Assertion (A): The function f:R-\(2n+1)(π)/(2):n Z\→(-∞,-1][1,∞) defined by f(x)= x is not one-one function in its domain. Reason (R): The line y=2 meets the graph of the function at more than one point. (A) Both (A) and (R) are true and (R) is the correct explanation of (A). (B) Both (A) and (R) are true but (R) is not the correct explanation of (A). (C) (A) is true but (R) is false. (D) (A) is false but (R) is true.

MathsCBSE Class 12 · Sample paper, session 2024-25 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics sample paper 2024-25: question 20

From the official CBSE sample question paper for 2024-25, 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-basedRelations and Functions

Assertion (A): The function $f : R - {(2 n + 1) \frac{π}{2} : n \in Z} \to (- \infty, - 1] \cup [1, \infty)$ defined by $f (x) = sec x$ is not one-one function in its domain.

Reason (R): The line $y = 2$ meets the graph of the function at more than one point.

(A)Both (A) and (R) are true and (R) is the correct explanation of (A).
(B)Both (A) and (R) are true but (R) is not the correct explanation of (A).
(C)(A) is true but (R) is false.
(D)(A) is false but (R) is true.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Find two values of $x$ with $sec x = 2$ .

Hint 2

Recall the horizontal line test for one-one functions.

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.

$sec x = 2$ at $x = π /3$ and $x = - π /3$ (and more), so the line $y = 2$ cuts the graph at many points; (R) true.
By the horizontal line test, $sec x$ is not one-one; (A) true and (R) explains it. Option (A).
1 mark

Answer: Option (A)

Where the marks are

Uses horizontal line test with $y = 2$ to show not one-one (1 mark)

Revise the chapter

Chapter: Relations and Functions (notes, formulas, where marks are lost and every past question)
Topic: One-One and Onto Functions

Practise this chapterBoard-style questions from Relations and Functions, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2024-25: 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.

CBSE Class 12 Mathematics sample paper 2024-25: question 20

Hints

Step-by-step solution

Revise the chapter

More questions from Relations and Functions