MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 37

From the official CBSE sample question paper for 2026-27, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedArithmetic Progressions

Delhi's pollution is a severe, often seasonal issue caused by a combination of factors like high vehicular and industrial emissions, dust from construction, and crop burning in surrounding states. In a school, students of classes I to XII thought of planting trees in and around the school to reduce air pollution.

It was decided that the number of trees that each section of each class will plant be three more than the double of the class in which they are studying, e.g., a section of class IV will plant 11 trees. If in the given school, there are two sections of each class, then answer the following questions:

(i)
If number of trees planted by students class-wise follow arithmetic progression, then find the common difference.
1 mark
(ii)
What is the number of trees planted by students of class VI?
1 mark
(iii)(A)
What is the total number of trees planted by the students of given school?
2 marks
OR
(iii)(B)
Identify the class that planted 34 trees.
2 marks

Figure in the paper: Two illustrations side by side. Left: a grey image of a field with crop burning, showing flames and smoke rising over dry stalks. Right: an illustration of a factory with several smoke-emitting chimneys, a car on the left, a tree on the right, and a group of people standing in between. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

Open one hint at a time and try again before the next.

Hint 1

Find how many trees one section of class n plants, then remember there are two sections.

Hint 2

Write the number of trees for classes I, II and III to see the AP and its first term.

Hint 3

For the total, use $S_{n} = \frac{n}{2} {2 a + (n - 1) d}$ with 12 classes. For 34 trees, set the class-n expression equal to 34.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Each section of class $n$ plants $2 n + 3$ trees. With 2 sections, class $n$ plants $2 (2 n + 3)$ trees. Class I: $2 (5) = 10$ ; Class II: $2 (7) = 14$ ; Class III: $2 (9) = 18$ ; ... This gives the AP 10, 14, 18, 22, ...
(i) Common difference $d = 14 - 10 = 4$
1 mark
(ii) Class VI: $2 {2 (6) + 3} = 2 \times 15 = 30$ trees
1 mark
(iii)(A) There are 12 classes, so $n = 12$ , $a = 10$ , $d = 4$ . Then $S_{12} = \frac{n}{2} {2 a + (n - 1) d} = \frac{12}{2} {2 (10) + 11 (4)}$
1 mark
(iii)(A) $= 6 \times (20 + 44) = 6 \times 64 = 384$ trees
1 mark
(iii)(B) Let class $n$ plant 34 trees: $2 (2 n + 3) = 34$
1 mark
(iii)(B) $2 n + 3 = 17$
½ mark
(iii)(B) $n = 7$ , i.e. Class VII planted 34 trees.
½ mark

Answer: (i) 4; (ii) 30 trees; (iii)(A) 384 trees; (iii)(B) Class VII

Where the marks are

(i) Finds the common difference 4 (1 mark)
(ii) Class VI plants 2(2×6+3) = 30 trees (1 mark)
(iii)(A) Uses $S_{n}$ with n = 12, a = 10, d = 4 (1 mark); total 384 (1 mark)
(iii)(B) Forms 2(2n+3) = 34 (1 mark); 2n+3 = 17 (½ mark); n = 7, Class VII (½ mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 37

Hints

Step-by-step solution

Revise the chapter

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