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In Questions 19 and 20, an… (Class 10 Maths 2023, Q20)

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

CBSE Class 10 Mathematics Standard 2023: question 20

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedReal Numbers

In Questions 19 and 20, an Assertion (A) statement is followed by a statement of Reason (R). Select the correct option out of the following.

Assertion (A): The perimeter of is a rational number.

Reason (R): The sum of the squares of two rational numbers is always rational.

  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 but 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.

Figure in the paper: Right-angled triangle ABC with the right angle at B. AB = 2 cm (vertical side), BC = 3 cm (horizontal base), and hypotenuse AC joining A (top) to C (bottom right). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/1/1.

Hints

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

Hint 1

Find the hypotenuse AC first.

Hint 2

Is rational? Is ?

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. By Pythagoras, cm, which is irrational.

  2. Perimeter , which is irrational. So A is false.

  3. R: if are rational, then is rational (rationals are closed under multiplication and addition). So R is true. Option (D).

    1 mark

Answer: Option (D)

Where the marks are

  • Finds , shows the perimeter is irrational and R is true, option (D) (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paper2023 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.