilogram and second) so the answer also comes out in SI. NCERT Class 11 Physics, Chapter 1 follows SI units throughout.

The commonest trap is mixing km/h with m/s. To convert, multiply km/h by 1000 and divide by 3600, which is the same as multiplying by 5/18. So 72 km/h = 72 × 5/18 = 20 m/s.

Other usual slips are cm left unconverted to m, grams to kg, and minutes to seconds.

After converting, make a one-line estimate with round numbers before you do the exact sum. Round g (acceleration due to gravity) to 10 m/s², 72 km/h to 20 m/s, and so on. The estimate is a separate quick calculation, so it can disagree with your exact answer and warn you.

The pass test is a scan of the values you are about to substitute. A km, cm, gram, minute or hour anywhere is a fail. A few formulas use only ratios, where the same unit on both sides cancels. If you are unsure which kind you have, convert anyway. The estimate passes when you can do it in a few seconds with round numbers.

Run three tests before you move on. The unit must match the Required quantity, the size must agree with a rough estimate, and the sign must match the direction the story describes. Each test passes or fails in seconds.

• Unit: a height must end in metres. If it ends in (km/h)²/(m/s²), the setup failed.
• Size: compare the exact answer with the estimate you made in Step 3. If they differ by a factor of two or more, redo the steps.
• Sign: pick a positive direction and keep it. A negative velocity means motion opposite to that direction. In optics the same rule applies to distances: fix the sign convention before you substitute.

In MHT-CET, when the options are formulas, dimensions can remove wrong ones before you calculate anything. Suppose a question asks for the time period of a simple pendulum and the options are √(L/g), √(g/L), L/g and Lg (ignoring numerical factors such as 2π). Length has dimension [L] and g has [LT⁻²], so L/g has dimension [T²]. Only √(L/g) has dimension [T], so the other three can be crossed out. Dimensions cannot catch a wrong pure number such as ½ or 2π, so use this to remove options, not to confirm one.

After a mock test, our 45-minute mock error log turns your mistakes into a retry plan. Add one column of your own: which step failed (Write, Pick, Convert or Check). A pattern in that column tells you what to practise.

Run all four steps on this question: a stone is fired straight up from level ground by a catapult at 72 km/h, ignoring air resistance. (a) How high does it rise? (b) What is its velocity 3 s after release?

We use g = 9.8 m/s² (acceleration due to gravity near Earth's surface, as in NCERT Chapter 2), with upward as positive. Rounding g to 10 m/s² is only for the mental check. In an exam, use the g value the question gives.

Write.

• u = 72 km/h, upward
• v at the top = 0
• a = −g = −9.8 m/s²
• Required: height H

Pick. v² = u² + 2as with s = H and v = 0, so H = u²/(2g).

Convert and estimate. u = 72 km/h = 72 × 5/18 = 20 m/s. With g ≈ 10 m/s², H ≈ u²/20 = 20²/20 = 20 m. Putting the unconverted 72 into the same estimate would give 72²/20 ≈ 260 m, which no catapult stone reaches, so the slip is flagged before the exact sum.

Calculate. H = (20 m/s)² / (2 × 9.8 m/s²) = 400 m²/s² ÷ 19.6 m/s² = 20.4 m.

Check. The unit is metres, as the question requires. 20.4 m agrees with the estimate of 20 m. The sign is positive, which is above the start.

The wrong route. Using 72 directly: 72² / (2 × 9.8) = 5184 / 19.6 ≈ 264 m. The unit is not metres, and 264 m against an estimate of 20 m fails the size check.

Part (b). Given t = 3 s, Required v. v = u + at = 20 m/s + (−9.8 m/s²)(3 s) = 20 − 29.4 = −9.4 m/s. The sign check makes this real. The stone reaches its top at 20 ÷ 9.8 ≈ 2.04 s, which is before 3 s, so it is already coming down, and a negative velocity is correct.

Run the same four lines in both exams. Write them out in full in a Maharashtra HSC answer; our 12th HSC Physics study plan covers every chapter for Boards and MHT-CET. Do them mentally in MHT-CET, where you choose one of four options.

The 2026 MHT-CET brochure sets out these rules in Section 7:

• Questions are multiple-choice with four options and one correct answer.
• There is no negative marking.
• Questions appear on screen one at a time.
• Calculators are not allowed in the examination hall.
• Physics and Chemistry share the first 90 minutes.

As of October 2026, treat all of this as the 2026 format, which may change when the State CET Cell publishes its 2027 brochure.

Our calculation: 90 minutes is 5,400 seconds. Split evenly across 100 Physics and Chemistry questions (50 Physics, as in our previous-year question (PYQ) practice plan, and 50 Chemistry, as on our MHT-CET exam pattern page), that is an average of 54 seconds per question. It is an average across both subjects, not a time per numerical.

The brochure advises candidates not to spend too much time on any one question, and there is no negative marking, so our recommendation is to mark your best option and move on when a numerical runs well past its share.

Three habits keep the routine honest: write the unit on every line, write the formula in symbols before numbers, and name the failed step on every wrong answer. You can check each one at a glance. A bare number anywhere in your working, a formula with no letters, or a wrong answer in your log that just says "mistake" means the habit has slipped.

Practise on PYQs one chapter at a time, and run all four lines on every question. This is our recommendation, not an official target:

1. Start small. Take 5 to 10 questions from one chapter, using our checked PYQ library, and write all four lines in full with the solutions closed.
2. Add a timer. Time the whole set, not each question. If one question runs well past its share, mark your best option and move on.
3. Log the failed step. For every wrong answer, note Write, Pick, Convert or Check.
4. Drill the step that appears most. Then retry the questions you missed after a few days.

Our MHT-CET Physics PYQ practice plan shows how to organise those questions by chapter. To see how we teach, read about learning physics with RG Sir.

• Simple Harmonic Motion Formulas: Pick the Right One
• Wave Optics Formulas: Pick the Right One in 3 Questions
• How to Study Engineering Mechanics: SPPU Plan