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DIRECTIONS: In the question… (Class 10 Maths 2023, Q19)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2023: question 19

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, 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: In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option out of the following.

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

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

  1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. (B)Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of 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 2023 board paper, set 30/4/1.

Hints

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

Hint 1

Write 366 and 365 as complete weeks plus some extra days.

Hint 2

Count how many of the possible extra days (or pairs of days) include a Sunday.

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 and 2 extra days. The extra pair of days can be one of 7 equally likely pairs: (Sun, Mon), (Mon, Tue), …, (Sat, Sun). Two of these pairs contain a Sunday, so . Hence A is true.

  2. A non-leap year has 365 days, which is 52 weeks and 1 extra day. That extra day is a Sunday in 1 case out of 7, so , not . Hence R is false.

  3. A is true but R is false. The answer is option (C).

    1 mark

Answer: Option (C): A true, R false

Where the marks are

  • Chooses 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 paper2023 board paper, set 30/4/1 (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.