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Class 7 Maths competency-based questions 2026-27: what they look like, with 8 of our own

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A competency-based question gives you a real situation, a small table of numbers or two linked statements, and asks you to choose the right mathematics and use it, instead of repeating a worked method. This guide shows what the NCERT Class 7 Maths book, Ganita Prakash Part I, says about the kind of thinking it wants, how to answer these questions, and then 8 practice questions of our own, two each from four chapters, with worked answers.

The 8 questions are our own, drafted with AI help. Every number was re-computed by a script and every answer was checked against the textbook page named under it, but no practising teacher has reviewed them yet. The data in the questions is made up for practice. If you find a mistake, please tell us.

What the Class 7 book asks for

Ganita Prakash Part I, the Grade 7 Maths textbook (Reprint 2026-27), says in its opening pages that it follows NEP 2020 and the 2023 school curriculum framework (NCF-SE). Its "About the Book" says mathematics should build logical reasoning, creative problem solving and clear communication, not only arithmetic skills. It also says the classroom should not expect a blind use of methods, but should encourage many ways of solving a problem, and that its problems are linked to daily-life situations.

That is what a competency-based question tests. In Class 7 there is no board exam, so your school sets the tests, but the questions in the book's "Figure it Out" sets, and the ones it marks "Math Talk" and "Try This", already work this way. In the Class 10 board papers, CBSE makes about half the questions competency-focused; our Class 10 Maths competency-based questions guide explains that pattern.

How to answer them

The four choices used for every assertion-reason question below: (a) both are true and the reason explains the assertion; (b) both are true but the reason does not explain the assertion; (c) the assertion is true but the reason is false; (d) the assertion is false but the reason is true.

Large Numbers Around Us (Chapter 1)

Question 1. A newspaper headline says, "Over 50 lakh people live in our three districts." The census table it quotes gives (made-up numbers): District A 18,45,230; District B 9,72,640; District C 24,08,915. (a) Is the headline right? By how much is the total above or below 50 lakh? (b) Round the total to the nearest lakh. (c) How many more people live in the largest district than in the smallest?

Answer: (a) yes, by 2,26,785; (b) about 52 lakh; (c) 14,36,275. (a) 18,45,230 + 9,72,640 + 24,08,915 = 52,26,785, and 52,26,785 − 50,00,000 = 2,26,785. (b) The total lies between 52 lakh and 53 lakh, and 26,785 is less than half a lakh, so it rounds to 52,00,000. (c) The largest is C and the smallest is B: 24,08,915 − 9,72,640 = 14,36,275. (Reading lakhs and placing commas, page 4.)

Question 2. Assertion: A city of 1 crore people has 100 times as many people as a town of 1 lakh. Reason: The Indian and the American systems place commas in large numbers differently. Choose (a), (b), (c) or (d).

Answer: (b), both are true but the reason does not explain the assertion. 100 lakhs make 1 crore (page 8), so 1 crore is 100 times 1 lakh. The book's table shows that the two systems put commas in different places (page 8), which is true, but it says nothing about why a crore is 100 lakh.

Arithmetic Expressions (Chapter 2)

Question 3. A science museum charges ₹60 for each student and ₹90 for each adult. A class of 38 students goes with 4 teachers, and the museum takes ₹200 off the group's bill. (a) Write the bill as one expression and find its value. (b) Meena writes the bill as (38 + 4) × (60 + 90) − 200. What has she done wrong, and how far off is her answer?

Answer: (a) 38 × 60 + 4 × 90 − 200 = ₹2,440; (b) she charged every person both prices, and her answer is ₹3,660 too high. (a) The expression has three terms: 38 × 60 = 2,280, 4 × 90 = 360, and −200. The terms are worked out first and then added: 2,280 + 360 − 200 = 2,440 (page 31). (b) Her expression gives 42 × 150 − 200 = 6,100. It charges all 42 people ₹60 and ₹90 each. 6,100 − 2,440 = 3,660.

Question 4. Assertion: 8 + 12 × 5 = 100. Reason: When an expression has no brackets, its terms are worked out first and then added. Choose (a), (b), (c) or (d).

Answer: (d), the assertion is false but the reason is true. The reason is the book's rule (page 31). Using it, the terms are 8 and 12 × 5 = 60, so the value is 8 + 60 = 68, not 100. The value 100 comes from adding 8 + 12 first, which the rule does not allow.

A Peek Beyond the Point (Chapter 3)

Question 5. A school weather club records the rain each day for one week, in millimetres (made-up readings): Monday 12.5, Tuesday 0, Wednesday 3.75, Thursday 21.2, Friday 8.05, Saturday 0.6, Sunday 4. (a) What was the total rain for the week? (b) How much more rain fell on the wettest day than on the day with the least rain (not counting Tuesday)? (c) The club said, "More than 5 cm of rain fell this week." Were they right?

Answer: (a) 50.1 mm; (b) 20.6 mm; (c) yes, just: 5.01 cm. (a) 12.5 + 0 + 3.75 + 21.2 + 8.05 + 0.6 + 4 = 50.1 mm. (b) Thursday had the most, 21.2 mm, and Saturday the least, 0.6 mm: 21.2 − 0.6 = 20.6 mm. (c) Since 1 cm = 10 mm (page 64), 50.1 mm = 5.01 cm, which is more than 5 cm by 0.01 cm.

Question 6. Assertion: 0.7 is greater than 0.65. Reason: Of two decimals, the one with more digits after the decimal point is always the greater. Choose (a), (b), (c) or (d).

Answer: (c), the assertion is true but the reason is false. Decimals are compared place by place, as whole numbers are (page 72): both have 0 ones, and in the tenths place 7 is more than 6, so 0.7 is greater. 0.65 has more digits but is the smaller number, which shows the reason is false.

Working with Fractions (Chapter 8)

Question 7. A khichdi recipe for 4 people uses 3/4 cup of rice and 2/3 cup of moong dal. (a) How much of each is needed for 6 people? (b) How much of each is needed for just 2 people?

Answer: (a) 1 1/8 cups of rice and 1 cup of dal; (b) 3/8 cup of rice and 1/3 cup of dal. (a) 6 people is 6/4 = 3/2 times the recipe. Rice: 3/4 × 3/2 = 9/8 = 1 1/8 cups. Dal: 2/3 × 3/2 = 6/6 = 1 cup. To multiply fractions, multiply the numerators and multiply the denominators (page 182). (b) 2 people is half the recipe. Rice: 3/4 × 1/2 = 3/8 cup. Dal: 2/3 × 1/2 = 2/6 = 1/3 cup.

Question 8. Assertion: 15 ÷ 3/5 is more than 15. Reason: Dividing by a fraction that lies between 0 and 1 gives an answer larger than the number being divided. Choose (a), (b), (c) or (d).

Answer: (a), both are true and the reason explains the assertion. Dividing by 3/5 is the same as multiplying by 5/3, so 15 ÷ 3/5 = 15 × 5/3 = 25, which is more than 15. The divisor 3/5 is less than 1, and the chapter's summary says a divisor of that kind always gives a quotient bigger than the dividend (pages 189 and 198).

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Sources

All opened and read on 4 November 2026. Page numbers are the printed page numbers of the textbook.

The mathematics in each answer is from the textbook pages named. The situations, data, questions and worked answers are our own, and every number was re-checked by script. This guide is general information; follow your teacher and the textbook.

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