ASSERTION (A): The relation f:\1,2,3,4\→\x,y,z,p\ defined by f=\(1,x),(2,y),(3,z)\ is a bijective function. REASON (R): The function f:\1,2,3\→\x,y,z,p\ such that f=\(1,x),(2,y),(3,z)\ is one-one. (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 2023-24 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics sample paper 2023-24: question 20

From the official CBSE sample question paper for 2023-24, 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 relation $f : {1, 2, 3, 4} \to {x, y, z, p}$ defined by $f = {(1, x), (2, y), (3, z)}$ is a bijective function.

REASON (R): The function $f : {1, 2, 3} \to {x, y, z, p}$ such that $f = {(1, x), (2, y), (3, z)}$ is one-one.

(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 2023-24.

Hints

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

Hint 1

Does every element of the domain have an image?

Hint 2

In R, are the images all distinct?

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.

A: the element 4 has no image, so $f$ is not even a function. A is false.
R: 1, 2 and 3 have distinct images $x$ , $y$ , $z$ , so $f$ is one-one. R is true. The answer is option (D).
1 mark

Answer: Option (D)

Where the marks are

A false (4 has no image); R true (distinct images) (1 mark)

Revise the chapter

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

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 2023-24: every question, by section.

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CBSE Class 12 Mathematics sample paper 2023-24: question 20

Hints

Step-by-step solution

Revise the chapter

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