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Directions: Question numbers 19… (Class 10 Maths 2026, Q19)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2026: question 19

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedProbability

Directions: Question numbers 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.

Assertion (A): The probability that a leap year has 53 Mondays is .

Reason (R): The probability that a non-leap year has 53 Mondays is .

  1. (a)Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  2. (b)Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  3. (c)Assertion (A) is true, but Reason (R) is false.
  4. (d)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

How many days are left over after 52 complete weeks?

Hint 2

List the possible extra day(s) and count those that contain a Monday.

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.

  1. A leap year has 366 days, which is 52 weeks + 2 extra days. The 2 extra days can be one of 7 consecutive pairs (Sun–Mon, Mon–Tue, …, Sat–Sun). Two of these pairs contain a Monday, so P = . Assertion is true.

  2. A non-leap year has 365 days, which is 52 weeks + 1 extra day. That day is Monday in 1 case out of 7, so P = , not . Reason is false. Option (c).

    1 mark

Answer: Option (c): A is true, R is false

Where the marks are

  • Identifies A true (2/7) and R false (1/7), option (c) (1 mark)

Revise the chapter

  • Chapter: Probability (notes, formulas, where marks are lost and every past question)
Practise this chapterBoard-style questions from Probability, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/1/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.