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Assertion (A): If 5 + √(7) is a… (Class 10 Maths 2023, Q19)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2023: question 19

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, 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-basedQuadratic Equations

Assertion (A): If is a root of a quadratic equation with rational co-efficients, then its other root is .

Reason (R): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.

Choose the correct option out of the following:

  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.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

What is the conjugate of ?

Hint 2

Ask whether the reason directly gives you the assertion.

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. R is true: irrational (surd) roots of a quadratic with rational coefficients occur in conjugate pairs .

  2. Hence the other root is , so A is true and R correctly explains it. Option (A).

    1 mark

Answer: Option (A)

Where the marks are

  • Both statements true and R explains A (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 30/6/1 (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.