Numerical value questions in JEE Main

Each subject in JEE Main ends with five numerical value questions — fifteen in all, worth sixty marks. They often look like ordinary problems. The difference is what is missing: there are no options to check your answer against, no way to eliminate, and no lucky guesses. Under the current scheme, a wrong entry also costs a mark.

That makes Section B the purest test of whether you can carry a solution all the way to a correct number. The good news is that the skills involved are specific and trainable.

How Section B works

When numerical questions were first introduced, wrong answers in this section carried no penalty; negative marking has applied here since the 2022 exam. From 2021 to 2024, candidates also chose 5 of 10 numerical questions per subject; from 2025 there are just five, all compulsory. Old advice such as "always fill something in Section B" dates from the no-penalty years and is now wrong.

When to attempt

The rule is simple: attempt a numerical question when you have worked out an answer, and not otherwise. A typed guess without a method has almost no chance of matching the exact value, so on average it costs close to one mark.

That does not mean you should be timid. If you have a complete solution and are reasonably confident, enter it. The +4/−1 balance strongly favours attempting a worked answer.

The traps, with worked examples

Most lost marks in Section B are not concept gaps. They are one of a handful of predictable slips.

Trap 1: answering a different quantity

Question: A ball is dropped from rest from a height of 45 m. Taking g = 10 m/s², find its speed (in m/s) just before it hits the ground.

Solution: Time to fall: h = ½gt², so 45 = ½ × 10 × t², giving t² = 9 and t = 3 s. Speed v = gt = 10 × 3 = 30 m/s.

Check with energy: v² = 2gh = 2 × 10 × 45 = 900, so v = 30 m/s.

A candidate who stops at the time and enters 3 has solved most of the problem and still lost a mark. Underline what is asked before you start and read it again before you type.

Trap 2: units

Question: A sound wave of frequency 500 Hz travels at 340 m/s. Find its wavelength in centimetres.

Solution: λ = v ÷ f = 340 ÷ 500 = 0.68 m = 68 cm.

Entering 0.68 is a correct calculation in the wrong unit, and it scores −1. Convert to the unit the question asks for as the very last step, and write the unit beside every intermediate value.

Trap 3: the "x × 10ⁿ" format

JEE often asks, for example: "the wavelength is x × 10⁻² m. Find x." Using the value above, 0.68 m = 68 × 10⁻² m, so x = 68.

The answer is the number x, not the full quantity. Rewrite your result in the given form and read off x.

Trap 4: rounding

If a question asks for the nearest integer and your answer is 4.62, the entry is 5, not 4.62 or 4. Round only at the end; rounding early can move the final answer across the boundary.

Trap 5: last-step arithmetic

Question: α and β are the roots of x² − 7x + 10 = 0. Find α² + β².

Solution: α + β = 7 and αβ = 10. So α² + β² = (α + β)² − 2αβ = 49 − 20 = 29.

Check by solving: the roots are 2 and 5, and 4 + 25 = 29. A quick independent check like this catches most last-step slips.

Accuracy habits that work

• Underline the quantity asked and its unit before solving.
• Write units through the whole solution, not just at the end.
• Check with a second method where it is cheap: energy as well as kinematics, solving the quadratic directly, a limiting case.
• Sanity-check the size of the answer. A car's speed of 3,000 m/s or a pH of 17 means something went wrong.
• Read the entry instruction for decimals, rounding or the x × 10ⁿ form.

How to practise

• Solve previous years' numerical questions chapter by chapter, always to a final typed-style number, never stopping at "the method is clear".
• Time them: most should take three to five minutes.
• Keep a separate section of your error notebook for Section B slips, labelled by trap type. After a month you will know your own weak habit.
• Physical chemistry, mechanics, current electricity and algebra are natural sources of numerical questions. See the physical chemistry numericals guide and maths numerical questions.

Practice set

Give each answer as a number in the unit asked.

1. A car starts from rest and accelerates uniformly at 2 m/s² for 5 s. Find the distance covered, in metres.
2. Resistors of 6 Ω and 3 Ω are connected in parallel across a 12 V battery of negligible internal resistance. Find the current drawn from the battery, in amperes.
3. What volume of 0.1 M HCl, in mL, exactly neutralises 20 mL of 0.25 M NaOH?
4. What mass of NaOH (molar mass 40 g/mol), in grams, is needed to make 250 mL of a 0.2 M solution?
5. Find the modulus of the complex number 3 + 4i.
6. Find the sum of the first 20 natural numbers.

Answers

1. 25. s = ½at² = ½ × 2 × 25 = 25 m.
2. 6. Parallel resistance = (6 × 3) ÷ (6 + 3) = 18 ÷ 9 = 2 Ω. Current = 12 ÷ 2 = 6 A.
3. 50. NaOH = 0.25 × 20 = 5 mmol. HCl needed = 5 mmol, so volume = 5 ÷ 0.1 = 50 mL.
4. 2. Moles = 0.2 × 0.25 = 0.05 mol. Mass = 0.05 × 40 = 2 g.
5. 5. √(3² + 4²) = √25 = 5.
6. 210. n(n + 1) ÷ 2 = 20 × 21 ÷ 2 = 210.

What to do next

• Take the five numerical questions from each subject of a recent paper and solve them untimed, to a final number.
• Label any mistakes by trap type.
• In your next mock, time Section B separately for each subject.
• Review the JEE Main exam pattern so the marking scheme is fresh in mind.